Abstract

In this paper, we investigate the Fraunhofer diffraction of a class of partially coherent light diffracted by a circular aperture. It is shown that by the illumination of partially coherent light of the special spatial correlation function, the anomalous behaviors of the diffraction patterns are found. We find that the decrease of the spatial coherence of the light in the aperture leads to the drastic changes of the diffraction pattern. Specifically, when the light in the aperture is fully coherent, the diffraction pattern is just an Airy disc. However, as the coherence decreases, the diffraction pattern becomes an annulus, and the radius of the annulus increases with the decrease of the coherence. Flattened annuli can be achieved, when the parameters characterizing the correlation of the partially coherent light are chosen with suitable values. Potential applications of modulating the coherence to achieve desired diffraction patterns are discussed.

© 2003 Optical Society of America

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References

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IEEE J. Quant. Electron. (1)

J. Pu and S. Nemoto, �??Spectral shifts and spectral switches in diffraction of partially coherent light by a circular aperture,�?? IEEE J. Quant. Electron. 36, 1407-1411 (2000).
[CrossRef]

J. Appl. Phys. (1)

J. Turunen, E. Tervonen, and A. T. Friberg, �??Acousto-optic control and modulation of optical coherence by electronically synthesized holographic grating,�?? J. Appl. Phys. 67, 49-59 (1990).
[CrossRef]

J. Opt. Soc. Am A (1)

S. Anand, B. K. Yadav, and H. C. Kandpal, �??Experimental study of the phenomenon of N �? 1 spectral switch due to diffraction of partially coherent light,�?? J. Opt. Soc. Am A 19, 2223-2228 (2002).
[CrossRef]

J. Opt. Soc. Am. A (5)

Jpn. J. Appl. Phys. (1)

Y. Ohtsuka, �??Optical coherence reduction by an amplitude modulated ultrasonic wave,�?? Jpn. J. Appl. Phys. 17, 1775-1780 (1978).
[CrossRef]

Opt. Commun. (1)

T. Asakura, �??Diffraction of partially coherent light by an apodized slit aperture,�?? Opt. Commun. 5, 279-284 (1972).
[CrossRef]

Optica Acta (1)

T. S. C. Som and S. C. Biswas, �??The far-field diffraction properties of apertures I. Circular apertures with Besinc correlated illumination,�?? Optica Acta 17, 925-942 (1970).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Illustration and geometry of the diffraction of partially coherent light by a circular aperture of radius a.

Fig. 2.
Fig. 2.

The correlation function µ(Δρ) as a function of Δρ in the case of a/ = 1, (a) ε s = 0.9, (b) ε s = 0.6 and (c) ε s = 0.4, respectively.

Fig. 3
Fig. 3

(a). The diffraction pattern; (b). the corresponding intensity distribution I(v) as a function of the diffraction angle v. a/ = 0, ε s = 0.9. The maximum intensity is normalized to unity.

Fig. 4
Fig. 4

(a). The diffraction pattern; (b). the corresponding intensity distribution I(v) as a function of the diffraction angle v. a / = 1, ε s = 0.9. (The intensity I(v) is normalized to have the maximum intensity unity in the case of complete coherence. This applies to Figs. 58)

Fig. 5
Fig. 5

(a). The diffraction pattern; (b). the corresponding intensity distribution I(v) as a function of the diffraction angle v. a / = 2, ε s = 0.9.

Fig. 6
Fig. 6

(a). The diffraction pattern; (b). the corresponding intensity distribution I(v) as a function of the diffraction angle v. a / = 4, ε s = 0.9.

Fig. 7
Fig. 7

(a). The diffraction pattern; (b). the corresponding intensity distribution I(v) as a function of the diffraction angle v. a / = 4, ε s = 0.4.

Fig.8
Fig.8

(a). The diffraction pattern; (b). the corresponding intensity distribution I(v) as a function of the diffraction angle v. a / = 5, ε s = 0.4.

Equations (9)

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W ( ρ 1 , ρ 2 ) = W ( ρ 1 ρ 2 ) = s 0 μ ( ρ 1 ρ 2 ) ,
μ ( ρ 1 ρ 2 ) = 1 1 ε s 2 Besinc ( k ρ 1 ρ 2 b ) ε s 2 1 ε s 2 Besinc ( k ρ 1 ρ 2 ε s b )
I ( r , z ) = ( k 2 π z ) 2 A W ( ρ 1 ρ 2 ) exp { ik ( ρ 1 ρ 2 ) . r z } d ρ 1 d ρ 2
I ( v ) = 2 S 0 ( k a 2 z ) 2 { 1 1 ε s 2 0 1 C ( u ) Besinc [ 7.664 ( a L ¯ ) u ] J 0 ( 7.664 uv ) udu
ε s 2 1 ε s 2 0 1 C ( u ) Besinc [ 7.664 ( a L ¯ ) ε s u ] J 0 ( 7.664 uv ) udu }
C ( u ) = ( 2 π ) { cos −1 ( u ) u ( 1 u 2 ) 1 2 } .
L ¯ = 3.832 kb .
v = 3.832 ka ( r z ) ( 3.832 ka ) θ ,
θ r z

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