Abstract

We demonstrate the ability to measure the system modulation transfer function (MTF) of both color and monochrome charge-coupled-device (CCD) video camera systems with a liquid-crystal-display (LCD) projector. Test matrices programmed to the LCD projector were chosen primarily to have a flat power spectral density (PSD) when averaged along one dimension. We explored several matrices and present results for a matrix produced with a random-number generator, a matrix of sequency-ordered Walsh functions, a pseudorandom Hadamard matrix, and a pseudorandom uniformly redundant array. All results are in agreement with expected filtering. The Walsh matrix and the Hadamard matrix show excellent agreement with the matrix from the random-number generator. We show that shift-variant effects between the LCD array and the CCD array can be kept small. This projector test method offers convenient measurement of the MTF of a low-cost video system. Such characterization is useful for an increasing number of machine vision applications and metrology applications.

© 2000 Optical Society of America

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  7. W. Hon-Sum, “Effect of knife-edge skew on MTF measurements of CCD imagers employing a knife-edge,” Opt. Eng. 30, 1394–1398 (1991).
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  8. M. Marchywka, D. G. Socker, “Modulation transfer function measurement techniques for small-pixel detectors,” Appl. Opt. 31, 7198–7213 (1992).
    [CrossRef] [PubMed]
  9. J. E. Greivenkamp, A. E. Lowman, “Modulation transfer function measurements of sparse-array sensors using a self-calibrating fringe pattern,” Appl. Opt. 33, 5029–5036 (1994).
    [CrossRef] [PubMed]
  10. N. Guérineau, J. Primot, M. Tauvy, M. Caes, “Modulation transfer function measurement of an infrared focal plane array by use of the self-imaging property of a canted periodic target,” Appl. Opt. 38, 631–637 (1999).
    [CrossRef]
  11. G. Boreman, E. L. Dereniak, “Method for measuring modulation transfer function of charge-coupled devices using laser speckle,” Opt. Eng. 25, 148–150 (1986).
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    [CrossRef]
  13. A. Daniels, G. D. Boreman, A. D. Ducharme, E. Sapir, “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34, 860–868 (1995).
    [CrossRef]
  14. E. J. van Zwet, H. W. Zandbergen, “Measurement of the modulation transfer function of a slow-scan CCD camera on a TEM using a thin amorphous film as a test signal,” Ultramicroscopy 64, 49–55 (1996).
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  17. Z. Chen, M. A. Karim, “Effects of indented interframe cross talk in charge-coupled device detection of discrete displays,” Appl. Opt. 38, 314–324 (1999).
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  18. M. Sjödahl, P. Synnergren, “Measurement of shape by using projected random patterns and temporal digital speckle photography,” Appl. Opt. 38, 1990–1997 (1999).
    [CrossRef]
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  26. K. G. Beauchamp, Applications of Walsh and Related Functions (Academic, San Diego, Calif., 1977).
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  30. J. G. Proakis, Digital Communications (McGraw-Hill, New York, 1995), pp. 422–423.
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    [CrossRef]
  44. T. Lomheim, L. Schumann, R. Shima, J. Thompson, W. Woodward, “Electro-optical hardware considerations in measuring the imaging capability of scanned TDI charge-coupled imagers,” Opt. Eng. 29, 911–927 (1990).
    [CrossRef]

1999 (4)

1996 (2)

W. Astar, “New power-efficient optical filter for detector array modulation transfer function measurement by laser speckle,” Opt. Eng. 35, 2761–2764 (1996).
[CrossRef]

E. J. van Zwet, H. W. Zandbergen, “Measurement of the modulation transfer function of a slow-scan CCD camera on a TEM using a thin amorphous film as a test signal,” Ultramicroscopy 64, 49–55 (1996).
[CrossRef]

1995 (3)

W. Na, J. K. Paik, C. H. Lee, “An image restoration system for a single-CCD color camcorder,” IEEE Trans. Consumer Electron. 41, 563–571 (1995).
[CrossRef]

