Abstract

The characteristics of 2-D holographic scanners utilizing a concave auxiliary reflector are analyzed. The total resolution capability of the scanner is discussed in detail for the scanner operated at both finite and infinite conjugations, and the factors limiting resolution are indicated. The resolution considerations lead to a near-optimal design procedure which is used in design examples for typical applications in the visible, millimeter, and ultrasonic wavelength regions.

© 1981 Optical Society of America

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References

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  1. C. S. Ih, Appl. Opt. 16, 2137 (1977).
    [CrossRef] [PubMed]
  2. C. S. Ih, Appl. Opt. 17, 748 (1978).
    [CrossRef] [PubMed]
  3. C. S. Ih, N. S. Kopeika, E. LeDet, Appl. Opt. 19, 2041 (1980).
    [CrossRef] [PubMed]
  4. C. S. Ih, B. Waeber, J. Opt. Soc. Am. 68, 1443 (1978).
  5. C. S. Ih, N. Kong, T. Giriappa, Appl. Opt. 17, 1582 (1978).
    [CrossRef] [PubMed]
  6. C. S. Ih, K. Yen, “Computer Generated Holograms for Scanners Utilizing a Concave AR,” to be published.
  7. C. S. Ih, K. Yen, “Holographic Scanners Utilizing an Aspheric AR,” to be published.
  8. Another possible application is for laser radar: C. S. Ih, in Digest of Topical Meeting on Coherent Laser Radar for Atmospheric Sensing (Optical Society of America, Washington, D.C., 1980), paper ThA5.

1980 (1)

1978 (3)

1977 (1)

Giriappa, T.

Ih, C. S.

C. S. Ih, N. S. Kopeika, E. LeDet, Appl. Opt. 19, 2041 (1980).
[CrossRef] [PubMed]

C. S. Ih, N. Kong, T. Giriappa, Appl. Opt. 17, 1582 (1978).
[CrossRef] [PubMed]

C. S. Ih, Appl. Opt. 17, 748 (1978).
[CrossRef] [PubMed]

C. S. Ih, B. Waeber, J. Opt. Soc. Am. 68, 1443 (1978).

C. S. Ih, Appl. Opt. 16, 2137 (1977).
[CrossRef] [PubMed]

C. S. Ih, K. Yen, “Computer Generated Holograms for Scanners Utilizing a Concave AR,” to be published.

Another possible application is for laser radar: C. S. Ih, in Digest of Topical Meeting on Coherent Laser Radar for Atmospheric Sensing (Optical Society of America, Washington, D.C., 1980), paper ThA5.

C. S. Ih, K. Yen, “Holographic Scanners Utilizing an Aspheric AR,” to be published.

Kong, N.

Kopeika, N. S.

LeDet, E.

Waeber, B.

C. S. Ih, B. Waeber, J. Opt. Soc. Am. 68, 1443 (1978).

Yen, K.

C. S. Ih, K. Yen, “Computer Generated Holograms for Scanners Utilizing a Concave AR,” to be published.

C. S. Ih, K. Yen, “Holographic Scanners Utilizing an Aspheric AR,” to be published.

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

C. S. Ih, B. Waeber, J. Opt. Soc. Am. 68, 1443 (1978).

Other (3)

C. S. Ih, K. Yen, “Computer Generated Holograms for Scanners Utilizing a Concave AR,” to be published.

C. S. Ih, K. Yen, “Holographic Scanners Utilizing an Aspheric AR,” to be published.

Another possible application is for laser radar: C. S. Ih, in Digest of Topical Meeting on Coherent Laser Radar for Atmospheric Sensing (Optical Society of America, Washington, D.C., 1980), paper ThA5.

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Figures (8)

Fig. 1
Fig. 1

Basic holographic scanner with concave auxiliary reflector illustrating scanner parameters: (a) side view; (b) front view.

Fig. 2
Fig. 2

Finite conjugation geometry.

