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Characteristics of a Television Photometer†
Characteristics of a Television Photometer? Y . NOZAWA Sniithsonian Aetrophysical Obsewatory, Cumbridge, 2Classtcchuaetts, U . S . A .
INTRODUCTION The Celescope/Uvicon broad-band ultra-violet integrating television photometer’.’ is ;L complex, non-linear, multi-parameter instrument. The mathematical model necessary t o calibrate the instrument is a set of non-linear multi-variable equations. Although a rigorous analysis may be suitable where high accuracy is required and ample time and the help of a large digital computer are available, it is not practical for use in field measurement, which requires quick rather t,hari accurate results. ln this paper a simplified mathematical model suitable for field use is therefore given. The television photometer discussed here is an ultra-violet sensitive, integrating, broad-band photometer, which is usually referred t o as the “Celesrope”. It will be launched in an Earth orbit some time in November 1968, as a part of the Orbiting Astronomical Observatory (OAO) satellite.$ As shown in a simplified sehernatic diagram in Fig. I , the optical system fornis a point image from star light (or from the photon flux emitted by a stellar atmosphere) on the photocathode of the image tube. The optical system consists of two reflecting mirrors and an optical filter which defines the passband of the Celescope. The camera tube, which is called the Uvicon, was developed by Westinghouse as an ultra-violet-sensitive SEC vidicon-type camera tube.3 The incoming photons are converted to photoelectrons, then t o electrical charges on an SEC target. As tthe electron charge on thc target is read out in digital scan, the output signal becomes a sort of amplitude-modulated pulse train. The height of the pulses is digitized by the on-board data-handling system
t T h s work was supported by Contract NAS3-1535 from the National Aeronautics aiitl Space Administration. 1 Noto added March 1969: OAO was xucrt~ssfdlylaunched 011 the 15th Dectmhrr 1968 arut thc C”e1escopcIS still transmitting data 801
892
Y . NOZAWA
and transmitted to the ground in coded form. On the ground, the digital television picture is reconstructed and a computer processes the picture to determine the input photon flux. Faceplate From star
------ma
mirror
electronics
mirror
FIG.1. Schematic diagram of the Celescope television photometer.
Figure 2 indicates a portion of a reconstructed picture. A complete picture consists of a 251 x 256 matrix, each element of the matrix representing the intensity of the corresponding dot in the television picture, the x,y coordinates of which correspond to column and row of the matrix, The intensity is quantized up to 127 levels. 5 6 5 6 3 4 4
b 0 6 4 4 6 1
4
4
4
6
4
5
4
5 5 3 5 6 8 4 8 5
6
b 4 4 4 4 5 1 4 4
6 10
b 6 5 5 4 4 4 5 8
9
11
5
6
7 5 6
6
4
6
7 8 7
5 5
4 5
4 2
5 4
5 4
5
6
4
6 3
3 5
5 4
5 7
5 3
5 5
6 3
4
3 5
FIG.
7
4
4 7
11
10
15
16 18 8 1 2 5 e
10
4 4
4 6 5 4 4 6 4
6 4 4 6 4 6 7
5 1 1
4 4 3 2 3 4 6
8
3 5 4 5 5 5 4 8
4 6 4 4 3 5 4 6
5 6 4 4 5 7 6 0
8 1 1 1 0 5 1 0 8 8 1 0 1 3 1 0 1 1 1 5 1 3 23 19 18 14 1 1 21 3 0 25 24 16 a 29 32 29 24 23 6 25 26 32 28 2 1 6 2 5 2 8 3 0 2 8 9 4 l 4 3 0 1 9 7 5 6
6 5 4 4 3 4 6
5 4 5
6 8 b
5
6
3
4 5 4 6 4 4 4 4
5
5 5 6 4 4 4 5 3 4
4
5 6 4 5
6
5
3 5 5
4
4
4 6
8 0
6 6
5 5
6 1
5 4
4 6
4 5
4
4 4 4
4
5
5
4
4
5
5
4
4
5
5 6
2 5
6 3
5 2
3 3
4 5
5 4
3 7
4 6
2 6
1 4
6 5
5 5
4 6
6 4
5 4
5 4
3 5
4 3
4 4
2. A portion of the reconstructed digital television picture.
Figure 2 represents a typical output picture for a point-source input, and as can be seen, a point-source input is spread over an area in the output picture. The numerical output corresponding to input intensity is the summation of values for all elements in an image area minus the
CHARACTERISTICS O F A TELEVISION PHOTOMETER
893
sum of bacligrouiid-noise intensity values.
