Abstract

Interferenceless coded aperture correlation holography (I-COACH) is an incoherent opto-digital technique for imaging 3D objects. In I-COACH, the light scattered from an object is modulated by a coded phase mask (CPM) and then recorded by a digital camera as an object digital hologram. To reconstruct the image, the object hologram is cross-correlated with the point spread function (PSF)—the intensity response to a point at the same object’s axial location recorded with the same CPM. So far in I-COACH systems, the light from each object point has scattered over the whole camera area. Hence, the signal-to-noise ratio per camera pixel is lower in comparison to the direct imaging in which each point is imaged to a single image point. In this work, we consider the midway between the camera responses of a single point and of a continuous pattern over the entire camera area. The light in this study is focused onto a set of dots randomly distributed over the camera plane. With this technique, we show that there is a PSF with a best number of dots, yielding an image with a maximum product of the signal-to-noise ratio and the image visibility and a maximum value of structural similarity.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Non-linear adaptive three-dimensional imaging with interferenceless coded aperture correlation holography (I-COACH)

Mani R. Rai, A. Vijayakumar, and Joseph Rosen
Opt. Express 26(14) 18143-18154 (2018)

References

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2019 (2)

2018 (7)

M. R. Rai, A. Vijayakumar, and J. Rosen, “Extending the field of view by a scattering window in an I-COACH system,” Opt. Lett. 43(5), 1043–1046 (2018).
[Crossref] [PubMed]

M. R. Rai, A. Vijayakumar, and J. Rosen, “Non-linear adaptive three-dimensional imaging with interferenceless coded aperture correlation holography (I-COACH),” Opt. Express 26(14), 18143–18154 (2018).
[Crossref] [PubMed]

A. Bulbul, A. Vijayakumar, and J. Rosen, “Superresolution far-field imaging by coded phase reflectors distributed only along the boundary of synthetic apertures,” Optica 5(12), 1607–1616 (2018).
[Crossref]

J. N. Mait, G. W. Euliss, and R. A. Athale, “Computational imaging,” Adv. Opt. Photonics 10(2), 409–483 (2018).
[Crossref]

J.-P. Liu, T. Tahara, Y. Hayasaki, and T.-C. Poon, “Incoherent digital holography: A review,” Appl. Sci. (Basel) 8(1), 143 (2018).
[Crossref]

S. Mukherjee, A. Vijayakumar, M. Kumar, and J. Rosen, “3D imaging through scatterers with interferenceless optical system,” Sci. Rep. 8(1), 1134 (2018).
[Crossref] [PubMed]

S. Mukherjee and J. Rosen, “Imaging through scattering medium by adaptive non-linear digital processing,” Sci. Rep. 8(1), 10517 (2018).
[Crossref] [PubMed]

2017 (5)

2016 (1)

M. N. Lakshmanan, J. A. Greenberg, E. Samei, and A. J. Kapadia, “Design and implementation of coded aperture coherent scatter spectral imaging of cancerous and healthy breast tissue samples,” J. Med. Imaging (Bellingham) 3(1), 013505 (2016).
[Crossref] [PubMed]

2015 (3)

J. A. Greenberg, M. N. Lakshmanan, D. J. Brady, and A. J. Kapadia, “Optimization of a coded aperture coherent scatter spectral imaging system for medical imaging,” Proc. SPIE 9412, 94125E (2015).

M. J. DeWeert and B. P. Farm, “Lensless coded-aperture imaging with separable Doubly-Toeplitz masks,” Opt. Eng. 54(2), 023102 (2015).
[Crossref]

Y. Kashter, Y. Rivenson, A. Stern, and J. Rosen, “Sparse synthetic aperture with Fresnel elements (S-SAFE) using digital incoherent holograms,” Opt. Express 23(16), 20941–20960 (2015).
[Crossref] [PubMed]

2013 (1)

2012 (1)

D. S. Kittle, D. L. Marks, and D. J. Brady, “Design and fabrication of an ultraviolet-visible coded aperture snapshot spectral imager,” Opt. Eng. 51(7), 071403 (2012).
[Crossref]

2011 (2)

2009 (1)

2004 (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

1995 (1)

1988 (1)

1984 (1)

1978 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35(2), 237–246 (1972).

Athale, R. A.

J. N. Mait, G. W. Euliss, and R. A. Athale, “Computational imaging,” Adv. Opt. Photonics 10(2), 409–483 (2018).
[Crossref]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Brady, D. J.

J. A. Greenberg, M. N. Lakshmanan, D. J. Brady, and A. J. Kapadia, “Optimization of a coded aperture coherent scatter spectral imaging system for medical imaging,” Proc. SPIE 9412, 94125E (2015).

