Abstract

In this paper, we propose a single-shot three-dimensional imaging technique. This is achieved by simply placing a normal thin scattering layer in front of a two-dimensional image sensor, making it a light-field-like camera. The working principle of the proposed technique is based on the statistical independence and spatial ergodicity of the speckle produced by the scattering layer. Thus, the local point responses of the scattering layer should be measured in advance and are used for image reconstruction. We demonstrate the proposed method with proof-of-concept experiments and analyze the factors that affect its performance.

© 2021 Optical Society of America

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References

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2020 (1)

Z. Cai, J. Chen, G. Pedrini, W. Osten, X. Liu, and X. Peng, “Lensless light-field imaging through diffuser encoding,” Light Sci. Appl. 9, 1–9 (2020).
[Crossref]

2019 (2)

M. Liao, D. Lu, G. Pedrini, W. Osten, G. Situ, W. He, and X. Peng, “Extending the depth-of-field of imaging systems with a scattering diffuser,” Sci. Rep. 9, 7165 (2019).
[Crossref]

R. Horisaki, Y. Okamoto, and J. Tanida, “Single-shot noninvasive three-dimensional imaging through scattering media,” Opt. Lett. 44, 4032–4035 (2019).
[Crossref]

2018 (5)

2017 (6)

2016 (1)

K. Lee and Y. Park, “Exploiting the speckle-correlation scattering matrix for a compact reference-free holographic image sensor,” Nat. Commun. 7, 1–7 (2016).
[Crossref]

2015 (2)

M. Takeda, A. K. Singh, D. N. Naik, G. Pedrini, and W. Osten, “Holographic correloscopy–unconventional holographic techniques for imaging a three-dimensional object through an opaque diffuser or via a scattering wall: a review,” IEEE Trans. Ind. Inf. 12, 1631–1640 (2015).
[Crossref]

J. Liu, T. Xu, W. Yue, J. Sun, and G. Situ, “Light-field moment microscopy with noise reduction,” Opt. Express 23, 29154–29162 (2015).
[Crossref]

2014 (2)

J.-H. Park, S.-K. Lee, N.-Y. Jo, H.-J. Kim, Y.-S. Kim, and H.-G. Lim, “Light ray field capture using focal plane sweeping and its optical reconstruction using 3D displays,” Opt. Express 22, 25444–25454 (2014).
[Crossref]

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

2013 (1)

2011 (3)

D. N. Naik, R. K. Singh, T. Ezawa, Y. Miyamoto, and M. Takeda, “Photon correlation holography,” Opt. Express 19, 1408–1421 (2011).
[Crossref]

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
[Crossref]

J. Geng, “Structured-light 3D surface imaging: a tutorial,” Adv. Opt. Photon. 3, 128–160 (2011).
[Crossref]

2009 (1)

2007 (1)

2006 (1)

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94, 591–607 (2006).
[Crossref]

1991 (1)

1990 (1)

I. Freund, “Looking through walls and around corners,” Physica A 168, 49–65 (1990).
[Crossref]

1980 (1)

J. S. Lim and H. Nawab, “Techniques for speckle noise removal,” Proc. SPIE 243, 35–45 (1980).
[Crossref]

Antipa, N.

Barth, E.

A. Kolb, E. Barth, R. Koch, and R. Larsen, “Time-of-flight cameras in computer graphics,” in Computer Graphics Forum (Wiley Online Library, 2010), Vol. 29, pp. 141–159.

Bishara, W.

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
[Crossref]

Bostan, E.

Brédif, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Tech. Rep. (Stanford University Computer Science Tech Report CSTR, 2005).

Brooker, G.

Cai, Z.

Z. Cai, J. Chen, G. Pedrini, W. Osten, X. Liu, and X. Peng, “Lensless light-field imaging through diffuser encoding,” Light Sci. Appl. 9, 1–9 (2020).
[Crossref]

Chen, J.

Z. Cai, J. Chen, G. Pedrini, W. Osten, X. Liu, and X. Peng, “Lensless light-field imaging through diffuser encoding,” Light Sci. Appl. 9, 1–9 (2020).
[Crossref]

Chen, N.

Crozier, K. B.

Dang, C.

Duval, G.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Tech. Rep. (Stanford University Computer Science Tech Report CSTR, 2005).

Ezawa, T.

Feng, S.

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
[Crossref]

Fink, M.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

Frank, W. Y.

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
[Crossref]

Freund, I.

I. Freund, “Looking through walls and around corners,” Physica A 168, 49–65 (1990).
[Crossref]

Geng, J.

Gigan, S.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

Gonglewski, J. D.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 2015).

