FOCOIVA Lens: A Scanner in the Lateral and Longitudinal Directions.

We propose what to our knowledge is a novel optical system that can scan an optical axis simultaneously in the perpendicular and the longitudinal directions (a two-dimensional scanner), which we have named the FOCOIVA (acronym for focal constant and image variable) lens system. We give the equations for first-order analysis and also the equations of motion for the lenses. Examples calculated with these equations are presented, and finally we give the optical designs for the writing system that will be used for a reader of digital documents.

Ronchi test with a square grid.

We use a square grid in the Ronchi test. This grid allows processing of both the X and the Y directions when calculating optical path difference. We use trapezoidal integration to analyze the new patterns, since it does not have the smoothing drawback at the edges of the wave front.

Exact Design of Aplanatic Microscope Objectives consisting of Two Conic Mirrors.

The necessary equations are derived for the design of aplanatic microscope objectives consisting of two mirrors, one concave and the other convex. The first-order parameters are calculated along with the conic constants of the mirrors, determined by means of an exact analysis to arrive at an aplanatic system.

Multiple-path telescope: third-order design.

Exact results for the magnification and effective focal length of a multiple-path telescope are presented. We present analytical results for the third-order design of this system, using the Seidel sums for the five aberration terms. Numerical calculations are used throughout to corroborate these results. Third-order aberrations remain small or at least stable as the number of paths is increased.