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  1. A. VanderLugt, Proc. IEEE 54, 1055 (1966).
    [CrossRef]
  2. R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 120–134.
  3. F. P. Carlson, Introduction to Applied Optics for Engineers (Academic, New York, 1977), pp. 56–76.
  4. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), pp. 360, 391ff.
  5. M. O. Hagler, Appl. Opt. 10, 2783 (1971).
    [CrossRef] [PubMed]
  6. F. P. Carlson, R. E. Francois, Proc. IEEE 65, 10 (1977).
    [CrossRef]
  7. Equation (2) shows that the Fourier transform of ψ is essentially ψ* and generalizes to two dimensions in the obvious way: ∫∫ dxdyψ(x,y;ρ) exp[−jk(ax + by)] = j(λ/ρ)ψ*(a,b;1/ρ). See Table I of Ref. 6.
  8. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 87–88.

1977

F. P. Carlson, R. E. Francois, Proc. IEEE 65, 10 (1977).
[CrossRef]

1971

1966

A. VanderLugt, Proc. IEEE 54, 1055 (1966).
[CrossRef]

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 120–134.

Carlson, F. P.

F. P. Carlson, R. E. Francois, Proc. IEEE 65, 10 (1977).
[CrossRef]

F. P. Carlson, Introduction to Applied Optics for Engineers (Academic, New York, 1977), pp. 56–76.

Collier, R. J.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 120–134.

Francois, R. E.

F. P. Carlson, R. E. Francois, Proc. IEEE 65, 10 (1977).
[CrossRef]

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), pp. 360, 391ff.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 87–88.

Hagler, M. O.

Lin, L. H.

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 120–134.

VanderLugt, A.

A. VanderLugt, Proc. IEEE 54, 1055 (1966).
[CrossRef]

Appl. Opt.

Proc. IEEE

F. P. Carlson, R. E. Francois, Proc. IEEE 65, 10 (1977).
[CrossRef]

A. VanderLugt, Proc. IEEE 54, 1055 (1966).
[CrossRef]

Other

R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971), pp. 120–134.

F. P. Carlson, Introduction to Applied Optics for Engineers (Academic, New York, 1977), pp. 56–76.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), pp. 360, 391ff.

Equation (2) shows that the Fourier transform of ψ is essentially ψ* and generalizes to two dimensions in the obvious way: ∫∫ dxdyψ(x,y;ρ) exp[−jk(ax + by)] = j(λ/ρ)ψ*(a,b;1/ρ). See Table I of Ref. 6.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 87–88.

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Figures (1)

Fig. 1
Fig. 1

Simple optical system.

Equations (15)

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ψ ( x , y ; ρ ) exp [ j k ρ 2 ( x 2 + y 2 ) ] ,
d x ψ ( x ; ρ ) exp ( j k a x ) = j λ ρ ψ * ( a ; 1 ρ ) ,
I = d x ψ ( x ; ρ ) rect ( x / W ) exp ( j k a x )
rect ( x ) = [ 1 , | x | 1 2 0 , otherwise .
I = j λ ρ d ξ ψ * ( a ξ; 1 / ρ ) W λ sinc ( W ξ / λ ) ,
I = j λ ρ ψ * ( a ; 1 ρ ) d θ ψ * ( θ ; λ 2 / W 2 ρ ) exp ( j 2 π a ρ W θ ) sinc ( θ ) .
I = j λ ρ ψ * ( a ; 1 / ρ ) W 2 ρ j λ d ξ rect ( a ρ W ξ ) ψ ( ξ ; W 2 ρ ) .
lim α α ψ ( x ; α ) = j λ δ ( x )
d x ψ ( x ; ρ ) rect ( x / W ) exp ( j k a x ) = j λ ρ ψ * ( a ; 1 / ρ ) rect ( a ρ W )
d x d y ψ ( x , y ; ρ ) rect ( x / W ) rect ( y / W ) exp [ j k ( a x + b y ) ] = j λ ρ ψ * ( a , b ; 1 / ρ ) rect ( a / ρ W ) rect ( b / ρ W ) ,
t ( x 2 , y 2 ) = t L ψ * ( x 2 , y 2 ; f ) rect ( x 2 / W ) rect ( y 2 / W ) ,
u 3 ( x 3 , y 3 ) = k d 3 2 π j exp ( j k D 3 ) d x 2 d y 2 ψ ( x 3 x 2 , y 3 y 2 ; d 3 ) t ( x 2 , y 2 ) · k d 2 2 π j exp ( j k D 2 ) d x 1 d y 1 ψ ( x 2 x 1 , y 2 y 1 ; d 2 ) u 1 ( x 1 , y 1 ) ,
u 3 ( x 3 , y 3 ) = t L d 2 j λ d 3 j λ exp [ j k ( D 2 + D 3 ) ] ψ ( x 3 , y 3 ; d 3 ) · d x 1 d y 1 u 1 ( x 1 , y 1 ) ψ ( x 1 , y 1 ; d 2 ) · d x 2 d y 2 ψ ( x 2 , y 2 ; d 2 + d 3 f ) rect ( x 2 W ) rect ( y 2 W ) · exp { j k [ x 2 ( d 2 x 1 + d 3 x 3 ) + y 2 ( d 2 y 1 + d 3 y 3 ) ] } .
u 3 ( x 3 , y 3 ) = t L j λ d 3 d 2 d 2 2 d 2 + d 3 f × exp [ j k ( D 2 + D 3 ) ] ψ ( x 3 , y 3 ; d 3 d 3 2 d 2 + d 3 f ) · d x 1 d y 1 ψ ( x 1 , y 1 ; d 2 d 2 2 d 2 + d 3 f ) · rect [ d 2 x 1 + d 3 x 3 ( d 2 + d 3 f ) W ] rect [ d 2 y 1 + d 3 y 3 ( d 2 + d 3 f ) W ] u 1 ( x 1 , y 1 ) · exp [ j k d 2 2 d 2 + d 3 f ( d 3 d 2 x 1 x 3 + d 3 d 2 y 1 y 3 ) ] .
u 3 ( x 3 , y 3 ) = t L j λ F exp ( j k 2 F ) d x 1 d y 1 u 1 ( x 1 , y 1 ) rect ( x 1 + x 3 W ) · rect ( y 1 + y 3 W ) exp [ j 2 π ( x 3 λ F x 1 + y 3 λ F y 1 ) ]

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