NASA Logo, National Aeronautics and Space Administration

National Aeronautics and Space Administration

Goddard Space Flight Center

Astrophysics Science Division | Sciences and Exploration

This website is kept for archival purposes only and is no longer updated.

skip to content
Coded Aperture Imaging in High-Energy Astronomy banner

REFERENCES OF PAPERS ON CODED APERTURE IMAGING

Status: August 11, 2005; Prepared by: Jean in 't Zand, SRON


Paper count: 140


The following list concerns papers that deal with the principle and details of coded aperture imaging (i.e., aperture designs, camera configurations, reconstruction designs and related subjects). This list is a personal non-exhaustive compilation of papers which in my mind are most relevant mainly to astrophysical applications.

New entries are highlighted with NEW!.

If you have a preprint of a paper on coded-aperture imaging, I'd appreciate it very much if you send me a copy!

Ables, J.G.: 1968, Proc. Astron. Soc. Australia, 1, 172
Fourier Transform Photography: A New Method for X-ray Astronomy
In comparison with all other branches of astronomy, X-ray astronomy suffers from a relative dearth of image forming devices. No X-ray lens is known and image formation by reflection requires glancing incidence optics which have small fields of view and are extremely difficult to fabricate, even for small apertures (about 2 cm^2) now employed. The only other imaging device which has been successfully employed is the simplest of all, the pinhole camera. Pinhole cameras with resolutions better than 10^-3~rad are easily constructed, but the apertures are very small--not greater than about 10^-4 cm^2. The new instrument described here is closely related to the pinhole camera and may be viewed as an attempt to overcome the aperture restrictions of this simple device.
Ballesteros, F.J., Sanchez, F., Reglero, V., Porras, E., Perez, F., Robert, A.: 1996, preprint
Imaging in X-ray with Coded-Aperture Masks
Imaging reconstruction methods for coded mask telescopes devoted to study celestial X and gamma ray sources, normally fall on correlation methods, using Fast Fourier Transforms to increase the computational speed. In very complex telescopes these methods are succesful because they allow to reconstruct the images quickly. However, there is an intrinsic loss of angular resolution when using such imaging reconstruction methods. In this paper we describe alternative reconstruction methods that can be used for not very complex coded mask telescopes, obtaining better results. We have found that the E-M algorithm (a maximum likelihood method) give us the best results in the case of LEGRI (Low Energy Gamma Ray Imager) which consists of 10x10 pixeled detector plane together with a 14x14 coded mask.
Barrett, H.H., Horrigan, F.A.: 1973, Appl. Opt., 12, 2686
Fresnel Zone Plate Imaging of Gamma Rays; Theory
The use of a Fresnel zone plate as a coded aperture for imaging incoherent radiation such as gamma rays has been previously reported. The coded image is in many respects similar to a hologram and can be decoded or reconstructed with a coherent optical system. In this paper, the general theory of coded-aperture imaging is presented, first for an arbitrary code and the for an on-axis zone plate, an off-axis zone plate, and a one-dimensional zone plate (or linear chirp). With the on-axis plate, a matched imaging condition is suggested as a guide to optimizing image contrast. With the off-axis zone plate and the linear chirp, it is necessary to use a half-tone screen to spatially heterodyne the object spectrum into the passband of the aperture. In all three cases, expressions for the resolution, depth of field, field of view and relative efficiency are derived. A simplified noise analysis is presented, and some practical system constraints are discussed.
Barrett, H.H., DeMeester, G.D.: 1974, Appl. Opt., 13, 1100
Quantum Noise in Fresnel Zone Plate Imaging
A Fresnel zone plate, used as a coded aperture, offers a great advantage in geomegric collection efficiency over a conventional pinhole or collimator. We present a detailed analysis of the signla-to-noise ratio (SNR) of a quantum-limited zone plate camera. The magnitude and spatial distribution of the noise field and its dependence on the source distribution and the characteristics of the optical processing system are derived. It is shown that the largest SNR advantage occurs for a point source, while for very large, uniform sources there may be a slight net disadvantage using a zone plate. it is also shown that optical processing does not give the highest possible SNR.
Barthelmy, S.D.: 2004, SPIE 5165, 139 NEW!
Burst Alert Telescope (BAT) on the Swift MIDEX mission
The Burst Alert telescope (BAT) is one of 3 instruments on the Swift MIDEX spacecraft to study gamma-ray bursts (GRBs). The BAT instrument is the instrument that first detects the GRB and localizes the burst direction to an accuracy of 1-4 arcmin within 20 sec after the start of the event. These locations cause the spacecraft to autonomously slew to point the two narrow-FOV instruments at the burst location within 20-70 sec to make follow-up x-ray and optical observations. BAT is a wide-FOV coded-aperture instrument with a CdZnTe detector plane. The detector plane is composed of 32,768 pieces of CdZnTe (4x4x2mm), and the coded-aperture mask is composed of ~52,000 pieces of lead (5x5x1mm) with a 1-m separation between mask and detector plane. The BAT operates over the 15-150 keV energy range with ~6 keV resolution, a sensitivity of 0.2 ph/cm2-sec, and a 1.4 sr (half-coded) FOV. We expect to detect >100 GRBs/yr for a 2-year mission. The BAT also performs an all-sky hard x-ray survey with a sensitivity of ~2 mCrab (systematic limit) and as a hard x-ray transient monitor.
Bassani, L., Butler, R.C., Caroli, E., Di Cocco, G., Natalucci, L., Spizzichino, A., Stephen, J.B.: 1989, Astron. Lett. and Communications, 27, 321
Simulated Observations of Low Energy Gamma Ray Sources
A series of Monte-Carlo simulated observations of gamma ray sources has been obtained for the Zebra telescope, using recent observational data. The results of the simulations are analyzed in order to assess both the sensitivity and imaging capability of the instrument during a typical balloon flight. It is shown that sources like the Crab nebula, the quasar 3C273, and the Seyfert galaxy NGC4151 will be observable over the entire energy range of the instrument (0.2-10 MeV) at the few tens of sigma confidence level and will be located with an accuracy of the order of a few arcminutes. Furthermore, the simulations furnish an estimate of the capability of the telescope to resolve complex structured sources such as SS433 or crowded regions of the sky like that of the Galactic Center.
Braga, J., Villela, T., Jayanthi, U.B., D'Amico, F., Neri, J.A.: 1991, Exp. Astron., 2, 101
A New Mask-Antimask Coded-Aperture Telescope for Hard X-ray Astronomy
A new imaging balloon-borne telescope for hard X-rays in the energy range from 30 to 100 keV is described. The imaging capability is provided by the use of an extended URA-based coded mask. With only one motor and suitable stop bins, we can rotate a carbon-fibre wheel with most of the mask elements attached to it by 180 deg, and a bar, which is also part of the mask pattern and is allowed to rotate freely over the wheel, by 90 deg; this combined rotation creates an antimask of the original mask, except for the central element. This is a novel and elegant manner of providing an antimask without additional weight and complex mechanical manipulations. We show that the use of antimasks is a very effective method of eliminating systematic variations in the background map over the position sensitive detector area. The expected sensitivity of the instrument for the 30-100 keV range is of the order of 7X10^-5 photons cm^-2 s^-1 keV^-1, for an integration time of 10^4 seconds at a residual atmosphere of 3.5 g cm^-2. This telescope will provide imaging observations of bright galactic hard X-ray sources with an angular resolution of ~2 deg. in a 10 deg by 10 deg FOV, which is defined by a collimator placed in front of the detector system. We are particularly interested in the galactic center region, where recent imaging results in X-rays have shown the presence of an interesting source field. Results of computer simulations of the imaging system are reported.
Brown, C.M.: 1972, Ph.D. Thesis, University of Chicago
Multiplex Imaging with Random Arrays
The signal-to-noise ratio in the image from a pinhole camera can be improved by replacing the single pinhole with many pinholes. Pictures from such cameras are subjected to a posteriori interpretation (postprocessing) which collects the images from all the pinholes into a single, stronger image. When the images from individual pinholes overlap on the film, we say they are multiplexed; advantages can then accrue both from better utilization of information gathering and storage resources and from nonlinear detector response. While the latter effect is best explored experimentally, the linear phenomena in such a system may be treated theoretically. The system is an example of a multiplexing system using correlation coding and decoding methods. Multiplexing systems have in common the goal of increasing the rate in a noisy channel by sending through it a superposition of several encoded messages. The imaging process is equivalent to encoding and decoding messages by correlation with binary arrays. In the absence of a priori information about the messages to be sent, this coding can induce a loss of information, an uncertainty inherent to the technique. Promising methods for synthesis of code arrays inducing low uncertainty are reviewed, and no better two-dimensional codes are found for aperiodic correlation than random arrays whose characteristics have been improved slightly by iterative methods. In the imaging application, the coding induces uncertainty in the form of two kinds of intensity inaccuracies: one of low and one of high spatial frequency. The usual postprocessing technique (optical matched filtering) is unsatisfactory in multiplexing systems. Although it has some optimal noise-rejection properties, in multiplexing it can cause an unacceptable amount of low spatial frequency inaccuracy. Two new postporcessing schemes are introduced (mismatched filtering and pseudomatched filtering involving image subtraction) which can remove this low spatial frequency inaccuracy, at the same time lessening the inaccuracies of high spatial frequency. Detailed models of the inherent uncertainty are developed for the three postprocessing schemes. The uncertainty produced by correlation coding methods is modelled as a quasi- statistical nosie process whose amplitude is proportional to the signal strength. Two common physical processes, proportional to the square root of the signal and independent of the signal, are mentioned and their effects evaluated. The most promising coding schemes (nonmultiplexing, aperiodic correlation coding, psuedoperiodic correlation coding with multiplexing) are compared using an expression which includes the effects from all the noise processes. The conditions are found under which each scheme is to be preferred. Multiplexing is known to yield and advantage if signal-independent noise is dominant; it is found that in the imaging system, multiplexing can yield an advantage even if other forms of noise are dominant. Technniques are illustrated and qualitative and quantitative predictions of the theory are tested.
Brown, C.: 1974, Journal of Applied Physics, 45, 1806
Multiplex imaging with multiple-pinhole cameras
When making photographs in x rays or gamma rays with a multiple-pinhole camera, the individual images of an extended object such as the sun may be allowed to overlap; then the situation is in many ways analogous to that in a multiplexing device such as a Foruier spectroscope. Some advantages and problems arising with such use of the camera are discussed, and expressions are derived to describe the relative efficay of three exposure/postprocessing schemes using mutliple-pinhole cameras.
Bryan, R.K., Skilling, J.: 1980, Mon. Not. R. Astr. Soc., 191, 69
Deconvolution by Maximum Entropy, as Illustrated by Application to the Jet of M87
We present an improved method of deconvolving blurred and noisy data, appropriate for pictures of the sky taken with astronomical telescopes. The maximum entropy criterium gives the smoothest possible structure of the sky consistent with the observed image. Our improvements lie in the consistency test; we force the noise to have its correct statistical distribution. This provides greater resolution and more accurate fitting. The method is illustrated by deconvolving an optical photograph of the nuclear regions of M87.
Budtz-Joergensen, C., Lund, N., Westergaard, N., et al.: 2004, SPIE 5165, 139 NEW!
EM-X: the x-ray monitor on INTEGRAL
The INTEGRAL X-ray monitor, JEM-X, (together with the two gamma ray instruments, SPI and IBIS) provides simultaneous imaging with arcminute angular resolution in the 3-35 keV band. The good angular resolution and low energy response of JEM-X plays an important role in the detection and identification of gamma ray sources as well as in the analysis and scientific interpretation of the combined X-ray and gamma ray data. JEM-X is a coded aperture X-ray telescope consisting of two identical detectors. Each detector has a sensitive area of 500 cm2, and views the sky through its own coded aperture mask. The coded masks are located 3.4 m above the detector windows. The detector field of view is constrained by X-ray collimators (6.6 FOV, FWHM).
Busboom, A., Elders-Boll, H., Schotten, H.D.: 1997, Proc. ICASSP-97, 2817
Combinatorial Design of Near-Optimum Masks for Coded Aperture Imaging
In coded aperture imaging the attainable quality of the reconstructed images strongly depends on the choice of the aperture pattern. Optimum mask patterns can be designed from binary arrays with constant sidelobes of their periodic autocorrelation function, the so-called URAs. However, URAs exist for a restricted number of aperture sizes and open fractions only. Using a mismatched filter decoding scheme, artifact-free reconstructions can be obtained even if the aperture array violates the URA condition. A general expression and an upper bound for the signal-to-noise ratio as a function of the aperture array and the relative detector noise level are derived. Combinatorial optimization algorithms, such as the great Deluge algorithm, are employed for the design of near-optimum aperture arrays. The signal-to-noise ratio of the reconstructions is predicted to be only slightly inferior to the URA case while no restrictions with respect to the aperture size or open fraction are imposed.
Busboom, A., Schotten, H.D., Elders-Boll, H.: 1997, J. Opt. Soc. Am. A, 14, 1058
Coded Aperture Imaging with Multiple Measurements
In coded aperture imaging, only aperture arrays consisting of (0,1) elements are physically realizable. If multiple coded images are obtained with different aperture masks and the resulting detector images are suitably combined, a larger variety of aperture arrays, such as multilevel, complex-valued, vector-valued, or complementary arrays become applicable. We present a general theory of coded aperture imaging with multiple measurements. An image reconstruction scheme from the coded images is described that results in a maximum signal-to-noise ratio. Also, the design of sets of aperture arrays is addressed and explicitly solved for several important cases. It is shown how know classes of correlation arrays can be beneficially applied to coded aperture imaging.
Busboom, A., Elders-Boll, H., Schotten, H.D.: 1998, Exp. Astron., 8, 97
Uniformly Redundant Arrays
Uniformly redundant arrays (URAs) are two-dimensional binary arrays with constant sidelobes of their periodic autocorrelation function. They are widely agreed upon to be optimum mask patterns for coded aperture imaging, particularly in imaging systems with a cyclic coded mask. In this paper, a survey of all currently known construction methods for URAs is given and the sizes and open fractions of the arrays resulting from each construction method are pointed out. Alternatives to URAs for situations in which a URA does not exist, are discussed.
Busboom, A.. Lueke, H.D.: 2001, Appl. Opt., 40, 3894 NEW!
Hexagonal Binary Arrays With Perfect Correlation
Two-dimensional binary signals (arrays) with good autocorrelation properties are needed for coded-aperture imaging systems. In many astrophysical instruments, circular detectors with hexagonally packed detector elements are used, such that hexagonal coded apertures are often preferable to rectangular ones. A general method for folding a one-dimensional sequence into a hexagonal array is presented, by which the periodic or odd-periodic correlation properties of the original sequence are preserved. This method is applied to a known family of sequences with perfect odd-periodic correlation, yielding a new family of almost-binary and odd-perfect -or binary and almost odd-perfect -hexagonal arrays with optimum properties for coded-aperture imaging. The new odd-perfect arrays have near-uniform side lengths and exist for many more sizes than known families of even-periodic hexagonal arrays with good imaging properties.
Butler, R.C., Caroli, E., Di Cocco, G., Maggioli, P.P., Spizzichino, A., Charalambous, P.M., Dean, A.J., Drane, M., Gil, A., Stephen, J.B., Perotti, F., Villa, G., Badiali, M., La Padula, C., Polcaro, F., Ubertini, P.: 1984, Nucl. Instr. Methods Phys. Res., 221, 41
An Evaluation of the Background Introduced from the Coded Aperture Mask in the Low Energy Gamma-Ray Telescope Zebra
The background which arises from the presence of a coded aperture mask is evaluated. The major contributions which have been considered here are the interactions with the mask of the isotropic gamma ray background, a parallel gamma ray beam, neutrons and the effect of the mask element profile. It is shown that none of these factors contribute to a significant excess or modulation in the background counting rate over the detection plane. In this way the use of a passive rather than an active coded aperture mask is seen to be suitable for use in a low energy gamma ray telescope.
Byard, K., Dean, A.J., Goldwurm, A., Hall, C.J., Harding, J.S.J., Lei, F.: 1990, Astron. and Astrophys., 227, 634
Imaging USing HURA Coded Aperture with Discrete Pixel Detector Array
Hexagonal URA (HURA) coded apertures have important properties for gamma-ray imaging and they have been successfully used in conjunction with an Anger camera for astronomical gamma-ray observations. However, when coupled to a detector plane constructed from discrete pixels an inherent systematic noise due to the non-perfect overlap between mask elements and detector pixels can cause degradation of the image quality. Here we presents the results of computer simulations designed to evaluate the basic performance of a system employing a rotating HURA mask and two discrete detector pixel geometries: a square pixel detector (SPD) and a hexagonal pixel detector (HPD). Intrinsic systematic noise has been found to affect the quality of the system point spread function for both detector geometries. The noise varies with the mask orientation, the detector resolution and the source position, and is highly magnified by the background level. Special configurations for the HPD geometry have been identified for which a nearly perfect overlap of mask elements with detector pixels occurs at two mask orientations. Under these conditions the systematic noise is completely absent.
Byard, K.: 1992, Exp. Astron., 2, 227
Square Element Antisymmetric Coded Apertures
This paper describes a method for constructing square element coded aperture patterns which possess 90 deg antisymmetry. The resulting patterns now make possible the removal of systematic detector background noise from a square pixel detector by means of 'antimask' imaging using a single aperture, and without requiring full 180 deg aperture rotation
Cannon, T.M., Fenimore, E.E.: 1979, Appl. Opt., 18, 1052
Tomographical Imaging Using Uniformly Redundant Arrays

