Abstract

A two-wavelength interferometer is described that can be used to measure distances to rough surfaces with micrometer resolution. The measuring range can be made as large as several centimeters. Owing to the small numerical aperture of the object beam, the interferometer is particularly suitable in applications where a long working distance is required. The interferometer uses two single-frequency diode lasers to create a virtual two-wavelength laser. The equivalent wavelength of this laser can be easily tuned by changing the temperature of the laser diodes in opposite directions.

© 1988 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Tatsuno, Y. Tsunoda, “Diode Laser Direct Modulation Heterodyne Interferometer,” Appl. Opt. 26, 37 (1987).
    [CrossRef] [PubMed]
  2. H. Kikuta, K. Iwata, R. Nagata, “Distance Measurement by the Wavelength Shift of Laser Diode Light,” Appl. Opt. 25, 2976 (1986).
    [CrossRef] [PubMed]
  3. A. J. den Boef, “Interferometric Laser Rangefinder Using a Frequency Modulated Diode Laser,” Appl. Opt. 26, 4545 (1987).
    [CrossRef]
  4. C. Williams, H. K. Wickramasinghe, “Optical Ranging by Wavelength Multiplexed Interferometry,” J. Appl. Phys. 60, 1900 (1986).
    [CrossRef]
  5. T. Hayakawa et al., “Highly Reliable and Mode Stabilised Operation in V-Channeled Substrate Inner Stripe Laser on p-GaAs Substrate Emitting in the Visible Wavelength Region,” J. Appl. Phys. 53, 7224 (1982).
    [CrossRef]
  6. J. W. Goodman, “Statistical Properties of Laser Speckle Patterns” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, Berlin, 1975).
    [CrossRef]
  7. U. Vry, A. F. Fercher, “Higher-Order Statistical Properties of Speckle Fields and Their Application to Rough-Surface Interferometry,” J. Opt. Soc. Am. A 3, 988 (1986).
    [CrossRef]
  8. U. Vry, “Absolute Statistical Error in Two-Wavelength Rough Surface Interferometry (ROSI),” Opt. Acta 33, 1221 (1986).
    [CrossRef]
  9. A. F. Fercher, H. Z. Hu, U. Vry, “Rough Surface Interferometry with a Two-Wavelength Heterodyne Speckle Interferometer,” Appl. Opt. 24, 2181 (1985).
    [CrossRef] [PubMed]

1987 (2)

1986 (4)

H. Kikuta, K. Iwata, R. Nagata, “Distance Measurement by the Wavelength Shift of Laser Diode Light,” Appl. Opt. 25, 2976 (1986).
[CrossRef] [PubMed]

C. Williams, H. K. Wickramasinghe, “Optical Ranging by Wavelength Multiplexed Interferometry,” J. Appl. Phys. 60, 1900 (1986).
[CrossRef]

U. Vry, “Absolute Statistical Error in Two-Wavelength Rough Surface Interferometry (ROSI),” Opt. Acta 33, 1221 (1986).
[CrossRef]

U. Vry, A. F. Fercher, “Higher-Order Statistical Properties of Speckle Fields and Their Application to Rough-Surface Interferometry,” J. Opt. Soc. Am. A 3, 988 (1986).
[CrossRef]

1985 (1)

1982 (1)

T. Hayakawa et al., “Highly Reliable and Mode Stabilised Operation in V-Channeled Substrate Inner Stripe Laser on p-GaAs Substrate Emitting in the Visible Wavelength Region,” J. Appl. Phys. 53, 7224 (1982).
[CrossRef]

den Boef, A. J.

Fercher, A. F.

Goodman, J. W.

J. W. Goodman, “Statistical Properties of Laser Speckle Patterns” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, Berlin, 1975).
[CrossRef]

Hayakawa, T.

T. Hayakawa et al., “Highly Reliable and Mode Stabilised Operation in V-Channeled Substrate Inner Stripe Laser on p-GaAs Substrate Emitting in the Visible Wavelength Region,” J. Appl. Phys. 53, 7224 (1982).
[CrossRef]

Hu, H. Z.

Iwata, K.

Kikuta, H.

Nagata, R.

Tatsuno, K.

Tsunoda, Y.

Vry, U.

Wickramasinghe, H. K.

C. Williams, H. K. Wickramasinghe, “Optical Ranging by Wavelength Multiplexed Interferometry,” J. Appl. Phys. 60, 1900 (1986).
[CrossRef]

Williams, C.

C. Williams, H. K. Wickramasinghe, “Optical Ranging by Wavelength Multiplexed Interferometry,” J. Appl. Phys. 60, 1900 (1986).
[CrossRef]

Appl. Opt. (4)

J. Appl. Phys. (2)

C. Williams, H. K. Wickramasinghe, “Optical Ranging by Wavelength Multiplexed Interferometry,” J. Appl. Phys. 60, 1900 (1986).
[CrossRef]

T. Hayakawa et al., “Highly Reliable and Mode Stabilised Operation in V-Channeled Substrate Inner Stripe Laser on p-GaAs Substrate Emitting in the Visible Wavelength Region,” J. Appl. Phys. 53, 7224 (1982).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

U. Vry, “Absolute Statistical Error in Two-Wavelength Rough Surface Interferometry (ROSI),” Opt. Acta 33, 1221 (1986).
[CrossRef]

