Abstract

Expressions are derived for the primary longitudinal and transverse chromatic aberrations of a lens system as summations of terms over all the singlet components of the system. Each term in these summations is the product of the partial dispersion of the glass of the lens with a certain coefficient which is easily calculated from the data of a paraxial trace, and specifies the contribution made by the lens to the corresponding primary chromatic aberration of the final image. The coefficients are called the primary chromatic coefficients of the system. In addition, the coefficients provide a rapid means of analyzing the complete secondary spectrum of the system, and afford a clear guide to the adjustment of the primary chromatic aberrations insofar as it is desired to do this by the selection of different glass types.

© 1946 Optical Society of America

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References

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  1. A. E. Conrady, Applied Optics and Optical Design (Oxford University Press, London, 1929), pp. 312–313.

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design (Oxford University Press, London, 1929), pp. 312–313.

Other (1)

A. E. Conrady, Applied Optics and Optical Design (Oxford University Press, London, 1929), pp. 312–313.

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Figures (2)

Tables (3)

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Table II Detailed computation of the contributions to the primary longitudinal chromatic aberration made by the three pairs of components of a wide angle Ross Xpres type photographic objective for various spectral ranges.

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Table III Computation of the change of the secondary spectrum, lk-lDk, due to change of glass in two components of the system.

Equations (24)

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L c h C = N u l i N k u k 2 ( δ N N δ N N ) ,
L c h C = N u l i p r N k u k ( δ N N δ N N ) = L c h C u k ( i p r i ) .
d l i = l i d u i / u i .
u = u + i i = u + i ( 1 n ) ,
u / n = i ,
d l i = l i u i n i d n i / u i = l i i i d n i / u i .
N k d l k u k 2 = N i d l i u i 2
d l k = N i u i l i l i N k u k 2 d n i ,
l k / n i = N i u i l i l i / N k u k 2 = N i y i i i / N k u k 2 .
l k N h = l k n 1 n 1 N h + l k n 2 n 2 N h , = l k n 1 N h ( N h 1 N h ) + l k n 2 N h ( N h N h + 1 ) , = N 1 y 1 i 1 N k u k 2 . N h 1 N h 2 + N 2 y 2 i 2 N k u k 2 . 1 N h + 1 , = 1 N k u k 2 ( n 1 y 1 i 1 + y 2 i 2 ) , = 1 N k u k 2 ( y 1 i 1 + y 2 i 2 ) .
l r k = l d k + l k N a ( N r N d ) a + l k N b ( N r N d ) b + = l d k Σ a l k N h ( N r N d ) h .
l v k = l d k + Σ l k N h ( N v N d ) h .
l c h = l r k l v k = Σ l k N h ( N r N v ) h .
l c h = Σ l k N h P h ,
l c h / P h = l k / N h .
l k / N a , f = 991.833 , l k / N b , e = 1087.38 , l k / N c , d = 270.091.
l C k = 106.525 + 0.226 = 106.751 , l F k = 106.525 0.335 = 106.190 , l c h C F = 0.561.
l C k = 106.748 , l F k = 106.181 , l c h C F = 0.567 ,
d h i = l i d u i p r , = l i u i p r n i d n i , = l i i i p r d n i .
d h k = N i u i d h i / N k u k ,
h k / n i = N i y i i i p r / N k u k .
h k / n i = u k ( i i p r / i i ) ( l k / n i ) .
h k N h = 1 N k u k ( y 1 i p r 1 + y 2 i p r 2 ) h ,
t c h = h r k h v k = Σ h k N k ( N r N v ) h .