Abstract

A general analysis of the image fill-factor influence on Zernike-type phase contrast filtering is presented. We define image fill factor as the ratio of the object support area over the illuminating area. We first consider binary-phase objects and then generalize to arbitrarily quantized and continuous-phase objects. Numerical simulations are presented for binary- and quadratic-phase objects, where the contrast of the output image is evaluated as a function of the image fill factor, image phase variations, and filter phase. The results obtained show that the image fill factor can significantly modify the contrast and irradiance of the contrasted image.

© 2002 Optical Society of America

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References

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  1. F. Zernike, “Diffraction theory of knife-edge test and its improved form, the phase contrast,” Mon. Not. R. Astron. Soc. 94, 371–378 (1934).
  2. C. S. Anderson, “Fringe visibility, irradiance, and accuracy in common path interferometers for visualization of phase disturbances,” Appl. Opt. 34, 7474–7485 (1995).
    [CrossRef] [PubMed]
  3. J. Glückstad, “Phase contrast image synthesis,” Opt. Commun. 130, 225–230 (1996).
    [CrossRef]
  4. A. W. Lohmann, J. Schwider, N. Streibl, J. Thomas, “Array illuminator based on phase contrast,” Appl. Opt. 27, 2915–2921 (1988).
    [CrossRef] [PubMed]
  5. J. Glückstad, “Adaptive array illumination and structured light generated by spatial zero-order self-phase modulation in a Kerr medium,” Opt. Commun. 120, 194–203 (1995).
    [CrossRef]
  6. J. Glückstad, “Graphic method for analyzing common path interferometers,” Appl. Opt. 37, 8151–8152 (1998).
    [CrossRef]
  7. J. Glückstad, P. C. Mogensen, “Reconfigurable ternary-phase array illuminator based on the generalized phase contrast method,” Opt. Commun. 173, 169–175 (2000).
    [CrossRef]
  8. J. Glückstad, P. C. Mogensen, “Optimal phase contrast in common-path interferometry,” Appl. Opt. 40, 268–282 (2001).
    [CrossRef]

2001 (1)

2000 (1)

J. Glückstad, P. C. Mogensen, “Reconfigurable ternary-phase array illuminator based on the generalized phase contrast method,” Opt. Commun. 173, 169–175 (2000).
[CrossRef]

1998 (1)

1996 (1)

J. Glückstad, “Phase contrast image synthesis,” Opt. Commun. 130, 225–230 (1996).
[CrossRef]

1995 (2)

C. S. Anderson, “Fringe visibility, irradiance, and accuracy in common path interferometers for visualization of phase disturbances,” Appl. Opt. 34, 7474–7485 (1995).
[CrossRef] [PubMed]

J. Glückstad, “Adaptive array illumination and structured light generated by spatial zero-order self-phase modulation in a Kerr medium,” Opt. Commun. 120, 194–203 (1995).
[CrossRef]

1988 (1)

1934 (1)

F. Zernike, “Diffraction theory of knife-edge test and its improved form, the phase contrast,” Mon. Not. R. Astron. Soc. 94, 371–378 (1934).

Anderson, C. S.

Glückstad, J.

J. Glückstad, P. C. Mogensen, “Optimal phase contrast in common-path interferometry,” Appl. Opt. 40, 268–282 (2001).
[CrossRef]

J. Glückstad, P. C. Mogensen, “Reconfigurable ternary-phase array illuminator based on the generalized phase contrast method,” Opt. Commun. 173, 169–175 (2000).
[CrossRef]

J. Glückstad, “Graphic method for analyzing common path interferometers,” Appl. Opt. 37, 8151–8152 (1998).
[CrossRef]

J. Glückstad, “Phase contrast image synthesis,” Opt. Commun. 130, 225–230 (1996).
[CrossRef]

J. Glückstad, “Adaptive array illumination and structured light generated by spatial zero-order self-phase modulation in a Kerr medium,” Opt. Commun. 120, 194–203 (1995).
[CrossRef]

Lohmann, A. W.

Mogensen, P. C.

J. Glückstad, P. C. Mogensen, “Optimal phase contrast in common-path interferometry,” Appl. Opt. 40, 268–282 (2001).
[CrossRef]

J. Glückstad, P. C. Mogensen, “Reconfigurable ternary-phase array illuminator based on the generalized phase contrast method,” Opt. Commun. 173, 169–175 (2000).
[CrossRef]

Schwider, J.

Streibl, N.

Thomas, J.

Zernike, F.

F. Zernike, “Diffraction theory of knife-edge test and its improved form, the phase contrast,” Mon. Not. R. Astron. Soc. 94, 371–378 (1934).

Appl. Opt. (4)

Mon. Not. R. Astron. Soc. (1)

F. Zernike, “Diffraction theory of knife-edge test and its improved form, the phase contrast,” Mon. Not. R. Astron. Soc. 94, 371–378 (1934).

Opt. Commun. (3)

J. Glückstad, P. C. Mogensen, “Reconfigurable ternary-phase array illuminator based on the generalized phase contrast method,” Opt. Commun. 173, 169–175 (2000).
[CrossRef]

J. Glückstad, “Adaptive array illumination and structured light generated by spatial zero-order self-phase modulation in a Kerr medium,” Opt. Commun. 120, 194–203 (1995).
[CrossRef]

J. Glückstad, “Phase contrast image synthesis,” Opt. Commun. 130, 225–230 (1996).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Binary phase image.

Fig. 2
Fig. 2

Contrast as a function of the input image phase difference and fill factor for filter phases of (a) π/4, (b) π/2, (c) 3π/4, and (d) π rad. The fill factor varies from 0.01 to 0.99.

Fig. 3
Fig. 3

Same as in Fig. 2, except that the fill factor is 0.25.

Fig. 4
Fig. 4

Same as Fig. 2, except that the fill factor is 0.75.

Fig. 5
Fig. 5

Output object (a) and background (b) intensities as a function of the input image phase difference and fill factor for a filter phase of π rad. The fill factor varies from 0.01 to 0.99.

Fig. 6
Fig. 6

Fringe visibility as a function of the fill factor for filter phases of (a) π/4, (b) π/2, (c) 3π/4, and (d) π rad. The input is a 2π dynamic-range quadratic-phase object. The fill factor varies from 0.01 to 1.

Fig. 7
Fig. 7

Same as Fig. 6, except that the input is a 10π dynamic-range quadratic-phase object.

Fig. 8
Fig. 8

Output intensity for a 10π (a) and 2π (b) dynamic-range quadratic-phase input object. The fill factor is 0.5 and the filter phase is π/2.

Equations (7)

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Zr=1+limc0circrcexpiα-1,
F0  1-ρexpiϕs+ρ expiϕo.
gx, y=f-x, -y+expiα-11-ρexpiϕs+ρ expiϕo2,
gx, y=f-x, -y+expiα-11-ρ+ρ expiΔo2,
F0  1-ρexpiϕs+m=1nρm expiϕm,
gx, y=f-x, -y+expiα-11-ρ+m=1nρm expiΔm2,
gx, y=f-x, -y+expiα-11-ρ+1ATObject supportexpiϕox, ydxdy2,

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