Caroli, E., Butler, R.C., Di Cocco, G., Maggioli, P.P., Natalucci, L., Spizzichino, A.: 1984, Il Nuovo Cimento, 7, 786
Coded Masks in X- and gamma-Ray Astronomy: the Problem of the Signal-to-Noise Ratio Evaluation
Coded-mask telescopes are presently considered as one of the best solutions for producing images of the sky in hard X-ray and gamma-ray astronomy, because they can posses optimum signal-to-noise ratio (SNR), which is crucial in an energy range in which the expected fluxes are generally low compared with the background. For a given field of the sky, the values of the SNR, associated with each pixel of the reconstructed image, depend on both the mask design and the decoding technique employed. The expressions for the SNR of a variety of replicated masks are derived for the cases of the inversion and the correlation methods, in different conditions of background and source fluxes. For the inversion method, the SNR is found to be simply inversely proportional to the square root of the trace of the matrix associated with the mask, but generally in the case of the correlation method the SNR is limited by an additional systematic term due to the cross-talk between sources in the field of view. The effect of this term can be avoided by choosing a uniformly redundant array pattern.
Caroli, E., Stephen, J.B., Di Cocco, G., Natalucci, L., Spizzichino, A.: 1987, Space Sci. Rev., 45, 349
Coded Aperture Imaging in X- and Gamma-Ray Astronomy
Coded aperture imaging in high energy astronomy represents an important technical advance in instrumentation over the full energy range over X-rays till gamma-rays and is playing a unique role in those spectral ranges where other techniques become ineffective or impracticable due to limitations connected to the physics of interactions of photons with matter. The theory underlying this method of indirect imaging is of strong relevance both in design optimization of new instruments and in the data analysis process. The coded aperture imaging method is herein reviewed with emphasis on topics of mainly practicle interest along with a description of already developed and forthcoming implementations.
Charalambous, P.M., Dean, A.J., Stephen, J.B., Young, N.G.S., Gourlay, A.R.: 1984, Nucl. Instr. Methods Phys. Res., 221, 56
Aberrations in Gamma-Ray Imaging Systems
The aberrations present in a coded aperture imaging system have a fundamentally different origin to those found in a focused optical instrument. A series of laboratory tests is described in which masks with carefully controlled defects were employed to generate non-perfect gamma-ray images, so that the magnitude of the aberrations introduced could be quantitively investigated. The results of these test are presented and the extend to which they affect the design of a practical gamma-ray imaging system is discussed.
Charalambous, P.M., Dean, A.J., Stephen, J.B., Young, N.G.S.: 1984, Appl. Opt., 23, 4118
Aberrations in Gamma-Ray Coded Aperture Systems
Laboratory test have been performed to investigate the quality of gamma-ray images which may be obtained using the coded aperture mask technique. A number of potential sources of image defects are examined both theoretically and experimentally, and the methods in which these may be minimized eliminated are studied. It is shown that good quality gamma-ray images may be produced by efficient design and control of the imaging system.
Connell, P.H., Skinner, G.K.: 1995, "Imaging in High Energy Astronomy" (eds. L. Bassani & G. di Cocco; Kluwer Academic Publishers), p. 143
Development of the "CAPTIF" Software Facility for the Simulation of Coded Aperture Telescopes and Its Application to "INTEGRAL" and Other Instruments
To support the development of the next generation of coded aperture telescopes, a software facility has been developed to simulate the response of any mask/detector configuration and the observation of various photon sources, allowing its sensitivity and imaging properties to be evaluated. The system is suitable for any instrument which can be defined by four components: a coded mask, an array of detectors, an identical array of detector collimators and an outer shield. It allows for rotating or alternating masks, for flexibility in the choice of mask/detector shape and for off-axis effects inherent in a mask of finite thickness with exponential absorption. Facilities are also provided to simulate point or extended sources, and an observation program consisting of a sequence of parameters describing the pointing direction, orientation and exposure of the device. Detector count simulations and image reconstructions have been performed for the evaluation of various designs proposed for the INTEGRAL instruments and for a small, balloon carried coded aperture telescope.
Covault, C.E., Grindlay, J.E., Manandhar, R.P, Braga, J.: 1991, IEEE Trans. on Nucl. Sci., 38, 591
Techniques for Removing Non-uniform Background in Coded-Aperture Imaging on the Energetic X-ray Imaging Telescope Experiment
The coded-aperture technique for reconstructing images for a position-sensitive detector looking through a stationary URA mask requires that the background illumination be distributed uniformly across the surface of the detector. Non-uniformities in the background are typical of balloon and space-borne detectors, ad introduce large artifacts into the reconstructed image, with a subsequent noise of SNR. Here we describe a technique, employed for EXITE to remove the systematic effects of non-uniform background. We explore the time-dependence of intensity and two-dimensional shape of the background detector image during the flight. We construct a "flat field" image from observations where X-ray sources were absent from the field of view. We demonstrate that this technique can successfully reduce RMS fluctuations to within a few percents of ideal Poisson statistics.
Daniel, G.J.: 1984, Nucl. Instr. Methods Phys. Res., 221, 67
Image Restoration and Processing Methods
This review will stress the importance of using image restoration techniques that deal with incomplete, inconsistent, and noisy data and do not introduce spurious features into the processed image. No single image is equally suitable for both the resolution of detail and the accurate measurement of intensity. A good general purpose technique is the maximum entropy method and the basis and use of this will be discussed.
Desai, U.D., Gaither, C.C.: 1995, "Imaging in High Energy Astronomy" (eds. L. Bassani & G. di Cocco; Kluwer Academic Publishers), p. 227
Solar X-ray Imaging Telescope
A design concept is presented for a new solar X-ray telescope for use on a small satellite. Imaging with high angular resolution will be achieved by using two Fresnel zone plates (FZPs), separated by a distance of up to a few meters, acting as a coder (Mertz, L., SPIE, 1159, 14, 1989). Such paired FZPs provide two-dimensional spatial coding in the form of parellel fringes whose frequency and orientation are dependent on the off-axis location of a point source. Extended sources have correspondingly more complex spatial coding patterns. One advantage of this scheme is the capability for all aximuth viewing over a range of source sizes. Also, the image-plane detector needs only moderate spatial resolution to achieve fine angular resolution. As compared with rotating modulation collimators, less stringent alignment is required and, given adequate flux, the time resolution is not restricted by the bi-grid rotation rate. With a 4 cm plate diameter and a separation of 2 meters, angular resolution of about 10 seconds of arc over a few degrees is possible. The proposed detector array will use avelanche photodiodes and/or silicon PIN diodes at the lowest energies, and CsI(Tl) viewed by APDs at higher energies. The instrument will be compact, low in power, light in weight, and ideally suited for solar studies on a small satellite.
Dicke, R.H.: 1968, Astrophys. J., 153, L101
Scatter-Hole Cameras for X-Rays and Gamma Rays
A pinhole camera for which the entrance area, covered with a very large number of randomly distributed pinholes, is 50% open is shown to be a very effective way of forming images of a complex of X-ray stars. A simple statistical trick is used to reduce the multidunious overlapping images into a single image. Less than forty detected photons are needed to form an image of a star.
Ducros, G., Ducros, R.: 1984, Nucl. Instr. Methods Phys. Res., 221, 49
Statistical Analysis for Coded Aperture gamma-ray Telescope
We have developed a statistical analysis of the image recorded by a photon sensitive detector associated with a coded mask for the French gamma ray telescope SIGMA, in the energy range 20-2000 keV. The aperture of the telescope is not limited to the size of the mask. In the first part, we describe the principle of the image analysis based on the least squares method with a fit function generated and tested term after term. The statistical test is performed on the F distribution followed by the relative improvement of chi^2 when the fit function has an additional term. The second part deals with digital processing aspects: the adjustment on the method to reduce computation time, and the analysis results of two simulated images.
Fenimore, E.E., Cannon, T.M.: 1977, Proc. of Digital Signal Processing Symposium
Uniformly Redundant Arrays
A recent development in coded aperture imaging has removed the basic limitation on the quality of the reconstructed images when a correlation analysis is used. A pattern of holes for the aperture has been designed that has an autocorrelation that is perfectly flat. The pattern is referred to as a uniformly redundant array (URA) and combined the high transmission characteristics of the random arrays and Fresnel zone plate with the flat sidelobe advantage of the non-redundant pinhole array. An analysis procedure has been developed (balanced correlation) which, when combined with the URA, gives a system point-spread function which is exactly a delta function. Computer simulations have been used to demonstrate that, with random arrays, the balanced correlation is able to improve the reconstructed images by orders of magnitude. Additional orders of magnitude improvement are possible if the URA pattern is used.
Fenimore, E.E.: 1978, Appl. Opt., 17, 3562
Coded Aperture Imaging: Predicted Performance of Uniformly Redundant Arrays
URA's have autocorrelation functions with perfectly flat sidelobes. The URA combines the high transmission characteristics of the random array with the flat sidelobe advantage of the non-redundant pinhole arrays. A general expression for the SNR has been developed for the URA as a function of the type of object being imaged and the design parameters of the aperture. The SNR expression is used to obtain and expression for the optimum aperture transmission. Currently, the only 2-D URAs known have a transmission of 1/2. This, however, is not a severe limitation because the use of the non-optimum transmission of 1/2 never causes a reduction in the SNR of more than 30%. The predicted performance of the URA system is compared to the images obtainable from a single pinhole camera. Because the reconstructed image of the URA contains virtually uniform noise regardless of the original object's structure, the improvement over the single pinhole camera is much larger for the bright points than it is for the low intensity points. For a detector with high background noise, the URA will always give a much better image than the single pinhole camera regardless of the structure of the object. In the case of a detector with low background noise, the improvement of the URA relative to the single pinhole camera will have lower limit of ~2f^-1/2, where f is the fraction of the field of view that is uniformly filled with object.
Fenimore, E.E., Cannon, T.M.: 1978, Appl. Opt., 17, 337
Coded Aperture Imaging with Uniformly Redundant Arrays
URA's have autocorrelation functions with perfectly flat sidelobes. The URA combines the high transmission characteristics of the random array with the flat sidelobe advantage of the non-redundant pinhole arrays. This gives the URA the capability to image low-intensity, low-contrast sources. Furthermore, whereas the inherent noise in random array imaging puts a limit on the obtainable SNR, the URA has no such limit. Computer simulations show that the URA with significant shot and background noise is vastly superior to random array techniques without noise. Implementation permits a detector which is smaller than its random array counterpart.
Fenimore, E.E., Cannon, T.M., Miller, E.L..: 1978, Proc. SPIE, 149, 232
Comparison of Fresnel Zone Plates and Uniformly Redundancy Arrays
Several imaging systems in laser fusion, e-beam fusion, and astronomy employ a Fresnel zone plate (FZP) as a coded aperture. The recent development of URAs promises several improvements in these systems. The first advantage of URA is the fact that its modulation transfer function (MTF) is the same as the MTF of a single pinhole, whereas the MTF of an FZP is an erratic function including some small values. This means that if inverse filtering is used, the URA will be less susceptible to noise. If a correlation analysis is used, the FZP will produce artifacts whereas the URA has no artifact (assuming planar sources). Both the FZP and URA originated from functions which had flat MTFs. However, practical considerations in the implementation of the FZP detracted from its good characteristics whereas the URA was only mildly affected. The second advantage of the URA is that it better utilizes the available detector area. With the FZP, the aperture should be smaller than the detector in order to obtain the full angular resolution corresponding to the thinnest zone. The cyclic nature of the URA allows one to mosaic it in such a way that the entire detector area collect photons from all of the sources within the field of view while maintaining the full angular resolution. If the FZP is as large (or larger) than the detector, all parts of the source will not be resolved with the same resolution. The FZP does have some advantages, in particular its radial symmetry eases the alignment problem; it has a convenient optical decoding method; and higher diffraction order reconstruction might provide better spatial resolution.
Fenimore, E.E.: 1979, LASL Mini Review
X-Ray Imaging Using Uniformly Redundant Arrays

