Abstract

The size of infrared camera systems can be reduced by collecting low-resolution images in parallel with multiple narrow-aperture lenses rather than collecting a single high-resolution image with one wide-aperture lens. We describe an infrared imaging system that uses a three-by-three lenslet array with an optical system length of 2.3 mm and achieves Rayleigh criteria resolution comparable with a conventional single-lens system with an optical system length of 26 mm. The high-resolution final image generated by this system is reconstructed from the low-resolution images gathered by each lenslet. This is accomplished using superresolution reconstruction algorithms based on linear and nonlinear interpolation algorithms. Two implementations of the ultrathin camera are demonstrated and their performances are compared with that of a conventional infrared camera.

© 2008 Optical Society of America

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  1. S. Ogata, J. Ishida, and T. Sasano, "Optical sensor array in an artificial compound eye," Opt. Eng. 33, 3649-3655 (1994).
    [CrossRef]
  2. J. S. Sanders and C. E. Halford, "Design and analysis of apposition compound eye optical sensors," Opt. Eng. 34, 222-235 (1995).
    [CrossRef]
  3. K. Hamanaka and H. Koshi, "An artificial compound eye using a microlens array and its application to scale invariant processing," Opt. Rev. 3, 264-268 (1996).
    [CrossRef]
  4. G. A. Horridge, "Apposition eyes of large diurnal insects as organs adapted to seeing," Proc. R. Soc. London 207, 287-309 (1980).
    [CrossRef]
  5. J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Marimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, "Thin observation module by bound optics (TOMBO): concept and experimental verification," Appl. Opt. 40, 1806-1813 (2001).
    [CrossRef]
  6. K. Nitta, R. Shogenji, S. Miyatake, and J. Tanida, "Image reconstruction for thin observation module by bound optics by using the iterative backprojection method," Appl. Opt. 45, 2893-2900 (2006).
    [CrossRef] [PubMed]
  7. A. V. Kanaev, D. A. Scribner, J. R. Ackerman, and E. F. Fleet, "Analysis and application of multiframe superresolution processing for conventional imaging systems and lenslet arrays," Appl. Opt. 46, 4320-4328 (2007).
    [CrossRef] [PubMed]
  8. E. Dowski and K. Kubala, "Reducing size, weight, and cost in a LWIR imaging system with wavefront coding," Proc. SPIE 5407, 66-73 (2004).
    [CrossRef]
  9. R. Willett, I. Jermyn, R. Nowak, and J. Zerubia, "Wavelet-based superresolution in astronomy," in Proceedings of Astronomical Data Analysis Software and Systems (Astronomical Society of the Pacific, 2003), Vol. 314, p. 107.
  10. M. Shankar, R. Willett, N. P. Pitsianis, R. Te Kolste, C. Chen, R. Gibbons, and D. J. Brady, "Ultra-thin multiple-channel LWIR imaging systems," Proc. SPIE 6294, 629411 (2006).
    [CrossRef]
  11. T. J. Schulz, "Multiframe blind deconvolution of astronomical images," J. Opt. Soc. Am. A 10, 1064-1073 (1993).
    [CrossRef]
  12. M. Figueiredo and R. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Trans. Image Process. 12, 906-916 (2003).
    [CrossRef]
  13. S. Mallat, A Wavelet Tour of Signal Processing (Academic, 1998).
  14. L. Landweber, "An iteration formula for Fredholm integral equations of the first kind," Am. J. Math. 73, 615-624 (1951).
    [CrossRef]
  15. M. Figueiredo and R. Nowak, "Wavelet-based image estimation: an empirical Bayes approach using Jeffreys' noninformative prior," IEEE Trans. Image Process. 10, 1322-1331 (2001).
    [CrossRef]
  16. W. H. Richardson, "Bayesian-based iterative method of image restoration," J. Opt. Soc. Am. 62, 55-59 (1972).
    [CrossRef]
  17. L. B. Lucy, "An iterative technique for the rectification of observed distributions," Astron. J. 7, 745-754 (1974).
    [CrossRef]

2007 (1)

