Abstract

We present experimental results showing that the reverse phase contrast (RPC) technique is a viable method for the generation of a binary phase distribution from a spatially varying amplitude pattern using Fourier plane filtering techniques. Experimental results are shown for the generation of a binary 0-π phase only distribution using either an amplitude mask or a spatial light modulator to provide the input and the results are shown to be in agreement with theoretical predictions for the RPC technique.

© 2002 Optical Society of America

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References

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  1. Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high-efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
    [CrossRef]
  2. P. C. Mogensen, J. Glückstad, “Phase-only optical decryption of a fixed mask,” Appl. Opt. 40, 1226–1235 (2001).
    [CrossRef]
  3. C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
    [CrossRef]
  4. S. Jutamulia, “Phase-only Fourier transform of an optical transparancy,” Appl. Opt. 33, 280–282 (1994).
    [CrossRef] [PubMed]
  5. J. Glückstad, P. C. Mogensen, “Optimal phase contrast in common-path interferometry,” Appl. Opt. 40, 268–282 (2001).
    [CrossRef]
  6. F. Zernike, “How I discovered phase contrast,” Science 121, 345–349 (1955).
    [CrossRef] [PubMed]
  7. J. Glückstad, P. C. Mogensen, “Reverse phase contrast for the generation of phase-only spatial light modulation” Opt. Commun. 197, 261–266 (2001).
    [CrossRef]
  8. J. Glückstad, “A method and an apparatus for generating a phase modulated wavefront,” U.S. patent application 60/257,093 (priority date 22Dec.2000).

2001 (3)

1994 (1)

1991 (1)

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

1955 (1)

F. Zernike, “How I discovered phase contrast,” Science 121, 345–349 (1955).
[CrossRef] [PubMed]

Denz, C.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Fukuchi, N.

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high-efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
[CrossRef]

Glückstad, J.

P. C. Mogensen, J. Glückstad, “Phase-only optical decryption of a fixed mask,” Appl. Opt. 40, 1226–1235 (2001).
[CrossRef]

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

J. Glückstad, P. C. Mogensen, “Reverse phase contrast for the generation of phase-only spatial light modulation” Opt. Commun. 197, 261–266 (2001).
[CrossRef]

J. Glückstad, “A method and an apparatus for generating a phase modulated wavefront,” U.S. patent application 60/257,093 (priority date 22Dec.2000).

Hara, T.

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high-efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
[CrossRef]

Igasaki, Y.

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high-efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
[CrossRef]

Jutamulia, S.

Kobayashi, Y.

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high-efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
[CrossRef]

Mogensen, P. C.

Pauliat, G.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Roosen, G.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Toyoda, H.

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high-efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
[CrossRef]

Tschudi, T.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Wu, M.

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high-efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
[CrossRef]

Yoshida, N.

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high-efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
[CrossRef]

Zernike, F.

F. Zernike, “How I discovered phase contrast,” Science 121, 345–349 (1955).
[CrossRef] [PubMed]

Appl. Opt. (3)

Opt. Commun. (2)

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

J. Glückstad, P. C. Mogensen, “Reverse phase contrast for the generation of phase-only spatial light modulation” Opt. Commun. 197, 261–266 (2001).
[CrossRef]

Science (1)

F. Zernike, “How I discovered phase contrast,” Science 121, 345–349 (1955).
[CrossRef] [PubMed]

Other (2)

J. Glückstad, “A method and an apparatus for generating a phase modulated wavefront,” U.S. patent application 60/257,093 (priority date 22Dec.2000).

Y. Kobayashi, Y. Igasaki, N. Yoshida, N. Fukuchi, H. Toyoda, T. Hara, M. Wu, “Compact high-efficiency electrically addressable phase-only spatial light modulator,” in Diffractive/Holographic Technologies and Spatial Light Modulators VII, I. Cindrich, S. H. Lee, R. L. Sutherland, eds., Proc. SPIE3951, 158–165 (2000).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Generic reverse phase contrast system. A filter (described by the parameters A, B, and θ) in the Fourier plane of a 4-f setup converts a binary amplitude distribution into a binary phase modulation. Because it is an imaging operation, the phase modulation will be spatially identical to that of the amplitude mask.

