Interferogram Analysis Methods Research Articles

Preliminary study of photomask pattern inspection by beam-shaped knife-edge interferometry

This paper presents a photomask inspection and defect analysis technique to accurately measure the pattern dimensions and to detect the defects of the photomask in a convenient, fast, reliable manner. The beam-shaped knife-edge interferometry (BSKEI) was developed to collect the interferogram created by the superposition of the reference incident wave and the edge-diffracted wave while scanning the photomask. BSKEI consists of a pulsed laser diode, an aperture, an objective lens, and a fiber-coupled photodiode. The objective lens enabled the beam shaping to create a spherical wave as a new source of light, and the beam shaping was effective to enhance the spatial frequency of the interferogram. The interferograms were characterized based on a Fresnel number model, and the corresponding interferogram analysis methods were developed. BSKEI produced different interferograms according to the photomask patterns and defects while scanning the photomask. As a result, BSKEI is capable of the measurement of pattern width, opening width, line-edge quality, and opening area surface quality of the photomask, and is expected to be an alternative tool for critical dimension metrology in many semiconductor applications.

Mean gradient descent: an optimization approach for single-shot interferogram analysis.

Complex object wave recovery from a single-shot interference pattern is an important practical problem in interferometry and digital holography. The most popular single-shot interferogram analysis method involves Fourier filtering of the cross term, but this method suffers from poor resolution. To obtain full pixel resolution, it is necessary to model the object wave recovery as an optimization problem. The optimization approach typically involves minimizing a cost function consisting of a data consistency term and one or more constraint terms. Despite its potential performance advantages, this method is not used widely due to several tedious and difficult tasks such as empirical tuning of free parameters. We introduce a new optimization approach, mean gradient descent (MGD), for single-shot interferogram analysis that is simple to implement. MGD does not have any free parameters whose empirical tuning is critical to the object wave recovery. The MGD iteration does not try to achieve minimization of a cost function but instead aims to reach a solution point where the data consistency and the constraint terms balance each other. This is achieved by iteratively progressing the solution in the direction that bisects the descent directions associated with the error and constraint terms. Numerical illustrations are shown for recovery of a step phase object from its corresponding off-axis as well as on-axis interferograms simulated with multiple noise levels. Our results show full pixel resolution as evident from the recovery of the phase step and excellent rms phase accuracy relative to the ground truth phase map. The concept of MGD as presented here can potentially find applications to a wider class of optimization problems.

Video-Based Interferogram Analysis for Measuring Influence of Vibration to White Light Interferometry

In this paper, we present a video-based interferogram analysis method for measuring the influence of vibration on white light interferometer in terms of undesired change in optical path difference between reference and sample arms. The measurement principle is based on the analysis of interferograms which involves tracking and converting change in interferograms to physical change in optical path difference. The method proposed uses the original sensor in interferometer for data acquisition as such no additional hardware is required. Such an approach ensures that the properties of interferometer such as the bandwidth of sensor are considered and the vibration pattern recorded is close to the effective influence of vibration. With our method, the influence of vibration on white light interferometer and the performance of vibration isolation system can be objectively quantified and measured.

Real-time holographic interferometry using photorefractive sillenite crystals with phase-stepping technique

This work presents a holographic interferometer that uses the photorefractive sillenite crystals in diffusive regimen whose configuration exhibits diffraction anisotropy for real-time holographic interferometry. The writing–reading process of holographic interferogram was done in real-time, connected with an interferogram-analysis method that uses the phase-stepping technique for quantitative measurement of changes on an object. The holographic interferograms from the analyzed surface were captured and they were used to calculate the phase map with four-frame technique. The unwrapping process used was the cellular-automata technique. We obtained quantitative results for some applications: measurements of micro-rotation of surfaces, punctual micro-displacements on an aluminum plate, stress on a dog's jaw, among others; adding new promising applications possibilities for basic research, dentistry and technological areas.

Phase-shifting real-time holographic interferometry that uses bismuth silicon oxide crystals

A bismuth silicon oxide crystal is used in the diffusion regime as a dynamic recording medium in a real-time holographic interferometer based on anisotropic self-diffraction. This device is connected with an interferogram-analysis method that uses the phase-shifting technique for quantitative measurement of diffusive-reflecting object deformations. In addition to the usual error sources in phase shifting, the temporal interferogram erasure is studied and is found weakly perturbative for the measured phase. It is shown that quantitative measurements are possible for low-intensity object beams (8 µW/cm(2)) and a large observed area. Apractical situation of defect monitoring in a composite structure is presented.