Abstract

Recent advances in Fresnel incoherent correlation holography (FINCH) increase the signal-to-noise ratio in hologram recording by interference of images from two diffractive lenses with focal lengths close to the image plane. Holograms requiring short reconstruction distances are created that reconstruct poorly with existing Fresnel propagation methods. Here we show a dramatic improvement in reconstructed fluorescent images when a 2D Hamming window function substituted for the disk window typically used to bound the impulse response in the Fresnel propagation. Greatly improved image contrast and quality are shown for simulated and experimentally determined FINCH holograms using a 2D Hamming window without significant loss in lateral or axial resolution.

© 2013 Optical Society of America

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References

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    [CrossRef]

2013 (1)

P. Bouchal and Z. Bouchal, J. Europ. Opt. Soc. 8, 13011 (2013).
[CrossRef]

2012 (3)

2011 (3)

2010 (1)

D. J. A. McKechan, C. Robinson, and B. S. Sathyaprakash, Class. Quantum Grav. 27, 084020 (2010).
[CrossRef]

2008 (1)

J. Rosen and G. Brooker, Nat. Photonics 2, 190 (2008).
[CrossRef]

2007 (1)

1978 (1)

F. J. Harris, Proc. IEEE 66, 51 (1978).
[CrossRef]

Bouchal, P.

Bouchal, Z.

Brooker, G.

Chmelik, R.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 2005).

Hamming, R. W.

R. W. Hamming, Digital Filters (Prentice-Hall, 1977), Sec. 5.8.

Harris, F. J.

F. J. Harris, Proc. IEEE 66, 51 (1978).
[CrossRef]

Kapitan, J.

Katz, B.

Kelner, R.

Lai, X.

Lv, X.

McKechan, D. J. A.

D. J. A. McKechan, C. Robinson, and B. S. Sathyaprakash, Class. Quantum Grav. 27, 084020 (2010).
[CrossRef]

Robinson, C.

D. J. A. McKechan, C. Robinson, and B. S. Sathyaprakash, Class. Quantum Grav. 27, 084020 (2010).
[CrossRef]

Rosen, J.

Sathyaprakash, B. S.

D. J. A. McKechan, C. Robinson, and B. S. Sathyaprakash, Class. Quantum Grav. 27, 084020 (2010).
[CrossRef]

Siegel, N.

Smith, J. O.

J. O. Smith, Spectral Audio Signal Processing (W3K, 2011).

Wang, V.

Zeng, S.

Zhao, Y.

Zhou, Z.

Class. Quantum Grav. (1)

D. J. A. McKechan, C. Robinson, and B. S. Sathyaprakash, Class. Quantum Grav. 27, 084020 (2010).
[CrossRef]

J. Europ. Opt. Soc. (1)

P. Bouchal and Z. Bouchal, J. Europ. Opt. Soc. 8, 13011 (2013).
[CrossRef]

Nat. Photonics (1)

J. Rosen and G. Brooker, Nat. Photonics 2, 190 (2008).
[CrossRef]

Opt. Express (5)

Opt. Lett. (2)

Proc. IEEE (1)

F. J. Harris, Proc. IEEE 66, 51 (1978).
[CrossRef]

Other (3)

R. W. Hamming, Digital Filters (Prentice-Hall, 1977), Sec. 5.8.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, 2005).

J. O. Smith, Spectral Audio Signal Processing (W3K, 2011).

Supplementary Material (1)

» Media 1: AVI (1070 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

(a) and (b) Formation and reconstruction of single-point holograms (PSFs) in two FINCH configurations. Objective lenses and other ancillary optics are omitted. (a) Plane and spherical wave and long reconstruction distance. (b) Two spherical waves at the same camera distance but a much smaller recording PSF and shorter reconstruction distance. SLM, spatial light modulator; f d 1 , signal beam focal length; f d 2 reference beam focal length; z h , SLM-detector distance; | z r | , reconstruction distance. (c) Example profiles of disk and Hamming window functions.

Fig. 2.
Fig. 2.

(a) Calculated x z PSF I of the reconstructed image of a single point through focus, reconstructed with disk-windowed PSF H h d . (b)  x z PSF I calculated using the Hamming-windowed PSF H h h . (c)  z -profiles through peak pixel of reconstructions, serving as a measure of relative z resolution. (d)  x y profiles of the reconstructions at best focus.

Fig. 3.
Fig. 3.

In (a) and (b), respectively, FINCH reconstructions of the same USAF pattern hologram recorded with dual-lens pattern FINCH (from Fig. 7, top center in [8]), reconstructed with the disk-windowed PSF H and with the Hamming-windowed PSF H . Intensity profiles through the lines indicated are shown in (c) and (d). (e) The visibilities of the Group 9 Element 3 bars, as described in [8], from FINCH images of the sample above, at, or below the objective focal plane. The images were reconstructed with either the disk window (red, round points and dashed line) or the Hamming window (blue square points, solid line). The visibility of these features in ordinary wide-field fluorescence microscopy is provided to show that the super-resolving characteristics of FINCH are maintained when using the Hamming window function.

Fig. 4.
Fig. 4.

Reconstructed images of pollen grains from holograms captured with short reconstruction distance. (a)–(c) With disk-windowed PSF H . (d)–(f) or Hamming-windowed PSF H . Images 39 [(a) and (d)], 46 [(b) and (e)], and 67 [(c) and (f)] of 100 reconstructed sections from the same holograms are shown. Full series is online (Media 1, top series Hamming window, bottom series disk window). Intensity profiles through three spines at three planes of focus (g)–(i) for disk window (red) or Hamming window (blue).

Fig. 5.
Fig. 5.

Contrast in at-focus reconstructed images plotted against PSF width of the image. (a) Lateral (xy) PSF I . (b) Axial (xz) PSF I . The dashed boxes denote a group of window functions with roughly comparable performance. (a) Window function parameters in quadrant (i): Gaussian, 2.5; Dolph–Chebychev, 3; Tukey, 0.1; (ii): Gaussian, 3.5; Dolph–Chebychev, 4; Tukey, 0; Planck, 1, 0.9, and 0.75; (iii): Tukey, 0.5, 0.9, and 1; Planck, 0.5, 0.1, and 0. (b) Window function parameters in quadrant (i): Gaussian, 2.5; Dolph–Chebychev, 3; Tukey, 0 and 0.1; (ii): Gaussian, 3.5; Dolph–Chebychev, 4; Planck, 1, 0.9, and 0.75; (iii): Tukey, 0.5, 0.9, and 1; Planck, 0.5, 0.1, and 0.

Tables (1)

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Table 1. Normalized Image Point-Spread Function ( PSF I ) Widths for Windowed Holographic Point-Spread Functions ( PSF H )

Equations (6)

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u ( x , y ; z ) = | F 2 D 1 { F 2 D [ g ( x , y ) ] × F 2 D [ h ( x , y ; z ) ] } | ,
h ( x , y ; z ) = exp [ i π λ z ( x 2 + y 2 ) ] .
N min = λ z / Δ 2 .
h ( n x , n y ; z ) = w d ( n r ; N min ) × exp [ i π Δ 2 λ z ( n x 2 + n y 2 ) ] ,
w d ( n r ; N min ) = { 1 , n r N min 2 0 , otherwise .
w h ( n r ; N min ) = { α β cos [ 2 π ( n r N min 2 ) N min ] , n r N min 2 0 , otherwise ,

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