Abstract

Volume holographic imaging (VHI) is a promising biomedical imaging tool that can simultaneously provide multi-depth or multispectral information. When a VHI system is probed with a broadband source, the intensity spreads in the horizontal direction, causing degradation of the image contrast. We theoretically analyzed the reason of the horizontal intensity spread, and the analysis was validated by the simulation and experimental results of the broadband impulse response of the VHI system. We proposed a deconvolution method to reduce the horizontal intensity spread and increase the image contrast. Imaging experiments with three different objects, including bright field illuminated USAF test target and lung tissue specimen and fluorescent beads, were carried out to test the performance of the proposed method. The results demonstrated that the proposed method can significantly improve the horizontal contrast of the image acquire by broadband VHI system.

© 2016 Optical Society of America

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References

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  1. A. Sinha and G. Barbastathis, “Volume holographic imaging for surface metrology at long working distances,” Opt. Express 11(24), 3202–3209 (2003).
    [Crossref] [PubMed]
  2. W. Liu, G. Barbastathis, and D. Psaltis, “Volume holographic hyperspectral imaging,” Appl. Opt. 43(18), 3581–3599 (2004).
    [Crossref] [PubMed]
  3. Y. Lv, J. Zhang, F. Liu, J. Shi, H. Guang, J. Bai, and J. Luo, “Spectral selective fluorescence molecular imaging with volume holographic imaging system,” J. Innov. Opt. Heal. Sci. 09(5), 1650010 (2016).
    [Crossref]
  4. Y. Luo, P. J. Gelsinger-Austin, J. M. Watson, G. Barbastathis, J. K. Barton, and R. K. Kostuk, “Laser-induced fluorescence imaging of subsurface tissue structures with a volume holographic spatial-spectral imaging system,” Opt. Lett. 33(18), 2098–2100 (2008).
    [Crossref] [PubMed]
  5. C. Y. Lin, W. T. Lin, H. H. Chen, J. M. Wong, V. R. Singh, and Y. Luo, “Talbot multi-focal holographic fluorescence endoscopy for optically sectioned imaging,” Opt. Lett. 41(2), 344 (2016).
    [Crossref] [PubMed]
  6. W. Liu, D. Psaltis, and G. Barbastathis, “Real-time spectral imaging in three spatial dimensions,” Opt. Lett. 27(10), 854–856 (2002).
    [Crossref]
  7. A. Sinha and G. Barbastathis, “Broadband volume holographic imaging,” Appl. Opt. 43(27), 5214–5221 (2004).
    [Crossref] [PubMed]
  8. W. Sun and G. Barbastathis, “Rainbow volume holographic imaging,” Opt. Lett. 30(9), 976–978 (2005).
    [Crossref] [PubMed]
  9. E. E. de Leon, J. W. Brownlee, P. Gelsinger-Austin, and R. K. Kostuk, “Dual-grating confocal-rainbow volume holographic imaging system designs for high depth resolution,” Appl. Opt. 51(29), 6952–6961 (2012).
    [Crossref] [PubMed]
  10. Y. Lv, J. Zhang, D. Zhang, W. Cai, N. Chen, and J. Luo, “In vivo simultaneous multispectral fluorescence imaging with spectral multiplexed volume holographic imaging system,” J. Biomed Opt. 21(6), 060502 (2016).
    [Crossref]
  11. D. Walter, A. Liu, E. Franklin, D. Macdonald, B. Mitchell, and T. Trupke, “Contrast enhancement of luminescence images via point-spread deconvolution,” in Proceedings of IEEE Photovoltaic Specialists Conference (PVSC) (IEEE, 2012), pp. 307–312.
  12. H. H. Chen, S. B. Oh, X. Zhai, J. C. Tsai, L. C. Cao, G. Barbastathis, and Y. Luo, “Wigner analysis of three dimensional pupil with finite lateral aperture,” Opt. Express 23(4), 4046–4054 (2015).
    [Crossref] [PubMed]
  13. Se Baek Oh, “Volume holographic pupils in ray, wave, statistical optics, and wigner space,” Ph.D. dissertation (Massachusetts Institute of Technology, 2009).
  14. P. Wissmann, Se Baek Oh, and G. Barbastathis, “Simulation and optimization of volume holographic imaging systems in zemax,” Opt. Express 16(10), 7516–7524 (2008).
    [Crossref] [PubMed]
  15. P. Günter, J. Huignard, and G. Barbastathis, “The transfer function of volume holographic optical systems,” in Photorefractive Materials and Their Applications 3, H. E. Fellows, ed. (Springer, 2007).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  19. J. Shi, F. Liu, H. Pu, S. Zuo, J. Luo, and J. Bai, “An adaptive support driven reweighted l1-regularization algorithm for fluorescence molecular tomography,” Biomed. Opt. Express 5(11), 4039–4052 (2014).
    [Crossref] [PubMed]
  20. B. Amizic, L. Spinoulas, R. Molina, and A. K. Katsaggelos, “Compressive blind image deconvolution,” IEEE Transactions on Image Processing A Publication of the IEEE Signal Processing Society 22(10), 3994–4006 (2013).
    [Crossref] [PubMed]
  21. B. A. Scalettar, J. R. Swedlow, J. W. Sedat, and D. A. Agard, “Dispersion, aberration and deconvolution in multi-wavelength fluorescence images,” J. Microsc-Oxford 182(Pt 1), 50–60 (1996).
    [Crossref]
  22. H. Yang, Y. Chiao, P. Huang, and S. Lai, “Blind image deblurring with modified richardson-lucy deconvolution for ringing artifact suppression,” in Proceedings of Advances in Image and Video Technology - Pacific Rim Symposium, Y. Ho, ed. (Springer, 2011), pp. 240–251.

