Abstract

We describe a variation of the liquid-flat technique for determining the absolute flatness of a 240-mm-diameter optical surface to an accuracy better than 1/100λ in both its horizontal (three-point support) and vertical orientations. Using the appropriate mathematics to calculate the surface deformation of a disk due to gravity, we achieved verification of the method by comparing measurements carried out on a pair of optical flats and a liquid reference surface.

© 1998 Optical Society of America

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References

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  1. G. D. Dew, “A method for the precise evaluation of interferograms,” J. Sci. Instrum. 41, 160–162 (1964).
    [CrossRef]
  2. G. D. Dew, “Systems of minimum deflection supports for optical flats,” J. Sci. Instrum. 43, 809–811 (1966).
    [CrossRef]
  3. G. D. Dew, “Some observations on the long-term stability of optical flats,” Opt. Acta 21, 609–614 (1974).
    [CrossRef]
  4. G. Schulz, J. Grzana, “Absolute flatness testing by the rotation method with optimal measuring-error compensation,” Appl. Opt. 31, 3767–3780 (1992).
    [CrossRef] [PubMed]
  5. C. Ai, J. C. Wyant, “Absolute testing of flats by using even and odd functions,” Appl. Opt. 32, 4698–4705 (1993).
    [CrossRef] [PubMed]
  6. K-E. Elssner, A. Vogel, J. Grzana, G. Schulz, “Establishing a flatness standard,” Appl. Opt. 33, 2437–2446 (1994).
    [CrossRef] [PubMed]
  7. J. Grzana, “Absolute testing of optical flats at points on a square grid: error propagation,” Appl. Opt. 33, 6654–6661 (1994).
    [CrossRef]
  8. L. A. Selke, “Theoretical elastic deflections of a thick horizontal circular mirror on a ring support,” Appl. Opt. 9, 149–153 (1970).
    [CrossRef] [PubMed]
  9. E. Reissner, “On bending of elastic plates,” Q. Appl. Math. 5, 55–68 (1947).
  10. S. Timoshenko, Theory of Plates and Shells (McGraw-Hill, New York, 1959).

1994

1993

1992

1974

G. D. Dew, “Some observations on the long-term stability of optical flats,” Opt. Acta 21, 609–614 (1974).
[CrossRef]

1970

1966

G. D. Dew, “Systems of minimum deflection supports for optical flats,” J. Sci. Instrum. 43, 809–811 (1966).
[CrossRef]

1964

G. D. Dew, “A method for the precise evaluation of interferograms,” J. Sci. Instrum. 41, 160–162 (1964).
[CrossRef]

1947

E. Reissner, “On bending of elastic plates,” Q. Appl. Math. 5, 55–68 (1947).

Ai, C.

Dew, G. D.

G. D. Dew, “Some observations on the long-term stability of optical flats,” Opt. Acta 21, 609–614 (1974).
[CrossRef]

G. D. Dew, “Systems of minimum deflection supports for optical flats,” J. Sci. Instrum. 43, 809–811 (1966).
[CrossRef]

G. D. Dew, “A method for the precise evaluation of interferograms,” J. Sci. Instrum. 41, 160–162 (1964).
[CrossRef]

Elssner, K-E.

Grzana, J.

Reissner, E.

E. Reissner, “On bending of elastic plates,” Q. Appl. Math. 5, 55–68 (1947).

Schulz, G.

Selke, L. A.

Timoshenko, S.

S. Timoshenko, Theory of Plates and Shells (McGraw-Hill, New York, 1959).

Vogel, A.

Wyant, J. C.

Appl. Opt.

J. Sci. Instrum.

G. D. Dew, “A method for the precise evaluation of interferograms,” J. Sci. Instrum. 41, 160–162 (1964).
[CrossRef]

G. D. Dew, “Systems of minimum deflection supports for optical flats,” J. Sci. Instrum. 43, 809–811 (1966).
[CrossRef]

Opt. Acta

G. D. Dew, “Some observations on the long-term stability of optical flats,” Opt. Acta 21, 609–614 (1974).
[CrossRef]

Q. Appl. Math.

E. Reissner, “On bending of elastic plates,” Q. Appl. Math. 5, 55–68 (1947).

Other

S. Timoshenko, Theory of Plates and Shells (McGraw-Hill, New York, 1959).

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Figures (8)

Fig. 1
Fig. 1

Layout of the blank and oil assembly.

Fig. 2
Fig. 2

(a) Difference between flat 1 at 0° azimuthal orientation and the oil flat; rms 0.024λ, p–v (peak to valley) 0.99λ. (b) Difference between flat 2 at 0° azimuthal orientation and the oil flat; rms 0.018λ, p–v 0.088λ.

Fig. 3
Fig. 3

(a) Difference between flat 1 (average) and the oil flat; rms 0.020λ, p–v 0.063λ. (b) Difference between flat 2 (average) and the oil flat; rms 0.13λ, p–v 0.53λ.

Fig. 4
Fig. 4

Difference between flat 1 and flat 2 at 0° azimuthal orientation and flat 1 uppermost; rms 0.0053λ, p–v 0.036λ.

Fig. 5
Fig. 5

Discrepancy in interferograms between average of flat 1 on flat 2 and a typical single measurement; rms 0.0014λ, p–v 0.012λ.

Fig. 6
Fig. 6

Deformation of optical blank due to gravity; rms 0.038λ, p–v 0.13λ.

Fig. 7
Fig. 7

(a) Absolute flatness of flat 1; rms 0.0045λ, p–v 0.019λ. (b) Absolute flatness of flat 2; rms 0.0053λ, p–v 0.028λ.

Fig. 8
Fig. 8

(a) Discrepancy between theory and experiment as a contour and an isometric plot; rms 0.0036λ, p–v 0.026λ. (b) Discrepancy between theory and experiment as a profile plot in the x direction; rms 0.0036λ, p–v 0.026λ.

Tables (1)

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Table 1 Values for Parameters Appearing in Eq. (1)

Equations (2)

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w = W 1 + ν 8 π D r 2 - r 1 2 2 D 1 + ν r 2 2 1 C s - 2 C n + 1 + ν ln r 1 r 2 + 1 + 3 ν 4 + 1 8 - 3 - 5 ν r 1 4 r 2 2 + 4 1 - ν r 2 r 1 2 r 1 2 - 1 + ν r 4 r 2 2 ,
w r = 0 = 0.0362 Wr 1 2 / D .

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