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2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture

A new Coded Aperture design. We are getting ready to purchase a new Low Energy Coded Aperture chip. We do not do this often; the cost is about 15K$ each. We have decided that the Fresnel Zone Plate will not be useful and can be replaced with an alternate Coded Aperture.

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2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture

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  1. A new Coded Aperture design We are getting ready to purchase a new Low Energy Coded Aperture chip. We do not do this often; the cost is about 15K$ each. We have decided that the Fresnel Zone Plate will not be useful and can be replaced with an alternate Coded Aperture. Possibly, an alternative design, including gold thickness and pattern, will provide improved resolution (especially) at low beam energy. In this talk, I will discuss a means to evaluated different coded aperture designs in different conditions, To this end, I have revised the image calculation program to output images with a common normalization for all conditions: energy and filters. The images, and image differences, can be compared. The normalization to number-of-photons is unknown, but the same for all images. investigate the current Coded Aperture at 2.085 and 1.8 GeV, with varying gold thickness, compare the Coded Aperture to the Pinhole, investigate a preliminary design for a new Coded Aperture. 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 1

  2. The standard Coded Aperture design has a total vertical opening of 150 μm, distributed over a total distance of 280 μm. This total distance projects to 3.34 * 280 μm = 935 μm on the detector. With 2.085 GeV beam energy, with Diamond filter, the average transmitted light on the detector, relative to straight-through, is calculated from the images from the images to be 270/1246 = 0.22 . ( A simpler calculation based on the pattern predicts a ratio 150 * 3.34 /1600 = 0.31 ) The other loss, 0.22/0.31, is due to the silicon substrate. The current Coded Aperture with 7 μm beam size, 2.085 GeV, 4.0μm diamond, 2.5μm silicon, 0.7μm gold. (red) straight-through: no gold, no silicon. x-ray energy distribution “incident on gold” (blue) <E x-ray > = 3.50 KeV The CA works because of the high average transparency. 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 2

  3. The Pinhole (without silicon filtering), has average transmission, 0.092 . (ref: CA with 0.7μm gold was 0.22 ). From a simple calculation, using the Pinhole opening, expect 45 * 3.34 /1600 = 0.094 Without the silicon filtering, the average x-ray energy, “incident on gold” (blue) is reduced to <E x-ray > = 3.19 KeV The Pinhole, 45μm slit width, with 7 μm beam size, 2.085 GeV, 4.0μm diamond, no silicon, “10μm gold”. (red) straight-through: no gold, no silicon. The Pinhole works with less transmission because the light is concentrated in one peak. The feature width limits the resolution at small beam size. 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 3

  4. “Evaluate” the resolving power of the Pinhole. In the plot below, compare the image for 9μm beam size (blue) relative to 7μm beam size (red) . Define the relative χ2/dof as… χ2 /dof = 1/(#bins) ∑bin ( PHi (9μm) - PHi (7μm) )2 / ( PHi (7μm) ) . This is the sum over bins of differences (squared) due to the beam spread, relative to statistical accuracy (squared). In this case, comparing 9μm vs.7μm, with the Pinhole, χ2 /dof =0.243 . The pulse height is not calibrated to number-of-photons. I do not evaluate the beam smeared image above 10 μm because I integrate over a limited number of bins. 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 4

  5. Coded Aperture, 2.085 GeV, with Diamond “Evaluate” the resolving power of the Coded Aperture; with 0.7 μm gold thickness, χ2 /dof =0.614 . As expected, this is better than the Pinhole, ref: χ2 /dof =0.243 . We have seen agreement between Coded Aperture and the Pinhole measurements from December data. Fluctuations in the single turn measurements indicated that the Coded Aperture measurement is more accurate. Shown at right are the images for 0.7 μm, 0.3 μm, and 10 μm gold. With the 0.3 μm gold, the image dips below the baseline, the minimum-to-maximum swing is larger when compared to maximum gold. the total transmission, and statistical weight, is higher. There is a large background, but it is not in phase. 0.3 μm gold 0.7 μm gold 10 μm gold 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 5

  6. 2.085 GeV, with Diamond GAP is optimized at 45 μm subtractor ~18 μm χ2 /dof is shown as a function of beam size. for both Coded Aperture and Pinhole. This is for a constant δσ/σ (not constant δσ). Note: the Pinhole increases to a maximum at a beam size slightly higher than the subtractor (16μm), while the Coded Aperture is best at low beam size. Note: calculations for beam sizes below the detector pixel size are not useful. 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 6

  7. Coded Aperture, 2.085 GeV, with Diamond Resolving power as a function of gold thickness. χ2 /dof is maximum with 0.50 μm gold. I do not advocate 0.5 microns; 0.7 is OK and may be more robust. The transmission is shown relative to 2.085 GeV, diamond, straight through. Increased gold thickness reduces the total transmission. 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 7

