Pattern Design of Diffractive Optical Sensor Elements for Multiplex Interferometry

In interferometric optical sensors, phase information is extracted from the modulated light intensity. In the case of free-standing interferometers, operating through the far-field interferogram, multiplex phase detection is not trivial. Multipinhole or multimicrodisk interferometry are examples of common-path interferometers that allow multiplex interferometric phase detection. Thereby an unambiguous interference pattern is required, with no overlap of multiple spatial frequencies. A common pattern in multipinhole interferometry is a circular arrangement. To increase the element density of the pattern, Golomb rulers are an interesting concept. Golomb rulers and rectangles are known from sonar and radar applications. Recently, they were applied for encoding in quantum information systems. In this publication, we investigate different pattern designs of circular diffractors that produce unique spatial frequencies. We introduce design algorithms. The optimization criteria are the uniqueness of the spatial frequencies, which show no overlap with any other frequency, and the density of the microdisk pattern. Golomb patterns increase the element density by about 30% compared to the circular pattern. Depending on the pattern area, the density of the circular Archimedes spiral surpasses by up to 13% the density of a square Golomb pattern, referenced to a circular area. To validate the theoretically designed patterns, examples are fabricated on the basis of photonic crystal microdisk elements and are characterized optically.