Juan C. Escalera

Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator

We show that both a lens and a nonuniform amplitude transmission filter can be encoded simultaneously onto a twisted nematic liquid-crystal spatial light modulator (SLM) working in the phase-only mode. The inherent equivalent apodization that is due to the pixelated structure of the SLM is compensated for. In addition, different types of nonuniform transmission pupil such as transverse apodizing, transverse hyperresolving, and axial hyperresolving (multifocusing) filters are implemented. The excellent agreement between numerical and experimental results shows the capability of this method to encode amplitude apodizers on a phase-only SLM.

Programmable axial apodizing and hyperresolving amplitude filters with a liquid-crystal spatial light modulator

Amplitude-transmitting filters for apodizing and hyperresolving applications can be easily implemented by use of a two-dimensional programmable liquid-crystal spatial light modulator operating in a transmission-only mode. Experimental results are in excellent agreement with theoretical predictions. This approach can permit the analysis of various filter designs and can allow the filters to be changed rapidly to modify the response of an optical system.

Depth of focus increase by multiplexing programmable diffractive lenses

A combination of several diffractive lenses written onto a single programmable liquid crystal display (LCD) is proposed for increasing the Depth of Focus (DOF) of the imaging system as a whole. The lenses are spatially multiplexed in a random scheme onto the LCD. The axial irradiance distribution produced by each lens overlaps with the next one producing an extended focal depth. To compare the image quality of the multiplexed lenses, the Modulation Transfer Function (MTF) is calculated. Finally we obtain the experimental Point Spread Functions (PSF) for these multiplexed lenses and experimental results in which an extended object is illuminated under spatially incoherent monochromatic light. We compare the images obtained in the focal plane and in some defocused planes with the single lens and with three multiplexed lenses. The experimental results confirm that the multiplexed lenses produce a high increase in the depth of focus.

Polychromatic axial behavior of axial apodizing and hyperresolving filters

The polychromatic behavior in defocused planes produced by different types of axial apodizing and hyperresolvingfilter is studied. The image quality is determined by comparing the illuminance and chromaticity distributions of the aberration free system with different filters and without a filter. The comparison is done in equivalent planes according to the normalized illuminance.

Simple expressions for performance parameters of complex filters, with applications to super-Gaussian phase filters

To study the three-dimensional (3-D) behavior produced by complex filters, we have extended the expressions for the axial and the transverse gain to the case in which the best image plane is not near the paraxial focus. Super-Gaussian phase filters are proposed to control the 3-D image response of an optical system. Super-Gaussian phase filters depend on several parameters that modify the shape of the phase filter, producing tunable control of the 3-D response of the optical system. The filters are capable of producing a wide range of optical effects: transverse superresolution with high depth of focus, 3-D superresolution, and transverse apodization with different axial responses.

Supergaussian rings: focusing properties

Abstract Bessel beams remain invariant as they propagate in free-space. Attempts to implement them make use of narrow ring apertures. Here we propose the use of apertures having supergaussian ring profiles, which contain the narrow ring as a limiting case. Numerically evaluated plots show the focusing properties of this new type of apertures.

Axially invariant pupil filters

Abstract We establish general conditions that complex and real valued pupil filters must satisfy to produce an identical axial response. We show several conditions that permit the generation of families of filters with identical axial response but with different transverse response. In particular we show results for supergaussian rings that depend on three parameters. Two of the parameters can determine the shape of the axial response achieving arbitrarily high focal depth. For a given axial response the third parameter controls the transverse response, permitting the attainment of super-resolution up to a limit. Loss of light throughput and the sidelobes increase are also studied. The axial behaviour is also studied for the case of optical systems with high aperture. The introduction of a generalized pupil function allows the determination of the conditions to obtain axially invariant pupil filters.

High focal depth imaging of small structures

The image intensity of small structures is considered under the influence of nonuniform pupils, which are apodizing and/or hyperresolving in the radial or axial direction. The predicted features of the aerial images of these structures are explained with the discussion of the 3D response functions and of the apparent transfer function. Differences occur between small lines and squares. In contrast to the 3D point response the 3D response function of the line is influenced by the coherence parameter.

Inherent apodization of lenses encoded on liquid-crystal spatial light modulators

Focusing diffractive optical elements encoded in liquid-crystal spatial light modulators yields an inherent equivalent apodization of the focused spot as a result of the pixelated nature of these devices and the finite extent of each pixel. We present a theoretical explanation for and experimental evidence of this effect. We demonstrate an experimental procedure for measuring the apodization and a method to compensate for this effect.

Symmetry properties with pupil phase-filters

Pupil filters can modify the three dimensional response of an optical system. In this paper, we study different pupil symmetries that produce a predictable image behavior. We show that different pupil-filters that satisfy certain symmetry conditions can produce axial responses which are either identical or mirror reflected. We also establish the differences in the symmetry properties between amplitude-only filters and phase-only filters. In particular, we are interested in phase filters that produce transverse superresolution with axial superresolution or high depth of focus.