Fenimore, E.E., Cannon, T.M., Van Hulsteyn, D.B., Lee, P.: 1979, Appl. Opt., 18, 945
Uniformly Redundant Arrays Imaging of LAser Driven Compressions: Preliminary Results

Fenimore, E.E.: 1980, Appl. Opt., 19, 2465
Coded Aperture Imaging: the Modulation Transfer Function for Uniformly Redundant Arrays
Coded aperture imaging uses many pinholes to increase the SNR for intrinsically weak sources when the radiation can be neither reflected nor refracted. Effectively, the signal is multiplexed onto an image and then decoded, often by computer, to form a reconstructed image. We derive the modulation transfer function (MTF) of such a system employing URAs. We show that the MTF of a URA system is virtually the same as the MTF of an individual pinhole regardless of the shape or size of the pinhole. Thus, only the location of the pinholes is important for optimum multiplexing and decoding. The shape and the size of the pinholes can then be selected based on other criteria. For example, one can generate self-supporting patterns, useful for energies typically encountered in the imaging of laser driven compressions or in soft X-ray astronomy. Such patterns contain holes all of the same size, easing the etching or plating fabrication efforts for the apertures. A new reconstruction method is introduced called delta-decoding. It improves the resolution capabilities of a coded aperture system ny mitigating a blur often introduced during the reconstruction step.
Fenimore, E.E., Blake, R.L.: 1980, Rev. Sci. Instrum., 51(4), 445
Random array grid collimators
X-ray collimators using grid patterns which are random offer several significant advantages ovre collimators using periodic grids. In particular, random array grid collimators (RAGC's) eliminate the requirement that there be very closely spaced grids if a wide field of obscuration outside the central peak is desired. The RAGC should be less susceptibel to systematic off-axis leaks, and the RAGC has a better high energy response than a periodic grid collimator. The random array technique can also be used to produce converging or diverging collimators. A general theory is presented which predicts the angular response of a RAGC. It is shown that pure random arrays have two problems: there are strong wings in the response function and the patterns are not self-supporting. Restrictions on the randomness of the pattern are suggested which eliminate these problems but at the price of putting an upper limit on the available throughput. However, even in the worst case, the upper limit for a two-dimensional collimator is as high as 23%. In other cases, throughputs the order of 40% are possible with two-dimensional collimators and of 50% with one-dimensional collimators with a large collecting area. Suggestions are presented for easing the fabrication efoort of the grids.
Fenimore, E.E., Cannon, T.M.: 1981, Appl. Opt., 20, 1858
Uniformly Redundant Arrays: Digital Reconstruction Methods
Several new digital reconstruction techniques for coded aperture imaging are developed which are especially applicable to URAs. The techniques provide improved resolution without upsetting the artifact-free nature of URAs. Two new techniques are described; one which allows self-supporting arrays and one which avoids (or at least mitigates) a blur which has been associated with previous correlation analyses. Each of the methods and their resolution improvements are demonstrated with reconstruction of a laser-driven compression. Particular emphasis has been placed on the special sampling required of the encoded picture and the decoding function if artifacts are to be avoided. For large URAs, it is known that another new digital technique, periodic decoding, is much faster. Periodic decoding does produce artifacts, but they usually are negligible.
Fenimore, E.E., Weston, G.S.: 1981, Appl. Opt., 20, 3058
Fast Delta Hadamard Transform
In many fields (e.g. spectroscopy, imaging spectroscopy, photo-acoustic imaging, coded aperture imaging) binary bit patters known as m sequences are used to encode (by multiplexing) a series of measurements in order to obtain a larger throughput. The observed measurements must be decoded to obtain the desired spectrum (or images in case of coded aperture imaging). Decoding in the past has used a technique called the fast Hadamard transform (FHT) whose chief advantage is that it can reduce the computational effort from N^2 multiplies to NlogN additions or subtractions. However, the FHT has the disadvantage that it does not readily allow one to sample more finely than the number of bits used in the m sequence. This can limit the obtainable resolution and cause confusion near the sample boundaries (phasing errors). We have developed both 1-D and 2-D methods (called fast delta Hadamard transforms, FDHT) which overcome both the above limitations. Applications of the FDHT are discussed in the context of Hadamard spectroscopy and coded aperture imaging with URAs. Special emphasis has been placed on how the FDHT can unite techniques used by both of these fields into the same mathematical basis.
Fenimore, E.E.: 1983, Appl. Opt., 22, 826
Large Symmetric Pi-Transformations for Hadamard Transforms

