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 (2)

1993 (1)

1992 (1)

1974 (1)

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

1970 (1)

1966 (1)

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

1964 (1)

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

1947 (1)

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. (5)

J. Sci. Instrum. (2)

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 (1)

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

Q. Appl. Math. (1)

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

Other (1)

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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