Alberic Boivin

Energy Flow in the Neighborhood of the Focus of a Coherent Beam

In a previous paper [ Phys. Rev.138, B1561 ( 1965)] some new results were presented relating to the structure of the electromagnetic field near the focus of a coherent beam emerging from an aplanatic optical system. The present paper supplements the previous one by providing detailed analysis of the behavior of the Poynting vector in the focal region of such a beam. In particular, diagrams showing the flow lines and the contours of constant amplitude of the time-averaged Poynting vector are given. The energy flow is found to have vortices near certain points of the focal plane. Two diagrams showing the behavior of the flow near a typical vortex are also included.

On the Theory of Diffraction by Concentric Arrays of Ring-Shaped Apertures

Lommel’s problem, the diffraction of spherical waves by a circular aperture and opaque disk, is extended to the case of a concentric array of ring-shaped apertures with arbitrary distribution of circle radii. The evaluation of the diffracted amplitude resulting from the entire array by the obvious process of numerical summation, applied to amplitude expressions pertaining to the sequence of circles involved, is found unsuitable and, instead, series expansions are investigated in which the location of the off-axis observation point and the interference effects of the ring openings are formally separated. The already available solutions of Lommel’s problem are examined from this viewpoint, and two new expansions in complex power series are derived. By means of two novel multiplication theorems for Lommel’s functions of two variables, convenient expansions in series of these functions are obtained for the amplitude diffracted by the annular array, thus affording the basis of a general theory of diffraction by ring systems, including the case of phase-reversal construction. Furthermore, equivalent general expressions are directly obtained from the power series formulas mentioned previously. A first application is made to the special case of the Soret zone plate. Finally Hopkins’ assumption of radially non-uniform amplitude is briefly dealt with in connection with the circular aperture and the annular systems.

An Axial Form of the Sampling Theorem and its Application to Optical Diffraction

The sampling theorem is used to obtain expressions for the diffracted amplitude G(y, z) at any point in space, once the distribution along the axis G(y, 0) is known at the sampling points. In the case of a circular symmetrical pupil, G(y, 0) is simply the Fourier transform of the pupil function. The real or imaginary parts of G(y, z) may be obtained either from the real or from the imaginary part of G(y, 0). By suitable oversampling, the real part of G(y, z) may be found from its imaginary part, and vice versa. A technique for the synthesis of antenna patterns is suggested.

Concepts and Techniques of Microwave Optics

The fast-developing domain of microwave optics is surveyed, with main emphasis on those aspects of interest to optical scientists. Special attention is devoted to the newer trends in that field of research. The following aspects are covered: diffraction theory of microwave optics, microwave optical instruments, beam waveguides, and components for millimeter waves.

Optimized Amplitude Filtering for Superresolution Over a Restricted Field

In the application of Friedens impulse-generating filter to super-resolution, the characteristics of the point response as well as those of the filter are seen to depend on the extent of the restricted field. Here curves are presented that show how the filter and its diffraction pattern change with field extent, and the behaviour of some pertinent figures of merit is examined under various conditions. For a given field extent it is found that (1) the resolution gain eventually increases linearly with the order M to which the point response approximates the delta function, (2) the filter transmission ratio exhibits a maximum for a certain value of M and eventually settles to the levels characteristic of the Zernike polynomials and (3) the Strehl central-irradiance ratio and the encircled-energy ratio for the restricted field drop without limit once M exceeds the superresolution threshold. The trade-off between resolution gain, central irradiance and field extent is also investigated.

Optical Filter Synthesis by Holographic Methods

By use of a recently developed formulation of scalar diffraction theory, any complex amplitude filter can be considered as a generalized zone plate. By placing sources having suitable amplitude and phase characteristics at the foci, we can reconstruct the filter function in the pupil plane. The amplitudes of the sources are related in a simple way to the Fourier-series expansion of the pupil function. The techniques of holography can be used to record complex-amplitude filters on photographic film. If three-beam holography is used and if the filter function is real, only real sources are needed.

Real-time curvature radii measurements using diffraction edge waves

A laser beam impinging at grazing incidence on a 3-D surface produces a diffraction edge wave whose obliquity factor contains, among other things, the information concerning the local radius of curvature of the surface in the plane of incidence. In this paper we show how to retrieve this curvature radius information from light irradiance measurements of the edge wave and from exact electromagnetic diffraction calculations. This new method of optical metrology gives the curvature radius of a surface in the incident plane and at a given point by a single measurement at that point, while other techniques depend on a scanning or a mapping in the vicinity of the point of interest. Moreover, a measuring system using this diffractional method is very easily implemented and can yield a precision in the 5–10-μm range. Experimental results are presented for six metallic circular cylinders and two metallic spheres.

Electromagnetic diffraction of a three-dimensional Gaussian laser beam at grazing incidence upon a large absorbing circular cylinder

We present an expression for the electromagnetic-diffraction edge wave produced by a three-dimensional Gaussian beam at grazing incidence upon an absorbing circular cylinder whose radius is much greater than the wavelength. The good conductor and the perfect conductor are included as special cases. Moreover, the edge-wave expression is valid in the Fresnel region as well as in the far field.

Apport du Canada français aux progrès récents de l’optique

For a number of years, optics, mainly in the area of diffraction, has been pursued with increasing vigor at Laval University. The present article summarizes the contributions of this French-Canadian group. After a brief historical outline, the following topics are surveyed: circular gratings, axially symmetrical diffraction patterns with both phase and amplitude variation, the factor of encircled energy and apodization, millimeter-wave optics, optical convolution, iterated diffraction in connection with beam waveguides and resonators, structure of focal region for wide angle systems, and holography.For a number of years, optics, mainly in the area of diffraction, has been pursued with increasing vigor at Laval University. The present article summarizes the contributions of this French-Canadian group. After a brief historical outline, the following topics are surveyed: circular gratings, axially symmetrical diffraction patterns with both phase and amplitude variation, the factor of encircled energy and apodization, millimeter-wave optics, optical convolution, iterated diffraction in connection with beam waveguides and resonators, structure of focal region for wide angle systems, and holography.

Un nouveau theoreme d'echantillonnage pour le degre de coherence complexe en vue de la reconstitution d'une source lumineuse isotrope

Resume We present a new sampling theorem for the complex degree of coherence γ of the field emitted by a circularly symmetric incoherent source. Our analysis is based on an expansion in Zernike polynomials of the source luminance. We show that the latter may be reconstructed from measurements of the γ function over discrete pairs of points.