Achromatic fourier processor with holographic optical lenses

An optical Fourier processor that allows the use of broadband light sources and colored inputs is designed, fabricated, and tested. We develop a design technique based on phase manipulation in the Fourier plane to construct an image processor that provides a chromatically corrected image making use of the good aberrations behavior of symmetrical optical systems. Only a small number of diffractive lenses and one achromatic refractive lens are required to obtain a real image. We verify our design experimentally using holographic lenses, which are presented, owing to their versatility, as a good alternative to expensive blazed diffractive elements.     

White-light implementation of the Wigner-distribution function with an achromatic processor

A temporally incoherent optical processor that combines diffractive and refractive components is proposed for performing two different operations simultaneously: an achromatic image along an axis and an achromatic one-dimensional Fourier transformation along the orthogonal axis. These properties are properly employed to achieve the achromatic white-light display of the Wigner-distribution function associated with a one-dimensional real signal, with high redundancy and variable scale.     

二元光学折/衍混合消色差望远物镜设计

首先从光栅衍射理论出发导出衍射光学元件的色散公式，并进一步推导出用一种材料进行折／衍混合消色差望远物镜设计的公式。最后给出全折射型、一个混合型消色差和一个改进型消色差望远物镜的例子，并进行了比较。结果说明，混合型透镜的性能优于全折射型透镜，而改进型消色差物镜的总体性能优于原混合消色差物镜     

Integrated diffractive andrefractive elements for spectrum shaping

Diffractive elements can be designed for spectrum shaping in the Fourier or Fresnel plane by iterative methods. It is necessary to use a Fourier lens and the wavelength for which the diffractive elements were designed to get the required spectrum shaping at the Fourier plane. Using a different wavelength will cause chromatic aberration. We deal with the combination of refractive and diffractive elements and two or more different diffractive elements on the same element to get appropriate beam shaping of light sources with a multiple spectral output. Simulations are preformed that transform the profile of a He-Ne laser with a Nd:YAG laser source, and shape the trapezoidal beam profile of an excimer laser into a Gaussian beam is also considered.     

Lensless anamorphic Fourier transform hologram recorded with prism systems

A novel configuration for recording a lensless anamorphic Fourier transform hologram of a given object's light distribution is proposed. The method is based on the use of prism anamorphic optical systems coupled with phase cancellation at the hologram plane. Anamorphic systems with cylindrical lenses and prisms are critically evaluated through computer simulations for their suitability in anamorphic Fourier transform holographic configurations. A complete theoretical analysis and experimental demonstration of the recording and reconstruction of a lensless anamorphic Fourier transform hologram are presented.     

Spectral properties of multiorder diffractive lenses

Diffractive lenses have been traditionally designed with the first diffracted order. The spectral characteristics of diffractive lenses operating in higher diffracted orders differ significantly from the first-order case. Multiorder diffractive lenses offer a new degree of freedom in the design of broadband and multispectral optical systems that include diffractive optical elements. It is shown that blazing the surface-relief diffractive lens for higher diffraction orders enables the design of achromatic and apochromatic singlets. The wavelength-dependent optical transfer function and the associated Strehl ratio are derived for multiorder diffractive lenses. Experiments that illustrate lens performance in two spectral bands are described, and the results show excellent agreement with the theoretical predictions.     

Development of a phase-displacement equation for panoramic interferometry

We developed the parametric equations that are needed to quantify the modulations in the sensitivity vector that occur when the phase-displacement equation is applied to make panoramic interferometric measurements. The measurement system relies on two collinear panoramic annular lenses, one to illuminate and the other to image their surroundings. When a coherent light source is used and a reference beam is added, interference occurs over the region of interest defined by the illuminating and viewing lenses. A holographic system is used to demonstrate the approach and quantify the analysis. We obtained interference fringes in real time by comparing holograms recorded before and after a section of cylindrical pipe is displaced relative to the measurement system. The annular images and the holographic fringes are acquired and stored digitally in a computer system, and image transformation algorithms are applied to remove optical distortions in the holographic patterns. Excellent agreement is obtained when the fringe loci are compared with those predicted on the basis of theory.     

