Abstract

Compared to traditional imaging system, diffuser camera is an easy-built imaging system to capture the light field with small form factor. Its imaging target can be reconstructed by deconvolving the sensor images with the point-spread-function (PSF) at the corresponding depth. However, the existing method to obtain the PSFs is generally relied on measuring point-source-responses at several depths which presents high complexity and low reliability. In this paper, we propose a theoretical PSF model for the diffuser camera by estimating the diffuser’s phase based on projection model and deriving the image response at any depth by forward Fourier optics to enable the reconstruction of the object at any depth. The experimental results demonstrate the effectiveness of the proposed model in terms of the correlation between the captured PSFs and our model derived PSFs, the correlation between the ground truth image and reconstructed images under different depths, and the correlation between the images reconstructed by real captured PSFs and the images reconstructed by our model derived PSFs. The objects at different depths can be correctly reconstructed by our theoretically derived PSFs, which benefits the application of diffuser camera for much lower complexity.

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

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  25. Light shaping diffuser, https://www.luminitco.com/products/light-shaping-diffusers .

2018 (3)

2017 (3)

2013 (1)

2010 (1)

2007 (1)

M. Singh and A. Kumar, “Optical encryption and decryption using a sandwich random phase diffuser in the Fourier plane,” Opt. Eng. 46(5), 055201 (2007).
[Crossref]

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]

2003 (2)

V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A 20(1), 40–55 (2003).
[Crossref] [PubMed]

J. Yao and G. C. K. Chen, “Holographic diffuser for diffuse infrared wireless home networking,” Opt. Eng. 42(2), 1–8 (2003).

2002 (1)

Y. T. Lu and S. Chi, “Fabrication of light-shaping diffusion screens,” Opt. Commun. 214(1), 55–63 (2002).

1983 (1)

1982 (1)

1972 (1)

Antipa, N.

N. Antipa, G. Kuo, R. Heckel, B. Mildenhall, E. Bostan, R. Ng, and L. Waller, “DiffuserCam: lensless single-exposure 3D imaging,” Optica 5(1), 1–9 (2018).
[Crossref]

N. Antipa, S. Necula, R. Ng, and L. Waller, “Single-shot diffuser-encoded light field imaging,” 2016 IEEE International Conference on Computational Photography (ICCP), Evanston, IL, pp. 1–11 (2016).

Berkner, K.

Bostan, E.

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]

Chen, G. C. K.

J. Yao and G. C. K. Chen, “Holographic diffuser for diffuse infrared wireless home networking,” Opt. Eng. 42(2), 1–8 (2003).

Chen, Y.

Chi, S.

Y. T. Lu and S. Chi, “Fabrication of light-shaping diffusion screens,” Opt. Commun. 214(1), 55–63 (2002).

Dai, Q.

Elser, V.

Fienup, J. R.

He, H.

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8(1), 4585 (2018).
[Crossref] [PubMed]

Heckel, R.

Hoshizawa, T.

K. Tajima, T. Shimano, Y. Nakamura, M. Sao, and T. Hoshizawa, “Lensless light-field imaging with multi-phased fresnel zone aperture,” 2017 IEEE International Conference on Computational Photography (ICCP), Stanford, CA, pp. 1–7 (2017).
[Crossref]

Isaacson, K.

Jin, X.

Kim, G.

Kumar, A.

M. Singh and A. Kumar, “Optical encryption and decryption using a sandwich random phase diffuser in the Fourier plane,” Opt. Eng. 46(5), 055201 (2007).
[Crossref]

Kuo, G.

Liang, H.

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8(1), 4585 (2018).
[Crossref] [PubMed]

Lin, P. D.

Liu, C. S.

Liu, L.

Liu, Y.

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8(1), 4585 (2018).
[Crossref] [PubMed]

Lu, Y. T.

Y. T. Lu and S. Chi, “Fabrication of light-shaping diffusion screens,” Opt. Commun. 214(1), 55–63 (2002).

Menon, R.

Mildenhall, B.

Nakamura, Y.

