Abstract

A system approach to acquire a three-dimensional object distribution is presented using a compact and cost efficient camera system with an engineered point spread function. The corresponding monocular setup incorporates a phase-only computer-generated hologram in combination with a conventional imaging objective in order to optically encode the axial information within a single two-dimensional image. The object’s depth map is calculated using a novel approach based on the power cepstrum of the image. The in-plane RGB image information is restored with an extended depth of focus by applying an adapted Wiener filter. The presented approach is tested experimentally by estimating the three-dimensional distribution of an extended passively illuminated scene.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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  1. J. Salvi, J. Pagès, and J. Batlle, “Pattern codification strategies in structured light systems,” Pattern Recogn. 37(4), 827–849 (2004).
    [Crossref]
  2. M. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2000).
  3. D. Huang, E. Swanson, and C. Lin, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
    [Crossref] [PubMed]
  4. M. Z. Brown, D. Burschka, and G. D. Hager, “Advances in computational stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 25(8), 993–1008 (2003).
    [Crossref]
  5. Y. Schechner and N. Kiryati, “Depth from defocus vs. stereo: How different really are they?” Int. J. Comput. Vision 39(2), 141–162 (2000).
    [Crossref]
  6. M. Subbarao and G. Surya, “Depth from defocus: a spatial domain approach,” Int. J. Comput. Vision 13(3), 271–294 (1994).
    [Crossref]
  7. R. Horisaki and J. Tanida, “Multi-channel data acquisition using multiplexed imaging with spatial encoding,” Opt. Express 18(22), 429–432 (2010).
    [Crossref]
  8. R. Horisaki and J. Tanida, “Preconditioning for multiplexed imaging with spatially coded PSFs,” Opt. Express 19(13), 573–583 (2011).
    [Crossref]
  9. T. Georgiev, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution tradeoffs in integral photography,” in Proceedings of the Eurographics Symposium on Rendering (2006), pp. 263–272.
  10. A. Lumsdaine and T. Georgiev, “The focused plenoptic camera,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2009), pp. 1–8.
  11. D. Miau, O. Cossairt, and S. Nayar, “Focal sweep videography with deformable optics,” in Proceedings of IEEE International Conference on Computational Photography (IEEE, 2013), pp. 1–8.
    [Crossref]
  12. P. Llull, X. Yuan, L. Carin, and D. Brady, “Image translation for single-shot focal tomography,” Optica 2, 822–825, (2015).
    [Crossref]
  13. A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Transactions on Graphics 26(3), 70 (2007).
    [Crossref]
  14. A. Levin, S. Hasinoff, and P. Green, “4D frequency analysis of computational cameras for depth of field extension,” ACM Transactions on Graphics 28(3), 97 (2007).
  15. S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16(5), 3484–3489 (2008).
    [Crossref] [PubMed]
  16. A. Greengard, Y. Y. Schechner, and R. Piestun, “Depth from diffracted rotation,” Opt. Lett. 31(2), 181–183 (2006).
    [Crossref] [PubMed]
  17. S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. 109(3), 675–679 (2012).
    [Crossref] [PubMed]
  18. S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106(9), 2995–2999 (2009).
    [Crossref] [PubMed]
  19. S. Quirin and R. Piestun, “Depth estimation and image recovery using broadband, incoherent illumination with engineered point spread functions [Invited],” Appl. Opt. 52(1), 367–376 (2013).
    [Crossref]
  20. T. Niihara, R. Horisaki, and M. Kiyono, “Diffraction-limited depth-from-defocus imaging with a pixel-limited camera using pupil phase modulation and compressive sensing,” Appl. Phys. Express 8, 012501 (2014).
    [Crossref]
  21. H.-C. Eckstein, M. Stumpf, P. Schleicher, S. Kleinle, A. Matthes, U. D. Zeitner, and A. Bräuer, “Direct write grayscale lithography for arbitrary shaped micro-optical surfaces,” presented at the 20th Microoptics Conference, Fukuoka, Japan, 25–28 Oct. 2015.
  22. G. Grover, S. Quirin, Callie Fiedler, and Rafael Piestun, “Photon efficient double-helix PSF microscopy with application to 3D photo-activation localization imaging,” Biomed. Opt. Express 82(11), 3010–3020 (2011).
    [Crossref]
  23. M. Cannon, “Blind deconvolution of spatially invariant image blurs with phase,” IEEE Trans. Acoust. Speech Signal Process. 24, 230–2351976).
  24. P. W. Smith and N. Nandhakumar, “An improved power cepstrum based stereo correspondence method for textured scenes,” IEEE Trans. Pattern Anal. Mach. Intell. 18(3), 338–348 (1996).
    [Crossref]
  25. A. M. Noll, “Short-time spectrum and ”cepstrum” techniques for vocal-pitch detection,” J. Acoust. Soc. Am. 36(2), 296–302 (1964).
    [Crossref]
  26. A. M. Noll, “Cepstrum pitch determination,” J. Acoust. Soc. Am. 41(2), 293–309 (1967).
    [Crossref] [PubMed]
  27. R. Rom, “On the cepstrum of two-dimensional functions (Corresp.),” IEEE Trans. Inf. Theory 21(2), 214–217 (1975).
    [Crossref]
  28. W. K. Pratt, Digital Image Processing (John Wiley & Sons, 2007).
    [Crossref]

