Abstract

Two-wavelength double heterodyne interferometry is applied for topographic measurements on optically rough target surfaces. A two-wavelength He–Ne laser and a matched grating technique are used to improve system stability and to simplify heterodyne frequency generation.

© 1991 Optical Society of America

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References

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  1. O. Kwon, J. C. Wyant, C. R. Hayslett, “Rough Surface Interferometry at 10.6 μm,” Appl. Opt. 19, 1862–1869 (1980).
    [CrossRef] [PubMed]
  2. M. V. R. K. Murty, R. P. Shukla, “An Oblique Incidence Interferometer,” Opt. Eng. 15, 451 (1976).
  3. J. C. Wyant, “Testing Aspherics Using Two-Wavelength Holography,” Appl. Opt. 10, 2113–2118 (1971).
    [CrossRef] [PubMed]
  4. F. M. Kuchel, H. J. Tiziani, “Real-Time Contour Holography Using BSO Crystals,” Opt. Commun. 38, 17 (1981).
    [CrossRef]
  5. C. Polhemus, “Two-Wavelength Interferometry,” Appl. Opt. 12, 2071–2074 (1973).
    [CrossRef] [PubMed]
  6. A. F. Fercher, H. Z. Hu, U. Vry, “Rough Surface Interferometry with a Two-Wavelength Heterodyne Speckle Interferometer,” Appl. Opt. 24, 2181–2288 (1985).
    [CrossRef] [PubMed]
  7. R. Dandliker, R. Thalmann, D. Prongue, “Two-Wavelength Laser Interferometry Using Super-Heterodyne Detection,” Proc. Soc. Photo-Opt. Instrum. Eng. 813 (1987).

1987 (1)

R. Dandliker, R. Thalmann, D. Prongue, “Two-Wavelength Laser Interferometry Using Super-Heterodyne Detection,” Proc. Soc. Photo-Opt. Instrum. Eng. 813 (1987).

1985 (1)

1981 (1)

F. M. Kuchel, H. J. Tiziani, “Real-Time Contour Holography Using BSO Crystals,” Opt. Commun. 38, 17 (1981).
[CrossRef]

1980 (1)

1976 (1)

M. V. R. K. Murty, R. P. Shukla, “An Oblique Incidence Interferometer,” Opt. Eng. 15, 451 (1976).

1973 (1)

1971 (1)

Dandliker, R.

R. Dandliker, R. Thalmann, D. Prongue, “Two-Wavelength Laser Interferometry Using Super-Heterodyne Detection,” Proc. Soc. Photo-Opt. Instrum. Eng. 813 (1987).

Fercher, A. F.

Hayslett, C. R.

Hu, H. Z.

Kuchel, F. M.

F. M. Kuchel, H. J. Tiziani, “Real-Time Contour Holography Using BSO Crystals,” Opt. Commun. 38, 17 (1981).
[CrossRef]

Kwon, O.

Murty, M. V. R. K.

M. V. R. K. Murty, R. P. Shukla, “An Oblique Incidence Interferometer,” Opt. Eng. 15, 451 (1976).

Polhemus, C.

Prongue, D.

R. Dandliker, R. Thalmann, D. Prongue, “Two-Wavelength Laser Interferometry Using Super-Heterodyne Detection,” Proc. Soc. Photo-Opt. Instrum. Eng. 813 (1987).

Shukla, R. P.

M. V. R. K. Murty, R. P. Shukla, “An Oblique Incidence Interferometer,” Opt. Eng. 15, 451 (1976).

Thalmann, R.

R. Dandliker, R. Thalmann, D. Prongue, “Two-Wavelength Laser Interferometry Using Super-Heterodyne Detection,” Proc. Soc. Photo-Opt. Instrum. Eng. 813 (1987).

Tiziani, H. J.

F. M. Kuchel, H. J. Tiziani, “Real-Time Contour Holography Using BSO Crystals,” Opt. Commun. 38, 17 (1981).
[CrossRef]

Vry, U.

Wyant, J. C.

