Abstract

Multiple-wavelength optical fields on a detecting plane of an interferometer are generated from the interference signals detected for an object surface. The generated optical fields are backpropagated along the optical axis. An optical field along the optical axis is reconstructed by summing the backpropagated fields over the multiple wavelengths. The intensity and phase distributions of the reconstructed optical field provide the position of the object surface with an accuracy of a few nanometers.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]

2002

1997

1994

H. J. Tiziani, B. Franze, and P. Haible, J. Mod. Opt. 44, 1485 (1994).
[CrossRef]

1986

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Figures (5)

Fig. 1
Fig. 1

Sinusoidal phase-modulating interferometer using multiple wavelengths for step-profile measurement.

Fig. 2
Fig. 2

Simulation results of the backpropagation method at (a) σ = 0.2 rad and (b) σ = 0.4 rad .

Fig. 3
Fig. 3

Simulation results of the unwrapped phase distribution at σ = 0.2 rad that is used in the phase gradient method.

Fig. 4
Fig. 4

Measurement result of an optical surface with a step shape of about 1000 μ m height.

Fig. 5
Fig. 5

Distributions of I R and Φ R at points A and B, whose x-coordinates are (a) 2 mm and (b) 6 mm , respectively, on the line of y = 4 mm in Fig. 4.

Tables (1)

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Table 1 Simulation Results of the Backpropagation Method and the Phase Gradient Method

Equations (9)

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λ m = λ 0 + m Δ λ m = 0 , 1 , , M 1 ,
S ( t , m ) = A m + B m cos ( Z cos ω c t + α m ) ,
D ( m ) = B m exp ( j α m ) m = 0 , 1 , , M 1 .
U m ( L ) = D ( m ) exp [ j ( 2 π λ m ) L ] .
U R ( L ) = m = 0 M 1 U m ( L ) = U R exp ( j Φ R ) .
U R = sin [ π ( B λ λ 0 2 ) L D ] sin [ π ( Δ λ λ 0 2 ) L D ] ,
Φ R = ( 2 π λ C ) L D ,
λ C = λ 0 + [ ( M 1 ) Δ λ 2 ] .
L max = λ 0 2 Δ λ ,

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