Abstract

This paper presents a coded pinhole lens imaging system consisting of a pinhole array aperture, followed by a thin convex lens, mounted onto a standard DSLR camera body. The combination of pinhole and lens incurs two questions: (1) Is the new camera based on pinhole or lens imaging principle? (2) Can the lens improve the imaging quality? The study reveals that the camera is based on pinhole imaging, but the lens can improve its optical resolution from 0.44 mm (pinhole size) to 0.042 mm, leading to a significant improvement in imaging quality. The numerous pinholes on the aperture also improve the camera’s light throughput ability over single pinhole camera. The camera could be used for applications where a large depth of field is required while the illumination condition is poor.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2015 (1)

2014 (2)

W. Wen, S. Wang, Y. Zou, H. Li, S. Liu, G. Tang, Y. Lu, and Z. Guo, “Design of moderator of a compact accelerator-driven neutron source for coded source imaging,” Phys. Procedia 60, 144–150 (2014).
[Crossref]

M. J. DeWeert and B. P. Farm, “Lensless coded aperture imaging with separable doubly-toeplitz masks,” Proc. SPIE 91090, Q91091 (2014).

2012 (1)

2011 (1)

2007 (5)

C. Slinger, M. Eismann, N. Gordon, K. Lewis, G. McDonald, M. McNie, D. Payne, K. Ridley, M. Strens, G. De Villiers, and R. Wilson, “An investigation of the potential for the use of a high resolution adaptive coded aperture system in the mid-wave infrared,” Proc. SPIE 6714(8), 671408 (2007).
[Crossref]

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Trans. Graph. 26(3), 701–709 (2007).
[Crossref]

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Trans. Graph. 26(3), 6901–6912 (2007).
[Crossref]

M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

S. R. Gottesman, “Coded apertures: past, present, and future application and design,” Proc. SPIE 6714(5), 671405 (2007).
[Crossref]

2006 (1)

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

1992 (1)

E. H. Adelson and J. Y. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14(2), 99–106 (1992).
[Crossref]

1989 (1)

1987 (1)

E. Caroli, J. B. Stephen, G. Dicocco, L. Natalucci, and A. Spizzichino, “Coded aperture imaging in X-ray and gamma-ray astronomy,” Space Sci. Rev. 45(3–4), 349–403 (1987).
[Crossref]

1986 (1)

S. R. Gottesman and E. J. Schneid, “PNP - a new class of coded aperture arrays,” IEEE Trans. Nucl. Sci. 33(1), 745–749 (1986).
[Crossref]

1978 (1)

1971 (1)

1968 (1)

R. H. Dicke, “Scatter-hole cameras for X-rays and gamma rays,” Astrophys. J. 153, L101–L106 (1968).
[Crossref]

1967 (1)

Adelson, E. H.

E. H. Adelson and J. Y. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14(2), 99–106 (1992).
[Crossref]

Agrawal, A.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Trans. Graph. 26(3), 6901–6912 (2007).
[Crossref]

Arce, G. R.

Arguello, H.

Asif, M. S.

M. S. Asif, A. Ayremlou, A. Veeraraghavan, R. Baraniuk, and A. Sankaranarayanan, “FlatCam: Replacing Lenses with Masks and Computation”, Proceedings of IEEE International Conference on Computer Vision Workshop (ICCVW), 2015, pp. 663–666.
[Crossref]

Ayremlou, A.

M. S. Asif, A. Ayremlou, A. Veeraraghavan, R. Baraniuk, and A. Sankaranarayanan, “FlatCam: Replacing Lenses with Masks and Computation”, Proceedings of IEEE International Conference on Computer Vision Workshop (ICCVW), 2015, pp. 663–666.
[Crossref]

Baraniuk, R.

M. S. Asif, A. Ayremlou, A. Veeraraghavan, R. Baraniuk, and A. Sankaranarayanan, “FlatCam: Replacing Lenses with Masks and Computation”, Proceedings of IEEE International Conference on Computer Vision Workshop (ICCVW), 2015, pp. 663–666.
[Crossref]

Brédif, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Computer Science Technical Report CSTR2, 11 (2005).

