A. Walther

Radiometry and Coherence

The basic laws of photometry are derived from the theory of partial coherence by considering a generalized form of the Van Cittert–Zernike theorem.

Propagation of the generalized radiance through lenses

We prove that in a large and significant class of cases the generalized radiance is, except for transmission losses, invariant along light rays traversing a lens.

Lenses, Wave Optics, and Eikonal Functions*

An approximate solution to the problem of a light wave propagating through a lens is obtained by systematically replacing the integrals required to solve the problem by their stationary-phase approximation. This approach is shown to yield (1) geometrical optics in its eikonal form, and (2) a diffraction theory of image formation applicable to lenses with large apertures and fields.

Problem in the determination of correlation functions. II

This Letter extends the treatment of an earlier note. This time we take into account corrections in the correlation function that must be made when both the mean slope as well as the mean reference level are not known. Again the true correlation function requires the solution of an integral equation.

Angle eikonals for a perfect zoom system.

I show that it is possible to choose the eikonals for the lens groups of a zoom lens such that extended objects at infinity are imaged perfectly, without any aberrations, at all zoom settings.

Eikonal theory and computer algebra II

I show how computer algebra can be used to turn the study of aberrations from a thorny branch of lens theory into a practical design tool. After a discussion of the underlying mathematics two applications are shown: the well-known problem of a lens used at different magnifications and the analysis of an unusual afocal element.

Irreducible aberrations of a lens used for a range of magnifications

In practical photography a lens must form a high-quality image at a variety of magnifications. It has, however, been known for more than a century that no lens can be designed that is perfect at more than one conjugate. It follows that lenses designed for a range of magnifications must have residual aberrations that cannot be corrected no matter how complicated the lens is made. In this paper it is shown how these residual aberrations can be calculated.

Zoom lenses and computer algebra

I show how computer algebra can be of material help in determining the potential quality of various zoom lens arrangements. One fortuitous result of this work is a proof that, when the object is kept at infinity, it is possible in principle to design zoom lenses for which all third-, fifth-, and seventh-order aberrations are corrected over a continuous range of zoom settings limited only by the restriction that the lens groups may not run into each other.

Approximate kernel for wave propagation from a curved surface

We used the stationary-phase approximation to derive an approximate kernel for the propagation of a monochromatic wave specified on a curved source plane.