Abstract

To reach the limiting resolution of a digital holographic system and improve the displaying quality of the reconstructed image, the subdivision convolution algorithm and the subdivision Fresnel algorithm are presented, respectively. The obtained results show that the lateral size of the reconstructed image obtained by two kinds of subdivision algorithms is the same in the central region of the reconstructed image-plane; moreover, the size of the central region is in proportional to the recording distance. Importantly, in the central region of the reconstructed image-plane, the reconstruction can be performed by the subdivision Fresnel algorithm instead of the subdivision convolution algorithm effectively, and, based on these subdivision approaches, both the displaying quality and the resolution of the reconstructed image can be improved significantly. Furthermore, in the reconstruction of the digital hologram with the large numerical aperture, the computer's memory consumed and the calculating time resulting from the subdivision Fresnel algorithm is significantly less than those from the subdivision convolution algorithm.

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  1. J. W. Goodman and P. W. Lawrence, “Digital image formulation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
    [CrossRef]
  2. D. D. Aguayo, F. Mendoza Santoyo, M. H. De la Torre-I, M. D. Salas-Araiza, C. Caloca-Mendez, and D. A. Gutierrez Hernandez, “Insect wing deformation measurements using high speed digital holographic interferometry,” Opt. Express 18(6), 5661–5667 (2010).
    [CrossRef] [PubMed]
  3. F. Joud, F. Laloë, M. Atlan, J. Hare, and M. Gross, “Imaging a vibrating object by Sideband Digital Holography,” Opt. Express 17(4), 2774–2779 (2009).
    [CrossRef] [PubMed]
  4. C. Trillo, A. F. Doval, F. Mendoza-Santoyo, C. Pérez-López, M. de la Torre-Ibarra, and J. L. Deán, “Multimode vibration analysis with high-speed TV holography and a spatiotemporal 3D Fourier transform method,” Opt. Express 17(20), 18014–18025 (2009).
    [CrossRef] [PubMed]
  5. C. J. Mann, P. R. Bingham, V. C. Paquit, and K. W. Tobin, “Quantitative phase imaging by three-wavelength digital holography,” Opt. Express 16(13), 9753–9764 (2008).
    [CrossRef] [PubMed]
  6. F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17(15), 13071–13079 (2009).
    [CrossRef] [PubMed]
  7. M. Salvador, J. Prauzner, S. Köber, K. Meerholz, J. J. Turek, K. Jeong, and D. D. Nolte, “Three-dimensional holographic imaging of living tissue using a highly sensitive photorefractive polymer device,” Opt. Express 17(14), 11834–11849 (2009).
    [CrossRef] [PubMed]
  8. W. Sun, J. Zhao, J. Di, Q. Wang, and L. Wang, “Real-time visualization of Karman vortex street in water flow field by using digital holography,” Opt. Express 17(22), 20342–20348 (2009).
    [CrossRef] [PubMed]
  9. X. Wu, G. Gréhan, S. Meunier-Guttin-Cluzel, L. Chen, and K. Cen, “Sizing of particles smaller than 5 microm in digital holographic microscopy,” Opt. Lett. 34(6), 857–859 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. J. W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005).
  12. U. Schnars and W. Jueptner, Digital Holography (Springer, Berlin, 2005).
  13. L. P. Chen and X. X. Lu, “The recording of digital hologram at short distance and reconstruction using convolution approach,” Chin. Phys. B 18(1), 189–194 (2009).
  14. A. V. Oppenheim, Signals & Systems (Pearson Education, Singapore, 1997).
  15. Q. Fan, J. L. Zhao, and S. Li, “Detail displaying and vision aberration rectifying of reconstructed image in digital holography,” Chin. J. Lasers 32, 1401–1405 (2005).
  16. H. Li, L. Zhong, Z. Ma, and X. Lu, “Joint approach of the sub-holograms in on-axis lensless Fourier phase-shifting synthetic aperture digital holography,” Opt. Commun. 284(9), 2268–2272 (2011).
    [CrossRef]

2011

H. Li, L. Zhong, Z. Ma, and X. Lu, “Joint approach of the sub-holograms in on-axis lensless Fourier phase-shifting synthetic aperture digital holography,” Opt. Commun. 284(9), 2268–2272 (2011).
[CrossRef]