A. V. Kanaev, D. A. Scribner, J. R. Ackerman, and E. F. Fleet, "Analysis and application of multiframe superresolution processing for conventional imaging systems and lenslet arrays," Appl. Opt. 46, 4320-4328 (2007).
[CrossRef] [PubMed]

2006 (2)

K. Nitta, R. Shogenji, S. Miyatake, and J. Tanida, "Image reconstruction for thin observation module by bound optics by using the iterative backprojection method," Appl. Opt. 45, 2893-2900 (2006).
[CrossRef] [PubMed]

M. Shankar, R. Willett, N. P. Pitsianis, R. Te Kolste, C. Chen, R. Gibbons, and D. J. Brady, "Ultra-thin multiple-channel LWIR imaging systems," Proc. SPIE 6294, 629411 (2006).
[CrossRef]

2004 (1)

E. Dowski and K. Kubala, "Reducing size, weight, and cost in a LWIR imaging system with wavefront coding," Proc. SPIE 5407, 66-73 (2004).
[CrossRef]

2003 (1)

M. Figueiredo and R. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Trans. Image Process. 12, 906-916 (2003).
[CrossRef]

2001 (2)

M. Figueiredo and R. Nowak, "Wavelet-based image estimation: an empirical Bayes approach using Jeffreys' noninformative prior," IEEE Trans. Image Process. 10, 1322-1331 (2001).
[CrossRef]

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Marimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, "Thin observation module by bound optics (TOMBO): concept and experimental verification," Appl. Opt. 40, 1806-1813 (2001).
[CrossRef]

1996 (1)

K. Hamanaka and H. Koshi, "An artificial compound eye using a microlens array and its application to scale invariant processing," Opt. Rev. 3, 264-268 (1996).
[CrossRef]

1995 (1)

J. S. Sanders and C. E. Halford, "Design and analysis of apposition compound eye optical sensors," Opt. Eng. 34, 222-235 (1995).
[CrossRef]

1994 (1)

S. Ogata, J. Ishida, and T. Sasano, "Optical sensor array in an artificial compound eye," Opt. Eng. 33, 3649-3655 (1994).
[CrossRef]

1993 (1)

T. J. Schulz, "Multiframe blind deconvolution of astronomical images," J. Opt. Soc. Am. A 10, 1064-1073 (1993).
[CrossRef]

1980 (1)

G. A. Horridge, "Apposition eyes of large diurnal insects as organs adapted to seeing," Proc. R. Soc. London 207, 287-309 (1980).
[CrossRef]

1974 (1)

L. B. Lucy, "An iterative technique for the rectification of observed distributions," Astron. J. 7, 745-754 (1974).
[CrossRef]

1972 (1)

W. H. Richardson, "Bayesian-based iterative method of image restoration," J. Opt. Soc. Am. 62, 55-59 (1972).
[CrossRef]

1951 (1)

L. Landweber, "An iteration formula for Fredholm integral equations of the first kind," Am. J. Math. 73, 615-624 (1951).
[CrossRef]

Ackerman, J. R.

A. V. Kanaev, D. A. Scribner, J. R. Ackerman, and E. F. Fleet, "Analysis and application of multiframe superresolution processing for conventional imaging systems and lenslet arrays," Appl. Opt. 46, 4320-4328 (2007).
[CrossRef] [PubMed]

Brady, D. J.

M. Shankar, R. Willett, N. P. Pitsianis, R. Te Kolste, C. Chen, R. Gibbons, and D. J. Brady, "Ultra-thin multiple-channel LWIR imaging systems," Proc. SPIE 6294, 629411 (2006).
[CrossRef]

Chen, C.

M. Shankar, R. Willett, N. P. Pitsianis, R. Te Kolste, C. Chen, R. Gibbons, and D. J. Brady, "Ultra-thin multiple-channel LWIR imaging systems," Proc. SPIE 6294, 629411 (2006).
[CrossRef]

Dowski, E.

E. Dowski and K. Kubala, "Reducing size, weight, and cost in a LWIR imaging system with wavefront coding," Proc. SPIE 5407, 66-73 (2004).
[CrossRef]

Figueiredo, M.

