Abstract

We report two kinds of Fresnel-type computer-generated hologram, namely, an intensity variable hologram and a wavelength demultiplexing hologram. The former shows that diffraction intensity can be controlled almost independently by the spatial frequencies of the holograms. The latter shows wavelength demultiplexing holograms. Combining the former intensity-controlled holograms, uniform diffraction intensity of different wavelengths can be realized.

© 1992 Optical Society of America

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References

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  1. S. H. Lee, “Recent advances in computer generated hologram applications,” Opto Photon. 1, 18–23 (1990).
    [CrossRef]
  2. A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
    [CrossRef] [PubMed]
  3. S. M. Sze, Physics of Semiconductor Devices2nd ed. (Wiley, New York1981), pp. 186–187.

1990

S. H. Lee, “Recent advances in computer generated hologram applications,” Opto Photon. 1, 18–23 (1990).
[CrossRef]

1967

Lee, S. H.

S. H. Lee, “Recent advances in computer generated hologram applications,” Opto Photon. 1, 18–23 (1990).
[CrossRef]

Lohmann, A. W.

Paris, D. P.

Sze, S. M.

S. M. Sze, Physics of Semiconductor Devices2nd ed. (Wiley, New York1981), pp. 186–187.

Appl. Opt.

Opto Photon.

S. H. Lee, “Recent advances in computer generated hologram applications,” Opto Photon. 1, 18–23 (1990).
[CrossRef]

Other

S. M. Sze, Physics of Semiconductor Devices2nd ed. (Wiley, New York1981), pp. 186–187.

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Figures (10)

Fig. 1
Fig. 1

Coordinates of the holographic experiments.

Fig. 2
Fig. 2

Ten intensity levels of a unit element cell.

Fig. 3
Fig. 3

Schematic of the interference fringes between a point source and a plane wave.

Fig. 4
Fig. 4

Schematic of the interference fringes between multipoint sources and a plane wave.

Fig. 5
Fig. 5

Positions of two different wavelength spots in the focal plane.

Fig. 6
Fig. 6

Positions of five different wavelength spots in the focal plane.

Fig. 7
Fig. 7

Positions of five different wavelength spots in the focal plane.

Fig. 8
Fig. 8

Photograph of five different intensity spots.

Fig. 9
Fig. 9

Diffraction patterns of five different spatial frequency holograms: (a) 5.4 lines/mm, (b) 7.4 lines/mm, (c) 9.4 lines/mm, (d) 11.5 lines/mm, and (e) 14.8 lines/mm.

Fig. 10
Fig. 10

Relation between spatial frequencies and diffracted-beam intensities.

Tables (4)

Tables Icon

Table I Minimum Resolution or Maximum Spatial Frequency That Can Be Obtained by Our Hologram-Producing System

Tables Icon

Table II Data of the Wavelength Division Hologram

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Table III Data of the Wavelength Division Hologram

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Table IV Data of the Intensity Division Holograma

Equations (8)

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A 1 ( x , y , 0 ) = a exp [ i k ( x cos α x + y cos α y ) ] ,
A 2 ( x , y , 0 ) = ( a 0 / z 0 ) exp ( i k z 0 ) exp { ( i k / 2 z 0 ) × [ ( x x 0 ) 2 + ( y y 0 ) 2 ] } ,
( x 2 + y 2 + z 0 2 ) 1 / 2 = z 0 [ 1 + ( x / z 0 ) 2 / 2 + ( y / z 0 ) 2 / 2 ] .
I ( x , y , z ) = | A 1 ( x , y , z ) + A 2 ( x , y , z ) | 2 = | A 1 ( x , y , z ) | 2 + | A 2 ( x , y , z ) | 2 + A 1 ( x , y , z ) A 2 ( x , y , z ) * + A 1 ( x , y , z ) * A 2 ( x , y , z ) ,
I ( x , y , 0 ) = a 2 + a 0 2 / z 0 + ( a a 0 / z 0 ) × cos ( k { [ ( x x 0 ) 2 + ( y y 0 ) ] 2 / 2 z 0 + z 0 ( x cos α x + y cos α y ) } ) .
Δ I ( x , y , 0 ) = ( a a 0 / z 0 ) cos ( k { [ ( x x 0 ) 2 + ( y y 0 ) 2 ] / ( 2 z 0 ) + z 0 } ) .
Δ I ( x , y , 0 ) = ( a a 0 / z 0 ) cos ( k { [ ( x x 0 ) 2 + ( y y 0 ) 2 ] / ( 2 z 0 ) + z 0 } ) + ( a a 1 / z 1 ) cos ( k { [ ( x x 1 ) 2 + ( y y 1 ) 2 ] / ( 2 z 1 ) + z 1 } ) + + ( a a i / z i ) cos ( k { [ ( x x i ) 2 + ( y y i ) 2 ] / ( 2 z i ) + z i } ) + + ( a a N / z n ) cos ( k [ ( x x N ) 2 + ( y y N ) 2 ] / ( 2 z N ) + z N } ) ,
Δ I ( x , y , 0 ) = ( ( a a 0 / z 0 ) cos { k [ ( x x 0 ) 2 + ( y y 0 ) 2 ] / ( 2 z 0 ) + z 0 } + ( a a 1 / z 1 ) cos { k [ ( x x 1 ) 2 + ( y y 1 ) 2 ] / ( 2 z 1 ) + z 1 } + + ( a a N / z N ) cos { k [ ( x x N ) 2 + ( y y N ) 2 ] / ( 2 z N ) + z N } ) / ( a a 0 / z 0 + a a 1 / z 1 + + a a N / z N ) .

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