Profilometry by phase-shifted Talbot images

Fringe projector with submillimeter fringe spacing at a meter-scale field of view

State-of-the-art fringe projection systems generate fringe patterns using digital light projectors (DLP). The axial uncertainty is limited by the smallest fringe period and is directly related to the pixel count. This results in limited accuracy of current DLP systems that affect applications such as in situ measurements for laser powder bed fusion systems, where a submillimeter fringe period is needed for field-of views larger than 500m m×500m m. This work presents a scalable fringe projection technique that enables the generation of stable fringe patterns over a large field of view spanning several meters while maintaining submillimeter fringe periods. This system uses geometric phase gratings to enable variable fringe spacing and fringe orientation capabilities. The system shears a coherent beam in the Fourier plane using a pair of geometric polarization gratings. The separation between the gratings directly affects the fringe spacing, and the orientation of the gratings affects the fringe orientation. The depth of focus is only limited by the coherence of the light source, enabling high fringe periods even on tilted planes. The system is designed with a single path configuration, making the system more robust to environmental noise. With a rotating linear polarizer, we demonstrate that phase-shifting methods could be employed to acquire phase information about the object. This paper employs a single-shot Fourier transform phase estimation technique to process the intensity maps acquired using projected fringe patterns. Further, we demonstrate the capabilities of the system to produce submillimeter fringe spacing and the ability to project fringes on larger scales for measurements.

Enhanced microwave metrology using an optical grating in Rydberg atoms

An enhanced measurement of the microwave (MW) electric (E) field is proposed using an optical grating in Rydberg atoms. Electromagnetically induced transparency (EIT) of Rydberg atoms appears driven by a probe field and a control field. The EIT transmission spectrum is modulated by an optical grating. When a MW field drives the Rydberg transition, the central principal maximum of the grating spectrum splits. It is interesting to find that the magnitude of the sharp grating spectrum changes linearly with the MW E-field strength, which can be used to measure the MW E-field. The simulation result shows that the minimum detectable E-field strength is nearly 1/8 of that without gratings, and its measurement accuracy could be enhanced by about 60 times. Other discussion of MW metrology based on a grating spectrum is also presented.

Diffraction by gratings with random fill factor

In this work, we analyze the diffraction produced by Ronchi gratings where the fill factor is not constant, but presents random fluctuations around its nominal value. This effect can be produced while developing the grating with etchers since the process can be slightly unpredictable. We obtain the theoretical formalism to describe the intensity produced by the grating at near and far field, showing that smoothing of the self-images is produced at the near field and, consequently, cancellation of higher diffraction orders is obtained at the far field. In addition, different nominal fill factors produce different diffraction behaviors in terms of the randomness. We corroborate the analytical formalism using a direct integration method based on the Rayleigh-Sommerfeld formula and conclude that the numerical results are in high agreement with the theoretical predictions.

Diffraction by random Ronchi gratings

In this work, we obtain analytical expressions for the near-and far-field diffraction of random Ronchi diffraction gratings where the slits of the grating are randomly displaced around their periodical positions. We theoretically show that the effect of randomness in the position of the slits of the grating produces a decrease of the contrast and even disappearance of the self-images for high randomness level at the near field. On the other hand, it cancels high-order harmonics in far field, resulting in only a few central diffraction orders. Numerical simulations by means of the Rayleigh-Sommerfeld diffraction formula are performed in order to corroborate the analytical results. These results are of interest for industrial and technological applications where manufacture errors need to be considered.

Self-imaging of partially coherent light in graded-index media

We demonstrate that partially coherent light beams of arbitrary intensity and spectral degree of coherence profiles can self-image in linear graded-index media. The results can be applicable to imaging with noisy spatial or temporal light sources.

Diffraction by metallic planar gratings

In this work, a kind of grating that, to our knowledge, has not yet been analyzed for diffractive purposes is proposed. The mentioned grating consists of metallic intercalated slits of two different metals on a glass substrate. The main characteristic and peculiarity of the proposed grating is that it is totally planar, without any slopes or grooves. We analyze the intensity distribution at the near- and far-field produced by the grating. The method used is rigorous-coupled wave analysis. We show how the metallic layer thickness is a crucial parameter to achieve the highest efficiency of the diffraction orders and, therefore, the highest contrast of the diffracted fringes. To conclude, we investigate how parameters such as the period, duty cycle, wavelength, or the used metals affect the diffracted field. Some nonexpected behaviors have been found. As we demonstrate by comparing with other kinds of gratings, the proposed grating would be useful in applications in which fringes are needed in both the front and back sides of the grating.

Grating-based at-wavelength metrology of hard x-ray reflective optics

A mean of characterizing the tangential shape of a hard x-ray mirror is presented. Derived from a group of methods operating under visible light, its application in the x-ray domain using an x-ray absorption grating allows recovery of the mirror shape with nanometer accuracy and submillimeter spatial resolution. The method works with incoherent light, does not require any a priori information about the mirror characteristics and allows shape reconstruction of x-ray reflective optics under thermal and mechanical working conditions.

Continuous self-imaging regime with a double-grating mask

We analyze the Talbot effect produced by a mask composed of two diffraction gratings. Combinations with phase and amplitude gratings have been studied in the near-field regime. For a two-phase-gratings configuration, the Talbot effect is canceled, even when using monochromatic light; that is, the intensity distribution is nearly independent of the distance from the mask to the observation plane. Therefore, the mechanical tolerances of devices that use the Talbot effect may be improved. In addition, the spatial frequency of the fringes is quadrupled, which improves the accuracy of devices that employ this mask. An experimental verification for the best case two phase gratings, has also been performed, validating the theoretical results.

Fringe projection with a sinusoidal phase grating

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.

Automated collimation testing using a temporal phase shifting technique in Talbot interferometry

We propose a quantitative approach toward the detection of collimation of a coherent optical beam. For detection of collimation position of the collimator, a temporal phase shifting technique has been incorporated into Talbot interferometry. The slope of the phase maps depicts the collimation position of the collimator. This technique offers high precision, accuracy, and provides automated output.

Talbot effect with rough reflection gratings

The Talbot effect is analyzed when steel tape gratings are used. These gratings are made on a steel substrate, and, because of the manufacture process, both levels of the grating are rough with different roughness parameters. A theoretical analysis based on Fresnel regime, which considers the statistical properties of roughness, is developed. Analytical formulas that show a decreasing exponential dependence on the intensity in terms of the distance between the grating and the observation plane are obtained, and an experimental verification is also performed.

Two-wavelength Talbot effect and its application for three-dimensional step-height measurement

The phenomenon of Talbot self-image shift by changing the wavelength of the illuminating light is described and demonstrated experimentally. A periodic grating is illuminated by light with wavelengths lambda1 and lambda2 generated by two lasers, and the Talbot self-images are recorded along the longitudinal direction at individual wavelengths. The Talbot self-image shift due to the change in the wavelength of light is implemented for the measurement of the three-dimensional step height of a large discontinuous object without any phase ambiguity problem. Fourier-transform fringe analysis was used to determine the maximum contrast of the high-visibility bands for the measurement of the step height of the object. The main advantages of the proposed system are nonmechanical scanning, high stability because of its common path geometry, compactness, and a wide range of measurement as compared to interferometric three- dimensional profilers.