Fenimore, E.E.: 1986, Appl. Opt., 26, 2760
Time-Resolved and Energy-Resolved Aperture Images with URA-tagging
Coded aperture imaging with URAs is the standard technique for imaging above the limit of grazing incident X-ray telescopes. It is an ideal technique for high-energy astrophysics because it has a high throughput, excellent performance on point sources, and the ability to simultaneously measure signal and background. However, many sources of interest in high-energy astrophysics are time variable or require detailed energy spectra. Until now, to obtain a single time (or energy) sample, the photons from the particular time (or energy) interval must be formed into an encoded pattern, then processed to obtain an image for that sample. Therefore, massive computations are required to cover the entire time and energy parameter space. We present a new method of coded aperture analysis called URA-tagging, which provides time and/or energy resolved histories of sources with known positions without using a correlation operation. It can easily reduce the computation time by orders of magnitude compared to the next fastest method, the fast delta Hadamard transform. URA-tagging can also correct for improperly encoded images or motion blurred images. Whereas previous methods for quantifying performance have not taken into account the finite resolution or the quantized sampling, URA-tagging provides a SNR equation that includes all such effects. URA-tagging analysis explains why delta-decoding has a somewhat poorer SNR than balanced correlation: naively, one would expect the better resolution to yield a better SNR. In addition, we show that complementary URAs (exchanged opaque and transparent elements) have different properties, and those with an even number of transparent elements should be preferred.
Finger, M.H., Prince, T.A.: 1995, "Imaging in High Energy Astronomy" (eds. L. Bassani & G. di Cocco; Kluwer Academic Publishers), p. 373
The Photon Statistics of Point Source Correlation Images in Coded Aperture Imaging
We discuss continuous source images for coded aperture gamma-ray telescopes that employ a mask-antimask pair in conjunction with a continuous position sensitive detector. The images discussed are constructed by correlation of the measured mask-antimask differenced count rates with the expected point source response. Results are presented on flux and point source location errors for background dominated observations. These show the impact of the detector's position resolution on the telescope's flux sensitivity and source location accuracy. We also discuss the expected frequency of noise peaks of a given significance in the image.
Finger, M.H., Prince, T.A.: 1995, "Imaging in High Energy Astronomy" (eds. L. Bassani & G. di Cocco; Kluwer Academic Publishers), p. 221
Useful Classes of Redundant Arrays for Imaging Applications
We discuss several classes of redundant arrays. These arrays have applications for indirect imaging in a variety of fields including coded-aperture imaging, interferometric radio imaging, and optical imaging in the presence of atmospheric trubulence. The specific classes we will discuss are all based on Galois fields and include: antisymmetric redundant arrays (ARAs) which have as a subset the hexagonal uniformly redundant arrays (HURAs), non-redundant arrays (NRAs), and the general class of quadratic residue arrays (QRAs).
Frieden, B.R.: 1972, J. Opt. Soc. Am., 62, 511
Restoring with Maximum Likelihood and Maximum Entropy
Given M sampled image values of an incoherent object, what can be deduced as the most likely object? Using a communication theory model for the process of image formation, we find that the most likely objects has a maximum entropy and is represented by a restoring formula that is positive and not band limited. The derivation is an adaption to optics of a formulation by Jaynes for unbiased estimates of positive probability functions. The restoring formula is tested, via computer simulation, upon noisy images of objects consisting of random impulses. These are found to be well restored, with resolution often exceeding the Rayleigh limit and with a complete absence of spurious details. The proviso is that the noise in each image input must not exceed about 40% of the signal image. The restoring method is applied to experimental data consisting of line spectra. Results are consistent with those of the computer simulations.
Grindlay, J., Prince, T.A., Gehrels, N., Tueller, J., Hailey, C.J., Ramsey, B.D., Weisskopf, M.C., Ubertini, P., Skinner, G.K.: 1995, Proc. SPIE, 2518, 202
Energetic X-ray Imaging Survey Telescope
Grindlay, J., Prince, T.A., Harrison, F., Gehrels, N., Hailey, C.J., Ramsey, B.D., Weisskopf, M.C., Skinner, G.K., Ubertini, P.: 1997, in "All Sky X-ray Observations in the Next Decade", Proc. Riken Workshop, eds. M. Matsuoka and N. Kawai, 247
Proposed (to) EXIST: Hard X-ray Imaging All Sky Survey/Monitor
Grindlay, J.: 1998, Adv. Sp. Res., 21(7), 999
Balloon-Borne Hard X-ray Imaging and Future Surveys
Grindlay, J., Hong, J.: 2003, SPIE 5168, 402 NEW!
Optimizing wide-field coded aperture imaging: radial mask holes and scanning
Imaging at hard X-ray energies (~10-600 keV) over very large fields of view (~60 per telescope) is required to conduct a high sensitivity all-sky and all-time survey for black holes. The proposed Energetic X-ray Imaging Survey Telescope (EXIST) could achieve the high sensitivity required for the mission science objectives by scanning an array of wide-field coded aperture telescopes with aperture mask holes radially aligned to minimize auto-collimation by the thick (~7mm) masks required for high energy imaging. Simulation results from a preliminary design study are reported which quantify the improvement in off-axis imaging sensitivity vs. the conventional case with mask holes all perpendicular to the mask. Such masks can be readily constructed from a stacked laminate of thin (1mm) laser-etched W sheets. An even more dramatic increase in coded aperture imaging sensitivity, and dynamic range, for a realistic telescope and imaging detector with typical systematic errors can be achieved by continuously scanning the field of view of the telescope over the source region to be imaged. Simulation results are reported for detectors with systematic errors 1-10%, randomly distributed but unknown in each detector pixel. For the simplified case of a 1-D coded aperture telescope scanning along its pattern, the systematics are removed identically. Results are also presented for the 2-D case with both 1-D and partial 2-D scanning which demonstrate the feasibility of a coded aperture scanning telescope with systematic errors achieving nearly Poisson-limited sensitivity for signal/background ratios S/B ~ 10-4, in constrast to limits typically ~10-100X worse that have been actually achieved by pointed or dithered coded aperture telescopes flown (or proposed) previously.
Goldwurm, A., Byard, K., Dean, A.J., Hall, C.J., Harding, J.S.J.: 1990, Astron. and Astrophys., 227, 640
Laboratory Images with HURA Coded Apertures
In this paper we consider the possibility of using hexagonally uniformly redundant array (HURA) coded apertures for high energy gamma ray telescopes where discrete pixel detectors with low positional resolution are generally used. Results of laboratory tests carried out to study the performance of a coded aperture system using both a stationary and rotating HURA mask with a discrete pixel detector are presented and compared to computer simulations. The tests confirm the simulation results indicating that such a system, when the standard cross-correlation deconvolution is applied, suffers from an intrinsic systematic noise due to the asymmetrical mismatch between the mask elements and the detector pixels. To reduce this coding error which is inherent to the system two techniques have been developed and tested. For a stationary mask, a special configuration using hexagonal pixel detector has been identified for which mask elements are binned nearly exactly by the pixels and no coding error is present. An efficient and fast algorithm, based on mean count subtraction and weighted deconvolution, has also been developed in order to reduce the coding error when a proper design of the system is infeasible or when a rotating mask is used. Both of the above techniques have been proved to be effective, the second being more suitable for rotating masks for which the coding error is smoothed in the convolution stage by the mask rotation.
Goldwurm, A.: 1995, Exp. Astron., 6, 9
Imaging techniques applied to the coded mask sigma telescope
After more than four and a half years of succesful operation aboard the Russian GRANAT space observatory, the French soft gamma-ray telescope SIGMA can be considered a milestone in the application of the coded mask aperture technique to high energy astronomy. The unprecedented imaging performance attained by SIGMA, coupled to the long observation time have yielded impressive results. Here I briefly describe the SIGMA imaging system and review the standard imaging reconstruction techniques and analysis procedures applied to the SIGMA data.
Gorenstein, P., Helmken, H., Gursky, H.: 1976, Astrophys. Space Sci., 42, 89
Localization of Gamma-Ray Bursts with Wide Field Multiple Pinhole Camera System in Near Earth Orbit
A multiple pinhole camera system has been designed and proposed for a small satellite of the SAS type for the detection and localization of gamma-ray bursts. The instrument consists of a three unit array of detectors each of which includes a semi-cylindrical collimator surrounding a two-dimensional position-sensitive detector. The collimator contains slits of 1 mm width that are cut parallel to the axis of the cylinder. The slits are randomly arranged in azimuth around the cylinder. X-rays may enter the counter through several surfaces. The point at which photoelectric interaction takes place is determined in two dimensions in a plane perpendicular to the cylinder axis. Each unit of the system determines the position of a burst to a great circle. An intersection of two (or three) great circles provides the precise positions. The field of view of the instrument is 2.7pi ster, essentially the entire region of the sky not occulted by the Earth. It is designed to operate in 20-100 keV. An instrument sized to fit a SAS spacecraft has a sensitivity of better than 10^- erg cm^-2 for bursts whose intense phase occur in less than a total of three seconds. For stronger bursts (larger than 10^-5 erg cm^-2) the location precision is better than a minute of arc.
Gottesman, S.R., Schneid, E.J.: 1986, IEEE Trans. on Nucl. Sci., 33, 745
PNP: A New Class of Coded Aperture Arrays
We report on a new class of coded aperture arrays which has all the desirable imaging characteristics of the URA, yet is constructible in dimensions which are forbidden to that design. In addition, the new arrays (called PNP arrays, for pseudo-noise product) are of self-supporting geometry, simplifying fabrication and making them ideal candidates for situations where active collimators are employed, as for example in high-energy gamma-ray imaging. A unique and important feature of all PNP arrays is the ability to produce reconstructed images whose noise is uniform regardless of the original source structure. A comparison of the predicted performance of the PNP, URA, GEOMETRIC, and PINHOLE designs is presented.
Gottesman, S.R., Fenimore, E.E.: 1989, Appl. Opt., 28, 4344
New Family of Binary Arrays for Coded Aperture Imaging
We introduce a new family of binary arrays for use in coded aperture imaging which are predicted to have properties and sensitivity (SNR) equal to that of the URA. The new arrays, called MURA (modified URA), have decoding coefficients all of which are unimodular, resulting in a reconstructed image with noise terms completely independent of image-source structure. Although the new arrays are derived from quadratic residues, they do not belong to the cyclic difference set or set of pseudo-noise sequences and consequently are constructable in configurations forbidden for those designs, thus providing the user with a wider selection of aperture patterns to match his particular needs. With the addition of MURAs to the family of binary arrays, all prime numbers can now be used for making optimal coded apertures, increasing the number of available square patterns by more than a factor of 3.
Gourlay, A.R., Stephen, J.B., Young, N.G.S.: 1984, Nucl. Instr. Methods Phys. Res., 221, 54
Geometrically Designed Coded Aperture Mask Arrays
New geometric coded aperture mask designs are proposed, with certain perfect decoding properties. Two of the new designs are compared with a quadratic residue URA mask when used in forming images of conventional hospital gamma camera.
Gourlay, A.R., Young, N.G.S.: 1984, Appl. Opt., 23, 4111
Coded Aperture Imaging: A Class of Flexible Mask Designs
A general class of coded aperture masks woth certain perfect decoding properties are described. These masks are flexible in design in terms of both their shape and openness ratio.
Graziani, C., Lamb, D.Q., Slawinski, R., 1997, preprint, to appear in proceedings of RIKEN workshop on "All-Sky X-ray Observations in the Next Decade"
Determination of X-ray Transient Source Positions by Bayesian Analysis of Coded Aperture Data
We present a new method of transient point source deconvolution for coded-aperture X-ray detectors. Our method is based upon the calculation of the likelihood function and its interpretation as a probability density for the transient source position by an apllication of Bayes' theorem. The method obtains point estimates of source positions by finding the maximum of this probability density, and interval estimates of prescribed probability by choosing suitable contours of constant probability density. We give the results of simulations that we performed to test the method. These estimates underline the intuitively plausible properties of the method and provide a sound quantative basis for the design of coded-aperture systems.
Grebenev, S.A., Pavlinsky, M.N., Sunyaev, R.A.: 1995, "Imaging in High Energy Astronomy" (eds. L. Bassani & G. di Cocco; Kluwer Academic Publishers), p. 155
X-ray Imaging with ART-P/GRANAT
We discuss the use of a wavelet transform for the subtraction of nonuniform background and for filtering images obtained with the coded-mask X-ray telescope ART-P aboard the Granat spacecraft.
Grindlay, J.E., Barrett. D., Lum, K.S.K., Manandhar, R.P., Robbason, B., Vance, S.: 1995, "Imaging in High Energy Astronomy" (eds. L. Bassani & G. di Cocco; Kluwer Academic Publishers), p. 213
New Wavelet Methods for Flatfielding Coded Aparture Images
We describe preliminary results from a new investigation we have undertaken for the processing of "flatfield" images used in coded aperture imaging analysis to remove spatial variations in detector background. We have explored wavelet methods for multiresolution smoothing of detector background images which preserve both high and low spatial frequency components of the detector background. Whereas original EXITE images, from the EXITE1 detector and telescope, wre processed with a high-statistics average detector background image for a subtartive flatfield, any temporal variations in background shape would be better removed using the observations themselves, appropriately smoothed, to define the background shape. Wavelt smoothing, combined with a pointing program including small dither offsets (planned for EXITE2), appears to be a promising technique. Preliminary results of actual EXITE1 image analysis and simulations are presented.
Gull, S.F., Daniel, G.J.: 1978, Nature, 272, 686
Image Reconstruction from Incomplete and Noisy Data
Results are presented of a powerful technique for image reconstruction by a maximum entropy method, which is sufficiently fast to be useful for large and complicated images. Although our examples are taken from the fields of radio and X-ray astronomy, the technique is immediately applicable in spectroscopy, electron microscopy, X-ray crystallography, geophysics and virtually any type of optical image processing. Applied to radioastronomical data, the algorithms reveals details not seen by conventional analysis, but which are known to exist.
Gunson, J., Polychronopulos, B.: 1976, Mon. Not. R. Astr. Soc., 177, 485
Optimum Design of a Coded Mask X-Ray Telescope for Rocket Applications
A review of the principles of current X-ray telescopes is made with particular emphasis on two-step imaging techniques involving coded masks. The merits and limitations of the various types of coding masks in use are examined in detail. The limitations are shown to arise from the finite nature of practical masks. By postulating periodicity, 'optimum masks' can be constructed with ideal imaging qualities. The theory of the design of such masks and practical considerations involved in the design of a rocket-borne X-ray telescope system are discussed in full, with particular attention paid to resolution, field of view and image noise. The main emphasis throughout the paper is on one-dimensional masks but two-dimensional are also studied. It is concluded that optimum masks could prove very valuable in astronomical applications and also in other fields such able in astronomical applications and also in other fields such as radiography, where high imaging quality coupled with high sensitivity and low cost are of utmost importance.
Haberl, F.: 1984, Diplomarbeit, MPI-Garching
Untersuchungen an einer Kodierten Lochkamera fuer Astronomische Messungen im Harten Roentgenbereich