2010

2009

F. Joud, F. Laloë, M. Atlan, J. Hare, and M. Gross, “Imaging a vibrating object by Sideband Digital Holography,” Opt. Express 17(4), 2774–2779 (2009).
[CrossRef] [PubMed]

C. Trillo, A. F. Doval, F. Mendoza-Santoyo, C. Pérez-López, M. de la Torre-Ibarra, and J. L. Deán, “Multimode vibration analysis with high-speed TV holography and a spatiotemporal 3D Fourier transform method,” Opt. Express 17(20), 18014–18025 (2009).
[CrossRef] [PubMed]

F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17(15), 13071–13079 (2009).
[CrossRef] [PubMed]

M. Salvador, J. Prauzner, S. Köber, K. Meerholz, J. J. Turek, K. Jeong, and D. D. Nolte, “Three-dimensional holographic imaging of living tissue using a highly sensitive photorefractive polymer device,” Opt. Express 17(14), 11834–11849 (2009).
[CrossRef] [PubMed]

W. Sun, J. Zhao, J. Di, Q. Wang, and L. Wang, “Real-time visualization of Karman vortex street in water flow field by using digital holography,” Opt. Express 17(22), 20342–20348 (2009).
[CrossRef] [PubMed]

X. Wu, G. Gréhan, S. Meunier-Guttin-Cluzel, L. Chen, and K. Cen, “Sizing of particles smaller than 5 microm in digital holographic microscopy,” Opt. Lett. 34(6), 857–859 (2009).
[CrossRef] [PubMed]

L. P. Chen and X. X. Lu, “The recording of digital hologram at short distance and reconstruction using convolution approach,” Chin. Phys. B 18(1), 189–194 (2009).

2008

2006

2005

Q. Fan, J. L. Zhao, and S. Li, “Detail displaying and vision aberration rectifying of reconstructed image in digital holography,” Chin. J. Lasers 32, 1401–1405 (2005).

1967

J. W. Goodman and P. W. Lawrence, “Digital image formulation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[CrossRef]

Aguayo, D. D.

Amato-Grill, J.

Atlan, M.

Bingham, P. R.

Caloca-Mendez, C.

Cen, K.

Chen, L.

Chen, L. P.

L. P. Chen and X. X. Lu, “The recording of digital hologram at short distance and reconstruction using convolution approach,” Chin. Phys. B 18(1), 189–194 (2009).

Cheong, F. C.

De la Torre-I, M. H.

de la Torre-Ibarra, M.

Deán, J. L.

Di, J.

Dixon, L.

Doval, A. F.

Dreyfus, R.

Fan, Q.

Q. Fan, J. L. Zhao, and S. Li, “Detail displaying and vision aberration rectifying of reconstructed image in digital holography,” Chin. J. Lasers 32, 1401–1405 (2005).

Goodman, J. W.

J. W. Goodman and P. W. Lawrence, “Digital image formulation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[CrossRef]

Gréhan, G.

Grier, D. G.

Gross, M.

Gutierrez Hernandez, D. A.

Hare, J.

Jeong, K.

Joud, F.

Kim, M. K.

Köber, S.

Laloë, F.

Lawrence, P. W.

J. W. Goodman and P. W. Lawrence, “Digital image formulation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[CrossRef]

Li, H.

H. Li, L. Zhong, Z. Ma, and X. Lu, “Joint approach of the sub-holograms in on-axis lensless Fourier phase-shifting synthetic aperture digital holography,” Opt. Commun. 284(9), 2268–2272 (2011).
[CrossRef]

Li, S.

Q. Fan, J. L. Zhao, and S. Li, “Detail displaying and vision aberration rectifying of reconstructed image in digital holography,” Chin. J. Lasers 32, 1401–1405 (2005).

Lu, X.

H. Li, L. Zhong, Z. Ma, and X. Lu, “Joint approach of the sub-holograms in on-axis lensless Fourier phase-shifting synthetic aperture digital holography,” Opt. Commun. 284(9), 2268–2272 (2011).
[CrossRef]

Lu, X. X.

L. P. Chen and X. X. Lu, “The recording of digital hologram at short distance and reconstruction using convolution approach,” Chin. Phys. B 18(1), 189–194 (2009).

Ma, Z.

