FRINGE 2005 (Stuttgart) Preprint Interpreting interferometric height measurements using the instrument transfer function Peter de Groot and Xavier Colonna de Lega Zygo Corporation Laurel Brook Rd, Middlefield, CT 06455, USA 1 Introduction Of the various ways of characterizing a system, one of the most appeal- ing is the instrument transfer function or ITF. The ITF describes system response in terms of an input signal’s frequency content. An every-day example is the graph of the response of an audio amplifier or media player to a range of sound frequencies. It is natural therefore to characterize surface profiling interferometers according to their ITF. This is driven in part by developments in precision optics manufacturing, which increasingly tolerance components as a func- tion of spatial frequency [1]. Metrology tools must faithfully detect pol- ishing errors over a specified frequency range, and so we need to know how such tools respond as a function of lateral feature size. Here we review the meaning, applicability, and calculation of the ITF for surface profiling interferometers. This review leads to useful rules of thumb as well as some cautions about what can happen when we apply the concept of a linear ITF to what is, fundamentally, a nonlinear system. Ex- perimental techniques and example results complete the picture. Our approach is informal, as is appropriate for a conference paper. The foundation for a rigorous understanding of the ITF is well documented in the literature, including the well-known books by Goodman [2]. 2 Linear systems ITF is most commonly understood to apply to linear systems, which share certain basic properties that lend themselves naturally to frequency analysis. Principally, the response of a linear system is the sum of the re- sponses that each of the component signals would produce individually. Copyright 2005 Society of Photo-Optical Instrumentation Engineers. This paper will be published in Proceedings of SPIE and is made available as an electronic preprint with permission of SPIE. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.