A. Daniels, G. D. Boreman, A. D. Ducharme, E. Sapir, “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34, 860–868 (1995).
[CrossRef]

D. N. Sitter, J. S. Goddard, R. K. Ferrell, “Method for the measurement of the modulation transfer function of sampled imaging systems from bar-target patterns,” Appl. Opt. 34, 746–751 (1995).
[CrossRef] [PubMed]

1994 (1)

1992 (1)

1991 (3)

S. E. Reichenbach, S. K. Park, R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[CrossRef]

W. Hon-Sum, “Effect of knife-edge skew on MTF measurements of CCD imagers employing a knife-edge,” Opt. Eng. 30, 1394–1398 (1991).
[CrossRef]

G. Marsaglia, A. Zaman, “A new class of random number generators,” Ann. Appl. Probability 1, 462–480 (1991).
[CrossRef]

1990 (2)

T. Lomheim, L. Schumann, R. Shima, J. Thompson, W. Woodward, “Electro-optical hardware considerations in measuring the imaging capability of scanned TDI charge-coupled imagers,” Opt. Eng. 29, 911–927 (1990).
[CrossRef]

J. E. Greivenkamp, “Color dependent optical prefilter for the suppression of aliasing artifacts,” Appl. Opt. 29, 676–684 (1990).
[CrossRef] [PubMed]

1989 (1)

1988 (1)

S. Park, K. Miller, “Random number generators: good ones are hard to find,” Commun. ACM 31, 1192–1201 (1988).
[CrossRef]

1986 (1)

G. Boreman, E. L. Dereniak, “Method for measuring modulation transfer function of charge-coupled devices using laser speckle,” Opt. Eng. 25, 148–150 (1986).
[CrossRef]

1985 (1)

G. Marsaglia, “Matrices and the structure of random number sequences,” Linear Algebr. Appl. 67, 147–157 (1985).
[CrossRef]

1984 (1)

1982 (1)

W. Wittenstein, J. C. Fontanella, A. R. Newberry, J. Baars, “The definition of the OTF and the measurement of aliasing for sampled imaging systems,” Opt. Acta 29, 41–50 (1982).
[CrossRef]

1980 (1)

1978 (1)

1923 (1)

J. L. Walsh, “A closed set of orthogonal functions,” Ann. J. Math. 55, 5–24 (1923).

1893 (1)

M. J. Hadamard, “Résolution d’une question relative aux déterminants,” Bull. Sci. Math. A 17, 240–246 (1893).

1867 (1)

J. Sylvester, “Thoughts on inverse orthogonal matrices, simultaneous sign-successions, and tessellated pavements in two or more colours, with applications to Newton’s Rule, ornamental tile work, and the theory of numbers,” Philos. Mag. Ser. 4 34, 461–475 (1867).

Astar, W.

W. Astar, “New power-efficient optical filter for detector array modulation transfer function measurement by laser speckle,” Opt. Eng. 35, 2761–2764 (1996).
[CrossRef]

Baars, J.

W. Wittenstein, J. C. Fontanella, A. R. Newberry, J. Baars, “The definition of the OTF and the measurement of aliasing for sampled imaging systems,” Opt. Acta 29, 41–50 (1982).
[CrossRef]

Beauchamp, K. G.

K. G. Beauchamp, Applications of Walsh and Related Functions (Academic, San Diego, Calif., 1977).

Becklund, O. A.

C. S. Williams, O. A. Becklund, Introduction to the Optical Transfer Function (Wiley, New York, 1989), pp. 149–158.

Boreman, G.

G. Boreman, E. L. Dereniak, “Method for measuring modulation transfer function of charge-coupled devices using laser speckle,” Opt. Eng. 25, 148–150 (1986).
[CrossRef]

Boreman, G. D.

A. Daniels, G. D. Boreman, A. D. Ducharme, E. Sapir, “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34, 860–868 (1995).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), pp. 484–490.

Caes, M.

Cannon, T. M.

Chen, Z.

Daniels, A.

