Abstract

A novel configuration that combines a linearly polarized He–Ne laser and a birefringent lens to produce a common-path polarized optical heterodyne profilometer with respect to the heterodyned P and S waves has been set up. In this profilometer a linear polarized frequency-stabilized He–Ne laser was used with an acousto-optical modulator to replace the Zeeman laser as the light source that had two polarization eigenstates in different temporal frequencies. The proposed interferometer shows a more symmetric and ideal common-path structure than the conventional optical heterodyne profilometers with the Zeeman laser. The phase error aroused by the elliptical polarization and the nonorthogonality of the two eigenpolarization modes of the Zeeman laser can be reduced. The system’s resolution in the vertical direction reaches 2 Å, and in a 27-μm scanning range the repeatability of the surface profile measurements is shown to be 5 Å.

© 1998 Optical Society of America

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References

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1997

W. Zhou, Z. Zhou, G. Chi, “Investigation of common path interference profilometry,” Opt. Eng. 36, 3172–3175 (1997).
[CrossRef]

B. Li, J. W. Liang, “Effect of polarization mixing on the dual wavelength heterodyne interferometer,” Appl. Opt. 36, 3668–3672 (1997).
[CrossRef] [PubMed]

1994

1993

1992

1989

1988

1987

1986

1984

C. C. Huang, “Optical heterodyne profilometer,” Opt. Eng. 23, 365–369 (1984).
[CrossRef]

1981

1975

Balakshy, I.

I. Balakshy, J. A. Hassan, “Polarization effects in acousto-optic interaction,” Opt Eng. 32, 746–751 (1993).
[CrossRef]

Barger, R. L.

Bodwin, H. M.

Chi, G.

W. Zhou, Z. Zhou, G. Chi, “Investigation of common path interference profilometry,” Opt. Eng. 36, 3172–3175 (1997).
[CrossRef]

Cohen, S. C.

Dandliker, R.

Ek, L.

Faller, J. E.

Hall, J. L.

Hassan, J. A.

I. Balakshy, J. A. Hassan, “Polarization effects in acousto-optic interaction,” Opt Eng. 32, 746–751 (1993).
[CrossRef]

Huang, C. C.

C. C. Huang, “Optical heterodyne profilometer,” Opt. Eng. 23, 365–369 (1984).
[CrossRef]

Li, B.

Liang, J. W.

Lin, Y.

Nibaner, T. M.

Ohta, N.

Pantzer, D.

Politch, J.

Prongué, D.

Schill, J.

Sommargren, G.

Tanaka, K.

Thalmann, R.

Wang, R. W.

Wu, Y.

Wu, Y. Z.

Xie, Y.

Zhou, W.

W. Zhou, Z. Zhou, G. Chi, “Investigation of common path interference profilometry,” Opt. Eng. 36, 3172–3175 (1997).
[CrossRef]

Zhou, Z.

W. Zhou, Z. Zhou, G. Chi, “Investigation of common path interference profilometry,” Opt. Eng. 36, 3172–3175 (1997).
[CrossRef]

Appl. Opt.

Opt Eng.

I. Balakshy, J. A. Hassan, “Polarization effects in acousto-optic interaction,” Opt Eng. 32, 746–751 (1993).
[CrossRef]

Opt. Eng.

W. Zhou, Z. Zhou, G. Chi, “Investigation of common path interference profilometry,” Opt. Eng. 36, 3172–3175 (1997).
[CrossRef]

C. C. Huang, “Optical heterodyne profilometer,” Opt. Eng. 23, 365–369 (1984).
[CrossRef]

Opt. Lett.

Other

Fujian CASIX laser Inc., Fujian, China.

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Figures (3)

Fig. 1
Fig. 1

Experimental setup of the common-path optical heterodyne profilometer: I, isolater; AO1, AO2, acousto-optic modulators; BS1, BS2, beam splitters; L1, lens; PBS, polarized beam splitter; D1, D2, drivers; M1, M2, reflection mirrors; BF1, BF2, bandpass filters; Dp, Ds, photodetectors; PC, personal computer.

Fig. 2
Fig. 2

Repeated surface profile of an optical flat driven by a PZT stage. The hysterisis effect of the PZT scans different paths in each measurement.

Fig. 3
Fig. 3

Profile of the test surface in a 27-μm scanning range (a) in the forward direction, (b) in the backward direction. The measurement is repeated 6 times with 5-Å repeatability.

Tables (1)

Tables Icon

Table 1 Phase Contributions of Different Parameters and Variations

Equations (15)

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I p Δ ω t = | A P 1 exp i ω 1 t + ϕ p 1 + A P 2 × exp i ω 2 t + ϕ p 2 | 2 = I p 1 + I p 2 + 2 I p 1 I p 2 1 / 2 × cos Δ ω t + ϕ p 1 - ϕ p 2 ,
I s Δ ω t = | A s 1 exp i ω 1 t + ϕ s 1 + A s 2 × exp i ω 2 t + ϕ s 2 | 2 = I s 1 + I s 2 + 2 I s 1 I s 2 × cos Δ ω t + ϕ s 1 - ϕ s 2 ,
I p 1 I p 2 I s 1 I s 2 1 / 2 ,
ϕ = 2 ω 0 h c + 2 ω 2 h c - Δ ω c   z ps ,
Δ ϕ = 2 c ω 0 Δ h + ω 2 Δ h + Δ ω 0 h + Δ ω 2 h - Δ ω Δ z ps 2 - z ps Δ Δ ω 2 .
Δ h c 2 ω 0   Δ ϕ = λ 4 π   Δ ϕ .
E p 1 = A p 1 exp i ω 0 + ω 1 t + k 1 z 1 + z p ,
E s 1 = A s 1 exp i ω 0 + ω 1 t + k 1 z 1 + z s ,
E p 2 = A p 2 exp i ω 0 + ω 2 t + k 2 z 2 + z p + 2 z c ,
E s 2 = A s 2 exp i ω 0 + ω 2 t + k 2 z 2 + z s + 2 z av ,
I p Δ ω t = | A p 1 exp i ω 1 + ω 0 t + k 1 z 1 + z p + A p 2 exp i ω 2 + ω 0 t + k 2 z 2 + z p + 2 z c | 2 2 A p 1 A p 2 cos Δ ω t + k 2 z 2 + z p + 2 z c - k 1 z 1 + z p ,
I s Δ ω t = | A s 1 exp i ω 1 + ω 0 t + k 1 z 1 + z s + A s 2 exp i ω 2 + ω 0 t + k 2 z 2 + z s + 2 z av | 2 - 2 A s 1 A s 2 cos Δ ω t + k 2 z 2 + z s + 2 z av - k 1 ( z 1 + z s .
ϕ = 2 k 2 z c - z av + k 1 - k 2 z s - z p = 2 ω 0 c   h + 2 ω 2 c   h - Δ ω c   z ps ,
Δ ϕ = 2 c ω 0 Δ h + ω 2 Δ h + Δ ω 0 h + Δ ω 2 h - Δ ω Δ z ps 2 - z ps Δ Δ ω 2 .
Δ h c 2 ω 0   Δ ϕ = λ 4 π   Δ ϕ .

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