Abstract

Three approaches for visualization of transparent micro-objects from holographic data using phase-only SLMs are described. The objects are silicon micro-lenses captured in the near infrared by means of digital holographic microscopy and a simulated weakly refracting 3D object with size in the micrometer range. In the first method, profilometric/tomographic data are retrieved from captured holograms and converted into a 3D point cloud which allows for computer generation of multi-view phase holograms using Rayleigh-Sommerfeld formulation. In the second method, the microlens is computationally placed in front of a textured object to simulate the image of the textured data as seen through the lens. In the third method, direct optical reconstruction of the micrometer object through a digital lens by modifying the phase with the Gerchberg-Saxton algorithm is achieved.

© 2013 Optical Society of America

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References

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  1. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett.24(5), 291–293 (1999).
    [CrossRef] [PubMed]
  2. Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express17(1), 266–277 (2009).
    [CrossRef] [PubMed]
  3. L. Onural, F. Yaras, and H. Kang, “Digital holographic three-dimensional video displays,” Proc. IEEE99(4), 576–589 (2011).
    [CrossRef]
  4. SUSS MicroOptics, http://www.suss-microoptics.com/
  5. F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett.31(2), 178–180 (2006).
    [CrossRef] [PubMed]
  6. F. Charrière, J. Kühn, T. Colomb, F. Montfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, “Characterization of microlenses by digital holographic microscopy,” Appl. Opt.45(5), 829–835 (2006).
    [CrossRef] [PubMed]
  7. D. Ghiglia and M. Pritt, Two-Dimensional Phase Unwrapping (J. Wiley & Sons, 1998).
  8. U. Schnars and W. Juptner, Digital Holography (Springer, 2005).
  9. E. Stoykova, A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3D Time-Varying Scene Capture Technologies – A Survey,” IEEE TCSVT17(11), 1568–1586 (2007).
  10. J. P. Waters, “Holographic image synthesis utilizing theoretical method,” Appl. Phys. Lett.9(11), 405–407 (1966).
    [CrossRef]
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  12. H. Kang, T. Yamaguchi, H. Yoshikawa, S. C. Kim, and E. S. Kim, “Acceleration method of computing a compensated phase-added stereogram on a graphic processing unit,” Appl. Opt.47(31), 5784–5789 (2008).
    [CrossRef] [PubMed]
  13. F. Yaraş, H. Kang, and L. Onural, “Circular holographic video display system,” Opt. Express19(10), 9147–9156 (2011).
    [CrossRef] [PubMed]
  14. F. Yaraş, “Three-dimensional holographic video display systems using multiple spatial light modulators,” Ph.D.dissertation (Bilkent University, 2011).
  15. R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).
  16. G. Liu and P. Scott, “Phase retrieval and twin-image elimination for in-line Fresnel holograms,” J. Opt. Soc. Am. A4(1), 159–165 (1987).
    [CrossRef]

2011

L. Onural, F. Yaras, and H. Kang, “Digital holographic three-dimensional video displays,” Proc. IEEE99(4), 576–589 (2011).
[CrossRef]

F. Yaraş, H. Kang, and L. Onural, “Circular holographic video display system,” Opt. Express19(10), 9147–9156 (2011).
[CrossRef] [PubMed]

2009

2008

2007

E. Stoykova, A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3D Time-Varying Scene Capture Technologies – A Survey,” IEEE TCSVT17(11), 1568–1586 (2007).

2006

1999

1987

1972

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).

1966

J. P. Waters, “Holographic image synthesis utilizing theoretical method,” Appl. Phys. Lett.9(11), 405–407 (1966).
[CrossRef]

Alatan, A.

E. Stoykova, A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3D Time-Varying Scene Capture Technologies – A Survey,” IEEE TCSVT17(11), 1568–1586 (2007).

Badizadegan, K.

Benzie, P.

E. Stoykova, A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3D Time-Varying Scene Capture Technologies – A Survey,” IEEE TCSVT17(11), 1568–1586 (2007).

Bevilacqua, F.

Charrière, F.

Choi, W.

Colomb, T.

Cuche, E.