Hammersley, A.P., Skinner, G.K.: 1984, Nucl. Instr. Methods Phys. Res., 221, 45
Data Processing of Imperfectly Coded Images
The theory of mask coding is well established for perfect coding systems, but imperfections in practical situations produce new data processing problems. The Spacelab 2 telescopes are fully coded systems, but some complications arise as parts of the detector are obscured by a strengthening cross. The effects of this sort of obscuration on image quality and ways of handling them will be discussed.
Hammersley, A.P.: 1986, Ph.D. Thesis, University of Birmingham
The Reconstruction of Coded Mask Data under Conditions Realistic to X-Ray Astronomy Observations

Hammersley, A.P., Ponman, T.J., Skinner, G.K.: 1992, Nucl. Instr. Methods Phys. Res., A311, 585
Reconstruction of images from a coded-aperture box camera
Methods for reconstruction of images from coded-aperture box cameras are discussed. A fast reconstruction method for unbiased reconstruction is presented and examples of its for unbiased reconstruction is presented and examples of its application to simulated and real data are given. An iterative procedure to further reduce coding noise is proposed and its effectiveness quantified.
In 't Zand, J.J.M.: 1992, Ph.D. Thesis, University of Utrecht
A coded-mask imager as monitor of galactic X-ray sources

In 't Zand, J.J.M., Heise, J., Jager, R.: 1994, Astron. and Astrophys., 288, 665
The optimum open fraction of coded apertures with an application to the wide field X-ray cameras of SAX
We consider issues that concern the mathematical description of coded aperture patterns. Primarily this involves the relation between the open fraction of such patterns and the signal-to-noise ratio of imaged point sources. A refinement of the corresponding theory is introduced, taking into account the spatial response of the coded aperture camera. From this we predict that patterns with an open fraction of less than 0.5 can enhance the performance of coded aperture cameras to bright sources, as opposed to what was previously thought. As an application of the refined theory, we tested candidate open fractions in the instrumental configuration of two identical, wide field, coded aperture X-ray cameras (1.8-30 keV), that will be part of the X-ray satellite SAX (to be launched in late 1995). These tests consisted of numerical simulations of several types of observations, and show that open fractions between 0.25 and 0.33 are to be favored for the SAX cameras. The improvement in signal-to-noise ratio with respect to the commonly used open fraction of 0.5 is up to 30%. WHenever telemetry limits the data coverage, this profit may well be larger. We also address additional aperture constraints as applied to the SAX cameras, such as the aperture geometry and pattern. From this analysis we propose a new type of coded aperture pattern for the SAX cameras with an open fraction equal to 0.33, which possesses near-ideal mathematical properties.
In 't Zand, J.J.M., Fenimore, E.E., Kawai, N., Yoshida, Y., Matsuoka, M., Yamauchi, M.: 1995, "Imaging in High Energy Astronomy" (eds. L. Bassani & G. di Cocco; Kluwer Academic Publishers), p. 137
Imaging Design of the Wide Field X-Ray Monitor onboard the HETE satellite
The High-Energy Transient Experiment (HETE), to be launched in 1995, will study Gamma-Ray Bursts in an unprecedented wide wavelength range fromm Gamma- and X-ray to UV wavelengths. The X-ray range (2 to 25 keV) will be covered by 2 perpendicularly oriented 1-dimensional coded aperture cameras. These instruments cover a wide field of view of 2 sr and have a relatively large potential to locate GRBs to a fraction of a degree, which is an order of magnitude better than BATSE. The imaging design of these coded aperture cameras relates to the design of the coded apertures and the decoding algorithm. The aperture pattern is to a large extent determined by the high background in this wide field application abd the low number of pattern elements (~100) in each direction. The result is a random pattern with an open fraction of 33%. An onboard decoding algorithm is dedicated to the localization of a single point source.
Jayanthi, U.B., Braga, J.: 1991, Nucl. Instr. Methods Phys. Res., A310, 685
Physical Implementation of an Antimask in URA Based Coded Mask Systems
X- and gamma-ray astronomy experiments which employ rectangular URA coded masks alone show artifacts in the images reconstructed due to the nonuniform background levels in the detector plane. The employment of a separate antimask in addition to the mask in observations is useful to eliminate this problem. We propose here a method to implement the antimask with the same mask, utilizing the antisymmetric properties in the mask pattern, thereby avoiding the need for a separate antimask in an experiment. Simulations performed with this mask-antimask system are presented to show its advantages.
Jimenez, J., Olmos, P., de Pablos, J.L., Perez, J.M.: 1991, Appl. Opt., 30, 549
Gamma Ray Imaging Using Coded aperture Masks: a Computer Simulation Approach
The gamma-ray imaging using coded aperture masks as focusing elements is an extended technique for static position sensitive detectors. Several transfer functions have been proposed to implement mathematically the set of holes in the mask, the uniformly redundant array collimator being the most popular design. A considerable amount of work has been done to improve the digital methods to deconvolve the gamma-ray image, formed at the detector plane, with this transfer function. Here we present a study of the behavior of these techniques when applied to the geometric shadows produced by a set of point emitters. Comparison of the shape of the object reconstructed from these shadows with that resulting from the analytical reconstruction is performed, defining the validity ranges of the usual algorithmic approximations reported in the literature. Finally, a set of improvements are discussed.
Jupp, I.D., Green, A.R., Dean, A.J.: 1995, "Imaging in High Energy Astronomy" (eds. L. Bassani & G. di Cocco; Kluwer Academic Publishers), p. 203
Optimised Sampling for Hexagonal Array Coded Mask Telescopes
The sensitivity of hexagonal geometry, gamma-ray coded aperture telescopes has been studied in order to investigate the trade-off between the nominal angular resolution and the mean reconstructed image signal to noise (SNR) that occurs when a pixellated detector array is used and images are retrieved by a simple correlation analysis. Without high fine sampling of the coded mask by the detector plane, the image SNR is seriously comprimised if the source under observation lies close to a sky pixel boundary. Increasing the integer sampling partially restores the image SNR, but at the expense of the angular resolution. A method for improving the image SNR across the sky pixel boundaries has been investigated, resulting in sky images that are free from the SNR modulation encountered with integer fine sampling of the shadowgram, and without any significant loss in angular resolution.
Jupp, I.D., Green, A.R., Dean, A.J.: 1995, "Imaging in High Energy Astronomy" (eds. L. Bassani & G. di Cocco; Kluwer Academic Publishers), p. 209
Imaging with Two Angular Scales Using Coded Mask Techniques
Coded aperture telescopes employing a high angular resolution specifically for accurate point source imaging, are subject to a severe loss in sensitivity with respect to the extended source imaging capability. However, by choosing a mask with a larger element size the telescope becomes sensitive to more extended regions, but consequently there will be considerable source confusion in crowded fields. This paper describes two systems which simultaneously take images of point sources and extended regions over the same energy range.
Kohman, T.P.: 1989, Rev. Sci. Instrum., 60, 3396
Coded-aperture X- or gamma-ray telescope with least-squares image reconstruction. I - Design considerations. II - Computer simulation
This paper presents a method for reconstructing a multiplex image in a coded-aperture device for imaging X-ray or gamma-rays by using the least-squares solution of an overdetermined set of simultaneous equations connecting the object, the aperture, and the image. It is shown that a completely open auxiliary aperture of carefully chosen size and position, placed ahead of the coded aperture can limit the number of object pixels to less than the number of image pixels, a necessary condition for yielding an overdetermined set of equations. Various aspects of implementing the design as a practical X-ray or gamma-ray telescope for flight aboard an orbiting satellite or stratospheric balloon are discussed. A computer program developed for simulating the operation of this telescope is described, and the results of simulations are presented, demonstrating the feasibility of this approach to coded-aperture imaging.
Kohman, T.P.: 1997, Rev. Sci. Instrum., 68, 2404
Coded-aperture X- or gamma-ray telescope with least squares image reconstruction. III - Data acquisition and analysis enhancements
The previously described design of a cosmic X- or gamma-ray telescope with least-squares image reconstruction has been enhanced to provide for mask-antimask opereration. This cancels and eliminates uncertainties in the detector background. The simulations of its operation have been made more realistic by incorporating instrumental blurring of sources. A second-stage least squares procedure determines the precise positions and total fluxes of point sources responsible for clusters of above-background pixels in the field resulting from the first-stage reconstruction. Another program converts source positions in the image plane to celestial coordinates and vice versa, the image being a gnomic projection of a region of the sky. A complete sky-to-sky simulation of the imaging process is presented. It is demonstrated that the point-spread function of the overall imaging process is essentially perfect.
Kopilovich, L.E., Sodin, L.G.: 1994, Mon. Not. R. Astr. Soc., 266, 357
Synthesis of coded masks for gamma-ray and X-ray telescopes
We propose the synthesis of coded masks for gamma-ray and X-ray telescopes with square or rectangular apertures, using two-dimensional difference sets. Compared with masks employed at present, these facilitate a significant increase in the capability to choose both the size and the fraction of the 'open' pixels, i.e. the telescope resolution and sensitivity. We also point out the possibility of constructing masks on the basis of two-dimensional generalized difference sets, which considerably increase the number of feasible variants.
Lei, F., Fraser-Mitchell J., Yearworth, M.: 1991, Exp. Astron., 1, 285
A Comparison of Different Imaging Techniques in Low Energy gamma-Ray Astronomy
Three main imaging techniques used in low energy gamma-ray (20-1000 keV) astronomy are briefly described. Their imaging capabilities are first compared from the point of view of image formation, then simulated images of the Galactic Center are produced using these three techniques. The image qualities are evaluated with respect to their ability to determine the locations and intensities of point sources in the presence of background and diffuse emission.
Lei, F., Palmer, M.J., Jupp, I.D., Ramsden, D.: 1995, "Imaging in High Energy Astronomy" (eds. L. Bassani & G. di Cocco; Kluwer Academic Publishers), p. 255
A Novel System for the Location of GRBs
A long standing problem in the identification of GRBs is the inability of current instruments to provide rapidly an accurate source location. An accuracy of a few acrminutes is required to allow follow-up observations at other wavelengths to be meaningful. An imaging system which employs one-dimensional coded masks in conjunction with silicon strip detectors can be used to locate bursts with an accuracy within a few acrminutes. The field of view of such an instrument could be more than 2 sr. This paper addresses the imaging principles and the design of a gamma-ray burst telescope which uses this technology.
Lueke, H.D., Busboom, A.: 1997, Appl. Opt., 36, 6612
Binary Arrays with Perfect Odd-periodic Autocorrelation
Arrays with good autocorrelation functions are required for coded aperture imaging. A generalized folding procedure is derived that permits the construction of arrays with good autocorrelation properties from well correlating sequences for many array sizes. This synthesis method is applied to the construction of approximately square binary arrays with a single zero element and perfect odd-periodic autocorrelation functions. In additions, new binary arrays with constant sidelobes of their periodic autocorrelation functions (uniformly redundant arrays) can be generated with the generalized folding method.
Lueke, H.D., Busboom, A.: 1998, Appl. Opt., 37, 856
Mismatched filtering of periodic and odd-periodic binary arrays
Arrays with good correlation properties are required for coded-aperture imaging, as well as for other applications of two-dimensional signal processing. Since binary arrays with perfect periodic autocorrelation functions exist for only a few sizes, mismatched filtering is discussed. Mismatched filtering entirely suppresses any sidelobes of the periodic autocorrelation function at the expense of a slightly reduced signal-to-noise ratio. New construction methods for binary arrays are presented for which this loss, with respect to periodic or odd-periodic correlation, converges to zero with an increasing array size.
Lund, N.: 1985, SPIE Proc., 597, 95
The Watch Gamma-Burst Detector for Eureca-I
The Watch gamma-burst detector will be flown for the first time on the ESA microgravity satellite EURECA-I. EURECA is a retrievable satellite (...) planned for March 1988 (...) The unique feature of Watch is its capability for real time localizations of the sources of strong gamma-ray bursts. The expected source localization accuracy is about 10 arcminutes. The aim for the future is to supplement it with a rapidly moving optical telescope (...) Watch will not only study gamma bursts but also detected hard X-ray transients and monitor the X-ray sky in the energy band from 5 to 120 keV.
Machanda, R.K.: 1995, "Imaging in High Energy Astronomy" (eds. L. Bassani & G. di Cocco; Kluwer Academic Publishers), p. 171
HEXIT: High Energy X-ray Imaging Telescope
A balloon-borne High Energy X-ray Imaging Telescope is presently being developed for imaging studies in 20 keV to 1 MeV energy region. The payload consists of a 40 cm diameter 'Phoswich Anger Camera' made of NaI(Tl) and CsI(Na) scintillation crystals viewed by 13 phototubes and a URA-based coded mask, mounted on a servo-stabilized alta-azimuth platform. This paper described the design characteristics and laboratory performance of the detector system.
Maggioli, P.P., Caroli, E., Natalucci, L., Spizzichino, A.: 1984, Nucl. Instr. Methods Phys. Res., 221, 82
A Numerical Method for Recognition of Virtual Images in Coded Mask Telescopes
A problem with telescopes utilizing replicated structure coded masks is the possible occurrence of virtual images. A numerical method to discriminate virtual from real images, and to determine their correct location in the field of view, is described. The performance and reliability of this method, based on eight "ad hoc" modifications of the coding array, have been investigated by Monte Carlo simulations.
Makishima, K., Miyamoto, S., Murakami, T. et al.: 1977, Proc. New Instrumentation for Space Astronomy (vd. Hucht & Vaiana
Modulation Collimator as an Imaging Device
Recent developments in the concept of the modulation collimator as an imaging device are summarized. In particular, we discuss a system of modulation collimators, tentatively called as the multi-pitch modulation collimator of the Fourier-transform telescope, which reconciles a large dynamic range of the source resolution with the high sensitivity, i.e. the brightness of the reconstructed source image (...) Results of simulation calculation are presented for modest instrumental conditions.
McConnell, M.L., Forrest, D.J., Chupp, E.L., Dunphy, P.P.: 1982, IEEE Trans. Nucl. Sc., NS-29, 155
A Coded Aperture Gamma Ray Telescope
A gamma ray telescope is being developed to operate in the energy range 100 keV to 5 MeV utilizing coded aperture imaging. The design incorporates a mask pattern based on a Uniformly Redundant Array (URA), which has been shown to have ideal imaging characteristics. A mask anti-mask procedure is used to eliminate the effects of any possible systematic variations in detector background rates. The detector array is composed of 35 elements of the high-Z material Bismuth Germanate (BGO). Results of laboratory testing of the imaging properties will be presented. A southern hemisphere balloon flight is planned for 1982 with the goal of observing the 0.511 MeV radiation from the Galactic Center. Computer calculations show that a point source of this radiation can be located to within +/- 1 degree.
Mertz, L.: 1968, Proc. Symp. Modern Optics
A Dilute Image Transform with Application to an X-Ray Star Camera
If a Ronchi grating rotates in an image plane, then each image point experiences a quasi-orthogonal modulation. The resulting sum forms a one dimensional transform of the two dimensional image...
Miyamoto, S.: 1977, Space Sci. Instrum., 3, 473
Hadamard Transform X-Ray Telescope
A Hadamard transform X-ray telescope is a type of Dicke's random hole X-ray camera for observing the X-ray sky. Instead of making a random pattern mask, a cyclic Hadamard matrix or PN sequence is used to make the mask pattern for this telescope. With this mask and a position sensitive X-ray detector, one can get Hadamard transformed image data of the X-ray sky and easily reconstruct the X-ray sky image from the observed data. The Hadamard matrix can be used to make one dimensional X-ray telescope as well as two-dimensional telescopes. In the case that spurious counts on the detector are predominant over image counts and background counts, the SNR advantage of this telescope is sqrt{N}/2 compared to the slat type X-ray telescope of the same angular resolution, where N is the number of position sensitive detector cells and N+1 is the order of the cyclic Hadamard matrix employed to make this mask.
Miyamoto, S., Tsunemi, M., Tsuno, K.: 1981, Nucl. Instr. Methods Phys. Res., 180, 557
Some Characteristics of Hadamard Transform X-Ray Telescopes
The characteristics of the Hadamard transform X-ray telescope (HTXT) are investigated and the following results are obtained: (1) the statistical error of the image, reconstructed by the HTXT, is uniform all over the image, which is different from the case of a pinhole camera. (2) The SNR of the HTXT is much better than that of the pinhole camera in the case that spurious counts are predominant over the counts due to the X-ray image. (3) The statistical error of the image, which is obtained by summing of several image elements of an HTXT of a finer angular resolution to get a fixed angular resolution is worse that obtained by the HTXT which is designed to the final angular resolution beforehand. (4) Even in the case that data of some detector cells are lost, the image can be reconstructed. (5) All detector cells of the HTXT must see the same X-ray image through the Hadamard mask, otherwise the error due to the fluctuating number of mask holes is introduced. (6) The image reconstructed by the HTXT becomes obscure by the amount of the positional resolution of the X-ray detector in the case that the positional resolution is larger than the cell of the detector. (7) The Hadamard transform imaging system described in this paper is also applicable to other fields such as plasma and a medical diagnoses with slight alteration of the system and is expected to have the same characteristics as the HTXT.
Natalucci, L., Soggiu, M.E.: 1995, "Imaging in High Energy Astronomy" (eds. L. Bassani & G. di Cocco; Kluwer Academic Publishers), p. 149
Scientific Design and Opitmization of a Coded Mask Hard X-Ray Telescope
The design of a coded mask X-ray instrument depends on a combination of factors: its target function (monitor, spectroscope, etc.), the field of view, the energy range and, therefore, the detection device. Recently, the high pressures attainable in gas detectors for use in space and the outcome of ultrafast electronics techniques have made proportional counters well suited for observations in the energy range from a few keV up to 200 keV. In this medium-hard X-ray range, the use of a large area detector must be coupled to an efficient shielding to reduce cosmic diffuse background. In this paper, the criteria which have been adopted in the design of the MART-LIME experiment on board SPECTRUM X/GAMMA are described, with emphasis on the imaging characteristics.
Nelson, E.D., Fredman, M.L.: 1970, J. Opt. Soc. Am., 60, 1664
Hadamard Spectroscopy
The basic concept of Hadamard spectroscopy is presented. General methods are given for the construction of cyclic measurement matrices. A new algorithm, which permits adaptation of the fast HAdamard transform to the calculation of spectral intensities when the measurement matrices are cyclic, is introduced. Some applications are also briefly discussed.
Nottingham, M.R.: 1993, Ph.D. Thesis, University of Birmingham (UK)
X-ray observations of the galactic centre utilising a new analytical Technique
A new technique for the analysis of data from coded mask telescopes is introduced. It is shown that this new technique called 'Maximum Likelihood Fitting' (MALF), has several advantages over conventional techniques espacially in the reduction of coding noise from the 'box cameras' design of coded mask telescopes. The new technique is then used with data obtained by the TTM coded mask instrument when the instrument was pointing in the direction of the galactic centre region. Using the MALF technique it was possible to solve for the intensity (in different energy channels) of the small scale (1 degree) diffuse emission which is seen emanating from the galactic nucleus. This would be the first time that accurate spectral measurements of this source have been obtained, however no spatial information could be obtained as an assumed distribution had to be used. All of the point sources whci were inthe field of view of the instrument during the observations of the galactic centre were also analysed using a variaty of spectral models to try and obtain as much information about individual sources and also to investigate the differences observed between the various groups of X-ray binaries.
Nugent, K.A.: 1987, Appl. Opt., 26, 563
Coded Aperture Imaging: a Fourier Analysis
Coded aperture imaging is analyzed in Fourier space and the conditions for obtaining artifact-free 3-D images are obtained. It is deduced that an infinite square array of coding apertures will obey these conditions. A finite array is considered and it is shown that, after a certain coordinate transformation has been performed, the finite aperture acts to bandlimit the spatial frequencies in the image. This results is used to deduce a sampling theorem for coded apertures which places limits on the artifact-free 3-D information that may be obtained. It is thus deduced that 3-D information with a resolution greater than the limits placed here may only be obtained by extrapolating the data to larger viewing angles.
Palmer, D., Prince, T.A.: 1987, IEEE Trans. on Nucl. Sci., 34, 71
A Laboratory Demonstration of High-Resolution Hard X-Ray and Gamma-Ray imaging using Fourier-Transform Techniques
A laboratory imaging system has been developed to study the use of Fourier-transform techniques in high-resolution hard X-ray and gamma-ray imaging, with particular emphasis on possible application to high-energy astronomy. We discuss considerations for the design of a Fourier-transform imager and describe the instrumentation used in the laboratory studies. Several analysis methods for image reconstruction are discussed including the CLEAN algorithm and maximum entropy methods. Images obtained using these methods are presented.
Palmer, D.: 1992, Ph. D. Thesis, California Institute of Technology
Gamma-ray Imaging Observations of Supernova 1987a
The Caltech imaging gamma-ray telescope has made four balloon flights from Alice Springs, Australia, to observe the hard X-ray and gamma-ray emission from Supernova 1987a as it evolved between 1987 May and 1989 April. We have detected gamma-rays with the time behavior and spectral signature expected from freshly-synthesized readioisotopes embedded in a cloud of ejecta. In particular, we detect the 847 and 1238 keV gamma-ray lines produced by the decay of 56Co, and the continuum spectrum expected from Compton scattering of these gamma-rays. The results of these observations are compared with other measurements and with theoretical models of supernovae, and it is found that our results are consistent with core-collapse models for SN 1987a in which the centrally-produced radioisotopes have propagated outwards to mix with the ejecta.
Palmieri, T.M.: 1974, Astrophys. Space Sci., 26, 431
An X-Ray Telescope Sensitive at High Energies
A telescope is described which is capable of producing images of point sources of x-rays without recourse to reflection optics. A mathematical approach to the operation and to the SNR properties of the telescope is presented. This is followed by several examples of its response and a discussion of detectors that could be used with the device.
Palmieri, T.M.: 1974, Astrophys. Space Sci., 28, 277
Multiplex Methods and Advantages in X-Ray Astronomy
The multiplex advantage is defined and applied in considering various techniques presently used in X-ray astronomy. It is concluded that the multiplex advantage will be useful in evaluating future techniques to be used in X-ray astronomy.
Patterson, T.G.: 1990, Ph.D. Thesis, University of Birmingham
A Survey of the Galactic Bulge, Large Magellanic Cloud and Cygnus Region with A Simple Configuration Coded Mask X-Ray Telescope

