Abstract

We describe a simple system for achieving real-time phase-difference amplification of interferograms. We arrange the interferogram such that it contains high-spatial-frequency carrier fringes and project it onto the write side of an optically addressed phase-only spatial light modulator. The resultant phase pattern on the modulator is read out by two readout beams, and diffraction by the carrier fringes provides the spatial heterodyning that is necessary for achieving phase-difference amplification. We present results that demonstrate real-time phase-difference amplification by as much as a factor of 10.

© 2000 Optical Society of America

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References

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  1. K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. 26, p. 249.
  2. O. Bryngdahl, A. W. Lohmann, “Interferograms are image holograms,” J. Opt. Soc. Am. 58, 141–142 (1968).
    [CrossRef]
  3. K. Matsumoto, M. Takashima, “Phase difference amplification by nonlinear holograms,” J. Opt. Soc. Am. 60, 30–33 (1970).
    [CrossRef]
  4. O. Bryngdahl, “Longitudinally reversed shearing interferometry,” J. Opt. Soc. Am. 59, 142–145 (1969).
    [CrossRef]
  5. K. Matsuda, C. H. Freund, P. Hariharan, “Phase-difference amplification using longitudinally reversed shearing interferometry: an experimental study,” Appl. Opt. 20, 2763–2765 (1981).
    [CrossRef] [PubMed]
  6. K. Frieschlad, M. Kuchel, K. H. Scguster, U. Wegmann, W. Kaiser, “Real time wavefront measurement with lambda/10 fringe spacing for the optical shop,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. Grover, ed. Proc. SPIE1332, 18–24 (1991).

1981 (1)

1970 (1)

1969 (1)

1968 (1)

Bryngdahl, O.

Creath, K.

K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. 26, p. 249.

Freund, C. H.

Frieschlad, K.

K. Frieschlad, M. Kuchel, K. H. Scguster, U. Wegmann, W. Kaiser, “Real time wavefront measurement with lambda/10 fringe spacing for the optical shop,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. Grover, ed. Proc. SPIE1332, 18–24 (1991).

Hariharan, P.

Kaiser, W.

K. Frieschlad, M. Kuchel, K. H. Scguster, U. Wegmann, W. Kaiser, “Real time wavefront measurement with lambda/10 fringe spacing for the optical shop,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. Grover, ed. Proc. SPIE1332, 18–24 (1991).

Kuchel, M.

K. Frieschlad, M. Kuchel, K. H. Scguster, U. Wegmann, W. Kaiser, “Real time wavefront measurement with lambda/10 fringe spacing for the optical shop,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. Grover, ed. Proc. SPIE1332, 18–24 (1991).

Lohmann, A. W.

Matsuda, K.

Matsumoto, K.

Scguster, K. H.

K. Frieschlad, M. Kuchel, K. H. Scguster, U. Wegmann, W. Kaiser, “Real time wavefront measurement with lambda/10 fringe spacing for the optical shop,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. Grover, ed. Proc. SPIE1332, 18–24 (1991).

Takashima, M.

Wegmann, U.

K. Frieschlad, M. Kuchel, K. H. Scguster, U. Wegmann, W. Kaiser, “Real time wavefront measurement with lambda/10 fringe spacing for the optical shop,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. Grover, ed. Proc. SPIE1332, 18–24 (1991).

Appl. Opt. (1)

J. Opt. Soc. Am. (3)

Other (2)

K. Frieschlad, M. Kuchel, K. H. Scguster, U. Wegmann, W. Kaiser, “Real time wavefront measurement with lambda/10 fringe spacing for the optical shop,” in Optical Testing and Metrology III: Recent Advances in Industrial Optical Inspection, C. Grover, ed. Proc. SPIE1332, 18–24 (1991).

K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. 26, p. 249.

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Figures (7)

Fig. 1
Fig. 1

General arrangement for real-time phase-difference amplification with a LCSLM.

Fig. 2
Fig. 2

Experimental setup. M, mirror; L, lens; BS, beam splitter.

Fig. 3
Fig. 3

Result of measuring the step height of the test object by using a Talystep profilometer. The step height was ∼50 nm and gave rise to an optical path difference in the Michelson interferometer of 48 nm (double pass; the refractive index of SiO2 is 1.48).

Fig. 4
Fig. 4

Interference fringes produced by the Michelson interferometer with the phase object in place.

Fig. 5
Fig. 5

Interference fringes obtained at the CCD camera with the following phase-amplification factors: (a) 0 (0th orders); (b) 2 (±1st orders); (c) 6 (±3rd orders); (d) 8 (±4th orders).

Fig. 6
Fig. 6

Interference fringes obtained at the CCD camera with higher input intensity to the LCSLM, giving greater nonlinearity. Amplitude factors are (a) 6 (±3rd orders); (b) 8 (±4th orders); (c) 10 (±5th orders); (d) 12 (±6th orders).

Fig. 7
Fig. 7

Interference fringes obtained at the CCD camera with no phase object in the Michelson interferometer. The separation of orders in the focal plane of L4 was 4 mm. (a) Fringes obtained between ±1st orders, (b) fringes obtained between ±2nd orders.

Equations (10)

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Ix, y=2A21+cosφx, y,
φx, y=ϕx, y+αx,
E1x, y=expjβxexp(j2A2K1+cosϕx, y+αx),
E2x, y=exp-jβxexp(j2A2K1+cosϕx, y+αx),
exp(j2A2K1+cosϕx, y+αx)=expj2A2Kn=-n= Jn2A2Kexpjnϕx, y+αx+π/2.
E1x, y=expj2A2Kexpjβxn=-n= Jn2A2K×expjnϕx, y+αx+π/2,
E2x, y=expj2A2Kexp-jβxn=-n= Jn2A2K×expjnϕx, y+αx+π/2.
E1x, y=Jn2A2Kexp-jnϕx, y+π/2,
E2x, y=Jn2A2Kexpjnϕx, y+π/2.
IOut=|E1+E2|2=2Jn2A2K21+cos2nϕx, y.

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