Dasari, R. R.

Depeursinge, C.

Emery, Y.

Fang-Yen, C.

Feld, M. S.

Gerchberg, R.

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).

Grammalidis, N.

E. Stoykova, A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3D Time-Varying Scene Capture Technologies – A Survey,” IEEE TCSVT17(11), 1568–1586 (2007).

Kang, H.

Kim, E. S.

Kim, S. C.

Kuehn, J.

Kühn, J.

Liu, G.

Malassiotis, S.

E. Stoykova, A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3D Time-Varying Scene Capture Technologies – A Survey,” IEEE TCSVT17(11), 1568–1586 (2007).

Marian, A.

Marquet, P.

Montfort, F.

Onural, L.

L. Onural, F. Yaras, and H. Kang, “Digital holographic three-dimensional video displays,” Proc. IEEE99(4), 576–589 (2011).
[CrossRef]

F. Yaraş, H. Kang, and L. Onural, “Circular holographic video display system,” Opt. Express19(10), 9147–9156 (2011).
[CrossRef] [PubMed]

Ostermann, J.

E. Stoykova, A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3D Time-Varying Scene Capture Technologies – A Survey,” IEEE TCSVT17(11), 1568–1586 (2007).

Piekh, S.

E. Stoykova, A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3D Time-Varying Scene Capture Technologies – A Survey,” IEEE TCSVT17(11), 1568–1586 (2007).

Sainov, V.

E. Stoykova, A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3D Time-Varying Scene Capture Technologies – A Survey,” IEEE TCSVT17(11), 1568–1586 (2007).

Saxton, W.

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).

Scott, P.

Stoykova, E.

E. Stoykova, A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3D Time-Varying Scene Capture Technologies – A Survey,” IEEE TCSVT17(11), 1568–1586 (2007).

Sung, Y.

Theobalt, C.

E. Stoykova, A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3D Time-Varying Scene Capture Technologies – A Survey,” IEEE TCSVT17(11), 1568–1586 (2007).

Thevar, T.

E. Stoykova, A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3D Time-Varying Scene Capture Technologies – A Survey,” IEEE TCSVT17(11), 1568–1586 (2007).

Waters, J. P.

J. P. Waters, “Holographic image synthesis utilizing theoretical method,” Appl. Phys. Lett.9(11), 405–407 (1966).
[CrossRef]

Weible, K.

Yamaguchi, T.

Yaras, F.

F. Yaraş, H. Kang, and L. Onural, “Circular holographic video display system,” Opt. Express19(10), 9147–9156 (2011).
[CrossRef] [PubMed]

L. Onural, F. Yaras, and H. Kang, “Digital holographic three-dimensional video displays,” Proc. IEEE99(4), 576–589 (2011).
[CrossRef]

Yoshikawa, H.

Zabulis, X.

E. Stoykova, A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3D Time-Varying Scene Capture Technologies – A Survey,” IEEE TCSVT17(11), 1568–1586 (2007).

Appl. Opt.

Appl. Phys. Lett.

J. P. Waters, “Holographic image synthesis utilizing theoretical method,” Appl. Phys. Lett.9(11), 405–407 (1966).
[CrossRef]

IEEE TCSVT

E. Stoykova, A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3D Time-Varying Scene Capture Technologies – A Survey,” IEEE TCSVT17(11), 1568–1586 (2007).

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Optik (Stuttg.)

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).

Proc. IEEE

L. Onural, F. Yaras, and H. Kang, “Digital holographic three-dimensional video displays,” Proc. IEEE99(4), 576–589 (2011).
[CrossRef]

Other

SUSS MicroOptics, http://www.suss-microoptics.com/

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

D. Ghiglia and M. Pritt, Two-Dimensional Phase Unwrapping (J. Wiley & Sons, 1998).

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

F. Yaraş, “Three-dimensional holographic video display systems using multiple spatial light modulators,” Ph.D.dissertation (Bilkent University, 2011).

