Signal-to-noise ratios for the Wide Field Camera and Planetary Camera of the Space Telescope were calculated as a function of integration time. Models of the optical systems and CCD detector arrays were used with a 27th visual magnitude point source and a 25th visual magnitude per arc-sq. second extended source. A 23rd visual magnitude per arc-sq. second background was assumed. The models predicted signal-to-noise ratios of 10 within 4 hours for the point source centered on a signal pixel. Signal-to-noise ratios approaching 10 are estimated for approximately 0.25 x 0.25 arc-second areas within the extended source after 10 hours integration

Zissa, D. E.

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Q /I
NASA
Technical
' ,lemorandum
NASA TM -86472
SIGNAL-TO-NOISE RATIO FOR THE WIDE
FIELD /PLANETARY CAMERA OF THE
SPACE TELESCOPE
By D. E. Zissa
Information and Electronic Systems Laboratory
October 1984
(NASA-TM-86472) SIGNAL-TC-NOISE RATIO FOR	 N84-35235
THE WIDE FIELD-PLANETARY CAMERA OF THE SPACE
TELESCOPE (NASA) 12 p BC A02/MF A01
CSCL 03A	 Unc:las
G3/89 24078
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National Aeronautics and
Space Adm,n!strat(on
George C. Marshall Space Flight Center
MSFC - Form 3190 (Rev. May 1983)
Ten UUlr-Al or:DAOT CTAMMAOM TITt R PAr Fr
i. REPORTNO, z,	 GOVERNMENT ACCESSION NO. 3,	 RECIPIENT I S CATALOG NO.
NASA TM-86472
4,	 TITLE AND SUBTITLE b,	 REPORT DATE
Signal-to-Noise Ratio for the Wide Field/Planetary October 19846,	 PERFORMING ORGANIZATION CuDECamera of the Space Telescope
7,	 AUTHOR(S) S. PERFORMING ORGANIZATION REPOR r it
D. E.	 Zissa
9.	 PERFORMING ORGANIZATION NAME AND ADDRESS 10.	 WORK UNIT NO.
George C. Marshall Space Flight Center 1 1.	 CONTRACT OR GRANT NO.
Marshall Space Flight Center, AL	 35812
13, TYPE OF REPORT & PERIOD COVERED
12.	 SPONSORING AGENCY NAME AND ADDRESS
National Aeronautics and Space Administration Technical Memorandum
Washington, D.C. 	 20546 14,	 SPONSORING AGENCY CODE
15, SUPPLEMENTARY NOTES
Prepared by Information and Electronic Systems Laboratory.
16,	 ABSTRACT
l Signal-to-noise ratios for the Wide Field Camera and Planetary Camera of the
Space Telescope have been calculated as a function of integration time.
	
