Abstract

We introduce a framework of focal-plane coding schemes for multichannel sampling in optical systems. A particular objective is to develop an ultrathin imager without compromising image resolution. We present a complete f/2.1 optical system with a thickness of 2.2mm. The resolution is maintained in the thin optical system by an integrated design of the encoding scheme, the process of making the coding elements, and the decoding algorithms.

© 2008 Optical Society of America

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  1. A. Papoulis, “Generalized sampling expansion,” IEEE Trans. Circuit Syst. 24, 652-654 (1977).
    [CrossRef]
  2. N. Nguyen, P. Milanfar, and G. Golub, “A computationally efficient superresolution image reconstruction algorithm,” IEEE Trans. Image Process. 10, 573-583 (2001).
    [CrossRef]
  3. S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20, 21-36 (2003).
    [CrossRef]
  4. H. Ur and D. Gross, “Improved resolution from subpixel shifted pictures,” CVGIP: Graph. Models Image Process. 54, 181-186 (1992).
    [CrossRef]
  5. M. A. Fiddy and T. J. Hall, “Nonuniqueness of superresolution techniques applied to sampled data,” J. Opt. Soc. Am. 71, 1406-1407 (1981).
  6. R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, and E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247-260(1998).
    [CrossRef]
  7. Z. Lin and H.-Y. Shum, “Fundamental limits of reconstruction-based superresolution algorithms under local translation,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 83-97(2004).
    [CrossRef] [PubMed]
  8. Y. Lu and M. Inamura, “Super-resolution of undersampled and subpixel shifted image sequence by pyramid iterative back-projection ,” IEICE Trans. Inf. Syst. E85D, 1929-1937(2002).
  9. J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, “Thin observation module by bound optics (TOMBO): Concept and experimental verification ,” Appl. Opt. 40, 1806-1813 (2001).
  10. D. J. Brady, M. Feldman, N. Pitsianis, J. P. Guo, A. Portnoy, “Compressive optical montage photography,”Proc. SPIE 5907, 590708 (2005).
    [CrossRef]
  11. N. P. Pitsianis, D. J. Brady, and X. Sun, “Sensor-layer image compression based on the quantized cosine transform,” Proc. SPIE 5817, 250 (2005).
    [CrossRef]
  12. A. D. Portnoy, N. P. Pitsianis, D. J. Brady, J. Guo, M. A. Fiddy, M. R. Feldman, and R. D. T. Kolste, “Thin digital imaging systems using focal-plane coding,” Proc. SPIE 6065, 60650F(2006).
    [CrossRef]
  13. R. Mait, J. Athale, and J. van der Gracht, “Evolutionary paths in imaging and recent trends,” Opt. Express 11, 2093-2101(2003).
    [CrossRef] [PubMed]
  14. N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, M. A. Fiddy, T. Suleski, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 43-51 (2006).
  15. J. Tanida, R. Shogenji, Y. Kitamura, K. Yamada, M. Miyamoto, and S. Miyatake, “Color imaging with an integrated compound imaging system,” Opt. Express 11, 2109-2117 (2003).
    [CrossRef] [PubMed]
  16. C. Van Loan, Computational Frameworks for the Fast Fourier Transform (Society for Industrial and Applied Mathematics, 1992).
    [CrossRef]

2006

A. D. Portnoy, N. P. Pitsianis, D. J. Brady, J. Guo, M. A. Fiddy, M. R. Feldman, and R. D. T. Kolste, “Thin digital imaging systems using focal-plane coding,” Proc. SPIE 6065, 60650F(2006).
[CrossRef]

N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, M. A. Fiddy, T. Suleski, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 43-51 (2006).

2005

D. J. Brady, M. Feldman, N. Pitsianis, J. P. Guo, A. Portnoy, “Compressive optical montage photography,”Proc. SPIE 5907, 590708 (2005).
[CrossRef]

N. P. Pitsianis, D. J. Brady, and X. Sun, “Sensor-layer image compression based on the quantized cosine transform,” Proc. SPIE 5817, 250 (2005).
[CrossRef]

2004

Z. Lin and H.-Y. Shum, “Fundamental limits of reconstruction-based superresolution algorithms under local translation,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 83-97(2004).
[CrossRef] [PubMed]

2003

2002

Y. Lu and M. Inamura, “Super-resolution of undersampled and subpixel shifted image sequence by pyramid iterative back-projection ,” IEICE Trans. Inf. Syst. E85D, 1929-1937(2002).