Appl. Opt. (4)

Opt. Commun. (1)

F. M. Kuchel, H. J. Tiziani, “Real-Time Contour Holography Using BSO Crystals,” Opt. Commun. 38, 17 (1981).
[CrossRef]

Opt. Eng. (1)

M. V. R. K. Murty, R. P. Shukla, “An Oblique Incidence Interferometer,” Opt. Eng. 15, 451 (1976).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

R. Dandliker, R. Thalmann, D. Prongue, “Two-Wavelength Laser Interferometry Using Super-Heterodyne Detection,” Proc. Soc. Photo-Opt. Instrum. Eng. 813 (1987).

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Figures (6)

Fig. 1
Fig. 1

Schematic double heterodyne interferometry setup.

Fig. 2
Fig. 2

Double heterodyne interferometer with solid-state matched gratings.

Fig. 3
Fig. 3

Double heterodyne interferometer with a rotational matched grating.

Fig. 4
Fig. 4

(Upper part) superposition of heterodyne frequencies; (lower part) squared and band-pass filtered heterodyne beat signal.

Fig. 5
Fig. 5

Phase response from a target distance variation of 100 μm.

Fig. 6
Fig. 6

Topography obtained from two successive line scans on a milled aluminum sample with step heights of 5 μm and 10 μm and superimposed by periodic height variations from the scan table.

Equations (12)

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a 1 = A 1 exp [ i ( 2 π v 1 t - 4 π v 1 c z ) ] ,
a 2 = A 2 exp [ i ( 2 π v 2 t - 4 π v 2 c z ) ] ,
a 3 = A 3 exp [ i ( 2 π ( v 1 + f 1 ) t - 2 π v 1 + f 1 c l 1 ) ] ,
a 4 = A 4 exp [ i ( 2 π ( v 2 + f 2 ) t - 2 π v 2 + f 2 c l 2 ) ] .
I = a 1 + a 3 2 + a 2 + a 4 2 = ( a 1 + a 3 ) ( a 1 * + a 3 * ) + ( a 2 + a 4 ) ( a 2 * + a 4 * ) .
I = A 1 2 + A 2 2 + A 3 2 + A 4 2 + 2 A 1 A 3 cos ( 2 π f 1 t + 4 π v 1 c z - 2 π v 1 + f 1 c l 1 ) + 2 A 2 A 4 cos ( 2 π f 2 t + 4 π v 2 c z - 2 π v 2 + f 2 c l 2 ) .
I 2 = 2 A 1 2 A 3 2 + 2 A 2 2 A 4 2 + 2 A 1 2 A 3 2 cos ( 4 π f 1 t + 8 π v 1 c z - 4 π v 1 + f 1 c l 1 ) + 2 A 2 2 A 4 2 cos ( 4 π f 2 t + 8 π v 2 c z - 4 π v 2 + f 2 c l 2 ) + 4 A 1 A 2 A 3 A 4 cos ( 2 π ( f 1 - f 2 ) t + 4 π v 1 - v 2 c z - 2 π v 1 + f 1 c l 1 + 2 π v 2 + f 2 c l 2 ) 4 A 1 A 2 A 3 A 4 cos ( 2 π ( f 1 + f 2 ) t + 4 π v 1 + v 2 c z - 2 π v 1 + f 1 c l 1 - 2 π v 2 + f 2 c l 2 )
ϕ = 4 π ( v 1 - v 2 c ) z - 2 π ( v 1 l 1 - v 2 l 2 c ) ,
δ ϕ = ϕ v 1 δ v 1 + ϕ v 2 δ v 2 + ϕ l 1 δ l 1 + ϕ l 2 δ l 2 , δ ϕ = ( 4 π z c - 2 π l 1 c ) δ v 1 + ( - 4 π z c + 2 π l 2 c ) δ v 2 - 2 π v 1 c δ l 1 + 2 π v 2 c δ l 2 .
δ ϕ = 2 π c Δ l δ v + 2 π λ ef δ l ,
Δ α = 2 λ v f m ,
Δ α = λ 2 g 1 - ( λ 1 g ) 2 - λ 1 g 1 - ( λ 2 g ) 2 ,

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