Supplementary Material (2)

» Media 1: AVI (3069 KB)     
» Media 2: AVI (1542 KB)     

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Figures (10)

Fig. 1
Fig. 1

(Top) - image-plane off-axis holograms of silicon microlenses captured at 1.28 μm with a digital holographic microscope; (bottom) - profilometric reconstruction of the microlenses from the captured holograms.

Fig. 2
Fig. 2

(a) - 3D refractive index distribution of a simulated 3D transparent object with the refractive index values in different regions; (b) - simulated complex amplitudes (magnitudes and wrapped phases) of holograms of the transparent object; from right to the left illumination of the object is at 0, 70, 120 and 180 degrees.

Fig. 3
Fig. 3

Conversion of the data obtained from the profilometric or tomographic reconstruction into a 3D computer graphic model (point cloud), and computer generation of multi-view phase-only holograms from the point cloud data by using Rayleigh-Sommerfeld diffraction model; O( x,y,z ) - object wave, R( x,y,z ) - reference wave.

Fig. 4
Fig. 4

Continuous optical reconstruction of pure phase objects within 24° and 32° viewing zone by using a circular holographic display; (a) – video recording of reconstruction of a silicon microlens from profilometric data (Media 1); (a)-(c) – enlarged parts from the single-frame excerpts of reconstruction of microlenses; (g) – video recording of reconstruction of a micrometer object given by a 3D refractive index distribution obtained by means of optical diffraction tomography (Media 2); (g)-(i) - enlarged parts from single-frame excerpts.

Fig. 5
Fig. 5

Visualization of a textured pattern by means of a microlens with a focal distance f, that is reconstructed from an off-axis hologram and whose wrapped phase distribution is applied to the phase-only SLM.

Fig. 6
Fig. 6

Algorithm to visualize the textured pattern with a microlens, reconstructed from an off-axis hologram (only phase distributions are applied to a phase-only SLM).

Fig. 7
Fig. 7

Display of a textured pattern at λ2 = 532 nm by means of a microlens, whose wrapped phase distribution is reconstructed from a hologram, recorded in the near infrared region at λ1 = 1280 nm and applied as a phase distribution to a SLM; (top) - square microlens; (bottom) – circular microlens.

Fig. 8
Fig. 8

(a) - full complex amplitude at the hologram plane and the image reconstructed from it; (b) - phase at the hologram plane and the image reconstructed from it; (c) - schematic representation of the Gerchberg-Saxton algorithm between the SLM plane and the plane of the reconstructed image; numerical reconstruction in Figs. (a) and (b) is made for 0.532 μm wavelength and pixel period of 8 μm.

Fig. 9
Fig. 9

Schematic of the Gerchberg-Saxton algorithm for improving the image quality at reconstruction by modifying the phase.

Fig. 10
Fig. 10

(a) - numerical reconstruction of the phase object in the micrometer range from holographic data after applying the Gerchberg-Saxton algorithm to modify phase distribution; (b) – optical reconstruction at λ2 = 532 nm with a single SLM after incorporation of a digital lens at the SLM plane; the size of the reconstructed 3D shape is 6 mm.

Equations (8)

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O( x,y )= p=1 N a op r p exp{ j( k r p + φ p ), }
r p = ( x p ξ ) 2 + ( y p η ) 2 + z p 2
W( x,y )=exp( jk x 2 D h )exp[ jk k 2 ( y+ h SLM 2 ) 2 D h + D s ],
t( x ˜ , y ˜ )= p=1 M q=1 M rect[ x ˜ ( 2p1 ) Δ t Δ t , y ˜ ( 2q1 ) Δ t Δ t ] ,
G ± ( l,m,d )=exp{ ± 2πd λ j 1 ( l N x 2 ) 2 ( λ N x Δ ) 2 ( m N y 2 ) 2 ( λ N y Δ ) 2 }
L ˜ ( x,y )=exp{ πi x 2 + y 2 λ f dl }
O( ξ,η )= a O ( ξ,η )exp{ jk φ O ( ξ,η ) }= 1 { [ O( x,y ) ]× G ( d ) }
O i ( x,y )= a O i ( x,y )exp{ jk φ O i ( x,y ) }= 1 { [ O( ξ,η ) ]× G + ( d ) },

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