Phillipps, S., Davies, J.: 1991, Mon. Not. R. Astr. Soc., 251, 105
A Cross-Correlation Method for Surface Photometry
We apply the cross-correlation technique familiar in spectral matching to the two-dimensional case of surface photometry of galaxies with low surface brightness, i.e. to a problem of surface photometry with low signal-to-noise ratio. Comparison with normal profiling methods shows a considerable improvement in accuracy with photometric parameters can be obtained. In particular, for simulated image representing objects like GP1444a which are fairly large but have extremely low surface brightness, we find errors of only ~2 and 3 percent in the scalelength and central intensity, smaller by a factor ~6 than the errors obtained from intensity profiles.
Ponman, T.J.: 1984, Nucl. Instr. Methods Phys. Res., 221, 72
Maximum Entropy Methods
For some years now two different entropy expressions have been in use for maximum entropy image restoration and there has been some controversy over which one is appropriate for a given problem. Her two further entropies are presented and it is argued that there is no single correct algorithm. The properties of the four different methods are compared using simple 1-D simulations with a view to showing how they can be used together to gain as much information as possible about the original object.
Ponman, T.J., Hammersley, A.P., Skinner, G.K.: 1987, Nucl. Instr. Methods Phys. Res., A262, 419
Error Analysis for a Noncyclic Imaging System
The imaging properties of the "coded aperture box camera", a noncyclic coded mask system in which mask and detector are the same size, are investigated under the assumption of random positioning of the mask holes. Each source in the field of view generates noise due to the imperfect coding, in addition to the Poisson and detector noise present in a cyclic coded mask imager. Equations are presented for the magnitude and spatial variation of each of these three sources of noise, and their validity is confirmed by simulations. For a small number of sources the coding variance from each can simply be superposed to a good approximation. In the case of many sources the coding variance is less than the superposition value. The box camera has advantage over a collimated cyclic imager, particularly for wide field imaging, provided that coding errors are not too large compared to Poisson and detector noise.
Pratt, W.K., Kane, J., Andrews, H.C.: 1969, Proc. IEEE, 57, 58
Hadamard Transform Image Coding
The introduction of the fast Fourier transform algorithm has led to the development of the Fourier transform image coding technique whereby the two-dimensional Fourier transform of an image is transmitted over a channel rather than the image itself. This development has further led to a related image coding technique in which an image is transformed by a Hadamard matrix operator. The Hadamard matrix is a square array of plus and minus ones whose rows and columns are orthogonal to one another. A high-speed computational algorithm, similar to the fast Fourier transform algorithm, which performs the Hadamard transformation has been developed. Since only real number additions and subtractions are required with the Hadamard transform, an order of magnitude speed advantage is possible compared to the complex number Fourier transform. Transmitting the Hadamard transform of an image rather than the spatial representation of the image provides a potential toleration to channel errors and the possibility of reduced bandwidth transmission.
Proctor, R.J., Skinner, G.K., Willmore, A.P.: 1979, Mon. Not. R. Astr. Soc., 187, 633
The Design of Optimum Coded Mask X-Ray Telescopes