K. Tajima, T. Shimano, Y. Nakamura, M. Sao, and T. Hoshizawa, “Lensless light-field imaging with multi-phased fresnel zone aperture,” 2017 IEEE International Conference on Computational Photography (ICCP), Stanford, CA, pp. 1–7 (2017).
[Crossref]

Necula, S.

N. Antipa, S. Necula, R. Ng, and L. Waller, “Single-shot diffuser-encoded light field imaging,” 2016 IEEE International Conference on Computational Photography (ICCP), Evanston, IL, pp. 1–11 (2016).

Ng, R.

N. Antipa, G. Kuo, R. Heckel, B. Mildenhall, E. Bostan, R. Ng, and L. Waller, “DiffuserCam: lensless single-exposure 3D imaging,” Optica 5(1), 1–9 (2018).
[Crossref]

N. Antipa, S. Necula, R. Ng, and L. Waller, “Single-shot diffuser-encoded light field imaging,” 2016 IEEE International Conference on Computational Photography (ICCP), Evanston, IL, pp. 1–11 (2016).

Osten, W.

A. K. Singh, G. Pedrini, M. Takeda, and W. Osten, “Scatter-plate microscope for lensless microscopy with diffraction limited resolution,” Sci. Rep. 7(1), 10687 (2017).
[Crossref] [PubMed]

Palmer, R.

Pedrini, G.

A. K. Singh, G. Pedrini, M. Takeda, and W. Osten, “Scatter-plate microscope for lensless microscopy with diffraction limited resolution,” Sci. Rep. 7(1), 10687 (2017).
[Crossref] [PubMed]

Richardson, W. H.

Sao, M.

K. Tajima, T. Shimano, Y. Nakamura, M. Sao, and T. Hoshizawa, “Lensless light-field imaging with multi-phased fresnel zone aperture,” 2017 IEEE International Conference on Computational Photography (ICCP), Stanford, CA, pp. 1–7 (2017).
[Crossref]

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]

Shimano, T.

K. Tajima, T. Shimano, Y. Nakamura, M. Sao, and T. Hoshizawa, “Lensless light-field imaging with multi-phased fresnel zone aperture,” 2017 IEEE International Conference on Computational Photography (ICCP), Stanford, CA, pp. 1–7 (2017).
[Crossref]

Shroff, S. A.

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]

Singh, A. K.

A. K. Singh, G. Pedrini, M. Takeda, and W. Osten, “Scatter-plate microscope for lensless microscopy with diffraction limited resolution,” Sci. Rep. 7(1), 10687 (2017).
[Crossref] [PubMed]

Singh, M.

M. Singh and A. Kumar, “Optical encryption and decryption using a sandwich random phase diffuser in the Fourier plane,” Opt. Eng. 46(5), 055201 (2007).
[Crossref]

Tajima, K.

K. Tajima, T. Shimano, Y. Nakamura, M. Sao, and T. Hoshizawa, “Lensless light-field imaging with multi-phased fresnel zone aperture,” 2017 IEEE International Conference on Computational Photography (ICCP), Stanford, CA, pp. 1–7 (2017).
[Crossref]

Takeda, M.

A. K. Singh, G. Pedrini, M. Takeda, and W. Osten, “Scatter-plate microscope for lensless microscopy with diffraction limited resolution,” Sci. Rep. 7(1), 10687 (2017).
[Crossref] [PubMed]

Teague, M. R.

Waller, L.

N. Antipa, G. Kuo, R. Heckel, B. Mildenhall, E. Bostan, R. Ng, and L. Waller, “DiffuserCam: lensless single-exposure 3D imaging,” Optica 5(1), 1–9 (2018).
[Crossref]

N. Antipa, S. Necula, R. Ng, and L. Waller, “Single-shot diffuser-encoded light field imaging,” 2016 IEEE International Conference on Computational Photography (ICCP), Evanston, IL, pp. 1–11 (2016).

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]

Xie, X.

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8(1), 4585 (2018).
[Crossref] [PubMed]

Xu, X.

