Detecting X-ray pulses

The Problem

The first job of the DSP code is to detect pulses in the data stream. Detecting initial pulses is easy; the hard part is finding small secondary pulses on top of large ones. Here is a 200eV secondary pulse (blue) 2 milliseconds after a 10keV initial pulse (red).

As you can see, the secondary pulse is barely noticeable. However, it is still a valid signal from a perfectly good X-ray, which needs to be counted. Furthermore, if it were not detected, the calculated pulseheight of the 10keV pulse would be affected. Thus it is very important that the CDP can detect secondary pulses even when they are much smaller than the initial pulse.

Use The Derivative, Luke

The pulse detection algorithm is based on using a smoothed derivative (slope) of the data. We use the derivative so that DC level of the data doesn't affect the detection of pulses. The derivative is calculated by convolving the data with a boxcar derivative function. That is, to find the derivative at time T, we multiply several data points on each side of point T by the corresponding point in an array that looks like this: (The number of samples—the length of the "boxcar"—is an adjustable parameter.) The smoothed derivative is the sum of those multiplications.

This convolution smoothes the data as well as finding the derivative. The derivatives of the two pulses shown above look as shown here.

The initial pulse is detected when the derivative exceeds a fixed threshold. This threshold must be set low enough so that even the smallest pulses will be detected, but high enough that the noise in the system will not cause false triggers.

Notice that the single-pulse (blue) and double-hit (red) derivative traces are nearly indistinguishable. In particular, the derivative doesn't go above (or even near) zero when the second pulse happens. So using the derivative hasn't directly helped to identify double-hits. To do that we need to compare the actual derivative to the value we would expect from a single pulse.

The Adjusted Derivative

Here is an expanded view of the area indicated above. The data containing a secondary pulse is clearly distinguishable from the single pulse. We just need to be more sophisticated than a simple threshold.

The CDP software maintains a copy of what the single-pulse derivative shape is. Then when a pulse occurs, the expected derivative shape is scaled and subtracted from the calculated derivative to form the adjusted derivative.

The adjusted derivative is then used in place of the derivative for detection of secondary pulses. The adjusted derivative is compared to a threshold, and a secondary pulse is detected when it exceeds that threshold. (Actually, it's slightly more complicated than that, but that's the basic idea.)

Counting Down

Once an initial pulse has been detected, the CDP begins counting down the length of a Hi-res data record. This is the number of samples needed by the PHA algorithm to calculate the pulseheight to the highest possible resolution. If it reaches zero without detecting any secondary pulses, the event is flagged as a hi-res record and processed. If a secondary pulse does occur, the initial pulse will be processed as either a Mid-res or Low-res event, and the counter will reset to the full Hi-res length. Further secondary pulses will be treated the same way.

CDP Pulse height analysis