2001

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, “Thin observation module by bound optics (TOMBO): Concept and experimental verification ,” Appl. Opt. 40, 1806-1813 (2001).

N. Nguyen, P. Milanfar, and G. Golub, “A computationally efficient superresolution image reconstruction algorithm,” IEEE Trans. Image Process. 10, 573-583 (2001).
[CrossRef]

1998

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, and E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247-260(1998).
[CrossRef]

1992

H. Ur and D. Gross, “Improved resolution from subpixel shifted pictures,” CVGIP: Graph. Models Image Process. 54, 181-186 (1992).
[CrossRef]

1981

1977

A. Papoulis, “Generalized sampling expansion,” IEEE Trans. Circuit Syst. 24, 652-654 (1977).
[CrossRef]

Armstrong, E. E.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, and E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247-260(1998).
[CrossRef]

Athale, J.

Barnard, K. J.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, and E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247-260(1998).
[CrossRef]

Bognar, J. G.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, and E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247-260(1998).
[CrossRef]

Brady, D. J.

N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, M. A. Fiddy, T. Suleski, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 43-51 (2006).

A. D. Portnoy, N. P. Pitsianis, D. J. Brady, J. Guo, M. A. Fiddy, M. R. Feldman, and R. D. T. Kolste, “Thin digital imaging systems using focal-plane coding,” Proc. SPIE 6065, 60650F(2006).
[CrossRef]

N. P. Pitsianis, D. J. Brady, and X. Sun, “Sensor-layer image compression based on the quantized cosine transform,” Proc. SPIE 5817, 250 (2005).
[CrossRef]

D. J. Brady, M. Feldman, N. Pitsianis, J. P. Guo, A. Portnoy, “Compressive optical montage photography,”Proc. SPIE 5907, 590708 (2005).
[CrossRef]

Feldman, M.

D. J. Brady, M. Feldman, N. Pitsianis, J. P. Guo, A. Portnoy, “Compressive optical montage photography,”Proc. SPIE 5907, 590708 (2005).
[CrossRef]

Feldman, M. R.

A. D. Portnoy, N. P. Pitsianis, D. J. Brady, J. Guo, M. A. Fiddy, M. R. Feldman, and R. D. T. Kolste, “Thin digital imaging systems using focal-plane coding,” Proc. SPIE 6065, 60650F(2006).
[CrossRef]

N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, M. A. Fiddy, T. Suleski, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 43-51 (2006).

Fiddy, M. A.

N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, M. A. Fiddy, T. Suleski, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 43-51 (2006).

A. D. Portnoy, N. P. Pitsianis, D. J. Brady, J. Guo, M. A. Fiddy, M. R. Feldman, and R. D. T. Kolste, “Thin digital imaging systems using focal-plane coding,” Proc. SPIE 6065, 60650F(2006).
[CrossRef]

M. A. Fiddy and T. J. Hall, “Nonuniqueness of superresolution techniques applied to sampled data,” J. Opt. Soc. Am. 71, 1406-1407 (1981).

Golub, G.

N. Nguyen, P. Milanfar, and G. Golub, “A computationally efficient superresolution image reconstruction algorithm,” IEEE Trans. Image Process. 10, 573-583 (2001).
[CrossRef]

Gross, D.

H. Ur and D. Gross, “Improved resolution from subpixel shifted pictures,” CVGIP: Graph. Models Image Process. 54, 181-186 (1992).
[CrossRef]

Guo, J.

A. D. Portnoy, N. P. Pitsianis, D. J. Brady, J. Guo, M. A. Fiddy, M. R. Feldman, and R. D. T. Kolste, “Thin digital imaging systems using focal-plane coding,” Proc. SPIE 6065, 60650F(2006).
[CrossRef]

Guo, J. P.

D. J. Brady, M. Feldman, N. Pitsianis, J. P. Guo, A. Portnoy, “Compressive optical montage photography,”Proc. SPIE 5907, 590708 (2005).
[CrossRef]

Hall, T. J.

Hardie, R. C.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, and E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247-260(1998).
[CrossRef]

Ichioka, Y.

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, “Thin observation module by bound optics (TOMBO): Concept and experimental verification ,” Appl. Opt. 40, 1806-1813 (2001).

Inamura, M.

Y. Lu and M. Inamura, “Super-resolution of undersampled and subpixel shifted image sequence by pyramid iterative back-projection ,” IEICE Trans. Inf. Syst. E85D, 1929-1937(2002).

Ishida, K.