Mitigating Chromatic Dispersion with Hybrid Optical Metasurfaces

Metasurfaces control various properties of light via scattering across a large number of subwavelength‐spaced nanostructures. Although metasurfaces appear to be ideal photonic platforms for realizing and designing miniaturized devices, their chromatic aberrations have hindered the large‐scale deployment of this technology in numerous applications. Wavelength‐dependent diffraction and resonant scattering effects usually limit their working operation wavelengths. In refractive optics, chromatic dispersion is a significant problem and is generally treated by cascading multiple lenses into achromatic doublets, triplets, and so on. Recently, broadband achromatic metalenses in the visible have been proposed to circumvent chromatic aberration but their throughput efficiency is still limited. Here, the dispersion of refractive components is corrected by leveraging the inherent dispersion of metasurfaces. Hybrid refractive‐metasurface devices, with nondispersive refraction in the visible, are experimentally demonstrated. The dispersion of this hybrid component, characterized by using a Fourier plane imaging microscopy setup, is essentially achromatic over about 150 nm in the visible. Broadband focusing with composite plano‐convex metasurface lenses is also proposed. These devices could find applications in numerous consumer optics, augmented reality components, and all applications including imaging for which monochromatic performance is not sufficient.     

Holographic optical elements in the presence of spherical aberration and focus error: Some remarks on imaging quality

Abstract

When aberrations are small, it is possible to use wave aberration variance to obtain the position of the best image plane in both conventional and holographic optical systems. However, when aberrations increase, this measurement is not sufficient and it does not provide the correct plane position for the best image. In this paper, two alternative methods for evaluating image quality in spherically aberrated on-axis holographic lenses are compared. These two methods are the standard deviation of the distribution of light intensity and entropy. Both methods are based on the calculation of the diffraction integral and the subsequent analysis of the distribution of light intensity as a probability density function for each image plane being analysed. Even though the results obtained with both methods are identical when aberrations are small, only entropy provides the best image when the value of these aberrations increases.     

Speckle suppression in holographic projection displays using temporal integration of speckle images from diffractive optical elements

Speckles on images in holographic projection displays (HPDs) were efficiently suppressed by the temporal sum of two diffractive images generated from diffractive optical elements (DOEs). Using a modified iterative Fourier transform algorithm, we obtained pairs of phase-only DOEs that generated the diffractive images with high negative correlation coefficients of -0.827 and -0.490 in the one-dimensional and the two-dimensional simulations, respectively. The suppression ratios of the speckles in the two simulations were 0.301 and 0.457, which were 61% and 35% lower, respectively, than the sum of the two uncorrelated images. We have successfully demonstrated that the sum of two negatively correlated images from DOEs can effectively reduce the image speckles and improve the image quality in HPD systems.     

Application of holographic diffractive doublets as collimators for highly elliptical light beams edge emitted from diode lasers

Two schemes for collimation of diode laser light beams with high cross-sectional ellipticity by means of a doublet of holographic diffractive elements are proposed and designed; one of the schemes is realized and tested. In both the schemes the first element of the doublet collimates the beam in the plane of the longer axis of the ellipse, and the second element collimates it in the perpendicular plane. Each element simulates a cylindrical lens. The set-up with the focal line of the cylindrical beam oriented perpendicular to the meridional plane is realized experimentally. The elements are holographic surface-relief gratings recorded in photoresist. For recording, only homocentric diverging beams are used, which minimizes potential aberrations and optical dirt. The parameters of the elements are computed using four equations, including one equation for compensation of the aberration of the lowest order. The doublet is proposed for the He—Ne red wavelength. A collimated He—Ne laser beam is employed for quality testing of collimation in a reverse way, with this beam impinging upon the second element. Characteristics of an outgoing beam from the first element of the doublet are recorded with a charge-coupled device camera. Calculated spot diagrams are compared with cylindrical focal lines captured separately from both the elements.     

Refractive and diffractive properties of planar micro-optical elements

The refractive and the diffractive properties of planar micro-optical elements are investigated. The transition between purely refractive and purely diffractive planar microlenses is numerically simulated for the example of differently designed phase-matched Fresnel elements. Results obtained from numerical simulations and experiments show that the refractive and diffractive types exhibit a distinctly different behavior in the presence of small fabrication errors or wavelength deviations. Based on these results, design rules for various applications, including low- and high-numerical-aperture lenses and hybrid refractive-diffractive elements, are derived. For a high-numerical-aperture (? /# = 1.0) lens the experimental characterization of the irradiance distribution in the image space is presented and shown to agree well with theoretical predictions.     

Diffractive-refractive behavior of kinoform lenses

The connection between the diffractive behavior and the refractive behavior of kinoform lenses is investigated. The image-forming capabilities of the diffractive element are found to be expressed as an interference pattern that is due to a set of associated refractive lenses corresponding to each zone of the kinoform. The coefficient modulating the contribution of each refracting zone is determined. The term linking the point-spread function of a refractive lens and a diffractive lens is also obtained. Spectral and spatial aspects are compared as the diffractive element approaches the refractive limit.     