M. Figueiredo and R. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Trans. Image Process. 12, 906-916 (2003).
[CrossRef]

M. Figueiredo and R. Nowak, "Wavelet-based image estimation: an empirical Bayes approach using Jeffreys' noninformative prior," IEEE Trans. Image Process. 10, 1322-1331 (2001).
[CrossRef]

Fleet, E. F.

A. V. Kanaev, D. A. Scribner, J. R. Ackerman, and E. F. Fleet, "Analysis and application of multiframe superresolution processing for conventional imaging systems and lenslet arrays," Appl. Opt. 46, 4320-4328 (2007).
[CrossRef] [PubMed]

Gibbons, R.

M. Shankar, R. Willett, N. P. Pitsianis, R. Te Kolste, C. Chen, R. Gibbons, and D. J. Brady, "Ultra-thin multiple-channel LWIR imaging systems," Proc. SPIE 6294, 629411 (2006).
[CrossRef]

Halford, C. E.

J. S. Sanders and C. E. Halford, "Design and analysis of apposition compound eye optical sensors," Opt. Eng. 34, 222-235 (1995).
[CrossRef]

Hamanaka, K.

K. Hamanaka and H. Koshi, "An artificial compound eye using a microlens array and its application to scale invariant processing," Opt. Rev. 3, 264-268 (1996).
[CrossRef]

Horridge, G. A.

G. A. Horridge, "Apposition eyes of large diurnal insects as organs adapted to seeing," Proc. R. Soc. London 207, 287-309 (1980).
[CrossRef]

Ichioka, Y.

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Marimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, "Thin observation module by bound optics (TOMBO): concept and experimental verification," Appl. Opt. 40, 1806-1813 (2001).
[CrossRef]

Ishida, J.

S. Ogata, J. Ishida, and T. Sasano, "Optical sensor array in an artificial compound eye," Opt. Eng. 33, 3649-3655 (1994).
[CrossRef]

Ishida, K.

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Marimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, "Thin observation module by bound optics (TOMBO): concept and experimental verification," Appl. Opt. 40, 1806-1813 (2001).
[CrossRef]

Jermyn, I.

R. Willett, I. Jermyn, R. Nowak, and J. Zerubia, "Wavelet-based superresolution in astronomy," in Proceedings of Astronomical Data Analysis Software and Systems (Astronomical Society of the Pacific, 2003), Vol. 314, p. 107.

Kanaev, A. V.

A. V. Kanaev, D. A. Scribner, J. R. Ackerman, and E. F. Fleet, "Analysis and application of multiframe superresolution processing for conventional imaging systems and lenslet arrays," Appl. Opt. 46, 4320-4328 (2007).
[CrossRef] [PubMed]

Kondou, N.

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Marimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, "Thin observation module by bound optics (TOMBO): concept and experimental verification," Appl. Opt. 40, 1806-1813 (2001).
[CrossRef]

Koshi, H.

K. Hamanaka and H. Koshi, "An artificial compound eye using a microlens array and its application to scale invariant processing," Opt. Rev. 3, 264-268 (1996).
[CrossRef]

Kubala, K.

E. Dowski and K. Kubala, "Reducing size, weight, and cost in a LWIR imaging system with wavefront coding," Proc. SPIE 5407, 66-73 (2004).
[CrossRef]

Kumagai, T.

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Marimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, "Thin observation module by bound optics (TOMBO): concept and experimental verification," Appl. Opt. 40, 1806-1813 (2001).
[CrossRef]

Landweber, L.

L. Landweber, "An iteration formula for Fredholm integral equations of the first kind," Am. J. Math. 73, 615-624 (1951).
[CrossRef]

Lucy, L. B.

L. B. Lucy, "An iterative technique for the rectification of observed distributions," Astron. J. 7, 745-754 (1974).
[CrossRef]

Mallat, S.

S. Mallat, A Wavelet Tour of Signal Processing (Academic, 1998).

Marimoto, T.

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Marimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, "Thin observation module by bound optics (TOMBO): concept and experimental verification," Appl. Opt. 40, 1806-1813 (2001).
[CrossRef]

Miyatake, S.

