Abstract

A binary holographic technique for infrared laser beam multiplexing is described. The technique was used to generate amplitude distribution matched and phase matched local oscillators for a heterodyne IR imaging detector array. It uses a high accuracy interlaced binary diffraction grating to multiplex single LO wave fronts.

© 1983 Optical Society of America

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References

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  2. A. Siegman, Proc. IEEE 54, 1350 (1966).
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  5. W.-H. Lee, Appl. Opt. 9, 639 (1970).
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  6. C. B. Burckhardt, Appl. Opt. 9, 1949 (1970).
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  7. C. K. Hsueh, A. A. Sawchuk, Appl. Opt. 17, 3874 (1978).
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  9. A. W. Lohmann, D. P. Paris, Appl. Opt. 6, 1739 (1967).
    [CrossRef] [PubMed]
  10. W.-H. Lee, Appl. Opt. 18, 2152 (1979).
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  11. H. Dammann, K. Goertler, Opt. Commun. 3, 312 (1971).
    [CrossRef]
  12. W. Rudin, Proc. Am. Math. Soc. 10, 855 (1959).
    [CrossRef]
  13. D. R. Anderson, Proc. IRE 49, 357 (1961).
  14. R. L. Frank, S. A. Zadoff, IRE Trans. Inf. Theory IT-8, 381 (1962).
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  15. M. R. Schroeder, IEEE Trans. Inf. Theory IT-16, 85 (1970).
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  16. H. Akahori, Appl. Opt. 12, 2336 (1973).
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  23. M. Neviere, Proc. Soc. Photo-Opt. Instrum. Eng. 240, 139 (1980).
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  25. W. Steinmann, Phys. Status Solidi 28, 437 (1968).
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  26. D. W. Sweeney, W. H. Stevenson, D. K. Campbell, G. Shaffer, Appl. Opt. 15, 2959 (1976).
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1983 (1)

1981 (1)

1980 (1)

M. Neviere, Proc. Soc. Photo-Opt. Instrum. Eng. 240, 139 (1980).

1979 (1)

1978 (1)

1976 (2)

1974 (1)

1973 (2)

1971 (2)

T. S. Huang, Proc. IEEE 59, 1335 (1971).
[CrossRef]

H. Dammann, K. Goertler, Opt. Commun. 3, 312 (1971).
[CrossRef]

1970 (5)

1968 (1)

W. Steinmann, Phys. Status Solidi 28, 437 (1968).
[CrossRef]

1967 (1)

1966 (2)

1962 (1)

R. L. Frank, S. A. Zadoff, IRE Trans. Inf. Theory IT-8, 381 (1962).
[CrossRef]

1961 (1)

D. R. Anderson, Proc. IRE 49, 357 (1961).

1959 (1)

W. Rudin, Proc. Am. Math. Soc. 10, 855 (1959).
[CrossRef]

1941 (1)

Akahori, H.

Anderson, D. R.

D. R. Anderson, Proc. IRE 49, 357 (1961).

Bachman, C.

C. Bachman, Laser Radar Systems and Techniques (Artech, Dedham, Mass., 1979).

Beaglehole, D.

D. Beaglehole, D. Hunderi, Phys. Rev. B 2, 309 (1970).
[CrossRef]

Brown, B. R.

Burckhardt, C. B.

Campbell, D. K.

Dallas, W. J.

Dammann, H.

H. Dammann, K. Goertler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Fano, U.

Ford, G. W.

Frank, R. L.

R. L. Frank, S. A. Zadoff, IRE Trans. Inf. Theory IT-8, 381 (1962).
[CrossRef]

Gabel, R. A.

Gallagher, M. C.

M. C. Gallagher, IEEE Trans. Inf. Theory IT-22, 622 (1976).
[CrossRef]

M. C. Gallagher, B. Liu, Appl. Opt. 12, 2328 (1973).
[CrossRef] [PubMed]

Goertler, K.

H. Dammann, K. Goertler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Hsueh, C. K.

Huang, T. S.

T. S. Huang, Proc. IEEE 59, 1335 (1971).
[CrossRef]

Hunderi, D.