Ranieri, M., Badiali, D., Cardini, D., Emanuale, A., Auriemma, G.: 1981, Journ. Brit. Interplan. Society, 34, 135
Coded Aperture Telescopes for Hard X-ray Astronomy
The coded aperture technique and its applications to a balloon borne hard X-ray telescope is described; results of Monte Carlo simulation are presented and the experimental apparatus is illustrated.
Reglero, V. et al.: 1996, preprint
Low Energy Gamma Ray Imager on MINISAT-01
The Low Energy Gamma Ray Imager (LEGRI) is one of two astronomical instruments on the MINISAT-01 mission and is devoted to exploring the hard X-ray and low gamma-ray emission of the celestial bodies. MINISAT-01 launch is due for December 1996 by a Pegasus launcher in the Canary Islands area. A coded mask coupled to a 100 pixel detector plane formed by 80 HgI2 and 20 CdZnTe solid state detectors provide good imaging capability at 20-100 keV spectral region. Around 40 objects are going to be monitored during the 2 years of MINISAT 01 nominal life time. The Galactic Center region, black hole candidates, neutron stars in binary systems and hard X-ray emitters are among the LEGRI targets. (...) In this paper we present a review of the LEGRI technologies, main subsystems, operations plan and some detail about the LEGRI collaboration and management system.
Rideout, R.M., Skinner, G.K.: 1995, "Imaging in High Energy Astronomy" (eds. L. Bassani & G. di Cocco; Kluwer Academic Publishers), p. 167
The Coded Mask Design and Test Flight Results of a Small Array Germanium Telescope
A small germanium array detector had been incorporated into a coded mask telescope and was flown as a piggy-back experiment on the NASA/GRIS high altitude balloon payload. The flight, on the 24th September 1993 from Fort Sumner, New Mexico, succesfully demonstrated the use of a compact 3X3 germanium array detector to achieve good imaging of X-ray and gamma-ray sources. This paper describes the techniques used to select a suitable coded mask pattern for the telescope as well giving a brief overview of flight results. Comparisons are made of the imaging ability of several different classes of coded mask patterns. By applying constraints to the design of the otherwise 'random' coded mask patterns, the performance in terms of point source resolution is seen to be better than that of masks based on cyclic difference sets and 'constraint-less' random masks.
Rideout, R.M., Skinner, G.K.: 1996, Astron. Astroph., in press
Minimum Error Image Reconstruction for Coded Mask Telescopes
A new method is proposed for reconstructing the data from coded aperture X/gamma-ray telescopes. This technique, based on the Wiener criterion, is essentially a generalization of existing Wiener filtering methods but is not confined to systems with position independent point source response functions. The reconstruction method trades off the image degrading effects of statistical detector noise with the effects of imperfect source field coding, to produce a minimum error source field estimate. It offers advantages if the coding properties of the mask-detector configuration considered are not 'ideal' and is particularly useful where multiple dithered observations are made of a given source field. The proposed methid is applied to simulated data and to data from a recent balloon flight of an experimental coded mask telescope. It is shown to give better quality images than those formed by more conventional methods.
Robert, A. et al.: 1996, preprint
LEGRI Science Operation Center and Observing Programme
(...) In this paper a brief description of the LEGRI Observing Programme is presented together with the estimations of LEGRI sensitivity and the description of the different SOC tasks.
Roques, J.P.: 1987, Appl. Opt., 26, 3862
Fast Decoding Algorithms for Uniformly Redundant Arrays
Coded mask aperture imaging techniques are now used in various fields, in particular in X-ray and gamma-ray astronomy. With such systems it is possible to construct apertures which have autocorrelation functions with perfectly flat sidelobes. For quadratic residue arrays (URAs), we have developed fast deconvolution algorithms based on conventional decoding methods but taking advantage of the mathematical properties of the decoding matrices. Balanced decoding, delta decoding, and finely sampled decoding are discussed.
Rothschild, R.E., Matteson, J.L., Heindl, W.A., et al.: 1995 SPIE
The Continuous Hard X-ray Imager for Astrophysics (CHIP) (proposed coded aperture imaging mission between 2 and 100 keV with CdZnTe detectors and an array of flat coded apertures)
Schmitz-Fraysse, M-C., Stephen, J.B.: 1995, "Imaging in High Energy Astronomy" (eds. L. Bassani & G. di Cocco; Kluwer Academic Publishers), p. 189
Advanced Techniques of Image Correction for the Coded Mask Telescope SIGMA
The position sensitive detector of the SIGMA telescope, a variety of the Anger camera, suffers from intrinsic non unifromity defects. In order to maximize the signal to noise ratio of the observed gamma-ray sources, the removal of the systematic defects should be nearly perfect. In this paper we describe and give the achieved performances of some correction methods. In particular, we describe an adaptive filtering method which is atomatically adjusted for the best possible signal to noise ratio.
Shevgaonkar, R.K.: 1986, Astron. and Astrophys., 162, 349
Maximum Entropy Method for Phase-Unstable Aperture Synthesis
An application of the maximum entropy method to closure data is described here. It is shown that although the basic principle of the method is to obtain a brightness distribution which has highest entropy the closure phases play a prominent role in giving the correct reconstruction especially when the distributions are complex and the measurements are large. The method gives faithful reconstruction for the observed random phase error up to plus minus 150 deg. The method can be used as an alternative to the routinely used 'self-calibration' technique to improve the astronomical images obtained from the phase unstable interferometers. For large fields of view when due to repetitive use of CLEAN the 'self-calibration' method becomes time consuming. MEM with closure phase may have a computational advantage. For extended sources as the performance of CLEAN deteriorates the maximum entropy method could be superior to the self-calibration.
Sims, M., Turner, M.J.L., Willingale, R.: 1980, Space Sci. Instrum., 5, 109
A Wide Field X-Ray Camera
A Wide Field of View Camera based on the Dicke or Coded Mask principle is described. It is shown that this type of instrument is more sensitive than a pinhole camera, or than a scanning survey of a given region of sky for wide field conditions. The design of a practical camera is discussed and the sensitivity and performance of the chosen design are evaluated by means of computer simulations. The Wiener Filter and Maximum Entropy Methods of deconvolution are described and these methods are compared with each other and cross-correlation using data from the computer simulations. It is shown that the analytic expressions for sensitivity used by other workers are confirmed by the simulations, and that ghost images caused by incomplete coding can be substantially eliminated by the use of the Wiener Filter and the MAximum Entropy Method, with some penalty in computer time for the latter. The cyclic mask configuration is compared with the simple mask camera. It is shown that when the diffuse X-ray background dominates, the simple system is more sensitive and has the better angular resolution. When sources dominate the simple system is less sensitive. It is concluded that the simple coded mask camera is the best instrument for wide field imaging of the X-ray sky.
Sims, M.: 1981, Ph.D. Thesis, University of Leicester
A Wide Field Camera for X-Ray Astronomy

Sims, M., Willingale, R., Turner, M.J.L.: 1984, Nucl. Instr. Methods Phys. Res., 221, 77
Computer Simulations of the Performance of Practical Designs of Coded Aperture Cameras
The coded aperture camera is an instrument suitable for many applications in X- and gamma-ray imaging. In this paper the effect of a partially obscuring window support is considered using a computer simulation technique. This allows the signal to noise in the decoded image to be evaluated for practical designs of camera, a process which is difficult to carry out using an analytical approach. The sensitivity of simple and cyclic forms of camera is determined for real celestial X-ray source distributions under both source and diffuse background dominated conditions. The image obtained is shown to be degraded but not destroyed by the interference of the window support, and the simple form of camera is shown to be more sensitive than the cyclic form for wide fields of view.
Sims, M., Turner, M.J.L., Willingale, R.: 1985, Nucl. Instr. Methods Phys. Res., 228, 512
The Influence of Disturbing Effects on the Performance of a Wide Field Coded Mask X-Ray Camera
The coded aperture telescope, or Dicke camera, is seen as an instrument suitable for many applications in X-ray and gamma ray imaging. In this paper the effects of a partially obscuring window mask support or collimator, a detector with limited spatial resolution, and motion of the camera during image integration are considered using a computer simulation of the performance of such a camera. Cross correlation and the Wiener filter are used to deconvolve the data. It is shown that while these effects cause a degradation in performance this is in no case catastrophic. Deterioration of the image is shown to be greatest where strong sources are present in the field of view and is quite small (~10%) when diffuse background is the major element. A comparison between the cyclic mask camera and the simple mask camera is made under various conditions and it is shown that the simple mask camera has a moderate advantage particularly when imaging a wide field of view.
Skilling, J.: 1984, Nature, 309, 748
The Maximum Entropy Method

Skinner, G.K.: 1980, J. Brit. Interplanetary Soc., 33, 333
Imaging of Cosmic X-Ray Sources Using Coded Mask Techniques