A. Daniels, G. D. Boreman, A. D. Ducharme, E. Sapir, “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34, 860–868 (1995).
[CrossRef]

Dereniak, E. L.

G. Boreman, E. L. Dereniak, “Method for measuring modulation transfer function of charge-coupled devices using laser speckle,” Opt. Eng. 25, 148–150 (1986).
[CrossRef]

Ducharme, A. D.

A. Daniels, G. D. Boreman, A. D. Ducharme, E. Sapir, “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34, 860–868 (1995).
[CrossRef]

Fenimore, E. E.

Ferrell, R. K.

Fontanella, J. C.

W. Wittenstein, J. C. Fontanella, A. R. Newberry, J. Baars, “The definition of the OTF and the measurement of aliasing for sampled imaging systems,” Opt. Acta 29, 41–50 (1982).
[CrossRef]

Goddard, J. S.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), pp. 137–154.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), pp. 68–73.

Gottesman, S. R.

Greivenkamp, J. E.

Guérineau, N.

Hadamard, M. J.

M. J. Hadamard, “Résolution d’une question relative aux déterminants,” Bull. Sci. Math. A 17, 240–246 (1893).

Harmuth, H. F.

H. F. Harmuth, Sequency Theory: Foundations and Applications (Academic, San Diego, Calif., 1984).

Harwit, M.

M. Harwit, N. J. A. Sloane, Hadamard Transform Optics (Academic, San Diego, Calif., 1979), pp. 212–214.

Holst, G. C.

G. C. Holst, CCD Arrays, Cameras, and Displays, 2nd ed., Vol PM57 of SPIE Monographs and Handbooks Series (JCD Publishing, Winter Park, Fla. and SPIE Optical Engineering Press, Bellingham, Wash., 1998).

Hon-Sum, W.

W. Hon-Sum, “Effect of knife-edge skew on MTF measurements of CCD imagers employing a knife-edge,” Opt. Eng. 30, 1394–1398 (1991).
[CrossRef]

Jack, K.

K. Jack, Video Demystified, 2nd ed. (Hightext Publications, San Diego, Calif., 1996).

Kaczynski, M.

Karim, M. A.

Lee, C. H.

W. Na, J. K. Paik, C. H. Lee, “An image restoration system for a single-CCD color camcorder,” IEEE Trans. Consumer Electron. 41, 563–571 (1995).
[CrossRef]

Levy, E.

Lipson, S. G.

Lomheim, T.

T. Lomheim, L. Schumann, R. Shima, J. Thompson, W. Woodward, “Electro-optical hardware considerations in measuring the imaging capability of scanned TDI charge-coupled imagers,” Opt. Eng. 29, 911–927 (1990).
[CrossRef]

Lowman, A. E.

Marchywka, M.

Marsaglia, G.

G. Marsaglia, A. Zaman, “A new class of random number generators,” Ann. Appl. Probability 1, 462–480 (1991).
[CrossRef]

G. Marsaglia, “Matrices and the structure of random number sequences,” Linear Algebr. Appl. 67, 147–157 (1985).
[CrossRef]

G. Marsaglia, “A current view of random number generators,” Keynote Address, in Computer Science and Statistics: 16th Symposium on the Interface, L. Billard, ed. (North-Holland, Elsevier, Amsterdam, 1985), pp. 3–10.

G. Marsaglia, “Random number generation,” in Encyclopedia of Computer Science and Engineering, A. Ralston, ed. (Van Nostrand Reinhold, New York, 1983), pp. 1260–1264.

Miller, K.

S. Park, K. Miller, “Random number generators: good ones are hard to find,” Commun. ACM 31, 1192–1201 (1988).
[CrossRef]

Na, W.

W. Na, J. K. Paik, C. H. Lee, “An image restoration system for a single-CCD color camcorder,” IEEE Trans. Consumer Electron. 41, 563–571 (1995).
[CrossRef]

Narayanswamy, R.

S. E. Reichenbach, S. K. Park, R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[CrossRef]

Newberry, A. R.

