Abstract

In this paper, we present a novel method for pinhole optics with variable pinhole arrays. The imaging system is based on a time multiplexing method using variable and moving pinhole arrays. The improved resolution and signal-to-noise ratio are achieved with improved light intensity in the same exposure time, compared with that of a one-pinhole system. This new configuration preserves the advantages of pinhole optics while solving the resolution limitation problem and the long exposure time of such systems. The system also can be used as an addition to several existing optical systems, which use visible and invisible light and x-ray systems.

© 2014 Optical Society of America

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References

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  1. E. W. H. Selwyn, “The pin-hole camera,” Photographic J. 90B, 47–52 (1950).
  2. L. C. Martin and W. T. Welford, Technical Optics, Vol. I (Pitman, 1966).
  3. A. C. Hardy and F. Perrin, The Principles of Optics (McGraw-Hill, 1932).
  4. R. Kingslake, Lenses in Photography, rev., ed. (A. S. Barnes and Company, 1963).
  5. L. Mertz and N. O. Young, “Fresnel transformations of images,” in Proceedings of International Conference on Optical Instruments and Techniques (Chapman and Hall, 1961), pp. 305–310.
  6. R. H. Dicke, “Scatter-hole cameras for x-rays and gamma rays,” Astrophys. J. 153, L101–L106 (1968).
    [CrossRef]
  7. J. G. Ables, “Fourier transform photography: a new method for x-ray astronomy,” Proc. Astron. Soc. Aust. 1, 172–173 (1968).
  8. H. H. Barrett, D. T. Wilson, and G. D. Demeester, “The use of half-tone screens in Fresnel zone plate imaging of incoherent sources,” Opt. Commun. 5, 398–401 (1972).
    [CrossRef]
  9. H. H. Barrett and F. A. Horrigan, “Fresnel zone plate image of gamma rays; theory,” Appl. Opt. 12, 2686–2702 (1973).
    [CrossRef]
  10. R. Accorsi and R. C. Lanza, “Near-field artifact reduction in coded aperture imaging,” Appl. Opt. 40, 4697–4705 (2001).
    [CrossRef]
  11. R. Accorsi, F. Gasparini, and R. C. Lanza, “Optimal coded aperture patterns for improved SNR in nuclear medicine imaging,” Nucl. Instrum. Methods Phys. Res. A 474, 273–284 (2001).
    [CrossRef]
  12. R. Accorsi, F. Gasparini, and R. C. Lanza, “A coded aperture for high-resolution nuclear medicine planar imaging with a conventional anger camera: experimental results,” IEEE Trans. Nucl. Sci. 48, 2411–2417 (2001).
    [CrossRef]
  13. E. H. Adelson and J. Y. A. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99–106 (1992).
  14. M. Aggarwal and N. Ahuja, “Split aperture imaging for high dynamic range,” Int’l. J. Comp. Vis. 58, 7–17 (2004).
  15. R. Ng, “Fourier slice photography,” ACM Trans. Graph. 24, 735–744 (2005).
  16. T. Georgiev, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution tradeoffs in integral photography,” in Proceedings of Eurographics Symposium on Rendering, T. Akenine-Möller and W. Heidrich, eds. (The Eurographics Association, 2006), pp. 263–272.
  17. M. Mcguire, W. Matusik, B. Chen, J. F. Hughes, H. Pfister, and S. Nayar, “Optical splitting trees for high-precision monocular imaging,” IEEE Comp. Graphics App. 27, 32–42 (2007).
  18. P. Green, W. Sun, W. Matusik, and F. Durand, “Multi-aperture photography,” ACM Trans. Graph. 26, 68 (2007).
    [CrossRef]
  19. E. E. Fenimore and T. M. Cannon, “Coded aperture imaging with uniformly redundant arrays,” Appl. Opt. 17, 337–347 (1978).
    [CrossRef]
  20. A. Busboom, H. Elders-Boll, and H. D. Schotten, “Uniformly redundant arrays,” Exp. Astro. 8, 97–123 (1998).
  21. S. R. Gottesman and E. E. Fenimore, “New family of binary arrays for coded aperture imaging,” Appl. Opt. 28, 4344–4352 (1989).
    [CrossRef]
  22. 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).
    [CrossRef]

2007 (2)

M. Mcguire, W. Matusik, B. Chen, J. F. Hughes, H. Pfister, and S. Nayar, “Optical splitting trees for high-precision monocular imaging,” IEEE Comp. Graphics App. 27, 32–42 (2007).

