The influence of wave aberrations: an operator approach

Abstract

The wave departures from sphericity known as Seidel's primary-or third-order aberrations are represented by a differential operator that modifies the diffraction-limited image. We show that the complex amplitude at any point over the aberrant image can be obtained from certain terms of the Taylor series expansion of the diffraction limited image. This approach allows us to describe the propagation of an aberrant wave front in terms of its aberration coefficients. Furthermore, it can also be applied to implement an optical or an electronic procedure for simulating aberrant images.Nous representons par un opkrateur diffkrentiel, modifiant I'image diffractionnelle idkale, I'effet sur celle-ci des Ccarts ondulatoires relativement a la sphkre, connus sous le nom d'aberrations de Seidel primaires, ou du troisikme ordre. Nous dCmontrons qu'en tout point de I'image entachke d'aberrations I'amplitude complexe peut Ctre obtenue ii partir de certains termes du dkveloppement de Taylor de I'image diffractionnelle idkale. Suivant cette voie il devient possible de dkcrire la propagation d'un front d'onde aberrant en termes de ses coefficients d'aberration. De plus on peut la mettre en oeuvre via des moyens optiques ou klectroniques capables de simuler des images entachkes d'aberrations.

Continuous order derivative for optical signals and images

“…It is worth noting that the second-order Bayliss-Turkel condition improves on the scalar Sommerfeld radiation condition by three powers of the variable r. Equation (22) is similar in that it improves on Eq. (4) by three powers of r.…”