2016 (3)

Y. Lv, J. Zhang, F. Liu, J. Shi, H. Guang, J. Bai, and J. Luo, “Spectral selective fluorescence molecular imaging with volume holographic imaging system,” J. Innov. Opt. Heal. Sci. 09(5), 1650010 (2016).
[Crossref]

Y. Lv, J. Zhang, D. Zhang, W. Cai, N. Chen, and J. Luo, “In vivo simultaneous multispectral fluorescence imaging with spectral multiplexed volume holographic imaging system,” J. Biomed Opt. 21(6), 060502 (2016).
[Crossref]

C. Y. Lin, W. T. Lin, H. H. Chen, J. M. Wong, V. R. Singh, and Y. Luo, “Talbot multi-focal holographic fluorescence endoscopy for optically sectioned imaging,” Opt. Lett. 41(2), 344 (2016).
[Crossref] [PubMed]

2015 (1)

2014 (2)

2013 (1)

B. Amizic, L. Spinoulas, R. Molina, and A. K. Katsaggelos, “Compressive blind image deconvolution,” IEEE Transactions on Image Processing A Publication of the IEEE Signal Processing Society 22(10), 3994–4006 (2013).
[Crossref] [PubMed]

2012 (1)

2011 (1)

2008 (2)

2005 (1)

2004 (2)

2003 (1)

2002 (1)

1996 (1)

B. A. Scalettar, J. R. Swedlow, J. W. Sedat, and D. A. Agard, “Dispersion, aberration and deconvolution in multi-wavelength fluorescence images,” J. Microsc-Oxford 182(Pt 1), 50–60 (1996).
[Crossref]

Agard, D. A.

B. A. Scalettar, J. R. Swedlow, J. W. Sedat, and D. A. Agard, “Dispersion, aberration and deconvolution in multi-wavelength fluorescence images,” J. Microsc-Oxford 182(Pt 1), 50–60 (1996).
[Crossref]

Amizic, B.

B. Amizic, L. Spinoulas, R. Molina, and A. K. Katsaggelos, “Compressive blind image deconvolution,” IEEE Transactions on Image Processing A Publication of the IEEE Signal Processing Society 22(10), 3994–4006 (2013).
[Crossref] [PubMed]

Andalman, A.

Bai, J.

