Abstract

A hologram of hyperbolic fringes generated by double exposure is presented in this paper. The principle and experimental results of using it to measure optical coherence are given as well.

© 1990 Optical Society of America

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References

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  1. J. W. Goodman, Fourier Optics (McGraw-Hill, New York, 1968), p. 255.
  2. J. W. Wyant, “Double Frequency Grating Lateral Shearing Interferometer,” Appl. Opt. 12, 2057–2060 (1973).
    [CrossRef] [PubMed]
  3. Xie Jianping, Ming Hai, Sheng Dingyuan, “Holographic Young’s Interferometer,” Chin. J. Sci. Instrum. 9, 234–239 (1988).
  4. Xie Jianping, Yao Kun, Ming Hai, “Measurement of Optical Coherence with Holographic Shearing Interferometer,” Acta Opt. Sin. 5, 103–106 (1985).

1988 (1)

Xie Jianping, Ming Hai, Sheng Dingyuan, “Holographic Young’s Interferometer,” Chin. J. Sci. Instrum. 9, 234–239 (1988).

1985 (1)

Xie Jianping, Yao Kun, Ming Hai, “Measurement of Optical Coherence with Holographic Shearing Interferometer,” Acta Opt. Sin. 5, 103–106 (1985).

1973 (1)

Dingyuan, Sheng

Xie Jianping, Ming Hai, Sheng Dingyuan, “Holographic Young’s Interferometer,” Chin. J. Sci. Instrum. 9, 234–239 (1988).

Goodman, J. W.

J. W. Goodman, Fourier Optics (McGraw-Hill, New York, 1968), p. 255.

Hai, Ming

Xie Jianping, Ming Hai, Sheng Dingyuan, “Holographic Young’s Interferometer,” Chin. J. Sci. Instrum. 9, 234–239 (1988).

Xie Jianping, Yao Kun, Ming Hai, “Measurement of Optical Coherence with Holographic Shearing Interferometer,” Acta Opt. Sin. 5, 103–106 (1985).

Jianping, Xie

Xie Jianping, Ming Hai, Sheng Dingyuan, “Holographic Young’s Interferometer,” Chin. J. Sci. Instrum. 9, 234–239 (1988).

Xie Jianping, Yao Kun, Ming Hai, “Measurement of Optical Coherence with Holographic Shearing Interferometer,” Acta Opt. Sin. 5, 103–106 (1985).

Kun, Yao

Xie Jianping, Yao Kun, Ming Hai, “Measurement of Optical Coherence with Holographic Shearing Interferometer,” Acta Opt. Sin. 5, 103–106 (1985).

Wyant, J. W.

Acta Opt. Sin. (1)

Xie Jianping, Yao Kun, Ming Hai, “Measurement of Optical Coherence with Holographic Shearing Interferometer,” Acta Opt. Sin. 5, 103–106 (1985).

Appl. Opt. (1)

Chin. J. Sci. Instrum. (1)

Xie Jianping, Ming Hai, Sheng Dingyuan, “Holographic Young’s Interferometer,” Chin. J. Sci. Instrum. 9, 234–239 (1988).

Other (1)

J. W. Goodman, Fourier Optics (McGraw-Hill, New York, 1968), p. 255.

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Figures (4)

Fig. 1
Fig. 1

Geometric diagram for making the hyperbolic fringe hologram.

Fig. 2
Fig. 2

Photograph of the holographic reconstructed fringes.

Fig. 3
Fig. 3

Geometric diagram for measuring coherence.

Fig. 4
Fig. 4

Photograph of moire fringes.

Tables (1)

Tables Icon

Table I Measurement Results of Optical Coherence

Equations (11)

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I 1 = 2 A 2 { 1 + cos [ k δ 1 ( x , y ) ] / 2 z 0 } ,
I 2 = A exp ( j k x sin ϕ ) + A exp ( j k x 2 / 2 z 0 ) 2 = 2 A 2 [ 1 + cos k δ 2 ( x , y ) / 2 z 0 ] ,
t ( x , y ) = β ( I 1 + I 2 ) = 4 A 2 β ( 1 + cos { k [ δ 1 ( x , y ) - δ 2 ( x , y ) ] / 4 z 0 } × cos { k [ δ 1 ( x , y ) + δ 2 ( x , y ) ] / 4 z 0 } ) .
x = x cos α - y sin α ; y = x sin α + y cos α ; α = π / 4 + θ / 2.
cos { k [ δ 1 ( x , y ) - δ 2 ( x , y ) ] / 4 z 0 } = cos [ k sin θ ( y 2 - x 2 ) / 4 z 0 ] .
t ( x , y ) = β A 2 { 4 + exp [ j k δ 1 ( x , y ) / 2 z 0 ] + exp [ - j k δ 1 ( x , y ) / 2 z 0 ] + exp [ j k δ 2 ( x , y ) / 2 z 0 ] + exp [ - j k δ 2 ( x , y ) / 2 z 0 ] } .
I A c 2 exp { j k [ δ 1 ( x , y ) + 2 z 0 x sin ϕ ] / 2 ( z 0 + z ) } + exp { j k [ δ 2 ( x , y ) + 2 z 0 x sin ϕ ] / 2 ( z 0 + z ) } 2 = 2 A c 2 { 1 + cos [ k sin θ · ( y 2 - x 2 ) / 4 ( z 0 + z ) ] } .
y 2 - x 2 = 4 n λ ( z + z 0 ) / sin θ ; y 2 - x 2 = 2 ( 2 n + 1 ) λ ( z + z 0 ) / sin θ .
s = z ( P 1 P 2 ) / ( z + z 0 ) = z r sin θ / ( z + z 0 ) ,
z 0 = z 0 λ 1 / λ 2 .
r = 1.22 λ f ( 1 + z 0 / z ) / l cos ϕ sin θ .

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