Abstract

This note describes a convenient working technique for measuring the minimum size focused spot formed by a lens system. The technique is routinely capable of measurement precision of better than ⅛λ. The theory of knife-edge scanning is presented, and the relationship of the measured spot profile to the actual spot profile is shown to be relatively insensitive to the acceptance solid angle of the photodetector. Finally, some typical results of high resolution microscope objectives are presented.

© 1977 Optical Society of America

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References

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  1. I. Gorog et al., Appl. Opt. 15, 1425 (1976).
    [Crossref] [PubMed]
  2. K. Compaan, P. Kramer, Phillips Tech. Rev. 33, 178 (1973).
  3. J. H. Bruning et al., Appl. Opt. 13, 2693 (1974).
    [Crossref] [PubMed]
  4. Y. Suzaki, A. Tachibana, Appl. Opt. 14, 2809 (1975).
    [Crossref] [PubMed]
  5. J. Corcoran, Laser Focus 61–62 (June1973).
  6. D. R. Skinner, R. E. Whitcher, J. Phys. E. 5, 237 (1972).
    [Crossref]
  7. J. A. Arnaud et al., Appl. Opt. 10, 2775 (1971).
    [Crossref] [PubMed]
  8. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

1976 (1)

1975 (1)

1974 (1)

1973 (2)

K. Compaan, P. Kramer, Phillips Tech. Rev. 33, 178 (1973).

J. Corcoran, Laser Focus 61–62 (June1973).

1972 (1)

D. R. Skinner, R. E. Whitcher, J. Phys. E. 5, 237 (1972).
[Crossref]

1971 (1)

Arnaud, J. A.

Bruning, J. H.

Compaan, K.

K. Compaan, P. Kramer, Phillips Tech. Rev. 33, 178 (1973).

Corcoran, J.

J. Corcoran, Laser Focus 61–62 (June1973).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Gorog, I.

Kramer, P.

K. Compaan, P. Kramer, Phillips Tech. Rev. 33, 178 (1973).

Skinner, D. R.

D. R. Skinner, R. E. Whitcher, J. Phys. E. 5, 237 (1972).
[Crossref]

Suzaki, Y.

Tachibana, A.

Whitcher, R. E.

D. R. Skinner, R. E. Whitcher, J. Phys. E. 5, 237 (1972).
[Crossref]

Appl. Opt. (4)

J. Phys. E. (1)

D. R. Skinner, R. E. Whitcher, J. Phys. E. 5, 237 (1972).
[Crossref]

Laser Focus 61–62 (1)

J. Corcoran, Laser Focus 61–62 (June1973).

Phillips Tech. Rev. (1)

K. Compaan, P. Kramer, Phillips Tech. Rev. 33, 178 (1973).

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (4)

Fig. 1
Fig. 1

Computed spot profiles for various acceptance numerical apertures (N.A.). The illumination wavefront has the intensity profile exp(−r2/2σ2) at the front focal plane with σ = 0.3f, f being the focal length and r the radial distance from the optical axis. The intensity scale is normalized by assuming the peak intensity of the N.A. = 1.0 case to be 1. x = 0 is the optical axis.

Fig. 2
Fig. 2

Schematic diagram of the knife-edge scanning apparatus.

Fig. 3
Fig. 3

Photograph of the integrated scanner–interferometer stage mounted on its xyz stage.

Fig. 4
Fig. 4

Oscilloscope photograph of the measurement of a submicron focused spot (lens—Leitz F1 100, N.A. = 0.95, λ = 4416 Å).

Tables (1)

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Table I Measurements of Microscope Objectives

Equations (6)

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E ( x ) = ½ [ 1 + sgn ( x ) ] ,
sgn ( x ) = ( + 1 x > 0 , - 1 x < 0.
p ( K , Δ ) = a ( k ) e ( K ) exp ( i K Δ ) ,
a ( K ) = - A ( x ) exp ( - i K x ) d x , e ( K ) = ½ δ ( K ) + 1 i K ,
S ( x ) = d d Δ p ( 0 , Δ ) 2 Δ = x .
S ( x ) α A ( x ) x A ( u ) d u .

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