Byard, K.

Candès, E. J.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

Cannon, T. M.

Caroli, E.

E. Caroli, J. B. Stephen, G. Dicocco, L. Natalucci, and A. Spizzichino, “Coded aperture imaging in X-ray and gamma-ray astronomy,” Space Sci. Rev. 45(3–4), 349–403 (1987).
[Crossref]

Chi, W.

Cuadros, A. P.

De Villiers, G.

C. Slinger, M. Eismann, N. Gordon, K. Lewis, G. McDonald, M. McNie, D. Payne, K. Ridley, M. Strens, G. De Villiers, and R. Wilson, “An investigation of the potential for the use of a high resolution adaptive coded aperture system in the mid-wave infrared,” Proc. SPIE 6714(8), 671408 (2007).
[Crossref]

DeWeert, M. J.

M. J. DeWeert and B. P. Farm, “Lensless coded aperture imaging with separable doubly-toeplitz masks,” Proc. SPIE 91090, Q91091 (2014).

Dicke, R. H.

R. H. Dicke, “Scatter-hole cameras for X-rays and gamma rays,” Astrophys. J. 153, L101–L106 (1968).
[Crossref]

Dicocco, G.

E. Caroli, J. B. Stephen, G. Dicocco, L. Natalucci, and A. Spizzichino, “Coded aperture imaging in X-ray and gamma-ray astronomy,” Space Sci. Rev. 45(3–4), 349–403 (1987).
[Crossref]

Durand, F.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Trans. Graph. 26(3), 701–709 (2007).
[Crossref]

Duval, G.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Computer Science Technical Report CSTR2, 11 (2005).

Eismann, M.

C. Slinger, M. Eismann, N. Gordon, K. Lewis, G. McDonald, M. McNie, D. Payne, K. Ridley, M. Strens, G. De Villiers, and R. Wilson, “An investigation of the potential for the use of a high resolution adaptive coded aperture system in the mid-wave infrared,” Proc. SPIE 6714(8), 671408 (2007).
[Crossref]

Farm, B. P.

M. J. DeWeert and B. P. Farm, “Lensless coded aperture imaging with separable doubly-toeplitz masks,” Proc. SPIE 91090, Q91091 (2014).

Fenimore, E. E.

Fergus, R.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Trans. Graph. 26(3), 701–709 (2007).
[Crossref]

Figueiredo, M.

M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

Freeman, W. T.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Trans. Graph. 26(3), 701–709 (2007).
[Crossref]

George, N.

Gordon, N.

C. Slinger, M. Eismann, N. Gordon, K. Lewis, G. McDonald, M. McNie, D. Payne, K. Ridley, M. Strens, G. De Villiers, and R. Wilson, “An investigation of the potential for the use of a high resolution adaptive coded aperture system in the mid-wave infrared,” Proc. SPIE 6714(8), 671408 (2007).
[Crossref]

Gottesman, S. R.

S. R. Gottesman, “Coded apertures: past, present, and future application and design,” Proc. SPIE 6714(5), 671405 (2007).
[Crossref]

S. R. Gottesman and E. E. Fenimore, “New family of binary arrays for coded aperture imaging,” Appl. Opt. 28(20), 4344–4352 (1989).
[Crossref] [PubMed]

S. R. Gottesman and E. J. Schneid, “PNP - a new class of coded aperture arrays,” IEEE Trans. Nucl. Sci. 33(1), 745–749 (1986).
[Crossref]

Guo, Z.

W. Wen, S. Wang, Y. Zou, H. Li, S. Liu, G. Tang, Y. Lu, and Z. Guo, “Design of moderator of a compact accelerator-driven neutron source for coded source imaging,” Phys. Procedia 60, 144–150 (2014).
[Crossref]

Hanrahan, P.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Computer Science Technical Report CSTR2, 11 (2005).

Horowitz, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Computer Science Technical Report CSTR2, 11 (2005).

