The theory of image formation is formulated in terms of the coherence function in the object plane, the diffraction distribution function of the image-forming system and a function describing the structure of the object. There results a four-fold integral involving these functions, and the complex conjugate functions of the latter two. This integral is evaluated in terms of the Fourier transforms of the coherence function, the diffraction distribution function and its complex conjugate. In fact, these transforms are respectively the distribution of intensity in an 'effective source', and the complex transmission of the optical system-they are the data initially known and are generally of simple form. A generalized 'transmission factor' is found which reduces to the known results in the simple cases of perfect coherence and complete incoherence. The procedure may be varied in a manner more suited to non-periodic objects. The theory is applied to study inter alia the influence of the method of illumination on the images of simple periodic structures and of an isolated line.

On the diffraction theory of optical images

A new type of interferometer is described by means of which the asphericity of an optical wavefront can be measured, by testing it against itself with lateral displacement or shear. Continuous control of the amount of this shear, and of the meridional or sagittal fringes is obtained in white light.

A wavefront shearing interferometer

A two-beam interferometer illuminates a sample surface with light at grazing incidence angles for the purpose of analyzing a surface characteristic such as surface topography. The interferometer includes a diffractive-optic beam splitter, which separates an incoming light beam into measurement and reference beams and a diffractive-optic beam combiner, which produces an output beam by interfering portions of the reference beam with reflected portions of the measurement beam. Those portions of the reference wavefront and the measurement wavefront that interfere originate from substantially the same portion of the initial illumination wavefront.

Grazing incidence interferometer and method

SUMMARY

A systematic account is given, in relation to amorphous and paracrystalline (especially biological) material, of electron scattering and image formation for the range of electron energy from 50 to 100 keV. Contrast mechanisms in both elastic and inelastic scattering are discussed and image formation is considered under both scattering contrast and phase contrast conditions.

Mechanisms of contrast and image formation of biological specimens in the transmission electron microscope

Methods of detecting extrasolar planets: I. Imaging

A theoretical expression has been derived for the intensity distribution in the diffrimoscopic image for a straight edge under partially coherent illumination. Computations have been made to see (a) the effect of the degree of coherence, (b) the effect of the width of the aperture, and (c) the effect of obstacle width. It has been shown that the dark fringe appears exactly in the position of the geometric image of the edge and that the fringe width is practically independent of the degree of coherence and of the obstacle width but is inversely proportional to the width of the aperture.

Diffrimoscopic Image Formation under Partially Coherent Illumination (Straight Edge)

A simple, common path inverting interferometer is described. The interference pattern shows the anti-symmetrical wavefront error about the axis of inversion and the path difference is always zero at the centre of the pattern. It is shown that, in this interferometter, collimation errors have negligible effect. The interferometer is suitable for testing concave mirrors and convex lenses.

A Simple Inverting Interferometer

An inverting interferometer based on the double-passed Fizeau interferometer is described. The fringe irradiance distribution of the interferometer is derived and it is shown that the inclination of the rays has negligible effect. Its use for testing the parallelism between two optical surfaces and for the measurement of the variation of their optical separation is also discussed.

An Inverting Fizeau Interferometer

The intensity distributions in the diffrimoscopic (dark-field) images have been derived for objects with periodically varying transmission. Detailed studies have been made of the effects of the degree of coherence, the spatial frequency y and the ratio of the width of lighter strip to the period of the object. It has been shown that the dark fringe appears near the geometric image of the edge separating the normally bright and dark regions and that the contrast in the diffrimoscopic image is independent of the contrast in the object. For rectangular wave periodic objects with equal widths of dark and bright strips the image intensity distribution is symmetrical about the dark fringe. When the widths of the dark and bright strips are not equal, the intensity distributions, in general, are asymmetrical but the distributions can be made symmetrical by taking suitable values of r, the ratio of the numerical apertures of the collimator and the objective. In symmetrical distributions the centre of the dark frin...

Dark-field (Diffrimoscopic) Images of Periodic Objects (Partially Coherent Illumination)

The intensity distributions have been computed in the dark-field images of coherently illuminated objects with periodically varying transmission. To get this dark field an obstacle is placed centrally in the back focal plane of the imaging system and the image so formed is called the diffrimoscopic image. The image is characterized by the appearance of a dark fringe at the geometric image of the edges of the object. The effect of the width of the obstacle and the aperture of the imaging system on image intensity distribution have been studied. It has been shown that the dark fringes appear exactly at the geometric image of the edges separating the light and dark regions of a rectangular wave object. The width of the dark fringe is inversely proportional to the aperture width. The position and the width of the dark fringe are independent of the width of the obstacle which affects mainly the intensity away from the dark fringe.

D. Sen

Papers

Diffrimoscopic Image Formation under Partially Coherent Illumination (Straight Edge)

A Simple Inverting Interferometer

An Inverting Fizeau Interferometer

Dark-field (Diffrimoscopic) Images of Periodic Objects (Partially Coherent Illumination)

Dark-field (Diffrimoscopic) Images of Periodic Objects (Coherent Illumination)