Y. Lv, J. Zhang, F. Liu, J. Shi, H. Guang, J. Bai, and J. Luo, “Spectral selective fluorescence molecular imaging with volume holographic imaging system,” J. Innov. Opt. Heal. Sci. 09(5), 1650010 (2016).
[Crossref]

J. Shi, F. Liu, H. Pu, S. Zuo, J. Luo, and J. Bai, “An adaptive support driven reweighted l1-regularization algorithm for fluorescence molecular tomography,” Biomed. Opt. Express 5(11), 4039–4052 (2014).
[Crossref] [PubMed]

Barbastathis, G.

H. H. Chen, S. B. Oh, X. Zhai, J. C. Tsai, L. C. Cao, G. Barbastathis, and Y. Luo, “Wigner analysis of three dimensional pupil with finite lateral aperture,” Opt. Express 23(4), 4046–4054 (2015).
[Crossref] [PubMed]

J. M. Castro, J. Brownlee, Y. Luo, E. de Leon, J. K. Barton, G. Barbastathis, and R. K. Kostuk, “Spatial spectral volume holographic systems: resolution dependence on effective thickness,” Appl. Opt. 50(7), 1038–1046 (2011).
[Crossref] [PubMed]

P. Wissmann, Se Baek Oh, and G. Barbastathis, “Simulation and optimization of volume holographic imaging systems in zemax,” Opt. Express 16(10), 7516–7524 (2008).
[Crossref] [PubMed]

Y. Luo, P. J. Gelsinger-Austin, J. M. Watson, G. Barbastathis, J. K. Barton, and R. K. Kostuk, “Laser-induced fluorescence imaging of subsurface tissue structures with a volume holographic spatial-spectral imaging system,” Opt. Lett. 33(18), 2098–2100 (2008).
[Crossref] [PubMed]

W. Sun and G. Barbastathis, “Rainbow volume holographic imaging,” Opt. Lett. 30(9), 976–978 (2005).
[Crossref] [PubMed]

A. Sinha and G. Barbastathis, “Broadband volume holographic imaging,” Appl. Opt. 43(27), 5214–5221 (2004).
[Crossref] [PubMed]

W. Liu, G. Barbastathis, and D. Psaltis, “Volume holographic hyperspectral imaging,” Appl. Opt. 43(18), 3581–3599 (2004).
[Crossref] [PubMed]

A. Sinha and G. Barbastathis, “Volume holographic imaging for surface metrology at long working distances,” Opt. Express 11(24), 3202–3209 (2003).
[Crossref] [PubMed]

W. Liu, D. Psaltis, and G. Barbastathis, “Real-time spectral imaging in three spatial dimensions,” Opt. Lett. 27(10), 854–856 (2002).
[Crossref]

P. Günter, J. Huignard, and G. Barbastathis, “The transfer function of volume holographic optical systems,” in Photorefractive Materials and Their Applications 3, H. E. Fellows, ed. (Springer, 2007).

Barton, J. K.

Brownlee, J.

Brownlee, J. W.

Broxton, M.

Cai, W.

Y. Lv, J. Zhang, D. Zhang, W. Cai, N. Chen, and J. Luo, “In vivo simultaneous multispectral fluorescence imaging with spectral multiplexed volume holographic imaging system,” J. Biomed Opt. 21(6), 060502 (2016).
[Crossref]

Cao, L. C.

Castro, J. M.

Chen, H. H.

Chen, N.

Y. Lv, J. Zhang, D. Zhang, W. Cai, N. Chen, and J. Luo, “In vivo simultaneous multispectral fluorescence imaging with spectral multiplexed volume holographic imaging system,” J. Biomed Opt. 21(6), 060502 (2016).
[Crossref]

Chiao, Y.

H. Yang, Y. Chiao, P. Huang, and S. Lai, “Blind image deblurring with modified richardson-lucy deconvolution for ringing artifact suppression,” in Proceedings of Advances in Image and Video Technology - Pacific Rim Symposium, Y. Ho, ed. (Springer, 2011), pp. 240–251.

Cohen, N.

de Leon, E.

de Leon, E. E.

Deisseroth, K.

Franklin, E.

