Applications of Coherence Theory in Microscopy and Interferometry*

Fraunhofer diffraction patterns produced by a narrow rectangular aperture having a non-uniform illumination with partially coherent light are presented. Graphs of intensity distributions in the diffraction patterns for three cases of amplitude filters and four forms of the mutual coherence at the slit are given. An increase in the half-width at half-height (H.W.H.H.) and a decrease in the intensity at the centre are observed. Tolerances for the value of the correlation interval in the aperture based on .the Strehl intensity criterion have been calculated for various amplitude filters.

Section: Introductionmentioning

confidence: 99%

Fraunhofer Diffraction in Partially Space Coherent Light by Slit Aperture with Amplitude Filters

Singh

Gupta

1970

“…where y(xo, Yo) is the effective source distribution [3][4][5][6][7][8] and contains the information about the spatial coherence of the illumination, a(x) is the (inverse) Fourier transform of the complex amplitude transmittance of the object, f(x, y) is the pupil function, which describes the amplitude transmittance and aberrations of the imaging system, and the asterisk denotes complex conjugate. This may be written as…”

Section: Derivation Of Equationmentioning

confidence: 99%

“…In order to carry out such an examination we shall explicitly employ the theory of partially-coherent image formation as developed by Hopkins [3][4][5][6] for one dimensional objects to the procedure employed for determining the OTF, on the assumption that the illumination is incoherent.…”

Section: Introductionmentioning

confidence: 99%

“…We shall assume that the conditions of linearity required [5] are satisfied, either by the optical system or by application of the effective source theorem [6,7]; in practice this is conveniently arranged by imaging the source onto the entrance pupil of the lens under test, in which case the, so called, 'effective source' distribution is simply the geometric image of the source [6], provided the condenser is itself incoherently illuminated [3][4][5][6]8]. …”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Influence of Spatial Coherence on the Monochromatic Optical Transfer Function

Shaw

1986

It is widespread practice to measure the optical transfer function (OTF) by scanning the images of 'simple' objects. However, the illumination used in such systems is (generally) partially coherent, and not incoherent as is required by theory. The influence of spatial coherence is explicitly examined in order to obtain a general equation for the observed OTF for the case of onedimensional test objects. The equation is applied to the case of a 'perfect' rotationally symmetric lens, using a slit object, and, on comparing the results with the true (incoherent) OTF of such a lens, significant differences have been found.

“…In other words, we treat the geometrical and spectral effects separately. This seems to be justified, since Hopkins [3] showed that very often the general degree of coherence is a product of two factors, which are influenced only by the spectral width, and by the geometrical width of the source, respectively. It is sufficient, but not necessary, for the separation of the two influences that ygeo or yspec is nearly unity.…”

Section: U )mentioning

confidence: 99%

Grating Diffraction Spectra as Coherent Light Sources for Two- or Three-beam Interferometry

1962

It is common practice in two-beam and three-beam interferometry to obtain coherent light sources by using slits in a coherent field (division of wave-front) or by means of suitable mirror devices (division of amplitude). The purpose of this paper is to show that better coherence properties may be realized if one uses grating diffraction spectra as coherent light sources. As a result one may use a source larger than what is permissible in a conventional slit-interference set-up and thereby gain in photometric efficiency. Further, it is shown that the fringes with slit interference are, in general, inhomogeneously distributed in space. The proposed method of interference between the disturbances from the different grating spectra does not suffer from these disadvantages. Also one gets achromatic fringes, and hence the grating interference technique is ideally suited for interferometry in the ultra-violet or infra-red region of the spectrum. The physical reason for the achromacy of the fringes is easy to understand, if one considers the fringes as images of the grating produced by lenses which have no chromatic aberrations. Finally, other interferometric devices have also been discussed in terms of coherence.