Fig. 3
Fig. 3

Infinite conjugation geometry.

Fig. 4
Fig. 4

Normalized minimum scan radius vs magnification factor.

Fig. 5
Fig. 5

Normalized maximum total resolution vs magnification factor.

Fig. 6
Fig. 6

Maximum magnification factor vs number of holograms/row on the disk surface.

Fig. 7
Fig. 7

Geometric aspect ratio vs magnification factor.

Fig. 8
Fig. 8

Geometric aspect ratio vs scan radius normalized with respect to the minimum scan radius.

Equations (46)

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α h = 2 π / N ,
h t = 2 sin ( α h / 2 ) .
h r = h t cos ψ .
r m = 1 + d m tan ψ ,
r a = r m sin φ ,
r = 1 + 1 2 n 1 h r ,
d b = d m r a cos φ ,
p a = d m cos ψ ,
φ = π 4 + ψ 2 .
p b = r a p a 2 P a r a ,
p e = p b P a h r cos ψ = p b P a h t .
δ = p b p a = p e h t = cos ψ + d m sin ψ d m ( 2 sin φ sin ψ ) cos ψ ,
r e = p b r m
d m = ( 1 + δ ) cos ψ 2 δ sin φ ( 1 + δ ) sin ψ .
x 0 = r m , y 0 = d m .
x 1 = r , y 1 = d b + ( r a 2 r 2 ) 1 / 2 .
m a = 2 ( y 1 y 0 )
y 2 = y 0 1 2 k m a , x 2 = [ r a 2 ( y 2 d b ) 2 ] 1 / 2 ,
o s = ε λ ( r s r e ) p e = ε λ ( r s r e ) δ h t ,
l h = α h r s ,
l υ = N n 1 n 2 o s ,
S h = Int l h o s ,
S υ = N n 1 n 2 .
μ = l h l υ = 4 π sin ( π / N ) ε λ N 2 n 1 n 2 δ ( r s r s r e ) .
k m a r s min + x 2 = n 1 p e r s min r e .
r s min = k m a r e + n 1 p e x 2 k m a n 1 P e .
l υ g = k m a ( r s r e ) + ( n 1 2 ) p e ( r s + x 2 ) r 3 + x 2 ,
μ g = l h l υ g = 2 π r s N l υ g ,
T = S h S υ = μ ( N n 1 n 2 ) 2 ,
T = 4 π n 1 n 2 sin ( π / N ) ε λ δ ( r s r s r e ) .
τ = ε λ 4 π T = n 1 n 2 sin ( π / N ) δ ( r s r s r e ) .
α s = ε λ p e .
α υ g = 2 tan 1 [ k m a 2 ( x 2 + r c ) ] α υ ,
r c = k m a r e ( n 1 2 ) P e x 2 k m a + ( n 1 2 ) P e ,
α υ = N n 1 n 2 α s .
T = α h α s · α υ α s = 4 π n 1 n 2 sin ( π / N ) ε λ δ ,
τ = n 1 n 2 sin ( π / N ) δ ,
μ = α h α υ = 4 π sin ( π / N ) ε λ N 2 n 1 n 2 δ ,
μ μ g = π N tan 1 [ k m a 2 ( x 2 + r c ) ] .
ψ = sin 1 ( λ / D ) .
N n 1 n 2 = ( T / μ ) 1 / 2 .
lim r s min τ max = n 1 n 2 sin ( π / N ) δ max ,
τ = ε λ 4 π T = ε Λ 4 π R T ,
R = ε Λ T 4 π τ = ε Λ μ N 2 n 1 n 2 4 π sin ( π / N ) 1 δ ( r s r e r s ) ,
( a ) n 1 P e = 2 n 1 sin ( π / N ) δ < k m a , ( b ) r s r s min , ( c ) μ μ g ,
R = ε Λ T 4 π τ = ε Λ μ N 2 n 1 n 2 4 π sin ( π / N ) 1 δ ,

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