W. Wittenstein, J. C. Fontanella, A. R. Newberry, J. Baars, “The definition of the OTF and the measurement of aliasing for sampled imaging systems,” Opt. Acta 29, 41–50 (1982).
[CrossRef]

Opher-Lipson, M.

Paik, J. K.

W. Na, J. K. Paik, C. H. Lee, “An image restoration system for a single-CCD color camcorder,” IEEE Trans. Consumer Electron. 41, 563–571 (1995).
[CrossRef]

Park, S.

S. Park, K. Miller, “Random number generators: good ones are hard to find,” Commun. ACM 31, 1192–1201 (1988).
[CrossRef]

Park, S. K.

S. E. Reichenbach, S. K. Park, R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[CrossRef]

S. K. Park, R. Schowengerdt, M. Kaczynski, “Modulation transfer function analysis for sampled image systems,” Appl. Opt. 23, 2572–2582 (1984).
[CrossRef]

Peles, D.

Primot, J.

Proakis, J. G.

J. G. Proakis, Digital Communications (McGraw-Hill, New York, 1995), pp. 422–423.

Reichenbach, S. E.

S. E. Reichenbach, S. K. Park, R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[CrossRef]

Sapir, E.

A. Daniels, G. D. Boreman, A. D. Ducharme, E. Sapir, “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34, 860–868 (1995).
[CrossRef]

Schowengerdt, R.

Schumann, L.

T. Lomheim, L. Schumann, R. Shima, J. Thompson, W. Woodward, “Electro-optical hardware considerations in measuring the imaging capability of scanned TDI charge-coupled imagers,” Opt. Eng. 29, 911–927 (1990).
[CrossRef]

Shannon, R. R.

R. R. Shannon, The Art and Science of Optical Design (Cambridge U. Press, Cambridge, UK, 1997), pp. 265–333.
[CrossRef]

Shima, R.

T. Lomheim, L. Schumann, R. Shima, J. Thompson, W. Woodward, “Electro-optical hardware considerations in measuring the imaging capability of scanned TDI charge-coupled imagers,” Opt. Eng. 29, 911–927 (1990).
[CrossRef]

Sitter, D. N.

Sjödahl, M.

Sloane, N. J. A.

M. Harwit, N. J. A. Sloane, Hadamard Transform Optics (Academic, San Diego, Calif., 1979), pp. 212–214.

Socker, D. G.

Sylvester, J.

J. Sylvester, “Thoughts on inverse orthogonal matrices, simultaneous sign-successions, and tessellated pavements in two or more colours, with applications to Newton’s Rule, ornamental tile work, and the theory of numbers,” Philos. Mag. Ser. 4 34, 461–475 (1867).

Synnergren, P.

Tauvy, M.

Thompson, J.

T. Lomheim, L. Schumann, R. Shima, J. Thompson, W. Woodward, “Electro-optical hardware considerations in measuring the imaging capability of scanned TDI charge-coupled imagers,” Opt. Eng. 29, 911–927 (1990).
[CrossRef]

van Zwet, E. J.

E. J. van Zwet, H. W. Zandbergen, “Measurement of the modulation transfer function of a slow-scan CCD camera on a TEM using a thin amorphous film as a test signal,” Ultramicroscopy 64, 49–55 (1996).
[CrossRef]

Walsh, J. L.

J. L. Walsh, “A closed set of orthogonal functions,” Ann. J. Math. 55, 5–24 (1923).

Williams, C. S.

C. S. Williams, O. A. Becklund, Introduction to the Optical Transfer Function (Wiley, New York, 1989), pp. 149–158.

Wittenstein, W.

W. Wittenstein, J. C. Fontanella, A. R. Newberry, J. Baars, “The definition of the OTF and the measurement of aliasing for sampled imaging systems,” Opt. Acta 29, 41–50 (1982).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), pp. 484–490.

Woodward, W.

T. Lomheim, L. Schumann, R. Shima, J. Thompson, W. Woodward, “Electro-optical hardware considerations in measuring the imaging capability of scanned TDI charge-coupled imagers,” Opt. Eng. 29, 911–927 (1990).
[CrossRef]

Zaman, A.

