Walter D. Furlan

Polychromatic axial behavior of aberrated optical systems: Wigner distribution function approach

We propose a new method for the computation of the tristimuli values that correspond to the impulse response along the optical axis provided by an imaging optical system working under polychromatic illumination. We show that all the monochromatic irradiance distributions needed for this calculation can be obtained from the Wigner distribution function associated with a certain version of the pupil function of the system. The use of this single phase-space representation allows us to obtain the above merit function for aberrated systems with longitudinal chromatic aberration and primary spherical aberration. Some numerical examples are given to verify the accuracy of our proposal.

Focusing properties of diffractive lenses constructed with the aperiodic m-bonacci sequence

In this contribution we present a new family of diffractive lenses which are designed using the m-bonacci sequence. These lenses are a generalization of the Fibonacci Zone Plates previously reported. Diffractive elements of this type are called aperiodic zone plates because they are characterized by a radial profile that follows a given deterministic aperiodic sequence (Cantor set, Thue-Morse, Fibonacci...). Aperiodic lenses have demonstrated new interesting focusing and imaging properties that have found applications in different fields such as soft X-ray microscopy and spectral domain optical coherence tomography. Here, we show that m-bonacci zone plates are inherently bifocal lenses. We demonstrate that the relative separation of their foci depends on the m-value of the sequence and also can be correlated with the generalized golden ratio. As a particular case, the properties of the m-bonacci sequence with m=2 and m=3, called Fibonacci and Tribonacci Zone Plates respectively are discussed.

Polychromatic merit functions in terms of the Wigner distribution function

A method for the calculation of the axial illuminance and chromaticity as polychromatic merit functions of optical imaging systems is presented. We show that the Wigner distribution function of the pupil of the system allows us to obtain all the monochromatic components needed for the calculation of these parameters. From this single phase-space representation, the merit functions can be obtained in a polar fashion for a variable spherical and longitudinal chromatic aberrations. Numerical examples for an axially apodizing filter are shown.

Unconventional imaging with radial Walsh filters

In this work, we report the achievement of images obtained with radial Walsh filters. Derived from Walsh functions, radial Walsh filters are phase binary diffractive optical elements characterized by a set of equal-area concentric rings that take the phase values 0 or π, corresponding to +1 or -1 transmittance values of the corresponding Walsh function. Then, a radial Walsh filter can be re-interpreted as an aperiodic zone plate with self-similar multi-focusing properties under monochromatic illumination and, therefore, multi-imaging capabilities. We have implemented these unconventional lenses with a spatial light modulator and the first images obtained with this type of lenses are presented and evaluated.

Axial behavior of Cantor rings diffractals

Cantor ring diffractals describe rotationally symmetric pupils based on a polyadic Cantor set. The influence on the axial irradiance of several fractal descriptors including fractal dimension, number of gaps and stage of growth of such pupils are investigated. The analysis is performed through a new method for the computation of axial PSFs that uses a Wigner distribution function obtained from the pupil.

Axial irradiance computation using the Wigner Distribution Function: Assessment of the method

A new method for the computation of the tristimuli values that correspond to the impulse response along the optical axis provided by an imaging optical system working under polychromatic illumination is evaluated. A comparison between this method and the classical one of Hopkins and Yzuel shows that for systems with pupil functions of general profile it needs less computation time to obtain the same degree of accuracy.

Wigner distribution function applied to the calculation of the axial irradiance impulse response

We obtain that the irradiance impulse response along certain axes of an optical imaging system, that suffers from primary spherical aberration and longitudinal chromatic aberration, can be calculated from 1D integrations in a single 2D phase- space representation, the Wigner distribution function associated with a certain azimuthally-averaged version of the pupil of the system. This result is applied to study the response along the optical axis of unstable laser resonators and optical systems working under polychromatic illumination.