Models of
the optical systems and CCD detector arrays were used with a 27th visual magnitude
point source and a 25th visual magnitude per arc-second 2
 extended source.	 A 23rd
visual magnitude per arc-second 2
 background was assumed. 	 The models predicted
signal-to-noise ratios of 10 within 4 hours for the point source centered on a single
pixel.	 Signal-to-noise ratios approaching 10 are estimated for approximately 0. 25 x
	 r
0. 25 arc-second areas within the extended source after 10 hours integration.
1I
{ 17.	 KEY WORDS 18,	 DISTRIBUTION STATEMENT
Space Telescope, signal-to-noise ratios,
ray-trace models, optical instruments, Unclassified — Unlimited
I	 optics, telescopes, charge-coupled devices
)
19,	 SECURITY CLASSIF. (of this report) 20,	 SECURITY CLASSIF. (of this po li o) 21.	 NO. OF PAGES 22,	 PRICE
Unclassified Unclassified 11 NTIS
MBFC • F orm 3292 (May 1969)
For Halo by National Technical Information Service, Springfiel d, Virginia 22161
aTECHNICAI. MEMORANDUM
SIGNAL-TO-NOISE RATIO FOR THE WIDE FIELD /PLANETARY
CAMERA OF THE SPACE TELESCOPE
The signal-to-noise ratio has been estimated for the wide field camera (WFC)
and the planetary camera (PC) as a function of integration time. The following
paragraphs describe the effective flux, effective polychromatic point spread function,
and noise calculations.
The total number of CCD signal electrons from the whole point spread function
(PSF) or from a square arc-second solid angle for an extended source was deter-
mined as follows. First, the energy flux received from a solar type star of visual
magnitude m was taken as [ 11 :
I(m) = 3.72 x 10-9 x 10-0.4m erg cm -2 A -1 Sec-1
near 5500 A. Then the spectral distribution was assumed to be that of a blackbody
at 6000°K. (The results are not very sensitive to the assumed temperature since the
bandwidth of the visual filter is narrow compared to that of the blackbody.) Thee
the number of signal electrons in the entire PSF or square arc-second solid angle for
an extended source is
N = AtI(m) f (a/hc)B(a)Q(X)T(a)da
(all X)
where
A = unobscured aperture area [ 2]
t = integration time
X = wavelength
(x /hc) = photons per unit energy
B(X) = blackbody spectrum at 6000°K normalized to 1. at 5500
Q (X) = quantum efficiency of system [ 3]
T(X) = transmission of visual filter F306 [ 4]
The WFC and PC designs [ 5] were ray-traced; it was found that they are
basically perfect optical systerr,s from -the OTA through the central axis of each of
the WF/PC telescopes (rms wavelength error < X/300). For this study, several
4
n
t,
TRr 7"
l
1 1 	 ^
samples of X/13  rms random wave front error were applied (here X = 6328 A) . The
random distributions were smoothed by a gaussian distribution so that there were
about 5 cycles per aperture diameter. The aperture was assumed to be a circle of
1200 mm radius with a central obscuration of radius 396 mm. ''F" numbers of 12.9
and 30.0 were assumed for the WFC and PC, respectively. The polychromatic PSF's
Z	 were represented by 6 monochromatic PSF's weighted by the spectral distribution of
signal electrons. An assumed jitter of 0.007 arc-seconds rms was simulated by con-
volution with a gaussian distribution of tho appropriate width. The smearing effect
of charge transfer inefficiency in the CCD at the center of the 800 x 800 array was
included by assuming a typical value for charge transfer efficiency of 0.99996 [ 6, 7, 8] .(A central pixel's charge must be transferred 1200 times in the three-phase device) .
w	 Finally, smearing by charge carrier diffusion in the CCD was taken into account with iF	 a theorecical model [9,101 of a rear illuminat d CCD 10 microns thick with a 4.5
micron thick depletion region and with 5500 A incident light. The temperature of the
CCD was assumed to be -95°C. The theoretical model is supported by measurements
up to 33 cycles/mm spatial frequency for sample devices [7,8]. Formally, the fraction
of the total number of signal electrons in a given CCD detector area is
f f f AB(a)Q(a)T(X)NPSF(x,y,a) dxdyda
9
( given area, all X)
fXD(X)Q(a)T(X)dX
(a ll X)
4 w 	 where	 4 ,
ffNPSF(x,y,X)  dxdy = 1	 0 t
(all area)
and NPSF(x,y, a) is the continuous form of the effective polychromatic PSF at the
(BCD surface before weighting by the spectral distribution of signal electrons.
The rms noise in the signal was calculated as follows:
Y, _ (NS + N B + iDtnp + Q22 np)1/2
where :	 OF POOR QUALMN
E = rms noise electrons
N S = signal electrons
NT = background electrons
iD = dark current = 6 x 10 - 3 electrons /pixel /sec at -95 0 C [ 7]
t = integration time
2
i0
n  = number of detector pixels considered
a  = rms readout noise of CCD = 17.8 electrons/pixel [3]
