Abstract

A nonlinear filtering setup visualizes wavefront aberrations. In a single-beam scheme, however, the negative and positive phase shifts cannot be distinguished. As an improvement, a two-beam nonlinear scheme is proposed. It has self-aligning properties and mechanical stability, and can be used for remote testing of large optical objects such as photolithography masks, liquid crystal substrates, jet streams and turbulence.

© 2000 Optical Society of America

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References

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  1. P. Hariharan, Optical interferometry, (Academic Press, Sydney; Orlando, 1985).
  2. V.P. Linnik, “Simple interferometer for investigation of optical schemes,” C.R.Acad.Sci.USSR, 1, 208–10 (1933).
  3. C.R. Mercer, K. Creath, “Liquid crystal point-diffraction interferomeler,” Optics Letters, 19, 916–18 (1994).
    [CrossRef]
  4. R.N. Smartt, W.H. Steel, “Theory and application of point-diffraction interferometers,” Jap.J.Appl.Phys., 14, (Suppl. 141), 351–6 (1975).
  5. A. Naumov et al., “Dynamic image self-filtering,” Bulletin of Lebedev Physics Institute, 10, 8–13 (1987).
  6. K. Harada et al., “Nonlinear image self-filtering with liquid crystal spatial light modulator,” Optics and Laser Technology, 30, 147–55 (1988).
    [CrossRef]
  7. A. Vasiliev et al.Spatial Light Modulators (Radio I Svjaz’, Moscow, 1987).
  8. L.M. Blinov, V.G. Chigrinov, Electrooptic effects in liquid crystal materials (Springer-Verlag, New York, 1994).
    [CrossRef]
  9. P. Vashurin et al. “Image contrast enhancement with LC SLM,” Preprint Lebedev Physics Institute, 250, 1–27 (1985).
  10. H. Rehn, R. Kowarschik, “Real-time non-linear spatial filtering with a leaky OASLM,” Optics and Laser Technology, 30, 39–47 (1998).
    [CrossRef]

1998

H. Rehn, R. Kowarschik, “Real-time non-linear spatial filtering with a leaky OASLM,” Optics and Laser Technology, 30, 39–47 (1998).
[CrossRef]

1994

C.R. Mercer, K. Creath, “Liquid crystal point-diffraction interferomeler,” Optics Letters, 19, 916–18 (1994).
[CrossRef]

1988

K. Harada et al., “Nonlinear image self-filtering with liquid crystal spatial light modulator,” Optics and Laser Technology, 30, 147–55 (1988).
[CrossRef]

1987

A. Naumov et al., “Dynamic image self-filtering,” Bulletin of Lebedev Physics Institute, 10, 8–13 (1987).

1975

R.N. Smartt, W.H. Steel, “Theory and application of point-diffraction interferometers,” Jap.J.Appl.Phys., 14, (Suppl. 141), 351–6 (1975).

1933

V.P. Linnik, “Simple interferometer for investigation of optical schemes,” C.R.Acad.Sci.USSR, 1, 208–10 (1933).

Blinov, L.M.

L.M. Blinov, V.G. Chigrinov, Electrooptic effects in liquid crystal materials (Springer-Verlag, New York, 1994).
[CrossRef]

Chigrinov, V.G.

L.M. Blinov, V.G. Chigrinov, Electrooptic effects in liquid crystal materials (Springer-Verlag, New York, 1994).
[CrossRef]

Creath, K.

C.R. Mercer, K. Creath, “Liquid crystal point-diffraction interferomeler,” Optics Letters, 19, 916–18 (1994).
[CrossRef]

Harada, K.

K. Harada et al., “Nonlinear image self-filtering with liquid crystal spatial light modulator,” Optics and Laser Technology, 30, 147–55 (1988).
[CrossRef]

Hariharan, P.

P. Hariharan, Optical interferometry, (Academic Press, Sydney; Orlando, 1985).

Kowarschik, R.

H. Rehn, R. Kowarschik, “Real-time non-linear spatial filtering with a leaky OASLM,” Optics and Laser Technology, 30, 39–47 (1998).
[CrossRef]

Linnik, V.P.

