Abstract

The stability of the Shack-Hartmann sensor against mechanical disturbances from the environment can advantageously be exploited in highly sensitive wave front tests of surfaces. Here, a Fizeau-type multiple beam test is investigated. The enhancement of the phase sensitivity in a Fizeau-resonator formed by two high reflecting mirror surfaces enables tests in reflected light which includes also opaque surfaces. The multiplication of the sensitivity with the number of passes through the Fizeau resonator provides a big margin against the rather limited repeatability of wave front measurements with such a wave front sensor. The method has been tested for planeness Fizeau measurements. It could also be exploited in spherical Fizeau tests. But in the latter case the two spherical surfaces forming the resonator should have radii which differ only by e.g. 1mm.

© 2008 Optical Society of America

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References

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  1. G. Schulz, J. Schwider, "Interferometric testing of smooth surfaces," Progress in Optics, vol.XIII, E. Wolf, Ed., Elsivier Publisher New York, p.93 (1976)
    [CrossRef]
  2. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, "Digital wavefront measuring interferometry: some systematic error sources," Appl. Opt. 22, 3421-3432 (1983)
    [CrossRef] [PubMed]
  3. J. Schwider, "Advanced evaluation techniques in interferometry,"
  4. Progress in Optics XXVIII, E. Wolf, Ed., Elsivier Publisher New York 28, p.271-359 (1990)
  5. J. Hartmann, "Objektivuntersuchungen," Ztschr. für Instrumentenkunde 24 erstes Heft 1-21; zweites Heft 3-47; viertes Heft 97-117 (1904)
  6. B. Platt, R. Shack, "Lenticular Hartmann screen," Opt.Science Center Newslett. 515 (1971)
  7. D. Malacara, „Optical shop testing" 3-rd edition, J. Wiley and Sons Inc. Hoboken, New Jersey (2007)
  8. J. Pfund, N. Lindlein, J. Schwider, "Dynamic range expansion of a Shack-Hartmann-Sensor by using a modified unwrapping algorithm," Opt. Lett:  23995-997 (1998)
    [CrossRef]
  9. J. Pfund, N. Lindlein, J. Schwider, R. Burow, Th. Blümel, K.-E. Elssner, „Absolute sphericity measurement: a comparative study on the use of interferometry and a Shack-Hartmann sensor," Opt. Lett. 23742-744 (1998)
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  14. K.-E. Elssner, A. Vogel, J. Grzanna, and G. Schulz, "Establishing a flatness standard," Appl. Opt. 332437-2446 (1994)
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  18. S. Tolansky, „Multiple beam interferometry of surfaces and films" Oxford University Press, Oxford (1948)
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    [CrossRef]
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1998

J. Pfund, N. Lindlein, J. Schwider, "Dynamic range expansion of a Shack-Hartmann-Sensor by using a modified unwrapping algorithm," Opt. Lett:  23995-997 (1998)
[CrossRef]

J. Pfund, N. Lindlein, J. Schwider, R. Burow, Th. Blümel, K.-E. Elssner, „Absolute sphericity measurement: a comparative study on the use of interferometry and a Shack-Hartmann sensor," Opt. Lett. 23742-744 (1998)
[CrossRef]

1994

1993

1992

J. Schwider, "Fizeau- and Michelson-type interferograms and their relation to the absolute testing of optical surfaces," Optik 89113-117 (1992)

1983

1974

1973

G. Schulz, "Interferentielle Absolutprüfung zweier Flächen," Opt. Act. 20699-706 (1973)
[CrossRef]

1971

1969

P. Langenbeck, "Multi-pass interferometry," Appl. Opt. 8, 545-552 (1969)

1968

J. Schwider, „Informationssteigerung in der Vielstrahlinterferometrie," Opt. Acta 15351-372 (1968)
[CrossRef]

1967

G. Schulz, "Ein Interferenzverfahren zur absoluten Ebenheitsprüfung längs beliebiger Zentralschnitte," Opt. Act. 14375-388 (1967)
[CrossRef]

Appl. Opt.

Opt. Act.

