Centroid approach for estimating modulation peak in broad-bandwidth interferometry

An interferometric profiling method wherein time-domain interferometric measurements are performed by illuminating though a microscope objective a test surface and a reference surface aligned in an optical path and by scanning in time each of a plurality of predetermined adjacent regions of the test surface to provide an interference pattern detected on a corresponding plurality of regions of a photosensitive surface, said method comprising the following steps:

• (a) using a broad-bandwidth light source to illuminate the test surface and the reference surface while effecting a multi-step relative translation therebetween to produce a plurality of interference patterns and a corresponding plurality of irradiance signals on said photosensitive surface, such that an irradiance signal for each of said adjacent regions of the test surface is generated for a predetermined scanning position at each step of said relative translation and detected at said corresponding regions of the photosensitive surface;
• (b) estimating a relative-translation position corresponding to a peak value of a modulation function associated with said irradiance signal for each of said adjacent regions of the test surface;
• and
• (c) processing said relative-translation position to produce a topographic map of said test surface for on-line display;
• wherein said step (b) comprises the step of calculating a centroid value for a predetermined converging function of a first-order derivative of said irradiance signal and using said centroid value as a relative-translation position corresponding to a peak value of said modulation function.