G. Marsaglia, A. Zaman, “A new class of random number generators,” Ann. Appl. Probability 1, 462–480 (1991).
[CrossRef]

Zandbergen, H. W.

E. J. van Zwet, H. W. Zandbergen, “Measurement of the modulation transfer function of a slow-scan CCD camera on a TEM using a thin amorphous film as a test signal,” Ultramicroscopy 64, 49–55 (1996).
[CrossRef]

Ann. Appl. Probability (1)

G. Marsaglia, A. Zaman, “A new class of random number generators,” Ann. Appl. Probability 1, 462–480 (1991).
[CrossRef]

Ann. J. Math. (1)

J. L. Walsh, “A closed set of orthogonal functions,” Ann. J. Math. 55, 5–24 (1923).

Appl. Opt. (12)

E. E. Fenimore, T. M. Cannon, “Coded aperture imaging with uniformly redundant arrays,” Appl. Opt. 17, 337–347 (1978).
[CrossRef] [PubMed]

E. E. Fenimore, “Coded aperture imaging: the modulation transfer function for uniformly redundant arrays,” Appl. Opt. 19, 2465–2471 (1980).
[CrossRef] [PubMed]

S. K. Park, R. Schowengerdt, M. Kaczynski, “Modulation transfer function analysis for sampled image systems,” Appl. Opt. 23, 2572–2582 (1984).
[CrossRef]

S. R. Gottesman, E. E. Fenimore, “New family of binary arrays for coded aperture imaging,” Appl. Opt. 28, 4344–4352 (1989).
[CrossRef] [PubMed]

J. E. Greivenkamp, “Color dependent optical prefilter for the suppression of aliasing artifacts,” Appl. Opt. 29, 676–684 (1990).
[CrossRef] [PubMed]

J. E. Greivenkamp, A. E. Lowman, “Modulation transfer function measurements of sparse-array sensors using a self-calibrating fringe pattern,” Appl. Opt. 33, 5029–5036 (1994).
[CrossRef] [PubMed]

Z. Chen, M. A. Karim, “Effects of indented interframe cross talk in charge-coupled device detection of discrete displays,” Appl. Opt. 38, 314–324 (1999).
[CrossRef]

N. Guérineau, J. Primot, M. Tauvy, M. Caes, “Modulation transfer function measurement of an infrared focal plane array by use of the self-imaging property of a canted periodic target,” Appl. Opt. 38, 631–637 (1999).
[CrossRef]

M. Sjödahl, P. Synnergren, “Measurement of shape by using projected random patterns and temporal digital speckle photography,” Appl. Opt. 38, 1990–1997 (1999).
[CrossRef]

D. N. Sitter, J. S. Goddard, R. K. Ferrell, “Method for the measurement of the modulation transfer function of sampled imaging systems from bar-target patterns,” Appl. Opt. 34, 746–751 (1995).
[CrossRef] [PubMed]

E. Levy, D. Peles, M. Opher-Lipson, S. G. Lipson, “Modulation transfer function of a lens measured with a random target method,” Appl. Opt. 38, 679–683 (1999).
[CrossRef]

M. Marchywka, D. G. Socker, “Modulation transfer function measurement techniques for small-pixel detectors,” Appl. Opt. 31, 7198–7213 (1992).
[CrossRef] [PubMed]

Bull. Sci. Math. A (1)

M. J. Hadamard, “Résolution d’une question relative aux déterminants,” Bull. Sci. Math. A 17, 240–246 (1893).

Commun. ACM (1)

S. Park, K. Miller, “Random number generators: good ones are hard to find,” Commun. ACM 31, 1192–1201 (1988).
[CrossRef]

IEEE Trans. Consumer Electron. (1)

W. Na, J. K. Paik, C. H. Lee, “An image restoration system for a single-CCD color camcorder,” IEEE Trans. Consumer Electron. 41, 563–571 (1995).
[CrossRef]

Linear Algebr. Appl. (1)