G. Schulz, "Ein Interferenzverfahren zur absoluten Ebenheitsprüfung längs beliebiger Zentralschnitte," Opt. Act. 14375-388 (1967)
[CrossRef]

G. Schulz, "Interferentielle Absolutprüfung zweier Flächen," Opt. Act. 20699-706 (1973)
[CrossRef]

Opt. Acta

J. Schwider, „Informationssteigerung in der Vielstrahlinterferometrie," Opt. Acta 15351-372 (1968)
[CrossRef]

Opt. Lett

J. Pfund, N. Lindlein, J. Schwider, "Dynamic range expansion of a Shack-Hartmann-Sensor by using a modified unwrapping algorithm," Opt. Lett:  23995-997 (1998)
[CrossRef]

Opt. Lett.

Optik

J. Schwider, "Fizeau- and Michelson-type interferograms and their relation to the absolute testing of optical surfaces," Optik 89113-117 (1992)

Science Center Newslett.

B. Platt, R. Shack, "Lenticular Hartmann screen," Opt.Science Center Newslett. 515 (1971)

Other

D. Malacara, „Optical shop testing" 3-rd edition, J. Wiley and Sons Inc. Hoboken, New Jersey (2007)

J. Schwider, "Advanced evaluation techniques in interferometry,"

Progress in Optics XXVIII, E. Wolf, Ed., Elsivier Publisher New York 28, p.271-359 (1990)

J. Hartmann, "Objektivuntersuchungen," Ztschr. für Instrumentenkunde 24 erstes Heft 1-21; zweites Heft 3-47; viertes Heft 97-117 (1904)

M. Born and E. Wolf, „Principles of Optics" 6-th ed. Pergamon Press (1997)

S. Tolansky, „Multiple beam interferometry of surfaces and films" Oxford University Press, Oxford (1948)

G. Schulz, J. Schwider, "Interferometric testing of smooth surfaces," Progress in Optics, vol.XIII, E. Wolf, Ed., Elsivier Publisher New York, p.93 (1976)
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

SHS-setup for performing a Fizeau-type flatness test (The reflected light beams are deflected by 90° by means of the mirror surface of the prism positioned behind the slit aperture which is possible when the plate combination is slightly tilted out of the drawing plane)

Fig. 2.
Fig. 2.

Schematic ray path of the waves reflected from the two surfaces A, B with the absolute deviations from planeness a, b. It is assumed that the back side of the plates forms a small angle with the surfaces under test enabling suppression of the backside reflections by spatial filtering operations.

Fig. 3.
Fig. 3.

Enhancement of surface aberrations through multiple reflections in a Fizeau resonator. At the left: Reflected waves due to semitransparent highly reflecting reference and highly reflecting mirror under test. At the right: Perspective display of the waves coming to a focus in the focal plane of the collimator objective.

Fig. 4.
Fig. 4.

Basic aberration of the optical system measured against the first Fizeau reflection. The contour line distance is 0.5 waves.

Fig. 5.
Fig. 5.

Repeatability test for the SHS, Zernike-fit of degree 20, please note the change in the contour line distance by a factor of 50 compared to Fig. 4. The contour line distance is 0.01 waves.

Fig. 6.
Fig. 6.

Tilt indication for the case of the enhancement factors 10 (on the left) and 15(on the right) In this picture the measured wave aberration is shown in a mod 2π representation. The absence of big tilts can be inferred from the near parallel section through the wave front deformation. In case of a remaining tilt a picture similar to a fringe interferogram would be seen.

Fig. 7.
Fig. 7.

Difference between two runs (cont. line dist. λ/20) and a hard screen copy of the best adjustment (on the right). The first modulo (2π)-picture from the left shows the wave front without tilt removal. In a second run about 10 carrier fringes have been added to show the influence.

Fig. 8.
Fig. 8.

Deviation sums of the two surfaces AB, i.e., (a+b): AB(N=10) left; AB(N=20) middle, AB(N=30) right (which corresponds to enhancement factors of 10/20/30, or in wavelengths λ/20, λ/40, λ/60 or contour line distances: λ/40; λ/80, λ/120).

Fig. 9.
Fig. 9.

Deviation sums of two surfaces AC, i.e., (a+c); surfaces AD, i.e. (a+d) and Surfaces BD, i.e., (b+d): AC (N=20) left, AD (N=20) middle, BD (N=20) right, from contour line to contour line the surface deviations are varying by λ/80.

Equations (6)

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Δ W = W B W A = W ob + 2 na + 2 z { W ob + 2 na } = 2 z
with
z = z 0 ( a + b )
Δ W = W B W A W ob + 2 na + N 2 z { W ob + 2 na + 2 Mz } 2 ( N M ) z
with
z = z 0 ( a + b )

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