Abstract

We describe a simple method for measuring the radius of curvature by using Talbot interferometry in a noncollimated light beam. This scheme can also be used to determine the focal length of the collimating lens employed in the setup. Results of the measurements are presented. A discussion of achievable accuracies and the proper choice of parameters is included.

© 1992 Optical Society of America

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References

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  1. Y. Nakano, K. Murata. “Talbot interferometry for measuring the focal length of a lens,” Appl. Opt. 24, 3162–3166 (1985).
    [CrossRef] [PubMed]
  2. C. W. Chang, D. C. Su, “An improved technique of measuring the focal length of a lens,” Opt. Commun. 73, 257–262 (1989).
    [CrossRef]
  3. L. M. Bernardo, O. D. D. Soares, “Evaluation of the focal distance of a lens by Talbot interferometry,” Appl. Opt. 27, 296–301 (1988).
    [CrossRef] [PubMed]
  4. I. Glatt, O. Kafri, “Determination of the focal length of nonparaxial lenses by moiré deflectometry,” Appl. Opt. 26, 2507–2508 (1987).
    [CrossRef] [PubMed]
  5. O. Kafri, E. Keren, K. Kreske, Y. Zac, “Moiré deflectometry with a focused beam: radius of curvature, microscopy, and thickness analysis,” Appl. Opt. 29, 133–136 (1990).
    [CrossRef] [PubMed]
  6. M. P. Kothiyal, R. S. Sirohi, K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
    [CrossRef]
  7. M. P. Kothiyal, R. S. Sirohi, “Improved collimation testing using Talbot interferometry,” Appl. Opt. 26, 4056–4057 (1987).
    [CrossRef] [PubMed]
  8. D. W. Swift, “A simple moiré fringe technique for magnification checking,” J. Phys. E 7, 164–165 (1974).
    [CrossRef]
  9. S. Yokozeki, K. Patorski, K. Ohnishi, “Collimation method using Fourier imaging and moiré techniques,” Opt. Commun. 14, 401–405 (1975).
    [CrossRef]
  10. K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Curvature and focal length measurements using compensation of a collimated beam,” Opt. Laser Technol. (to be published).
  11. M. P. Kothiyal, K. V. Sriram, R. S. Sirohi, “Setting sensitivity in Talbot interferometry with modified gratings,” Opt. Laser Technol. (to be published).

1990 (1)

1989 (1)

C. W. Chang, D. C. Su, “An improved technique of measuring the focal length of a lens,” Opt. Commun. 73, 257–262 (1989).
[CrossRef]

1988 (2)

M. P. Kothiyal, R. S. Sirohi, K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[CrossRef]

L. M. Bernardo, O. D. D. Soares, “Evaluation of the focal distance of a lens by Talbot interferometry,” Appl. Opt. 27, 296–301 (1988).
[CrossRef] [PubMed]

1987 (2)

1985 (1)

1975 (1)

S. Yokozeki, K. Patorski, K. Ohnishi, “Collimation method using Fourier imaging and moiré techniques,” Opt. Commun. 14, 401–405 (1975).
[CrossRef]

1974 (1)

D. W. Swift, “A simple moiré fringe technique for magnification checking,” J. Phys. E 7, 164–165 (1974).
[CrossRef]

Bernardo, L. M.

Chang, C. W.

C. W. Chang, D. C. Su, “An improved technique of measuring the focal length of a lens,” Opt. Commun. 73, 257–262 (1989).
[CrossRef]

Glatt, I.

Kafri, O.

Keren, E.

Kothiyal, M. P.

M. P. Kothiyal, R. S. Sirohi, K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[CrossRef]

M. P. Kothiyal, R. S. Sirohi, “Improved collimation testing using Talbot interferometry,” Appl. Opt. 26, 4056–4057 (1987).
[CrossRef] [PubMed]

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Curvature and focal length measurements using compensation of a collimated beam,” Opt. Laser Technol. (to be published).

M. P. Kothiyal, K. V. Sriram, R. S. Sirohi, “Setting sensitivity in Talbot interferometry with modified gratings,” Opt. Laser Technol. (to be published).

Kreske, K.

Murata, K.

Nakano, Y.

Ohnishi, K.

S. Yokozeki, K. Patorski, K. Ohnishi, “Collimation method using Fourier imaging and moiré techniques,” Opt. Commun. 14, 401–405 (1975).
[CrossRef]

Patorski, K.

S. Yokozeki, K. Patorski, K. Ohnishi, “Collimation method using Fourier imaging and moiré techniques,” Opt. Commun. 14, 401–405 (1975).
[CrossRef]

Rosenbruch, K. J.