G. Marsaglia, “Matrices and the structure of random number sequences,” Linear Algebr. Appl. 67, 147–157 (1985).
[CrossRef]

Opt. Acta (1)

W. Wittenstein, J. C. Fontanella, A. R. Newberry, J. Baars, “The definition of the OTF and the measurement of aliasing for sampled imaging systems,” Opt. Acta 29, 41–50 (1982).
[CrossRef]

Opt. Eng. (6)

T. Lomheim, L. Schumann, R. Shima, J. Thompson, W. Woodward, “Electro-optical hardware considerations in measuring the imaging capability of scanned TDI charge-coupled imagers,” Opt. Eng. 29, 911–927 (1990).
[CrossRef]

S. E. Reichenbach, S. K. Park, R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[CrossRef]

W. Hon-Sum, “Effect of knife-edge skew on MTF measurements of CCD imagers employing a knife-edge,” Opt. Eng. 30, 1394–1398 (1991).
[CrossRef]

G. Boreman, E. L. Dereniak, “Method for measuring modulation transfer function of charge-coupled devices using laser speckle,” Opt. Eng. 25, 148–150 (1986).
[CrossRef]

W. Astar, “New power-efficient optical filter for detector array modulation transfer function measurement by laser speckle,” Opt. Eng. 35, 2761–2764 (1996).
[CrossRef]

A. Daniels, G. D. Boreman, A. D. Ducharme, E. Sapir, “Random transparency targets for modulation transfer function measurement in the visible and infrared regions,” Opt. Eng. 34, 860–868 (1995).
[CrossRef]

Philos. Mag. Ser. 4 (1)

J. Sylvester, “Thoughts on inverse orthogonal matrices, simultaneous sign-successions, and tessellated pavements in two or more colours, with applications to Newton’s Rule, ornamental tile work, and the theory of numbers,” Philos. Mag. Ser. 4 34, 461–475 (1867).

Ultramicroscopy (1)

E. J. van Zwet, H. W. Zandbergen, “Measurement of the modulation transfer function of a slow-scan CCD camera on a TEM using a thin amorphous film as a test signal,” Ultramicroscopy 64, 49–55 (1996).
[CrossRef]

Other (17)

Panasonic GP-KR222 Industrial Color CCD Data Sheet, Industrial Camera Division, One Panasonic Way, Secaucus, N.J. 07094; see also, Sony Semiconductor document files ICX038DNA.pdf (color CCD sensor) and CXA1391R.pdf (primary color separation), available at http://www.sel.sony.com/semi/ccdarea.html .

G. C. Holst, CCD Arrays, Cameras, and Displays, 2nd ed., Vol PM57 of SPIE Monographs and Handbooks Series (JCD Publishing, Winter Park, Fla. and SPIE Optical Engineering Press, Bellingham, Wash., 1998).

Panasonic GP-KR222 Industrial Color CCD Camera Operating Instructions (Panasonic, Secaucus, N.J. 07094).

Philips SAA7110 One Chip Front-end 1 (OCF1), Product Specification IC22, document file SAA7110 A 1.pdf, http://www-us2.semiconductors.philips.com/pip/SAA7110AWP , 1995, pp. 10–11. 59, 62–63.

K. Jack, Video Demystified, 2nd ed. (Hightext Publications, San Diego, Calif., 1996).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), pp. 68–73.

G. Marsaglia, “A current view of random number generators,” Keynote Address, in Computer Science and Statistics: 16th Symposium on the Interface, L. Billard, ed. (North-Holland, Elsevier, Amsterdam, 1985), pp. 3–10.

G. Marsaglia, “Random number generation,” in Encyclopedia of Computer Science and Engineering, A. Ralston, ed. (Van Nostrand Reinhold, New York, 1983), pp. 1260–1264.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), pp. 484–490.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), pp. 137–154.