P. Green, W. Sun, W. Matusik, and F. Durand, “Multi-aperture photography,” ACM Trans. Graph. 26, 68 (2007).
[CrossRef]

2005 (1)

R. Ng, “Fourier slice photography,” ACM Trans. Graph. 24, 735–744 (2005).

2004 (1)

M. Aggarwal and N. Ahuja, “Split aperture imaging for high dynamic range,” Int’l. J. Comp. Vis. 58, 7–17 (2004).

2001 (4)

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).
[CrossRef]

R. Accorsi and R. C. Lanza, “Near-field artifact reduction in coded aperture imaging,” Appl. Opt. 40, 4697–4705 (2001).
[CrossRef]

R. Accorsi, F. Gasparini, and R. C. Lanza, “Optimal coded aperture patterns for improved SNR in nuclear medicine imaging,” Nucl. Instrum. Methods Phys. Res. A 474, 273–284 (2001).
[CrossRef]

R. Accorsi, F. Gasparini, and R. C. Lanza, “A coded aperture for high-resolution nuclear medicine planar imaging with a conventional anger camera: experimental results,” IEEE Trans. Nucl. Sci. 48, 2411–2417 (2001).
[CrossRef]

1998 (1)

A. Busboom, H. Elders-Boll, and H. D. Schotten, “Uniformly redundant arrays,” Exp. Astro. 8, 97–123 (1998).

1992 (1)

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

1989 (1)

1978 (1)

1973 (1)

1972 (1)

H. H. Barrett, D. T. Wilson, and G. D. Demeester, “The use of half-tone screens in Fresnel zone plate imaging of incoherent sources,” Opt. Commun. 5, 398–401 (1972).
[CrossRef]

1968 (2)

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

J. G. Ables, “Fourier transform photography: a new method for x-ray astronomy,” Proc. Astron. Soc. Aust. 1, 172–173 (1968).

1950 (1)

E. W. H. Selwyn, “The pin-hole camera,” Photographic J. 90B, 47–52 (1950).

Ables, J. G.

J. G. Ables, “Fourier transform photography: a new method for x-ray astronomy,” Proc. Astron. Soc. Aust. 1, 172–173 (1968).

Accorsi, R.

R. Accorsi and R. C. Lanza, “Near-field artifact reduction in coded aperture imaging,” Appl. Opt. 40, 4697–4705 (2001).
[CrossRef]

R. Accorsi, F. Gasparini, and R. C. Lanza, “Optimal coded aperture patterns for improved SNR in nuclear medicine imaging,” Nucl. Instrum. Methods Phys. Res. A 474, 273–284 (2001).
[CrossRef]

R. Accorsi, F. Gasparini, and R. C. Lanza, “A coded aperture for high-resolution nuclear medicine planar imaging with a conventional anger camera: experimental results,” IEEE Trans. Nucl. Sci. 48, 2411–2417 (2001).
[CrossRef]

Adelson, E. H.

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

Aggarwal, M.

M. Aggarwal and N. Ahuja, “Split aperture imaging for high dynamic range,” Int’l. J. Comp. Vis. 58, 7–17 (2004).

Ahuja, N.

M. Aggarwal and N. Ahuja, “Split aperture imaging for high dynamic range,” Int’l. J. Comp. Vis. 58, 7–17 (2004).

Barrett, H. H.