V.P. Linnik, “Simple interferometer for investigation of optical schemes,” C.R.Acad.Sci.USSR, 1, 208–10 (1933).

Mercer, C.R.

C.R. Mercer, K. Creath, “Liquid crystal point-diffraction interferomeler,” Optics Letters, 19, 916–18 (1994).
[CrossRef]

Naumov, A.

A. Naumov et al., “Dynamic image self-filtering,” Bulletin of Lebedev Physics Institute, 10, 8–13 (1987).

Rehn, H.

H. Rehn, R. Kowarschik, “Real-time non-linear spatial filtering with a leaky OASLM,” Optics and Laser Technology, 30, 39–47 (1998).
[CrossRef]

Smartt, R.N.

R.N. Smartt, W.H. Steel, “Theory and application of point-diffraction interferometers,” Jap.J.Appl.Phys., 14, (Suppl. 141), 351–6 (1975).

Steel, W.H.

R.N. Smartt, W.H. Steel, “Theory and application of point-diffraction interferometers,” Jap.J.Appl.Phys., 14, (Suppl. 141), 351–6 (1975).

Vashurin, P.

P. Vashurin et al. “Image contrast enhancement with LC SLM,” Preprint Lebedev Physics Institute, 250, 1–27 (1985).

Vasiliev, A.

A. Vasiliev et al.Spatial Light Modulators (Radio I Svjaz’, Moscow, 1987).

Bulletin of Lebedev Physics Institute

A. Naumov et al., “Dynamic image self-filtering,” Bulletin of Lebedev Physics Institute, 10, 8–13 (1987).

C.R.Acad.Sci.USSR

V.P. Linnik, “Simple interferometer for investigation of optical schemes,” C.R.Acad.Sci.USSR, 1, 208–10 (1933).

Jap.J.Appl.Phys.

R.N. Smartt, W.H. Steel, “Theory and application of point-diffraction interferometers,” Jap.J.Appl.Phys., 14, (Suppl. 141), 351–6 (1975).

Optics and Laser Technology

K. Harada et al., “Nonlinear image self-filtering with liquid crystal spatial light modulator,” Optics and Laser Technology, 30, 147–55 (1988).
[CrossRef]

H. Rehn, R. Kowarschik, “Real-time non-linear spatial filtering with a leaky OASLM,” Optics and Laser Technology, 30, 39–47 (1998).
[CrossRef]

Optics Letters

C.R. Mercer, K. Creath, “Liquid crystal point-diffraction interferomeler,” Optics Letters, 19, 916–18 (1994).
[CrossRef]

Other

P. Hariharan, Optical interferometry, (Academic Press, Sydney; Orlando, 1985).

A. Vasiliev et al.Spatial Light Modulators (Radio I Svjaz’, Moscow, 1987).

L.M. Blinov, V.G. Chigrinov, Electrooptic effects in liquid crystal materials (Springer-Verlag, New York, 1994).
[CrossRef]

P. Vashurin et al. “Image contrast enhancement with LC SLM,” Preprint Lebedev Physics Institute, 250, 1–27 (1985).

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Figures (3)

Figure 1
Figure 1

Optical setup: PR, polarizing beam splitter; S and P, waves polarized orthogonally; α, angle between the beams; SLM, spatial light modulator; L1, L2, Fourier lenses; WF, investigated wavefront; POL, lineal polarizer; IP, interference pattern.

Figure 2
Figure 2

Interferogram of polymer stripes with nonlinear filtering (a) and without (b) nonlinear filtering, when the scheme turns into a regular shearing interferometer. The period of pattern is 20µm.

Figure 3
Figure 3

The trace of contact scanning for the object (where each 100nm of thickness variation corresponds approximately to the phase shift of 0.5 rad for the given polymer), Inset shows a surface profile reconstructed from the optical measurements.

Equations (5)

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E1 + E2  AE0 exp(ik · r + iφ(r)) + BE0 exp(ik1 · r)
E1 + E22  E02const + cosφ(r) + K · r
Eout(r) = ϕ(Ω)expiTϕ(Ω)2 exp(iΩ · r)dΩ
Eout = Ein + iβE02Einφ(Ω)φ(Ω)2exp(iΩ · r)dΩ
δϕ  βIφ2

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