Abstract

We present what we believe is a new technique for the focal-length measurement of positive lenses using Fizeau interferometery. The technique utilizes the Gaussian lens equation. The image distance is measured interferometrically in terms of the radius of curvature of the image-forming wavefront emerging from the lens. The radii of curvature of the image-forming wavefronts corresponding to two different axial object positions of known separation are measured. The focal length of the lens is determined by solving the equations obtained using the Gaussian lens equation for the two object positions. Results obtained for a corrected doublet lens of a nominal focal length of 200.0mm with a measurement uncertainty of ±2.5% is presented.

© 2009 Optical Society of America

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References

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2007 (2)

2005 (1)

2002 (2)

1999 (1)

1997 (1)

M. de Angelis, S. de Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A new approach to high accuracy measurement of the focal length of lenses using a digital Fourier transform,” Opt. Commun. 136, 370-374 (1997).
[CrossRef]

1995 (1)

1994 (1)

O. Prakash and R. S. Ram, “Determination of focal length of convex lenses using Newton's method,” J. Opt. (Paris) 25, 135-138 (1994).
[CrossRef]

1991 (1)

K. V. S. Ram, M. P. Kothiyal, and R. S. Sirohi, “Curvature and focal length measurements using compensation of a collimated beam,” Opt. Laser Technol. 23, 241-245 (1991).
[CrossRef]

1988 (1)

1983 (1)

M. V. R. K. Murty and R. P. Shukla, “Measurement of long radius of curvature,” Opt. Eng. 22, 231-235 (1983).

Anand, A.

Branes, T. H.

Chhaniwal, V. K.

Chung, P. S.

de Angelis, M.

M. de Angelis, S. de Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A new approach to high accuracy measurement of the focal length of lenses using a digital Fourier transform,” Opt. Commun. 136, 370-374 (1997).
[CrossRef]

de Nicola, S.

M. de Angelis, S. de Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A new approach to high accuracy measurement of the focal length of lenses using a digital Fourier transform,” Opt. Commun. 136, 370-374 (1997).
[CrossRef]

Faridi, M. S.

Ferraro, P.

M. de Angelis, S. de Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A new approach to high accuracy measurement of the focal length of lenses using a digital Fourier transform,” Opt. Commun. 136, 370-374 (1997).
[CrossRef]

Finizio, A.

M. de Angelis, S. de Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A new approach to high accuracy measurement of the focal length of lenses using a digital Fourier transform,” Opt. Commun. 136, 370-374 (1997).
[CrossRef]

Ilev, I. K.

Kafri, O.

Keren, E.

Kerske, M. K.

Kothiyal, M. P.

K. V. S. Ram, M. P. Kothiyal, and R. S. Sirohi, “Curvature and focal length measurements using compensation of a collimated beam,” Opt. Laser Technol. 23, 241-245 (1991).
[CrossRef]

Mastsuda, K.

Murty, M. V. R. K.

M. V. R. K. Murty and R. P. Shukla, “Measurement of long radius of curvature,” Opt. Eng. 22, 231-235 (1983).

Oreb, B. F.

Pierattini, G.

M. de Angelis, S. de Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A new approach to high accuracy measurement of the focal length of lenses using a digital Fourier transform,” Opt. Commun. 136, 370-374 (1997).
[CrossRef]

Prakash, O.

O. Prakash and R. S. Ram, “Determination of focal length of convex lenses using Newton's method,” J. Opt. (Paris) 25, 135-138 (1994).
[CrossRef]

Ram, K. V. S.

K. V. S. Ram, M. P. Kothiyal, and R. S. Sirohi, “Curvature and focal length measurements using compensation of a collimated beam,” Opt. Laser Technol. 23, 241-245 (1991).
[CrossRef]

Ram, R. S.

O. Prakash and R. S. Ram, “Determination of focal length of convex lenses using Newton's method,” J. Opt. (Paris) 25, 135-138 (1994).
[CrossRef]

Shakher, C.

Sheppard, C. J. R.

Shukla, R. P.

M. V. R. K. Murty and R. P. Shukla, “Measurement of long radius of curvature,” Opt. Eng. 22, 231-235 (1983).

Singh, P.

Sirohi, R. S.

P. Singh, M. S. Faridi, C. Shakher, and R. S. Sirohi, “ Measurement of focal length with phase-shifting Talbot interferometry,” Appl. Opt. 44, 1572-1576 (2005).
[CrossRef] [PubMed]

K. V. S. Ram, M. P. Kothiyal, and R. S. Sirohi, “Curvature and focal length measurements using compensation of a collimated beam,” Opt. Laser Technol. 23, 241-245 (1991).
[CrossRef]

Thakur, M.

Wen, J. F.

Xiang, Y.

Zhao, S.