General linear optical coordinate tranformations

New optical configurations for performing general coordinate transformation operations of shear, rotation, and their combination are presented. These configurations consist of refractive spherical and cylindrical lenses that are readily available. Typically, high-resolution imagery can be obtained, depending on the size of the input object, the illumination wavelength, and the f-number of the lenses. Basic and more general configurations are presented, along with experimental results clearly showing image shearing, rotation, and a combination of these with high-quality output imagery.     

White-light-modified Talbot array illuminator with a variable density of light spots

A flexible array illuminator, comprising only two conventional optical elements, with a variable density of bright white-light spots is presented. The key to our method is to obtain with a single diffractive lens an achromatic version of different fractional Talbot images, produced by free-space propagation, of the amplitude distribution at the back focal plane of a periodic refractive microlens array under a broadband point-source illumination. Some experimental results of our optical procedure are also shown.     

Collimating cylindrical diffractive lenses: rigorous electromagnetic analysis and scalar approximation

Practical collimating diffractive cylindrical lenses of 2, 4, 8, and 16 discrete levels are analyzed with a sequential application of the two-region formulation of the rigorous electromagnetic boundary-element method (BEM). A Gaussian beam of TE or TM polarization is incident upon the finite-thickness lens. F/4, F/2, and F/1.4 lenses are analyzed and near-field electric-field patterns are presented. The near-field wave-front quality is quantified by its mean-square deviation from a planar wave front. This deviation is found to be less than 0.05 free-space wavelengths. The far-field intensity patterns are determined and compared with the ones predicted by the approximate Fraunhofer scalar diffraction analysis. The diffraction efficiencies determined with the rigorous BEM are found to be generally lower than those obtained with the scalar approximation. For comparison, the performance characteristics of the corresponding continuous Fresnel (continuous profile within a zone but discontinuous at zone boundaries) and continuous refractive lenses are determined by the use of both the BEM and the scalar approximation. The diffraction efficiency of the continuous Fresnel lens is found to be similar to that of the 16-level diffractive lens but less than that of the continuous refractive lens. It is shown that the validity of the scalar approximation deteriorates as the lens f-number decreases.     

Cross talk in holographic memories with lensless phase-conjugate holograms

Recently holographic memory with lensless phase-conjugate holograms has attracted much attention because it opens up the possibility of compact holographic memories. We investigate cross-talk noise in compact holographic memories with angular multiplexing. It turns out that the optimum angular separation is the same as that for the Fourier plane hologram in the leading order and that the noise-to-signal ratio is independent of the positions in the output plane, similar to the case of the image plane hologram.     

Toward the diffraction limit with transmissive x-ray lenses in astronomy

We develop an analytical approach to refractive, blazed diffractive, and achromatic x-ray lenses of scalable dimensions for energies from 1 to 20 keV. Based on the parabolic wave equation, their wideband imaging properties are compared and optimized for a given spectral range. Low-Z lens materials for massive cores and rugged alternatives, such as polycarbonate or Si for flat Fresnel components, are investigated with respect to their suitability for diffraction-limited high-energy astronomy. Properly designed "hybrid" combinations can serve as an approach to x-ray telescopes with an enhanced efficiency throughout the whole considered band, nearly regardless of their inherent absorption.     

Diffractive-refractive hybrid corrector for achro- and apochromatic corrections of optical systems

The possibility is shown of achro- and apochromatic correction of an optical system with any residual chromatism by completing the system with a diffractive-refractive hybrid corrector comprising one diffractive lens and one or two refractive lenses.     

Achromatic fan-out diffractive system for white-light free-space optical interconnects

Abstract

A simple and versatile white-light fan-out diffractive system based on the achromatization of the fractional Talbot effect is proposed. This achromatic configuration is able to interconnect a single polychromatic point source with a 2-D array of optoelectronic microdevices with low residual chromatic aberration even for white light. The whole broadband beamsplitter system is formed by two simple diffractive optical elements, a periodic diffractive lenslet array and a diffractive lens, that are made with a direct laser writing technique giving high light efficiency. The focal amplitude distribution corresponding to the lenslet array produces, by free-space propagation, self-replicas with different density of light points. These patterns, in conjunction with the achromatization process carried out by the additional diffractive lens, are, in short, the key to achieving a set of undistorted white-light spots at the output plane with high uniformity and variable separation between them. Experimental results are also shown.