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, “Thin observation module by bound optics (TOMBO): Concept and experimental verification ,” Appl. Opt. 40, 1806-1813 (2001).

Kang, M. G.

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20, 21-36 (2003).
[CrossRef]

Kitamura, Y.

Kondou, N.

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, “Thin observation module by bound optics (TOMBO): Concept and experimental verification ,” Appl. Opt. 40, 1806-1813 (2001).

Kumagai, T.

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, “Thin observation module by bound optics (TOMBO): Concept and experimental verification ,” Appl. Opt. 40, 1806-1813 (2001).

Lin, Z.

Z. Lin and H.-Y. Shum, “Fundamental limits of reconstruction-based superresolution algorithms under local translation,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 83-97(2004).
[CrossRef] [PubMed]

Lu, Y.

Y. Lu and M. Inamura, “Super-resolution of undersampled and subpixel shifted image sequence by pyramid iterative back-projection ,” IEICE Trans. Inf. Syst. E85D, 1929-1937(2002).

Mait, R.

Milanfar, P.

N. Nguyen, P. Milanfar, and G. Golub, “A computationally efficient superresolution image reconstruction algorithm,” IEEE Trans. Image Process. 10, 573-583 (2001).
[CrossRef]

Miyamoto, M.

Miyatake, S.

J. Tanida, R. Shogenji, Y. Kitamura, K. Yamada, M. Miyamoto, and S. Miyatake, “Color imaging with an integrated compound imaging system,” Opt. Express 11, 2109-2117 (2003).
[CrossRef] [PubMed]

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, “Thin observation module by bound optics (TOMBO): Concept and experimental verification ,” Appl. Opt. 40, 1806-1813 (2001).

Miyazaki, D.

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, “Thin observation module by bound optics (TOMBO): Concept and experimental verification ,” Appl. Opt. 40, 1806-1813 (2001).

Morimoto, T.

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, “Thin observation module by bound optics (TOMBO): Concept and experimental verification ,” Appl. Opt. 40, 1806-1813 (2001).

Nguyen, N.

N. Nguyen, P. Milanfar, and G. Golub, “A computationally efficient superresolution image reconstruction algorithm,” IEEE Trans. Image Process. 10, 573-583 (2001).
[CrossRef]

Papoulis, A.

A. Papoulis, “Generalized sampling expansion,” IEEE Trans. Circuit Syst. 24, 652-654 (1977).
[CrossRef]

Park, M. K.

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20, 21-36 (2003).
[CrossRef]

Park, S. C.

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20, 21-36 (2003).
[CrossRef]

Pitsianis, N.

D. J. Brady, M. Feldman, N. Pitsianis, J. P. Guo, A. Portnoy, “Compressive optical montage photography,”Proc. SPIE 5907, 590708 (2005).
[CrossRef]

Pitsianis, N. P.

N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, M. A. Fiddy, T. Suleski, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 43-51 (2006).

A. D. Portnoy, N. P. Pitsianis, D. J. Brady, J. Guo, M. A. Fiddy, M. R. Feldman, and R. D. T. Kolste, “Thin digital imaging systems using focal-plane coding,” Proc. SPIE 6065, 60650F(2006).
[CrossRef]

N. P. Pitsianis, D. J. Brady, and X. Sun, “Sensor-layer image compression based on the quantized cosine transform,” Proc. SPIE 5817, 250 (2005).
[CrossRef]

Portnoy, A.

N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, M. A. Fiddy, T. Suleski, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 43-51 (2006).

D. J. Brady, M. Feldman, N. Pitsianis, J. P. Guo, A. Portnoy, “Compressive optical montage photography,”Proc. SPIE 5907, 590708 (2005).
[CrossRef]

Portnoy, A. D.

A. D. Portnoy, N. P. Pitsianis, D. J. Brady, J. Guo, M. A. Fiddy, M. R. Feldman, and R. D. T. Kolste, “Thin digital imaging systems using focal-plane coding,” Proc. SPIE 6065, 60650F(2006).
[CrossRef]

Shogenji, R.

Shum, H.-Y.

Z. Lin and H.-Y. Shum, “Fundamental limits of reconstruction-based superresolution algorithms under local translation,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 83-97(2004).
[CrossRef] [PubMed]

Suleski, T.

N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, M. A. Fiddy, T. Suleski, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 43-51 (2006).

Sun, X.

N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, M. A. Fiddy, T. Suleski, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 43-51 (2006).