R. R. Shannon, The Art and Science of Optical Design (Cambridge U. Press, Cambridge, UK, 1997), pp. 265–333.
[CrossRef]

C. S. Williams, O. A. Becklund, Introduction to the Optical Transfer Function (Wiley, New York, 1989), pp. 149–158.

The MathWorks, Inc, http://www.mathworks.com/support/solutions/v5/8542.shtml .

M. Harwit, N. J. A. Sloane, Hadamard Transform Optics (Academic, San Diego, Calif., 1979), pp. 212–214.

J. G. Proakis, Digital Communications (McGraw-Hill, New York, 1995), pp. 422–423.

K. G. Beauchamp, Applications of Walsh and Related Functions (Academic, San Diego, Calif., 1977).

H. F. Harmuth, Sequency Theory: Foundations and Applications (Academic, San Diego, Calif., 1984).

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Figures (8)

Fig. 1
Fig. 1

Sample regions of the binary test matrices: (a) the stochastic matrix from the random-number generator, (b) the sequency-ordered Walsh matrix, (c) the Sylvester-type Hadamard matrix, and (d) the URA.

Fig. 2
Fig. 2

2-D and averaged 1-D spatial frequency distributions, from -0.5 cycles/pixel to +0.5 cycles/pixel, for the binary stochastic matrix [(a) and (b)], the sequency-ordered Walsh matrix [(c) and (d)], the Hadamard matrix [(e) and (f)], and the URA [(g) and (horizontal)].

Fig. 3
Fig. 3

Schematic illustration of the experimental test station used to measure the video system MTF.

Fig. 4
Fig. 4

Frequency response of several filters: (a) pixel MTF; (b) typical MTF resulting from the combined effects of low-cost CCD lens optics, pixel MTF, and general camera processing; (c) vertical response due to field integration within the camera; and (d) frame grabber’s low-pass luminance filter that operates on the horizontal analog video signal.

Fig. 5
Fig. 5

Horizontal and vertical spatial frequency results are shown for each matrix, on a vertical log scale from 0.01 to 1, and over the spatial frequencies -0.5 cycles/pixel to +0.5 cycles/pixel. Respective results are shown for the binary stochastic matrix in (a) and (b), for the gray scale stochastic matrix in (c) and (d), for the Walsh functions in (e) and (f), for the Hadamard matrix in (g) and (horizontal), for the URA in (i) and (j), and for the 2 × 2 sampled Walsh functions in (k) and (l).

Fig. 6
Fig. 6

Horizontal (a) and vertical (b) MTF measurements for the color camera; results from the black-and-white stochastic matrix. The horizontal result is compared with theoretical curve based on the frame grabber’s luminance filter, and the vertical result is fitted with a third-order cosine least-squares fit, which incorporates field integration.

Fig. 7
Fig. 7

Monochrome CCD horizontal and vertical spatial frequency results are shown for the stochastic matrix, on a vertical log scale from 0.01 to 1, and over the spatial frequencies -0.5 cycles/pixel to +0.5 cycles/pixel. Curves for horizontal and vertical MTF: field integration mode (a) and (b), respectively, and frame accumulation mode (c) and (d), respectively. A higher vertical response is obtained with frame accumulation.

Fig. 8
Fig. 8

Least-squares cosine fits for monochrome camera with default frame-grabber filters for (a) vertical and (b) horizontal MTF. Curve (c) represents the horizontal MTF with the frame grabber’s antialias filter off, and (d) represents the horizontal MTF with the antialias filter off and the luminance low-pass notch filter bypassed to a boost filter.

Equations (11)

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

H2n=HnHnHnH¯n.
I=0.3R+0.59G+0.11B.
Tξ, η=FFTimagex, y.
PSDESTIMATEξ=|Tξ, η|2η.
PSDoutξ=|Hξ|2PSDINξ,
MTFξ=ηPSDOUTξ, η1/2ηPSDOUT0, η|EXTRAPOLATED1/2.
fNYQUIST=12d.
MTFsystem = MTFoptics MTFpixel MTFelectronics.
sξ, η=hx, y ** px, y.
sξ, η=11 ** pi, j.
sξ, η=a cbd ** pi j.

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