Skinner, G.K.: 1984, Nucl. Instr. Methods Phys. Res., 221, 33
Imaging with Coded-Aperture Masks
Coded-MAsk imaging systems may be considered as generalizations of the pinhole camera in which the "coding-plane" contains a carefully chosen pattern of transparent and opaque regions instead of a single pinhole. A variety of instruments result from selecting different coding patterns and from simple geometrical variations on the theme. The various schemes which have been proposed and used and the methods of interpreting the data obtained with them are reviewed and compared. Emphasis is placed on systems for X-ray astronomy.
Skinner, G.K., Ponman, T.J., Hammersley, A.P., Eyles, C.J.: 1987, Astrophys. Space Sci., 136, 337
Techniques for the Analysis of Data from Coded-Mask X-Ray Telescopes
Several techniques useful in the analysis of data from coded-mask telescopes are presented. Methods of handling changes in the instrument pointing direction are reviewed and ways of using FFT techniques to do the deconvolution considered. Emphasis is on techniques for optimally-coded systems, but it is shown that the range of systems included in this class can be extended through the new concept of 'partial cycle averaging'.
Skinner, G.K.: 1988, Astro. Lett. and Communications, 27, 199
The Spacelab 2 X-ray Telescope: Coded Mask Imaging in Orbit
The payload of the Spacelab 2 mission included a large coded mask telescope for X-ray observations in the 2.5-25 keV energy range. This is the first time that true sky images have been obtained in this energy range which is particularly important for the study of clusters of galaxies. It is also the first time that a critical evaluation of the coded mask technique used in orbital conditions has been possible. It is shown that both the sensitivity and the imaging quality obtained were very close to the theoretical expectation.
Skinner, G.K., Nottingham, M.R.: 1993, Nucl. Instr. Methods Phys. Res., A333, 540
Analysis of Data from Coded-Mask Telescopes by Maximum Entropy
Coded mask telescopes have proved of great utility in X- and gamma-ray astronomy. A coded mask telescope of a non-cyclic 'box-camera' design cab in some circumstances have a sensitivity advantage over an optimally coded cyclic configuration, but images reconstructed by a simple correlation technique are subject to various imperfections. A new method, maximum entropy likelihood fitting (MALF), for the analysis of data from non-cyclic coded mask telescopes is presented. MALF avoids artifacts due to strong sources and handles in an optimum way data affected by small-number statistics, by partial coding and by aspects of real systems such as finite detector depth and obscurations of parts of the detector.
Skinner, G.K., Grindlay, J.E: 1993, Astron. and Astrophys., 276, 673
Coded masks with two spatial scales
A new design is proposed for masks for wide-band coded aperture X-ray/gamma-ray telescopes. The masks contain both elements with a coarse spatial scale, which are opaque at all energies at which the telescope is to operate, and elements with finer structure which provide good angular resolution at low energies but which become transparent in the upper part of the energy range. It is shown that patterns exist which have very satisfactory imaging properties and that the sensitivity which is sacrificed to obtain the improvement in angular resolution is very small, even at intermediate energies where the fine mask in partially absorbing.
Skinner, G.K., Herring, J.R., Balthazor, R.L.: 1993, Proc. SPIE Vol. 1945, p. 465-477, Space Astronomical Telescopes and Instruments II, Pierre Y. Bely; James B. Breckinridge; Eds.
Coded mask telescope with a germanium array detector
Coded mask X-ray and gamma-ray telescopes are the only way of obtaining true images in the photon energy range from approximately 10 keV to a few MeV. The detectors used must be position sensitive, and the types employed in gamma-ray coded mask telescopes up to now have had limited energy resolution. With a view to developing position sensitive detectors which have the energy resolution attainable with Germanium we have procured and characterized in the laboratory a detector comprising a small array of high purity Germanium elements each 15 X 15 X 50 mm. Although having only nine elements, its construction is such that is should later be possible to build larger modules in the same way and finally to assemble modules into a large detector plane array. The nine element array is being incorporated into a coded mask telescope which will be tested in a balloon flight. Laboratory tests on the array detector and comparisons with simulations are reported and the anticipated performance of the small array telescope considered. The feasibility of a large instrument based on this approach, which is under study for a space mission, and its expected capabilities are discussed.
Skinner, G.K., Ponman, T.J., T.J.: 1994, Mon. Not. R. Astr. Soc., , preprint
On the properties of images from coded-mask telescopes
We consider coded-mask telescopes with cyclic mask patterns which are 'optimum', i.e. patterns which are based on uniformly redundant arrays (URAs), which can be derived using Cyclic Difference Sets. The properties of images obtained with different reconstruction arrays are compared to find the best options. In the usual case where the detector background is imperfectly known, it is easily shown that although the elements of an image reconstructed by any of the usual algorithms are nearly independent of each other and of the detector background, they cannot be perfectly so. The correlation between image elements which results is evaluated for various reconstruction algorithms and the circumstances in which it may be important are discussed. Although the effect is small when point sources are considered, it may be significant where sources of emission cover an appreciable fraction of the field of view. Masks based on 'modified URAs' lead to slightly worse interdependence of image pixels.
Skinner, G.K.: 1995, Exp. Astron., 6, 1
Coding (and decoding) coded mask telescopes
Many designs of masks for coded aperture telescopes have been proposed and a number of different configurations for instruments considered. Their advantages and disadvantages and some of the considerations involved in designing an instrument and in choosing a mask are reviewed. The methods of image reconstruction, which strongly influence the choice of design, are discussed and a way of quantifying the effectiveness of a mask pattern when used with a detector of finite resolution is presented.
Skinner, G.K., Rideout, R.M.: 1995, "Imaging in High Energy Astronomy" (eds. L. Bassani & G. di Cocco; Kluwer Academic Publishers), p. 177
A Compendium of Coded Mask Designs
Many different patterns have been proposed for coded masks, from Fresnel zone plates, through scatter-hole designs, to various patterns which are 'optimal' in different senses. We present a compendium of such patterns, with examples and their autocorrelation functions, together with a bibliography of associated literature.
Skinner, G.K., Balthazor, R.L., Herring, J.R.H., Rideout, R.M., Tueller, J., Barthelmy, S.D., Bartlett, L.M.: 1995, NIM A357, 580
A Balloon Flight Test of a Coded-Mask Telescope with a Multi-element Germanium Detector
The use of a small array of germanium detectors to obtain high spectral resolution X-ray and Gamma-ray images of astronomical objects has been demonstrated with a coded mask telescope flown as a piggy-back instrument on the NASA GRIS balloon payload. The design of the experimental telescope is dicussed and images of the Crab nebula and of Cygnus X-1 obtained during the flight are presented. The quality of the images is shown to be very close to that expected from simulations.
Stephen, J.B., Caroli, E., Di Cocco, G., Maggioli, P.P., Natalucci, L., Spizzichino, A.: 1987, Astron. and Astrophys., 185, 343
The Identification of Vignetted Sources in Coded Aperture Imaging
The next generation of gamma-ray telescopes will utilize the technique of coded apertures in order to provide high resolution images of the celestial sphere. This method, however, suffers from a disadvantage wherein vignetted sources are reconstructed in false positions with incorrect intensities. Most techniques of identifying these sources involve the use of time consuming iterative computer algorithms. One recent suggestion, however, allows fast decoding which is also accurate when there are a limited number of sources in the field of view and a high background level, as is the case for contemporary low energy gamma-ray instruments. This method has been examined in detail by means of Monte Carlo simulation in order to assess its accuracy and sensitivity.
Theinhardt, J., Burk, R., Kendziorra, E., Staubert, R.: 1984, Nucl. Instr. Methods Phys. Res., 221, 288
A Rotation Modulation Collimator for Imaging in High Energy X-Ray Astronomy
A rotation modulation collimator (RMC) for imaging of cosmic point X-ray sources for photon energies up to 100 keV has been built and tested. Results of computer simulations and laboratory testing with radioactive sources are presented.
Vigneau, D., Robinson, D.W.: 2003, SPIE 4851, 1326 NEW!
Large coded aperture mask for spaceflight hard x-ray images
The 2.6 square meter coded aperture mask is a vital part of the Burst Alert Telescope on the Swift mission. A random, but known pattern of more than 50,000 lead tiles, each 5 mm square, was bonded to a large honeycomb panel which projects a shadow on the detector array during a gamma ray burst. A two-year development process was necessary to explore ideas, apply techniques, and finalize procedures to meet the strict requirements for the coded aperture mask. Challenges included finding a honeycomb substrate with minimal gamma ray attenuation, selecting an adhesive with adequate bond strength to hold the tiles in place but flexible enough to allow the tiles to expand and contract without distorting the panel under large temperature gradients, and eliminating excess adhesive from all untiled areas. Finding an efficient way to bond the > 50,000 lead tiles to the panel while maintaining positional tolerances within +0.1 mm was no small task. In order to generate the desired bondline, adhesive was applied and allowed to cure to each tile. The 'pre-cured' tiles were located in a tool to maintain positional accuracy, wet adhesive was applied to the panel, and the wetted substrate was lowered to the tile surface with synchronized actuators. Using this procedure, the entire tile pattern was transferred to the large honeycomb panel in a single bond. The pressure for the bond was achieved by enclosing the entire system in a vacuum bag. Thermal vacuum and acoustic tests validated this approach. This paper discusses the methods, materials, and techniques used to fabricate this very large and unique coded aperture mask for the Swift mission.
Wild, W.J.: 1983, Opt. Lett., 8, 247
Dilute Uniformly Redundant Sequences For Use in Coded Aperture Imaging
A class of binary sequences with ideal autocorrelation properties is given for several lengths. These sequences possess the property that their periodic autocorrelation sidelobes are a constant unity; they represent a class of codes that are both uniformly redundant and nonredundant. Application to coded-aperture imaging is discussed.
Wild, W.J.: 1990, Appl. Opt., 29, 668
Gamma-ray Imaging Probes. 1: Formalism
A mathematical matrix formalism for a class of 1-D temporal coded aperture gamma-ray imaging probes is developed. Various code catagories are presented. Object estimation is discussed as well as the effect of noise on the reconstruction.
Wild, W.J.: 1990, Appl. Opt., 29, 672
Gamma-ray Imaging Probes. 2: Code Optimization
The Hotelling trace is used as a figure of merit for optimizing the azimuthal aperture in a coded aperture gamma-ray imaging system. We present simulations for a particular aperture size that incorporates the combined effects of signal and background variability, additive nonstationary noise, aperture code noise, and detector integration time. It is shown that crossing points occur wherein different codes are, in principle, optimal for short vs long detector count times. The optimization approach may be generalized to more complex coded aperture systems.
Willingale, R.: 1981, Mon. Not. R. Astr. Soc., 194, 359
Use of the Maximum Entropy Method in X-ray Astronomy
An algorithm used to apply the maximum entropy method in X-ray astronomy is described. It is easy to programma on a digital computer and fast enough to allow processing of two-dimensional images. The method gives good noise suppression without loss of instrumental resolution and has been successfully applied to several data analysis problems in X-ray astronomy. The restoration of a high-resolution image from the Einstein Observatory demonstrates the use of the algorithm.
Willingale, R., Sims, M., Turner, M.J.L.: 1984, Nucl. Instr. Methods Phys. Res., 221, 60
Advanced Deconvolution Techniques for Coded Aperture Imaging
The standard deconvolution technique for coded aperture imaging is cross correlation with the relevant mask pattern. In practice such an imaging system is imperfect, giving incomplete coding, and direct cross correlation with the mask introduces "ghosting" and enhanced noise fluctuations. This paper describes the application of image processing techniques such as the Wiener Filter and Maximum Entropy Method to deconvolve the recorded shadow pattern and illustrates the advantage of such methods using a computer simulation of a wide field camera for X-ray astronomy.
Willmore, A.P., Skinner, G.K., Eyles, C.J., Ramsey, B.: 1984, Nucl. Instr. Methods Phys. Res., 221, 284
A Coded Mask Telescope for the Spacelab 2 Mission
A dual coded mask telescope for the Spacelab 2 mission is now in the final stages of preparation at Birmingham University. It is due for launch in late 1984/early 1985 and will be by far the largest and most sophisticated such instrument to be flown in this time-frame. The design and capabilities of the telescope will be described.
Willmore, A.P., Bertram, D., Watt, M.P., Skinner, G.K., Ponman, T.J., Church, M.J., Herring, J.R.H., Eyles, C.J.: 1992, Mon. Not. R. Astr. Soc., 258, 621
Image Correction in a Coded Mask X-Ray Telescope
A large coded mask telescope was flown on the Spacelab 2 mission in 1985. This was the first time that large amounts of data from such an instrument had been obtained and much effort was devoted to optimizing the methods of reducing detector background effects and correcting of correcting and co-adding images. An unexpected problem was encountered in that small errors in energy calibration led to a large apparent detector background in the presence of bright sources. To provide background information for the scientific results from this instrument, and also because of their relevance to the analysis of data from other coded mask telescopes, we describe the data processing procedures adopted. They have led to an overall performance for the instrument which is close to that theoretically achievable.
Wunderer, C.B., Strong, A.W., Attie, D., et al.: 2003, SPIE 4851, 1269 NEW!
Imaging with the coded aperture gamma-ray spectrometer SPI aboard INTEGRAL
ESA's INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL) will be launched in October 2002. Its two main instruments are the imager IBIS and the spectrometer SPI. Both emply coded apertures to obtain directional information on the incoming radiation. SPI's detection plane consists of 19 hexagonal Ge detectors, its coded aperture has 63 tungsten-alloy elements of 30 mm thickness.

POPULAR PAPERS

In 't Zand, J.J.M., Jager R., Spaan, F.P.: 1988, Zenit, Dec. 1988, 414
COMIS: een Roentgen Camera aan Boord van MIR

Skinner, G.K.: 1988, Scientific American, Aug. 1988, 66
X-Ray Imaging with Coded Masks

Terwey, J.: 1987, Aarde en Kosmos, May 1987, 480
MIRakelse Telescopen

Wild, W.J.: 1987, Sky & Telescope, Aug. 1987, 126
A Gamma-Ray Pinhole Camera

These pages have been compiled by Jean in 't Zand. They are intended to provide general information for those interested in coded aperture imaging. Any citations should reference original papers as noted in the bibliography, and requests for further information about any of the papers should be directed to the authors thereof.