Luis A. González

Pixelated phase computer holograms for the accurate encoding of scalar complex fields

We discuss a class of phase computer-generated holograms for the encoding of arbitrary scalar complex fields. We describe two holograms of this class that allow high quality reconstruction of the encoded field, even if they are implemented with a low-resolution pixelated phase modulator. In addition, we show that one of these holograms can be appropriately implemented with a phase modulator limited by a reduced phase depth.

Optics of the average normal cornea from general and canonical representations of its surface topography

Generally, the analysis of corneal topography involves fitting the raw data to a parametric geometric model that includes a regular basis surface, plus some sort of polynomial expansion to adjust the more irregular residual component. So far, these parametric models have been used in their canonical form, ignoring that the observation (keratometric) coordinate system is different from corneal axes of symmetry. Here we propose, instead, to use the canonical form when the topography is referenced to the intrinsic corneal system of coordinates, defined by its principal axes of symmetry. This idea is implemented using the general expression of an ellipsoid to fit the raw data given by the instrument. Then, the position and orientation of the three orthogonal semiaxes of the ellipsoid, which define the intrinsic Cartesian system of coordinates for normal corneas, can be identified by passing to the canonical form, by standard linear algebra. This model has been first validated experimentally obtaining significantly lower values for rms fitting error as compared with previous standard models: spherical, conical, and biconical. The fitting residual was then adjusted by a Zernike polynomial expansion. The topographies of 123 corneas were analyzed obtaining their radii of curvature, conic constants, Zernike coefficients, and the direction and position of the optical axis of the ellipsoid. The results were compared with those obtained using the standard models. The general ellipsoid model provides more negative values for the conic constants and lower apex radii (more prolate shapes) than the standard models applied to the same data. If the data are analyzed using standard models, the resulting mean shape of the cornea is consistent with previous studies, but when using the ellipsoid model we find new interesting features: The mean cornea is a more prolate ellipsoid (apical power 50 D), the direction of the optical axis is about 2.3 degrees nasal, and the residual term shows three Zernike coefficients significantly higher than zero (third-order trefoil and fourth- and sixth-order spherical). These three nonzero Zernike coefficients are responsible for most of the higher-order aberrations of the average cornea. Finally, we propose and implement a simple method for three-dimensional registration of corneal topographies, passing from the general to the canonical form of the ellipsoid.

Computer-generated holograms with optimum bandwidths obtained with twisted-nematic liquid-crystal displays

We discuss a computer-generated hologram for encoding arbitrary complex modulation based on a commercial twisted-nematic liquid-crystal display. This hologram is implemented with the constrained complex modulation provided by the display in a phase-mostly configuration. The hologram structure and transmittance are determined to obtain on-axis signal reconstruction, maximum bandwidth, optimum efficiency, and high signal-to-noise ratio. We employed the proposed holographic code for the experimental synthesis of first-order Bessel beams.

Self-apodization of low-resolution pixelated lenses

We show that a pixelated lens with appropriate parameters exhibits an apodized point-spread function that originates in the finite size of the pixels pupil. We evaluate numerically the degree of apodization and the enlargement associated with the point-spread function in terms of the parameters that characterize the pixelated lens.

Programmable pixelated lens with long depth of focus for shape recovering applications

We show that long depth of focus can be achieved with a pixelated lens (PL) encoded onto a reconfigurable spatial light modulator (SLM). Our PL has a phase distribution similar to that of a conventional axilens. Additionally, our resulting reconfigurable PL is employed in a novel shape recovering system. A feature of this system is that no moving parts or motors are required to scan a three-dimensional object. Numerical simulations and experimental results are shown.

Encoding fully-complex transmittance with coupled amplitude-phase liquid-crystal modulator

We propose a holographic code for synthesis of fully-complex transmittance, which can be implemented employing a twisted-nematic liquid-crystal display, two linear polarizers, and a He-Ne laser. This simple setup provides a reduced phase range and amplitude modulation with significant variance. Our holographic code efficiently exploits this constrained modulation for the accurate encoding of arbitrary complex transmittance. Two experimental examples illustrate the good performance of the holographic code.

Improved simulated annealing algorithm for optimization of symmetrical diffractive elements

We present a modified simulated annealing algorithm for the design of diffractive optical elements whose basic cell is constrained by a symmetry similar to that of the reconstruction field. Compared with the conventional SA algorithm, our approach permits better designs with reduced computational efforts.

Laser line shape recovery system based on a double pixelated axilens

We describe a scanning system for shape recovery that employs a pair of one-dimensional interlaced axilenses encoded onto a reflective liquid-crystal spatial light modulator. The design of these axilenses with opposite depth presets allows the generation of a high-quality laser line pattern with extended depth of focus, which is applied in the shape recovery. Other attributes of the system allow the scanning of objects whose lateral dimensions are larger that those of the spatial light modulator itself. The high performance of the scanning system is demonstrated by its application to the shape recovery of ceramic objects.

Accurate Encoding Of Complex Optical Fields With Pixelated Phase‐Only Spatial Light Modulators

Point‐oriented phase computer‐generated holograms that encode complex scalar fields are proposed and discussed. These holograms allow the reconstruction of the encoded fields with high signal to noise ratio, even if they are implemented with a pixelated spatial light modulator. The good performance of these holograms is enabled by a significant reduction in the relative intensity of the high order diffraction field contributions that share the spatial frequency domain of the encoded field.

Modified encoding of fully complex modulation with coupled amplitude-phase spatial light modulator

In a previously reported holographic code for the synthesis of arbitrary complex fields with phase-only modulators, the amplitude is encoded by scaling the phase modulation. For the appropriate performance of this code, it is necessary to employ an ideal phase modulator, which can not be easily obtained with a standard liquid-crystal device. We generalize and improve the above holographic code in such a way that the desired complex function can be obtained by using the restricted phase-mostly modulation provided by a twisted-nematic liquid-crystal display, in a simple setup employing two polarizers and a He-Ne laser. A commercial liquid-crystal device employed in this setup only provides a phase modulation in a range smaller than 1.5π radians, coupled with an amplitude modulation with a significant variance. In spite of these restrictions, the quality of complex signals encoded with the modified holographic code is only affected by a marginal efficiency reduction. We present numerical simulations and experimental results regarding our proposal.