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8(1), 4585 (2018).
[Crossref] [PubMed]

Yao, J.

J. Yao and G. C. K. Chen, “Holographic diffuser for diffuse infrared wireless home networking,” Opt. Eng. 42(2), 1–8 (2003).

Zhou, J.

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8(1), 4585 (2018).
[Crossref] [PubMed]

Zhuang, H.

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8(1), 4585 (2018).
[Crossref] [PubMed]

Appl. Opt. (4)

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. Opt. Soc. Am. (2)

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

Opt. Commun. (1)

Y. T. Lu and S. Chi, “Fabrication of light-shaping diffusion screens,” Opt. Commun. 214(1), 55–63 (2002).

Opt. Eng. (2)

J. Yao and G. C. K. Chen, “Holographic diffuser for diffuse infrared wireless home networking,” Opt. Eng. 42(2), 1–8 (2003).

M. Singh and A. Kumar, “Optical encryption and decryption using a sandwich random phase diffuser in the Fourier plane,” Opt. Eng. 46(5), 055201 (2007).
[Crossref]

Opt. Express (2)

Optica (1)

Sci. Rep. (2)

A. K. Singh, G. Pedrini, M. Takeda, and W. Osten, “Scatter-plate microscope for lensless microscopy with diffraction limited resolution,” Sci. Rep. 7(1), 10687 (2017).
[Crossref] [PubMed]

X. Xie, H. Zhuang, H. He, X. Xu, H. Liang, Y. Liu, and J. Zhou, “Extended depth-resolved imaging through a thin scattering medium with PSF manipulation,” Sci. Rep. 8(1), 4585 (2018).
[Crossref] [PubMed]

Other (9)

R. Ng, M. Levoy, M. Bredif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a handheld plenopic camera,” Technical Report, Stanford University (2005).

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 SIGGRAPH, New York, NY, USA, Article 69 (2007).
[Crossref]

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM SIGGRAPH, New York, NY, USA, Article 70 (2007).
[Crossref]

K. Tajima, T. Shimano, Y. Nakamura, M. Sao, and T. Hoshizawa, “Lensless light-field imaging with multi-phased fresnel zone aperture,” 2017 IEEE International Conference on Computational Photography (ICCP), Stanford, CA, pp. 1–7 (2017).
[Crossref]

N. Antipa, S. Necula, R. Ng, and L. Waller, “Single-shot diffuser-encoded light field imaging,” 2016 IEEE International Conference on Computational Photography (ICCP), Evanston, IL, pp. 1–11 (2016).

M. F. Dickey, Laser Beam Shaping: Theory and Techniques, Second Edition (Crc, 2017).

J. W. Goodman, Introduction to Fourier optics (Roberts and Company Publishers, 2005).

D. G. Voelz, Computational Fourier Optics: A MATLAB Tutorial (SPIE, 2011).

Light shaping diffuser, https://www.luminitco.com/products/light-shaping-diffusers .

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Figures (10)

Fig. 1
Fig. 1 Optical configuration of a diffuser camera.
Fig. 2
Fig. 2 Experimental setup to estimate diffuser’s phase: (a) general architecture to obtain the near-field and far-field intensity distributions; (b) experimental setup to obtain the far-field intensity distribution
Fig. 3
Fig. 3 Phase estimation simulation: (a) Ground truth phase distribution; (b) Intensity distribution of the near field; (c) Far-field intensity distribution generated by Eq. (13); (d) Estimated phases.
Fig. 4
Fig. 4 Gerchberg-Saxton algorithm adapted for diffuser phase estimation illustration, where the known variables are near-field intensity and far-field intensity.
Fig. 5
Fig. 5 (a) Simulated object for reconstruction with physical size 0.35mm × 0.35mm; (b) Simulated sensor response; (c) The first row corresponds to the estimated phase with different errors, second row corresponds to the model derived PSFs using the phase in the first row, and the last row corresponds to the reconstruction results using the PSFs in the second row.
Fig. 6
Fig. 6 Simulation with a more complex object and phase distribution: (a) Simulated object for reconstruction with physical size 0.35mm × 0.35mm; (b) Simulated sensor response; (c) The first row corresponds to the estimated phase with different errors, second row corresponds to the model derived PSFs using the phase in the first row, and the last row corresponds to the reconstruction results using the PSFs in the second row.
Fig. 7
Fig. 7 Diffuser camera system: (a)Vertical and side view of the diffuser camera system; (b)Test samples used for reconstruction.
Fig. 8
Fig. 8 (a) Captured far-field intensity distribution; (b) Captured near-field intensity distribution; (c) Estimated phase distribution.
Fig. 9
Fig. 9 Comparison between the real captured PSFs, scaled PSFs and our model derived PSFs.
Fig. 10
Fig. 10 Reconstruction results comparison for: (a) Object 1; and (b) Object 2 using the captured PSFs, scaled PSFs and our model derived PSFs provided in Fig. 9 correspondingly.