D. Beaglehole, D. Hunderi, Phys. Rev. B 2, 309 (1970).
[CrossRef]

Lee, W.-H.

Liu, B.

Lohmann, A. W.

Neviere, M.

M. Neviere, Proc. Soc. Photo-Opt. Instrum. Eng. 240, 139 (1980).

Paris, D. P.

Rudin, W.

W. Rudin, Proc. Am. Math. Soc. 10, 855 (1959).
[CrossRef]

Sawchuk, A. A.

Schroeder, M. R.

M. R. Schroeder, IEEE Trans. Inf. Theory IT-16, 85 (1970).
[CrossRef]

Shaffer, G.

Siegman, A.

A. Siegman, Proc. IEEE 54, 1350 (1966).
[CrossRef]

Steinmann, W.

W. Steinmann, Phys. Status Solidi 28, 437 (1968).
[CrossRef]

Stevenson, W. H.

Sweeney, D. W.

Veldkamp, W. B.

Weber, W. H.

Zadoff, S. A.

R. L. Frank, S. A. Zadoff, IRE Trans. Inf. Theory IT-8, 381 (1962).
[CrossRef]

Appl. Opt. (12)

IEEE Trans. Inf. Theory (2)

M. C. Gallagher, IEEE Trans. Inf. Theory IT-22, 622 (1976).
[CrossRef]

M. R. Schroeder, IEEE Trans. Inf. Theory IT-16, 85 (1970).
[CrossRef]

IRE Trans. Inf. Theory (1)

R. L. Frank, S. A. Zadoff, IRE Trans. Inf. Theory IT-8, 381 (1962).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

H. Dammann, K. Goertler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (1)

D. Beaglehole, D. Hunderi, Phys. Rev. B 2, 309 (1970).
[CrossRef]

Phys. Status Solidi (1)

W. Steinmann, Phys. Status Solidi 28, 437 (1968).
[CrossRef]

Proc. Am. Math. Soc. (1)

W. Rudin, Proc. Am. Math. Soc. 10, 855 (1959).
[CrossRef]

Proc. IEEE (2)

A. Siegman, Proc. IEEE 54, 1350 (1966).
[CrossRef]

T. S. Huang, Proc. IEEE 59, 1335 (1971).
[CrossRef]

Proc. IRE (1)

D. R. Anderson, Proc. IRE 49, 357 (1961).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

M. Neviere, Proc. Soc. Photo-Opt. Instrum. Eng. 240, 139 (1980).

Other (1)

C. Bachman, Laser Radar Systems and Techniques (Artech, Dedham, Mass., 1979).

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Figures (14)

Fig. 1
Fig. 1

Characteristics of a binary reflection grating.

Fig. 2
Fig. 2

Concept of holographic LO generation.

Fig. 3
Fig. 3

Computer simulation of the multiplexed LO wave front.

Fig. 4
Fig. 4

Unit vector representation of the complex transmittance A(x,y).

Fig. 5
Fig. 5

Section of a conjugated holographic fringe pair.

Fig. 6
Fig. 6

Enlarged unit cell in the binary holographic mask.

Fig. 7
Fig. 7

Choices in carrier and information frequency placements: (a) orthogonal and collinear and (b) even and odd element multiplexers.

Fig. 8
Fig. 8

Optic wave front of a thirteenfold beam multiplexer with three dynamic range reduction phase codes: (a) no coding, (b) random binary coding, (c) Schroeder’s coding, and (d) random polyphase coding.

Fig. 9
Fig. 9

LO alignment dependence on grating accuracy.

Fig. 10
Fig. 10

Required grating accuracy vs diffraction angle for a LO placement 90% accurate.

Fig. 11
Fig. 11

Construction of the hologram from a unit cell by a step-and-repeat process.

Fig. 12
Fig. 12

Binary grating processing steps using IC device fabrication techniques.

Fig. 13
Fig. 13

SEM microphotographs of the holographic relief surface: (a) section of the pattern with T = 50 μm, κ = 6 μm, and d = 1.7 μm; and (b) a subsection where τ < λ.

