Abstract

We propose a generalized framework for quantitatively acquiring multidimensional complex objects based on single-shot phase imaging with a coded aperture (SPICA). In multidimensional SPICA, a propagating field from a multidimensional complex object is sieved by a coded aperture, the sieved field is modulated by an optical element, which is called coding optics, and then the resultant field is captured by a monochrome image sensor. The original complex field is reconstructed from the single captured intensity image by a phase retrieval algorithm with a support constraint of the coded aperture and a sparsity-based reconstruction algorithm based on compressive sensing. We also present theoretical conditions for the proposed method. As a demonstration, we numerically verified an application of this generalized framework for single-shot acquisition of depth-variant multispectral objects.

© 2015 Optical Society of America

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References

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2015 (1)

2014 (5)

2013 (1)

2012 (3)

2011 (1)

2010 (2)

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6, 506–509 (2010).
[Crossref]

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (1)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

2007 (1)

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Proc. 16, 2992–3004 (2007).
[Crossref]

1992 (1)

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

1984 (2)

R. H. T. Bates, “Uniqueness of solutions to two-dimensional Fourier phase problems for localized and positive images,” Comput. Vision, Graph. Image Process. 25, 205–217 (1984).
[Crossref]

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984).
[Crossref]

1982 (1)

Aino, M.

Banerjee, P. P.

Bates, R. H. T.

R. H. T. Bates, “Uniqueness of solutions to two-dimensional Fourier phase problems for localized and positive images,” Comput. Vision, Graph. Image Process. 25, 205–217 (1984).
[Crossref]

Batey, D. J.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref] [PubMed]

Bhaduri, B.

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Proc. 16, 2992–3004 (2007).
[Crossref]

Blu, T.

Brady, D. J.

Bunk, O.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Chacko, N.

Choi, K.

Claus, D.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref] [PubMed]

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Dierolf, M.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Dong, S.

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Info. Theory52, 1289–1306 (2006).
[Crossref]

Edwards, C.

Fatemi, E.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

Fienup, J. R.

Figueiredo, M. A. T.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Proc. 16, 2992–3004 (2007).
[Crossref]

Goddard, L. L.

Godden, T. M.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Horisaki, R.

Humphry, M. J.

Javidi, B.

Kewish, C. M.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

Liebling, M.

Lim, S.

Maiden, A. M.

Marks, D. L.

Menzel, A.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Nanda, P.

Nehmetallah, G.

Nguyen, T. H.

Ogura, Y.

Osher, S.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

Pfeiffer, F.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Pham, H.

Popescu, G.

Rivenson, Y.

Y. Rivenson and A. Stern, “Conditions for practicing compressive Fresnel holography,” Opt. Lett. 36, 3365–3367 (2011).
[Crossref] [PubMed]

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6, 506–509 (2010).
[Crossref]

Rodenburg, J. M.

Rudin, L. I.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

Schneider, P.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

Shiradkar, R.

Stern, A.

Streibl, N.

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984).
[Crossref]

Suman, R.

Tanida, J.

Thibault, P.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Tian, L.

Waller, L.

Wepf, R.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

Zheng, G.

Zhou, R.

Adv. Opt. Photon. (2)

Appl. Opt. (1)

Biomed. Opt. Express (1)

Comput. Vision, Graph. Image Process. (1)

R. H. T. Bates, “Uniqueness of solutions to two-dimensional Fourier phase problems for localized and positive images,” Comput. Vision, Graph. Image Process. 25, 205–217 (1984).
[Crossref]

IEEE Trans. Image Proc. (1)

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Proc. 16, 2992–3004 (2007).
[Crossref]

J. Disp. Technol. (1)

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6, 506–509 (2010).
[Crossref]

J. Opt. Soc. Am. A (2)

Nature (1)

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
[Crossref] [PubMed]

Opt. Commun. (1)

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Optica (1)

Phys. D (1)

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

Science (1)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Ultramicroscopy (1)

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref] [PubMed]

Other (3)

“The USC-SIPI Image Database,” http://sipi.usc.edu/database/ .

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

D. L. Donoho, “Compressed sensing,” IEEE Trans. Info. Theory52, 1289–1306 (2006).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of multidimensional SPICA.

Fig. 2
Fig. 2

Simulation of multidimensional SPICA. The (a) amplitude and (b) phase of a color object at the distance z1. The (c) amplitude and (d) phase of the color object at the distance z2. (e) A magnified image (pixel count, 30 × 30) of the coded aperture. (f) The captured intensity image. The (g) amplitude and (h) phase of the reconstruction at the distance z1. The (i) amplitude and (j) phase of the reconstruction at the distance z2. Phases are normalized in the interval [−π,π].

Fig. 3
Fig. 3

Effects for the reconstruction fidelity by (a) the measurement noise level and (b) the error of the CA-based support constraint.

Fig. 4
Fig. 4

Relationship between the relative sparsity q and the numbers Nz and Nλ of depth channels and spectral channels. The numerically and analytically calculated relative spar-sities q are shown with the blue dots and the red grid, respectively.

Equations (16)

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

a = M I coh Pf .
g = I inc | Ea | 2 .
a = [ M 0 0 0 0 M 0 0 0 0 0 0 M 0 ] × [ I 0 coh 0 0 0 I 0 coh 0 0 0 0 0 I 0 coh ] × [ P 1 , 1 0 0 0 P 2 , 1 0 0 0 0 0 P N c coh , N c inc ] f .
g = [ I 0 I 0 I 0 ] × | [ E 1 0 0 0 E 2 0 0 0 0 0 E N c inc ] a | 2 .
h ^ C inc ( U ) = ( | h C inc ( U ) | 2 g ( U ) C inc | h C inc ( U ) | 2 ) exp ( i arg ( h C inc ( U ) ) ) ,
f ^ = arg min f a ^ M I coh Pf 2 + τ ( f ) ,
A ( s , λ ) = M ( s ) P ( s x , z , λ ) F ( x , z , λ ) d x d z ,
G ( u ) = | P ( u s , z A , λ ) A ( s , λ ) d s | 2 d λ ,
z z min = N x δ x 2 λ ,
N CFH σ K log ( N x 2 N z ) N λ ,
z A z A min = ρ 2 D N λ δ x 2 λ ,
N P N P max = N x 2 ρ 2 D N λ .
1 ρ 2 D log ( N x 2 N z ) σ K N x 2 = σ q ,
δ x min = λ z N x δ x ,
δ z min = 4 λ z 2 N x 2 δ x 2 .
δ λ min = δ x 2 2.44 z A .

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