K. Nitta, R. Shogenji, S. Miyatake, and J. Tanida, "Image reconstruction for thin observation module by bound optics by using the iterative backprojection method," Appl. Opt. 45, 2893-2900 (2006).
[CrossRef] [PubMed]

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Marimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, "Thin observation module by bound optics (TOMBO): concept and experimental verification," Appl. Opt. 40, 1806-1813 (2001).
[CrossRef]

Miyazaki, D.

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Marimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, "Thin observation module by bound optics (TOMBO): concept and experimental verification," Appl. Opt. 40, 1806-1813 (2001).
[CrossRef]

Nitta, K.

Nowak, R.

M. Figueiredo and R. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Trans. Image Process. 12, 906-916 (2003).
[CrossRef]

M. Figueiredo and R. Nowak, "Wavelet-based image estimation: an empirical Bayes approach using Jeffreys' noninformative prior," IEEE Trans. Image Process. 10, 1322-1331 (2001).
[CrossRef]

R. Willett, I. Jermyn, R. Nowak, and J. Zerubia, "Wavelet-based superresolution in astronomy," in Proceedings of Astronomical Data Analysis Software and Systems (Astronomical Society of the Pacific, 2003), Vol. 314, p. 107.

Ogata, S.

S. Ogata, J. Ishida, and T. Sasano, "Optical sensor array in an artificial compound eye," Opt. Eng. 33, 3649-3655 (1994).
[CrossRef]

Pitsianis, N. P.

M. Shankar, R. Willett, N. P. Pitsianis, R. Te Kolste, C. Chen, R. Gibbons, and D. J. Brady, "Ultra-thin multiple-channel LWIR imaging systems," Proc. SPIE 6294, 629411 (2006).
[CrossRef]

Richardson, W. H.

W. H. Richardson, "Bayesian-based iterative method of image restoration," J. Opt. Soc. Am. 62, 55-59 (1972).
[CrossRef]

Sanders, J. S.

J. S. Sanders and C. E. Halford, "Design and analysis of apposition compound eye optical sensors," Opt. Eng. 34, 222-235 (1995).
[CrossRef]

Sasano, T.

S. Ogata, J. Ishida, and T. Sasano, "Optical sensor array in an artificial compound eye," Opt. Eng. 33, 3649-3655 (1994).
[CrossRef]

Schulz, T. J.

T. J. Schulz, "Multiframe blind deconvolution of astronomical images," J. Opt. Soc. Am. A 10, 1064-1073 (1993).
[CrossRef]

Scribner, D. A.

A. V. Kanaev, D. A. Scribner, J. R. Ackerman, and E. F. Fleet, "Analysis and application of multiframe superresolution processing for conventional imaging systems and lenslet arrays," Appl. Opt. 46, 4320-4328 (2007).
[CrossRef] [PubMed]

Shankar, M.

M. Shankar, R. Willett, N. P. Pitsianis, R. Te Kolste, C. Chen, R. Gibbons, and D. J. Brady, "Ultra-thin multiple-channel LWIR imaging systems," Proc. SPIE 6294, 629411 (2006).
[CrossRef]

Shogenji, R.

Tanida, J.

K. Nitta, R. Shogenji, S. Miyatake, and J. Tanida, "Image reconstruction for thin observation module by bound optics by using the iterative backprojection method," Appl. Opt. 45, 2893-2900 (2006).
[CrossRef] [PubMed]

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Marimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, "Thin observation module by bound optics (TOMBO): concept and experimental verification," Appl. Opt. 40, 1806-1813 (2001).
[CrossRef]

Te Kolste, R.

M. Shankar, R. Willett, N. P. Pitsianis, R. Te Kolste, C. Chen, R. Gibbons, and D. J. Brady, "Ultra-thin multiple-channel LWIR imaging systems," Proc. SPIE 6294, 629411 (2006).
[CrossRef]

Willett, R.

M. Shankar, R. Willett, N. P. Pitsianis, R. Te Kolste, C. Chen, R. Gibbons, and D. J. Brady, "Ultra-thin multiple-channel LWIR imaging systems," Proc. SPIE 6294, 629411 (2006).
[CrossRef]

R. Willett, I. Jermyn, R. Nowak, and J. Zerubia, "Wavelet-based superresolution in astronomy," in Proceedings of Astronomical Data Analysis Software and Systems (Astronomical Society of the Pacific, 2003), Vol. 314, p. 107.