Levin, A.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Trans. Graph. 26(3), 701–709 (2007).
[Crossref]

Levoy, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Computer Science Technical Report CSTR2, 11 (2005).

Lewis, K.

C. Slinger, M. Eismann, N. Gordon, K. Lewis, G. McDonald, M. McNie, D. Payne, K. Ridley, M. Strens, G. De Villiers, and R. Wilson, “An investigation of the potential for the use of a high resolution adaptive coded aperture system in the mid-wave infrared,” Proc. SPIE 6714(8), 671408 (2007).
[Crossref]

Li, H.

W. Wen, S. Wang, Y. Zou, H. Li, S. Liu, G. Tang, Y. Lu, and Z. Guo, “Design of moderator of a compact accelerator-driven neutron source for coded source imaging,” Phys. Procedia 60, 144–150 (2014).
[Crossref]

Liu, S.

W. Wen, S. Wang, Y. Zou, H. Li, S. Liu, G. Tang, Y. Lu, and Z. Guo, “Design of moderator of a compact accelerator-driven neutron source for coded source imaging,” Phys. Procedia 60, 144–150 (2014).
[Crossref]

Lu, Y.

W. Wen, S. Wang, Y. Zou, H. Li, S. Liu, G. Tang, Y. Lu, and Z. Guo, “Design of moderator of a compact accelerator-driven neutron source for coded source imaging,” Phys. Procedia 60, 144–150 (2014).
[Crossref]

McDonald, G.

C. Slinger, M. Eismann, N. Gordon, K. Lewis, G. McDonald, M. McNie, D. Payne, K. Ridley, M. Strens, G. De Villiers, and R. Wilson, “An investigation of the potential for the use of a high resolution adaptive coded aperture system in the mid-wave infrared,” Proc. SPIE 6714(8), 671408 (2007).
[Crossref]

McNie, M.

C. Slinger, M. Eismann, N. Gordon, K. Lewis, G. McDonald, M. McNie, D. Payne, K. Ridley, M. Strens, G. De Villiers, and R. Wilson, “An investigation of the potential for the use of a high resolution adaptive coded aperture system in the mid-wave infrared,” Proc. SPIE 6714(8), 671408 (2007).
[Crossref]

Mohan, A.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Trans. Graph. 26(3), 6901–6912 (2007).
[Crossref]

Natalucci, L.

E. Caroli, J. B. Stephen, G. Dicocco, L. Natalucci, and A. Spizzichino, “Coded aperture imaging in X-ray and gamma-ray astronomy,” Space Sci. Rev. 45(3–4), 349–403 (1987).
[Crossref]

Nayar, S.

C. Zhou and S. Nayar, “What are good apertures for defocus deblurring?” IEEE International Conference on Computational Photography (ICCP)2009, pp. 1–8.
[Crossref]

Ng, R.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Computer Science Technical Report CSTR2, 11 (2005).

Nowak, R.

M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

Payne, D.

C. Slinger, M. Eismann, N. Gordon, K. Lewis, G. McDonald, M. McNie, D. Payne, K. Ridley, M. Strens, G. De Villiers, and R. Wilson, “An investigation of the potential for the use of a high resolution adaptive coded aperture system in the mid-wave infrared,” Proc. SPIE 6714(8), 671408 (2007).
[Crossref]

Peitsch, C.

Raskar, R.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Trans. Graph. 26(3), 6901–6912 (2007).
[Crossref]

Ridley, K.

C. Slinger, M. Eismann, N. Gordon, K. Lewis, G. McDonald, M. McNie, D. Payne, K. Ridley, M. Strens, G. De Villiers, and R. Wilson, “An investigation of the potential for the use of a high resolution adaptive coded aperture system in the mid-wave infrared,” Proc. SPIE 6714(8), 671408 (2007).
[Crossref]

Romberg, J.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

Sankaranarayanan, A.

M. S. Asif, A. Ayremlou, A. Veeraraghavan, R. Baraniuk, and A. Sankaranarayanan, “FlatCam: Replacing Lenses with Masks and Computation”, Proceedings of IEEE International Conference on Computer Vision Workshop (ICCVW), 2015, pp. 663–666.
[Crossref]

Sayanagi, K.

