Improved performance in many optical instruments has been achieved by considering coherence effects in the design of the optical instrument. In this paper such improvements are reviewed by heuristically describing the fundamental principles of partial coherence which are required in the design of such instruments. Furthermore, these coherence effects, which arise from both coherent and incoherent sources of radiation, are illustrated by discussing a selected set of instruments in which improved performance has been achieved. These examples include high-resolution recording and analyzing instruments which use incoherent sources, as well as imaging and mensuration instruments which use coherent sources. A set of guidelines for determining when coherence effects influence system performance with respect to linearity, resolution and noise is also presented.
The accurate measurement of micrometer-size iinewidths on integrated-circuit photo casks and wafers requires more accurate edge detection tecnniques than traditional optical measuring systems can achieve. A scanning pnotometric optical microscope has the capability of determining edge location using an optical threshold with a resulting linewidth error much smaller than the Airy disc radius of the imaging oujective. However, the threshold corresponding to edge location is dependent upon the spatial coherence of the illumination. Analysis using tne theory of partial coherence has led to threshold equations witn corrections for contrast and optical phase difference at the line edge. Both the tneory and instrumentation which have been developed for measurements on both pnotomasks and wafers are described. Linewidths as small as 0.5 Âµm can be measured with a sensitivity of 0.01 µm and an estimated uncertainty of 0.05 µm.
The developments leading to the characterization of microdensitorneter optical performance, through application of the principles and methods of the theory of partial coherence, are briefly reviewed and a summary of the papers contributing to the current state of knowledge is given. The basic imaging equations are presented and briefly discussed. The problem of achieving effective incoherence in the system illumination with incandescent sources is also discussed and the current criterion evaluated. The development of a new criterion for effective incoherence is then undertaken and a more useful inequality is derived. In those instances where the maintaining of effectively incoherent illumination conflicts with the minimizing of flare -- a case common to systems with limited reduction factor for the influx subsystem -- it is shown that there is a performance tradeoff: linearity (which occurs with incoherent illumination) or flare (which occurs with excessive over-illumination of the sampling aperture). A quantitative relation between these is established and a procedure is outlined for reconfiguring the microdensitometer to meet coherence requirements with a minimum of excess flare.
Radiometry evolved over a long period of time around rather incoherent sources of thermal nature. Only during the last few years the effects of coherence have been begun to be taken into account in radiometric considerations of light sources. In this review article the fundamental concepts of conventional radiometry and of the theory of partial coherence will be first briefly recalled. The basic radiometric quantities, namely the radiance, the radiant emittance and the radiant intensity, associated with a planar source of any state of coherence will then be introduced. It will be pointed out that the radiant intensity, representing the primary measurable quantity, obeys in all circumstances the usual postulates of conventional radiometry, whereas the radiance and the radiant emittance turn out to be much more elusive concepts. The radiometric characteristics of light from incoherent and coherent sources as well as from a certain type of a partially coherent source, viz., the so-called quasihomogeneous source, will be analyzed. Quasihomogeneous sources are useful models for radiation sources that are usually found in nature. Lambertian sources will be discussed as examples.
Although the theory of partial coherence was formulated in a reasonably general form about a quarter of a century ago, it was not until a few years ago that this theory was begun to be applied to problems of radiation from partially coherent sources. In this review article the properties of the radiant intensity generated by a planar source of any state of coherence will be discussed. It will be first recalled that the radiant intensity can be expressed as a two-dimensional spatial Fourier transform of a correlation function of the field in the source plane, averaged over the source area. The characteristics of the radiation from several model sources will then be analyzed. With, the help of these results certain equivalence theorems relating to the radiant intensity from planar sources of entirely different degrees of spatial coherence will be reviewed and the underlying physical principles will be elucidated. A number of illustrative examples will also be given. Finally some very recent work, which has led to the construction of planar sources with controllable degrees of spatial coherence, will be described. Experiments carried out with these sources will be discussed; they verify the main relationships between the coherence properties of the source and the directionality of the light it generates.
The role of coherence in the study of speckle patterns is considered. It is shown that the type of coherence used in such analysis has an important difference from the "classical" coherence concepts. The analogy between speckle and thermal radiation is explored. The second-order coherence properties of speckle are summarized. Finally, some aspects of speckle that do not arise in classical coherence theory are discussed.
We shall consider here the basic theory used in determining intensity fluctuations and the fourth-order coherence function in random media like the atmosphere or ocean. The basic governing equations will be presented for light propagation in the atmosphere and high frequency sound propagation in the ocean. Perturbation solutions will be given, and the saturation effect will be discussed. Recent numerical work will be reviewed.
The potential limitation of a stochastic volume scatter on large aperture, ocean acoustic systems has resulted in the development of propagation and scattering models formulated in terms of two-point coherence functions. By incorporating two additional features, these models can be regarded as generalizations of those originally developed for a similar application, but which involved electromagnetic signals in the atmosphere. One feature is an inhomogeneous background medium, resulting in an acoustic channel, which is a necessary input in discussing long-range propagation. The second is an extreme anisotropy which characterizes the scattering mechanism operative in the ocean. The models are discussed in physical terms; and the differences effected by the above-described factors are emphasized.