2015 (1)

2014 (1)

T. Niihara, R. Horisaki, and M. Kiyono, “Diffraction-limited depth-from-defocus imaging with a pixel-limited camera using pupil phase modulation and compressive sensing,” Appl. Phys. Express 8, 012501 (2014).
[Crossref]

2013 (1)

S. Quirin and R. Piestun, “Depth estimation and image recovery using broadband, incoherent illumination with engineered point spread functions [Invited],” Appl. Opt. 52(1), 367–376 (2013).
[Crossref]

2012 (1)

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. 109(3), 675–679 (2012).
[Crossref] [PubMed]

2011 (2)

R. Horisaki and J. Tanida, “Preconditioning for multiplexed imaging with spatially coded PSFs,” Opt. Express 19(13), 573–583 (2011).
[Crossref]

G. Grover, S. Quirin, Callie Fiedler, and Rafael Piestun, “Photon efficient double-helix PSF microscopy with application to 3D photo-activation localization imaging,” Biomed. Opt. Express 82(11), 3010–3020 (2011).
[Crossref]

2010 (1)

R. Horisaki and J. Tanida, “Multi-channel data acquisition using multiplexed imaging with spatial encoding,” Opt. Express 18(22), 429–432 (2010).
[Crossref]

2009 (1)

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

2008 (1)

2007 (2)

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Transactions on Graphics 26(3), 70 (2007).
[Crossref]

A. Levin, S. Hasinoff, and P. Green, “4D frequency analysis of computational cameras for depth of field extension,” ACM Transactions on Graphics 28(3), 97 (2007).

2006 (1)

2004 (1)

J. Salvi, J. Pagès, and J. Batlle, “Pattern codification strategies in structured light systems,” Pattern Recogn. 37(4), 827–849 (2004).
[Crossref]

2003 (1)

M. Z. Brown, D. Burschka, and G. D. Hager, “Advances in computational stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 25(8), 993–1008 (2003).
[Crossref]

2000 (2)

Y. Schechner and N. Kiryati, “Depth from defocus vs. stereo: How different really are they?” Int. J. Comput. Vision 39(2), 141–162 (2000).
[Crossref]

M. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2000).

1996 (1)

P. W. Smith and N. Nandhakumar, “An improved power cepstrum based stereo correspondence method for textured scenes,” IEEE Trans. Pattern Anal. Mach. Intell. 18(3), 338–348 (1996).
[Crossref]

1994 (1)

M. Subbarao and G. Surya, “Depth from defocus: a spatial domain approach,” Int. J. Comput. Vision 13(3), 271–294 (1994).
[Crossref]

1991 (1)

D. Huang, E. Swanson, and C. Lin, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

1976 (1)

M. Cannon, “Blind deconvolution of spatially invariant image blurs with phase,” IEEE Trans. Acoust. Speech Signal Process. 24, 230–2351976).

1975 (1)

R. Rom, “On the cepstrum of two-dimensional functions (Corresp.),” IEEE Trans. Inf. Theory 21(2), 214–217 (1975).
[Crossref]

1967 (1)

A. M. Noll, “Cepstrum pitch determination,” J. Acoust. Soc. Am. 41(2), 293–309 (1967).
[Crossref] [PubMed]

1964 (1)

A. M. Noll, “Short-time spectrum and ”cepstrum” techniques for vocal-pitch detection,” J. Acoust. Soc. Am. 36(2), 296–302 (1964).
[Crossref]

Amann, M.

M. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2000).

Batlle, J.

J. Salvi, J. Pagès, and J. Batlle, “Pattern codification strategies in structured light systems,” Pattern Recogn. 37(4), 827–849 (2004).
[Crossref]

Biteen, J. S.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Bosch, T.

M. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2000).

Brady, D.

Bräuer, A.

H.-C. Eckstein, M. Stumpf, P. Schleicher, S. Kleinle, A. Matthes, U. D. Zeitner, and A. Bräuer, “Direct write grayscale lithography for arbitrary shaped micro-optical surfaces,” presented at the 20th Microoptics Conference, Fukuoka, Japan, 25–28 Oct. 2015.

Brown, M. Z.

M. Z. Brown, D. Burschka, and G. D. Hager, “Advances in computational stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 25(8), 993–1008 (2003).
[Crossref]

Burschka, D.

M. Z. Brown, D. Burschka, and G. D. Hager, “Advances in computational stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 25(8), 993–1008 (2003).
[Crossref]

Cannon, M.

M. Cannon, “Blind deconvolution of spatially invariant image blurs with phase,” IEEE Trans. Acoust. Speech Signal Process. 24, 230–2351976).

Carin, L.

Cossairt, O.

D. Miau, O. Cossairt, and S. Nayar, “Focal sweep videography with deformable optics,” in Proceedings of IEEE International Conference on Computational Photography (IEEE, 2013), pp. 1–8.
[Crossref]

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 the Eurographics Symposium on Rendering (2006), pp. 263–272.

Durand, F.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Transactions on Graphics 26(3), 70 (2007).
[Crossref]

Eckstein, H.-C.

H.-C. Eckstein, M. Stumpf, P. Schleicher, S. Kleinle, A. Matthes, U. D. Zeitner, and A. Bräuer, “Direct write grayscale lithography for arbitrary shaped micro-optical surfaces,” presented at the 20th Microoptics Conference, Fukuoka, Japan, 25–28 Oct. 2015.

Fergus, R.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Transactions on Graphics 26(3), 70 (2007).
[Crossref]

Fiedler, Callie

G. Grover, S. Quirin, Callie Fiedler, and Rafael Piestun, “Photon efficient double-helix PSF microscopy with application to 3D photo-activation localization imaging,” Biomed. Opt. Express 82(11), 3010–3020 (2011).
[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 Transactions on Graphics 26(3), 70 (2007).
[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 the Eurographics Symposium on Rendering (2006), pp. 263–272.

A. Lumsdaine and T. Georgiev, “The focused plenoptic camera,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2009), pp. 1–8.

Green, P.

A. Levin, S. Hasinoff, and P. Green, “4D frequency analysis of computational cameras for depth of field extension,” ACM Transactions on Graphics 28(3), 97 (2007).

Greengard, A.

Grover, G.

G. Grover, S. Quirin, Callie Fiedler, and Rafael Piestun, “Photon efficient double-helix PSF microscopy with application to 3D photo-activation localization imaging,” Biomed. Opt. Express 82(11), 3010–3020 (2011).
[Crossref]

Hager, G. D.

M. Z. Brown, D. Burschka, and G. D. Hager, “Advances in computational stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 25(8), 993–1008 (2003).
[Crossref]

Hasinoff, S.

A. Levin, S. Hasinoff, and P. Green, “4D frequency analysis of computational cameras for depth of field extension,” ACM Transactions on Graphics 28(3), 97 (2007).

Horisaki, R.

T. Niihara, R. Horisaki, and M. Kiyono, “Diffraction-limited depth-from-defocus imaging with a pixel-limited camera using pupil phase modulation and compressive sensing,” Appl. Phys. Express 8, 012501 (2014).
[Crossref]

R. Horisaki and J. Tanida, “Preconditioning for multiplexed imaging with spatially coded PSFs,” Opt. Express 19(13), 573–583 (2011).
[Crossref]

R. Horisaki and J. Tanida, “Multi-channel data acquisition using multiplexed imaging with spatial encoding,” Opt. Express 18(22), 429–432 (2010).
[Crossref]

Huang, D.

D. Huang, E. Swanson, and C. Lin, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

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 the Eurographics Symposium on Rendering (2006), pp. 263–272.

