Abstract

We report a method for measuring the effective focal length of a lens without knowing the degree of collimation or the location of the principal planes of the lens.

© 1989 Optical Society of America

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References

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  1. K. A. Hoagland, “Focal Length Determining System,” U.S. Pat.3,495,913 (17 Feb.1970).
  2. J. L. McLaughlin, “Focus-Position Sensing Using Laser Speckle,” Appl. Opt. 18, 1042 (1979).
    [CrossRef] [PubMed]
  3. P. T. Kaestner, “Apparatus for Determining Focus,” U.S. Pat.3,917,409 (4 Nov.1975).
  4. T. D. Wise, J. B. Young, “Precise Measurement of Effective Focal Length,” Appl. Opt. 22, 3918 (1983).
  5. J. L. Horner, J. R. Leger, “Pattern Recognition with Binary Phase-Only Filters,” Appl. Opt. 24, 609 (1985).
    [CrossRef] [PubMed]

1985 (1)

1983 (1)

T. D. Wise, J. B. Young, “Precise Measurement of Effective Focal Length,” Appl. Opt. 22, 3918 (1983).

1979 (1)

Hoagland, K. A.

K. A. Hoagland, “Focal Length Determining System,” U.S. Pat.3,495,913 (17 Feb.1970).

Horner, J. L.

Kaestner, P. T.

P. T. Kaestner, “Apparatus for Determining Focus,” U.S. Pat.3,917,409 (4 Nov.1975).

Leger, J. R.

McLaughlin, J. L.

Wise, T. D.

T. D. Wise, J. B. Young, “Precise Measurement of Effective Focal Length,” Appl. Opt. 22, 3918 (1983).

Young, J. B.

T. D. Wise, J. B. Young, “Precise Measurement of Effective Focal Length,” Appl. Opt. 22, 3918 (1983).

Appl. Opt. (3)

Other (2)

P. T. Kaestner, “Apparatus for Determining Focus,” U.S. Pat.3,917,409 (4 Nov.1975).

K. A. Hoagland, “Focal Length Determining System,” U.S. Pat.3,495,913 (17 Feb.1970).

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Figures (2)

Fig. 1
Fig. 1

Lens setup with and without true collimation. Focal length is fc, Δ1 is displacement of a point source, and Δ2 is the change in apparent focal length.

Fig. 2
Fig. 2

Proposed system for measuring focal length. It is invariant to the degree of collimation of the incoming light.

Equations (7)

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ν = μ / λ f ,
f = u n a / λ n .
A ( ν x , ν y ) = exp [ j π / λ f ( 1 d 0 / f c ) ( ν x 2 + ν y 2 ) ] s ( x , y ) × exp [ j 2 π ( ν x x + ν y y ) ] d x d y .
A ( u , υ ) = s ( x , y ) exp [ j 2 π λ ( x u f + y υ f + x 2 2 L + y 2 2 L ) ] d x d y .
A ( u , υ ) = a sinc ( π a u ) + j a λ f 2 / 4 π L u 2 [ ( 2 π 2 a 2 u 2 / λ 2 f 2 ) × sinc ( π a u ) 2 cos ( π a u ) ] .
I ( u , υ ) = a 2 sinc 2 ( 1.0 ) ( π a u ) + b 2 sinc 2 ( 10 5 ) ( π a u ) + 4 b 2 sinc ( 10 5 ) ( π a u ) cos ( π a u ) + 4 cos 2 ( 10 9 ) ( π a u ) ,
b = λ a f 2 4 π L u 2 ( 2 π 2 a 2 u 2 λ 2 f 2 )

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