Abstract

A novel (to our knowledge) approach for resolution improvement in digital holography is presented in this paper. The proposed method is based on recording the incoming interference field on a complementary metal-oxide semiconductor (CMOS) camera with subpixel resolution. The method takes advantage of the small pixel size of the CMOS sensor, while overcoming the reduced fill factor. This paper describes the experimental and numerical procedures. The improvement of the obtainable optical resolution, image quality, and phase measurement accuracy are demonstrated within this paper.

© 2011 Optical Society of America

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References

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  1. T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).
  2. Interference of object wave with a plane reference wave.
  3. Interference of object wave with a spherical reference wave that originates from the object plane.
  4. F. Le Clerc and M. Gross, “Synthetic-aperture experiment in the visible with on-axis digital heterodyne holography,” Opt. Lett. 26, 1550–1552 (2001).
    [CrossRef]
  5. J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. 27, 2179–2181 (2002).
    [CrossRef]
  6. T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803(2007).
    [CrossRef]
  7. D. Claus, “High-resolution digital holographic synthetic aperture applied to deformation measurement and extended depth of field method,” Appl. Opt. 49, 3187–3198 (2010).
    [CrossRef]
  8. L. Granero, V. Micó, Z. Zalevsky, and J. Garcia, “Synthetic aperture super-resolved microscopy in digital lensless Fourier holography by time and angular multiplexing of the object information,” Appl. Opt. 49, 845–857 (2010).
    [CrossRef]
  9. J. Kornis and B. Gombköto, “Application of super image methods in digital holography,” Proc. SPIE 5856, 245–253(2005).
  10. Obtained by rotation of two quarter-wave plates in the reference arm.
  11. G. D. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems (SPIE Press, 2001), Vol.  TT52.
  12. L. Z. Cai, Q. Liu, and X. L. Yang, “Generalized phase-shifting interferometry with arbitrary unknown phase steps for diffraction objects,” Opt. Lett. 29, 183–185 (2004).
    [CrossRef]
  13. A. W. Lohmann and S. Sinzinger, Optical Information Processing (Universitätsverlag Ilmenau, 2006).
  14. J. Di, J. Zhao, H. Jiang, P. Zhang, Q. Fan, and W. Sun, “High-resolution digital holographic microscopy with a wide field of view based on a synthetic aperture technique and use of linear CCD scanning,” Appl. Opt. 47, 5654–5659(2008).
    [CrossRef]

2010 (2)

2008 (1)

2007 (1)

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803(2007).
[CrossRef]

2005 (1)

J. Kornis and B. Gombköto, “Application of super image methods in digital holography,” Proc. SPIE 5856, 245–253(2005).

2004 (1)

2002 (1)

2001 (1)

Boreman, G. D.

G. D. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems (SPIE Press, 2001), Vol.  TT52.

Cai, L. Z.

Claus, D.

Di, J.

Fan, Q.

Garcia, J.

Gombköto, B.

J. Kornis and B. Gombköto, “Application of super image methods in digital holography,” Proc. SPIE 5856, 245–253(2005).

Granero, L.

Gross, M.

Jiang, H.

Kornis, J.

J. Kornis and B. Gombköto, “Application of super image methods in digital holography,” Proc. SPIE 5856, 245–253(2005).

Kreis, T.

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803(2007).
[CrossRef]

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).

Le Clerc, F.

Liu, Q.

Lohmann, A. W.

A. W. Lohmann and S. Sinzinger, Optical Information Processing (Universitätsverlag Ilmenau, 2006).

Massig, J. H.

Micó, V.

Schlüter, K.

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803(2007).
[CrossRef]

Sinzinger, S.

A. W. Lohmann and S. Sinzinger, Optical Information Processing (Universitätsverlag Ilmenau, 2006).

Sun, W.

Yang, X. L.

Zalevsky, Z.

Zhang, P.

Zhao, J.

