Abstract

The effect of employing coherent illumination (such as a laser source in scanning optical systems) upon image content is investigated with particular reference to the microdensitometer system. The method of investigation involves the application of coherence theory to the imaging process in systems where the small-angle approximations can be made and the optics of the system are diffraction limited. The output of the system is determined for a sharp-edged object as the area illuminated in the object plane or the width of the illuminating slit is varied. A system configuration is found in which the edge image does not exhibit the usual ringing or diffraction fringes associated with coherent illumination.

© 1966 Optical Society of America

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References

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  1. H. Gamo, in Progress in Optics, ed. by E. Wolf (North-Holland Publishing Co., Amsterdam, 1964), Vol. III, pp. 271–274, treats the microdensitometer system using coherence theory. However, a specific object is not considered. Gamo includes the possibility of nonuniformity of the photodetecting surface whereas we assume uniform sensitivity.
  2. M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), Chap. X.
  3. W. H. Steel, Proc. Roy. Soc. (London) A249, 574 (1958). A constant phase factor usually is included in expression (2); however, under the small-angle approximation we assume curvature of the entrance and exit pupils, and the factor can be set equal to unity. In the imaging systems considered here, the “far-field approximation” is allowed between successive planes owing to the effect of the lenses in the system.
  4. This analysis does not include coupling of the mode of the laser or a nonuniform phase distribution of the wave amplitudes at the illuminating slit. However, an analysis of these effects can be made within the framework of the analysis present in this paper.
  5. The case where the area illuminated in the object plane is large has already been considered in a previous paper: R. E. Kinzly, J. Opt. Soc. Am. 55, 1002 (1965).

1965 (1)

1958 (1)

W. H. Steel, Proc. Roy. Soc. (London) A249, 574 (1958). A constant phase factor usually is included in expression (2); however, under the small-angle approximation we assume curvature of the entrance and exit pupils, and the factor can be set equal to unity. In the imaging systems considered here, the “far-field approximation” is allowed between successive planes owing to the effect of the lenses in the system.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), Chap. X.

Gamo, H.

H. Gamo, in Progress in Optics, ed. by E. Wolf (North-Holland Publishing Co., Amsterdam, 1964), Vol. III, pp. 271–274, treats the microdensitometer system using coherence theory. However, a specific object is not considered. Gamo includes the possibility of nonuniformity of the photodetecting surface whereas we assume uniform sensitivity.

Kinzly, R. E.

Steel, W. H.

W. H. Steel, Proc. Roy. Soc. (London) A249, 574 (1958). A constant phase factor usually is included in expression (2); however, under the small-angle approximation we assume curvature of the entrance and exit pupils, and the factor can be set equal to unity. In the imaging systems considered here, the “far-field approximation” is allowed between successive planes owing to the effect of the lenses in the system.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), Chap. X.

J. Opt. Soc. Am. (1)

Proc. Roy. Soc. (London) (1)

W. H. Steel, Proc. Roy. Soc. (London) A249, 574 (1958). A constant phase factor usually is included in expression (2); however, under the small-angle approximation we assume curvature of the entrance and exit pupils, and the factor can be set equal to unity. In the imaging systems considered here, the “far-field approximation” is allowed between successive planes owing to the effect of the lenses in the system.

Other (3)

This analysis does not include coupling of the mode of the laser or a nonuniform phase distribution of the wave amplitudes at the illuminating slit. However, an analysis of these effects can be made within the framework of the analysis present in this paper.

H. Gamo, in Progress in Optics, ed. by E. Wolf (North-Holland Publishing Co., Amsterdam, 1964), Vol. III, pp. 271–274, treats the microdensitometer system using coherence theory. However, a specific object is not considered. Gamo includes the possibility of nonuniformity of the photodetecting surface whereas we assume uniform sensitivity.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), Chap. X.

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Figures (3)

Fig. 1
Fig. 1

Microdensitometer optical system. C, condenser; O, objective; P, photomultiplier tube; S, aperture stop of the illuminating microscope; A, entrance aperture of the imaging system; ➀, plane of the illuminating slit; ➂, object plane; ➄, plane of image and scanning aperture. Planes ➀, ➂, ➄ are conjugate.

Fig. 2
Fig. 2

Normalized irradiance in the image of an edge as a function of the half-width, m, of the illuminating slit. Coherent illumination is assumed. The dashed curve (– – –) shows agreement to the case where the complete object plane is coherently illuminated. The scanning aperture is a delta function or narrow slit.

Fig. 3
Fig. 3

Normalized irradiance trace in the image of an edge for illuminating slit half-width of 3.0 u′ units and varying scanning slit width, L. Coherent illumination of the illuminating slit is assumed.

Equations (6)

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J ( x 1 , x 2 ) = V ( x 1 , t ) V * ( x 2 , t ) ,
J ( x 1 , x 2 ) = J ( ξ 1 , ξ 2 ) exp [ i ( x i ξ 1 - x 2 · ξ 2 ) ] d ξ 1 d ξ 2 .
J ( x 1 , x 2 ) = J ( x 1 , x 2 ) T ( x 1 ) T * ( x 2 ) .
x 1 = x 2 = x .
I 5 ( x , t ) = - T 3 ( u 1 , t ) T 3 * ( u 2 , t ) J 3 ( u 1 , u 2 ) × sinc ( u 1 + x ) sinc ( u 2 + x ) d u 1 d u 2 ,
I 6 ( u , m , L ) = - L L [ u sinc ( u + x ) × { S i ( u + m ) R - S i ( u - m ) R } d u ] 2 d x ,