Abstract

Paper II of this series demonstrates that spherical lens elements combined with spherical mirrors may provide well-corrected and achromatized ultraviolet microscope objectives. The present paper presents a further study of several types of catadioptric Schwarzschild systems which provide microscope objectives relatively easy to construct, convenient to use, and for which ultraviolet and visual range performance characteristics are not compromised. Several modifications with numerical apertures within the range 0.4 to 1.0 are presented.

© 1950 Optical Society of America

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References

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  1. D. S. Grey and P. H. Lee, J. Opt. Soc. Am. 39, 719 (1949).
    [Crossref] [PubMed]
  2. D. S. Grey, J. Opt. Soc. Am. 39, 723 (1949).
    [Crossref] [PubMed]
  3. The Schwarzschild objectives reported by Burch are based on aspheric mirrors. C. R. Burch, Proc. Phys. Soc. London 59, 41 (1947).
    [Crossref]
  4. The objectives used by Brumberg provide a weak lens between the convex mirror and the long conjugate focus. The only apparent function of this lens is to correct chromatic aberration introduced by the cover slip. E. M. Brumberg, Nature (London) 152, 357 (1943).
    [Crossref]
  5. For a discussion of glycerin-sugar-water mixtures for immersion liquids, see L. C. Martin and B. K. Johnson, J. Sci. Inst. 5, 380 (1928).
    [Crossref]

1949 (2)

1947 (1)

The Schwarzschild objectives reported by Burch are based on aspheric mirrors. C. R. Burch, Proc. Phys. Soc. London 59, 41 (1947).
[Crossref]

1943 (1)

The objectives used by Brumberg provide a weak lens between the convex mirror and the long conjugate focus. The only apparent function of this lens is to correct chromatic aberration introduced by the cover slip. E. M. Brumberg, Nature (London) 152, 357 (1943).
[Crossref]

1928 (1)

For a discussion of glycerin-sugar-water mixtures for immersion liquids, see L. C. Martin and B. K. Johnson, J. Sci. Inst. 5, 380 (1928).
[Crossref]

Brumberg, E. M.

The objectives used by Brumberg provide a weak lens between the convex mirror and the long conjugate focus. The only apparent function of this lens is to correct chromatic aberration introduced by the cover slip. E. M. Brumberg, Nature (London) 152, 357 (1943).
[Crossref]

Burch, C. R.

The Schwarzschild objectives reported by Burch are based on aspheric mirrors. C. R. Burch, Proc. Phys. Soc. London 59, 41 (1947).
[Crossref]

Grey, D. S.

Johnson, B. K.

For a discussion of glycerin-sugar-water mixtures for immersion liquids, see L. C. Martin and B. K. Johnson, J. Sci. Inst. 5, 380 (1928).
[Crossref]

Lee, P. H.

Martin, L. C.

For a discussion of glycerin-sugar-water mixtures for immersion liquids, see L. C. Martin and B. K. Johnson, J. Sci. Inst. 5, 380 (1928).
[Crossref]

J. Opt. Soc. Am. (2)

J. Sci. Inst. (1)

For a discussion of glycerin-sugar-water mixtures for immersion liquids, see L. C. Martin and B. K. Johnson, J. Sci. Inst. 5, 380 (1928).
[Crossref]

Nature (London) (1)

The objectives used by Brumberg provide a weak lens between the convex mirror and the long conjugate focus. The only apparent function of this lens is to correct chromatic aberration introduced by the cover slip. E. M. Brumberg, Nature (London) 152, 357 (1943).
[Crossref]

Proc. Phys. Soc. London (1)

The Schwarzschild objectives reported by Burch are based on aspheric mirrors. C. R. Burch, Proc. Phys. Soc. London 59, 41 (1947).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1

The Schwarzschild mirrors illustrated above are the starting point for the design of a series of objectives. Lens elements are added to this basic pair of mirrors to increase the numerical aperture at which aberrations are corrected, to decrease the obscuring ratio, to seal the system against dust, and to provide a non-obscuring support for the convex mirror.

Fig. 2
Fig. 2

Lens components have been added to the Schwarzschild mirrors to provide an objective of numerical aperture 0.72, corrected for use in the wave-length region from 220 mμ through the visible spectrum. Nine percent of the objective aperture area is obscured by the convex mirror.

Fig. 3
Fig. 3

Variation in cover slip thickness from the thickness assumed in lens computation introduces spherical aberration. The total range of permissible variation in the distance from the object plane to the top of the cover slip is plotted above as a function of numerical aperture of the objective. The computation is based on permitting the thickness variation to introduce an amount of spherical aberration equal to 1 8 wave-length, or half the Rayleigh tolerance, at wave-length 250 mμ. The tolerance is proportional to wave-length. Computations are for cover slip index 1.5. The factors, X1⋯X104, associated with the curves indicate the factor by which the ordinate is to be multiplied to yield the tolerance for the corresponding abscissa, or NA, value.

Fig. 4
Fig. 4

This objective, computed for water immersion, can be well corrected at numerical apertures up to 0.90. Variation of magnification with wave-length may be eliminated, so that no eyepiece is necessary.

Fig. 5
Fig. 5

A method of eliminating the construction and mounting of a separate convex mirror element is illustrated above. The convex mirror is continuous with a lens surface, and is merely an aluminized spot thereon. The concave mirror is back surfaced; the front and refracting surface of this lens element provides a correction for the chromatic aberration of the lens element adjacent to the object.

Fig. 6
Fig. 6

Objectives similar to that of Fig. 5 may be given additional refractive components to provide correction at larger numerical apertures.

Fig. 7
Fig. 7

Another method of “eliminating” the convex mirror element is shown above. Numerical aperture 1.0, obscured area 9 percent. Residual aberrations shown in Figs. 8 to 10.

Fig. 8
Fig. 8

Spherical aberration in terms of phase retardation for Fig. 7 type objective. These curves were computed for a common focal setting at the three wave-lengths, and thus include the effect of the shift of the plane of best focus.

Fig. 9
Fig. 9

The shift of the plane of best focus for the objective of Fig. 7, and the total depth of focus at numerical aperture 1. The shift of the plane of best focus includes variation of spherical aberration with wave-length. The allowance of chromatic overcorrection to compensate an unachromatized eyepiece has been subtracted from these residuals.

Fig. 10
Fig. 10

Offense against the sine condition for the objective of Fig. 5. Negative offense against the sine condition means an increase in magnification.

Fig. 11
Fig. 11

If the Schwarzschild pair of spherical mirrors is used without auxiliary lens elements, the obscuring ratio decreases as the magnification for which the objective is computed is decreased. If third-order coma and spherical aberration are both zero, the obscured area varies with magnification as shown in this figure.

Equations (4)

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R 1 R 2 = 3 2 - R 1 d - ( 5 4 - R 1 d ) 1 2 .
Q = 3 d R 2 - R 1 R 2 - 2 R 1 d R 2 ( d - R 1 ) .
M = { 1 - ( d / R 1 ) + 2 [ ( d / R 1 ) - 1 ] 1 2 } - 1 .
Q = [ 2 M + ( 5 M 2 - 6 M + 5 ) 1 2 ] [ 1 - M ] - 1 .