D. S. Kittle, D. L. Marks, and D. J. Brady, “Design and fabrication of an ultraviolet-visible coded aperture snapshot spectral imager,” Opt. Eng. 51(7), 071403 (2012).
[Crossref]

Bulbul, A.

Cannon, T. M.

Carnicer, A.

Chi, W.

DeWeert, M. J.

M. J. DeWeert and B. P. Farm, “Lensless coded-aperture imaging with separable Doubly-Toeplitz masks,” Opt. Eng. 54(2), 023102 (2015).
[Crossref]

Euliss, G. W.

J. N. Mait, G. W. Euliss, and R. A. Athale, “Computational imaging,” Adv. Opt. Photonics 10(2), 409–483 (2018).
[Crossref]

Farm, B. P.

M. J. DeWeert and B. P. Farm, “Lensless coded-aperture imaging with separable Doubly-Toeplitz masks,” Opt. Eng. 54(2), 023102 (2015).
[Crossref]

Fenimore, E. E.

Fienup, J. R.

George, N.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35(2), 237–246 (1972).

Gianino, P. D.

Greenberg, J. A.

M. N. Lakshmanan, J. A. Greenberg, E. Samei, and A. J. Kapadia, “Design and implementation of coded aperture coherent scatter spectral imaging of cancerous and healthy breast tissue samples,” J. Med. Imaging (Bellingham) 3(1), 013505 (2016).
[Crossref] [PubMed]

J. A. Greenberg, M. N. Lakshmanan, D. J. Brady, and A. J. Kapadia, “Optimization of a coded aperture coherent scatter spectral imaging system for medical imaging,” Proc. SPIE 9412, 94125E (2015).

Hayasaki, Y.

J.-P. Liu, T. Tahara, Y. Hayasaki, and T.-C. Poon, “Incoherent digital holography: A review,” Appl. Sci. (Basel) 8(1), 143 (2018).
[Crossref]

Hong, K.

Horner, J. L.

Javidi, B.

Juvells, I.

Kapadia, A. J.

M. N. Lakshmanan, J. A. Greenberg, E. Samei, and A. J. Kapadia, “Design and implementation of coded aperture coherent scatter spectral imaging of cancerous and healthy breast tissue samples,” J. Med. Imaging (Bellingham) 3(1), 013505 (2016).
[Crossref] [PubMed]

J. A. Greenberg, M. N. Lakshmanan, D. J. Brady, and A. J. Kapadia, “Optimization of a coded aperture coherent scatter spectral imaging system for medical imaging,” Proc. SPIE 9412, 94125E (2015).

Kashter, Y.

Kelner, R.

Kittle, D. S.

D. S. Kittle, D. L. Marks, and D. J. Brady, “Design and fabrication of an ultraviolet-visible coded aperture snapshot spectral imager,” Opt. Eng. 51(7), 071403 (2012).
[Crossref]

Kumar, A.

Kumar, M.

S. Mukherjee, A. Vijayakumar, M. Kumar, and J. Rosen, “3D imaging through scatterers with interferenceless optical system,” Sci. Rep. 8(1), 1134 (2018).
[Crossref] [PubMed]

M. Kumar, A. Vijayakumar, and J. Rosen, “Incoherent digital holograms acquired by interferenceless coded aperture correlation holography system without refractive lenses,” Sci. Rep. 7(1), 11555 (2017).
[Crossref] [PubMed]

Lakshmanan, M. N.

M. N. Lakshmanan, J. A. Greenberg, E. Samei, and A. J. Kapadia, “Design and implementation of coded aperture coherent scatter spectral imaging of cancerous and healthy breast tissue samples,” J. Med. Imaging (Bellingham) 3(1), 013505 (2016).
[Crossref] [PubMed]

J. A. Greenberg, M. N. Lakshmanan, D. J. Brady, and A. J. Kapadia, “Optimization of a coded aperture coherent scatter spectral imaging system for medical imaging,” Proc. SPIE 9412, 94125E (2015).

Lee, B.

Liu, J.-P.

J.-P. Liu, T. Tahara, Y. Hayasaki, and T.-C. Poon, “Incoherent digital holography: A review,” Appl. Sci. (Basel) 8(1), 143 (2018).
[Crossref]

Mait, J. N.

J. N. Mait, G. W. Euliss, and R. A. Athale, “Computational imaging,” Adv. Opt. Photonics 10(2), 409–483 (2018).
[Crossref]

Marks, D. L.