Other (1)

J. W. Goodman, “Statistical Properties of Laser Speckle Patterns” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, Berlin, 1975).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Setup of the interferometer. The two laser beams with wavelengths λ1 and λ2 are mixed with a polarizing beam splitter PBS1. After this the combined laser beams are split into a reference beam and an object beam with a neutral beam splitter NPBS. Both the ongoing and returning object beams are spatially filtered (SF) and phase modulated (PM) with a vibrating mirror. Mirror M s is used to scan the object beam across the optically rough surface of the object. The second polarizing beam splitter (PBS2) is used to separate the individual phase-modulated interference patterns cos(2πΔx1 + ϕ1) and cos(2πΔx2 + ϕ2). Both interference patterns are detected with two photodiodes and processed to yield two height signals C and S.

Fig. 2
Fig. 2

Schematic setup of the electronic hardware processing of the two interference patterns P1(t) and P2(t). For the sake of clarity the low-noise preamplifiers used to amplify P1(t) and P2(t) have not been shown. Both time-varying interference patterns are synchronously amplified (PSD1 through PSD4) using two distinct reference signals. One reference signal (f0) is used to detect the amplitude of the fundamental frequency of P j (t), while the second reference signal (2f0) is used to detect the amplitude of the first harmonic P j (t). The four resulting signals, f1, f2, g1, and g2, are sent to a computational unit containing high-precision four-quadrant multipliers. The outputs of this computational unit are signals A1A2 sin(Δωτ0) and A1A2 cos(Δωτ0). Finally, those signals are processed by a normalization circuit to eliminate the unknown quantity A1A2 thus producing two height signals C and S.

Fig. 3
Fig. 3

Calculated plot of the height signals C and S as a function of Δωτ0. The continuous line is the calculated shape of C and S, and the dashed line indicates the straight line approximation. The error that is introduced by using the straight line approximation rather than the exact form of C and S is indicated in the figure for a value of S = −0.25. The error varies periodically as a function of the phase Δωτ0. The amplitude of the error is ~0.027π.

Fig. 4
Fig. 4

Results of the measurement of field curvature: (A) and (B) measured values of C and S, respectively; (C) the reconstructed OPD (optical path difference) in the interferometer.

Fig. 5
Fig. 5

Results of a measurement of C and S as a function of position on a slightly tilted plastic sample. The noise is mainly due to small normalization errors in the normalization and linearization circuit. The overall shape of C and S can best be observed by inspecting the figures at grazing incidence to the printed page.

Fig. 6
Fig. 6

(A) Results of a measurement of a part of a spherically shaped bowl used in an x-ray image intensifier. The original measurement, consisting of 1000 points, has been smoothed with a 30-points averaging window. The same profile, measured with a mechanical profilometer, is shown in (B). The positions where the profile has been measured are indicated by dots. Owing to a nonlinearity error of the scan mirror used in the interferometer, small scaling errors are present in the horizontal scale of (A).

Fig. 7
Fig. 7

Measurement results of a dented brass plate. The dent was introduced by bending and reflattening the plate. No smoothing has been applied to this measurement.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

P j ( t ) = P j 0 + γ j 2 P j 0 + 2 γ j P j 0 cos [ ω j τ 0 + ω j Δ τ ^ cos ( 2 π f 0 t ) ] , j = 1 , 2 .
P j 1 ( t ) = 4 γ j P j 0 sin ( ω j τ 0 ) J 1 ( ω j Δ τ ^ ) cos ( 2 π f 0 t ) ,
P j 2 ( t ) = 4 γ j P j 0 cos ( ω j τ 0 ) J 2 ( ω j Δ τ ^ ) cos ( 2 π 2 f 0 t ) , j = 1 , 2 .
f j = P j 1 ( t ) cos ( 2 π f 0 t ) = A j 1 sin ( ω j τ 0 ) ,
g j = P j 2 ( t ) cos ( 2 π 2 f 0 t ) = A j 2 cos ( ω j τ 0 ) , j = 1 , 2 .
g 1 g 2 + f 1 f 2 = A 1 A 2 cos ( Δ ω τ 0 ) ,
f 1 g 2 f 2 g 1 = A 1 A 2 sin ( Δ ω τ 0 ) ,
C ( Δ ω τ 0 ) = A 1 A 2 cos ( Δ ω τ 0 ) | A 1 A 2 cos ( Δ ω τ 0 ) | + | A 1 A 2 sin ( Δ ω τ 0 ) | ,
S ( Δ ω τ 0 ) = A 1 A 2 sin ( Δ ω τ 0 ) | A 1 A 2 cos ( Δ ω τ 0 ) | + | A 1 A 2 sin ( Δ ω τ 0 ) | .
p ( I 1 , I 2 , ϕ ) = exp [ I 1 + I 2 2 I 1 I 2 | μ | cos ( ϕ ) 1 | μ | 2 ] 2 π ( 1 | μ | 2 ) .
μ = A 1 * A 2 = exp ( 2 π i Δ x λ eq ) exp ( 8 π 2 δ h 2 λ eq 2 ) ;
δ ϕ 2 = 0 0 π π ϕ 2 p ( I 1 , I 2 , ϕ ) d ϕ d I 1 d I 2 ,

Metrics