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Digital sinusoidal fringe generation with defocusing for profilometry: exponential binary vs squared binary patterns

Defocusing binary patterns to generate digital sinusoidal fringe patterns with a digital-light-processing projector has been pivotal in phase measurement profilometry with fringe projection techniques. However, despite all its merits, squared binary defocusing (SBD) has been borne with limitations: (1) limited defocusing range; (2) difficulty in quantifying the amount of defocus together with non-negligible residual high-frequency harmonic phase errors. Recently, three-dimensional profilometry with exponential fringe projection has been successfully demonstrated to be robust to high-order harmonics and related phase errors. In this paper, we compare the potential errors for digital sinusoidal fringe generation with both binary-exponential defocusing (BED) and squared binary defocusing (SBD) induced by varying the degree of defocusing specifically at low levels of defocus or extended defocusing range. Results show that in most scenarios, the error for the BED method is smaller than that of the SBD method especially at extended defocusing range. Therefore, generating a sinusoidal fringe image using a BED method seems to be appealing and promising for three-dimensional profilometry with projector defocusing at an extended defocusing or projection range.