D. S. Kittle, D. L. Marks, and D. J. Brady, “Design and fabrication of an ultraviolet-visible coded aperture snapshot spectral imager,” Opt. Eng. 51(7), 071403 (2012).
[Crossref]

Martín-Badosa, E.

Martinez-Corral, M.

Mu, G.-G.

Mukherjee, S.

S. Mukherjee, A. Vijayakumar, M. Kumar, and J. Rosen, “3D imaging through scatterers with interferenceless optical system,” Sci. Rep. 8(1), 1134 (2018).
[Crossref] [PubMed]

S. Mukherjee and J. Rosen, “Imaging through scattering medium by adaptive non-linear digital processing,” Sci. Rep. 8(1), 10517 (2018).
[Crossref] [PubMed]

Ogura, Y.

Park, J.-H.

Poon, T.-C.

J.-P. Liu, T. Tahara, Y. Hayasaki, and T.-C. Poon, “Incoherent digital holography: A review,” Appl. Sci. (Basel) 8(1), 143 (2018).
[Crossref]

Rai, M. R.

Ratnam Rai, M.

Rivenson, Y.

Rosen, J.

M. R. Rai, A. Vijayakumar, Y. Ogura, and J. Rosen, “Resolution enhancement in nonlinear interferenceless COACH with point response of subdiffraction limit patterns,” Opt. Express 27(2), 391–403 (2019).
[Crossref] [PubMed]

M. R. Rai, A. Vijayakumar, and J. Rosen, “Superresolution beyond the diffraction limit using phase spatial light modulator between incoherently illuminated objects and the entrance of an imaging system,” Opt. Lett. 44(7), 1572–1575 (2019).
[Crossref] [PubMed]

A. Bulbul, A. Vijayakumar, and J. Rosen, “Superresolution far-field imaging by coded phase reflectors distributed only along the boundary of synthetic apertures,” Optica 5(12), 1607–1616 (2018).
[Crossref]

M. R. Rai, A. Vijayakumar, and J. Rosen, “Extending the field of view by a scattering window in an I-COACH system,” Opt. Lett. 43(5), 1043–1046 (2018).
[Crossref] [PubMed]

M. R. Rai, A. Vijayakumar, and J. Rosen, “Non-linear adaptive three-dimensional imaging with interferenceless coded aperture correlation holography (I-COACH),” Opt. Express 26(14), 18143–18154 (2018).
[Crossref] [PubMed]

S. Mukherjee and J. Rosen, “Imaging through scattering medium by adaptive non-linear digital processing,” Sci. Rep. 8(1), 10517 (2018).
[Crossref] [PubMed]

S. Mukherjee, A. Vijayakumar, M. Kumar, and J. Rosen, “3D imaging through scatterers with interferenceless optical system,” Sci. Rep. 8(1), 1134 (2018).
[Crossref] [PubMed]

M. Kumar, A. Vijayakumar, and J. Rosen, “Incoherent digital holograms acquired by interferenceless coded aperture correlation holography system without refractive lenses,” Sci. Rep. 7(1), 11555 (2017).
[Crossref] [PubMed]

A. Vijayakumar, Y. Kashter, R. Kelner, and J. Rosen, “Coded aperture correlation holography system with improved performance [Invited],” Appl. Opt. 56(13), F67–F77 (2017).
[Crossref] [PubMed]

A. Vijayakumar and J. Rosen, “Interferenceless coded aperture correlation holography-a new technique for recording incoherent digital holograms without two-wave interference,” Opt. Express 25(12), 13883–13896 (2017).
[Crossref] [PubMed]

M. Ratnam Rai, A. Vijayakumar, and J. Rosen, “Single camera shot interferenceless coded aperture correlation holography,” Opt. Lett. 42(19), 3992–3995 (2017).
[Crossref] [PubMed]

A. Bulbul, A. Vijayakumar, and J. Rosen, “Partial aperture imaging by systems with annular phase coded masks,” Opt. Express 25(26), 33315–33329 (2017).
[Crossref]

Y. Kashter, Y. Rivenson, A. Stern, and J. Rosen, “Sparse synthetic aperture with Fresnel elements (S-SAFE) using digital incoherent holograms,” Opt. Express 23(16), 20941–20960 (2015).
[Crossref] [PubMed]

Samei, E.

M. N. Lakshmanan, J. A. Greenberg, E. Samei, and A. J. Kapadia, “Design and implementation of coded aperture coherent scatter spectral imaging of cancerous and healthy breast tissue samples,” J. Med. Imaging (Bellingham) 3(1), 013505 (2016).
[Crossref] [PubMed]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35(2), 237–246 (1972).

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Stern, A.

