Results

The slope, intercept, and RMS deviation of a linear fit of the energy scale of the ACIS flight devices are listed in Table 4.5. Pulse height as a function of energy is fit to the relation $PH(ADU) = Slope \times Energy(eV) + Intercept$.

 

CCD Quadrant A Quadrant B Quadrant C Quadrant D

Slope (ADU/eV) Intercept (ADU) RMS (eV) Slope (ADU/eV) Intercept (ADU) RMS (eV) Slope (ADU/eV) Intercept (ADU) RMS (eV) Slope Intercept RMS

i0 0.2636 0.81 3.75 0.2573 0.65 4.03 0.2662 0.77 3.52 0.2582 0.60 4.06

i1 0.2622 0.38 3.50 0.2559 -0.09 3.97 0.2596 0.36 4.34 0.2616 0.07 3.80

i2 0.2731 -0.98 3.10 0.2839 -1.07 3.35 0.2825 0.07 3.59 0.2745 0.43 3.67

i3 0.2582 1.19 4.68 0.2588 1.25 4.65 0.2542 1.25 4.51 0.2592 1.09 4.55

s0 0.2725 -0.12 4.69 0.2677 -0.54 3.35 0.2574 0.13 4.02 0.2565 -0.34 3.40

s1 0.2359 -22.00 14.80 0.2182 -27.07 22.37 0.2234 -24.86 20.23 0.2297 -25.33 18.84

s2 0.2602 0.03 3.75 0.2715 0.15 5.27 0.2640 -0.51 4.25 0.2692 -0.54 6.33

s3 0.2262 -17.33 11.16 0.2158 -19.88 13.99 0.2186 -19.65 13.18 0.2273 -22.80 13.66

s4 0.2328 -1.09 3.80 0.2272 -0.58 6.16 0.2301 -0.72 5.76 0.2391 -0.96 4.55

s5 0.2534 -0.16 3.09 0.2576 -0.13 3.18 0.2601 0.18 2.70 0.2114 0.46 4.32

 

The residual errors from the linear energy scale fit for the front illuminated devices are shown in Figure 4.5. The residual errors from the linear energy scale fit for the back illuminated devices are shown in Figure 4.6. Note that Figure 4.5 and Figure 4.6 are on different vertical scales. Random errors for the line center locations are much less than 1 eV.

  

Figure 4.5: Linear Energy Scale Residuals for the Front Illuminated Devices

  

Figure 4.6: Linear Energy Scale Residuals for the Back Illuminated Devices

The FWHM for the ACIS flight devices is shown in Figure 4.7. In Figure 4.7 the points for the front illuminated devices are the average of the four quadrants, while the points for the back illuminated devices show each quadrant separately. The values for the front illuminated devices are listed in Table 4.6. The values for the back illuminated devices are listed in Table 4.7. The "NA" indicates that a data point is not available. The 277 eV measurement was made only for the S-array. Many of the DCM energies were taken with only i3, s1 and s3 on. One of the DCM sets was taken with only the I-array.

  

Figure 4.7: Average FWHM versus Energy

 

Energy 277 525 1380 1487 1740 1770 2035 4500 4509 6399 8040

Source C-K O-K DCM Al-K Si-K DCM DCM DCM Ti-K Fe-K Cu-K

i0 NA 50.8 NA 73.7 83.7 NA 81.8 NA 120.4 145.9 169.5

i1 NA 50.9 NA 73.3 83.1 NA 80.7 NA 119.9 145.1 169.7

i2 NA 53.7 NA 77.8 89.4 NA 85.6 NA 128.7 155.2 179.1

i3 NA 49.6 67.0 71.8 81.8 77.4 79.7 114.5 118.6 144.0 168.2

s0 45.8 54.9 NA 77.3 86.7 NA NA NA 123.5 149.8 175.7

s2 39.6 52.0 NA 74.6 84.6 NA 82.7 NA 122.6 149.0 172.2

s4 37.3 49.8 NA 69.5 78.9 NA NA NA 111.3 134.9 159.9

s5 38.8 48.4 NA 69.2 79.3 NA NA NA 113.3 137.3 161.4

 

 

Energy 277 525 1380 1487 1740 2035 4500 4509 6399 8040

Source C-K O-K DCM Al-K DCM DCM DCM Ti-K Fe-K Cu-K

s1 A 92.8 139.6 143.8 150.3 154.0 NA 205.9 209.0 232.8 242.1

B 82.6 128.6 135.9 140.5 147.8 NA 205.3 208.6 225.3 234.5

C 84.9 130.1 135.5 138.2 146.4 NA 210.5 207.5 229.5 234.0

D 99.5 152.9 159.0 162.3 170.1 NA 233.5 235.0 264.6 275.8

s3 A 73.7 104.5 96.5 105.3 103.9 115.0 141.0 147.4 167.0 180.9

B 72.1 101.3 95.8 102.6 102.2 110.4 145.1 150.8 170.8 185.5

C 70.0 102.1 94.9 102.5 102.1 112.9 140.0 143.6 161.3 176.5

D 89.0 131.2 124.5 135.1 134.5 149.0 193.5 199.4 227.7 241.3

 

The spectral resolution as a function of energy for the front illuminated devices is shown as a solid line in Figure 4.7 and is described by

$$FWHM(E) = \sqrt{ (FWHM_{0})^{2} + 2.35^{2} Fano \times w \times E}$$ (16)

Note that here we treat FWHM₀ as an empirical parameter. In the simplest model for spectral resolution (see section  4.1) one expects

$$FWHM_{0} = 2.35 \times \sigma \times w$$ (17)

The expected value of $Fano \times w$ in silicon detectors at -120 $\mbox{$^{\circ}$}$ C is $0.115 \times 3.73 = 0.429$.

FWHM₀ and $Fano \times w$ for each quadrant of each front illuminated device is shown in Table 4.8.

 

$$Fano \times w$$ Chip FWHM₀

i0 26.56 0.516

i1 26.49 0.517

i2 26.02 0.513

i3 23.77 0.514

s0 32.09 0.519

s2 25.88 0.509

s4 29.73 0.552

s5 27.56 0.518