Beam geometry, alignment, and wavefront aberration effects on interferometric differential wavefront sensing

Abstract

Heterodyne interferometry is a widely accepted methodology with high resolution in many metrology applications. As a functionality enhancement, differential wavefront sensing (DWS) enables simultaneous measurement of displacement, pitch, and yaw using a displacement interferometry system and a single beam incident on a plane mirror target. The angular change is measured using a weighted phase average between symmetrically adjacent quadrant photodiode pairs. In this paper, we present an analytical model to predict the scaling of differential phase signals based on fundamental Gaussian beams. Several numerical models are presented to discuss the effects of physical beam parameters, detector size, system alignment errors, and beam wavefront aberrations on the DWS technique. The results of our modeling predict rotational scaling factors and a usable linear range. Furthermore, experimental results show the analytically predicted scaling factor is in good agreement with empirical calibration. Our three degree-of-freedom interferometer can achieve a resolution of 0.4 nm in displacement and 0.2 μrad in pitch and yaw simultaneously.

Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology

“…The majority of the 25.5 nm standard deviation is contributed to those two transient sections; however, we have previously demonstrated that this schematic can achieve sub-nanometer levels of accuracy and resolution for displacement. 26,27 Since the motion of the moving target introduces a Doppler shift to the measurement signal, the theoretical maximum measurement speed should satisfy |v m | < f s λ/2, where v m is the maximum moving stage velocity, f s is the split frequency in our system, and λ is the wavelength of the laser source. The current heterodyne frequency in our measurement system is set to 70 kHz which corresponds to a 0.022 m/s maximum stage velocity.…”

“…Although pitch and yaw measurements operate with the same interferometric principles, the linear range is limited to nominally 100 µrad as estimated in the previous work. 27 Straightness measurement range is based on a combination of beam diameter and PSD active area. Based on our experimental beam diameter (3.3 mm) and PSD dimensions (25 mm × 25 mm), the straightness range is 10 mm.…”

“…where φ represents detected phase of quadrant A, B, C, or D, L pitch and L yaw represent a calibrated equivalent length in pitch and yaw measurements that is primarily dependent on beam diameter, detector size, alignment errors, and beam wavefront. A detailed description for this three DOF interferometer 26 and a model which effectively predicts the equivalent lengths (L pitch and L yaw ) with high accuracy 27 are shown in our previous work.…”

Embedded Sensor System for Five-degree-of-freedom Error Detection on Machine Tools

“…Chen developed a 2-beam 6-DOF measurement system based on a straightness interferometer with rotational error compensation. Gillmer and Yu [14][15][16] developed a single beam 6-DOF measurement system based on Polarization Optics and wavefront aberration effects.…”

Fake tilts in differential wavefront sensing

“…Differential wavefront sensing -where the angle between the interfering wavefronts is measured via the phase difference between the travelling fringes detected by segmented photodiodes -makes it possible to simultaneously measure both the target translation and tilts with a single laser beam [1][2][3][4]. The working principles, operation, measurement equation, and effect of mismatches and aberrations are reported in [5][6][7].…”