Optical Reciprocity Research Articles

Non-destructive optical and magneto-optical analysis of inhomogeneously doped semiconductors

Extremely large gradients of the complex refractive index exist within microstructures used by modern semiconductor technology. A matrix calculation method of multilayer structures is presented for the non-destructive electrical and structural characterization of inhomogeneously doped semiconductors. This concept includes coherent multiple reflections within the refractive index profile as well as incoherent multiple reflections within the whole wafer in the cases with and without an applied magnetic field and also yields the spacial distribution of free carrier profiles as of transitions between different crystal phases by using the least-squares fit procedures. According to the theorem of optical and magneto-optical (MO) reciprocity the accuracy of the method is enhanced by using the asymmetrical optical reflectivity and the asymmetrical differential MO reflectance.

A versatile directional reflectance model for natural water bodies, submerged objects, and moist beach sands

A directional reflectance model is derived that is based upon the same multiple scattering concepts as were employed in a previously published vegetation reflectance model. The scattering phase functions utilize the “model equivalent” Lambertian panel approximation for each scattering species. The model exhibits the property of optical reciprocity and offers consistent procedures for calculating directional reflectance of turbid water bodies of any depth, particulate content, and bottom vegetation cover, as well as the apparent reflectance of an isolated submerged object, such as a Secchi disc. Moist beach sands are considered to be extremely turbid water where air voids are also a scattering species.

Reduction of fading in atmospheric optical communication links by application of optical reciprocity theory

Reduction of fading in atmospheric optical communication links by application of optical reciprocity theory

Reciprocal Optical System for Measuring the State of Focus of Reflected Images

A reciprocal-imaging optical system for monitoring the position of a specular reflecting surface (e.g., the back surface of a photographic film) is described. The technique involves imaging an illuminated pattern onto the reflecting surface, and reimaging the reflection back through the same optical system onto the original pattern. If the first image is in focus on the reflecting surface, then by optical reciprocity, the returned image is congruent with and superimposed upon the original source pattern. As the reflecting surface moves out of the image plane, some of the returned light falls beyond the input pattern and is intercepted by the monitoring system. Thus, intercepted light is nominally zero with the mirror in the image plane, and increases with displacement in either direction away from focus. The case of a uniformly illuminated circular source pattern imaged by a circular lens is analyzed, and the intercepted light as a function of mirror position is determined both analytically and experimentally. The critical parameters in the design of the system are identified and the effects of optical misalignment are discussed.

Numerical solution of the Boltzmann Transport Equation

A numerical model for solution of the linear Boltzmann Transport Equation is formulated. By applying the same techniques used in the derivation of the analytic equation, a discrete analog of the Boltzmann equation is derived for a finite cell in phase space. Initially undetermined coefficients in the analog are determined by requiring the numerical formulation to include properties (e.g., particle conservation) of the analytic equation. Terms occurring in the finite-cell analog are defined, and two treatments of the angular dependence are illustrated. A discrete ordinates representation is derived based on a connected straight-line-angular representation. This formulation maintains optical reciprocity and may be generalized. The second portion of the paper describes the systematic derivation of difference relations necessary to complete solution of the numerical formulation. Both representation schemes, based on assumed forms of particle fluxes in the cell, and characteristic schemes are examined. Difficulties encountered in extrapolations made by the use of representation schemes are clarified, and insight is gained for methods that can be used to prevent flux oscillations in numerical calculations.