A hard x-ray/medium energy gamma-ray telescope is being developed using coded-aperture imaging. The image recorded on the detector has to be cross correlated to deconvolve the sky map. This map suffers from blurring due to the spatial resolution of the position sensitive detector and to the simple point spread function of the cross-correlation method. We have developed and tested an iterative method which improves the separating power of the reconstructed maps. The results and limits of the method are discussed.
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Characteristics of the Reconstructed Image Resulting from an FSBC Analysis for the SIGMA Experiment as a Function of the Spatial Resolution of the Position Sensitive Detectora
(% of the total contribution in the central pixel)
Separating power (pixels)
3.8
5.5
29
52.1%
11
(40 keV)
(≈18′20″)
2.8
4.5
27
61.2%
9
(70 keV)
(≈15′)
1.8
4.5
23
74.2%
9
(130 keV)
(≈15′)
1.2
4.5
21
81.2%
9
(300 keV)
(≈15′)
For KK = 8, a pixel corresponds to a 1.175-mm wide square.
HWHM = halfwidth at half-maximum.
FWZI = full width at zero intensity.
Table II
Operating Thresholds in Sensitivity and Separating Power for the Iterative Algorithm for the Resolution of Two Point Sources of Equal Intensity as a Function of the Spatial Resolution of the Position Sensitive Detectora
Spatial resolution of the position sensitive detector HWHMb (mm)
Operating thresholds for the iterative algorithm
Sensitivity
Separating power
3.8
≈20σ
6 pixels
(40 keV)
(≈10′00″)
2.8
≈17σ
5 pixels
(70 keV)
(≈8′20″)
1.8
≈15σ
4 pixels
(130 keV)
(≈6′40″)
1.2
≈12σ
3 pixels
(300 keV)
(≈5′00″)
Correspondences with energy are given for the SIGMA experiment; correspondences with minutes of arc are given for an FSBC performed with KK = 8.
HWHM = halfwidth at half-maximum.
Table III
Deconvolution of Two Point Sources Contributing 1,144,000 Counts Each on the Detector, i.e., 300σ Confidence with Respect to the Backgrounda
Spatial resolution of the position sensitive detector HWHMb (mm)
Deconvolution of 2 point sources of equal intensity by the iterative algorithm
Distance between the 2 sources (pixels)
Obtained contribution (106 counts)
Number of iterations required
3.8
6 pixels
2.299
268
(40 keV)
(≈10′00″)
2.8
5 pixels
2.301
170
(70 keV)
(≈8′20″)
1.8
4 pixels
2.297
131
(130 keV)
(≈6′40″)
1.2
3 pixels
2.305
71
(300 keV)
(≈5′00″)
Correspondences with energy are given for the SIGMA experiment; correspondences with minutes of arc are given for an FSBC performed with KK = 8.
HWHM = halfwidth at half-maximum.
Tables (3)
Table I
Characteristics of the Reconstructed Image Resulting from an FSBC Analysis for the SIGMA Experiment as a Function of the Spatial Resolution of the Position Sensitive Detectora
(% of the total contribution in the central pixel)
Separating power (pixels)
3.8
5.5
29
52.1%
11
(40 keV)
(≈18′20″)
2.8
4.5
27
61.2%
9
(70 keV)
(≈15′)
1.8
4.5
23
74.2%
9
(130 keV)
(≈15′)
1.2
4.5
21
81.2%
9
(300 keV)
(≈15′)
For KK = 8, a pixel corresponds to a 1.175-mm wide square.
HWHM = halfwidth at half-maximum.
FWZI = full width at zero intensity.
Table II
Operating Thresholds in Sensitivity and Separating Power for the Iterative Algorithm for the Resolution of Two Point Sources of Equal Intensity as a Function of the Spatial Resolution of the Position Sensitive Detectora
Spatial resolution of the position sensitive detector HWHMb (mm)
Operating thresholds for the iterative algorithm
Sensitivity
Separating power
3.8
≈20σ
6 pixels
(40 keV)
(≈10′00″)
2.8
≈17σ
5 pixels
(70 keV)
(≈8′20″)
1.8
≈15σ
4 pixels
(130 keV)
(≈6′40″)
1.2
≈12σ
3 pixels
(300 keV)
(≈5′00″)
Correspondences with energy are given for the SIGMA experiment; correspondences with minutes of arc are given for an FSBC performed with KK = 8.
HWHM = halfwidth at half-maximum.
Table III
Deconvolution of Two Point Sources Contributing 1,144,000 Counts Each on the Detector, i.e., 300σ Confidence with Respect to the Backgrounda
Spatial resolution of the position sensitive detector HWHMb (mm)
Deconvolution of 2 point sources of equal intensity by the iterative algorithm
Distance between the 2 sources (pixels)
Obtained contribution (106 counts)
Number of iterations required
3.8
6 pixels
2.299
268
(40 keV)
(≈10′00″)
2.8
5 pixels
2.301
170
(70 keV)
(≈8′20″)
1.8
4 pixels
2.297
131
(130 keV)
(≈6′40″)
1.2
3 pixels
2.305
71
(300 keV)
(≈5′00″)
Correspondences with energy are given for the SIGMA experiment; correspondences with minutes of arc are given for an FSBC performed with KK = 8.
HWHM = halfwidth at half-maximum.