Schneid, E. J.

S. R. Gottesman and E. J. Schneid, “PNP - a new class of coded aperture arrays,” IEEE Trans. Nucl. Sci. 33(1), 745–749 (1986).
[Crossref]

Slinger, C.

C. Slinger, M. Eismann, N. Gordon, K. Lewis, G. McDonald, M. McNie, D. Payne, K. Ridley, M. Strens, G. De Villiers, and R. Wilson, “An investigation of the potential for the use of a high resolution adaptive coded aperture system in the mid-wave infrared,” Proc. SPIE 6714(8), 671408 (2007).
[Crossref]

Spizzichino, A.

E. Caroli, J. B. Stephen, G. Dicocco, L. Natalucci, and A. Spizzichino, “Coded aperture imaging in X-ray and gamma-ray astronomy,” Space Sci. Rev. 45(3–4), 349–403 (1987).
[Crossref]

Stephen, J. B.

E. Caroli, J. B. Stephen, G. Dicocco, L. Natalucci, and A. Spizzichino, “Coded aperture imaging in X-ray and gamma-ray astronomy,” Space Sci. Rev. 45(3–4), 349–403 (1987).
[Crossref]

Strens, M.

C. Slinger, M. Eismann, N. Gordon, K. Lewis, G. McDonald, M. McNie, D. Payne, K. Ridley, M. Strens, G. De Villiers, and R. Wilson, “An investigation of the potential for the use of a high resolution adaptive coded aperture system in the mid-wave infrared,” Proc. SPIE 6714(8), 671408 (2007).
[Crossref]

Tang, G.

W. Wen, S. Wang, Y. Zou, H. Li, S. Liu, G. Tang, Y. Lu, and Z. Guo, “Design of moderator of a compact accelerator-driven neutron source for coded source imaging,” Phys. Procedia 60, 144–150 (2014).
[Crossref]

Tao, T.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

Tumblin, J.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Trans. Graph. 26(3), 6901–6912 (2007).
[Crossref]

Veeraraghavan, A.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Trans. Graph. 26(3), 6901–6912 (2007).
[Crossref]

M. S. Asif, A. Ayremlou, A. Veeraraghavan, R. Baraniuk, and A. Sankaranarayanan, “FlatCam: Replacing Lenses with Masks and Computation”, Proceedings of IEEE International Conference on Computer Vision Workshop (ICCVW), 2015, pp. 663–666.
[Crossref]

Wang, J. Y.

E. H. Adelson and J. Y. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14(2), 99–106 (1992).
[Crossref]

Wang, S.

W. Wen, S. Wang, Y. Zou, H. Li, S. Liu, G. Tang, Y. Lu, and Z. Guo, “Design of moderator of a compact accelerator-driven neutron source for coded source imaging,” Phys. Procedia 60, 144–150 (2014).
[Crossref]

Wen, W.

W. Wen, S. Wang, Y. Zou, H. Li, S. Liu, G. Tang, Y. Lu, and Z. Guo, “Design of moderator of a compact accelerator-driven neutron source for coded source imaging,” Phys. Procedia 60, 144–150 (2014).
[Crossref]

Wilson, R.

C. Slinger, M. Eismann, N. Gordon, K. Lewis, G. McDonald, M. McNie, D. Payne, K. Ridley, M. Strens, G. De Villiers, and R. Wilson, “An investigation of the potential for the use of a high resolution adaptive coded aperture system in the mid-wave infrared,” Proc. SPIE 6714(8), 671408 (2007).
[Crossref]

Wright, S.

M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

Young, M.

Zhou, C.

C. Zhou and S. Nayar, “What are good apertures for defocus deblurring?” IEEE International Conference on Computational Photography (ICCP)2009, pp. 1–8.
[Crossref]

Zou, Y.