N. P. Pitsianis, D. J. Brady, and X. Sun, “Sensor-layer image compression based on the quantized cosine transform,” Proc. SPIE 5817, 250 (2005).
[CrossRef]

T. Kolste, R. D.

A. D. Portnoy, N. P. Pitsianis, D. J. Brady, J. Guo, M. A. Fiddy, M. R. Feldman, and R. D. T. Kolste, “Thin digital imaging systems using focal-plane coding,” Proc. SPIE 6065, 60650F(2006).
[CrossRef]

Tanida, J.

J. Tanida, R. Shogenji, Y. Kitamura, K. Yamada, M. Miyamoto, and S. Miyatake, “Color imaging with an integrated compound imaging system,” Opt. Express 11, 2109-2117 (2003).
[CrossRef] [PubMed]

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, “Thin observation module by bound optics (TOMBO): Concept and experimental verification ,” Appl. Opt. 40, 1806-1813 (2001).

TeKolste, R. D.

N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, M. A. Fiddy, T. Suleski, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 43-51 (2006).

Ur, H.

H. Ur and D. Gross, “Improved resolution from subpixel shifted pictures,” CVGIP: Graph. Models Image Process. 54, 181-186 (1992).
[CrossRef]

van der Gracht, J.

Van Loan, C.

C. Van Loan, Computational Frameworks for the Fast Fourier Transform (Society for Industrial and Applied Mathematics, 1992).
[CrossRef]

Watson, E. A.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, and E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247-260(1998).
[CrossRef]

Yamada, K.

J. Tanida, R. Shogenji, Y. Kitamura, K. Yamada, M. Miyamoto, and S. Miyatake, “Color imaging with an integrated compound imaging system,” Opt. Express 11, 2109-2117 (2003).
[CrossRef] [PubMed]

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, “Thin observation module by bound optics (TOMBO): Concept and experimental verification ,” Appl. Opt. 40, 1806-1813 (2001).

CVGIP: Graph. Models Image Process.

H. Ur and D. Gross, “Improved resolution from subpixel shifted pictures,” CVGIP: Graph. Models Image Process. 54, 181-186 (1992).
[CrossRef]

IEEE Signal Process. Mag.

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20, 21-36 (2003).
[CrossRef]

IEEE Trans. Circuit Syst.

A. Papoulis, “Generalized sampling expansion,” IEEE Trans. Circuit Syst. 24, 652-654 (1977).
[CrossRef]

IEEE Trans. Image Process.

N. Nguyen, P. Milanfar, and G. Golub, “A computationally efficient superresolution image reconstruction algorithm,” IEEE Trans. Image Process. 10, 573-583 (2001).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

Z. Lin and H.-Y. Shum, “Fundamental limits of reconstruction-based superresolution algorithms under local translation,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 83-97(2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

Opt. Eng.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, and E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247-260(1998).
[CrossRef]

Opt. Express

Proc. SPIE

D. J. Brady, M. Feldman, N. Pitsianis, J. P. Guo, A. Portnoy, “Compressive optical montage photography,”Proc. SPIE 5907, 590708 (2005).
[CrossRef]

N. P. Pitsianis, D. J. Brady, and X. Sun, “Sensor-layer image compression based on the quantized cosine transform,” Proc. SPIE 5817, 250 (2005).
[CrossRef]

A. D. Portnoy, N. P. Pitsianis, D. J. Brady, J. Guo, M. A. Fiddy, M. R. Feldman, and R. D. T. Kolste, “Thin digital imaging systems using focal-plane coding,” Proc. SPIE 6065, 60650F(2006).
[CrossRef]

Super-resolution of undersampled and subpixel shifted image sequence by pyramid iterative back-projection

Y. Lu and M. Inamura, “Super-resolution of undersampled and subpixel shifted image sequence by pyramid iterative back-projection ,” IEICE Trans. Inf. Syst. E85D, 1929-1937(2002).

Thin observation module by bound optics (TOMBO): Concept and experimental verification

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, “Thin observation module by bound optics (TOMBO): Concept and experimental verification ,” Appl. Opt. 40, 1806-1813 (2001).

Other

C. Van Loan, Computational Frameworks for the Fast Fourier Transform (Society for Industrial and Applied Mathematics, 1992).
[CrossRef]

N. P. Pitsianis, D. J. Brady, A. Portnoy, X. Sun, M. A. Fiddy, T. Suleski, M. R. Feldman, and R. D. TeKolste, “Compressive imaging sensors,” Proc. SPIE 6232, 43-51 (2006).