The numerical output is called “Sigma”, the final output of the C’elescope instrument.
THE TELEVISION PHOTOMETER Thc television photometer can bc separated into three major subsystems. I , an optical sub-system, which consists of telescope optics mid filter; 2, the Uvicon television tuhe, u hicli includes the photoc.;tthocte, SXC target, and high-voltage power supply and 3 , an electronics sub-system, which includes camera electronics, and data-handling and processing electronics. T h r cliaracteristics of the optical sub-system can be expressed by an attenuation factor A , which tn:xj- he a function of temperatiire T. my-intersecting positions r and y and wavelength A. Measurements indicate t h a t reflectance arid transmittance of mirrors and filters are uniform within 2% a t any position on t h e surface for a given wtlvelcngth. It, maytherefore be considered that A is independent of the l ~ o i n tof intersection of the optical components and the incoming ray. The temperature characteristics of reflectance are negligible, but t h e traiisinittnnce of some filters (especially Li F) hiive temperature coefficients t h a t are as high as 1.6 >( 1 0 - 3 / 0 C ” and are wavelength dependent. A mathematical model of the optical sub-system c m therefore be simplified t o A(h, ,r, y, 5“) w A ( > ,T ) for LiF, and A(A) for others. The hasic problem in the use of a tclcvision camera as a photometric sensor is reprodurcability of output for the same input in the same environrnent. ‘Fable I shows tlie resiilts of a study of the change of response with change in operating parameters. From these data and tlie plttnned operational procedure, it, is expected t h a t the output of the Celescope for the same input will vary less than *3yo in normal circumstances and within 10% in the worst environmental conditions. The parametric study also indicates that the transfer function for the Uvicon tube must be determined for a specific configuration of the tuhe and associated electronics, specifir operational procedure, and a given environment#,rather than simply for the IJvicon tube itself. For our experiment, all Uvicon tubes are assembled as a camera module that, includes the pre-amplifier, t h e tleflexion amplifiers, and the voltage divider for the various grids nnd the target. The Uvicon is then calibrated as a camera rnodiile. The electronics portion of the input -output function is, in general, a. simple gaili-function with some temperature dependence and requires ing portion may have a no further discussion here. The datn-pro significant effect on the input-output function, since Sigma is sensitive to the types of algorithm used. Although this effect is very prominent
+
Y . NOZAWA
894
TABLEI Output, variation due t o parameter change Parameter
F-2 voltage G1 voltage Gun voltage High voltage Target voltage Raster size G5 voltage Raster position Superscan amplitude Operational seqiiencc
Sensitivity of output change (yo) due to parameter change 200-300 1-12 1-1 1 1-1.4 0.8-0.9 0.3-0.9 0.1-0' 13 negligible negligible * 6 depending on choice of operational sequence
a t low and high values of Sigma, it has almost no effect on the intermediate values in which we are interested. The discussion of this problem will therefore be omitted here. CAMERA-MODULE TRANSFER FUNCTION When a 14-hole (or 26-hole) reticle is placed in front of the Uvicon face-plate and is illuminated by a monochromatic (usually 2537 8) collimated beam, the transfer functions for the Uvicon camera module that correspond to 14 (or 26) different image positions can be determined simultaneously. Figure 3 shows an example of such a transfer measurement. The transfer function varies considerably with the location of the image on the face-plate of the Uvicon. The curves in Pig. 3, with the proper interpolation formula can be used for final data processing, but are not suitable for field use. The variation of transfer function due t o image location is a combined result of two non-uniformities; the quantum yield of the photocathode and the electron amplification factor in the SEC target. It is obvious that there are no simple relations among the curves shown in Fig. 3. I n general, the relation between the input (the number F of integrated photons) and the output Sigma (Z) can be expressed as where f ( x , y) is the response of the system a t (x,y), x and y being
CIIARACTERJYTICS O F A TELEVISION PHOTOMETEIt
1
I
"
/
'
"
'
"
I
'
I
Number of #ri!egroled ;Iho!,>ns t
FIG.3. C'atric!ra-ill~rtlt~lr transfbr function. Wuvrlcngth, 2537 atmospheric proxsurc.