Fig. 14
Fig. 14

Infrared (10.6-μm) apodized detector scan past the focused wave front generated by the thirteen-element LO beam multiplexer.

Tables (2)

Tables Icon

Table I Dynamic Range Compression Phase Codes (in Radians) and Normalization Factors γ0

Tables Icon

Table II Beam Multiplexer Design Parameters

Equations (32)

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A ( x , y ) = A 0 n = 0 N δ ( y - 2 n b ) 2 J 1 ( a r ) a r ,
A ( u , v ) = 1 2 π A 0 n = 0 N exp ( j 2 π n α v ) · circ ( u / a , v / a ) .
A ( x , y ) = [ 2 f ( x , y ) - 1 ] sin ( θ ) + j cos ( θ ) ,
θ = 2 π / λ ( n 0 - 1 ) d ,
h ( x , y ) = n = - { sin [ n π q ( x , y ) ] n π } exp [ j n ϕ ( x , y ) ]
h ( x , y ) = n = - ( 1 / π n ) exp [ j n ϕ ( x , y ) ] .
U ( x 0 , y , z ) = n = - N / 2 + N / 2 exp [ j ( 2 π n α y + ψ n ) ] · exp { - j k [ z + x sin ( β ) ] } .
1 π { exp [ j ϕ ( y ) ] - exp [ - j ϕ ( y ) ] } = n = - N / 2 + N / 2 exp [ j ( 2 π n α y + ψ n ) ] .
ϕ ( y ) = arcsin { γ 0 [ ½ + n = 1 N / 2 cos ( 2 π n α y + ψ n ) ] } .
x 1 = ϕ ( y ) 2 π T + m T , x 2 = - ϕ ( y ) + π 2 π T + m T .
a o = [ 2 q ( x ) - 1 ] sin ( θ ) + j cos ( θ ) , a n = ± 1 ± ( N - 1 ) / 2 = 2 sin [ n π q ( x ) ] n π sin ( θ ) ,
q ( x ) = ½ + 1 2 2 N m = 1 N cos ( 2 π m α x + ψ m ) ,
θ ( x ) = arcsin [ ½ + 1 2 2 N m = 1 N γ m cos ( 2 π m α x + ψ m ) ] ,
x ( fringe ) = ϕ ( x ) 2 π T + n T ,
ϕ ( x ) = arcsin { γ [ ½ + 1 2 N m = 1 N cos ( 2 π m α x + ψ m ] } .
ϕ ( y ) = arcsin { γ m = 0 N / 2 cos [ 2 π ( m + ½ ) α y + ψ m ] } .
max | m = 1 N cos ( 2 π m α y + ψ m ) | N 1 / 2 .
| n = 1 N ɛ m cos ( 2 π m α y + ψ m ) | 2 N ,
ψ m = π m 2 / N .
k = 2 π ( d + s F ) ,
d = 2.44 ( λ F / ξ D ) ,
Δ ϕ = arcsin ( d + s 10 F )
Δ T = λ Δ ϕ cos ( β ) sin 2 ( β ) .
P ( ϕ ) = { N p / 2 π ϕ π / N p , 0 ϕ > π / N p ,
ϕ ( x , y ) = ϕ ( x , y ) + ɛ ( x , y ) ( 2 π T ) ,
mse ( ϕ ) = E [ exp [ j ϕ ( x , y ) ] - exp { j [ ϕ ( x , y ) + ɛ ( x , y ) 2 π / T ] } 2 ] ,
rmse ( ϕ ) = 2 [ 1 - N p / π sin ( π / N p ) ] π / ( 3 N p ) rad .
κ = ½ [ ( T / 2 ) ( 1 - μ / 2 ) - τ ]
( - κ / T ) 2 π ϕ ( y ) ( κ / T ) 2 π
γ 0 = ( 1 1 + 2 N - 1 ) sin ( 2 π κ / T ) .
Δ ϕ = π Δ [ ( 1 - μ / 2 ) T - μ ] ,
sin ( β ) + sin ( 90 - β ) = λ / T ,

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