What Is Phase Shifting Interferometry?

Phase shifting interferometry is an optical measurement technique that quantifies the phase difference between two coherent wavefronts by recording a sequence of interference patterns, each captured at a known phase offset between the reference and test beams. The resulting data yields a full-field, three-dimensional surface map with sub-nanometer height resolution, making the technique the standard for characterizing optical flats, lenses, mirrors, and precision-machined components. The method draws on optical physics, signal processing, and precision mechanical engineering.

Classical two-beam interferometry reveals surface topography through the spacing and curvature of interference fringes, but locating fringe centers by eye or by image processing limits accuracy and resolution. Phase shifting interferometry replaces that subjective analysis with a rigorous algebraic framework: by stepping the reference phase through a known sequence, typically four positions separated by 90 degrees, the measurement system captures enough data at every detector pixel to solve directly for the optical path difference at that point.

The Phase-Stepping Algorithm

The intensity recorded at each pixel in a phase-shifting interferometer follows the expression I = B + A cos(phi + alpha), where B is the dc background, A is the fringe contrast, phi is the local phase difference to be measured, and alpha is the applied phase step. Recording intensities at four phase steps of 0, pi/2, pi, and 3pi/2 and combining them in an arctangent formula yields phi at every point simultaneously. This approach, pioneered and documented in detail by James Wyant at the University of Arizona Optical Sciences Center, eliminated the need to find fringe centers and made it practical to transfer interferometric data directly to a computer for automated analysis.

The phase step is most commonly introduced by a piezoelectric transducer (PZT) that moves the reference mirror in controlled increments. Nonlinearity in PZT motion introduces phase errors; self-calibrating algorithms that use additional intensity frames can reduce this sensitivity substantially. An alternative approach uses a tunable diode laser and varies the wavelength to produce the required phase shifts without any moving mirror, improving vibration immunity.

Measurement Range and Accuracy

A single-wavelength PSI measurement resolves height variations only within a window of one-half wavelength, roughly 316 nm for a 633 nm helium-neon laser source, before phase wrapping makes the result ambiguous. Two-wavelength PSI extends the unambiguous measurement range by combining data from two laser wavelengths to synthesize a much longer equivalent wavelength, allowing measurement of steeper slopes and larger steps. The Newport guide to phase-shifting interferometry for optical surface quality describes the relation phi = 4 pi h / lambda, which ties measured phase directly to surface height, and explains how modern tunable laser sources simplify implementation.

Measurement repeatability below 1 nm is routinely achieved in controlled environments. Sensitivity to vibration remains the principal limitation of conventional PSI; dynamic interferometers address this by acquiring all phase-shifted frames simultaneously using polarization optics and multiple cameras, allowing measurements in environments that would defeat sequential-capture systems.

Algorithms and Error Sources

Beyond the basic four-bucket algorithm, researchers have developed five-step, seven-step, and Carré algorithms that trade data-collection time for reduced sensitivity to specific error sources such as phase-shifter miscalibration or laser intensity drift. Spurious reflections in Fizeau and Twyman-Green interferometer cavities produce parasitic fringe patterns that corrupt phase maps; a body of published work on PSI error correction addresses these through wavelength-tuning methods and coherence selection.

Applications

Phase shifting interferometry has applications across precision measurement and fabrication, including:

• Optical flat and lens characterization during manufacturing
• Hard disk surface flatness and read/write head air-bearing measurement
• Semiconductor wafer bow and surface roughness inspection
• Microelectromechanical systems (MEMS) component geometry verification
• Astronomical mirror and telescope optics qualification