Fringe projection with a sinusoidal phase grating

Abstract

Phase-shifting profilometry requires projection of sinusoidal fringes on a 3D object. We analyze the visibility and frequency content of fringes created by a sinusoidal phase grating at coherent illumination. We derive an expression for the intensity of fringes in the Fresnel zone and measure their visibility and frequency content for a grating that has been interferometrically recorded on a holographic plate. Both evaluation of the systematic errors due to the presence of higher harmonics by simulation of a profilometric measurement and measurement of 3D coordinates of test objects confirm the good performance of the sinusoidal phase grating as a projective element. In addition, we prove theoretically that in comparison with a sinusoidal amplitude grating this grating produces better quality of fringes in the near-infrared region. Sinusoidal phase gratings are fabricated easily, and their implementation in fringe projection profilometry facilitates construction of portable, small size, and low-cost devices.

Continuous casting slab surface crack depth measurement using sinusoidal phase grating method

“…Figure 1 illustrates the fringe projection technique diagram in which a sinusoidal grating is projected onto the surface of object through a grating projector. 15 In Fig. 1, P is the centre of the projector's exit pupil, I is the centre of the camera lens entrance pupil, w is the distance from both P and I and L is the distance from both P and the reference plane.…”

“…Figure 1 illustrates the fringe projection technique diagram in which a sinusoidal grating is projected onto the surface of object through a grating projector. 15…”

“…The deformed grating phase which is related to pixel position and height distributions is given by 7 where Z ( m , n ) is the object height of the m th horizontal and the n th vertical pixel-counters (mm), and P is the fringe projection period (s).…”

“…The use of projected fringes for the measurement of surface profile is a well developed technology. 7,8 The sinusoidal fringes are projected onto the object surface by a conventional imaging system. If the projection and observation directions are different, the phase distribution of the measured fringe pattern includes information on the surface height profile of the object.…”

Relaxation of the Talbot condition in generalized grating imaging

“…These effects have been used in many applications, which include periodic pattern projection [12][13][14], optical shearing interferometry [15][16][17][18][19], array illuminators [20,21], X-ray interferometry [22][23][24], and matter-wave interferometry [25]. These applications will become more important because fabrication techniques of micro-elements including gratings are making much progress.…”