Fig. 2
Fig. 2

Argand diagrams showing: (a) the complex solution vectors omin) and o(1) plotted from Eq. (6) for the constant-intensity background condition (equal resultant vector lengths) with a phase modulation of Δϕ0. (b) The much simpler case that arises from the choice of ψ c = π that results in a summation of real-valued vectors (shown displaced from the real axis for clarity).

Fig. 3
Fig. 3

Experimental setup for the implementation and characterization of the RPC method. A plane wave front produced by a laser diode (LD) and beam expander (BE) is incident on a spatial filtering 4-f system (lenses L1 and L2) that uses a phase only filter to generate a phase modulation from an amplitude mask (AM) placed in the same plane as an iris IR1. The output-phase distribution is visualized by an interferometer, the reference arm of which is formed by the mirrors (M1 and M2) and the beam splitters (BS1 and BS2), and the diameter of which is controlled by an iris (IR2). The resulting fringe pattern is recorded with a CCD camera.

Fig. 4
Fig. 4

Experimental results for the matching of the aperture (IR1 in Fig. 3) to the phase filter. These show an example of (a) a correctly matched aperture and incorrectly sized apertures that are either (b) too small or (c) too large for the filter-size being used.

Fig. 5
Fig. 5

Experimental results in which (a) an amplitude mask (a section of the United States Air Force target) is imaged and the iris adjusted to give a constant amplitude background. Reducing the iris size (b) results in imaging of the amplitude mask, while increasing the aperture size (c) produces contrast reversal of the image.

Fig. 6
Fig. 6

Interferometric measurement of a phase modulation generated by the RPC method, which shows (a) the resultant π-phase shift superimposed on a constant-amplitude background generated from the correctly matched aperture and amplitude object [as shown in Fig. 5(a)] and (b) the elimination of the phase shift that occurs when the aperture is no longer correctly matched.

Fig. 7
Fig. 7

Simplified Argand diagrams for the experimental system, where C = -2 and αmin = 0, which shows the conditions for (a) a correctly matched aperture fulfilling the constant-intensity-background condition, (b) an aperture that is too small, which gives the condition |o(1)| > |o(0)| corresponding to a standard imaging operation of the input-amplitude mask, (c) shows the result of using an oversized aperture that produces a contrast reversal between the input and output of the system, such that |o(1)| < |o(0)|, where dark sections of the input mask appear brightest and vice versa. In (d) we show what can happen when the input aperture is very much larger than it should be, so that |o(0)| ≫ |o(1)|, and for Eq. (8) to hold, we determine that there is no phase shift between the two resultant vectors o(0) and o(1). Referring to the interferometric measurement of the output image shown in Fig. 6(b), we see that we have a condition of contrast reversal without phase shift.

Fig. 8
Fig. 8

Experimental results for the generation of phase modulation by use of an SLM operating as the input-amplitude modulator. These show (a) an image of the input-amplitude distribution without the filter in place and (b) the interference fringe measurement of the output-phase modulation. Examination of the fringes reveals that we achieve a phase modulation of π.

Equations (8)

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ox, y=Aαx, y+Kα¯CexpiψC.
αx, y=αminforx, y  min1 forx, y  max.
C=CexpiψC=BA-1expiθ-1.
K=1-J02πΔrΔrfλ-1f-1.
α¯=minαmin+maxπΔr2 =1+αmin-1F.
αmin+Kα¯CexpiψC=1+Kα¯CexpiψC.
expiΔϕ0=αmin+Kα¯CexpiψC1+Kα¯CexpiψC .
ox, y=αx, y-CKα¯.

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