Abstract

A technique is described for obtaining interferometric data on an optical system without modification of the system, and using the detector intrinsic to the system. A pair of coherent point sources is imaged by the system and examined in an out-of-focus position. The period of the resulting fringe pattern is used to determine the focus position unambiguously. The structure of the fringe pattern indicates other system errors. An experiment to verify the practicality of the technique is described.

© 1971 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. G. Baker, Nat. Bur. Stand. Circ. 526 (U.S. GPO, Washington, D.C., 1954), p. 117.
  2. R. R. Shannon, in Applied Optics and Optical Design, R. Kingslake, Ed. (Academic Press, New York, 1965), Vol. 3, p. 183.
  3. G. Toraldo di Francia, Nat. Bur. Stand. Circ. 526 (U.S. GPO, Washington, D.C., 1954), p. 161.
  4. M. V. R. K. Murty, Appl. Opt. 3, 531, 853 (1964).
    [CrossRef]
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 259.
  6. W. H. Steel, Interferometry (Cambridge U. P., London, 1967).
  7. C. Rodriguez-Torres, “Multiple Source Testing of Camera Systems,” M.S. Thesis, U. of Arizona, Tucson (1970). Also published as Optical Sciences Center (University of Arizona) Tech. Rept. 54 (1970).

1964 (1)

M. V. R. K. Murty, Appl. Opt. 3, 531, 853 (1964).
[CrossRef]

Baker, J. G.

J. G. Baker, Nat. Bur. Stand. Circ. 526 (U.S. GPO, Washington, D.C., 1954), p. 117.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 259.

Murty, M. V. R. K.

M. V. R. K. Murty, Appl. Opt. 3, 531, 853 (1964).
[CrossRef]

Rodriguez-Torres, C.

C. Rodriguez-Torres, “Multiple Source Testing of Camera Systems,” M.S. Thesis, U. of Arizona, Tucson (1970). Also published as Optical Sciences Center (University of Arizona) Tech. Rept. 54 (1970).

Shannon, R. R.

R. R. Shannon, in Applied Optics and Optical Design, R. Kingslake, Ed. (Academic Press, New York, 1965), Vol. 3, p. 183.

Steel, W. H.

W. H. Steel, Interferometry (Cambridge U. P., London, 1967).

Toraldo di Francia, G.

G. Toraldo di Francia, Nat. Bur. Stand. Circ. 526 (U.S. GPO, Washington, D.C., 1954), p. 161.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 259.

Appl. Opt. (1)

M. V. R. K. Murty, Appl. Opt. 3, 531, 853 (1964).
[CrossRef]

Other (6)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 259.

W. H. Steel, Interferometry (Cambridge U. P., London, 1967).

C. Rodriguez-Torres, “Multiple Source Testing of Camera Systems,” M.S. Thesis, U. of Arizona, Tucson (1970). Also published as Optical Sciences Center (University of Arizona) Tech. Rept. 54 (1970).

J. G. Baker, Nat. Bur. Stand. Circ. 526 (U.S. GPO, Washington, D.C., 1954), p. 117.

R. R. Shannon, in Applied Optics and Optical Design, R. Kingslake, Ed. (Academic Press, New York, 1965), Vol. 3, p. 183.

G. Toraldo di Francia, Nat. Bur. Stand. Circ. 526 (U.S. GPO, Washington, D.C., 1954), p. 161.

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 (3)

Fig. 1
Fig. 1

A displacement from the focal plane, in imaging two coherent point sources, causes a fringe pattern with a characteristic fringe period to appear at each plane.

Fig. 2
Fig. 2

Region of overlap of the two image cones near focus. Labels indicate the meaning of the symbols used in the text.

Fig. 3
Fig. 3

Best linear fit for the fringe period measured for three different sets of pinhole separation. A common best focus value of −45 μm was found. Each data point for the resolution curve represents an average value from two measurements. The abscissa represents both fringe period and resolution.

Equations (24)

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

p = α a = ( λ / d ) a .
a = ( d / λ ) p .
n ( λ + δ λ ) - n λ 0.1 λ
δ λ / λ 1 / 10 n .
b / ( f + a ) = d / f
b = d [ ( f + a ) / f ] = d [ 1 + ( a / f ) ] .
c / a = 1 / ( F / no . )
c = a / ( F / no . ) ,
e = 2 [ ( c / 2 ) - b ] = 2 { [ a / ( F / no . ) ] - d }
N = e p = 2 [ a / ( F / no . ) ] - d ( λ / d ) a = 2 d λ a ( a F / no . - d ) .
a ( F / no . ) - d > 0 ,
a > ( F / no . ) d .
n · 8 λ ( F / no . ) 2 > ( F / no . ) · m λ ( F / no . ) ,
n > m / 8.
N = 2 m [ 1 - ( m / 8 n ) ] ,
p = λ ( a / d ) = ( n / m ) [ 8 λ ( F / no . ) ] = ( 8 n / m ) ( p 0 ) ,
p / p 0 = 5 = 8 n / m .
5 = 2 ( m ) ( 1 - 0.2 ) = 1.6 m ,
m = 3.1.
8 n / m = 5 , n = [ 5 · ( 3.1 ) ] / 8 = 1.94.
a = ( d / λ ) p
δ a = a [ ( δ d / d ) + ( δ p / p ) ]
δ a ( focal depth ) = δ a 8 λ ( F / no . ) 2 = n δ d / p 0 m + δ p / p 0 8 n / m .
δ a ( focal depth ) = ( 1.94 ) ( 0.25 3.1 + 1 5 ) = 0.55.

Metrics