I
" 1 1
I
I
'
895 I
l
A; terrrpcraturo
"5°C;
x-Co-ordinate
FIG.4. Uniforlnit,y correction factor for tho rulr1or.u-tnotlrlle. Wavelength, 2537 A. Point's marked S arc positions at which the rurves s h o w n in Fig. 4 wcrc obtained.
the image coordinates of the input and corresponding output. To simplity this relittion, it is assumed t h a t
m,Y) [F(J",!/)I
=
"(.r, ?/).fo(Fo),
896
Y. NOZAWA
where U ( x ,y) is the uniformity correction factor shown in Fig. 4, and F, is the input a t a standardized point, usually the center of the raster. All transfer functions can now be normalized into a single standard transfer fiinction fo( Po). If for normalization a point on the transfer function is chosen at the middle of the range (point R in curve 8 in Fig. 3), then for a point a t the centre of the raster the full line shown in Fig. 5 is obtained. To obtain the normalized response a t other points of incidence the uniformity transfer functions shown in Pig. 4 must be used. Such responses will be within the shaded portion shown in Fig. 5.
10
102
103
104
lo5
Number of integrated photons Fo
Fro. 5. Standnrdizecl transfer function for the camera-module. Solid line, stantlarclizctl function fo(F,)a t centre of raster; shacleed portion, envelope of riorrnalizetl trunsfrr funrtions a t other input positions. Wavelength, 2537 A; tcinperature, 25°C; atmospheric pressure.
When an unknown number of photons F , a t wavelength 2537 A are integrated and the output Sigma is obtained, the input a t any point will be determined by the formula R
c
where Z, is the standardized output, for the standard transfer function f o ( F o )in Fig. 5 . If the input light is monochromatic but not of wavelength 2537 A , then the input will be obtained by
where k(h) is a relative quantum yield a t wavelength X with respect to
('HAHACTERISTICS OF A TELEVISION
897
PHOTOMETER
wavelength 2537 .!. If, itistead of being monochromatic, the input lias a continuous spec$runi, then the equivalent input F, can be input, Po and the true determined. l'hr relatioit Iwtweeri ec~i~ivaleiit input is I
k',
(;Y(h,.r, 7J) q(h)tlh,
,,/
~
h
wliere tex is t81ir*vxI)osure (or integrating) time; #(A, .r. y) is the spectral sensitivity of tlic. qiiantuni yicild betwern X m d A dh a t location .r, y; n ~ i t y(X) l is tlw input intensity (I)lioton flux) between h and h dh per unit t i ~ n e . 14'01. i i sini~~lifietl rtiod(.l, it ('tin be assumed that
+
LS(h, .t', y) wherc V(.r,y) is cathode. 'I'hrii
--
+
F(X. .//),S"(h),
non-uniformity c.orrec.tion factor for the photo-
ii
m
/,,l'(J*, y)J",(h) y(X) dh.