H. H. Barrett and F. A. Horrigan, “Fresnel zone plate image of gamma rays; theory,” Appl. Opt. 12, 2686–2702 (1973).
[CrossRef]

H. H. Barrett, D. T. Wilson, and G. D. Demeester, “The use of half-tone screens in Fresnel zone plate imaging of incoherent sources,” Opt. Commun. 5, 398–401 (1972).
[CrossRef]

Busboom, A.

A. Busboom, H. Elders-Boll, and H. D. Schotten, “Uniformly redundant arrays,” Exp. Astro. 8, 97–123 (1998).

Cannon, T. M.

Chen, B.

M. Mcguire, W. Matusik, B. Chen, J. F. Hughes, H. Pfister, and S. Nayar, “Optical splitting trees for high-precision monocular imaging,” IEEE Comp. Graphics App. 27, 32–42 (2007).

Curless, B.

T. Georgiev, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution tradeoffs in integral photography,” in Proceedings of Eurographics Symposium on Rendering, T. Akenine-Möller and W. Heidrich, eds. (The Eurographics Association, 2006), pp. 263–272.

Demeester, G. D.

H. H. Barrett, D. T. Wilson, and G. D. Demeester, “The use of half-tone screens in Fresnel zone plate imaging of incoherent sources,” Opt. Commun. 5, 398–401 (1972).
[CrossRef]

Dicke, R. H.

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

Durand, F.

P. Green, W. Sun, W. Matusik, and F. Durand, “Multi-aperture photography,” ACM Trans. Graph. 26, 68 (2007).
[CrossRef]

Elders-Boll, H.

A. Busboom, H. Elders-Boll, and H. D. Schotten, “Uniformly redundant arrays,” Exp. Astro. 8, 97–123 (1998).

Fenimore, E. E.

Gasparini, F.

R. Accorsi, F. Gasparini, and R. C. Lanza, “Optimal coded aperture patterns for improved SNR in nuclear medicine imaging,” Nucl. Instrum. Methods Phys. Res. A 474, 273–284 (2001).
[CrossRef]

R. Accorsi, F. Gasparini, and R. C. Lanza, “A coded aperture for high-resolution nuclear medicine planar imaging with a conventional anger camera: experimental results,” IEEE Trans. Nucl. Sci. 48, 2411–2417 (2001).
[CrossRef]

Georgiev, T.

T. Georgiev, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution tradeoffs in integral photography,” in Proceedings of Eurographics Symposium on Rendering, T. Akenine-Möller and W. Heidrich, eds. (The Eurographics Association, 2006), pp. 263–272.

Gottesman, S. R.

Green, P.

P. Green, W. Sun, W. Matusik, and F. Durand, “Multi-aperture photography,” ACM Trans. Graph. 26, 68 (2007).
[CrossRef]

Hardy, A. C.

A. C. Hardy and F. Perrin, The Principles of Optics (McGraw-Hill, 1932).

Horrigan, F. A.

Hughes, J. F.

M. Mcguire, W. Matusik, B. Chen, J. F. Hughes, H. Pfister, and S. Nayar, “Optical splitting trees for high-precision monocular imaging,” IEEE Comp. Graphics App. 27, 32–42 (2007).

Ichioka, Y.

Intwala, C.

T. Georgiev, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution tradeoffs in integral photography,” in Proceedings of Eurographics Symposium on Rendering, T. Akenine-Möller and W. Heidrich, eds. (The Eurographics Association, 2006), pp. 263–272.

Ishida, K.

Kingslake, R.

R. Kingslake, Lenses in Photography, rev., ed. (A. S. Barnes and Company, 1963).

Kondou, N.

Kumagai, T.

Lanza, R. C.