D. Walter, A. Liu, E. Franklin, D. Macdonald, B. Mitchell, and T. Trupke, “Contrast enhancement of luminescence images via point-spread deconvolution,” in Proceedings of IEEE Photovoltaic Specialists Conference (PVSC) (IEEE, 2012), pp. 307–312.

Gelsinger-Austin, P.

Gelsinger-Austin, P. J.

Grosenick, L.

Guang, H.

Y. Lv, J. Zhang, F. Liu, J. Shi, H. Guang, J. Bai, and J. Luo, “Spectral selective fluorescence molecular imaging with volume holographic imaging system,” J. Innov. Opt. Heal. Sci. 09(5), 1650010 (2016).
[Crossref]

Günter, P.

P. Günter, J. Huignard, and G. Barbastathis, “The transfer function of volume holographic optical systems,” in Photorefractive Materials and Their Applications 3, H. E. Fellows, ed. (Springer, 2007).

Hansen, P. C.

P. C. Hansen, J. G. Nagy, and D. P. O’Leary, Deblurring Images: Matrices, Spectra, and Filtering (SIAM, 2006).
[Crossref]

Horowitz, M.

Huang, P.

H. Yang, Y. Chiao, P. Huang, and S. Lai, “Blind image deblurring with modified richardson-lucy deconvolution for ringing artifact suppression,” in Proceedings of Advances in Image and Video Technology - Pacific Rim Symposium, Y. Ho, ed. (Springer, 2011), pp. 240–251.

Huignard, J.

P. Günter, J. Huignard, and G. Barbastathis, “The transfer function of volume holographic optical systems,” in Photorefractive Materials and Their Applications 3, H. E. Fellows, ed. (Springer, 2007).

Katsaggelos, A. K.

B. Amizic, L. Spinoulas, R. Molina, and A. K. Katsaggelos, “Compressive blind image deconvolution,” IEEE Transactions on Image Processing A Publication of the IEEE Signal Processing Society 22(10), 3994–4006 (2013).
[Crossref] [PubMed]

Kostuk, R. K.

Lai, S.

H. Yang, Y. Chiao, P. Huang, and S. Lai, “Blind image deblurring with modified richardson-lucy deconvolution for ringing artifact suppression,” in Proceedings of Advances in Image and Video Technology - Pacific Rim Symposium, Y. Ho, ed. (Springer, 2011), pp. 240–251.

Levoy, M.

Lin, C. Y.

Lin, W. T.

Liu, A.

D. Walter, A. Liu, E. Franklin, D. Macdonald, B. Mitchell, and T. Trupke, “Contrast enhancement of luminescence images via point-spread deconvolution,” in Proceedings of IEEE Photovoltaic Specialists Conference (PVSC) (IEEE, 2012), pp. 307–312.

Liu, F.

Y. Lv, J. Zhang, F. Liu, J. Shi, H. Guang, J. Bai, and J. Luo, “Spectral selective fluorescence molecular imaging with volume holographic imaging system,” J. Innov. Opt. Heal. Sci. 09(5), 1650010 (2016).
[Crossref]

J. Shi, F. Liu, H. Pu, S. Zuo, J. Luo, and J. Bai, “An adaptive support driven reweighted l1-regularization algorithm for fluorescence molecular tomography,” Biomed. Opt. Express 5(11), 4039–4052 (2014).
[Crossref] [PubMed]

Liu, W.

Luo, J.

Y. Lv, J. Zhang, F. Liu, J. Shi, H. Guang, J. Bai, and J. Luo, “Spectral selective fluorescence molecular imaging with volume holographic imaging system,” J. Innov. Opt. Heal. Sci. 09(5), 1650010 (2016).
[Crossref]

Y. Lv, J. Zhang, D. Zhang, W. Cai, N. Chen, and J. Luo, “In vivo simultaneous multispectral fluorescence imaging with spectral multiplexed volume holographic imaging system,” J. Biomed Opt. 21(6), 060502 (2016).
[Crossref]

J. Shi, F. Liu, H. Pu, S. Zuo, J. Luo, and J. Bai, “An adaptive support driven reweighted l1-regularization algorithm for fluorescence molecular tomography,” Biomed. Opt. Express 5(11), 4039–4052 (2014).
[Crossref] [PubMed]

Luo, Y.

