## 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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### Equations (6)

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(1)
$$J({\mathbf{x}}_{1},{\mathbf{x}}_{2})=\u3008V({\mathbf{x}}_{1},t)V*({\mathbf{x}}_{2},t)\u3009,$$
(2)
$$J({\mathbf{x}}_{1},{\mathbf{x}}_{2})=\int \int J({\mathrm{\xi}}_{1},{\mathrm{\xi}}_{2})\hspace{0.17em}\text{exp}[i({\mathbf{x}}_{i}{\mathrm{\xi}}_{1}-{\mathbf{x}}_{2}\xb7{\mathrm{\xi}}_{2})]d{\mathrm{\xi}}_{1}d{\mathrm{\xi}}_{2}.$$
(3)
$${J}^{\prime}({\mathbf{x}}_{1},{\mathbf{x}}_{2})=J({\mathbf{x}}_{1},{\mathbf{x}}_{2})T({\mathbf{x}}_{1})T*({\mathbf{x}}_{2}).$$
(4)
$${\mathbf{x}}_{1}={\mathbf{x}}_{2}=\mathbf{x}.$$
(5)
$${I}_{5}(x,t)=\underset{-\infty}{\overset{\infty}{\int \int}}{T}_{3}({u}_{1},t){T}_{3}*({u}_{2},t){J}_{3}({u}_{1},{u}_{2})\times \text{sinc}({u}_{1}+x)\hspace{0.17em}\text{sinc}({u}_{2}+x)d{u}_{1}d{u}_{2},$$
(6)
$${I}_{6}({u}^{\prime},m,L)=\underset{-L}{\overset{L}{\int}}{\left[\underset{{u}^{\prime}}{\overset{\infty}{\int}}\text{sinc}(u+x)\times \{Si(u+m)R-Si(u-m)R\}du\right]}^{2}dx,$$