Kiryati, N.

Y. Schechner and N. Kiryati, “Depth from defocus vs. stereo: How different really are they?” Int. J. Comput. Vision 39(2), 141–162 (2000).
[Crossref]

Kiyono, M.

T. Niihara, R. Horisaki, and M. Kiyono, “Diffraction-limited depth-from-defocus imaging with a pixel-limited camera using pupil phase modulation and compressive sensing,” Appl. Phys. Express 8, 012501 (2014).
[Crossref]

Kleinle, S.

H.-C. Eckstein, M. Stumpf, P. Schleicher, S. Kleinle, A. Matthes, U. D. Zeitner, and A. Bräuer, “Direct write grayscale lithography for arbitrary shaped micro-optical surfaces,” presented at the 20th Microoptics Conference, Fukuoka, Japan, 25–28 Oct. 2015.

Lescure, M.

M. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2000).

Levin, A.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Transactions on Graphics 26(3), 70 (2007).
[Crossref]

A. Levin, S. Hasinoff, and P. Green, “4D frequency analysis of computational cameras for depth of field extension,” ACM Transactions on Graphics 28(3), 97 (2007).

Lin, C.

D. Huang, E. Swanson, and C. Lin, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Liu, N.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Llull, P.

Lord, S. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Lumsdaine, A.

A. Lumsdaine and T. Georgiev, “The focused plenoptic camera,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2009), pp. 1–8.

Matthes, A.

H.-C. Eckstein, M. Stumpf, P. Schleicher, S. Kleinle, A. Matthes, U. D. Zeitner, and A. Bräuer, “Direct write grayscale lithography for arbitrary shaped micro-optical surfaces,” presented at the 20th Microoptics Conference, Fukuoka, Japan, 25–28 Oct. 2015.

Miau, D.

D. Miau, O. Cossairt, and S. Nayar, “Focal sweep videography with deformable optics,” in Proceedings of IEEE International Conference on Computational Photography (IEEE, 2013), pp. 1–8.
[Crossref]

Moerner, W. E.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Myllyla, R.

M. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2000).

Nandhakumar, N.

P. W. Smith and N. Nandhakumar, “An improved power cepstrum based stereo correspondence method for textured scenes,” IEEE Trans. Pattern Anal. Mach. Intell. 18(3), 338–348 (1996).
[Crossref]

Nayar, S.

D. Miau, O. Cossairt, and S. Nayar, “Focal sweep videography with deformable optics,” in Proceedings of IEEE International Conference on Computational Photography (IEEE, 2013), pp. 1–8.
[Crossref]

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

Niihara, T.

T. Niihara, R. Horisaki, and M. Kiyono, “Diffraction-limited depth-from-defocus imaging with a pixel-limited camera using pupil phase modulation and compressive sensing,” Appl. Phys. Express 8, 012501 (2014).
[Crossref]

Noll, A. M.

A. M. Noll, “Cepstrum pitch determination,” J. Acoust. Soc. Am. 41(2), 293–309 (1967).
[Crossref] [PubMed]

A. M. Noll, “Short-time spectrum and ”cepstrum” techniques for vocal-pitch detection,” J. Acoust. Soc. Am. 36(2), 296–302 (1964).
[Crossref]

Pagès, J.

J. Salvi, J. Pagès, and J. Batlle, “Pattern codification strategies in structured light systems,” Pattern Recogn. 37(4), 827–849 (2004).
[Crossref]

Pavani, S. R. P.

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. 109(3), 675–679 (2012).
[Crossref] [PubMed]

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16(5), 3484–3489 (2008).
[Crossref] [PubMed]

Piestun, R.

S. Quirin and R. Piestun, “Depth estimation and image recovery using broadband, incoherent illumination with engineered point spread functions [Invited],” Appl. Opt. 52(1), 367–376 (2013).
[Crossref]

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. 109(3), 675–679 (2012).
[Crossref] [PubMed]

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16(5), 3484–3489 (2008).
[Crossref] [PubMed]

A. Greengard, Y. Y. Schechner, and R. Piestun, “Depth from diffracted rotation,” Opt. Lett. 31(2), 181–183 (2006).
[Crossref] [PubMed]

Piestun, Rafael

G. Grover, S. Quirin, Callie Fiedler, and Rafael Piestun, “Photon efficient double-helix PSF microscopy with application to 3D photo-activation localization imaging,” Biomed. Opt. Express 82(11), 3010–3020 (2011).
[Crossref]

Pratt, W. K.

