Retrace error: interferometry's dark little secret

Abstract

Fizeau type phase measuring interferometers are widely used in the optics industry for surface metrology. Measurement of spherical surfaces requires the use of transmission spheres which are commercially available in various F-numbers. A basic assumption of Fizeau interferometry is that the light reflected off the reference surface, called the reference beam, and the light reflected off the surface being tested, called the test beam, follow a common path back through the optics. For this to be strictly true, we would need the surface being tested to be perfectly spherical and positioned exactly concentric with the reference surface. Measurement inaccuracy that results from failure to meet this condition is referred to as retrace error. Retrace error has been largely ignored with regard to testing nominally spherical surfaces, yet it can be significant when high test accuracy is needed. In this paper, the author identifies two types of retrace error resulting from the test setup: Axial; induced spherical aberration resulting from defocus, and Transverse; induced coma as a result of tilt. The magnitude and exact form of retrace error is shown to be a function of the optical design of the transmission sphere. It is shown that, for the most part, measurement accuracy is independent of the transmitted wavefront error of the transmission sphere. It is shown that retrace error can be modeled in a lens design program with excellent agreement to measurement data. Specific design examples will be presented, including improvements to minimize retrace error. The significance of retrace error to the test accuracy of both spherical and aspheric surfaces will be discussed.