R. Accorsi, F. Gasparini, and R. C. Lanza, “Optimal coded aperture patterns for improved SNR in nuclear medicine imaging,” Nucl. Instrum. Methods Phys. Res. A 474, 273–284 (2001).
[CrossRef]

R. Accorsi and R. C. Lanza, “Near-field artifact reduction in coded aperture imaging,” Appl. Opt. 40, 4697–4705 (2001).
[CrossRef]

R. Accorsi, F. Gasparini, and R. C. Lanza, “A coded aperture for high-resolution nuclear medicine planar imaging with a conventional anger camera: experimental results,” IEEE Trans. Nucl. Sci. 48, 2411–2417 (2001).
[CrossRef]

Martin, L. C.

L. C. Martin and W. T. Welford, Technical Optics, Vol. I (Pitman, 1966).

Matusik, W.

M. Mcguire, W. Matusik, B. Chen, J. F. Hughes, H. Pfister, and S. Nayar, “Optical splitting trees for high-precision monocular imaging,” IEEE Comp. Graphics App. 27, 32–42 (2007).

P. Green, W. Sun, W. Matusik, and F. Durand, “Multi-aperture photography,” ACM Trans. Graph. 26, 68 (2007).
[CrossRef]

Mcguire, M.

M. Mcguire, W. Matusik, B. Chen, J. F. Hughes, H. Pfister, and S. Nayar, “Optical splitting trees for high-precision monocular imaging,” IEEE Comp. Graphics App. 27, 32–42 (2007).

Mertz, L.

L. Mertz and N. O. Young, “Fresnel transformations of images,” in Proceedings of International Conference on Optical Instruments and Techniques (Chapman and Hall, 1961), pp. 305–310.

Miyatake, S.

Miyazaki, D.

Morimoto, T.

Nayar, S.

M. Mcguire, W. Matusik, B. Chen, J. F. Hughes, H. Pfister, and S. Nayar, “Optical splitting trees for high-precision monocular imaging,” IEEE Comp. Graphics App. 27, 32–42 (2007).

T. Georgiev, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution tradeoffs in integral photography,” in Proceedings of Eurographics Symposium on Rendering, T. Akenine-Möller and W. Heidrich, eds. (The Eurographics Association, 2006), pp. 263–272.

Ng, R.

R. Ng, “Fourier slice photography,” ACM Trans. Graph. 24, 735–744 (2005).

Perrin, F.

A. C. Hardy and F. Perrin, The Principles of Optics (McGraw-Hill, 1932).

Pfister, H.

M. Mcguire, W. Matusik, B. Chen, J. F. Hughes, H. Pfister, and S. Nayar, “Optical splitting trees for high-precision monocular imaging,” IEEE Comp. Graphics App. 27, 32–42 (2007).

Salesin, D.

T. Georgiev, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution tradeoffs in integral photography,” in Proceedings of Eurographics Symposium on Rendering, T. Akenine-Möller and W. Heidrich, eds. (The Eurographics Association, 2006), pp. 263–272.

Schotten, H. D.

A. Busboom, H. Elders-Boll, and H. D. Schotten, “Uniformly redundant arrays,” Exp. Astro. 8, 97–123 (1998).

Selwyn, E. W. H.

E. W. H. Selwyn, “The pin-hole camera,” Photographic J. 90B, 47–52 (1950).

Sun, W.

P. Green, W. Sun, W. Matusik, and F. Durand, “Multi-aperture photography,” ACM Trans. Graph. 26, 68 (2007).
[CrossRef]

Tanida, J.

Wang, J. Y. A.

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

Welford, W. T.

L. C. Martin and W. T. Welford, Technical Optics, Vol. I (Pitman, 1966).

Wilson, D. T.

H. H. Barrett, D. T. Wilson, and G. D. Demeester, “The use of half-tone screens in Fresnel zone plate imaging of incoherent sources,” Opt. Commun. 5, 398–401 (1972).
[CrossRef]

Yamada, K.

Young, N. O.

L. Mertz and N. O. Young, “Fresnel transformations of images,” in Proceedings of International Conference on Optical Instruments and Techniques (Chapman and Hall, 1961), pp. 305–310.

Zheng, K. C.