W. K. Pratt, Digital Image Processing (John Wiley & Sons, 2007).
[Crossref]

Quirin, S.

S. Quirin and R. Piestun, “Depth estimation and image recovery using broadband, incoherent illumination with engineered point spread functions [Invited],” Appl. Opt. 52(1), 367–376 (2013).
[Crossref]

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. 109(3), 675–679 (2012).
[Crossref] [PubMed]

G. Grover, S. Quirin, Callie Fiedler, and Rafael Piestun, “Photon efficient double-helix PSF microscopy with application to 3D photo-activation localization imaging,” Biomed. Opt. Express 82(11), 3010–3020 (2011).
[Crossref]

Rioux, M.

M. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2000).

Rom, R.

R. Rom, “On the cepstrum of two-dimensional functions (Corresp.),” IEEE Trans. Inf. Theory 21(2), 214–217 (1975).
[Crossref]

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 the Eurographics Symposium on Rendering (2006), pp. 263–272.

Salvi, J.

J. Salvi, J. Pagès, and J. Batlle, “Pattern codification strategies in structured light systems,” Pattern Recogn. 37(4), 827–849 (2004).
[Crossref]

Schechner, Y.

Y. Schechner and N. Kiryati, “Depth from defocus vs. stereo: How different really are they?” Int. J. Comput. Vision 39(2), 141–162 (2000).
[Crossref]

Schechner, Y. Y.

Schleicher, P.

H.-C. Eckstein, M. Stumpf, P. Schleicher, S. Kleinle, A. Matthes, U. D. Zeitner, and A. Bräuer, “Direct write grayscale lithography for arbitrary shaped micro-optical surfaces,” presented at the 20th Microoptics Conference, Fukuoka, Japan, 25–28 Oct. 2015.

Smith, P. W.

P. W. Smith and N. Nandhakumar, “An improved power cepstrum based stereo correspondence method for textured scenes,” IEEE Trans. Pattern Anal. Mach. Intell. 18(3), 338–348 (1996).
[Crossref]

Stumpf, M.

H.-C. Eckstein, M. Stumpf, P. Schleicher, S. Kleinle, A. Matthes, U. D. Zeitner, and A. Bräuer, “Direct write grayscale lithography for arbitrary shaped micro-optical surfaces,” presented at the 20th Microoptics Conference, Fukuoka, Japan, 25–28 Oct. 2015.

Subbarao, M.

M. Subbarao and G. Surya, “Depth from defocus: a spatial domain approach,” Int. J. Comput. Vision 13(3), 271–294 (1994).
[Crossref]

Surya, G.

M. Subbarao and G. Surya, “Depth from defocus: a spatial domain approach,” Int. J. Comput. Vision 13(3), 271–294 (1994).
[Crossref]

Swanson, E.

D. Huang, E. Swanson, and C. Lin, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Tanida, J.

R. Horisaki and J. Tanida, “Preconditioning for multiplexed imaging with spatially coded PSFs,” Opt. Express 19(13), 573–583 (2011).
[Crossref]

R. Horisaki and J. Tanida, “Multi-channel data acquisition using multiplexed imaging with spatial encoding,” Opt. Express 18(22), 429–432 (2010).
[Crossref]

Thompson, M. A.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Twieg, R. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Yuan, X.

Zeitner, U. D.

H.-C. Eckstein, M. Stumpf, P. Schleicher, S. Kleinle, A. Matthes, U. D. Zeitner, and A. Bräuer, “Direct write grayscale lithography for arbitrary shaped micro-optical surfaces,” presented at the 20th Microoptics Conference, Fukuoka, Japan, 25–28 Oct. 2015.

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 the Eurographics Symposium on Rendering (2006), pp. 263–272.

ACM Transactions on Graphics (2)

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Transactions on Graphics 26(3), 70 (2007).
[Crossref]

A. Levin, S. Hasinoff, and P. Green, “4D frequency analysis of computational cameras for depth of field extension,” ACM Transactions on Graphics 28(3), 97 (2007).