Tahara, T.

J.-P. Liu, T. Tahara, Y. Hayasaki, and T.-C. Poon, “Incoherent digital holography: A review,” Appl. Sci. (Basel) 8(1), 143 (2018).
[Crossref]

Tippie, A. E.

Vallmitjana, S.

Vijayakumar, A.

M. R. Rai, A. Vijayakumar, and J. Rosen, “Superresolution beyond the diffraction limit using phase spatial light modulator between incoherently illuminated objects and the entrance of an imaging system,” Opt. Lett. 44(7), 1572–1575 (2019).
[Crossref] [PubMed]

M. R. Rai, A. Vijayakumar, Y. Ogura, and J. Rosen, “Resolution enhancement in nonlinear interferenceless COACH with point response of subdiffraction limit patterns,” Opt. Express 27(2), 391–403 (2019).
[Crossref] [PubMed]

A. Bulbul, A. Vijayakumar, and J. Rosen, “Superresolution far-field imaging by coded phase reflectors distributed only along the boundary of synthetic apertures,” Optica 5(12), 1607–1616 (2018).
[Crossref]

M. R. Rai, A. Vijayakumar, and J. Rosen, “Extending the field of view by a scattering window in an I-COACH system,” Opt. Lett. 43(5), 1043–1046 (2018).
[Crossref] [PubMed]

M. R. Rai, A. Vijayakumar, and J. Rosen, “Non-linear adaptive three-dimensional imaging with interferenceless coded aperture correlation holography (I-COACH),” Opt. Express 26(14), 18143–18154 (2018).
[Crossref] [PubMed]

S. Mukherjee, A. Vijayakumar, M. Kumar, and J. Rosen, “3D imaging through scatterers with interferenceless optical system,” Sci. Rep. 8(1), 1134 (2018).
[Crossref] [PubMed]

M. Kumar, A. Vijayakumar, and J. Rosen, “Incoherent digital holograms acquired by interferenceless coded aperture correlation holography system without refractive lenses,” Sci. Rep. 7(1), 11555 (2017).
[Crossref] [PubMed]

A. Vijayakumar and J. Rosen, “Interferenceless coded aperture correlation holography-a new technique for recording incoherent digital holograms without two-wave interference,” Opt. Express 25(12), 13883–13896 (2017).
[Crossref] [PubMed]

A. Vijayakumar, Y. Kashter, R. Kelner, and J. Rosen, “Coded aperture correlation holography system with improved performance [Invited],” Appl. Opt. 56(13), F67–F77 (2017).
[Crossref] [PubMed]

M. Ratnam Rai, A. Vijayakumar, and J. Rosen, “Single camera shot interferenceless coded aperture correlation holography,” Opt. Lett. 42(19), 3992–3995 (2017).
[Crossref] [PubMed]

A. Bulbul, A. Vijayakumar, and J. Rosen, “Partial aperture imaging by systems with annular phase coded masks,” Opt. Express 25(26), 33315–33329 (2017).
[Crossref]

Wang, X.-M.

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Wang, Z.-Q.

Xiao, X.

Adv. Opt. Photonics (1)

J. N. Mait, G. W. Euliss, and R. A. Athale, “Computational imaging,” Adv. Opt. Photonics 10(2), 409–483 (2018).
[Crossref]

Appl. Opt. (7)

Appl. Sci. (Basel) (1)

J.-P. Liu, T. Tahara, Y. Hayasaki, and T.-C. Poon, “Incoherent digital holography: A review,” Appl. Sci. (Basel) 8(1), 143 (2018).
[Crossref]

IEEE Trans. Image Process. (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

J. Med. Imaging (Bellingham) (1)

M. N. Lakshmanan, J. A. Greenberg, E. Samei, and A. J. Kapadia, “Design and implementation of coded aperture coherent scatter spectral imaging of cancerous and healthy breast tissue samples,” J. Med. Imaging (Bellingham) 3(1), 013505 (2016).
[Crossref] [PubMed]

Opt. Eng. (2)

M. J. DeWeert and B. P. Farm, “Lensless coded-aperture imaging with separable Doubly-Toeplitz masks,” Opt. Eng. 54(2), 023102 (2015).
[Crossref]

D. S. Kittle, D. L. Marks, and D. J. Brady, “Design and fabrication of an ultraviolet-visible coded aperture snapshot spectral imager,” Opt. Eng. 51(7), 071403 (2012).
[Crossref]

Opt. Express (7)

Opt. Lett. (3)

Optica (1)

Optik (Stuttg.) (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35(2), 237–246 (1972).