T. Georgiev, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution tradeoffs in integral photography,” in Proceedings of Eurographics Symposium on Rendering, T. Akenine-Möller and W. Heidrich, eds. (The Eurographics Association, 2006), pp. 263–272.

ACM Trans. Graph. (2)

R. Ng, “Fourier slice photography,” ACM Trans. Graph. 24, 735–744 (2005).

P. Green, W. Sun, W. Matusik, and F. Durand, “Multi-aperture photography,” ACM Trans. Graph. 26, 68 (2007).
[CrossRef]

Appl. Opt. (5)

Astrophys. J. (1)

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

Exp. Astro. (1)

A. Busboom, H. Elders-Boll, and H. D. Schotten, “Uniformly redundant arrays,” Exp. Astro. 8, 97–123 (1998).

IEEE Comp. Graphics App. (1)

M. Mcguire, W. Matusik, B. Chen, J. F. Hughes, H. Pfister, and S. Nayar, “Optical splitting trees for high-precision monocular imaging,” IEEE Comp. Graphics App. 27, 32–42 (2007).

IEEE Trans. Nucl. Sci. (1)

R. Accorsi, F. Gasparini, and R. C. Lanza, “A coded aperture for high-resolution nuclear medicine planar imaging with a conventional anger camera: experimental results,” IEEE Trans. Nucl. Sci. 48, 2411–2417 (2001).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

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

Int’l. J. Comp. Vis. (1)

M. Aggarwal and N. Ahuja, “Split aperture imaging for high dynamic range,” Int’l. J. Comp. Vis. 58, 7–17 (2004).

Nucl. Instrum. Methods Phys. Res. A (1)

R. Accorsi, F. Gasparini, and R. C. Lanza, “Optimal coded aperture patterns for improved SNR in nuclear medicine imaging,” Nucl. Instrum. Methods Phys. Res. A 474, 273–284 (2001).
[CrossRef]

Opt. Commun. (1)

H. H. Barrett, D. T. Wilson, and G. D. Demeester, “The use of half-tone screens in Fresnel zone plate imaging of incoherent sources,” Opt. Commun. 5, 398–401 (1972).
[CrossRef]

Photographic J. (1)

E. W. H. Selwyn, “The pin-hole camera,” Photographic J. 90B, 47–52 (1950).

Proc. Astron. Soc. Aust. (1)

J. G. Ables, “Fourier transform photography: a new method for x-ray astronomy,” Proc. Astron. Soc. Aust. 1, 172–173 (1968).

Other (5)

L. C. Martin and W. T. Welford, Technical Optics, Vol. I (Pitman, 1966).

A. C. Hardy and F. Perrin, The Principles of Optics (McGraw-Hill, 1932).

R. Kingslake, Lenses in Photography, rev., ed. (A. S. Barnes and Company, 1963).

L. Mertz and N. O. Young, “Fresnel transformations of images,” in Proceedings of International Conference on Optical Instruments and Techniques (Chapman and Hall, 1961), pp. 305–310.

T. Georgiev, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution tradeoffs in integral photography,” in Proceedings of Eurographics Symposium on Rendering, T. Akenine-Möller and W. Heidrich, eds. (The Eurographics Association, 2006), pp. 263–272.

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Figures (10)

Fig. 1.
Fig. 1.

Schematic of the optical time multiplexed setup.

Fig. 2.
Fig. 2.

Time interval simulation: 2D pinholes arrays with a total of 17 holes (L=3). The sum of the three filters (top fair line) as compared to one single pinhole (thick line). The straight line is the maximum level of the one-pinhole reference level. The thin lines (one continuous and two dashed) are the three filters with different accumulation time. (a) The time interval is equal for each array (60 s); the filters’ sum G(u,v) transmission value is not higher than the reference single pinhole filter in all the spectral region of interest. (b) The time interval is not equal for each array (70, 70, 40 s, respectively); the filters’ sum G(u,v) transmission value is higher than the reference single pinhole filter in all the regions of interest. (c) Comparison between three systems: one-pinhole system (thick line). The multipinhole system with total 17 holes in the set of arrays (top fair line) and a multipinhole system with the same 17 holes in a single array (thin line). Any other random 17 holes in a single array will produce more extra zero points.

