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 space containing electric currents may be regarded as a field where energy is transform ed a t certain points into the electric and magnetic kinds by means of batteries, dynamos, thermoelectric actions, and so on, while in other parts of the field this energy is again transformed into heat, work done by electromagnetic forces, or any form of energy yielded by currents. Formerly a current was regarded as something travelling along a conductor, attention being chiefly directed to the conductor, and the energy which appeared at any part of the circuit, if considered at all, was supposed to be conveyed thither through the conductor by the current. But the existence of induced currents and of electromagnetic actions at a distance from a primary circuit from which they draw their energy, have led us, under the guidance of Faraday and Maxwell, to look upon the medium surrounding the conductor as playing a very important part in the development of the phenomena. If we believe in the continuity of the motion of energy, that is, if we believe that when it disappears at one point and reappears at another, it must have passed through the intervening space, we are forced .to conclude that the surrounding medium contains at least a part of the energy, and that it is capable of transferring it from point to point. Upon this basis Maxwell has investigated what energy is contained in the medium, and. he has given expressions which assign to each art of the field a quantity of energy depending on the electromotive and magnetic intensities, and on the nature of the matter at that part l regard to its specific inductive capacity and magnetic permeability. These expressions account, as far as we know, for the whole energy. According to Maxwell’s theory currents consist essentially in a certain distribution of energy in and around a conductor, accompanied by transformation and consequent movement of energy through the field.

http://rspl.royalsocietypublishing.org/content/36/228-231/186.full.pdf

On the Transfer of Energy in the Electromagnetic Field.

Summary The maximum visibility of the interferences obtainable from two points in a wave field is defined as their degree of coherence γ. By a simple statistical method general formulae are found for deducing γ from illumination data. For any extended lightsource γ is found equal to the amplitude in a certain diffraction image. It does not change by the use of a condensing lens, but depends only on the aperture of the illuminating cone. These properties are applied to the microscopic observation of objects in transmitted light.

The concept of degree of coherence and its application to optical problems

On spectroscopic resolving power

The geometrical optics design of a focusing grating coupler (FGC) is discussed for the situation in which the shape of the guided and free-space pencil and the diffraction geometry are general. A function that describes the so-called optical path-length defect in a general point of the FGC yields the spatial frequency components after differentiation. The wavefront diffracted by the FGC is analyzed at large values of the numerical aperture of the free-space wave by means of ray tracing. Spatial variation of the wave amplitude over the wavefront due to the progressive diffraction of the guided wave is not taken into account. Tolerances on the wavelength drift of the source, the waveguide properties, and the source position are given for an integrated optical disk pickup equipped with an FGC.

Joseph Braat

Papers

Analytic Design and Optimisation of Optical Systems

Foundations of Geometrical Optics

The Kramers–Kronig Dispersion Relations

V. S. Ignatowsky: Diffraction by a Lens of Arbitrary Aperture

Geometrical Theory of Optical Imaging