Appl. Opt. (1)

S. Quirin and R. Piestun, “Depth estimation and image recovery using broadband, incoherent illumination with engineered point spread functions [Invited],” Appl. Opt. 52(1), 367–376 (2013).
[Crossref]

Appl. Phys. Express (1)

T. Niihara, R. Horisaki, and M. Kiyono, “Diffraction-limited depth-from-defocus imaging with a pixel-limited camera using pupil phase modulation and compressive sensing,” Appl. Phys. Express 8, 012501 (2014).
[Crossref]

Biomed. Opt. Express (1)

G. Grover, S. Quirin, Callie Fiedler, and Rafael Piestun, “Photon efficient double-helix PSF microscopy with application to 3D photo-activation localization imaging,” Biomed. Opt. Express 82(11), 3010–3020 (2011).
[Crossref]

IEEE Trans. Acoust. Speech Signal Process. (1)

M. Cannon, “Blind deconvolution of spatially invariant image blurs with phase,” IEEE Trans. Acoust. Speech Signal Process. 24, 230–2351976).

IEEE Trans. Inf. Theory (1)

R. Rom, “On the cepstrum of two-dimensional functions (Corresp.),” IEEE Trans. Inf. Theory 21(2), 214–217 (1975).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (2)

P. W. Smith and N. Nandhakumar, “An improved power cepstrum based stereo correspondence method for textured scenes,” IEEE Trans. Pattern Anal. Mach. Intell. 18(3), 338–348 (1996).
[Crossref]

M. Z. Brown, D. Burschka, and G. D. Hager, “Advances in computational stereo,” IEEE Trans. Pattern Anal. Mach. Intell. 25(8), 993–1008 (2003).
[Crossref]

Int. J. Comput. Vision (2)

Y. Schechner and N. Kiryati, “Depth from defocus vs. stereo: How different really are they?” Int. J. Comput. Vision 39(2), 141–162 (2000).
[Crossref]

M. Subbarao and G. Surya, “Depth from defocus: a spatial domain approach,” Int. J. Comput. Vision 13(3), 271–294 (1994).
[Crossref]

J. Acoust. Soc. Am. (2)

A. M. Noll, “Short-time spectrum and ”cepstrum” techniques for vocal-pitch detection,” J. Acoust. Soc. Am. 36(2), 296–302 (1964).
[Crossref]

A. M. Noll, “Cepstrum pitch determination,” J. Acoust. Soc. Am. 41(2), 293–309 (1967).
[Crossref] [PubMed]

Opt. Eng. (1)

M. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging: a critical review of usual techniques for distance measurement,” Opt. Eng. 40(1), 10–19 (2000).

Opt. Express (3)

R. Horisaki and J. Tanida, “Multi-channel data acquisition using multiplexed imaging with spatial encoding,” Opt. Express 18(22), 429–432 (2010).
[Crossref]

R. Horisaki and J. Tanida, “Preconditioning for multiplexed imaging with spatially coded PSFs,” Opt. Express 19(13), 573–583 (2011).
[Crossref]

S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16(5), 3484–3489 (2008).
[Crossref] [PubMed]

Opt. Lett. (1)

Optica (1)

Pattern Recogn. (1)

J. Salvi, J. Pagès, and J. Batlle, “Pattern codification strategies in structured light systems,” Pattern Recogn. 37(4), 827–849 (2004).
[Crossref]

Proc. Natl. Acad. Sci. (2)

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. 109(3), 675–679 (2012).
[Crossref] [PubMed]

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. 106(9), 2995–2999 (2009).
[Crossref] [PubMed]

Science (1)

D. Huang, E. Swanson, and C. Lin, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Other (5)

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

A. Lumsdaine and T. Georgiev, “The focused plenoptic camera,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2009), pp. 1–8.

D. Miau, O. Cossairt, and S. Nayar, “Focal sweep videography with deformable optics,” in Proceedings of IEEE International Conference on Computational Photography (IEEE, 2013), pp. 1–8.
[Crossref]

W. K. Pratt, Digital Image Processing (John Wiley & Sons, 2007).
[Crossref]

H.-C. Eckstein, M. Stumpf, P. Schleicher, S. Kleinle, A. Matthes, U. D. Zeitner, and A. Bräuer, “Direct write grayscale lithography for arbitrary shaped micro-optical surfaces,” presented at the 20th Microoptics Conference, Fukuoka, Japan, 25–28 Oct. 2015.