H. Li, L. Zhong, Z. Ma, and X. Lu, “Joint approach of the sub-holograms in on-axis lensless Fourier phase-shifting synthetic aperture digital holography,” Opt. Commun. 284(9), 2268–2272 (2011).
[CrossRef]

Mann, C. J.

Meerholz, K.

Mendoza Santoyo, F.

Mendoza-Santoyo, F.

Meunier-Guttin-Cluzel, S.

Nolte, D. D.

Paquit, V. C.

Pérez-López, C.

Prauzner, J.

Salas-Araiza, M. D.

Salvador, M.

Sun, B.

Sun, W.

Tobin, K. W.

Trillo, C.

Turek, J. J.

Wang, L.

Wang, Q.

Wu, X.

Xiao, K.

Yu, L.

Zhao, J.

Zhao, J. L.

Q. Fan, J. L. Zhao, and S. Li, “Detail displaying and vision aberration rectifying of reconstructed image in digital holography,” Chin. J. Lasers 32, 1401–1405 (2005).

Zhong, L.

H. Li, L. Zhong, Z. Ma, and X. Lu, “Joint approach of the sub-holograms in on-axis lensless Fourier phase-shifting synthetic aperture digital holography,” Opt. Commun. 284(9), 2268–2272 (2011).
[CrossRef]

Appl. Phys. Lett.

J. W. Goodman and P. W. Lawrence, “Digital image formulation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[CrossRef]

Chin. J. Lasers

Q. Fan, J. L. Zhao, and S. Li, “Detail displaying and vision aberration rectifying of reconstructed image in digital holography,” Chin. J. Lasers 32, 1401–1405 (2005).

Chin. Phys. B

L. P. Chen and X. X. Lu, “The recording of digital hologram at short distance and reconstruction using convolution approach,” Chin. Phys. B 18(1), 189–194 (2009).

Opt. Commun.

H. Li, L. Zhong, Z. Ma, and X. Lu, “Joint approach of the sub-holograms in on-axis lensless Fourier phase-shifting synthetic aperture digital holography,” Opt. Commun. 284(9), 2268–2272 (2011).
[CrossRef]

Opt. Express

D. D. Aguayo, F. Mendoza Santoyo, M. H. De la Torre-I, M. D. Salas-Araiza, C. Caloca-Mendez, and D. A. Gutierrez Hernandez, “Insect wing deformation measurements using high speed digital holographic interferometry,” Opt. Express 18(6), 5661–5667 (2010).
[CrossRef] [PubMed]

F. Joud, F. Laloë, M. Atlan, J. Hare, and M. Gross, “Imaging a vibrating object by Sideband Digital Holography,” Opt. Express 17(4), 2774–2779 (2009).
[CrossRef] [PubMed]

C. Trillo, A. F. Doval, F. Mendoza-Santoyo, C. Pérez-López, M. de la Torre-Ibarra, and J. L. Deán, “Multimode vibration analysis with high-speed TV holography and a spatiotemporal 3D Fourier transform method,” Opt. Express 17(20), 18014–18025 (2009).
[CrossRef] [PubMed]

C. J. Mann, P. R. Bingham, V. C. Paquit, and K. W. Tobin, “Quantitative phase imaging by three-wavelength digital holography,” Opt. Express 16(13), 9753–9764 (2008).
[CrossRef] [PubMed]

F. C. Cheong, B. Sun, R. Dreyfus, J. Amato-Grill, K. Xiao, L. Dixon, and D. G. Grier, “Flow visualization and flow cytometry with holographic video microscopy,” Opt. Express 17(15), 13071–13079 (2009).
[CrossRef] [PubMed]

M. Salvador, J. Prauzner, S. Köber, K. Meerholz, J. J. Turek, K. Jeong, and D. D. Nolte, “Three-dimensional holographic imaging of living tissue using a highly sensitive photorefractive polymer device,” Opt. Express 17(14), 11834–11849 (2009).
[CrossRef] [PubMed]

W. Sun, J. Zhao, J. Di, Q. Wang, and L. Wang, “Real-time visualization of Karman vortex street in water flow field by using digital holography,” Opt. Express 17(22), 20342–20348 (2009).
[CrossRef] [PubMed]

Opt. Lett.

