Circular–linear grating Talbot interferometry with moiré Fresnel imaging for beam collimation

Abstract

The Talbot interferometer using different self-imaging structures is studied and applied for laser beam collimation. A circular-linear grating pair enables visual dynamic detection and computer moirégram analysis. Automatic single-frame processing is performed using a 2D continuous wavelet transform. Conducting moirégram imaging in the Fresnel field of a double-diffraction system is brought up to avoid using distortion-free objectives and simplify the experimental setup. Simulation and experimental results document the method properties and provide beautiful exemplification of the double-grating Fresnel diffraction theory developed earlier.

Dual self-image technique for beam collimation

“…Talbot interferometry is used suitably modified by Patorsky to prevent the continued displacement of the second grating. In this case, the accuracy is ±20 µm [16]. Also based on the Talbot effect, Wang obtained accuracy of ±10 −7 rad when he collimates monochromatic beams with a lens of focal distance f = 50 mm [?].…”

“…∆z is the distance between the source s and the focal point of the lens whose focal length is f and whose principal plane is H, z 0 is the distance between s and H, z 1 is the distance from H to the diffraction grating G whose period is p, z 2 = lz T is the distance from G to a CMOS sensor placed at one self-image plane and finally, p z is the period of the signal acquired by CMOS sensor. setup has been modified in different ways, by changing the periods of the gratings, by transverse shifting one of the gratings, etc [14,15,16]. Another method consists of replacing one of the linear gratings by a circular grating [16].…”

Lissajous figure-based single-frame collimation technique

“…Most of them are based on interferometry [1][2][3][4][5] or on self-imaging techniques [6][7][8][9]. In addition, several techniques have been proposed in the last years [10][11][12][13][14][15]. In particular, several collimation methods based on self-imaging that do not need a lateral displacement of the grating have been proposed, being these devices simple an stable.…”

“…In particular, several collimation methods based on self-imaging that do not need a lateral displacement of the grating have been proposed, being these devices simple an stable. In [11] one circular grating is used instead of a linear grating and in [12] the collimation degree of the beam is obtained by measuring the period of one self-image produced by an amplitude Ronchi grating and comparing it with that of the grating. Nevertheless, the experimental configuration needs to be performed very accurately, since the period of one self-image is compared to the period of the grating and misalignments or environmental variations may produce wrong and inaccurate results.…”

Phase-shifting lateral shearing interferometry using wedge-plate and interferometric grating

“…Errors in beam collimation may result in severe degradation of system performance. Automated interferogramanalysis-based techniques have been incorporated to improve the measurement characteristics [17][18][19][20][21]. The use of these techniques has increased the performance of the collimation test substantially.…”