Gross, H.

W. Singer, M. Totzek, and H. Gross, Handbook of Optical Systems (Wiley-VCH, 2005), Vol. 2.

Hanrahan, P.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Tech. Rep. (Stanford University Computer Science Tech Report CSTR, 2005).

He, W.

M. Liao, D. Lu, G. Pedrini, W. Osten, G. Situ, W. He, and X. Peng, “Extending the depth-of-field of imaging systems with a scattering diffuser,” Sci. Rep. 9, 7165 (2019).
[Crossref]

Heckel, R.

Heidmann, P.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

Herman, G. T.

G. T. Herman, Fundamentals of Computerized Tomography: Image Reconstruction from Projections (Springer, 2009).

Horisaki, R.

Horowitz, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Tech. Rep. (Stanford University Computer Science Tech Report CSTR, 2005).

Idell, P. S.

Isikman, S. O.

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
[Crossref]

Javidi, B.

M. Martnez-Corral and B. Javidi, “Fundamentals of 3D imaging and displays: a tutorial on integral imaging, light-field, and plenoptic systems,” Adv. Opt. Photon. 10, 512–566 (2018).
[Crossref]

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94, 591–607 (2006).
[Crossref]

Jo, N.-Y.

Katz, O.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8, 784–790 (2014).
[Crossref]

Kelly, D. P.

Kim, H.-J.

Kim, Y.-S.

Koch, R.

A. Kolb, E. Barth, R. Koch, and R. Larsen, “Time-of-flight cameras in computer graphics,” in Computer Graphics Forum (Wiley Online Library, 2010), Vol. 29, pp. 141–159.

Kolb, A.

A. Kolb, E. Barth, R. Koch, and R. Larsen, “Time-of-flight cameras in computer graphics,” in Computer Graphics Forum (Wiley Online Library, 2010), Vol. 29, pp. 141–159.

Kumar, M.

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

M. Kumar, A. Vijayakumar, and J. Rosen, “Incoherent digital holograms acquired by interferenceless coded aperture correlation holography system without refractive lenses,” Sci. Rep. 7, 1–11 (2017).
[Crossref]

Kuo, C. J.

C. J. Kuo and M. H. Tsai, Three-Dimensional Holographic Imaging (Wiley Online Library, 2002).

Kuo, G.

Larsen, R.

A. Kolb, E. Barth, R. Koch, and R. Larsen, “Time-of-flight cameras in computer graphics,” in Computer Graphics Forum (Wiley Online Library, 2010), Vol. 29, pp. 141–159.

Lau, R.

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
[Crossref]

Lee, K.

K. Lee and Y. Park, “Exploiting the speckle-correlation scattering matrix for a compact reference-free holographic image sensor,” Nat. Commun. 7, 1–7 (2016).
[Crossref]

Lee, S.-K.

Levoy, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Tech. Rep. (Stanford University Computer Science Tech Report CSTR, 2005).

Li, D.

Li, G.

W. Yang, G. Li, and G. Situ, “Imaging through scattering media with the auxiliary of a known reference object,” Sci. Rep. 8, 9614 (2018).
[Crossref]

G. Li, W. Yang, D. Li, and G. Situ, “Cyphertext-only attack on the double random-phase encryption: experimental demonstration,” Opt. Express 25, 8690–8697 (2017).
[Crossref]

Liao, M.

M. Liao, D. Lu, G. Pedrini, W. Osten, G. Situ, W. He, and X. Peng, “Extending the depth-of-field of imaging systems with a scattering diffuser,” Sci. Rep. 9, 7165 (2019).
[Crossref]

Lim, H.-G.

Lim, J. S.

J. S. Lim and H. Nawab, “Techniques for speckle noise removal,” Proc. SPIE 243, 35–45 (1980).
[Crossref]

Liu, J.

Liu, X.

Z. Cai, J. Chen, G. Pedrini, W. Osten, X. Liu, and X. Peng, “Lensless light-field imaging through diffuser encoding,” Light Sci. Appl. 9, 1–9 (2020).
[Crossref]

Liu, Y.

Y. Shi, Y. Liu, J. Wang, and T. Wu, “Non-invasive depth-resolved imaging through scattering layers via speckle correlations and parallax,” Appl. Phys. Lett. 110, 231101 (2017).
[Crossref]

Lu, D.

M. Liao, D. Lu, G. Pedrini, W. Osten, G. Situ, W. He, and X. Peng, “Extending the depth-of-field of imaging systems with a scattering diffuser,” Sci. Rep. 9, 7165 (2019).
[Crossref]

Martnez-Corral, M.