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Figures (10)

Fig. 1
Fig. 1

Focal-plane pixel masks for a 4 × 4 lenslet array based on the modified Hadamard coding scheme.

Fig. 2
Fig. 2

Unmounted refractive lenslet array.

Fig. 3
Fig. 3

Microscope image of the imaging sensor with a focal-plane coding element. The white dots and bars are alignment marks on the focal-plane coding element.

Fig. 4
Fig. 4

Focal-plane coding element under 100 × magnification. Two aperture patterns are visible. The period of the bottom grating is equal to the pixel pitch.

Fig. 5
Fig. 5

Impulse response scan of four adjacent pixels. Each line corresponds to a pixel’s intensity as a function of the relative position of a point source on the detector plane.

Fig. 6
Fig. 6

Pixel impulse response as a function of image location on detector plane.

Fig. 7
Fig. 7

Impulse response of a pixel masked with a 50% horizontal grating with period equal to the pixel pitch.

Fig. 8
Fig. 8

Impulse response of a pixel masked with a checkerboard with feature size equal to one quarter pixel.

Fig. 9
Fig. 9

Raw captured image from the multiple-aperture focal-plane-coded camera. Here, the target is a portion of an ISO-12233 Digital Still-Camera Resolution Chart.

Fig. 10
Fig. 10

Detail of the reconstruction (left) compared with the bicubic spline interpolation of the clear aperture image (right).

Tables (2)

Tables Icon

Table 1 Condition Numbers for the Decoding Process Associated with the Modified Hadamard Coding on K × K Lenslet Arrays

Tables Icon

Table 2 Condition Numbers Associated With the P × P Partition of N × N Detector Arrays

Equations (20)

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

g i j = - X / 2 X / 2 - Y / 2 Y / 2 s i j ( x , y , f ˜ ( x , y ) ) d x d y , f ˜ ( x , y ) = - - f ( ξ , η ) h ( α x - ξ , α y - η ) d ξ d η ,
P i j ( x , y ) = rect ( x Δ x - i ) rect ( y Δ y - j ) ,
s i j ( x , y , f ˜ ( x , y ) ) = P i j ( x , y ) f ˜ ( x , y ) .
g p q , i j = X / 2 X / 2 Y / 2 Y / 2 s p q , i j ( x , y , f ˜ ( x , y ) ) d x d y , f ˜ ( x , y ) = f ( ξ , η ) h ( β x ξ , β y η ) d ξ d η ,
s p q , i j ( x , y , f ˜ ( x , y ) ) = P i j ( x , y ) E p q ( f ˜ ( x , y ) ) = P i j ( x , y ) f ˜ ( x - δ p , y - δ q ) ,
s p q , i j ( p q , i j ) ( x , y , f ˜ ( x , y ) ) = P i j ( x , y ) H p q ( x , y ) f ˜ ( x , y ) ,
H p q = 1 2 ( ( H 4 e q ) ( H 4 e p T ) + e e T ) ,
H 3 = ( 1 1 1 1 - 1 1 1 1 - 1 ) , H 5 = ( H 4 e e T - 1 ) .
A ^ ( i , j , p , q ) = A ( p , q , i , j ) .
2 M i j = H p X i j H q + ( e T X i j e ) e e T ,
X i j = H p - 1 ( 2 M i j - M i j ( 1 , 1 ) e e T ) H q - 1 .
cond ( S P Q ) = ( P Q + 4 ) + ( P Q + 4 ) 2 - 4 2 4 .
A ^ = B P , M X B Q , N ,
( 1 + 2 cos ( π N + 1 ) 1 + 2 cos ( 2 ( N + 1 ) / 3 π N + 1 ) ) 2 < cond ( B 3 , N B 3 , N ) < ( 1 + 2 cos ( π N + 1 ) 1 + 2 cos ( 2 ( N + 1 ) / 3 π N + 1 ) ) 2 .
A B = [ a 11 B a 1 n B a m 1 B a m n B ] .
H 2 = ( 1 1 1 1 ) , H 2 n = H 2 H n , n = 2 k , k 1 .
vec [ M i j ] = 1 2 [ ( H P H Q ) + e e T ] vec [ X i j ] ,
H ˜ N = 1 2 H N ( I + 1 N H N T e e T ) = 1 2 H N ( I + e 1 e T ) .
( N + 3 N 1 0 N 1 1 0 0 0 I N 2 ) .
λ max = N + 4 + ( N + 4 ) 2 4 2 2 > 1 > λ min = N + 4 ( N + 4 ) 2 4 2 2 > 0.

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