Abstract

A new type of aspheric surface calibrator has been developed at the National Research Council of Canada. It employs a nonmechanical contact technique for measuring rotationally symmetrical uncoated concave optical surfaces which depart from a sphere by as much as 0.5 mm with a precision of 0.3 μm. Using two precise air bearings for providing rotations about two mutually perpendicular axes, a focused laser beam is scanned across the surface under test. A fringe counting process measures the difference in sag between the surface shape and some reference sphere. Two surfaces, one spherical and the other ellipsoidal, were measured to illustrate the practicality of such an instrument.

© 1981 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. G. Birch, F. J. Green, National Physical Laboratory, Optical Metrology 12, 1972 (internal report).
  2. J. B. Saunders, Appl. Opt. 9, 1623 (1970).
    [CrossRef] [PubMed]
  3. J. C. Wyant, Appl. Opt. 12, 2057 (1973).
    [CrossRef] [PubMed]
  4. J. Schneider, in Application de l’holographie comptes rendus du symposium international, Besançon, 1970, J.-C. Vienot et al., Eds. (Lab. de Physique Générale et Optique, U. Besançon, 1970).
  5. A. V. Lukin, K. S. Mustafin, Sov. J. Opt. Technol. 46, 237 (1979).
  6. A. Offner, Appl. Opt. 2, 153 (1963).
    [CrossRef]
  7. M. P. Rimmer, Appl. Opt. 9, 849 (1970).
    [CrossRef] [PubMed]
  8. D. R. Shafer, Appl. Opt. 18, 3863 (1979).
    [PubMed]
  9. K. G. Birch, Optik 36, 399 (1972).
  10. T. M. Leushina, Sov. J. Opt. Technol. 45, 544 (1978).
  11. J. G. Dil, P. F. Greve, W. Mesman, Appl. Opt. 17, 553 (1978).
    [CrossRef] [PubMed]
  12. T. L. Williams, Opt. Acta 25, 1155 (1978).
    [CrossRef]
  13. P. E. Klingsporn, Appl. Opt. 18, 2881 (1979).
    [CrossRef] [PubMed]
  14. L. D. Dickson, Appl. Opt. 9, 1854 (1970).
    [CrossRef] [PubMed]

1979 (3)

1978 (3)

T. M. Leushina, Sov. J. Opt. Technol. 45, 544 (1978).

T. L. Williams, Opt. Acta 25, 1155 (1978).
[CrossRef]

J. G. Dil, P. F. Greve, W. Mesman, Appl. Opt. 17, 553 (1978).
[CrossRef] [PubMed]

1973 (1)

1972 (1)

K. G. Birch, Optik 36, 399 (1972).

1970 (3)

1963 (1)

Birch, K. G.

K. G. Birch, Optik 36, 399 (1972).

K. G. Birch, F. J. Green, National Physical Laboratory, Optical Metrology 12, 1972 (internal report).

Dickson, L. D.

Dil, J. G.

Green, F. J.

K. G. Birch, F. J. Green, National Physical Laboratory, Optical Metrology 12, 1972 (internal report).

Greve, P. F.

Klingsporn, P. E.

Leushina, T. M.

T. M. Leushina, Sov. J. Opt. Technol. 45, 544 (1978).

Lukin, A. V.

A. V. Lukin, K. S. Mustafin, Sov. J. Opt. Technol. 46, 237 (1979).

Mesman, W.

Mustafin, K. S.

A. V. Lukin, K. S. Mustafin, Sov. J. Opt. Technol. 46, 237 (1979).

Offner, A.

Rimmer, M. P.

Saunders, J. B.

Schneider, J.

J. Schneider, in Application de l’holographie comptes rendus du symposium international, Besançon, 1970, J.-C. Vienot et al., Eds. (Lab. de Physique Générale et Optique, U. Besançon, 1970).

Shafer, D. R.

Williams, T. L.

T. L. Williams, Opt. Acta 25, 1155 (1978).
[CrossRef]

Wyant, J. C.

Appl. Opt. (8)

Opt. Acta (1)

T. L. Williams, Opt. Acta 25, 1155 (1978).
[CrossRef]

Optik (1)

K. G. Birch, Optik 36, 399 (1972).

Sov. J. Opt. Technol. (2)

T. M. Leushina, Sov. J. Opt. Technol. 45, 544 (1978).

A. V. Lukin, K. S. Mustafin, Sov. J. Opt. Technol. 46, 237 (1979).

Other (2)

K. G. Birch, F. J. Green, National Physical Laboratory, Optical Metrology 12, 1972 (internal report).

J. Schneider, in Application de l’holographie comptes rendus du symposium international, Besançon, 1970, J.-C. Vienot et al., Eds. (Lab. de Physique Générale et Optique, U. Besançon, 1970).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (16)

Fig. 1
Fig. 1

Schematic of the aspheric surface calibrator.