Yamada, K.

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Marimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, "Thin observation module by bound optics (TOMBO): concept and experimental verification," Appl. Opt. 40, 1806-1813 (2001).
[CrossRef]

Zerubia, J.

R. Willett, I. Jermyn, R. Nowak, and J. Zerubia, "Wavelet-based superresolution in astronomy," in Proceedings of Astronomical Data Analysis Software and Systems (Astronomical Society of the Pacific, 2003), Vol. 314, p. 107.

Am. J. Math. (1)

L. Landweber, "An iteration formula for Fredholm integral equations of the first kind," Am. J. Math. 73, 615-624 (1951).
[CrossRef]

Appl. Opt. (2)

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Marimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, "Thin observation module by bound optics (TOMBO): concept and experimental verification," Appl. Opt. 40, 1806-1813 (2001).
[CrossRef]

A. V. Kanaev, D. A. Scribner, J. R. Ackerman, and E. F. Fleet, "Analysis and application of multiframe superresolution processing for conventional imaging systems and lenslet arrays," Appl. Opt. 46, 4320-4328 (2007).
[CrossRef] [PubMed]

Appl. Opt. (1)

Astron. J. (1)

L. B. Lucy, "An iterative technique for the rectification of observed distributions," Astron. J. 7, 745-754 (1974).
[CrossRef]

IEEE Trans. Image Process. (2)

M. Figueiredo and R. Nowak, "Wavelet-based image estimation: an empirical Bayes approach using Jeffreys' noninformative prior," IEEE Trans. Image Process. 10, 1322-1331 (2001).
[CrossRef]

M. Figueiredo and R. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Trans. Image Process. 12, 906-916 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

W. H. Richardson, "Bayesian-based iterative method of image restoration," J. Opt. Soc. Am. 62, 55-59 (1972).
[CrossRef]

J. Opt. Soc. Am. A (1)

T. J. Schulz, "Multiframe blind deconvolution of astronomical images," J. Opt. Soc. Am. A 10, 1064-1073 (1993).
[CrossRef]

Opt. Eng. (2)

S. Ogata, J. Ishida, and T. Sasano, "Optical sensor array in an artificial compound eye," Opt. Eng. 33, 3649-3655 (1994).
[CrossRef]

J. S. Sanders and C. E. Halford, "Design and analysis of apposition compound eye optical sensors," Opt. Eng. 34, 222-235 (1995).
[CrossRef]

Opt. Rev. (1)

K. Hamanaka and H. Koshi, "An artificial compound eye using a microlens array and its application to scale invariant processing," Opt. Rev. 3, 264-268 (1996).
[CrossRef]

Proc. SPIE (1)

M. Shankar, R. Willett, N. P. Pitsianis, R. Te Kolste, C. Chen, R. Gibbons, and D. J. Brady, "Ultra-thin multiple-channel LWIR imaging systems," Proc. SPIE 6294, 629411 (2006).
[CrossRef]

Proc. R. Soc. London (1)

G. A. Horridge, "Apposition eyes of large diurnal insects as organs adapted to seeing," Proc. R. Soc. London 207, 287-309 (1980).
[CrossRef]

Proc. SPIE (1)

E. Dowski and K. Kubala, "Reducing size, weight, and cost in a LWIR imaging system with wavefront coding," Proc. SPIE 5407, 66-73 (2004).
[CrossRef]

Other (2)

R. Willett, I. Jermyn, R. Nowak, and J. Zerubia, "Wavelet-based superresolution in astronomy," in Proceedings of Astronomical Data Analysis Software and Systems (Astronomical Society of the Pacific, 2003), Vol. 314, p. 107.

S. Mallat, A Wavelet Tour of Signal Processing (Academic, 1998).

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Figures (16)

Fig. 1
Fig. 1

Optical layout of one channel of the multichannel LWIR imaging systems. The surface A contains the phase grating for the coded PSF system. S denotes the sag of the convex element. The optical system thickness is 2.3 mm.

