Snap-shot profilometry with the Empirical Mode Decomposition and a 3-layer color sensor

Abstract

Remote sensing finds more and more applications, from industrial control, to face recognition, not forgetting terrain surveying. This trend is well exemplified by fringe projection techniques, which enjoyed a considerable development in the recent years. In addition of high requirement in terms of measurement accuracy and spatial resolution, the end-users of full-field techniques show a growing interest for dynamic regimes. We report here what we believe to be the use for the first time of a CMOS 3-layer color sensor (Foveon X3) as the key element of a RGB fringe projection system, together with the processing specifically elaborated for this sensor. The 3-layer architecture allows the simultaneous recording of three phase-shifted fringe patterns and features the precious asset of an unambiguous relationship between the physical sensor pixel and the picture pixel and this for each color layer, on the contrary of common color sensor arrays (Bayer mosaic and tri-CCD). Due to the overlapping of the spectral responses of the layers, color transformation is mandatory to achieve the separation of the three phase-shifted RGB projected fringe patterns. In addition, we propose the use of the Empirical Mode Decomposition to equalize the non-uniform responses of the three layers. Although the conversion of the phase into a height is of primary importance in an actual measurement, it is not treated here, the literature being profuse on the central projection model. 6. P. Groot, "Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window," Appl. Opt. 34(22), 4723-4730 (1995). 7. D. W. Phillion, "General methods for generating phase-shifting interferometry algorithms," Appl. Opt. 36(31), 8098-8115 (1997). 8. Y. Surrel, "Design of algorithms for phase measurements by the use of phase stepping," Appl. Opt. 35(1), 51-60 (1996). 9. J. Novak, P. Novak, and A. Miks, "Multi-step phase-shifting algorithms insensitive to linear phase shift errors," ©2011 Optical Society of AmericaOpt. Commun. 281(21), 5302-5309 (2008). 10. X. Colonna de Lega, and P. Jacquot, "Deformation measurement with object-induced dynamic phase shifting," Appl. Opt. 35(25), 5115-5121 (1996). 11. C. Wust, and D. W. Capson, "Surface profile measurement using color fringe projection," Mach. Vis. Appl. 4(3), 193-203 (1991 550-558 (2010). 22. S. Equis, and P. Jacquot, "The empirical mode decomposition: a must-have tool in speckle interferometry?" Opt.Express 17(2), 611-623 (2009). 23. H. A. Aebischer, and S. Waldner, "Simple and effective method for filtering speckle interferometric phase fringe patterns," Opt. Commun. 162(4-6), 205-210 (1999).

Non-dissipative internal optical filtering with solution-grown perovskite single crystals for full-colour imaging

“…In addition to gains in optical efficiency, this design minimizes colour moiré and may, in principle, also allow higher spatial resolution. 11,12 The latter possibility, however, is limited in the case of silicon due to its indirect band gap, requiring thick absorptive layers. In addition, this configuration requires a more complex and costly manufacturing process.…”

Multi-colour microscopic interferometry for optical metrology and imaging applications

“…This approach makes the fringe acquisition as simple as in single-wavelength case. Three different approaches have been used for 3-colour recording:(a) Bayer filter 1-CCD sensor [52][53][54][55], (b) 3-CCD sensor [24,49,52,56], and (c) Foveon X3 sensor [46,52,57]. We will discuss these threestrategies for simultaneous recording of 3-colours in Section-4.…”

“…The Foveon X3 sensor based camera has been used in white-light interferometric applications [67], aerodynamic flow analysis using digital three-colour holographic interferometry [46,52], surface profiling using snap-shot fringe projection profilometry [57]. The RGB interferometry that uses a RGB CCD camera to acquire multiple wavelength interferograms simultaneously is a simpler, faster, and dynamic tool for metrology and imaging applications.…”

Dynamic temperature field measurements using a polarization phase-shifting technique

“…4 Nowadays, some authors present novel algorithms based on this property; for example, in the demodulation form, algorithms focused on harmonics rejections, and recently encountered more accurate results by proposing an extension of the phase-shifting unit cell. 5,6 Other single-shot systems are based on the use of a threelayer sensor to detect three wavelengths; these systems have been applied accurately by fringe projections profilometry 7 and digital holographic system. 8 Interferometric polarization phase-shifting techniques also have been employed before in different techniques; some of them are based on using Wollaston prisms and polarization gratings 9 by using a prism and a glass plate with different thicknesses, 10 and lately a system capable of acting as a fringe projection system, or a shearing interferometer by employing a Savart plate and liquid crystals.…”