Enrique E. Sicre

Misfocus tolerance seen by simple inspection of the ambiguity function

Since Woodward’s ambiguity function contains all the optical transfer functions with varying focus error, it can be applied to display visually the tolerance to focus error. We compare the tolerance to defocus of a transparent but finite extended pupil and a pupil with a central obscuration.

Phase Pupil Functions for Focal-Depth Enhancement Derived from a Wigner Distribution Function

A method for obtaining phase-retardation functions, which give rise to an increase of the image focal depth, is proposed. To this end, the Wigner distribution function corresponding to a specific aperture that has an associated small depth of focus in image space is conveniently sheared in the phase-space domain to generate a new Wigner distribution function. From this new function a more uniform on-axis image irradiance can be accomplished. This approach is illustrated by comparison of the imaging performance of both the derived phase function and a previously reported logarithmic phase distribution.

Fractional Fourier transform applied to spatial filtering in the Fresnel domain

The fractional Fourier transform can be optically defined through a phase-space coordinate rotation of the Wigner distribution function associated with the input signal. This operation can be achieved by performing three successive shearing processes, which are reduced to a free-space Fresnel diffraction originated by a scaled version of the input object illuminated with a spherical wave. This result is applied to describe the behavior of spatial filtering devices based on the self-imaging phenomenon (Fresnel spatial filters).

Quality parameters analysis of optical imaging systems with enhanced focal depth using the Wigner distribution function

An analysis of the Strehl ratio and the optical transfer function as imaging quality parameters of optical elements with enhanced focal length is carried out by employing the Wigner distribution function. To this end, we use four different pupil functions: a full circular aperture, a hyper-Gaussian aperture, a quartic phase plate, and a logarithmic phase mask. A comparison is performed between the quality parameters and test images formed by these pupil functions at different defocus distances.

Analysis of the Strehl ratio using the Wigner distribution function

Abstract The on-axis intensity distribution, or the Strehl ratio versus defocus, is described in a phase-space domain in terms of the Wigner distribution function. A coordinate transformation that is defined for a general annular aperture is employed to convert the pupil amplitude transmittance into a one-dimensional function. We show that the single display of the Wigner distribution function associated with this modified pupil contains all the values of the Strehl ratio along the optical axis. The analysis is performed for two primary aberrations: coma and astigmatism.

Interferometry Based on the Lau Effect a Quasi-ray Description

There are two families of interferometric devices incorporating two gratings and an extended source that are based on the Lau effect. In this paper the ray-optics techniques made possible by using the Wigner distribution function are used to provide a simple description of these two families. Some new features of these devices are identified and experimental results are reported.

Optical correlation based on the fractional Fourier transform

Some properties of optical correlation based on the fractional Fourier transform are analyzed. For a particular set of fractional orders, a filter is obtained that becomes insensitive to scale variations of the object. An optical configuration is also proposed to carry out the fractional correlation in a flexible way, and some experimental results are shown.

Real-time measurement of the meniscus shape using the Talbot effect

Abstract A method is presented to determine the shape of the meniscus in a liquid surface using the Talbot effect and digital image processing. A comparison between experimental data and a theoretical model is performed, from which the value of the surface-tension coefficient of the liquid can be derived.

A speckle method of gray level pseudocoloring

Abstract A simple method of pseudocoloring gray level images is proposed. It is based on Youngs fringes modulated speckle encoding of images. Reconstruction from a photographic register is obtained using two light beams with different wavelengths at the same time. Pseudocoloring is produced by the superposition of a (diffracted) direct image in one color and a (directly transmitted) contrast reversed image in another color.

Off-axis Analysis of the Strehl Ratio Using the Wigner Distribution Function

Abstract An approach based on the Wigner distribution function (WDF) is used for analysing the Strehl ratio behaviour for varying focus errors and object source locations. A relationship is found between the WDF of the pupil function and the WDF of the light field in the Fresnel region about the image plane. Tolerance criteria to defocus can be specified in terms of the ‘amplitude’ of the parageometrical rays that intersect a tilted optical axis defined by the locations of the object and image points.