Proc. SPIE (1)

J. A. Greenberg, M. N. Lakshmanan, D. J. Brady, and A. J. Kapadia, “Optimization of a coded aperture coherent scatter spectral imaging system for medical imaging,” Proc. SPIE 9412, 94125E (2015).

Sci. Rep. (3)

S. Mukherjee, A. Vijayakumar, M. Kumar, and J. Rosen, “3D imaging through scatterers with interferenceless optical system,” Sci. Rep. 8(1), 1134 (2018).
[Crossref] [PubMed]

S. Mukherjee and J. Rosen, “Imaging through scattering medium by adaptive non-linear digital processing,” Sci. Rep. 8(1), 10517 (2018).
[Crossref] [PubMed]

M. Kumar, A. Vijayakumar, and J. Rosen, “Incoherent digital holograms acquired by interferenceless coded aperture correlation holography system without refractive lenses,” Sci. Rep. 7(1), 11555 (2017).
[Crossref] [PubMed]

Other (4)

M. K. Kim, Digital Holography and Microscopy: Principles, Techniques, and Applications (Springer Verlag, 2011).

H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley, 2003).

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford Tech. Rep. CTSR 2005–02 (2005).

R. Ng, “Digital light field photography,” Ph.D. thesis (Stanford University, 2006).

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Figures (8)

Fig. 1
Fig. 1 Optical configuration of SI-COACH. L0, L1 – Refractive lenses: P- Polarizer; SLM - Spatial light modulator; DL – Diffractive lens; CPM - Coded phase mask.
Fig. 2
Fig. 2 Modified Gerchberg-Saxton algorithm for synthesizing the CPMs.
Fig. 3
Fig. 3 Experimental setup. BS1 and BS2 – Beam splitters; SLM – Spatial light modulator; NBS – National Bureau of Standards ; L0A, L0B and L1 – Refractive lenses; LED1 and LED2 – Identical light emitting diodes; CPM – Coded phase mask; DL – Diffractive lens; BPF – Band pass filter (λc = 632.8 nm and Δλ = 5 nm); P- Polarizer; - Polarization orientation perpendicular to the plane of the page.
Fig. 4
Fig. 4 (a-b) Images of the CPMs, (c-d) intensity PSFs and (e) bipolar PSF, (f-g) object intensity responses and (h) bipolar HOBJ for dot density of ψ = 0.000164.
Fig. 5
Fig. 5 (a) Visibility, (b) SNR, (c) ξ( ψ ), (d) SSIM, (e) Reconstructed image of SI-COACH for the best dot density and (f) Reconstructed image for full window I-COACH in case of low power illumination of the object.
Fig. 6
Fig. 6 (a) Visibility, (b) SNR, (c) ξ( ψ ), (d) SSIM, (e) Reconstructed image of SI-COACH for best dot density and (f) Reconstructed image for full window I-COACH in case of mid power illumination of the object.
Fig. 7
Fig. 7 (a) Visibility, (b) SNR, (c) ξ( ψ ), (d) SSIM, (e) Reconstructed image of SI-COACH for the best dot density and (f) Reconstructed image for full window I-COACH in case of high power illumination of the object.
Fig. 8
Fig. 8 Reconstruction results of object in (a) plane 1, (b) plane 2 separated by a distance of 15 cm.

Equations (7)

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I PSF ( r ¯ o ; r ¯ s )= | ν[ 1 λ z h ]F{ C 0 L( r ¯ s f )exp[ iΦ( r ¯ ) ] } | 2 = I PSF ( r ¯ o z h f r ¯ s ;0 ),
o( r ¯ s )= j N a j δ( r ¯ r ¯ j ) .
I OBJ ( r ¯ o )= j a j I PSF ( r ¯ o z h f r ¯ j ;0 ) .
H PSF ( r ¯ o )= I PSF,1 ( r ¯ o ) I PSF,2 ( r ¯ o ). H OBJ ( r ¯ o )= I OBJ,1 ( r ¯ o ) I OBJ,2 ( r ¯ o ).
I REC = H OBJ H PSF = F 1 { F{ H OBJ H PSF } } = F 1 { H ˜ OBJ H ˜ PSF * }= F 1 { H ˜ OBJ exp( iarg{ H ˜ PSF } ) },
I REC =( H OBJ + n 1 )( H PSF + n 2 )=( H PSF + n 1 )( H PSF + n 2 ) H PSF H PSF + H PSF n 2 + H PSF n 1 ,
SNR= H PSF H PSF | ( x,y )=( 0,0 ) Max ( x,y )( 0,0 ) { H PSF H PSF + H PSF n 2 + H PSF n 1 } ,

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