Lv, Y.

Y. Lv, J. Zhang, D. Zhang, W. Cai, N. Chen, and J. Luo, “In vivo simultaneous multispectral fluorescence imaging with spectral multiplexed volume holographic imaging system,” J. Biomed Opt. 21(6), 060502 (2016).
[Crossref]

Y. Lv, J. Zhang, F. Liu, J. Shi, H. Guang, J. Bai, and J. Luo, “Spectral selective fluorescence molecular imaging with volume holographic imaging system,” J. Innov. Opt. Heal. Sci. 09(5), 1650010 (2016).
[Crossref]

Macdonald, D.

D. Walter, A. Liu, E. Franklin, D. Macdonald, B. Mitchell, and T. Trupke, “Contrast enhancement of luminescence images via point-spread deconvolution,” in Proceedings of IEEE Photovoltaic Specialists Conference (PVSC) (IEEE, 2012), pp. 307–312.

Mitchell, B.

D. Walter, A. Liu, E. Franklin, D. Macdonald, B. Mitchell, and T. Trupke, “Contrast enhancement of luminescence images via point-spread deconvolution,” in Proceedings of IEEE Photovoltaic Specialists Conference (PVSC) (IEEE, 2012), pp. 307–312.

Molina, R.

B. Amizic, L. Spinoulas, R. Molina, and A. K. Katsaggelos, “Compressive blind image deconvolution,” IEEE Transactions on Image Processing A Publication of the IEEE Signal Processing Society 22(10), 3994–4006 (2013).
[Crossref] [PubMed]

Nagy, J. G.

P. C. Hansen, J. G. Nagy, and D. P. O’Leary, Deblurring Images: Matrices, Spectra, and Filtering (SIAM, 2006).
[Crossref]

O’Leary, D. P.

P. C. Hansen, J. G. Nagy, and D. P. O’Leary, Deblurring Images: Matrices, Spectra, and Filtering (SIAM, 2006).
[Crossref]

Oh, S. B.

Oh, Se Baek

P. Wissmann, Se Baek Oh, and G. Barbastathis, “Simulation and optimization of volume holographic imaging systems in zemax,” Opt. Express 16(10), 7516–7524 (2008).
[Crossref] [PubMed]

Se Baek Oh, “Volume holographic pupils in ray, wave, statistical optics, and wigner space,” Ph.D. dissertation (Massachusetts Institute of Technology, 2009).

Psaltis, D.

Pu, H.

Scalettar, B. A.

B. A. Scalettar, J. R. Swedlow, J. W. Sedat, and D. A. Agard, “Dispersion, aberration and deconvolution in multi-wavelength fluorescence images,” J. Microsc-Oxford 182(Pt 1), 50–60 (1996).
[Crossref]

Sedat, J. W.

B. A. Scalettar, J. R. Swedlow, J. W. Sedat, and D. A. Agard, “Dispersion, aberration and deconvolution in multi-wavelength fluorescence images,” J. Microsc-Oxford 182(Pt 1), 50–60 (1996).
[Crossref]

Shi, J.

Y. Lv, J. Zhang, F. Liu, J. Shi, H. Guang, J. Bai, and J. Luo, “Spectral selective fluorescence molecular imaging with volume holographic imaging system,” J. Innov. Opt. Heal. Sci. 09(5), 1650010 (2016).
[Crossref]

J. Shi, F. Liu, H. Pu, S. Zuo, J. Luo, and J. Bai, “An adaptive support driven reweighted l1-regularization algorithm for fluorescence molecular tomography,” Biomed. Opt. Express 5(11), 4039–4052 (2014).
[Crossref] [PubMed]

Singh, V. R.

Sinha, A.

Spinoulas, L.

B. Amizic, L. Spinoulas, R. Molina, and A. K. Katsaggelos, “Compressive blind image deconvolution,” IEEE Transactions on Image Processing A Publication of the IEEE Signal Processing Society 22(10), 3994–4006 (2013).
[Crossref] [PubMed]

Sun, W.

