Abstract

A dual-wavelength heterodyne differential interferometer was developed and tested together with scanning mechanics. To extend the range of unambiguity, two wavelengths were applied. This is important for measuring structures with surface discontinuities (reliefs, steps). The automatic adjustment of the interferometer with respect to the rotational symmetrical measuring surfaces (aspheres) is important. An adjustment is needed to scan the asphere through its vertex. Typical measurements on a sphere, an asphere, and steps are shown.

© 1996 Optical Society of America

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References

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  1. H. J. Tiziani, “Prospects of testing aspheric surfaces with computer-generated holograms,” in Aspheric Optics: Design, Manufacture, Testing, P. Kuttner, T. L. Williams, eds., Proc. SPIE235, 72–79 (1980).
  2. B. Dörband, “Die 3-Interferogramm-Methode zur automatischen Streifenauswertung in rechnergesteuerten digitalen Zweistrahlinterferometern,” Optik 60, 161–174 (1982).
  3. S. D. Fantone, “Holographic interferometer for testing molds and molded parts,” Appl. Opt. 22, 1121–1126 (1983).
    [PubMed]
  4. H. J. Tiziani, “On the application of synthetic holograms for testing aspheric surfaces,” in Conference Digest of ICO (Sapporo) (Internation Commission on Optics, 1984), pp. 390–391.
  5. B. Dörband, “Auslegung von Kompensationssystemen zur interferometrischen Prüfung asphärischer Flächen,” Optik 67, 1–20 (1984).
  6. B. Dörband, “Interferometrische Messtechnik zur Prüfung asphärischer Kontaklinsen,” Die Kontaktlinse 1, 14–31 (1985).
  7. B. Dörband, H. J. Tiziani, “Analysis of adjustment and shape errors when testing aspheric surfaces with computer generated holograms,” Appl. Opt. 24, 2604–2611 (1985).
    [CrossRef] [PubMed]
  8. B. Dörband, B. Packross, Huppertz, “Asphärische KL-Rückflächen im Vergleich,” Der Augenoptiker 2, 14–24 (1986).
  9. J. C. Wyant, “Testing aspherics using two-wavelength holography,” Appl. Opt. 10, 2113–2118 (1971).
    [CrossRef] [PubMed]
  10. C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071–2074 (1973).
    [CrossRef] [PubMed]
  11. F. Bien, M. Camac, H. J. Caulfield, S. Ezekiel, “Absolute distance measure by variable wavelength interferometry,” Appl. Opt. 20, 400–403 (1981).
    [CrossRef] [PubMed]
  12. G. E. Sommargren, “Optical heterodyne profilometry,” Appl. Opt. 20, 610–618 (1981).
    [CrossRef] [PubMed]
  13. A. F. Fercher, H. Z. Hu, U. Vry, “Rough surface interferometry with a two-wavelength heterodyne speckle interferometer,” Appl. Opt. 24, 2181–2188 (1985).
    [CrossRef] [PubMed]
  14. K. Creath, Y.-Y. Cheng, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Opt. Acta 32, 1455–1464 (1985).
    [CrossRef]
  15. R. Dändliker, R. Thalmann, D. Prongué, “Two-wavelength laser interferometry using superheterodyne detection,” Opt. Lett. 13, 339–341 (1988).
    [CrossRef] [PubMed]
  16. Z. Sodnik, E. Fischer, T. Ittner, H. Tiziani, “Two-wavelength double heterodyne interferometry using a matched grating technique,” Appl. Opt. 30, 3139–3144 (1991).
    [CrossRef] [PubMed]
  17. E. Heynacher, “Fertigung asphärischer Flächen durch form-gebende Bearbeitung und durch Abgieβen,” Optik 45, 249–267 (1976).
  18. M. Gottlieb, C. L. M. Ireland, J. M. Ley, Electro-optic and Acousto-optic Scanning and Deflection (Marcel Dekker, New York, 1983).
  19. A. Korpel, Acousto-optics (Marcel Dekker, New York, 1988).

1991 (1)

1988 (1)

1986 (1)

B. Dörband, B. Packross, Huppertz, “Asphärische KL-Rückflächen im Vergleich,” Der Augenoptiker 2, 14–24 (1986).

1985 (4)

B. Dörband, “Interferometrische Messtechnik zur Prüfung asphärischer Kontaklinsen,” Die Kontaktlinse 1, 14–31 (1985).

B. Dörband, H. J. Tiziani, “Analysis of adjustment and shape errors when testing aspheric surfaces with computer generated holograms,” Appl. Opt. 24, 2604–2611 (1985).
[CrossRef] [PubMed]

A. F. Fercher, H. Z. Hu, U. Vry, “Rough surface interferometry with a two-wavelength heterodyne speckle interferometer,” Appl. Opt. 24, 2181–2188 (1985).
[CrossRef] [PubMed]

K. Creath, Y.-Y. Cheng, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Opt. Acta 32, 1455–1464 (1985).
[CrossRef]

1984 (1)

B. Dörband, “Auslegung von Kompensationssystemen zur interferometrischen Prüfung asphärischer Flächen,” Optik 67, 1–20 (1984).