Tables (1)

Tables Icon

Table 1 Objective quality comparison using the ground truths in Fig. 7(b) as the references.

Equations (15)

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

U 2 ( x 2 , y 2 )= U 1 ( x 1 , y 1 ) h 1 ( x 2 - x 1 , y 2 -y 1 )d x 1 d y 1 ,
h 1 ( x 1 , y 1 , x 2 , y 2 )= exp(jk z 1 ) jλ z 1 exp{ jk 2 z 1 [ ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 ]},
U 2 ' =C( x 2 , y 2 ) U 2 ( x 2 , y 2 ),
C( x 2 , y 2 )={ 1,if ( x 2 2 + y 2 2 ) 1/2 r 0,otherwise.
U '' 2 ( x 2 , y 2 )= U 2 ' ( x 2 , y 2 )exp[j θ d ( x 2 , y 2 )].
h 2 ( x 2 , y 2 , x 3 , y 3 )= exp(jk z 2 ) jλ z 2 exp{ jk 2 z 2 [ ( x 3 x 2 ) 2 + ( y 3 y 2 ) 2 ]}.
h( x 1 , y 1 , x 3 , y 3 )= exp[jk( z 1 + z 2 )] λ 2 z 1 z 2 C( x 2 , y 2 )exp{ jk 2 z 1 [ ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 ]} exp{ jk 2 z 1 [ ( x 3 x 2 ) 2 + ( y 3 y 2 ) 2 ]}exp[i θ d ( x 2 , y 2 )]d x 2 d y 2
I( x 3 , y 3 )=| U 3 ( x 3 , y 3 ) | 2 .
U en ( x 2 , y 2 )=A( x 2 , y 2 ) e j θ e ( x 2 , y 2 ) =A( x 2 , y 2 )P( x 2 , y 2 ),
U ef ( x 2 ' , y 2 ' )=S( x 2 ' , y 2 ' )F{ U en ( x 2 , y 2 )}=S( x 2 ' , y 2 ' ) A ' ( x 2 ' , y 2 ' )*F{P( x 2 , y 2 )},
U dn ( x 2 , y 2 )=A( x 2 , y 2 )C( x 2 , y 2 ) e j[ θ e ( x 2 , y 2 )+ θ d ( x 2 , y 2 )] =K( x 2 , y 2 )P( x 2 , y 2 )D( x 2 , y 2 ),
U df ( x 2 ' , y 2 ' )=S( x 2 ' , y 2 ' ) K ' ( x 2 ' , y 2 ' )F[P( x 2 , y 2 )]F[D( x 2 , y 2 )]
U 2 ' ( x 2 ' , y 2 ' )= exp(jkf) jλf × U 2 ( x 2 , y 2 )C( x 2 + x 2 ' , y 2 + y 2 ' )exp[j 2π λf ( x 2 ' x 2 + y 2 ' y 2 )]d x 2 d y 2 ,
P ( A , B ) = m n ( A m n A ¯ ) ( B m n B ¯ ) ( m n ( A m n A ¯ ) 2 ) ( m n ( B m n B ¯ ) 2 ) ,
o ( k + 1 ) = o k ( I o k H H * ) ,

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