E',
(I
I n Fig. 6, the s ~ mi n~thc l t,lireth curves indicates the scatter due t o the variation ill V ( x ,g). I
.f 3% 2.0
z5 .?? B ."O
4-
1-
I
I
I
I
I
I
'
I
I
I
'
I
';v5l7A 1216~
a 160ea
I
'
-
-
The temperat iirv c+lec*tron the transfer function is also complicated. I n geiic~al,the tcinperaturr coeficknt, is not zero hut lies between -1- 0.00 I a i i d - O.oo3.5. A(*tuaJ values of the temperature coefficient again tlepeiid 011 iiiput If',, image locution ,r : ~ n dy, and wavelength A. For siinldifictl Inotlcl, i~ cviistmt vulue of 0.0025 has been chosen. TIi(vi tlit. rclatioii Iwtwren iiiput Po m t l output Z a t temperature other t h a t i roo111 tt~rnp"r"t1ilc beconlc~s P.E.I.D. -I<
898
Y . NOZAWA
+
where K ( T ) is the temperature correction factor 1 u T , T being the difference between the operating temperature and room temperature (25’C) and u is the temperature coefficient.
CONCLIJSION The relationship between the true input and the output for a television photometer can be expressed as m
and where q$, is the equivalent input photon flux (photons at 2537 A sec-l B is the effective aperture of the instrument (em2),A , is the attenuation factor for 2537 8, g‘(A) is the true input photon flux (photon sec-l cm-2 A-1), and A ( A ) is the spectral attenuation factor of the optical sub-system at wavelength A. On the basis of test results in a vacuum optical bench test, the actual accuracy of the simplified model has been determined t o be about a factor of 2 ( + I 0 0 to -50%, corresponding t o stellar magnitude error 0.8) in normal conditions, and a factor of 4 (corresponding t o stellar magnitude 1.5) for the worst, case.
REFERENCES Nozawa, Y., I n “Advances in Electronics a n d Electron Physics”, ed. by J. D. McOee, D. McMullan and E. Kalran, Vol. 22B, p. 866. Academic Press, London (1966). Davis, R. J., In “Advances in Electronics and Electron Physics”, ed. by J. D. McCee, D. McMullan a n d E. Kahan, Vol. 22B, p. 875. Academic Press, London (1966). Doughty, D. D., I n “Advances in Electronics and Electron Physics”, ed. by J. D. McGee, D. McMullan and E. Kahan, Vol. 22A, p. 261. Academic Press, London (1966).
INTRODUCTION The Celescope/Uvicon broad-band ultra-violet integrating television photometer’.’ is ;L complex, non-linear, multi-parameter instrument. The mathematical model necessary t o calibrate the instrument is a set of non-linear multi-variable equations. Although a rigorous analysis may be suitable where high accuracy is required and ample time and the help of a large digital computer are available, it is not practical for use in field measurement, which requires quick rather t,hari accurate results. ln this paper a simplified mathematical model suitable for field use is therefore given. The television photometer discussed here is an ultra-violet sensitive, integrating, broad-band photometer, which is usually referred t o as the “Celesrope”. It will be launched in an Earth orbit some time in November 1968, as a part of the Orbiting Astronomical Observatory (OAO) satellite.$ As shown in a simplified sehernatic diagram in Fig. I , the optical system fornis a point image from star light (or from the photon flux emitted by a stellar atmosphere) on the photocathode of the image tube. The optical system consists of two reflecting mirrors and an optical filter which defines the passband of the Celescope. The camera tube, which is called the Uvicon, was developed by Westinghouse as an ultra-violet-sensitive SEC vidicon-type camera tube.3 The incoming photons are converted to photoelectrons, then t o electrical charges on an SEC target. As tthe electron charge on thc target is read out in digital scan, the output signal becomes a sort of amplitude-modulated pulse train. The height of the pulses is digitized by the on-board data-handling system
t T h s work was supported by Contract NAS3-1535 from the National Aeronautics aiitl Space Administration. 1 Noto added March 1969: OAO was xucrt~ssfdlylaunched 011 the 15th Dectmhrr 1968 arut thc C”e1escopcIS still transmitting data 801
892
Y . NOZAWA
and transmitted to the ground in coded form. On the ground, the digital television picture is reconstructed and a computer processes the picture to determine the input photon flux. Faceplate From star
------ma
mirror
electronics
mirror
FIG.1. Schematic diagram of the Celescope television photometer.