Swedlow, J. R.

B. A. Scalettar, J. R. Swedlow, J. W. Sedat, and D. A. Agard, “Dispersion, aberration and deconvolution in multi-wavelength fluorescence images,” J. Microsc-Oxford 182(Pt 1), 50–60 (1996).
[Crossref]

Trupke, T.

D. Walter, A. Liu, E. Franklin, D. Macdonald, B. Mitchell, and T. Trupke, “Contrast enhancement of luminescence images via point-spread deconvolution,” in Proceedings of IEEE Photovoltaic Specialists Conference (PVSC) (IEEE, 2012), pp. 307–312.

Tsai, J. C.

Walter, D.

D. Walter, A. Liu, E. Franklin, D. Macdonald, B. Mitchell, and T. Trupke, “Contrast enhancement of luminescence images via point-spread deconvolution,” in Proceedings of IEEE Photovoltaic Specialists Conference (PVSC) (IEEE, 2012), pp. 307–312.

Watson, J. M.

Wissmann, P.

Wong, J. M.

Yang, H.

H. Yang, Y. Chiao, P. Huang, and S. Lai, “Blind image deblurring with modified richardson-lucy deconvolution for ringing artifact suppression,” in Proceedings of Advances in Image and Video Technology - Pacific Rim Symposium, Y. Ho, ed. (Springer, 2011), pp. 240–251.

Yang, S.

Zhai, X.

Zhang, D.

Y. Lv, J. Zhang, D. Zhang, W. Cai, N. Chen, and J. Luo, “In vivo simultaneous multispectral fluorescence imaging with spectral multiplexed volume holographic imaging system,” J. Biomed Opt. 21(6), 060502 (2016).
[Crossref]

Zhang, J.

Y. Lv, J. Zhang, F. Liu, J. Shi, H. Guang, J. Bai, and J. Luo, “Spectral selective fluorescence molecular imaging with volume holographic imaging system,” J. Innov. Opt. Heal. Sci. 09(5), 1650010 (2016).
[Crossref]

Y. Lv, J. Zhang, D. Zhang, W. Cai, N. Chen, and J. Luo, “In vivo simultaneous multispectral fluorescence imaging with spectral multiplexed volume holographic imaging system,” J. Biomed Opt. 21(6), 060502 (2016).
[Crossref]

Zuo, S.

Appl. Opt. (4)

Biomed. Opt. Express (1)

IEEE Transactions on Image Processing A Publication of the IEEE Signal Processing Society (1)

B. Amizic, L. Spinoulas, R. Molina, and A. K. Katsaggelos, “Compressive blind image deconvolution,” IEEE Transactions on Image Processing A Publication of the IEEE Signal Processing Society 22(10), 3994–4006 (2013).
[Crossref] [PubMed]

J. Biomed Opt. (1)

Y. Lv, J. Zhang, D. Zhang, W. Cai, N. Chen, and J. Luo, “In vivo simultaneous multispectral fluorescence imaging with spectral multiplexed volume holographic imaging system,” J. Biomed Opt. 21(6), 060502 (2016).
[Crossref]

J. Innov. Opt. Heal. Sci. (1)

Y. Lv, J. Zhang, F. Liu, J. Shi, H. Guang, J. Bai, and J. Luo, “Spectral selective fluorescence molecular imaging with volume holographic imaging system,” J. Innov. Opt. Heal. Sci. 09(5), 1650010 (2016).
[Crossref]

J. Microsc-Oxford (1)

B. A. Scalettar, J. R. Swedlow, J. W. Sedat, and D. A. Agard, “Dispersion, aberration and deconvolution in multi-wavelength fluorescence images,” J. Microsc-Oxford 182(Pt 1), 50–60 (1996).
[Crossref]

Opt. Express (4)

Opt. Lett. (4)

Other (5)

H. Yang, Y. Chiao, P. Huang, and S. Lai, “Blind image deblurring with modified richardson-lucy deconvolution for ringing artifact suppression,” in Proceedings of Advances in Image and Video Technology - Pacific Rim Symposium, Y. Ho, ed. (Springer, 2011), pp. 240–251.