Fig. 2
Fig. 2

Positions of the lenslets in each subaperture of the TOMBO IR system. The centers of the lenslets (indicated by the circles) are shifted by 70 μm in different directions with respect to the centers of the subapertures. The pitch of the lenslets in the horizontal direction is 1.3 mm and that in the vertical direction is 1.31 mm as shown.

Fig. 3
Fig. 3

Phase grating array used in the coded PSF system. The orientation of the gratings in each of the subapertures is different. The period of gratings 1, 3, 6, and 8 is 286.2 μm and that of gratings 2, 4, 5, and 7 is 401.6 μm. The center subaperture does not have a grating associated with it.

Fig. 4
Fig. 4

(a) Spot diagram of the optical system of the TOMBO system and (b) coded PSF system for the wavelength of 10 μm at the field angles of 0 and 10 . The black circle represents the diffraction-limited spot. The resulting shift in the spots due to the diffractive element in the coded PSF system is 80 μm.

Fig. 5
Fig. 5

Modulation transfer function of (a) the optical system of the TOMBO system and (b) the coded PSF system for the wavelength of 10 μm at the field angles of 0 and 10 . For each field angle, the tangential (T) and sagittal (S) MTFs are shown. Also shown is the diffraction-limited MTF.

Fig. 6
Fig. 6

Experimentally obtained point-spread functions of (a) the TOMBO system and (b) the coded PSF system. The shifts caused by the phase grating array is evident in (b).

Fig. 7
Fig. 7

Three IR camera systems—from left to right, the coded PSF system, the conventional single-aperture system, and the TOMBO system.

Fig. 8
Fig. 8

3 × 3 convex microlens array used in the cameras.

Fig. 9
Fig. 9

Raw images obtained from the IR cameras: (a) TOMBO camera, (b) coded PSF camera, and (c) conventional camera.

Fig. 10
Fig. 10

(a) Image obtained from a single lenslet of the TOMBO camera, (b) image after reconstruction using the LG technique on the TOMBO image, and (c) image after reconstruction using the wavelet-based EM technique on the TOMBO image.

Fig. 11
Fig. 11

(a) Image obtained from a single lenslet of the coded PSF camera, (b) image obtained after reconstruction using the LG algorithm on the coded PSF image, and (c) image after reconstruction using the R–L technique on the coded PSF image.

Fig. 12
Fig. 12

Frame wound with heating wires placed at an angle to observe the modulation from the three cameras.

Fig. 13
Fig. 13

(a) Reconstruction of the image of the wire frame from the TOMBO system and (b) the corresponding modulation obtained by plotting the intensity across all columns from one selected row from the reconstructed image.

Fig. 14
Fig. 14

(a) Reconstruction of the image of the wire frame from the coded PSF system and (b) the corresponding modulation obtained by plotting the intensity across all columns from one selected row from the reconstructed image.

Fig. 15
Fig. 15

(a) Image of the wire frame obtained from the conventional IR camera and (b) the corresponding modulation obtained by plotting the intensity across all columns from one selected row from the image.

Fig. 16
Fig. 16

Determination of two-point resolution of the cameras. Plots of the intensity along the row containing the point sources in the reconstructed image as the sources are brought closer together.

Equations (10)

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

x = H f + n .
f L G = arg min f γ ( f ) = f 2
= [ 1 1 0 0 0 1 1 0 0 0 1 1 ] .
f L G = arg min c ( N c f p ) 2 .
f L G = f p N ( N T T N ) 1 ( N ) T f p ,
x = H ( W θ + α n 1 ) z + n 2 ,
z ^ ( i ) = E [ z | x , θ ^ ( i ) ] .
z ^ ( i ) = f ^ ( i ) + α 2 σ 2 H T ( x H f ^ ( i ) ) .
θ ^ ( i + 1 ) = arg min θ { W θ z ^ ( i ) 2 2 2 α 2 + p e n ( θ ) }
f ^ ( k + 1 ) = f ^ ( k ) H T ( x H f ^ ( k ) ) ,

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