Figure 2 indicates a portion of a reconstructed picture. A complete picture consists of a 251 x 256 matrix, each element of the matrix representing the intensity of the corresponding dot in the television picture, the x,y coordinates of which correspond to column and row of the matrix, The intensity is quantized up to 127 levels. 5 6 5 6 3 4 4
b 0 6 4 4 6 1
4
4
4
6
4
5
4
5 5 3 5 6 8 4 8 5
6
b 4 4 4 4 5 1 4 4
6 10
b 6 5 5 4 4 4 5 8
9
11
5
6
7 5 6
6
4
6
7 8 7
5 5
4 5
4 2
5 4
5 4
5
6
4
6 3
3 5
5 4
5 7
5 3
5 5
6 3
4
3 5
FIG.
7
4
4 7
11
10
15
16 18 8 1 2 5 e
10
4 4
4 6 5 4 4 6 4
6 4 4 6 4 6 7
5 1 1
4 4 3 2 3 4 6
8
3 5 4 5 5 5 4 8
4 6 4 4 3 5 4 6
5 6 4 4 5 7 6 0
8 1 1 1 0 5 1 0 8 8 1 0 1 3 1 0 1 1 1 5 1 3 23 19 18 14 1 1 21 3 0 25 24 16 a 29 32 29 24 23 6 25 26 32 28 2 1 6 2 5 2 8 3 0 2 8 9 4 l 4 3 0 1 9 7 5 6
6 5 4 4 3 4 6
5 4 5
6 8 b
5
6
3
4 5 4 6 4 4 4 4
5
5 5 6 4 4 4 5 3 4
4
5 6 4 5
6
5
3 5 5
4
4
4 6
8 0
6 6
5 5
6 1
5 4
4 6
4 5
4
4 4 4
4
5
5
4
4
5
5
4
4
5
5 6
2 5
6 3
5 2
3 3
4 5
5 4
3 7
4 6
2 6
1 4
6 5
5 5
4 6
6 4
5 4
5 4
3 5
4 3
4 4
2. A portion of the reconstructed digital television picture.
Figure 2 represents a typical output picture for a point-source input, and as can be seen, a point-source input is spread over an area in the output picture. The numerical output corresponding to input intensity is the summation of values for all elements in an image area minus the
CHARACTERISTICS O F A TELEVISION PHOTOMETER
893
sum of bacligrouiid-noise intensity values.
The numerical output is called “Sigma”, the final output of the C’elescope instrument.
THE TELEVISION PHOTOMETER Thc television photometer can bc separated into three major subsystems. I , an optical sub-system, which consists of telescope optics mid filter; 2, the Uvicon television tuhe, u hicli includes the photoc.;tthocte, SXC target, and high-voltage power supply and 3 , an electronics sub-system, which includes camera electronics, and data-handling and processing electronics. T h r cliaracteristics of the optical sub-system can be expressed by an attenuation factor A , which tn:xj- he a function of temperatiire T. my-intersecting positions r and y and wavelength A. Measurements indicate t h a t reflectance arid transmittance of mirrors and filters are uniform within 2% a t any position on t h e surface for a given wtlvelcngth. It, maytherefore be considered that A is independent of the l ~ o i n tof intersection of the optical components and the incoming ray. The temperature characteristics of reflectance are negligible, but t h e traiisinittnnce of some filters (especially Li F) hiive temperature coefficients t h a t are as high as 1.6 >( 1 0 - 3 / 0 C ” and are wavelength dependent. A mathematical model of the optical sub-system c m therefore be simplified t o A(h, ,r, y, 5“) w A ( > ,T ) for LiF, and A(A) for others. The hasic problem in the use of a tclcvision camera as a photometric sensor is reprodurcability of output for the same input in the same environrnent. ‘Fable I shows tlie resiilts of a study of the change of response with change in operating parameters. From these data and tlie plttnned operational procedure, it, is expected t h a t the output of the Celescope for the same input will vary less than *3yo in normal circumstances and within 10% in the worst environmental conditions. The parametric study also indicates that the transfer function for the Uvicon tube must be determined for a specific configuration of the tuhe and associated electronics, specifir operational procedure, and a given environment#,rather than simply for the IJvicon tube itself. For our experiment, all Uvicon tubes are assembled as a camera module that, includes the pre-amplifier, t h e tleflexion amplifiers, and the voltage divider for the various grids nnd the target. The Uvicon is then calibrated as a camera rnodiile. The electronics portion of the input -output function is, in general, a. simple gaili-function with some temperature dependence and requires ing portion may have a no further discussion here. The datn-pro significant effect on the input-output function, since Sigma is sensitive to the types of algorithm used. Although this effect is very prominent