Appl. Opt. (3)

Opt. Eng. (1)

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803(2007).
[CrossRef]

Opt. Lett. (3)

Proc. SPIE (1)

J. Kornis and B. Gombköto, “Application of super image methods in digital holography,” Proc. SPIE 5856, 245–253(2005).

Other (6)

Obtained by rotation of two quarter-wave plates in the reference arm.

G. D. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems (SPIE Press, 2001), Vol.  TT52.

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).

Interference of object wave with a plane reference wave.

Interference of object wave with a spherical reference wave that originates from the object plane.

A. W. Lohmann and S. Sinzinger, Optical Information Processing (Universitätsverlag Ilmenau, 2006).

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Figures (12)

Fig. 1
Fig. 1

Nomenclature for coordinates in object plane, hologram plane, and reconstruction plane.

Fig. 2
Fig. 2

Schematic diagram of experimental recording setup.

Fig. 3
Fig. 3

Schematic diagram of the relative pixel positions for subpixel resolution sampling.

Fig. 4
Fig. 4

Combination procedure to obtain a subpixel hologram.

Fig. 5
Fig. 5

Simulation of the digital recording mechanism.

Fig. 6
Fig. 6

Pixel MTF for the normal pixel size (dotted curve) and half the pixel size employing the subpixel sampling method (solid curve).

Fig. 7
Fig. 7

Phase hologram and reconstruction at 191 mm recording distance for (a) an undersampled normal hologram with 3.5 μm pixel size, (b) subpixel sampled hologram without phase correction, and (c) subpixel sampled hologram with phase correction.

Fig. 8
Fig. 8

Schematic diagram of the phase-correction procedure.

Fig. 9
Fig. 9

(a) Cantilever with micrometer screw used for experiments, region of interest for intensity reconstruction and their profile lines for (b) subpixel sampled hologram at 191 mm recording distance and (c) normal hologram with 3.5 μm pixel size at 300 mm recording distance.

Fig. 10
Fig. 10

Segment of double-exposure phase maps for 191 mm recording distance (a) normal hologram with 3.5 μm pixel size, (b) subpixel sampled hologram with 1.75 μm pixel size.

Fig. 11
Fig. 11

Transmission setup for the recording of a Fourier hologram.

Fig. 12
Fig. 12

(a) Recorded intensity hologram 3000 × 3000 pixels, (b) modulus of calculated complex object wave 6000 × 6000 pixels, numerical reconstructions with field of view indicated by dashed line (c) without subpixel sampling method, (d) with subpixel sampling method, and (e), (f) corresponding areas of interest to determine smallest resolvable element.

Tables (1)

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Table 1 Theoretical and Practically Achieved Resolution

Equations (15)

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δ x = λ d N x Δ x ,
D x _ speckle = 2.44 λ d N x Δ x ,
d min = ( 2 x + N Δ x ) Δ x λ { in - line : x = X / 2 off - axis : x = 1.5 · X ,
d min = 2 x Δ x λ { in - line : x = X / 2 off - axis : x = 1.5 · X ,
H ( 2 x 1 , 2 y 1 ) = A ( x , y ) , H ( 2 x 1 , 2 y ) = B ( x , y ) , H ( 2 x , 2 y ) = C ( x , y ) , H ( 2 x , 2 y 1 ) = D ( x , y ) .
u d ( x ) = u ( x ) comb ( x Δ x ) .
u pixel ( x ) = u d ( x ) rect ( x Δ x ) = F 1 [ F { u d ( x , y ) } · sinc ( ν x Δ x ) ] ,
MTF pixel = | sinc ( ν x Δ x ) | .
B ( x , y ) = A ( 2 x 1 , 2 y ) .
Δ φ B = 1 N M x = 1 N y = 1 M ( B ( x , y ) B ( x , y ) ) .
u ( x , y ) = i exp ( i k d ) λ d exp [ i π λ d ( x 2 y 2 ) ] · F { u ( x , y ) ref * ( x , y ) exp ( i π λ d ( x 2 + y 2 ) ) } ,
SNR = 20 log ( X ¯ σ ) ,
Δ x = λ d N Δ x .
SBP in - line = N · M ,
η = SBP SBP in - line .

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