D. Walter, A. Liu, E. Franklin, D. Macdonald, B. Mitchell, and T. Trupke, “Contrast enhancement of luminescence images via point-spread deconvolution,” in Proceedings of IEEE Photovoltaic Specialists Conference (PVSC) (IEEE, 2012), pp. 307–312.

Se Baek Oh, “Volume holographic pupils in ray, wave, statistical optics, and wigner space,” Ph.D. dissertation (Massachusetts Institute of Technology, 2009).

P. Günter, J. Huignard, and G. Barbastathis, “The transfer function of volume holographic optical systems,” in Photorefractive Materials and Their Applications 3, H. E. Fellows, ed. (Springer, 2007).

P. C. Hansen, J. G. Nagy, and D. P. O’Leary, Deblurring Images: Matrices, Spectra, and Filtering (SIAM, 2006).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 The k-sphere diagrams for procedures of recording and readout VHG. (a) Two coherent plane waves interfere within the material and the recorded 3D interference pattern within the volume works as a 3D Fourier filter. (b) The VHG can be Bragg matched when the probe wave-vector coincides with the reference wave-vector in (a). (c) When the direction of the probe vector deviates Δθr from the reference vector, the Bragg matched condition is not satisfied, although the diffraction field can still be obtained. The diffraction efficiency is affected by the magnitude of the mismatch vector δkd. (d) For a grating vector, Kg can be Bragg matched with different pairs of wave-vector with corresponding tilting angles.
Fig. 2
Fig. 2 Schematic layout of a standard VHI system, where f1 and f 2 are the focal lengths of the objective lens and imaging lens, respectively. a and L are the lateral aperture and thickness of the VHG respectively. xf, xs, and xp represent the positions of the reference point source, signal point source and probe point source, respectively. θs is the inter-angle between the reference beam and signal beam.
Fig. 3
Fig. 3 Experimentally characterized horizontal blurring in the broadband VHI. The USAF test target chart is focused and illuminated with transmission mode. (a) Image acquired without using the VHG. (b) Diffracted image acquired with the VHG placed on the Fourier plane. The horizontal contrast shows a significant reduction, while the vertical contrast is less affected. The average plots of Group 3 Class 5 marked with blue and red dashed rectangles are provided in (a) and (b). And (c) and (d) are the intensity profiles along the line perpendicular to the stripes in (a) and (b), respectively.
Fig. 4
Fig. 4 The (a, b) simulation and (c, d) experimental measurements of probing a 4f VHI system with point source. Diffraction pattern of (a) monochromatic point source and (b) broadband point source. The simulation system consists a slab-shaped VHG with a = 22 mm, L = 1.8 mm, and the focal length of the objective lens and imaging lens are f1 = 100 mm and f2 = 75 mm, respectively. The experimental results of probing a 4f VHI system with (c) collimated monochromatic laser beam and (d) white light point source, respectively. The slab-shaped VHG has a diameter a = 22 mm, thickness L = 1.8 mm, the focal lengths of objective lens and imaging lens are f1 = 100 mm and f2 = 75 mm, respectively. The point source is created by illuminate a 25-μm pinhole with white light source. Each figure is normalized by its peak value.
Fig. 5
Fig. 5 Experimentally observed diffraction patterns along different horizontal positions. (a) The intensity profiles (marked with red line) when the 536 ± 20 nm (FWHM bandwidth 40 nm) point source passing through the peak of the main lobe. (b) The diffraction pattern of the 25 μm point source uniformly illuminated with a 536 ± 20 nm broadband source. (c) and (d) are the diffraction intensity fluctuations (marked with blue lines) during the process of moving the 536 ± 20 nm and 530 ± 5 nm point source horizontally. The distance of the movement is 2.0 mm. And the coefficient of variation (CV) around the mean diffraction intensity (marked with red line) of the 536 ± 20 nm point source is within 4.0%, while the CV of the 530 ± 5 nm point source is larger than 46.8%.
Fig. 6
Fig. 6 Images of the USAF test target captured by a standard broadband 4f VHI system. (a) and (b) are the images when the target is illuminate with 536 ± 20 nm and 530 ± 5 nm source in transmission mode, respectively. (c) The relationship between the lateral FOV and the bandwidth. (e) Image after deconvolution of (d) image acquired by broadband VHI system with the aforementioned optical model. The average plots of Group 3 Class 5 in (d) and (e) (marked with blue and red dashed rectangles, respectively) in (f) show that the image contrast is significantly improved.
Fig. 7
Fig. 7 Horizontal contrast comparison of the USAF test target at regions with different line widths. In each region, the image contrast is significantly alleviated by using the deconvolution method.
Fig. 8
Fig. 8 Images of broadband illuminated (536 ± 20 nm) lung tissue section, obtained from an eigth-week nude mouse. (a) The broadband illuminated image acquired by the 4f VHI system without using the VHG. (b) The deconvolution results of (a) with PSF acquired with the 4f VHI system without VHG. (c) The diffraction image acquired with the VHG placed on the Fourier plane of the 4f VHI system, and (d) the reconstructed image with the deconvolution method. The unit of these images in both the vertical and horizontal directions is the size of CCD pixel (6.45 μm in width).
Fig. 9
Fig. 9 The images of two adjacent 15 μm fluorescence beads. (a) The ground truth image acquired with the 4f VHI system without using the VHG. (b) The reconstructed rersult of (a) with the PSF acquired without using VHG. (c) The image acquired with the VHG on the Fourier plane of the 4f VHI system. (d) The reconstructed image of the two microspheres.
Fig. 10
Fig. 10 The extent of horizontal intensity spread as a function of the focal length of objective lens and the thickness of prerecorded VHG. (a) For a fixed magnification factor m, longer focal length results in larger spread extent. (b) For a fixed 4f system structure, increased thickness of the VHG results in better performance in suppressing the horizontal intensity spread.

