Abstract

The holographic packing density is derived for any plane in a coherently illuminated optical system. The gain in packing density relative to the object plane is given. A two-lens optical system in which a condenser lens provides high packing densities and an imaging lens provides sufficient resolution is superior to a system in which a single lens performs both functions.

© 1975 Optical Society of America

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References

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  1. A. Vander Lugt, Appl. Opt. 12, 1677 (1973).
  2. E. G. Ramberg [RCA Rev. 33, 5 (1972)] states that holography does not provide an increase over direct recording in terms of packing density. His analysis did not consider the more general case treated here wherein we show that, by using lenses, increased packing density can indeed be achieved while retaining all the benefits of holography.

1973 (1)

A. Vander Lugt, Appl. Opt. 12, 1677 (1973).

Vander Lugt, A.

A. Vander Lugt, Appl. Opt. 12, 1677 (1973).

Appl. Opt. (1)

A. Vander Lugt, Appl. Opt. 12, 1677 (1973).

Other (1)

E. G. Ramberg [RCA Rev. 33, 5 (1972)] states that holography does not provide an increase over direct recording in terms of packing density. His analysis did not consider the more general case treated here wherein we show that, by using lenses, increased packing density can indeed be achieved while retaining all the benefits of holography.

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Figures (7)

Fig. 1
Fig. 1

Single-lens optical system.

Fig. 2
Fig. 2

Two-lens optical system.

Fig. 3
Fig. 3

Image transmitted through the two-lens system with R1 = 0.5 and R2 = 0.045.

Fig. 4
Fig. 4

Magnified portion of transmitted image.

Fig. 5
Fig. 5

Transmitted image with R1 = 0.25 and R2 = 0.045 showing partial vignetting.

Fig. 6
Fig. 6

Transmitted image with R1 = 0.25 and R2 = 0.125, restoring the vignetted rays.

Fig. 7
Fig. 7

Transmitted image with R1 = 0 and R2 = 0.25 showing unavoidable vignetting.

Equations (27)

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ū ū = h ¯ / F u u = h / F } ,
ϕ = 2 η f .
R = 2 { | h | + | h ¯ | } / F ,
R = 2 { | λ f F | + | η | } / F .
R = ( 2 λ f F + 2 η ) / F
= R t + R 0 ,
ϕ = 1 2 λ ( 4 η 2 / F 2 R η ) .
ϕ η = 1 2 λ ( 8 η / F 2 R ) = 0 ,
R = 4 η / F
R 0 = R t .
ϕ max = R 0 η λ .
ρ = ϕ / D ,
D = 2 u ( l s ) + 2 η .
ρ = ϕ D = 2 η f 2 η = f bits / mm .
h t = h t u h ¯ t = h ¯ t ū } .
D = 2 { | h t | + | h ¯ t | } ,
D = 2 { h t u + h ¯ t ū } ; 0 t l ¯ .
u = λ f , h = u l = λ f l , ū = 0 , h ¯ = η u l ¯ = η , } u = h / F + u = u l / F + u = u ( 1 + l / F ) , u = h ¯ / F + u = η / F ,
D = { 2 λ f l + 2 λ f t ( 1 + l / F ) + 2 η ( 1 t / F ) }
D = { 2 λ f l + 2 λ f t ( 1 + l / F ) + ϕ f ( 1 t / F ) } .
ρ = ϕ / D = f ( 1 t / F ) [ 1 + 2 λ f l D 2 t λ f ( 1 + l / F D ]
ρ t = f ( 1 t / F ) [ 2 λ f ( 1 + l / F ) D ] ( 1 t / F ) 2 ( f / F ) [ 1 + 2 λ f l D 2 t λ f ( 1 + 1 / F ) D ] ( 1 t / F ) 2 = 0 ,
D = 2 λ f F
t = F .
ρ = ϕ / D = 2 η f 2 λ f F = η λ F bits / mm ,
ρ = ( R 0 / 2 λ ) .
G = R 0 / ( 2 λ f ) .

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