Theory of image formation using the Talbot effect

Effect of nonuniform pit structure on self-imaging of periodical gratings

Self-imaging possibilities for periodical gratings that have nonuniform pit structure are theoretically investigated. The diffraction of periodic arrays in the deep Fresnel region is analyzed according to the scalar diffraction theory. The expressions of the diffraction intensities of three different gratings that have binary square, binary circle, and Gaussian pit structure are considered. Talbot images of gratings with nonuniform pit structure are predicted to appear at multiple certain distances. The present paper shows that even a structure in short-range disorder may take on the self-imaging effect in a Fresnel field.

Phase anomalies in Talbot light carpets of self-images

An interesting feature of light fields is a phase anomaly, which occurs on the optical axis when light is converging as in a focal spot. Since in Talbot images the light is periodically confined in both transverse and axial directions, it remains an open question whether at all and to which extent the phase in the Talbot images sustains an analogous phase anomaly. Here, we investigate experimentally and theoretically the anomalous phase behavior of Talbot images that emerge from a 1D amplitude grating with a period only slightly larger than the illumination wavelength. Talbot light carpets are observed close to the grating. We concisely show that the phase in each of the Talbot images possesses an anomalous axial shift. We show that this phase shift is analogous to a Gouy phase of a converging wave and occurs due to the periodic light confinement caused by the interference of various diffraction orders. Longitudinal-differential interferometry is used to directly demonstrate the axial phase shifts by comparing Talbot images phase maps to a plane wave. Supporting simulations based on rigorous diffraction theory are used to explore the effect numerically. Numerical and experimental results are in excellent agreement. We discover that the phase anomaly, i.e., the difference of the phase of the field behind the grating to the phase of a referential plane wave, is an increasing function with respect to the propagation distance. We also observe within one Talbot length an irregular wavefront spacing that causes a deviation from the linear slope of the phase anomaly. We complement our work by providing an analytical model that explains these features of the axial phase shift.

Digital holographic interferometry for measurement of temperature in axisymmetric flames

In this paper, experimental investigations and analysis is presented to measure the temperature and temperature profile of gaseous flames using lensless Fourier transform digital holographic interferometry. The evaluations of the experimental results give the accuracy, sensitivity, spatial resolution, and range of measurements to be well within the experimental limits. Details of the experimental results and analysis are presented.

Talbot images of wavelength-scale amplitude gratings

By means of experiment and simulation, we achieve unprecedented insights into the formation of Talbot images to be observed in transmission for light diffracted at wavelength-scale amplitude gratings. Emphasis is put on disclosing the impact and the interplay of various diffraction orders to the formation of Talbot images. They can be manipulated by selective filtering in the Fourier plane. Experiments are performed with a high-resolution interference microscope that measures the amplitude and phase of fields in real-space. Simulations have been performed using rigorous diffraction theory. Specific phase features, such as singularities found in the Talbot images, are discussed. This detailed analysis helps to understand the response of fine gratings. It provides moreover new insights into the fundamental properties of gratings that often find use in applications such as, e.g., lithography, sensing, and imaging.

Measurement of temperature profile of a gaseous flame with a Lau phase interferometer that has circular gratings

We have investigated the utility of a Lau phase interferometer with circular gratings and a white-light source to measure the temperature and temperature profile of an axisymmetric flame. The temperature measured with a Lau phase interferometer is in good agreement with the temperature measured with a thermocouple and multilogger. Detailed theoretical analysis and experimental investigation are presented.