Equations (15)

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K g = k s k r ,
C t h r = I m a x I m i n I m a x + I m i n ,
h ( x , y ; x , y ) = s i n c [ a ( x λ p f 1 + x λ p f 2 x s x f λ f f 1 ) ] s i n c [ b ( y λ p f 1 + y λ p f 2 ) ] s i n c [ L 2 ( x 2 + y 2 λ p f 1 2 x 2 + y 2 λ p f 2 2 x s 2 y f 2 λ f f 1 2 ) ] ,
q ( x , y ) = p ( x , y ) h ( x , y ; x , y ) d x d y ,
μ = λ p λ f ,
q ( x , y ) = s i n c [ a x + μ m x s + m ( x μ x f ) λ p f 2 ] s i n c [ b y + m y λ p f 2 ] s i n c [ L ( μ m 2 x s 2 x 2 ) + m 2 ( x 2 μ x f 2 ) 2 λ p f 2 2 ] ,
x = μ m x s ,
x = μ m x s m Δ μ x f ,
| q ( x , y , μ ) | 2 = x , y d x d y 1 Δ μ 1 + Δ μ | p ( x , y , τ ) | 2 | h ( x , y ; x , y , τ ) | 2 d τ , = x , y d x d y 1 Δ μ 1 + Δ μ | p ( x , y , τ ) | 2 s i n c 2 [ a x + τ m x s + m x m τ x f λ p f 2 ] × s i n c 2 [ b y + m y λ p f 2 ] s i n c 2 [ L ( x s 2 x f 2 ) τ m 2 + ( x 2 + y 2 ) m 2 ( x 2 + y 2 ) ) 2 λ p f 2 2 ] d τ ,
I i m g ( x , y , μ ) = x , y d x d y 1 Δ μ 1 + Δ μ | g i l l u m ( x , y , τ ) | 2 | h ( x , y ; x , y , τ ) | 2 d τ ,
b = Ax + e ,
x f i l t = V f i l t 1 U T b ,
F O V = B θ s f o b j λ ¯ ,
P S N R = 10 × l o g 10 [ ( 2 n 1 ) 2 M S E ] ,
Δ x = m 2 λ f L f 1 θ s ,

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