Appl. Opt. (7)

J. Opt. (Paris) (1)

O. Prakash and R. S. Ram, “Determination of focal length of convex lenses using Newton's method,” J. Opt. (Paris) 25, 135-138 (1994).
[CrossRef]

Opt. Commun. (1)

M. de Angelis, S. de Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A new approach to high accuracy measurement of the focal length of lenses using a digital Fourier transform,” Opt. Commun. 136, 370-374 (1997).
[CrossRef]

Opt. Eng. (1)

M. V. R. K. Murty and R. P. Shukla, “Measurement of long radius of curvature,” Opt. Eng. 22, 231-235 (1983).

Opt. Laser Technol. (1)

K. V. S. Ram, M. P. Kothiyal, and R. S. Sirohi, “Curvature and focal length measurements using compensation of a collimated beam,” Opt. Laser Technol. 23, 241-245 (1991).
[CrossRef]

Opt. Lett. (1)

Other (1)

R.Kingslake, ed., Applied Optics and Optical Engineering (Academic, 1965), Vol. 1, pp. 208-226.

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Figures (8)

Fig. 1
Fig. 1

Wavefront representation of the object and image rays.

Fig. 2
Fig. 2

Illustration of the radius of the image-forming wavefront approaching a large value when the object is placed slightly away from the focal point of the lens.

Fig. 3
Fig. 3

Schematic of the experimental setup for the focal-length measurement.

Fig. 4
Fig. 4

Illustration of the circular fringes.

Fig. 5
Fig. 5

Schematic for the focal-length determination of a concave lens using a concave mirror of known radius of curvature.

Fig. 6
Fig. 6

Interference fringes formed due to the interference of the spherical wavefront with the plane reference wavefront during the initial alignment.

Fig. 7
Fig. 7

Interference fringes formed due to further translation of the mirror from the initial position.

Fig. 8
Fig. 8

Plot of the focal length measured for multiple measurements.

Equations (18)

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1 U + 1 V = 1 F
R v 1 = ( D 2 n + p D 2 n 8 p λ ) + S ,
U 2 U 1 = 2 x .
1 U 1 + 1 R v 1 = 1 F ,
1 ( U 1 + 2 x ) + 1 R v 2 = 1 F .
U 1 = x + x 2 + 2 x ( R v 1 R v 2 R v 1 R v 2 ) .
d U 1 = [ ( δ U 1 δ x ) 2 ( d x ) 2 + ( δ U 1 δ R v 1 ) 2 ( d R v 1 ) 2 + ( δ U 1 δ R v 2 ) 2 ( d R v 2 ) 2 ] 1 / 2 .
d U 1 = [ ( { x + k 1 x 2 + 2 x k 1 } 1 ) 2 ( d x ) 2 + ( x R v 2 2 ( R v 1 R v 2 ) 2 x 2 + 2 x k 1 ) 2 ( d R v 1 ) 2 + ( x R v 1 2 ( R v 1 R v 2 ) 2 x 2 + 2 x k 1 ) 2 ( d R v 2 ) 2 ] 1 / 2 .
d F = [ ( δ F δ U 1 ) 2 ( d U 1 ) 2 + ( δ F δ V 1 ) 2 ( d V 1 ) 2 ] 1 / 2 .
d F = [ ( V 1 2 ( U 1 + V 1 ) 2 ) 2 ( d U 1 ) 2 + ( U 1 2 ( U 1 + V 1 ) 2 ) 2 ( d V 1 ) 2 ] 1 / 2 ,
U 1 = x + x 2 + 2 x [ ( R v 1 + d ) ( R v 2 + d ) ( R v 1 R v 2 ) ] .
d U 1 = [ ( { x + k 2 x 2 + 2 x k 2 } 1 ) 2 ( d x ) 2 + ( x ( R v 2 + d ) 2 ( R v 1 R v 2 ) 2 x 2 + 2 x k 2 ) 2 ( d R v 1 ) 2 + ( x ( R v 1 + d ) 2 ( R v 1 R v 2 ) 2 x 2 + 2 x k 2 ) 2 ( d R v 2 ) 2 ] 1 / 2 .
d F = [ ( V 1 2 ( U 1 + V 1 ) 2 ) 2 ( d U 1 ) 2 + ( U 1 2 ( U 1 + V 1 ) 2 ) 2 ( d V 1 ) 2 ] 1 / 2 ,
V 1 M = R C ( R C + x 1 ) ( R C + 2 x 1 ) .
V 2 M = R C ( R C + x 1 + x 2 ) ( R C + 2 x 1 + 2 x 2 ) .
1 U 1 CV + 1 V 1 CV = 1 F ,
1 U 2 CV + 1 V 2 CV = 1 F .
U 1 CV = Δ U + Δ U 2 + 4 V 1 CV V 2 CV V 1 CV V 2 CV Δ U 2 .

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