Abstract

This paper explores the maximum optical power, i.e., the shortest focal length, that can be achieved with homogeneous materials given a cylindrical volume and a minimum-diameter constraint. An equation for the maximum optical power for a given lens diameter and two refractive indices is defined. For example, we determine that a 25.4-mm-diameter lens assembly cannot have an effective focal length of ≤6 mm using existing optical glasses in the visible.

© 1990 Optical Society of America

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References

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  1. G. C. Righini, G. Molesini, Appl. Opt. 27, 4193 (1988).
    [Crossref] [PubMed]
  2. R. A. Sampson, Philos. Trans. R. Soc. London 212, 149 (1913).
    [Crossref]
  3. E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), pp. 32–45.

1988 (1)

1913 (1)

R. A. Sampson, Philos. Trans. R. Soc. London 212, 149 (1913).
[Crossref]

Molesini, G.

O’Neill, E. L.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), pp. 32–45.

Righini, G. C.

Sampson, R. A.

R. A. Sampson, Philos. Trans. R. Soc. London 212, 149 (1913).
[Crossref]

Appl. Opt. (1)

Philos. Trans. R. Soc. London (1)

R. A. Sampson, Philos. Trans. R. Soc. London 212, 149 (1913).
[Crossref]

Other (1)

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), pp. 32–45.

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Figures (2)

Fig. 1
Fig. 1

Limiting lens geometry with α = 5 and k = 6.

Fig. 2
Fig. 2

Limiting lens power versus L/D for n2 =1.9525 in air (solid curve), n2 = 1.9525 in n1 = 1.33 (curve with crosses), and n2 = 1.6225 in air (curve with diamonds).

Equations (12)

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r α = ± D 4 ( α 2 + 1 α ) ,
ϕ α = n 2 n 1 r α = 4 Δ n D ( α α 2 + 1 ) ,
M = [ A B C A ] ,
A = n 2 ϕ α t α n 2 , B = ϕ α 2 t α 2 ϕ α n 2 n 2 , C = t α n 2 .
M s = M k = ( RTR ) k = RTRRTR RTRRTR ,
M s = M k = ( UD U 1 ) k = U D k U 1 .
1 2 [ ( A + BC ) k + ( A BC ) k B C [ ( A + BC ) k ( A BC ) k ] C B [ ( A + BC ) k ( A BC ) k ] ( A + BC ) k + ( A BC ) k ] ,
Φ α , k = [ 8 n 2 Δ n D 2 α 2 α 2 + 1 16 Δ n 2 D 2 α 2 ( α 2 + 1 ) 2 ] 1 / 2 × sin [ ( tan 1 { [ n 2 2 / ( n 2 4 Δ n α 2 + 1 ) 2 ] 1 } 1 / 2 ) k ] .
Φ α = ( 8 n 2 Δ n ) 1 / 2 D sin [ 2 L D ( 2 Δ n n 2 ) 1 / 2 ] .
VP ¯ = P V ¯ = D ( 8 n 2 Δ n ) 1 / 2 { sin [ 2 L D ( 2 Δ n n 2 ) 1 / 2 ] } 1 × { 1 cos [ 2 L D ( 2 Δ n n 2 ) 1 / 2 ] } .
L = D π 4 ( n 2 2 Δ n ) 1 / 2 ,
Φ max = ( 8 n 2 Δ n ) 1 / 2 D .

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