Fig. 3.
Fig. 3.

2D three-array design with total 17 pinholes. This is an expansion to two dimensions of the same 1D design.

Fig. 4.
Fig. 4.

Lena test image with a 1D array design. (a) Image obtained with one pinhole system and R=1 (normalized unit). Light intensity is low but with high resolution. (b) Image obtained with one pinhole system (R=1) with long exposure time (×5.6). Light intensity and resolution are high. (c) Image obtained with one pinhole system and R=1.5. Light intensity is high but with low resolution. (d) Reconstructed image in the multipinhole 1D array system with R=1. Light intensity and resolution are high. (e) Final captured image in the multipinhole 2D array system before decoding. (f) The reconstructed image in the multipinhole 2D array system with R=1. Light intensity of the image is very high with high resolution.

Fig. 5.
Fig. 5.

Same light intensity and exposure time with better contrast. The dashed line points out the cross section area. (a) One-pinhole system with R=1.5. (b) 1D multipinhole system with R=1. The light intensity and exposure time are the same in the two systems, while the contrast is better in the multipinhole system.

Fig. 6.
Fig. 6.

Gaussian noise and SNR improvement; long exposure time simulation. (a) Image captured with one and small pinhole (R=1). (b) SNR improvement obtained in the multipinhole system reconstruction image. (c) Image captured with one and large pinhole (R=1.5).

Fig. 7.
Fig. 7.

Constructed multipinhole array system.

Fig. 8.
Fig. 8.

Resolution experiment. Dashed line represents max resolution. (a) One pinhole (250 μm) system; better resolution but low light intensity. (b) One pinhole (350 μm) system; high light intensity but with bad resolution. (c) Multipinhole (250 μm) 1D array system; better resolution with high light intensity.

Fig. 9.
Fig. 9.

USAF 1951 resolution target.

Fig. 10.
Fig. 10.

(a) One pinhole (170 μm) system; better resolution but low light intensity. (b) One-pinhole (250 μm) system; better light intensity but with bad resolution. (c) One pinhole (350 μm) system; high light intensity but with bad resolution. (d) The captured image in the 2D multipinhole array system before decoding. (e) Multipinhole (170 μm) 2D array system; better resolution with high light intensity. The obtained image in the 1D array system was similar but with less light intensity.

Tables (4)

Tables Icon

Table 1. Total Counts Simulation Results: Lena Testa

Tables Icon

Table 2. 1D Design and 2D Design Properties: Lena Testa

Tables Icon

Table 3. Total Counts Results: Spoke Resolution Targeta

Tables Icon

Table 4. Total Counts Results: USAF 1951 Resolution Targeta

Equations (14)

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

sarray(l)(x,y)·tl=tl·n=1Ns(x+dx(l,n),y+dy(l,n))Ttotal=l=1Ltl,
Sarray(l)(u,v)·tl=tlsarray(l)(x,y)e2πi(ux+vy)dxdy.
Sarray(u,v)·tl=S(u,v)·F(u,v)·tl,
S(u,v)=s(x,y)e2πi(ux+vy)dxdyF(l)(u,v)=n=1Ne2πi(dx(l,n)u+dy(l,n)v).
l=1LSarray(l)(u,v)·tl=S(u,v)l=1LF(l)(u,v)·tl.
G(u,v)=l=1LF(l)(u,v)·tl.
S(u,v)=[l=1LSarray(l)(u,v)·tl]·G(u,v)1.
M=FZ.
θgeometric2R·Z+FZFθdiffraction0.61·λR.
R=0.61λF.
ρ=2.44λFR.
LII=NL·πRarray2πRone2.
LII=73·25023502=1.19.
LII=173·17223502=1.34

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