W. Wen, S. Wang, Y. Zou, H. Li, S. Liu, G. Tang, Y. Lu, and Z. Guo, “Design of moderator of a compact accelerator-driven neutron source for coded source imaging,” Phys. Procedia 60, 144–150 (2014).
[Crossref]

ACM Trans. Graph. (2)

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Trans. Graph. 26(3), 701–709 (2007).
[Crossref]

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Trans. Graph. 26(3), 6901–6912 (2007).
[Crossref]

Appl. Opt. (4)

Astrophys. J. (1)

R. H. Dicke, “Scatter-hole cameras for X-rays and gamma rays,” Astrophys. J. 153, L101–L106 (1968).
[Crossref]

IEEE J. Sel. Top. Signal Process. (1)

M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

IEEE Trans. Inf. Theory (1)

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

IEEE Trans. Nucl. Sci. (1)

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Figures (9)

Fig. 1
Fig. 1 Sketch of proposed coded pinhole lens imaging system.
Fig. 2
Fig. 2 Implementation details: (a) the pattern of the prototype 2 × 2 cyclic version coded aperture (the middle part outlined by a red square presents the basic pattern); (b) physical implementation–left panel: lithographed film (top) and prototype camera (bottom); right panel: front view (top) and rear view (bottom) of the prototype lens set.
Fig. 3
Fig. 3 PSF analysis. (a) PSF for the basic pattern of CA without consideration of pinhole diffraction; (b) diffraction pattern for single pinhole lens aperture (a square pinhole placed in front of a thin lens)
Fig. 4
Fig. 4 Diffraction analysis of a pinhole lens aperture with one square pinhole (d = 0.44 mm). (a) simulation using Fresnel model; (b) simulation using Fraunhofer model; (c-f) real test using ISO 100 and different exposure time (Tv 1/1000, 1/250, 1/60, and 1/8 respectively) from a point light source. It is noted that (c-f) are of different scales.
Fig. 5
Fig. 5 PSF in different forms. (a) Aused for Wiener deconvolution; (b) A ¯ (a sparse Toeplitz matrix) used for regularization reconstruction.
Fig. 6
Fig. 6 Recorded images for a point light source using ISO 100 and different exposure time: (a) Tv 1/1000; (b) Tv 1/250; (c) Tv 1/60; (d) Tv 1/8.
Fig. 7
Fig. 7 Raw recorded images on the sensor array: an R letter by (a) a pure pinhole array and (b) a pinhole array with a thin lens; a house by (c) a pure pinhole array and (d) a pinhole array with a thin lens.
Fig. 8
Fig. 8 Original images and reconstructions: (a) original; (b) Holga pinhole images; (c, d) reconstructions of pure pinhole-array imaging using Weiner deconvolution and TVQC respectively; (e, f) reconstructions of pinhole-array lens imaging using Weiner deconvolution and TVQC respectively.
Fig. 9
Fig. 9 Geometric arrangement of mask and sensors. (a) Ideally the sensor size is ¼ of the aperture size and just below the center of the aperture; when the sensor size is bigger, multiple copies will be formed: (b) an example of reconstruction from full recorded raw image (720 × 480 pixels) by Wiener deconvolution.

Tables (1)

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Table 1 Parameters for the Prototype System

Equations (12)

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p=s+ f×s u .
1 f' = 1 u + 1 v .
q=( 1 f f' )×s+ f×s u .
d=1.56 λf ,
P= i=1 n OH( xi,yi ) ,
A= i=1 n H(xi,yi) .
E(x',y',z;x,y,0)= iE0 λR e iKR e iK(x ' 2 +y ' 2 ) 2R W 2 W 2 H 2 H 2 e iK( x 2 + y 2 ) 2R e iK(x'x+y'y) 2R dxdy,
E(x',y',z;x,y,0)= i E 0 λR e iKR W 2 W 2 H 2 H 2 e iK(xx'+yy') R dxdy ,
P=XA+N,
p= A ¯ x+n,
W(f)= 1 H(f) [ | H(f) | 2 | H(f) | 2 + 1 σ ],
minTV(x)subject to A ¯ x p 2 ε,