1983 (1)

1982 (1)

B. Dörband, “Die 3-Interferogramm-Methode zur automatischen Streifenauswertung in rechnergesteuerten digitalen Zweistrahlinterferometern,” Optik 60, 161–174 (1982).

1981 (2)

1976 (1)

E. Heynacher, “Fertigung asphärischer Flächen durch form-gebende Bearbeitung und durch Abgieβen,” Optik 45, 249–267 (1976).

1973 (1)

1971 (1)

Bien, F.

Camac, M.

Caulfield, H. J.

Cheng, Y.-Y.

K. Creath, Y.-Y. Cheng, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Opt. Acta 32, 1455–1464 (1985).
[CrossRef]

Creath, K.

K. Creath, Y.-Y. Cheng, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Opt. Acta 32, 1455–1464 (1985).
[CrossRef]

Dändliker, R.

Dörband, B.

B. Dörband, B. Packross, Huppertz, “Asphärische KL-Rückflächen im Vergleich,” Der Augenoptiker 2, 14–24 (1986).

B. Dörband, “Interferometrische Messtechnik zur Prüfung asphärischer Kontaklinsen,” Die Kontaktlinse 1, 14–31 (1985).

B. Dörband, H. J. Tiziani, “Analysis of adjustment and shape errors when testing aspheric surfaces with computer generated holograms,” Appl. Opt. 24, 2604–2611 (1985).
[CrossRef] [PubMed]

B. Dörband, “Auslegung von Kompensationssystemen zur interferometrischen Prüfung asphärischer Flächen,” Optik 67, 1–20 (1984).

B. Dörband, “Die 3-Interferogramm-Methode zur automatischen Streifenauswertung in rechnergesteuerten digitalen Zweistrahlinterferometern,” Optik 60, 161–174 (1982).

Ezekiel, S.

Fantone, S. D.

Fercher, A. F.

Fischer, E.

Gottlieb, M.

M. Gottlieb, C. L. M. Ireland, J. M. Ley, Electro-optic and Acousto-optic Scanning and Deflection (Marcel Dekker, New York, 1983).

Heynacher, E.

E. Heynacher, “Fertigung asphärischer Flächen durch form-gebende Bearbeitung und durch Abgieβen,” Optik 45, 249–267 (1976).

Hu, H. Z.

Huppertz,

B. Dörband, B. Packross, Huppertz, “Asphärische KL-Rückflächen im Vergleich,” Der Augenoptiker 2, 14–24 (1986).

Ireland, C. L. M.

M. Gottlieb, C. L. M. Ireland, J. M. Ley, Electro-optic and Acousto-optic Scanning and Deflection (Marcel Dekker, New York, 1983).

Ittner, T.

Korpel, A.

A. Korpel, Acousto-optics (Marcel Dekker, New York, 1988).

Ley, J. M.

M. Gottlieb, C. L. M. Ireland, J. M. Ley, Electro-optic and Acousto-optic Scanning and Deflection (Marcel Dekker, New York, 1983).

Packross, B.

B. Dörband, B. Packross, Huppertz, “Asphärische KL-Rückflächen im Vergleich,” Der Augenoptiker 2, 14–24 (1986).

Polhemus, C.

Prongué, D.

Sodnik, Z.

Sommargren, G. E.

Thalmann, R.

Tiziani, H.

Tiziani, H. J.

B. Dörband, H. J. Tiziani, “Analysis of adjustment and shape errors when testing aspheric surfaces with computer generated holograms,” Appl. Opt. 24, 2604–2611 (1985).
[CrossRef] [PubMed]

H. J. Tiziani, “On the application of synthetic holograms for testing aspheric surfaces,” in Conference Digest of ICO (Sapporo) (Internation Commission on Optics, 1984), pp. 390–391.

H. J. Tiziani, “Prospects of testing aspheric surfaces with computer-generated holograms,” in Aspheric Optics: Design, Manufacture, Testing, P. Kuttner, T. L. Williams, eds., Proc. SPIE235, 72–79 (1980).

Vry, U.

Wyant, J. C.

Appl. Opt. (8)

Der Augenoptiker (1)

B. Dörband, B. Packross, Huppertz, “Asphärische KL-Rückflächen im Vergleich,” Der Augenoptiker 2, 14–24 (1986).

Die Kontaktlinse (1)

B. Dörband, “Interferometrische Messtechnik zur Prüfung asphärischer Kontaklinsen,” Die Kontaktlinse 1, 14–31 (1985).

Opt. Acta (1)

K. Creath, Y.-Y. Cheng, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Opt. Acta 32, 1455–1464 (1985).
[CrossRef]

Opt. Lett. (1)

Optik (3)

E. Heynacher, “Fertigung asphärischer Flächen durch form-gebende Bearbeitung und durch Abgieβen,” Optik 45, 249–267 (1976).

