Abstract

We developed a practical method to derive response functions that convert the amount of incident light to the counts of analog-to-digital conversion (A/D) of cameras for scientific imaging. In this method, we need a mechanism to accurately control the amount of incident light into cameras just within a limited dynamic range and at a limited number of steps. A variable brightness light source, which supplies the incident light into cameras, is also necessary, but we do not need to know its accurate brightness. Thus, this method enables us to derive the nonlinear response functions accurately with such a simple setup.

© 2011 Optical Society of America

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  1. I. K. Baldry, “Time-series spectroscopy of pulsating stars,” Ph.D. dissertation (University of Sydney, 1999).
  2. R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
    [CrossRef]
  3. A. Tajitsu, W. Aoki, S. Kawanomoto, and N. Narita, “Nonlinearity in the detector used in the Subaru Telescope High Dispersion Spectrograph,” Publ. Natl. Astron. Obs. Japan 13, 1–8 (2010).
  4. K. D. Mielenz and K. L. Eckerle, “Spectrophotometer linearity testing using the double aperture method,” Appl. Opt. 11, 2294–2303 (1972).
    [CrossRef] [PubMed]
  5. E. Theocharous, F. J. J. Clarke, L. J. Rogers, and N. P. Fox, “Latest measurement techniques at NPL for the characterization of infrared detectors and materials,” Proc. SPIE 5209, 228–239 (2003).
    [CrossRef]
  6. E. Theocharous, J. Ishii, and N. P. Fox, “Absolute linearity measurements on HgCdTe detectors in the infrared,” Appl. Opt. 43, 4182–4188 (2004).
    [CrossRef] [PubMed]
  7. E. Theocharous, “Absolute linearity measurements on a gold-black-coated deuterated L-alanine-doped triglycine sulfate pyroelectric detector,” Appl. Opt. 47, 3731–3736 (2008).
    [CrossRef] [PubMed]

2010 (1)

A. Tajitsu, W. Aoki, S. Kawanomoto, and N. Narita, “Nonlinearity in the detector used in the Subaru Telescope High Dispersion Spectrograph,” Publ. Natl. Astron. Obs. Japan 13, 1–8 (2010).

2008 (1)

2004 (1)

2003 (1)

E. Theocharous, F. J. J. Clarke, L. J. Rogers, and N. P. Fox, “Latest measurement techniques at NPL for the characterization of infrared detectors and materials,” Proc. SPIE 5209, 228–239 (2003).
[CrossRef]

1999 (1)

I. K. Baldry, “Time-series spectroscopy of pulsating stars,” Ph.D. dissertation (University of Sydney, 1999).

1993 (1)

R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
[CrossRef]

1972 (1)

Aoki, W.

A. Tajitsu, W. Aoki, S. Kawanomoto, and N. Narita, “Nonlinearity in the detector used in the Subaru Telescope High Dispersion Spectrograph,” Publ. Natl. Astron. Obs. Japan 13, 1–8 (2010).

Baldry, I. K.

I. K. Baldry, “Time-series spectroscopy of pulsating stars,” Ph.D. dissertation (University of Sydney, 1999).

Belmonte, J. A.

R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
[CrossRef]

Brown, T. M.

R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
[CrossRef]

Clarke, F. J. J.

E. Theocharous, F. J. J. Clarke, L. J. Rogers, and N. P. Fox, “Latest measurement techniques at NPL for the characterization of infrared detectors and materials,” Proc. SPIE 5209, 228–239 (2003).
[CrossRef]

Cram, L. E.

R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
[CrossRef]

Eckerle, K. L.

Fox, N. P.

E. Theocharous, J. Ishii, and N. P. Fox, “Absolute linearity measurements on HgCdTe detectors in the infrared,” Appl. Opt. 43, 4182–4188 (2004).
[CrossRef] [PubMed]

E. Theocharous, F. J. J. Clarke, L. J. Rogers, and N. P. Fox, “Latest measurement techniques at NPL for the characterization of infrared detectors and materials,” Proc. SPIE 5209, 228–239 (2003).
[CrossRef]

Frandsen, S.

R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
[CrossRef]

Gilliland, R. L.

R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
[CrossRef]

Ishii, J.

Kawanomoto, S.

A. Tajitsu, W. Aoki, S. Kawanomoto, and N. Narita, “Nonlinearity in the detector used in the Subaru Telescope High Dispersion Spectrograph,” Publ. Natl. Astron. Obs. Japan 13, 1–8 (2010).

Kjeldsen, H.

R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
[CrossRef]

McCarthy, J. K.

R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
[CrossRef]

Mielenz, K. D.

Narita, N.

A. Tajitsu, W. Aoki, S. Kawanomoto, and N. Narita, “Nonlinearity in the detector used in the Subaru Telescope High Dispersion Spectrograph,” Publ. Natl. Astron. Obs. Japan 13, 1–8 (2010).

Palmer, J.

R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
[CrossRef]

Parthasarathy, M.

R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
[CrossRef]

Peri, M. L.

R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
[CrossRef]

Petro, L.

R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
[CrossRef]

Rogers, L. J.

E. Theocharous, F. J. J. Clarke, L. J. Rogers, and N. P. Fox, “Latest measurement techniques at NPL for the characterization of infrared detectors and materials,” Proc. SPIE 5209, 228–239 (2003).
[CrossRef]

Schneider, H.

