Abstract

Using a technique that was previously developed for measuring the radius of curvature of spherical surfaces, an alternative method for testing cylindrical as well as toric lenses is presented. The basic equipment required is a nodal bench and a low power He–Ne laser.

© 1986 Optical Society of America

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References

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  1. H. F. Johnson, H. D. Wolpert, “Cylindrical Optics: How to Test Them,” Photonics Spectra 18, 55 (Apr.1984).
  2. R. S. Longhurst, Geometrical and Physical Optics (Wiley, New York, 1964), p. 68.
  3. A. Cornejo-Rodriguez, A. Cordero-Dávila, “Measurement of Radii of Curvature of Convex and Concave Surfaces Using a Nodal Bench and He–Ne Laser,” Appl. Opt. 19, 1743 (1980).
    [Crossref] [PubMed]
  4. R. Diaz-Uribe, A. Cornejo-Rodriguez, J. Pedraza-Contreras, O. Cardona-Nunez, A. Cordero-Davila, “Profile Measurement of a Conic Surface Using He–Ne Laser and a Nodal Bench,” Appl. Opt. 24, 2612 (1985);in Conference Digest, Optics in Modern Science & Technology, ICO-13, Sapporo, Japan (1984), p. 402.
    [Crossref] [PubMed]
  5. We adopt the definitions given in Ref. 1 for the errors of a cylindrical lens.
  6. B. J. Thompson, U. Rochester; private communication (1985).

1985 (1)

1984 (1)

H. F. Johnson, H. D. Wolpert, “Cylindrical Optics: How to Test Them,” Photonics Spectra 18, 55 (Apr.1984).

1980 (1)

Cardona-Nunez, O.

Cordero-Davila, A.

Cordero-Dávila, A.

Cornejo-Rodriguez, A.

Diaz-Uribe, R.

Johnson, H. F.

H. F. Johnson, H. D. Wolpert, “Cylindrical Optics: How to Test Them,” Photonics Spectra 18, 55 (Apr.1984).

Longhurst, R. S.

R. S. Longhurst, Geometrical and Physical Optics (Wiley, New York, 1964), p. 68.

Pedraza-Contreras, J.

Thompson, B. J.

B. J. Thompson, U. Rochester; private communication (1985).

Wolpert, H. D.

H. F. Johnson, H. D. Wolpert, “Cylindrical Optics: How to Test Them,” Photonics Spectra 18, 55 (Apr.1984).

Appl. Opt. (2)

Photonics Spectra (1)

H. F. Johnson, H. D. Wolpert, “Cylindrical Optics: How to Test Them,” Photonics Spectra 18, 55 (Apr.1984).

Other (3)

R. S. Longhurst, Geometrical and Physical Optics (Wiley, New York, 1964), p. 68.

We adopt the definitions given in Ref. 1 for the errors of a cylindrical lens.

B. J. Thompson, U. Rochester; private communication (1985).

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Figures (3)

Fig. 1
Fig. 1

Two-step procedure for measuring r: (a) finding the vertex position, (b) finding the center of curvature position. Full and broken lines represent the lens without and with rotation, respectively.

Fig. 2
Fig. 2

Measuring defects of a cylindrical lens: (a) decentering of one of the surfaces, (b) presence of a wedge.

Fig. 3
Fig. 3

(a) Diagram showing the effect of twisting a cylindrical surface. (b) When a cylindrical twisted surface is rotated an angle ϕ around the vertical axis Y, the reflected beam is deviated on the screen to points X0, Y0.

Equations (8)

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γ = 1 2 tan 1 ( h d ) 1 2 h d .
δ γ γ = δ h h + δ d d .
( x cos θ sin ϕ + y sin θ + z cos θ cos ϕ ) 2 + ( x cos ϕ z sin θ ) 2 = a 2
n = z a { sin ϕ cos ϕ sin 2 θ } i ̂ + { cos ϕ sin θ cos θ } j ̂ + { cos 2 ϕ sin 2 θ 1 } k ̂ .
r ̂ = { 2 sin ϕ cos ϕ sin 2 θ } i ̂ + { 2 cos ϕ sin θ cos θ } j ̂ + { 1 2 cos 2 ϕ sin 2 θ } k ̂ .
X 0 = 2 b sin ϕ cos ϕ sin 2 θ , and Y 0 = 2 b cos ϕ sin θ cos θ ,
θ Y 0 2 d ( π ϕ ) ,
δ θ θ = δ Y 0 Y 0 + δ d d + δ ϕ ( π ϕ ) .

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