Comparative analysis of image pre-filtering techniques for phase-shifted noise-affected interferograms.

Phase-shifting techniques are one of the most promising strategies to extract the phase information and retrieve the parameters of interest (e.g., refractive index, beam collimation, object shape, deformations, thickness, focal length, etc.) from interferograms. However, traditional phase-shifting techniques suffer from both internal and external noise, which reduce measurement accuracy. This paper reports a comparative analysis of the three commonly used filtering techniques, namely, Fourier, windowed Fourier, and wavelet filtering for noise reduction and accurate extraction of phase information from phase-shifted interferograms. Toward this, two basic types of noise (additive and multiplicative noise) are introduced in the simulated interferograms and processed using the pre-filtering strategies. The effect of second-order harmonics in the presence of noise is also examined. In addition, experimental demonstrations of the real-life applicability of the analyses are provided using the interferograms recorded on coherent (Talbot) and incoherent (Lau) grating shearing interferometers. High accuracy in the measurement of defocusing error of the lens is obtained using the filtering strategies. Further inferences and insights are drawn in favor of the pre-filtering techniques.

Automated collimation testing by determining the statistical correlation coefficient of Talbot self-images.

In this paper, we propose a simple, fast, and accurate technique for detection of collimation position of an optical beam using the self-imaging phenomenon and correlation analysis. Herrera-Fernandez et al. [J. Opt.18, 075608 (2016)JOOPDB0150-536X10.1088/2040-8978/18/7/075608] proposed an experimental arrangement for collimation testing by comparing the period of two different self-images produced by a single diffraction grating. Following their approach, we propose a testing procedure based on correlation coefficient (CC) for efficient detection of variation in the size and fringe width of the Talbot self-images and thereby the collimation position. When the beam is collimated, the physical properties of the self-images of the grating, such as its size and fringe width, do not vary from one Talbot plane to the other and are identical; the CC is maximum in such a situation. For the de-collimated position, the size and fringe width of the self-images vary, and correspondingly the CC decreases. Hence, the magnitude of CC is a measure of degree of collimation. Using the method, we could set the collimation position to a resolution of 1 µm, which relates to ±0.25 µ radians in terms of collimation angle (for testing a collimating lens of diameter 46 mm and focal length 300 mm). In contrast to most collimation techniques reported to date, the proposed technique does not require a translation/rotation of the grating, use of complicated phase evaluation algorithms, or an intricate method for determination of period of the grating or its self-images. The technique is fully automated and provides high resolution and precision.

Collimation testing using deflectometry in conjunction with windowed Fourier transform analysis.

In this paper, we demonstrate a simple automated procedure for the detection of collimation of an optical beam by incorporating the windowed Fourier fringe analysis technique into a deflectometric setup. The experimental arrangement consists of a deflectometry-based system in which light from a laser is expanded and passed through a collimating lens. The transmitted light illuminates a coarse sinusoidal grating. The grating image is directly captured through a charge-coupled device. Typical image patterns corresponding to "in-focus," "at-focus," and "out-of-focus" positions of an optical beam are recorded. Depending on the position of the collimating lens, the grating line spacing and the resulting phase of the emerging wavefront varies. Direct phase measurement using the windowed Fourier transform method has been used to obtain the slope map of the wavefront. The slope of the phase map depicts the diverging, collimated, or converging nature of the optical beam. The positioning error of light beam collimation was approximately 1 µm. The experimental arrangement is simple, low cost, and compact. The technique is fully automatic and provides high resolution, high precision, and good sensitivity.

Fingerprint detection and mapping using a phase shifted coherent gradient sensing technique.

In this paper, a full field technique for mapping a latent fingerprint using a coherent gradient sensing (CGS) sensor is proposed. Collimated light from an He-Ne laser illuminates a specimen comprising a fingerprint implanted onto a reflecting surface. Reflected light from the specimen is analyzed using the CGS sensor comprising a pair of gratings. Reflected light carries information regarding the depth and orientation of furrows and ridges in the fingerprint. The topological information of the fingerprint is retrieved using four-step phase shifting interferometry. Well-defined 2D and 3D phase plots have been reconstructed to map the topography of the human fingerprint. The recorded slope data reconstructs the information regarding the separation and depth of the ridges in the latent fingerprint. The proposed technique is noninvasive and full field and does not require any kind of chemical or physical treatment. The sensor is very simple, yields interferometric sensitivity, and has the advantages of easy alignment, compactness, and low cost.

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

A simple and robust method for introducing a phase-shifting test procedure in a wedge-plate shearing interferometer is proposed. The output of the wedge-plate lateral shearing interferometer (LSI) is superposed onto a sinusoidal grating, forming a moiré pattern. The in-plane translation of grating perpendicular to the grating lines is used for introducing a known amount of phase shifts in the interferometer. Direct measurement of phase using a four-step phase-shifting method is undertaken. The applicability of this devised phase-shifting wedge-plate LSI has been successfully tested for setting the collimation position of optical beams. Good accuracy and precision are achieved.

Slope measurement of bent plates using double grating shearing interferometry.

A grating-based shearing interferometeric setup for slope measurement of bent plates has been proposed. The specimen under test is illuminated by a collimated beam from the laser. Light reflected from the specimen passes through two identical holographic gratings placed in tandem. The grating frequency has been so chosen that the diffracted orders from each grating are separated out distinctly. Two first-order beams diffracted from each of the gratings superpose in space. In the resulting interferogram, the fringes due to slope information of the object are visualized. Mathematical formulation for experimental determination of slope values has been undertaken. Validation of the experimental results with theoretical predictions in case of cantilever beam provides good correlation. The main advantage of the technique has been the realization of very compact geometry without the need for spatial filtering arrangement commonly associated with the grating-based techniques used to date.

Automated collimation testing by incorporating the Fourier transform method in Talbot interferometry.

In this paper, we report an automated technique for collimation testing by incorporating Fourier fringe analysis of the recorded interferograms in Talbot interferometry. The triangular profile of Talbot interferometric fringes has been recorded using a CCD and computer system. The interferograms corresponding to the in-focus, at-focus, and out-of-focus positions of the collimating lens have been recorded. Direct phase measurement using the Fourier transform method has been used for detection of collimation positions. Good accuracy and precision in measurement have been achieved.