+
Y . NOZAWA
894
TABLEI Output, variation due t o parameter change Parameter
F-2 voltage G1 voltage Gun voltage High voltage Target voltage Raster size G5 voltage Raster position Superscan amplitude Operational seqiiencc
Sensitivity of output change (yo) due to parameter change 200-300 1-12 1-1 1 1-1.4 0.8-0.9 0.3-0.9 0.1-0' 13 negligible negligible * 6 depending on choice of operational sequence
a t low and high values of Sigma, it has almost no effect on the intermediate values in which we are interested. The discussion of this problem will therefore be omitted here. CAMERA-MODULE TRANSFER FUNCTION When a 14-hole (or 26-hole) reticle is placed in front of the Uvicon face-plate and is illuminated by a monochromatic (usually 2537 8) collimated beam, the transfer functions for the Uvicon camera module that correspond to 14 (or 26) different image positions can be determined simultaneously. Figure 3 shows an example of such a transfer measurement. The transfer function varies considerably with the location of the image on the face-plate of the Uvicon. The curves in Pig. 3, with the proper interpolation formula can be used for final data processing, but are not suitable for field use. The variation of transfer function due t o image location is a combined result of two non-uniformities; the quantum yield of the photocathode and the electron amplification factor in the SEC target. It is obvious that there are no simple relations among the curves shown in Fig. 3. I n general, the relation between the input (the number F of integrated photons) and the output Sigma (Z) can be expressed as where f ( x , y) is the response of the system a t (x,y), x and y being
CIIARACTERJYTICS O F A TELEVISION PHOTOMETEIt
1
I
"
/
'
"
'
"
I
'
I
Number of #ri!egroled ;Iho!,>ns t
FIG.3. C'atric!ra-ill~rtlt~lr transfbr function. Wuvrlcngth, 2537 atmospheric proxsurc.
I
" 1 1
I
I
'
895 I
l
A; terrrpcraturo
"5°C;
x-Co-ordinate
FIG.4. Uniforlnit,y correction factor for tho rulr1or.u-tnotlrlle. Wavelength, 2537 A. Point's marked S arc positions at which the rurves s h o w n in Fig. 4 wcrc obtained.
the image coordinates of the input and corresponding output. To simplity this relittion, it is assumed t h a t
m,Y) [F(J",!/)I
=
"(.r, ?/).fo(Fo),
896
Y. NOZAWA
where U ( x ,y) is the uniformity correction factor shown in Fig. 4, and F, is the input a t a standardized point, usually the center of the raster. All transfer functions can now be normalized into a single standard transfer fiinction fo( Po). If for normalization a point on the transfer function is chosen at the middle of the range (point R in curve 8 in Fig. 3), then for a point a t the centre of the raster the full line shown in Fig. 5 is obtained. To obtain the normalized response a t other points of incidence the uniformity transfer functions shown in Pig. 4 must be used. Such responses will be within the shaded portion shown in Fig. 5.
10
102
103
104
lo5
Number of integrated photons Fo
Fro. 5. Standnrdizecl transfer function for the camera-module. Solid line, stantlarclizctl function fo(F,)a t centre of raster; shacleed portion, envelope of riorrnalizetl trunsfrr funrtions a t other input positions. Wavelength, 2537 A; tcinperature, 25°C; atmospheric pressure.
