Spatial carrier interferometry from M temporal phase shifted interferograms: Squeezing Interferometry.

It is well known that having 3 temporal phase shifting (PS) interferograms we do not have many possibilities of using an algorithm with a desired frequency spectrum, detuning, and harmonic robustness. This imposes severe restrictions on the possibilities to demodulate such set of temporal interferograms. It would be nice to apply for example a 7 step PS algorithm to these 3 images in order to have more possibilities to phase demodulate them; even further, it would be even better to apply a quadrature filter having a spatial spread given by a real number to these 3 interferograms. In this paper we propose to do just that; namely we show how to demodulate a set of M-steps phase shifting images with a quadrature filter having a real-number as spatial spread. The interesting thing in this paper is to use a higher than M spread quadrature filter to demodulate our interferograms; in traditional PS interferometry one is stuck to the use of M step phase shifting formula to obtain the searched phase. Using a less than M PS formula is not interesting at all given that we would not use all the available information. The main idea behind the "squeezing" phase shifting method is to re-arrange the information of the M phase shifted fringe patterns in such a way to obtain a single carrier frequency interferogram (a spatio-temporal fringe image) and use any two dimensional quadrature filter to demodulate it. In particular we propose the use of Gabor quadrature filters with a spread given by real-numbers along the spatial coordinates. The Gabor filter may be designed in such way that we may squeeze the frequency response of the filter along any desired spatio-temporal dimension, and obtain better signal to noise demodulation ratio, and better harmonic rejection on the estimated phase.

Holographic interferometer to test optical surfaces.

A new interferometric method for testing optical surfaces is given. It is related to Murty's Fresnel zone plate interferometer and suggests the fruitful applications of holography to this branch of optics. In this paper a theoretical model that explains both interferometers is developed. Experimental results and pertinent comments are included.

Object surface for applying a modified hartmann test to measure corneal topography.

A modified Hartmann test is proposed for measuring corneal topography. The plane screen with holes used in the typical Hartmann test is replaced with a curved object surface. This object surface yields a plane image for a spherical mirror surface. We show that the object surface is an oval of revolution that can be modeled by an ellipsoid. The plane image will be formed by a square array of circular spots, all with the same diameter. To obtain the square array in the image, we calculated the spatial distribution of the spots on the object surface.

A review of methods for measuring corneal topography.

A review of some methods and their optical principles for measuring the corneal topography are presented in this paper. The concepts of principal curvatures and the ambiguity concerning the axial curvature of surfaces without symmetry of revolution are analyzed. These methods are divided into three groups according to the following optical principles: (1) specular reflection, which includes the Placido disk system, interferometry, and moiré deflectometry; (2) diffuse reflection, which includes moiré fringes, rasterstereography, and Fourier Transform Profilometry; and (3) scattered light, which includes the slitlamp system. We avoided describing the details of commercial instruments, only their working principles.

Analysis of interferograms with a spatial radial carrier or closed fringes and its holographic analogy.

It is well known that an interferogram can be demodulated to find the wave-front shape if a linear carrier is introduced. We show that it can also be demodulated if it has many closed fringes or a circular carrier appears. A basic assumption is that the carrier fringes are of a bandwidth adequate to contain the wave-front distortion. This phase determination, called here demodulation, is made in the space domain, as opposed to demodulation in Fourier space, but the low-pass filter characteristics must be properly chosen. For academic purposes a holographic analogy of this demodulation process is also presented, which shows that the common technique of multiplying by a sine function and a cosine function is equivalent to holographically reconstructing with a tilted-flat wave front. Alternatively, a defocused (spherical) wave front can be used as a reference to perform the reconstruction or demodulation of some closed-fringe interferograms.

Graphic tool to produce tailored symmetrical phase-shifting algorithms.

We employ the Fourier-transform graphic representation of a set of antisymmetrical and symmetrical sampling reference harmonics to obtain new symmetrical phase-shifting algorithms tailored to specific characteristics. As an example, a new detuning-insensitive seven-point algorithm, with a third signal harmonic insensitivity and which is detuning insensitive at this frequency, is derived.