Instantaneous wavefront measurement based on deflectometry

Abstract

The deflectometry enables high-precision wavefront measurement with large dynamic range. Traditional multi-step phase-shifting fringe-illumination deflectometric methods involve at least three sinusoidal phase-shifting fringe patterns and require a sequential projection, making it not feasible for the instantaneous measurement. In this paper, a colorcoded method with frequency-carrier patterns is proposed to achieve the instantaneous wavefront measurement based on deflectometry. With the color extraction from different channels, composite patterns in x and y directions can be well separated with a single shot. Then, the phase-shifting patterns encoded in different frequencies can be demodulated with the designed filters, by which the local wavefront slopes can be obtained simultaneously to reconstruct the wavefront under test. Both the numerical simulation and experiments are performed to validate the feasibility of proposed method. The proposed method provides a feasible way for the real-time and instantaneous measurement with large dynamic range based on deflectometry.

Deflectometry for specular surfaces: an overview

“…Further research [478][479][480][481][482][483][484][485][486][487][488][489] has provided an even better understanding of the available options [490]. An exciting new trend in multi-period coding is to use of the sum of individual phases (as opposed to the difference) to achieve narrow virtual fringe spacings that are no longer resolvable optically [370,[491][492][493][494][495]. The actual narrow fringe patterns are best designed so that their period (and their advancement during phase stepping) is an integer number of pixels.…”

“…Temporal position coding is the safest approach for complex objects; if one can assume that the fringe patterns do not deform much, it is also possible to encode the required frequencies into one phase-shifting sequence in a so-called composite fringe pattern [163,[495][496][497][498][499][500][501]. Above, we have discussed crossed fringes and how they must share the dynamic range, and the same is of course true of signals mixed for a pseudo-temporal phase shift.…”

“…The addition of color information allows simultaneous three-step phase shifting [352,[505][506][507], multi-frequency display [508], or direction separation by color [470,474,495,509], including simple multi-frequency coding for easier unwrapping. Even discrete codes have been explored for use with colors [430,510], and a combination of color and direction coding has been presented as well [511].…”

Deflectometry for specular surfaces: an overview

“…Further research (Osten et al, 1996;Surrel, 1997c;Towers et al, 2004;Xia and Liu, 2005;Falaggis et al, 2011;Falaggis et al, 2013;Falaggis et al, 2014;Li et al, 2016;Wei et al, 2017;Xiao et al, 2017;Allgeier et al, 2019;Petz et al, 2020b) has provided an even better understanding of the available options ). An exciting new trend in multi-period coding is to make use of the sum of individual phases (as opposed to the difference) to achieve narrow virtual fringe spacings that are no longer resolvable optically (Servin et al, 2015;Xiong et al, 2017;Servin et al, 2018;Wang, 2018;DeMars et al, 2019;Xie et al, 2019). The actual narrow fringe patterns are best designed so that their period (and their advancement during phase stepping) is an integer number of pixels.…”

“…Temporal position coding is the safest approach for complex objects; if one can assume that the fringe patterns do not deform much, it is also possible to encode the required frequencies into one phase-shifting sequence in a so-called composite fringe pattern (Li et al, 1997;Guan et al, 2003;Sansoni and Redaelli, 2005;Su and Liu, 2006;Kim et al, 2009;Liu et al, 2010;Kludt and Burke, 2018;Xie et al, 2019). Above, we have discussed crossed fringes and how they must share the dynamic range, and the same is of course true of signals mixed for a pseudo-temporal phase shift.…”