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 $PH(ADU) = Slope \times Energy(eV) + Intercept$.
 
 

Table 4.5: Energy Scale for ACIS Flight Devices

 

CCD	Quadrant A			Quadrant B			Quadrant C			Quadrant D
	Slope	Intercept	RMS	Slope	Intercept	RMS	Slope	Intercept	RMS	Slope	Intercept	RMS
	ADU/eV	ADU	eV	ADU/eV	ADU	eV	ADU/ev	ADU	eV	ADU/eV	ADU	eV
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

 
 

Table 4.6: Average FWHM (eV) for Front Illuminated Devices

 

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

 
 

Table 4.7: FWHM (eV) for Back Illuminated Devices

 

	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

$$FWHM(E) = \sqrt{ (FWHM_{0})^{2} + 2.35^{2} Fano \times w \times E}$$ (4.4)

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

$$FWHM_{0} = 2.35 \times \sigma \times w$$ (4.5)

The expected value of $Fano \times w$ in silicon detectors at -120 $\mbox{$^{\circ}$ }$ C is $0.135 \times 3.73 = 0.504$. FWHM₀ and $Fano \times w$ for each quadrant of each front illuminated device is shown in Table 4.8.
 
 

Table 4.8: Average Front Illuminated Devices FWHM₀ and $Fano \times w$

 

Chip	FWHM0	$Fano \times w$
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