When an unknown number of photons F , a t wavelength 2537 A are integrated and the output Sigma is obtained, the input a t any point will be determined by the formula R
c
where Z, is the standardized output, for the standard transfer function f o ( F o )in Fig. 5 . If the input light is monochromatic but not of wavelength 2537 A , then the input will be obtained by
where k(h) is a relative quantum yield a t wavelength X with respect to
('HAHACTERISTICS OF A TELEVISION
897
PHOTOMETER
wavelength 2537 .!. If, itistead of being monochromatic, the input lias a continuous spec$runi, then the equivalent input F, can be input, Po and the true determined. l'hr relatioit Iwtweeri ec~i~ivaleiit input is I
k',
(;Y(h,.r, 7J) q(h)tlh,
,,/
~
h
wliere tex is t81ir*vxI)osure (or integrating) time; #(A, .r. y) is the spectral sensitivity of tlic. qiiantuni yicild betwern X m d A dh a t location .r, y; n ~ i t y(X) l is tlw input intensity (I)lioton flux) between h and h dh per unit t i ~ n e . 14'01. i i sini~~lifietl rtiod(.l, it ('tin be assumed that
+
LS(h, .t', y) wherc V(.r,y) is cathode. 'I'hrii
--
+
F(X. .//),S"(h),
non-uniformity c.orrec.tion factor for the photo-
ii
m
/,,l'(J*, y)J",(h) y(X) dh.
E',
(I
I n Fig. 6, the s ~ mi n~thc l t,lireth curves indicates the scatter due t o the variation ill V ( x ,g). I
.f 3% 2.0
z5 .?? B ."O
4-
1-
I
I
I
I
I
I
'
I
I
I
'
I
';v5l7A 1216~
a 160ea
I
'
-
-
The temperat iirv c+lec*tron the transfer function is also complicated. I n geiic~al,the tcinperaturr coeficknt, is not zero hut lies between -1- 0.00 I a i i d - O.oo3.5. A(*tuaJ values of the temperature coefficient again tlepeiid 011 iiiput If',, image locution ,r : ~ n dy, and wavelength A. For siinldifictl Inotlcl, i~ cviistmt vulue of 0.0025 has been chosen. TIi(vi tlit. rclatioii Iwtwren iiiput Po m t l output Z a t temperature other t h a t i roo111 tt~rnp"r"t1ilc beconlc~s P.E.I.D. -I<
898
Y . NOZAWA
+
where K ( T ) is the temperature correction factor 1 u T , T being the difference between the operating temperature and room temperature (25’C) and u is the temperature coefficient.
CONCLIJSION The relationship between the true input and the output for a television photometer can be expressed as m
and where q$, is the equivalent input photon flux (photons at 2537 A sec-l B is the effective aperture of the instrument (em2),A , is the attenuation factor for 2537 8, g‘(A) is the true input photon flux (photon sec-l cm-2 A-1), and A ( A ) is the spectral attenuation factor of the optical sub-system at wavelength A. On the basis of test results in a vacuum optical bench test, the actual accuracy of the simplified model has been determined t o be about a factor of 2 ( + I 0 0 to -50%, corresponding t o stellar magnitude error 0.8) in normal conditions, and a factor of 4 (corresponding t o stellar magnitude 1.5) for the worst, case.
REFERENCES Nozawa, Y., I n “Advances in Electronics a n d Electron Physics”, ed. by J. D. McOee, D. McMullan and E. Kalran, Vol. 22B, p. 866. Academic Press, London (1966). Davis, R. J., In “Advances in Electronics and Electron Physics”, ed. by J. D. McCee, D. McMullan a n d E. Kahan, Vol. 22B, p. 875. Academic Press, London (1966). Doughty, D. D., I n “Advances in Electronics and Electron Physics”, ed. by J. D. McGee, D. McMullan and E. Kahan, Vol. 22A, p. 261. Academic Press, London (1966).