Fig. 2
Fig. 2

Two air bearing assemblies.

Fig. 3
Fig. 3

(a) Method A for performing radial scan across test surface; (b) method B for performing radial scan across test surface.

Fig. 4
Fig. 4

Reflection of signal beam from an aspherical surface.

Fig. 5
Fig. 5

Interference pattern obtained at the exit aperture of the interferometer.

Fig. 6
Fig. 6

Optical paths taken by signal beam when the upper bearing axis lies slightly behind the lower one.

Fig. 7
Fig. 7

Subassemblies for the upper air bearing.

Fig. 8
Fig. 8

Overlap region between signal and reference beam.

Fig. 9
Fig. 9

Optical paths taken by signal beam when the surface of the scanning mirror lies slightly in front of the upper bearing axis.

Fig. 10
Fig. 10

Error function b and sag difference Δ plotted as a function of deflection angle ϕ.

Fig. 11
Fig. 11

Sag differential between test surface and reference sphere.

Fig. 12
Fig. 12

Measured interferogram of the first item under test—concave spherical surface.

Fig. 13
Fig. 13

Interference fringes obtained by placing the first test surface in contact with a convex optical gauge.

Fig. 14
Fig. 14

Interference fringes obtained by placing the convex optical gauge in contact with its female counterpart.

Fig. 15
Fig. 15

Profile of ellipsoidal surface—second item under test.

Fig. 16
Fig. 16

Interferogram depicting departure of the ellipsoidal surface under test from its ideal shape.

Tables (3)

Tables Icon

Table I Misalignment Error as a Function of Scanning Angle

Tables Icon

Table II Sagitta of Ellipsoid and Parent Sphere as a Function of Semidiameter Together with the Fringe Count Rate

Tables Icon

Table III Sagitta of Ellipsoid and Some Chosen Reference Sphere as a Function of Semidiameter Together with the Fringe Count Rate

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

= ϕ λ / ( 2 ρ δ ) ,
ρ = ( 4 f λ ) / ( π d ) ,
= 4 sin ϕ
z = ± λ 2 sin 2 U .
sin U = 0.018 z             ( λ = 632.8 nm ) .
Δ = 2 f α .
r 0 = ( R 2 + 2 ) 1 / 2 , r 1 = ( R 2 + 2 + 2 R sin ϕ ) 1 / 2 , r 2 = ( R 2 + 2 - 2 R sin ϕ ) 1 / 2 .
r 0 = R ,             r 1 = R + sin ϕ ,             r 2 = R - sin ϕ .
D 0 = r 0 , D 1 = 0 - 1 + r 1 , D 2 = 0 - 2 + r 2 .
b = ( D 1 + D 2 ) / 2 - D 0 = 0.
0 = / cos ( π / 4 ) , 1 = / cos ( π / 4 - ϕ / 2 ) , 2 = / cos ( π / 4 + ϕ / 2 ) ,
r 0 = ( R 2 + 0 2 ) 1 / 2 , r 1 = ( R 2 + 1 2 - 2 R 1 sin ϕ ) 1 / 2 , r 2 = ( R 2 + 2 2 + 2 R 2 sin ϕ ) 1 / 2 .
r 0 = R , r 1 = R - 1 sin ϕ , r 2 = R + 2 sin ϕ .
b = [ 2 0 - 1 ( 1 + sin ϕ ) - 2 ( 1 - sin ϕ ) ] / 2.
Δ = ρ 2 c / { ( 1 - c 2 ρ 2 ) 1 / 2 [ 1 + ( 1 - c 2 ρ 2 ) 1 / 2 ] } ,
z R ( ρ ) = c 1 ρ 2 1 + ( 1 - c 1 2 ρ 2 ) 1 / 2 ,
z S ( ρ ) = c ρ 2 1 + [ 1 - ( 1 + Q ) c 2 ρ 2 ] 1 / 2 + A ρ 2 + B ρ 3 + C ρ 4 + D ρ 5 + ( ρ ) ,
Δ r = Δ z cos θ = ( z S - z R ) cos θ .
( ρ ) = z R - c ρ 2 1 + [ 1 - ( 1 + Q ) c 2 ρ 2 ] 1 / 2 - A ρ 2 - B ρ 3 - C ρ 4 - D ρ 5 + Δ r ( 1 - c 2 ρ 2 ) - 1 / 2 .
( ρ , ϕ ) = z R - c ρ 2 1 + [ 1 - ( 1 + Q ) c 2 ρ 2 ] 1 / 2 - A ρ 2 - B ρ 3 - C ρ 4 - D ρ 5 + Δ r ( 1 - c 2 ρ 2 ) - 1 / 2 - E ρ cos ( ϕ - ψ ) - F ,

Metrics