Abstract

Equations are given for the condition that the focal surface of a lens system remain at a predetermined position for a range of ambient temperatures. Simple methods of satisfying these equations for lens systems composed predominantly or entirely of plastic components are described.

© 1948 Optical Society of America

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  1. The same problem was studied simultaneously in England at Combined Optical Industries, Ltd. See Br. Pat.561,503.

Other (1)

The same problem was studied simultaneously in England at Combined Optical Industries, Ltd. See Br. Pat.561,503.

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Figures (1)

Fig. 1
Fig. 1

Athermalized telescope. Army T-108 telescope for use as sight on anti-tank guns. Although this telescope is only 3-power, the eyepiece and objective are 3″ in diameter to achieve a 1″ diameter exit pupil and 6″ eye relief. The eye relief was necessitated by the carriage jump of the gun. This extraordinary allowance for freedom of head movement required that the focus of the objective remain accurately at the aiming reticle for all possible temperatures of use. Athermalization of the focus was effected by use of a single glass element in the otherwise all-plastic lens system.

Equations (11)

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( 1 / S ) + ( 1 / S ) = ( n - 1 ) [ ( 1 / R a ) - ( 1 / R b ) ] .
( D T S / S 2 ) + ( D T S / ( S ) 2 ) = - [ ( 1 / R a ) - ( 1 / R b ) ] D T n + [ ( D T R a / R a 2 ) - ( D T R b / R b 2 ) ] ( n + 1 ) .
( D T S / S 2 ) + ( D T S / ( S ) 2 ) = ( 1 / f ) [ - ( D T n / ( n - 1 ) ) + E T ] .
( D T S / S 2 ) + ( D T S / ( S ) 2 ) = - 1 / f ν T ,
D T S N = - k = 1 k = N ( h 2 / f ν T ) k ,
F ( n ) = [ [ ( n 2 + 2 ) ( n + 1 ) / 2 n ] + 1 ] .
D T S N = - ( D T S 1 / S 1 2 ) - k = 1 k = N [ [ ( ϕ a h a 2 + ϕ b h b 2 ) / ν T ] + ( h a / S a ) 2 n 2 D T ( t / n ) + ( h b / S b ) 2 D T L ] k ,
D T S N / n 0 = ( S N / ( n 0 ) 2 ) D T ( n 0 ) - [ ( n 0 D T S 1 - S 1 D T n 0 ) / S 1 2 ] - k = 1 k = N [ [ ( ϕ a h a 2 + ϕ b h b 2 ) / ν T ] + ( h a / S a ) 2 n 2 D T ( t / n ) + ( h b / S b ) 2 D T L ] k .
[ ( h a / S a ) 2 n 2 D T ( t / n ) ] k
( h a / S a ) 2 n 2 D T ( t / n )
h k 2 [ - ( 2 / R ) 2 E T + ( 1 / S ) 2 D T L ] k .