Purpose

To determine the "crosstalk correction matrices" and "position correction arrays" for each IPC in order to make image corrections. In addition, data is taken to measure the IPC positioning capabilities including a determination of the useful region of the IPC window. The IPC positioning capabilities will be measured through determinations of "position errors" and position resolution.

Testing Setup and Procedure

The IPC position response is measured by illuminating the face of the IPC obscured by a hole pattern. The x-ray beam line and hole pattern described in section 5.2.4 are used. The 18 by 16 hole pattern used has 0.5 mm diameter holes with 6.26 mm spacing between holes in both directions.

5.5.1 Image Reconstruction

Position Encoding

The W&S cathode pattern is used as a two-dimensional readout system. For a given event, the amplitudes of the signals induced on the Wedge, Strip, and Zee depend in a unique way on the multiplication point for the event according to their facing areas. Since the facing areas for the Wedge and Strip increase linearly in the two orthogonal directions, the x and y coordinates for an event can be calculated according to the following equations.

where wedge, strip, and zee indicate the measured signal amplitudes for each of the three channels. Figure 5.5-1 displays the image produced using xu and yu when the hole pattern obscures the IPC face. The data displayed in Figure 5.5-1 was acquired by HE1 at a Gas Gain of 10,000. During data acquisition, the copper anode was installed in the x-ray source producing an x-ray excess at an energy of 8.05 keV. Only x-rays in the copper K(alpha) peak are plotted.

Position Corrections

Crosstalk Correction

A correction is applied to the Wedge, Strip, and Zee signal amplitudes to correct for crosstalk between the Wedge, Strip, and Zee electronics channels. The correction is prescribed by:

where R is the 3 by 3 "crosstalk correction matrix" and Wc, Sc, and Zc are the corrected values of the Wedge, Strip, and Zee signal amplitudes. The crosstalk correction matrix is calculated from the measured values of the capacitance between the Wedge and Strip (Cws), the Wedge and Zee (Cwz), the Strip and Zee (Csz) and the known capacitance of the coupling capacitors (C = 3.3 nF). The following equation is used to calculate the matrix R:

Table 21 gives the capacitances measured between the Wedge, Strip, and Zee electrodes.

Table 21: Capacitances between the Wedge, Strip, and Zee for the four IPCs:

Using the measured capacitances, the following crosstalk correction matrices are calculated.

The following equations are used to calculate the "crosstalk corrected" x and y coordinates for an event:

Figure 5.5-2 displays the image produced using the crosstalk corrected x and y coordinates using the same data displayed in Figure 5.5-1.

Correction using the Position Correction Array

A position correction is applied to the crosstalk corrected x and y coordinates based on the deviation of the hole images from the known hole positions. To make this correction, a "position correction array" is calculated for each IPC. The position correction arrays are simply arrays of the mean x and y coordinates of each hole image for data taken when the hole pattern obscures the IPC face. The mean x and y hole image coordinates are found through an iterative procedure. Each iteration consists of finding the mean x and y coordinates of the events which fall within an ellipse centered on the image centroid found in the previous iteration. The condition for convergence is that no x or y coordinate for any hole image changes by more than 0.1 mm between iterations. The "position error" is defined as the distance between each hole image centroid and the known location of the corresponding hole. It has been found that the two outer columns of hole images are not usable due to large "position errors" for images in these columns. Thus, there are two 16 by 16 position correction arrays for each IPC: one for the x coordinates and one for the y coordinates of the hole images. The position correction arrays for each IPC are given in the appendix.

The position correction arrays are calculated using data taken while the IPC Gas Gain is 10,000. For LE1, LE2, and HE1, the data is taken with the copper anode installed in the x-ray source providing an emission excess around 8.05 keV, while for HE2, the data is taken with the iron anode installed in the x-ray source providing an emission excess around 6.40 keV. The energies of the events used to find each position correction array are restricted to those events with energies near 8.05 keV for LE1, LE2, and HE1 and near 6.40 keV for HE2. By keeping 87% (± 1.5(sigma) of the events in the 8.05 keV x-ray peak, about 100,000 points are used to find the LE1 and LE2 position correction arrays. By keeping 95% (± 2(sigma) of the events in the 8.05 keV (for HE1) and 6.40 keV (for HE2) x-ray peaks, about 30,000 points are used to find the HE1 and HE2 position correction arrays.