Mavandadi, S.

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
[Crossref]

Mildenhall, B.

Miyamoto, Y.

Mukherjee, S.

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

Naik, D. N.

M. Takeda, A. K. Singh, D. N. Naik, G. Pedrini, and W. Osten, “Holographic correloscopy–unconventional holographic techniques for imaging a three-dimensional object through an opaque diffuser or via a scattering wall: a review,” IEEE Trans. Ind. Inf. 12, 1631–1640 (2015).
[Crossref]

D. N. Naik, R. K. Singh, T. Ezawa, Y. Miyamoto, and M. Takeda, “Photon correlation holography,” Opt. Express 19, 1408–1421 (2011).
[Crossref]

Nawab, H.

J. S. Lim and H. Nawab, “Techniques for speckle noise removal,” Proc. SPIE 243, 35–45 (1980).
[Crossref]

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, 1–9 (2018).
[Crossref]

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Tech. Rep. (Stanford University Computer Science Tech Report CSTR, 2005).

Okamoto, Y.

Orth, A.

Osten, W.

Z. Cai, J. Chen, G. Pedrini, W. Osten, X. Liu, and X. Peng, “Lensless light-field imaging through diffuser encoding,” Light Sci. Appl. 9, 1–9 (2020).
[Crossref]

M. Liao, D. Lu, G. Pedrini, W. Osten, G. Situ, W. He, and X. Peng, “Extending the depth-of-field of imaging systems with a scattering diffuser,” Sci. Rep. 9, 7165 (2019).
[Crossref]

M. Takeda, A. K. Singh, D. N. Naik, G. Pedrini, and W. Osten, “Holographic correloscopy–unconventional holographic techniques for imaging a three-dimensional object through an opaque diffuser or via a scattering wall: a review,” IEEE Trans. Ind. Inf. 12, 1631–1640 (2015).
[Crossref]

Ozcan, A.

S. O. Isikman, W. Bishara, S. Mavandadi, W. Y. Frank, S. Feng, R. Lau, and A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. USA 108, 7296–7301 (2011).
[Crossref]

Park, J.-H.

Park, Y.

K. Lee and Y. Park, “Exploiting the speckle-correlation scattering matrix for a compact reference-free holographic image sensor,” Nat. Commun. 7, 1–7 (2016).
[Crossref]

Pedrini, G.

Z. Cai, J. Chen, G. Pedrini, W. Osten, X. Liu, and X. Peng, “Lensless light-field imaging through diffuser encoding,” Light Sci. Appl. 9, 1–9 (2020).
[Crossref]

M. Liao, D. Lu, G. Pedrini, W. Osten, G. Situ, W. He, and X. Peng, “Extending the depth-of-field of imaging systems with a scattering diffuser,” Sci. Rep. 9, 7165 (2019).
[Crossref]

M. Takeda, A. K. Singh, D. N. Naik, G. Pedrini, and W. Osten, “Holographic correloscopy–unconventional holographic techniques for imaging a three-dimensional object through an opaque diffuser or via a scattering wall: a review,” IEEE Trans. Ind. Inf. 12, 1631–1640 (2015).
[Crossref]

Peng, X.

Z. Cai, J. Chen, G. Pedrini, W. Osten, X. Liu, and X. Peng, “Lensless light-field imaging through diffuser encoding,” Light Sci. Appl. 9, 1–9 (2020).
[Crossref]

M. Liao, D. Lu, G. Pedrini, W. Osten, G. Situ, W. He, and X. Peng, “Extending the depth-of-field of imaging systems with a scattering diffuser,” Sci. Rep. 9, 7165 (2019).
[Crossref]

Rai, M. R.

Rosen, J.

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

M. Kumar, A. Vijayakumar, and J. Rosen, “Incoherent digital holograms acquired by interferenceless coded aperture correlation holography system without refractive lenses,” Sci. Rep. 7, 1–11 (2017).
[Crossref]

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

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, 13883–13896 (2017).
[Crossref]

J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. 32, 912–914 (2007).
[Crossref]

Sahoo, S. K.

Sheridan, J. T.

Shi, Y.

Y. Shi, Y. Liu, J. Wang, and T. Wu, “Non-invasive depth-resolved imaging through scattering layers via speckle correlations and parallax,” Appl. Phys. Lett. 110, 231101 (2017).
[Crossref]

Singer, W.

W. Singer, M. Totzek, and H. Gross, Handbook of Optical Systems (Wiley-VCH, 2005), Vol. 2.

Singh, A. K.

