Abstract

A solution is given of the problem of the paraxial optical transfer coefficients of a centered lens system. Certain fundamental differential coefficients are developed which specify the rate of change of quantities defining the path of a paraxial ray in the final image space with the constructional parameters of the system, i.e., the surface curvatures, axial separations, and refractive indices. From these, other differential transfer coefficients are derived which specify the rate of change of the paraxial magnification, the focal length, and the positions of the paraxial image plane and the image principal plane with the constructional parameters of the system. The calculation of these coefficients is based on the results of a paraxial ray trace and lends itself to systematic arrangement for machine computation.

© 1946 Optical Society of America

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References

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  1. M. Herzberger, J. Opt. Soc. Am. 33, 651 (1943).
    [Crossref]
  2. R. E. Stephens, J. Opt. Soc. Am. 33, 684 (A) (1943).
  3. W. M. Stempel, J. Opt. Soc. Am. 33, 278 (1943).
    [Crossref]
  4. A. L. McAulay, Secret Papers, Optical Munitions Panel, Aust.Nov.1942.
  5. A. L. McAulay, Secret Papers, Opt. Mun. Panel, Aust.July, 1943.
  6. F. D. Cruickshank, Secret Papers, Opt. Mun. Panel, Nov.1942.
  7. F. D. Cruickshank, Secret Papers, Opt. Mun. Panel, Aust.May1943.
  8. A. E. Conrady, Applied Optics and Optical Design (Oxford University Press, London, 1929). Note. The work described in references 4–7 is in course of publication in the Proc. Phys. Soc. The following papers have appeared: A. L. McAulay and F. D. Cruickshank, Proc. Phys. Soc. 57, 302 (1945); F. D. Cruickshank, Proc. Phys. Sob. 57, 350 (1945).
    [Crossref]
  9. F. D. Cruickshank, J. Opt. Soc. Am., to be published.

1943 (3)

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design (Oxford University Press, London, 1929). Note. The work described in references 4–7 is in course of publication in the Proc. Phys. Soc. The following papers have appeared: A. L. McAulay and F. D. Cruickshank, Proc. Phys. Soc. 57, 302 (1945); F. D. Cruickshank, Proc. Phys. Sob. 57, 350 (1945).
[Crossref]

Cruickshank, F. D.

F. D. Cruickshank, J. Opt. Soc. Am., to be published.

F. D. Cruickshank, Secret Papers, Opt. Mun. Panel, Nov.1942.

F. D. Cruickshank, Secret Papers, Opt. Mun. Panel, Aust.May1943.

Herzberger, M.

McAulay, A. L.

A. L. McAulay, Secret Papers, Optical Munitions Panel, Aust.Nov.1942.

A. L. McAulay, Secret Papers, Opt. Mun. Panel, Aust.July, 1943.

Stempel, W. M.

Stephens, R. E.

R. E. Stephens, J. Opt. Soc. Am. 33, 684 (A) (1943).

J. Opt. Soc. Am. (3)

Other (6)

A. L. McAulay, Secret Papers, Optical Munitions Panel, Aust.Nov.1942.

A. L. McAulay, Secret Papers, Opt. Mun. Panel, Aust.July, 1943.

F. D. Cruickshank, Secret Papers, Opt. Mun. Panel, Nov.1942.

F. D. Cruickshank, Secret Papers, Opt. Mun. Panel, Aust.May1943.

A. E. Conrady, Applied Optics and Optical Design (Oxford University Press, London, 1929). Note. The work described in references 4–7 is in course of publication in the Proc. Phys. Soc. The following papers have appeared: A. L. McAulay and F. D. Cruickshank, Proc. Phys. Soc. 57, 302 (1945); F. D. Cruickshank, Proc. Phys. Sob. 57, 350 (1945).
[Crossref]

F. D. Cruickshank, J. Opt. Soc. Am., to be published.

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Figures (2)

Tables (1)

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Table I Typical computation of fundamental transfer coefficients.

Equations (55)

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y k = y k y 1 y 1 + y k u 1 u 1 ,
u k = u k y 1 y 1 + u k u 1 u 1 ,
y k y 1 u k u 1 y k u 1 u k y 1 = N 1 / N k .
f = 1 / u k y 1 ,
l f = y k y 1 / u k y 1 = f y k y 1 ,
l f = u k u 1 / u k y 1 = f u k u 1 .
y k = y k y i y i + y k u i u i ,
u k = u k y i y i + u k u i u i ,
y k y i u k u i y k u i u k y i = N i / N k .
y k u i d u i = d y k = y k y j d y j + y k u j d u j , = y k y j d j d u i + y k u j d u i ,
y k u i = y k y j d j + y k u j ;
u k u i = u k y j d j + u k u j .
y k u i = y k u i u i u i = y k u i n i ,
u k u i = u k u i n i .
y k y i d y i = y k y j d y j + y k u j d u j , = y k y j ( d j d u j + d y i ) + y k u j d u j , = ( y k y j d j + y k u j ) d u j + y k y j d y i , = y k u i u i y i d y i + y k y i d y i ,
y k y i = y k u i u i y i + y k y j ;
u k y i = u k u i u i y i + u k y j
y k / u k = 0 , y k / u k = 0 , u k / u k = 1 , u k / u k = n k , y k / y k = 1 , u k / y k = ( 1 n k ) / r k ,
( 1 r ) u = r i ,
N i = N i ,
u + i = u + i .
i / u = 1.
y c u = i ,
i / y = c ,
i / c = y .
u = u + ( 1 n ) i ,
u / u = n ,
u / y = ( 1 n ) c ,
u / c = ( 1 n ) y ,
u / n = i .
u k c i = u k u i u i c i ,
y k c i = y k u i u i c i .
u k n i = u k u i u i n i ,
y k n i = y k u i u i n i .
y k N h = y k n 1 n 1 N h + y k n 2 n 2 N h , = y k n 1 N h ( N h 1 N h ) + y k n 2 N h ( N h N h + 1 ) , = y k n 1 · N h 1 N h + y k n 2 · 1 N h + 1
u k N h = u k n 1 · N h 1 N h 2 + u k n 2 · 1 N h + 1 .
y k d i = y k y i y i d i = y k y i u i ,
u k d i = u k y i u i ,
d y k = y k u i d u i and d u k = u k u i d u i ,
l k u i = ( y k u i l k u k u i ) / u k ,
= C ( u i ) / u k ,
C ( u i ) = y k u i l k u k u i .
l k / y i = C ( y i ) / u k .
l k c i = l k u i u i c i , = C ( u i ) u i c i / u k , = C ( c i ) / u k ,
l k n i = C ( u i ) u i n i / u k , = C ( n i ) / u k ,
l k N h = l k n 1 N h 1 N h 2 + l k n 2 1 N h + 1 ,
l k d i = C ( y i ) y i d i / u k , = C ( d i ) / u k .
f c i = ( y 1 / u k 2 ) u k c i , = ( f / u k ) u k c i .
f d i = ( f / u k ) u k d i ,
f n i = ( f / u k ) u k n i ;
f N h = N h 1 N h 2 f n 1 + 1 N h + 1 f n 2 .
l p p = l f f ,
l p p c i = l f c i f c i ,
m = N 1 u 1 / N k u k .
m c i = N 1 u 1 N k 1 u k 2 u k c i , = ( m / u k ) u k c i ,