The position correction arrays can be used to correct any image using the following procedure. After the image centroids are found, vectors are calculated for each hole pointing from the image centers to the known hole positions. Once these vectors are calculated, the image can be corrected by shifting the events based on these vectors. During the application of the position correction to an image, for each event, the identities of the four closest hole image centroids in the position correction array to the event location are determined. A shift is then calculated for each event based on the vectors corresponding to these four hole image centroids with weighting determined by the proximity of the event to each of the four centroids. In Figure 5.5-3, a corrected image is displayed using the same data displayed in the two previous figures.

Checking the Correction

The position correction arrays are checked by applying the position correction to images from data (other than the data used to find the position correction arrays) taken when the hole pattern obscures the IPC face. After application of the position correction, the hole image centroids are found using the same iterative process described above, and an "error vector" is found for each hole image. The "error vector" is a vector pointing from the known hole positions to the hole image centroids. Figures 5.5-4a to 5.5-4c display the observed error vectors for LE1 when the position correction array is applied to 4.51 keV x-rays, 6.40 keV x-rays, and x-rays between 9 and 14 keV for each of three Gas Gains: 20,000, 10,000, and 5,000.

Figures 5.5-4d to 5.5-4f display the observed error vectors for LE2 when the position correction array is applied to 4.51 keV, 6.40 keV, and 8.05 keV x-rays for each of three Gas Gains: 20,000, 10,000, and 5,000. Figures 5.5-4g and 5.5-4i display the observed error vectors for HE1 when the position correction array is applied to 4.51 keV, 6.40 keV, and 8.05 keV x-rays for Gas Gains of 20,000 and 5,000, and Figure 5.5-4h displays the observed error vectors for HE1 when the position correction array is applied to 4.51 keV and 6.40 keV x-rays for a Gas Gain of 10,000. Figures 5.5-4j to 5.5-4l display the observed error vectors for HE2 when the position correction array is applied to 2.84 keV, 4.51 keV, and 6.40 keV x-rays for a Gas Gain of 20,000, 2.84 keV and 4.51 keV x-rays for a Gas Gain of 10,000, and 4.51 keV and 6.40 keV x-rays for a Gas Gain of 5,000.

In each figure, the graphs on the left display the error vectors for each hole magnified by a factor of five for clarity, while the graphs on the right show histograms of the magnitudes of the error vectors. In the graphs on the left, the holes which are blocked by the strong back are indicated with diamonds. The 55Fe calibration source is located between the two blocked holes in the HE1 and HE2 plots which are toward the center of the IPC window. The two blocked holes in the LE1 and LE2 plots in the locations corresponding to the two HE2 blocked holes mark the 55Fe calibration source locations for those IPCs. It should be noted that the calibration source location for HE1 is not the same as for the other IPCs because the HE1 strong back is rotated 180 ° about an axis that is perpendicular to the plane of the strong back relative to the strong back orientations for the other IPCs. Tables 22 to 25 contain the mean error magnitudes for LE1, LE2, HE1, and HE2 respectively.

Figures 5.5-5a and 5.5-5b show the error vectors and the error magnitudes observed when the position correction array is applied to 2.84 keV x-rays for Gas Gains of 10,000 and 20,000 for LE1 and LE2. In each figure, the two graphs on the left display the error vectors for each hole within the low energy window magnified by a factor of five for clarity, while the two graphs on the right show histograms of the magnitudes of the error vectors. In the two graphs on the left, the holes which are blocked by the strong back are indicated with diamonds. Table 26 presents the mean error magnitudes for each case.

Table 22: LE1 Mean Error Magnitudes:

Table 23: LE2 Mean Error Magnitudes:

Table 24: HE1 Mean Error Magnitudes:

Table 25: HE2 Mean Error Magnitudes:

Table 26: LE1 & LE2 Mean Errors Magnitudes in the Low Energy Window:

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