The random phase-front resulting from the reflection of a laser beam from a rough surface produces the spatially random optical intensity fluctuations commonly referred to as speckle patterns. If the rough surface moves with respect to the laser beam (so that independent samples of the rough surface are illuminated) or if the scattered beam propagates through the wind-blown turbulent atmosphere, a fixed detector observes a time-fluctuating optical field that can be analyzed using the techniques of coherence theory. Because most experiments measure the optical intensity, the extended Rayleigh-Sommerfield technique (developed earlier) is employed to investigate intensity fluctuations resulting from atmospheric propagation of a curved, random, beam-amplitude wave front that results from laser-beam reflection from a curved rough-surface. The normalized intensity covariance is calculated by extending the recently developed intensity fluctuation analysis to curved phase-fronts. Calculations show that the normalized intensity variance is minimized when the field point is at the focus of the source and there is no turbulence (unsaturated speckle propagation), whereas a maximum variance results when the source is perfectly co-herent (focused laser beam) and the atmosphere is turbulent. Intermediate results are obtained when the source is partially coherent and propagates in the turbulent atmosphere. Because a laser beam becomes partially coherent as it propagates through atmospheric turbulence, the method of smooth perturbations and the extended Huggens-Fresnel technique fail to predict observed beam characteristics in strong turbulence. Observed saturation phenomena are predicted by calculating the coherence properties of the beam at intervals in the propagation path.
This paper reviews the physical mechanisms by which atmospheric turbulence and aerosols induce temporal and spatial variations in the amplitude and phase of an optical wave. Using simple models for the interaction between light and the atmospheric constituents, it estimates the magnitude of such variations for typical atmospheric paths. Finally, the paper discusses the relevance of the coherence degradations to specific electro-optical applications.
This paper deals with the use of suitable transparencies for modifying either the coherence or the radiance of a light beam. These properties are used in different fields such as optical processing -non coherent holography, for instance - and in the generation of high directional beams from particular partially incoherent sources.
The lack of complete spatial incoherence of the optical field in the object plane of an imaging system results in a nonlinear relationship between the object and image intensity distributions. The problem of correcting such nonlinear distortions (which are quadratic and have a nonzero spread) by using post-detection image processing is addressed. A minimum mean-square-error linear filter is determined and its performance assessed by computer-simulated examples. Results of restoring images in a Kohler illumination system are obtained for different source sizes (i.e., different degrees of spatial coherence) and for different pupil sizes. Limits in which linearity is approached are determined.
A proposal is made of an attempt to control the coherence condition of illumination by ultrasonic waves. A progressive ultrasonic wave acts to change the spatial coherence factor periodically in a Raman - Nath regime. Some improvements are performed in a problem of two-point resolution as well as in a speckle removal with a phase-modulated laser beam. A randomly frequency-modulated ultrasonic wave allows us to obtain a decreasing coherence factor.
Optical image formation (and processing) is strongly affected by film grain noise. The noise effects depend on the spatial coherence of the illumination. In this paper we shall analyse these phenomena in the case of Kehler illumination. The effective transmittance of any photographic image is instrument dependant due to diffusion by the grain (Callier effect). Thus the question arises : what is the meaningful physical quantity in image formation ? The Callier effect directly influences the contrast of weak modulations, which happens to be maximum in symmetric partially coherent illumination. Ultimately, the detection of weak modulations is not limited by the contrast but the signal to noise ratio. Using reasonable statistical assumptions for the noise behaviour, the optimal conditions for weak modulation detection will be discussed. This study is primarily devoted to'imaging problems, but it results may be partly extended to double-slit microdensitometry. In that case however, the illumination setup makes the complete study more difficult than in the K8hler illumination case.
For several years, people have attempted to develop holographic movie systems. These systems, for the most part, have met with limited success and have not developed to the point of commercial application. The following research is an attempt to develop a system which would be a true holographic movie system, which would be for a large part, compatible to the present motion picture camera and motion picture projection systems. It is not in any way related with the multi-plex holograms that are used so extensively in display systems. This work has been done with the financial assistance of the Idaho State University Research Funds, and although most subsystems in the system have been tested, the total system has not been built because of the lack of funding and available resources. The camera system uses some very unique optical methods which enable the coherent length of the reference and the optics beams to be maintained over great distances, due to the repeatability of the longitudinal coherence path caused by the intermodulation of the optical cavity. The projection system has been tested using both an arrangement of mirrors and a scatter media in order to develop the image projected from the holograms which have been recorded. Although the angle of viewing is still somewhat limited, these angles have been shown to be within usable limits. This paper, in no way, is intended to present the ultimate solution to the problem of producing holographic movies, but instead is intenrced to present various ideas which have been developed in the hope that it will stimulate additional thought in this particular area and perhaps stimulate the development of additional and more sophis-ticated apparatus.
Optical heterodyne detection of partially coherent cross-spectrally pure radiation is considered. A general formulation of the problem based on the photodetection statistics is presented first. Effects of temporal and spatial coherence of the signal on the heterodyne detection efficiency are then presented. Four limiting cases classified by the signal radiation coherence properties are considered in detail. The heterodyne antenna property, local oscillator (LO) laser requirement, and effects of radiation statistics on the heterodyne efficiency are also considered.