M. Takeda, A. K. Singh, D. N. Naik, G. Pedrini, and W. Osten, “Holographic correloscopy–unconventional holographic techniques for imaging a three-dimensional object through an opaque diffuser or via a scattering wall: a review,” IEEE Trans. Ind. Inf. 12, 1631–1640 (2015).
[Crossref]

Singh, R. K.

Situ, G.

Stern, A.

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94, 591–607 (2006).
[Crossref]

Sun, J.

Takeda, M.

M. Takeda, A. K. Singh, D. N. Naik, G. Pedrini, and W. Osten, “Holographic correloscopy–unconventional holographic techniques for imaging a three-dimensional object through an opaque diffuser or via a scattering wall: a review,” IEEE Trans. Ind. Inf. 12, 1631–1640 (2015).
[Crossref]

D. N. Naik, R. K. Singh, T. Ezawa, Y. Miyamoto, and M. Takeda, “Photon correlation holography,” Opt. Express 19, 1408–1421 (2011).
[Crossref]

Tang, D.

Tanida, J.

Totzek, M.

W. Singer, M. Totzek, and H. Gross, Handbook of Optical Systems (Wiley-VCH, 2005), Vol. 2.

Tsai, M. H.

C. J. Kuo and M. H. Tsai, Three-Dimensional Holographic Imaging (Wiley Online Library, 2002).

Vijayakumar, A.

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Supplementary Material (1)

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» Supplement 1       Mathematical derivation

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Figures (4)

Fig. 1.
Fig. 1. Experimental setup for system calibration. A collimated laser beam converges to a spot in the R plane by lens L2. This point source produces a spherical wave and illuminates the whole ground glass, G. An aperture, A, mounted on a 2D translation stage is placed against G. By controlling the aperture’s position and window size, one can effectively illuminate only a certain block of the ground glass G. L1, L2, lenses; G, ground glass; A, aperture; P, linear polarizer; M1, M2, mirrors; R, reference plane; LASER, laser device.
Fig. 2.
Fig. 2. Experimental results: PSF calibration. (a) Recorded speckles of the reference point with the ground glass used as a whole. (b) PSF associated with block 3 located at $(3 \;{\rm mm}, 3 \;{\rm mm})$. (c) PSF associated with block 7 located at $(- 3 \;{\rm mm}, - 3 \; {\rm mm})$. (d) Recovered result using Eq. (7) with $\Delta z = 0$. (e) Reconstruction result at the corresponding aperture of (b). (f) Reconstruction result at the corresponding aperture of (c). (g)–(i) Recovered results of a point 3 cm away from the reference plane using Eq. (7) with $\Delta z = 0\;{\rm cm} $, $\Delta z = 1.5\;{\rm cm} $, and $\Delta z = 3\;{\rm cm} $, respectively.
Fig. 3.
Fig. 3. Experimental setup. After calibration, the synthesized 3D object composed of two spatially staggered characters is illuminated by incoherent light emitted from an LED with a central wavelength of 530 nm and a bandwidth of 20 nm. Then the combined beam propagates forward and passes through the ground glass G, giving rise to speckle patterns recorded by the camera. L1, lens; G, ground glass diffuser; A, aperture; P, linear polarizer; F, narrow bandpass filter; M3, M4, mirrors; BS1, BS2, beam splitters; T1, position where character “X” is placed; T2, position where character “3” is placed. LED, LED source.
Fig. 4.
Fig. 4. Experimental results of synthesized 3D object. (a) Recovered result at the view of the sub-aperture located in the bottom right corner. (b) Recovered result at the view of a bigger aperture located in the bottom right corner. (c) Recovered result using all the point spread functions with $\Delta z = 0\;{\rm mm} $. (d) Recovered result at the view of the sub-aperture located in the top left corner. (e) Recovered result at the view of a bigger aperture located in the top left corner. (f) Recovered result using all the point spread functions with $\Delta z = 50\;{\rm mm} $.

Equations (7)

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S ( r ) = | j = 1 n a j ( r r j ) | 2 = j = 1 n s j ( r r j ) + i = 1 n j = 1 , j i n a i ( r r i ) a j ( r r j ) ,
C j ( r ^ ) = s j ( r + r ^ ) S ( r ) d r .
C j ( r ^ ) = | Γ j ( r ^ ) | 2 + S ¯ s ¯ j ,
C j , I ( r , 0 ) = s j ( r r j ) I ( r ) ,
S ( r , Δ z ) = j = 1 n s j ( r r j , M Δ z ξ j z ) ,
C j , I ( r , Δ z ) = j C j , I ( r r j , M Δ z ξ j z ) .
C j , I ( r , Δ z ) = S ( r , Δ z ) I ( r ) .

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