Then the signal-to-noise ratio is NS/2:
Figures 1 and 2 show sample effective point spread functions after integration
over wavelength for the WFC and PC models, respectively. The full width of a pixel
is 0.6 x 10-3 in. or 0.100 and 0.043 arc-seconds for the WFC and PC, respectively.
Figures 3 through 6 show sample signal-to-noise ratios calculated for the WFC and PC
models for a single CCD pixel exposed to a point source of 27th magnitude. The
background was assumed to be 23rd magnitude per square arc-second. The cases
with the PSF centered on the pixel and centered on the pixel's corner are shown.
Figures 7 through 9 show the signal-to-noise ratio calculated for groups of pixels
exposed within an area of 25th magnitude per square arc-second source and 23rd
magnitude per square arc-second background. At the edge of an extended source
area the signal-to-noise ratios would be smaller due to smearing by the effective
point spread functions.
In the present model a 27th magnitude point source centered on a pixel with a
23rd magnitude per bgiiare arc-second background would result in a signal-to-noise
ratio of 10 in less than 4 hours for both the WFC and PC. The cases with the PSF
on a corner would not meet that specification with a single pixel. The WFC model
would have a signal-to-noise ratio of 10 in 10 hr for 2 x 2 pixels exposed within an
area of 23rd magnitude source and 27th magnitude background., However, at the
edge of an extended source area the signal-to-noise ratio would be smaller due to
smearing by the effective point spread function. The PC model would achieve a
signal-to-noise ratio of about 9 over 6 x 6 pixels under similar conditions.
1
3
ia
q
REFERENCES
1. Allen, C. W.: Astrophysical Quaml6ities. Third edition, The Athlone Press,
London, 1973, p. 197.
2. Updated Characteristics of the SI-to-OTA Optical Interfaces, Perlin Elmer
Report No. PR-706, May 1982.
3. Westphal, J. A.: The Wide Field Planetary Camera. NASA Report No. CP-
2244, August 1982, pp. .28-39.
4. LMSC Report No. D931340, p. 60.
5. WFPC Flight Equipment Optical System Dotdil Specification, Jet Propulsion
Laboratory, September 1980; Optical Schematic WF/PC System, Jet Propulsion
Laboratory, revised November 1979.
6. Barbe, D. F.: Imaging Devices Using the CCD Concept. Charge-Coupled
Devices: Technology and Applications, IEEE Press, New York, 1977, equation
(82), p. 147.
7. Landauer, F. P., Janesiek, J. R., Knapp, S. L., Blouke, M. Al., and Hall,
J. E.: An 800 x 800 CCD Imager for Space-Borne Scientific Imaging. Proc.
1978 Gov. Micro. Applications Conf. , !Monterey, CA, November 1978, p. 394.
8. Blouke, M. M., Janesiek, J. R., Hall, J. E., and Cowens, M. W.: Texas
Instruments (TI) 800 x 800 Charge-Coupled Device (CCD) Image Sensor, in
Solid State Imagers for Astronomy, SPIE Vol. 290, 1981, pp. 6-15.
9. Crowell, M. H., and Labuda, E. F.: The Silicon Diode Array Camera Tube,
Bell System Technical Journal 48, 1969, pp. 1481-1528.
10. Seib, D. H.: Carrier Diffusion Degradation of Modulation Transfer Function in
Charge Coupled Imagers, IEEE Trans. ED21, 1974, pp. 210-217.
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Figure 1.	 WFC, effective point spread function.
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Figure 2. PC, effective point spread function.
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Figure 3. WFC, 27th magnitude point source centered on pixel,
23rd magnitude per arc-see 2 background.
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Figure 4. WFC, 27th magnitude point source centered on pixel's corner,
23rd magnitude per arc-see2 background.
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Figure 5. PC, 27th magnitude point source centered on pixel,
23rd magnitude per 11pe-seC2 background.
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IMTEGRATIOM TIME tH"I)
Fiure 6
	
P (. 9.71-h Mn nit"ri p nint source 	 i-valfQ cornerg	
23rd magnitude per arc-sec t background.
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Figure 7. WFC, 25th magnitude per arc-sec t source on 2x2 pixels,
23rd magnitude per arc-sec 2 background.
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	 6.0	 73
	
16.0	 18.6	 15.0
IMTEOSATIOM TIME IHOOAf1
Figure 8. WFC , 25th magnitude per arc-sec 2 source on 3x3 pixels,
23rd magnitude per arc-sec 2 background.
t
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	 10.0	 11.9
INTEGRATION TIME (HOWS1
Figure 9. PC, 25th magnitude per arc-sec t source on 6x6 pixels,
23rd magnitude per arc-sec t background.
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Signal-to-noise ratio for the wide field-planetary camera of the Space Telescope

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