www.osa-opn.org OPTICS | ENGINEERING 10 | OPN Optics & Photonics News L ateral resolution quantiies our abil- ity to separate individual features from each other in an image. Traditional speciications for resolving power employ either single numbers, such as Rayleigh or Sparrow criteria, or detailed response information as a function of spatial period or frequency, as in the modulation transfer function (MTF). For straight- forward incoherent imaging of light and dark or contrasting colors, as in a camera or a telescope, these deinitions are clear and have well-known procedures for speciication conirmation. However, it is less clear how to deine resolving power for instruments that measure surface shape. Interferometry, for example, relies on the light wave phase as the fundamental metrology principle. he phase is tucked inside a sine or cosine function and must be extracted by a process that is more com- plex than simple intensity imaging—for example, by shifting the phase in a con- trolled way and recording what happens. As a practical reality, metrology instruments report 3-D surface proiles take special care to deine appl icable measurement conditions. Chief among these conditions is that the surface height deviations should be small with respect to the wavelength—less than 50 nm for visible light, especially if features are close to each other. If we respect this limitation, we can leverage traditional and familiar 2-D imaging deinitions to describe the 3-D topographical measure- ment properties. Specifying and verifying lateral resolution he most common lateral resolution speci ication for interferometers is a single number, expressing the smallest separation between features that can be distinguished in an image. For genera- tions this was the Rayleigh criterion, whereby two image points are considered resolved if the distance for the difraction maximum of one point image coincides with the irst minimum of the other. he more generous Sparrow criterion corresponds to the separation between that may difer from the feature’s shape, depending on its heights and separations. Consequently, surface proilers do not have generally applicable lateral resolu- tion speciications that are valid for all surface shapes. Although there are pub- lished drafts of international standards, there is not complete agreement among engineers on a deinition for the resolv- ing power for a real measurement of surface topography. In spite of this, users of 3-D optical proiling tools insist on lateral resolu- tion speciications and manufacturers are compelled to generate them. he good news is that it is possible to develop meaningful speciications for compari- son and evaluation, provided that we Interferometry relies on the light wave phase as the fundamental metrology principle. The Meaning and Measure of Lateral Resolution for Surface Profiling Interferometers Peter de Groot, Xavier Colonna de Lega, Daniel Sykora and Leslie Deck Optical interferometers for surface characterization provide detailed information about surface topography, and they carry specifications related to the ultimate resolving power for 3-D imaging. It is worthwhile for engineers to understand the meaning of these specifications and the methods for validating them. Zygo Corp.