Other

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

U. Schnars and W. Jueptner, Digital Holography (Springer, Berlin, 2005).

A. V. Oppenheim, Signals & Systems (Pearson Education, Singapore, 1997).

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Figures (7)

Fig. 1
Fig. 1

Coordinates relationship between the object-plane (xO,yO), the recorded hologram-plane(xH,yH) and the reconstructed image-plane(xI,yI).

Fig. 2
Fig. 2

Scheme for the process of the hologram's frequency domain zero-padding operation.

Fig. 3
Fig. 3

Recorded phase-shifting digital holograms (a) one of four-step phase-shifting digital holograms in the recording distance ZOH = 65.7mm, (b) one of four-step phase-shifting digital holograms in the recording distance ZOH = 27.64mm.

Fig. 4
Fig. 4

Reconstructed results obtained from the original hologram directly in the recording distance ZOH = 65.71mm: (a) the reconstructed image obtained by the convolution algorithm; (b) the reconstructed image obtained by Fresnel algorithm; (c)the magnification marked with the white real line in (a); (d)the magnification marked with the white real line in (b); (e)the intensity distribution of one column marked with the black real arrow line in (c); (f)the intensity distribution of one column marked with the black real arrow line in (d).

Fig. 5
Fig. 5

Reconstructed results obtained from the original hologram directly in the recording distance ZOH = 27.64 mm: (a) the reconstructed obtained by the convolution algorithm; (b) the reconstructed obtained by Fresnel algorithm; (c)the magnification marked the white real line in (a); (d)the magnification marked the white real line in (b); (e)the intensity distribution of one column marked with the black real arrow line in (c); (f)the intensity distribution of one column marked with the black real arrow line in (d).

Fig. 6
Fig. 6

Reconstructed results obtained from different subdivision approaches in the recording distance ZOH = 65.71mm (a) the reconstructed image obtained by the subdivision convolution algorithm in which the hologram is implemented by the zero-padding operation in frequency domain (b) the reconstructed image obtained by the subdivision Fresnel algorithm in which the hologram is directly implemented by the zero-padding operation; (c)the magnification marked the white real line in area in (a); (d) the Magnification marked the white real line in (b); (e)Intensity distribution of the same column marked with the black real arrow line in (c) and (d), respectively.

Fig. 7
Fig. 7

Reconstructed results obtained from different subdivision approaches in the recording distance ZOH = 27.64 mm (a) the reconstructed image obtained by the subdivision convolution algorithm in which the hologram is implemented by the zero-padding operation in frequency domain (b) the reconstructed image obtained by the subdivision Fresnel algorithm in which the hologram is directly implemented by the zero-padding operation; (c)the magnification marked the white real line in area in (a); (d) the Magnification marked the white real line in (b); (e)Intensity distribution of the same column marked with the black real arrow line in (c) and (d), respectively.

Equations (10)

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ξ= 1 ε = sinu λ = 1 λ L CCD /2 Z OH 2 + ( L CCD /2) 2
ξ= 1 ε = NA λ L CCD 2λ Z OH
O( x I , y I )= I( x H , y H ) C( x H , y H )g( x I x H , x I y H )d x H d y H
g( x I x H , y I y H )= Z HI jλ exp[ jk Z HI 2 + ( x I x H ) 2 + ( y I y H ) 2 ] Z HI 2 + ( x I x H ) 2 + ( y I y H ) 2
O( x I , y I )= F 1 { F [ I( x H , y H ) C( x H , y H ) ]F[ g( x I x H , y I y H ) ] }
Δ x I =Δ x H Δ y I =Δ y H
O( x I , y I )=A I( x H , y H )C( x H , y H )exp[j π λ Z HI ( x H 2 + y H 2 )]exp[j 2π λ Z HI ( x H x I + y H y I )]d x H d y H =A F 1 { I( x H , y H )C( x H , y H )exp[j π λ Z HI ( x H 2 + y H 2 )] }
A= 1 jλ Z HI exp(jk Z HI )exp[ jk 2 Z HI ( x I 2 + y I 2 )]
O(mΔ x I ,nΔ y I )=A F 1 { I(kΔ x H ,lΔ y H )C(kΔ x H ,lΔ y H )exp[ j π λ Z HI ( k 2 Δ x H 2 + l 2 Δ y H 2 ) ] }
Δ x I = λ Z HI MΔ x H , Δ y I = λ Z HI NΔ y H

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