B. Dörband, “Auslegung von Kompensationssystemen zur interferometrischen Prüfung asphärischer Flächen,” Optik 67, 1–20 (1984).

B. Dörband, “Die 3-Interferogramm-Methode zur automatischen Streifenauswertung in rechnergesteuerten digitalen Zweistrahlinterferometern,” Optik 60, 161–174 (1982).

Other (4)

H. J. Tiziani, “Prospects of testing aspheric surfaces with computer-generated holograms,” in Aspheric Optics: Design, Manufacture, Testing, P. Kuttner, T. L. Williams, eds., Proc. SPIE235, 72–79 (1980).

H. J. Tiziani, “On the application of synthetic holograms for testing aspheric surfaces,” in Conference Digest of ICO (Sapporo) (Internation Commission on Optics, 1984), pp. 390–391.

M. Gottlieb, C. L. M. Ireland, J. M. Ley, Electro-optic and Acousto-optic Scanning and Deflection (Marcel Dekker, New York, 1983).

A. Korpel, Acousto-optics (Marcel Dekker, New York, 1988).

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Figures (14)

Fig. 1
Fig. 1

Fabrication of aspherical lenses with high optical quality.

Fig. 2
Fig. 2

Heterodyne-interferometer scheme.

Fig. 3
Fig. 3

Scanning DW-H-DiI principle.

Fig. 4
Fig. 4

Interferometer with a measuring tube (right) and a rotational stage with a specimen mounting (left).

Fig. 5
Fig. 5

Scan geometry for the rotational scan of rotation-symmetrical aspherical shapes.

Fig. 6
Fig. 6

Interference of the beams after the second AOM.

Fig. 7
Fig. 7

Measurement of the spot distance for λ1 ≈ 810 nm and λ2 ≈ 830 nm for the best focusing state: (a) phase measurement; 1, λ1; 2, λ2; (b) amplitude measurement; 1, λ1; 2, λ2.

Fig. 8
Fig. 8

Shape measurement of a sphere (r = 15.179 mm), S = 34.725 μm, λ1 ≈ 810 nm. There are 32 measuring points.

Fig. 9
Fig. 9

Microstructure measurement of a sphere (r = 15.179 mm), S = 34.725 μm, λ1 ≈ 810 nm. There are 1024 measuring points.

Fig. 10
Fig. 10

High-precision measurement. Start-adjustment measurement (75% of the aperture) for an asphere; one-wavelength method (λ1 ≈ 810 nm), S = 34.7 μm, with an automatic focusing possibility. Median-filter window: 20 measuring points.

Fig. 11
Fig. 11

High-precision measurement. End-adjustment measurement (75% of aperture) for an asphere.

Fig. 12
Fig. 12

High-precision measurement. End measurement for determination of polynomial coefficients (99% of aperture) for an asphere.

Fig. 13
Fig. 13

Measured grating with a 400-nm step height, 32-μm width, and a period of 64 μm (nominal values). Measurements with two wavelengths successively, without a median filter and data shift and without data evaluation for both wavelengths.

Fig. 14
Fig. 14

Grating step; two-wavelength measurement. Median-filter window: 20 measuring points.

Tables (1)

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Table 1 Wavelength Dependence of Resolution and Image

Equations (17)

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I = | a 1 + a 2 | 2 = I 0 ( 1 + m cos Φ )
I 0 = A 1 2 + A 2 2 ,
m = 2 A 1 A 2 A 1 2 + A 2 2 ,
Φ = 4 π λ ( l 1 l 2 )
( l 1 l 2 ) max = λ 2 .
λ eff = Λ = λ 1 λ 2 | λ 1 λ 2 | .
tan α = l 1 l 2 S ,
α = arctan ( Φ λ 4 π S ) .
I 1 ( t ) = | a 00 + a 11 | 2 = A 00 2 + A 11 2 + 2 A 00 A 11 × cos [ 2 π ( f 1 f 2 ) t + 4 π λ 1 ( l 1 l 2 ) 4 π c f 1 l 2 ] ,
I ( t ) = A 1 2 + A 2 2 + 2 A 1 A 2 cos ( 2 π f t + 4 π ν c z ) .
z = λ 4 π Φ .
Δ z min = λ 4 π Δ Φ .
α AOM λ c g f
λ 1 ( AOM1 ) λ 2 ( AOM2 ) = f 2 f 1 .
Δ α AOM λ M c g Δ f .
Δ α AOM λ M 2 D max ,
D max c g 2 Δ f .

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