Abstract

The history of achromatic lenses is briefly reviewed. The latest development is the superachromat, which is corrected for four colors. Since the dispersion of glass can be represented by an equation containing four constants, the superachromat is practically corrected for all colors. The application of the superachromatic principle to thick lenses is described and it is shown that a compound lens can be made superachromatic by making each of its separate components superachromatic.

© 1963 Optical Society of America

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References

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  1. I. Newton, “A new theory about light and colours,” Phil. Trans.6, 3075ff. (1672). Reprinted in M. Roberts, E. R. Thomas, Newton and the Origin of Colours (Bell, London, 1934), pp. 71ff., and W. F. Magie, A Source Book in Physics (McGraw-Hill, New York, 1935), pp. 298ff.
    [CrossRef]
  2. I. Newton, Lectiones Opticae, etc. (London, 1728). Republished by J. Manfré Padua, 1773.
  3. For the history of the telescope between 1675 and 1830, see T. H. Court, M. von Rohr, Trans. Opt. Soc. London 30, 207 (1928–29).
    [CrossRef]
  4. For biographies of this brilliant optical engineer, who died all too young (1787–1826), see M. von Rohr, Trans. Opt. Soc. London 27, 277 (1925–26); Z. Insturmentenk. 46, 273 (1926).
    [CrossRef]
  5. M. Herzberger, Optica Acta 6, 197 (1959).
    [CrossRef]
  6. R. E. Stephens, J. Opt. Soc. Am. 49, 398 (1959); J. Opt. Soc. Am. 50, 1016 (1960).
    [CrossRef]
  7. M. Herzberger, Modern Geometrical Optics (Interscience, New York, 1958), Eq. (12.35).
  8. F. H. Perrin, H. O. Hoadley, J. Opt. Soc. Am. 38, 1040 (1948).
    [CrossRef]

1959 (2)

1948 (1)

Court, T. H.

For the history of the telescope between 1675 and 1830, see T. H. Court, M. von Rohr, Trans. Opt. Soc. London 30, 207 (1928–29).
[CrossRef]

Herzberger, M.

M. Herzberger, Optica Acta 6, 197 (1959).
[CrossRef]

M. Herzberger, Modern Geometrical Optics (Interscience, New York, 1958), Eq. (12.35).

Hoadley, H. O.

Newton, I.

I. Newton, Lectiones Opticae, etc. (London, 1728). Republished by J. Manfré Padua, 1773.

I. Newton, “A new theory about light and colours,” Phil. Trans.6, 3075ff. (1672). Reprinted in M. Roberts, E. R. Thomas, Newton and the Origin of Colours (Bell, London, 1934), pp. 71ff., and W. F. Magie, A Source Book in Physics (McGraw-Hill, New York, 1935), pp. 298ff.
[CrossRef]

Perrin, F. H.

Stephens, R. E.

von Rohr, M.

For the history of the telescope between 1675 and 1830, see T. H. Court, M. von Rohr, Trans. Opt. Soc. London 30, 207 (1928–29).
[CrossRef]

For biographies of this brilliant optical engineer, who died all too young (1787–1826), see M. von Rohr, Trans. Opt. Soc. London 27, 277 (1925–26); Z. Insturmentenk. 46, 273 (1926).
[CrossRef]

J. Opt. Soc. Am. (2)

Optica Acta (1)

M. Herzberger, Optica Acta 6, 197 (1959).
[CrossRef]

Trans. Opt. Soc. London (2)

For the history of the telescope between 1675 and 1830, see T. H. Court, M. von Rohr, Trans. Opt. Soc. London 30, 207 (1928–29).
[CrossRef]

For biographies of this brilliant optical engineer, who died all too young (1787–1826), see M. von Rohr, Trans. Opt. Soc. London 27, 277 (1925–26); Z. Insturmentenk. 46, 273 (1926).
[CrossRef]

Other (3)

I. Newton, “A new theory about light and colours,” Phil. Trans.6, 3075ff. (1672). Reprinted in M. Roberts, E. R. Thomas, Newton and the Origin of Colours (Bell, London, 1934), pp. 71ff., and W. F. Magie, A Source Book in Physics (McGraw-Hill, New York, 1935), pp. 298ff.
[CrossRef]

I. Newton, Lectiones Opticae, etc. (London, 1728). Republished by J. Manfré Padua, 1773.

M. Herzberger, Modern Geometrical Optics (Interscience, New York, 1958), Eq. (12.35).

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Figures (8)

Fig. 1
Fig. 1

Plot of P** = (nFn**)/(nFnC) vs P* = (nFn*)/(nFnC) for selected glasses, largely from Schott catalog 350-E, and certain other materials (○—fluorite; △—methyl methacrylate). The types of glass are designated as in the Schott catalog. The materials used for a superachrornat must lie on a straight line in this plot.

Fig. 2
Fig. 2

Color curves of the ten thin-lens superachromatic triplets listed in Table II on the basis of a 100-mm focal length.

Fig. 3
Fig. 3

Color curves of (A) typical apochromat, (S) superachromatic triplet A of Table II, and (AT) air-spaced fluorite triplet that approached superachromnatic correction, all for f′ = 100 mm.