R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
[CrossRef]

Stetson, P. B.

R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
[CrossRef]

Tajitsu, A.

A. Tajitsu, W. Aoki, S. Kawanomoto, and N. Narita, “Nonlinearity in the detector used in the Subaru Telescope High Dispersion Spectrograph,” Publ. Natl. Astron. Obs. Japan 13, 1–8 (2010).

Theocharous, E.

Vidal, I.

R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
[CrossRef]

Weiss, W. W.

R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
[CrossRef]

Appl. Opt. (3)

Astron. J. (1)

R. L. Gilliland, T. M. Brown, H. Kjeldsen, J. K. McCarthy, M. L. Peri, J. A. Belmonte, I. Vidal, L. E. Cram, J. Palmer, S. Frandsen, M. Parthasarathy, L. Petro, H. Schneider, P. B. Stetson, and W. W. Weiss, “A search for solar-like oscillations in the stars of M67 with CCD ensemble photometry on a network of 4 M telescopes,” Astron. J. 106, 2441–2476 (1993).
[CrossRef]

Proc. SPIE (1)

E. Theocharous, F. J. J. Clarke, L. J. Rogers, and N. P. Fox, “Latest measurement techniques at NPL for the characterization of infrared detectors and materials,” Proc. SPIE 5209, 228–239 (2003).
[CrossRef]

Publ. Natl. Astron. Obs. Japan (1)

A. Tajitsu, W. Aoki, S. Kawanomoto, and N. Narita, “Nonlinearity in the detector used in the Subaru Telescope High Dispersion Spectrograph,” Publ. Natl. Astron. Obs. Japan 13, 1–8 (2010).

Other (1)

I. K. Baldry, “Time-series spectroscopy of pulsating stars,” Ph.D. dissertation (University of Sydney, 1999).

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Figures (9)

Fig. 1
Fig. 1

(a) Sample drawing of a nonlinear response function between the amount of light input, I, and the output A/D count, S. (b) Drawing of the results of practically available measurements between the throughput, T, and the measured A/D count, S, under the brightness of the light source, B 1 B 3 . (c) Enlargement of two of the measured points in panel (b).

Fig. 2
Fig. 2

Instrumental setup for the measurements. Between a light source and the tested camera, a light modulator, which consists of two linear polarizers, is placed.

Fig. 3
Fig. 3

(a) Sample image taken in our measurements. A rectangle at the center shows the area used for the analysis. (b) Enlargement of the central area shown in panel (a). (c) Abnormal pixels in panel (b) are shown in black, and remaining normal pixels are shown in white.

Fig. 4
Fig. 4

(a) Measured A/D counts, S, at various transmission values, T, are shown with plus signs. Each curve represents the measurements carried out under the same brightness of the light source. (b) Relation between three of the measured points and calculated derivative d S / d T .

Fig. 5
Fig. 5

Relation between the measured A/D count, S, and the T d S / d T value. For each point, the upper and lower limits of T d S / d T are connected by a straight line. (b) Measured points shown in panel (a) except for those showing large ambiguity are plotted. Result of the fitting for these points is shown with a solid gray curve. (c) Enlargement of the low S range of panel (b). The fitted curve, shown with a thick solid gray curve, consists of three different analytical functions. They are shown by a dotted curve, a dashed curve, and a dash–dot curve, respectively. Ranges where the three functions are valid are labeled as I, II, and III.

Fig. 6
Fig. 6

Errors between the data and the fitting result shown in Fig. 5b are plotted with plus signs. Each curve connecting plus signs corresponds to one of the curves in Fig. 4a.

Fig. 7
Fig. 7

(a) Calculated nonlinear response function between the amount of light input, I, and the output A/D count, S, is shown with a solid gray curve. The measured points shown in Fig. 4a are also plotted with plus signs, which are scaled to fit the response function. (b) Enlargement of the low-I range of panel (a).

Fig. 8
Fig. 8

Errors between the data and the fitting result shown in Fig. 7a are plotted with plus signs. Each curve connecting plus signs corresponds to one of the curves in Fig. 4a.

Fig. 9
Fig. 9

(a), (b) Sample images taken with the tested camera at different transmission values, T (0.27 and 0.79, respectively). (c) Ratio of the A/D counts of the dark-corrected images in panels (a) and (b). The ratio within ± 25 % of the average is displayed. (d) Ratio of the nonlinearity compensated results of the dark- corrected images in panels (a) and (b).

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

S = f ( I ) .
S = f ( B T ) .
d S / d T ( S i + 1 S i ) / ( T i + 1 T i ) .
d S / d T = B d S / d I .
T d S / d T = T B d S / d I = I d S / d I .
I d S / d I = g ( S ) .
T d S / d T = g ( S ) .
I d S / d I = 0.5949 S 284.2 + 670.9 / [ 1 + exp { 0.003444 ( S 309.9 ) } ] ,
I d S / d I = 4.8318 S + 7725.1 31976.6 / [ 1 + exp { 0.000555 ( S 1990.7 ) } ] ,
I d S / d I = 0.9428 S 1232.8 + 73686675 / [ 1 + exp { 0.000853 ( S 11617.1 ) } ] .

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