Phase-shifting interferometry (PSI)^[2][3] is an optical metrology technique for measuring surface topography and wavefront shape to sub-nanometre precision.^[4] It works by recording a short sequence of interferograms, each captured with a known phase offset between the reference and object beams, then solving for the surface height at every pixel simultaneously.^[5][6] Height measurement repeatability is typically below 1 nm, independent of field size.^[1] Before PSI, the standard approach was to trace fringe centres in a static interferogram by eye or with image-processing software, which was a labour-intensive, sparse, and unable to resolve the sign of surface deviations from a single image.^[7]

The phase shift is most often introduced by a piezoelectric transducer (PZT) moving the reference mirror in steps of roughly a quarter wavelength of optical path between frames.^[8][9] With at least three frames, the three unknowns at each pixel namely, background intensity, fringe contrast, and surface phase, are over-determined and can be solved with an arctangent formula.^[10][11] The raw output is a wrapped phase map; a phase-unwrapping^[12] step removes the 2π jumps to give the final height map.^[13][14] PSI can be implemented in Twyman–Green, Fizeau, Mach–Zehnder, and common-path configurations.^[8]

P. Carré described a four-frame algorithm tolerant of unknown step sizes as early as 1966.^[15][16] The pivotal step toward practical use came in 1974, when Bruning and colleagues at Bell Laboratories built a fully digital, computer-controlled system for testing optical surfaces and lenses.^[17] This is often cited as the birth of modern PSI.^[6] Widespread industrial adoption came in the 1980s as affordable CCD arrays and desktop computers made real-time phase calculation possible.^[10] Comprehensive reviews by Creath (1988) and Greivenkamp and Bruning (1992) cemented PSI as the standard framework for precision interferometric metrology.^[18][19]

The four-step algorithm with π/2 steps is the most common basic form.^[10] Schwider and colleagues (1983) showed that a five-step variant largely cancels errors from PZT miscalibration.^[20] Hariharan, Oreb, and Eiju (1987) independently derived the same formula, now known as the Schwider–Hariharan algorithm.^[21] The main remaining error sources are mechanical vibration during acquisition, detector nonlinearity, and stray reflections; higher-order algorithms and simultaneous multi-channel designs have been developed to address each of these.^[22]

Common uses include optical component testing, semiconductor wafer and MEMS characterisation, and precision-engineering quality control.^[1][23]