Fig. 4
Fig. 4

Plot of P** vs P* for (A) an all-glass and (B) a fluorite superachromatie triplet.

Fig. 5
Fig. 5

Marginal spherical aberration and isoplanatism as a function of bending for triplets of 100-mm focal length made from the materials plotted in Fig. 4. The bending is indicated by the curvature of the first surface in reciprocal millimeters.

Fig. 6
Fig. 6

Superachromatic combinations of (A) two and (B) three all-glass, air-spaced triplets of 100-mm focal length with their error curves. The first two curves for each lens represent, left to right, spherical aberration and isoplanatism (coma) as a function of aperture; the third and fourth represent, respectively, distortion on the axis and departure from the Gaussian image point as a function of slope angle σ′ of emergent ray. Solid curves, F-line; broken curves, A′-line; dotted curves, h-line of spectrum. Combination B was designed for a comparatively small field. Distortion as defined here means the deviation of the intersection point of a ray with the image plane from the Gaussian image point. This is a generalization of the usual definition, which is restricted to principal rays.

Fig. 7
Fig. 7

Sketch of f/2.8 superachromatic Petzval-type lens in which two components are cemented fluorite superachromatic triplets.

Fig. 8
Fig. 8

Spot diagrams of f/2.8 Petzval-type lens sketched in Fig. 7 for each of three field angles and each of three axial positions measured from the Gaussian focus. The size of the first dark ring in the Airy pattern is indicated by the circle AD.

Tables (3)

Tables Icon

Table I Values of Universal Functions Appearing in Eq. (1) for Twelve Selected Wavelengths

Tables Icon

Table II Glass Constants of Ten Thin Superachromatic Triplets of Unit Powera

Tables Icon

Table III Glass Constants for Thin Color-Corrected Lenses of Unit Power, Powers of Individual Elements, and Sums of Absolute Values of These Powersa

Equations (23)

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λ 1 = λ * = 1.014 μ , λ 2 = λ C = 0.6563 μ , λ 3 = λ F = 0.4861 μ , and λ 4 = λ * * = 0.356 μ .
μ λ = a 1 ( λ ) μ * + a 2 ( λ ) μ C + a 3 ( λ ) μ F + a 4 ( λ ) μ * * ,
a 1 + a 2 + a 3 + a 4 = 1 ,
μ F - μ λ = a 1 ( μ F - μ * ) + a 2 ( μ F - μ C ) + a 4 ( μ F - μ * * ) .
ν λ = μ F / ( μ F - μ λ )
1 ν λ = a 1 1 ν * + a 2 1 ν C + a 4 1 ν * * .
P λ = ν C ν λ = μ F - μ λ μ F - μ C = n F - n λ n F - n C
P λ = a 1 P * + a 4 P * * + a 2 .
μ λ = μ F - μ F ( P λ / ν C ) .
μ λ = μ F - μ F ( a 1 P * + a 4 P * * + a 2 ) / ν C . Q . E . D .
ϕ = μ ( ρ - ρ ) ,
Φ = Σ ϕ i
Φ F - Φ λ = a 1 ( Φ F - Φ * ) + a 2 ( Φ F - Φ C ) + a 4 ( Φ F - Φ * * ) ,
Φ F - Φ λ = Σ ( ϕ F / ν λ ) .
Φ F - Φ C = 0 = Σ ϕ F / ν C , Φ F - Φ * = 0 = Σ ϕ F / ν * , Φ F - Φ * * = 0 = Σ ϕ F / ν * * .
ϕ F 1 / ν C 1 + ϕ F 2 / ν C 2 + ϕ F 3 / ν C 3 = 0 , ϕ F 1 / ν * 1 + ϕ F 2 / ν * 2 + ϕ F 3 / ν * 3 = 0 , ϕ F 1 / ν * * 1 + ϕ F 2 / ν * * 2 + ϕ F 3 / ν * * 3 = 0.
| 1 / ν C 1 1 / ν C 2 1 / ν C 3 1 / ν * 1 1 / ν * 2 1 / ν * 3 1 / ν * * 1 1 / ν * * 2 1 / ν * * 3 | ,
| 1 1 1 P * 1 P * 2 P * 3 P * * 1 P * * 2 P * * 3 | = 0 ,
ϕ 1 / ν C 1 : ϕ 2 / ν C 2 = ( P * 2 - P * 3 ) : ( P * 3 - P * 1 ) .
ϕ 2 / ν C 2 : ϕ 3 / ν C 3 = ( P * 3 - P * 1 ) : ( P * 1 - P * 2 ) .
ϕ 1 = k ( P * 2 - P * 3 ) ν C 1 , ϕ 2 = k ( P * 3 - P * 1 ) ν C 2 , ϕ 3 = k ( P * 1 - P * 2 ) ν C 3 ,
k = 1 / Σ ( ϕ 1 + ϕ 2 + ϕ 3 ) ,
P * 1 - P * 2 0.07 and P * 2 - P * 3 0.07.

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