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References

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  1. C.-Y. Han, Y. Ishii, K. Murata, “Reshaping Collimated Laser Beams with Gaussian Profile to Uniform Profiles,” Appl. Opt. 22, 3644 (1983).
    [CrossRef] [PubMed]
  2. O. Bryngdahl, “Geometrical Transformations in Optics,” J. Opt. Soc. Am. 64, 1092 (1974).
    [CrossRef]
  3. M. Robinson, A. M. Ariyaeeinia, “An Active Coordinate Imaging System for Robot Vision,” Proc SPIE, 657, 144 (1986).
  4. W.-H. Lee, “Binary Computer-Generated Holograms,” Appl. Opt. 18, 3661 (1979).
    [CrossRef] [PubMed]

1986 (1)

M. Robinson, A. M. Ariyaeeinia, “An Active Coordinate Imaging System for Robot Vision,” Proc SPIE, 657, 144 (1986).

1983 (1)

1979 (1)

1974 (1)

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Figures (1)

Fig. 1
Fig. 1

Computer-generated hologram showing curves of constant phase for Gaussian to square beam conversion.

Equations (12)

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ϕ x = 2 π u λ f ,             ϕ y = 2 π v λ f .
ϕ x = 2 π λ Z ( u - x ) ,             ϕ y = 2 π λ Z ( v - y ) ,
u / y = v / x .
I ( x ) = 0 x i ( s ) d s = 0 u o ( s ) d s = O ( u ) ,
d ϕ d x = 2 π λ [ u ( x ) - x Z ] .
d ϕ d u = 2 π λ [ u - x ( u ) Z ] .
ϕ x = 2 π λ [ u ( x ) - x Z ] ,             ϕ y = 2 π λ [ v ( y ) - y Z ] ,
ϕ ( x , y ) = 2 π λ x u ( x ) - x Z d x + 2 π λ y v ( y ) - y Z d y = ϕ X ( x ) + ϕ Y ( y ) .
i ( x , y ) exp { j [ ϕ X ( x ) + ϕ Y ( y ) ] } = i X ( x ) exp [ j ϕ X ( x ) ] i Y ( y ) exp [ j ϕ Y ( y ) ] ,
i ( x , y ) = exp ( - 2 x 2 / x 0 2 - 2 y 2 / y 0 2 ) = exp ( - 2 x 2 / x 0 2 ) exp ( - 2 y 2 / y 0 2 ) .
u = 2 u 0 k x 0 0 x exp ( - 2 s 2 / x 0 2 ) d s = u 0 k erf ( 2 x / x 0 ) ,
v = 2 v 0 k y 0 0 y exp ( - 2 s 2 / y 0 2 ) d s = v 0 k erf ( 2 y / y 0 ) ,

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