M. P. Kothiyal, R. S. Sirohi, K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[CrossRef]

Sirohi, R. S.

M. P. Kothiyal, R. S. Sirohi, K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[CrossRef]

M. P. Kothiyal, R. S. Sirohi, “Improved collimation testing using Talbot interferometry,” Appl. Opt. 26, 4056–4057 (1987).
[CrossRef] [PubMed]

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Curvature and focal length measurements using compensation of a collimated beam,” Opt. Laser Technol. (to be published).

M. P. Kothiyal, K. V. Sriram, R. S. Sirohi, “Setting sensitivity in Talbot interferometry with modified gratings,” Opt. Laser Technol. (to be published).

Soares, O. D. D.

Sriram, K. V.

M. P. Kothiyal, K. V. Sriram, R. S. Sirohi, “Setting sensitivity in Talbot interferometry with modified gratings,” Opt. Laser Technol. (to be published).

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Curvature and focal length measurements using compensation of a collimated beam,” Opt. Laser Technol. (to be published).

Su, D. C.

C. W. Chang, D. C. Su, “An improved technique of measuring the focal length of a lens,” Opt. Commun. 73, 257–262 (1989).
[CrossRef]

Swift, D. W.

D. W. Swift, “A simple moiré fringe technique for magnification checking,” J. Phys. E 7, 164–165 (1974).
[CrossRef]

Yokozeki, S.

S. Yokozeki, K. Patorski, K. Ohnishi, “Collimation method using Fourier imaging and moiré techniques,” Opt. Commun. 14, 401–405 (1975).
[CrossRef]

Zac, Y.

Appl. Opt. (5)

J. Phys. E (1)

D. W. Swift, “A simple moiré fringe technique for magnification checking,” J. Phys. E 7, 164–165 (1974).
[CrossRef]

Opt. Commun. (2)

S. Yokozeki, K. Patorski, K. Ohnishi, “Collimation method using Fourier imaging and moiré techniques,” Opt. Commun. 14, 401–405 (1975).
[CrossRef]

C. W. Chang, D. C. Su, “An improved technique of measuring the focal length of a lens,” Opt. Commun. 73, 257–262 (1989).
[CrossRef]

Opt. Laser Technol. (1)

M. P. Kothiyal, R. S. Sirohi, K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[CrossRef]

Other (2)

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Curvature and focal length measurements using compensation of a collimated beam,” Opt. Laser Technol. (to be published).

M. P. Kothiyal, K. V. Sriram, R. S. Sirohi, “Setting sensitivity in Talbot interferometry with modified gratings,” Opt. Laser Technol. (to be published).

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Figures (7)

Fig. 1
Fig. 1

Optical configuration for the testing of a concave surface.

Fig. 2
Fig. 2

Optical configuration for the testing of a convex surface.

Fig. 3
Fig. 3

Schematic of the modified gratings G1 and G2.

Fig. 4
Fig. 4

Moiré fringe patterns obtained (a) at the self-image plane and (b) away from the self-image plane. The orientation of the fringes reverses as we go from one side of the self-image plane to the other.

Fig. 5
Fig. 5

ΔRυ versus Rυ for f= 400 mm, δf = 1.2 mm, δx = 0.05 mm, and δD = 1 mm.

Fig. 6
Fig. 6

Δf versus f by using a concave surface for D′ = 800 mm, δD = 1 mm, δx = 0.05 mm.

Fig. 7
Fig. 7

Experimental arrangement for setting the gratings G1 and G2 at equal separations from the CBS.

Tables (2)

Tables Icon

Table I Calculated Values of the Radii of Curvature

Tables Icon

Table II Calculated Values of the Focal Length of the Collimating Lens

Equations (14)

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R υ = x f + D ,
x x = | f 2 | .
R υ = f 2 x f + D .
R x = f 2 x + f D .
h = ( n 1 ) t / n ,
R υ = ( f 2 x f + D h ) ,
R x = ( f 2 x + f D + h ) .
f = [ D x 1 x 2 ( x 2 x 1 ) ] 1 / 2
f = [ D x 1 x 2 ( x 1 x 2 ) ] 1 / 2
R υ + f = D x 2 ( x 2 x 1 ) + D 1 h ,
R x f = D x 2 ( x 1 x 2 ) D 1 + h .
Δ μ μ = Δ Z R Z ,
α = tan θ Δ μ 2 μ ,
Δ μ = 2 μα tan θ .

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