Abstract

The importance of spatial coherence of a pulsed ruby laser beam is pointed out. The spatial and temporal coherences of light are defined. Spatial coherence of the beams from a ruby laser, operating in either the Q-switched or normal lasing modes, is deduced from the degree of visibility of fringes formed by a Michelson interferometer in which the laser beam interferes with itself after being rotated 180°. The results are physically and analytically interpreted.

© 1978 Optical Society of America

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References

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  1. A. B. Booker, C. D. Clemnow, in Transformation de Fourier et Théorie des distributions, J. Arsac, Ed. (Dunod, Paris, 1961), Chap. 8.
  2. A. Lacourt, Thèse de doctorat, U. Besançon, France (1970).
  3. H. Madjidi-Zolbanine, Diplome d’Etudes Approfondis, U. Besançon, France (1972).
  4. G. DaCosta, J. Opt. Soc. Am. 66, 1085 (1976).

1976 (1)

G. DaCosta, J. Opt. Soc. Am. 66, 1085 (1976).

Booker, A. B.

A. B. Booker, C. D. Clemnow, in Transformation de Fourier et Théorie des distributions, J. Arsac, Ed. (Dunod, Paris, 1961), Chap. 8.

Clemnow, C. D.

A. B. Booker, C. D. Clemnow, in Transformation de Fourier et Théorie des distributions, J. Arsac, Ed. (Dunod, Paris, 1961), Chap. 8.

DaCosta, G.

G. DaCosta, J. Opt. Soc. Am. 66, 1085 (1976).

Lacourt, A.

A. Lacourt, Thèse de doctorat, U. Besançon, France (1970).

Madjidi-Zolbanine, H.

H. Madjidi-Zolbanine, Diplome d’Etudes Approfondis, U. Besançon, France (1972).

J. Opt. Soc. Am. (1)

G. DaCosta, J. Opt. Soc. Am. 66, 1085 (1976).

Other (3)

A. B. Booker, C. D. Clemnow, in Transformation de Fourier et Théorie des distributions, J. Arsac, Ed. (Dunod, Paris, 1961), Chap. 8.

A. Lacourt, Thèse de doctorat, U. Besançon, France (1970).

H. Madjidi-Zolbanine, Diplome d’Etudes Approfondis, U. Besançon, France (1972).

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Figures (4)

Fig. 1
Fig. 1

Experimental device. M1 is the spherical mirror with 60% reflectance and radius R = 50 cm. M2 is the plane mirror with 99.9% reflectance. M1M2 = 50 cm.

Fig. 2
Fig. 2

Fringes due to autocorrelation between the grains of the speckle are visible at the center.

Fig. 3
Fig. 3

Speckle pattern obtained by a Q-switched laser.

Fig. 4
Fig. 4

Representation of the Laue sphere around the object source (ruby), x and z are variables in the object space; U and W are reciprocal variables in the Fourier space. The point O′ is situated on the Laue sphere which has a radius R = 1/λ. d = the distance between the object source and the observation plane.

Equations (4)

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U 2 + V 2 + W 2 = 1 / λ 2 ,
A ( U , V , W ) = j / λ d s ( x , y , z ) × { exp [ j k ( U x + V y + W z ) ] } d x d y d z ,
A ( U , W ) = j / λ d s ( x , y ) exp [ ( j 2 π / λ ) ( U X + W Z ) ] d x d z ,
A ( U , W ) = K FT [ h ( x , z ) × d ( x , z ) ] = K FT [ h ( x , z ) ] FT [ d ( x , z ) ] = K H ( U , W ) D ( U , W ) ,

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