# Profilometry with digital fringe-projection at the spatial and temporal Nyquist frequencies

## TL;DR

This paper introduces a phase-demodulation method for digital fringe-projection profilometry that operates at the highest spatial and temporal Nyquist frequencies, enabling high-sensitivity 3D surface digitization without complex filtering.

## Contribution

It presents a novel approach that uses the highest Nyquist frequencies for spatial and temporal sampling, eliminating the need for spatial low-pass filtering and gamma calibration.

## Key findings

- Achieves high sensitivity in 3D surface digitization.
- Effectively rejects DC component and even harmonics with minimal phase shifts.
- Experimental results confirm the method's accuracy and robustness.

## Abstract

A phase-demodulation method for digital fringe-projection profilometry using the spatial and temporal Nyquist frequencies is presented. It allows us to digitize tridimensional surfaces using the highest spatial frequency ({\pi} radians per pixel) and consequently with the highest sensitivity for a given digital fringe projector. Working with the highest temporal frequency ({\pi} radians per temporal sample), the proposed method rejects the DC component and all even-order distorting harmonics using a bare-minimum 2-step phase shift. The proposed method is suitable for digitization of piece-wise continuous surfaces because it does not require spatial low-pass filtering. Gamma calibration is unnecessary because the projected fringes are binary, and the harmonics produced by the binary profile can be easily attenuated with a slight defocusing on the digital projector. Viability of the proposed method is supported by experimental results showing complete agreement with the predicted behavior.

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Source: https://tomesphere.com/paper/1706.08592