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Figures (6)

Fig. 1
Fig. 1

Schematic layout of the proposed image acquisition setup. A 3D object distribution is imaged by a conventional camera objective with an implemented glass substrate comprising the CGH surface profile. The lateral and axial object information is optically encoded within the raw image due to an engineered PSF and can be recovered by tailored image processing.

Fig. 2
Fig. 2

The phase distribution in the exit pupil plane of the hybrid optical system (a), the corresponding Modulation Transfer Function (MTF) (b), as well as the MTF of a conventional optical system (c) are plotted for an exemplary in- and out-of-focus object distance z1 and z2, respectively. Note that the CGH is slightly oversized with respect to the actual pupil size, which is indicated by the dashed circle in (a). The spatial frequencies of the displayed MTFs are normalized according to the optical cut-off frequency given by the wavelength λ and the system’s F-number. The engineered MTFs, shown in (b), exhibit a characteristic modulation with an axially dependent period 1/p(z) and orientation angle θ.

Fig. 3
Fig. 3

Schematic work flow of the proposed image acquisition and processing approach, which retrieves the depth information encoded in (pkl, θkl) and reconstructs the object distribution O′kl from a single subimage Ikl.

Fig. 4
Fig. 4

(a) Measured surface profile of realized CGH. The dashed circle indicates the aperture size of 10 mm with in the optical setup. (b) Measured relationship between object distance z and rotation angle θ for three different wavelengths. The insets display the shape of the PSF at 540 nm for the corresponding object distance.

Fig. 5
Fig. 5

(a) Nominal image distribution of the three-dimensional object scene, captured without the CGH. The two insets on the right side exemplarily highlight an in- and out-of-focus part of the object scene, respectively. (b) Raw, encoded image distribution of the scene using the CGH. The in- and out-of-focus insets exhibit the blurred twin image with a lateral shift according to the distance of the respective object part. (c) Decoded image. The exemplary text features, displayed in both insets, can clearly be identified after the removal of the twin image.

Fig. 6
Fig. 6

Retrieved depth map of the imaged, three-dimensional scene.

Equations (19)

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i = { i k l } = + o ( z ) * h ( z ) d z + n ,
h ( z ) h 0 * δ + ( z ) + h 0 * δ ( z ) ,
δ k l ± ( z ) = δ [ k ± p ( z ) cos ( θ ( z ) ) , l ± p ( z ) sin ( θ ( z ) ) ] ,
i = + o ( z ) * h 0 o 0 ( z ) * [ δ + ( p ( z ) , θ ( z ) ) + δ ( p ( z ) , θ ( z ) ) ] d z + n
w m n = { 1 if | m | , | n | | M / 2 | , | N / 2 | 0 else
I k l m n = i k + m , l + n w m n .
I k l = O k l * H 0 * [ δ + ( p k l , θ k l ) + δ ( p k l , θ k l ) ] + N k l ,
C k l = 𝒞 { I k l } : = 1 { log ( | { I k l } | 2 ) } .
C k l = 1 { log ( | { I 0 , k l + N k l } | 2 ) }
= 1 { log ( | { I 0 , k l } | 2 ) + log ( | 1 + { N k l } { I 0 , k l } | 2 ) }
= 𝒞 { I 0 , k l } + 1 { log ( | 1 + { N k l } { I 0 , k l } | 2 ) } ,
𝒞 { I 0 , k l } = 𝒞 { O k l * H 0 } + 𝒞 { [ δ + ( p k l , θ k l ) + δ ( p k l , θ k l ) ] } ,
I k l m n = { I k l } : = I k l m n { 1 4 [ 1 cos ( 2 π m M 1 ) ] [ 1 cos ( 2 π n N 1 ) ] } ,
C k l m n = { C k l m n if p min m 2 + n 2 / 2 p max , 0 else
I ^ k l = O ^ k l H ^ 0 D ^ k l + N ^ k l
D ^ k l m n = cos [ 2 π p k l { k cos ( θ k l ) + l sin ( θ k l ) } ] ,
H ^ 0 m n = 1 2 π σ ^ 2 exp ( m 2 + n 2 2 σ ^ 2 ) ,
O ^ k l = I ^ k l [ H ^ 0 * D ^ k l * | H ^ 0 D ^ k l | 2 + SNR k l 1 ] ,
o k l = m , n O k m , l n m n

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