  8. Pinhole, 1.8 GeV, No Diamond GAP is optimized at 73 μm subtractor ~29 μm “Evaluate” the resolving power of the pinhole In this case, comparing 9μm vs.7μm, with the pinhole, χ2 /dof =0.089 Recall, for 2.085, with Diamond, χ2 /dof =0.243 . The χ2 /dof is significantly reduced compared to 2.085 GeV; the Pinhole will not work at 1.8 GeV. (45 μm, not re-optimized) . 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 8

  9. Coded Aperture, 1.800 GeV, NO diamond With 1.8 GeV beam energy, and no diamond filter, the average x-ray energy, “incident on gold” (blue) is reduced to <E x-ray > = 1.96 KeV . ref: 2.085 GeV, with Diamond, <E x-ray > = 3.50 KeV The current Coded Aperture with 7 μm beam size, 1.800 GeV, NO diamond, 2.5μm silicon, 0.7μm gold. (red) straight-through: no gold, no silicon. The CA collected light is 270/1246=0.063 relative to 2.085 GeV straight-through. ref: 2.085 GeV, with Diamond, transmission =0.22 . The reduced light collection will affect the resolving power. 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 9

  10. Just for illustration, this shows the two images: 2.085 GeV, Diamond, 7 μm beam size, (blue) 1.800 GeV, No Diamond, 7μm beam size, scaled to equal area (red) . χ2 /dof = 40.9 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 10

  11. Coded Aperture, 1.800 GeV, NO diamond 0.3 μm gold “Evaluate” the resolving power of the Coded Aperture. With 0.7 μm gold, χ2 /dof =0.225 . As expected, this is worse than 2.085 Gev, with Diamond, χ2 /dof =0.614 Shown are the images for 0.7 μm, 0.3 μm, and 10 μm gold. With the 0.3 μm gold, AGAIN the image dips below the baseline, the minimum-to-maximum swing is larger when compared to maximum gold. the total transmission, and statistical weight, is higher. AGAIN, there is a large background, but it is not in phase. 0.7 μm gold 10 μm gold 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 11

  12. 1.800 GeV, No Diamond GAP is optimized at 73 μm subtractor ~29 μm χ2 /dof is shown as a function of beam size. for both Coded Aperture and Pinhole. This is for a constant δσ/σ (not constant δσ). Note: the Pinhole increases to a maximum at a beam size slightly higher than in the case of 2.085, with Diamond, while the Coded Aperture is best at low beam size. Note: calculations for beam sizes below the detector pixel size are not useful. 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 12

  13. Coded Aperture, 1.800 GeV, NO diamond Resolving power as a function of gold thickness. χ2 /dof is maximum with ~0.32 μm gold, but is always less than for 2.085 GeV with Diamond. The transmission is shown relative to 2.085 GeV, diamond, straight through. 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 13

  14. 1.800 GeV, No Diamond 0.7 μm gold Alternate CA This an early attempt; it is not optimized. DPP Standard BKH Nov 07 Oct 31 Total transmitting 171 150 120 μm Total range 312 280 290 μm χ2 /dof 0.296 0.226 0.141 7 μm beam 0.7 μm gold χ2 /dof 0.097 0.040 0.082 18 μm beam 0.7 μm gold The BKH Oct 31 pattern has low total transmission. A variation of my starting point, from the Oct 23 email, does not work at 1.8 GeV. 0.7 μm gold 0.7 μm gold 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 14

  15. 0.7 μm gold 2.085 GeV, with Diamond Alternate CA This an early attempt; it is not optimized. DPP Standard BKH Nov 07 Oct 31 χ2 /dof 1.080 0.614 0.404 0.7 μm gold The alternate CA provides improved resolving power at both 1.8 and 2.085 GeV. Hopefully, further refinement is possible. 0.7 μm gold 0.7 μm gold 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 15

  16. The analysis indicates at 2.085 GeV, with Diamond, at 7 μm beam size, the CA (0.7 μm gold) performs better than the Pinhole ,χ2 /dof =0.614 (CA)vs. 0.243 (PH), at 2.085 GeV, with Diamond, the optimum gold thickness is 0.5 μm, at 1.8 GeV, No Diamond, at 7 μm beam size, the pinhole is not usable, χ2 /dof =0.028 , at 1.8 GeV, No Diamond, at 7 μm beam size, the CA (0.7 μm gold) performs at about the resolution of the pinhole at 2.085GeV, χ2 /dof =0.225 , at 1.8 GeV, No Diamond, the optimum gold thickness is 0.32 μm, it is possible to design a new CA with improved resolution , the example shows improved χ2 /dof for both 1.8 GeV and 2.085 GeV. The peak-to-peak separation for the example CA is 10 pixels. (Is this small enough for beam motion?) I do not advocate gold thickness less than 0.6 μm because I think it is fragile. 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 2012-11-07 xBSM meeting, Dan Peterson, Coded Aperture 16

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