Serial transform optical correlator design principles

Optical correlators such as the 4f and VanderLugt optical systems have been an active area of research for many years; we refer to these types of optical system collectively as serial transform correlators (STCs). Despite being well known, misconceptions regarding the design of STCs are not uncommon. We show, for example, that one correlator configuration reported to suffer from a phase curvature problem in fact works correctly. We present and prove a simple set of rules to follow in the selection of a STC design that does not contain unnecessary constraints and that makes it easier to identify permissible optical systems. As examples, we discuss three representative types of correlator configuration, one of which is discussed in detail to highlight its practical advantages. A novel proof of the design rules is presented that does not depend on details such as what lenses or combination of lenses are used, what their focal lengths are, or what their locations are within the optical system. We also present a conventional Fourier optics proof.     

Application of nonperiodic phase structures in optical systems

Wide, nonperiodic stepped phase structures are studied to correct various parameter-dependent wave-front aberrations in optical systems. The wide nature of these phase structures makes them easy to manufacture with sufficient compensation of the wave-front aberrations. Wave-front aberration correction for both continuous and discrete parameter variations are studied. An analytical method is derived for the discrete parameter variations to find the optimal phase structure. Both theoretical and experimental results show that these nonperiodic phase structures can be used to make (1) lenses athermal (defocus and spherical aberration compensated), (2) lenses achromatic, (3) lenses with a large field of view, (4) lenses with a reduced field curvature, and (5) digital versatile disk objective lenses for optical recording that are compatible with compact disk readout.     

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.     

Calculation of focal positions in an optical head for parallel data processing with a monolithic four-beam laser diode

A method for calculating focal positions in a multibeam optical head by use of a multibeam laser diode, in which conditions for misalignment of the light source are taken into consideration, is introduced. One calculates the focal positions by using the practical characteristics of a monolithic four-beam laser diode and the practical specifications of the optics in an optical head. The results show that each focal position is defocused mainly as a result of curvature of the fields of the lenses. The adaptability of focal positions for various calculated conditions is discussed from the standpoint of depth of focus.     

Optical fractional Fourier transforms with complex orders

A definition of real and complex domains for the order of fractional Fourier transforms is introduced in association with diffraction either in free space or through real and complex lenses. The geometrical and the optical conditions that lead to real and complex orders of the fractional Fourier transforms and their relevance to cascading optical systems are discussed.     

Refractive index variation in compression molding of precision glass optical components

Compression molding of glass optical components is a high volume near net-shape precision fabrication method. In a compression molding process, a variation of the refractive index occurs along the radial direction of the glass component due to thermal treatment. The variation of refractive index is an important parameter that can affect the performance of optical lenses, especially lenses used for high precision optical systems. Refractive index variations in molded glass lenses under different cooling conditions were investigated using both an experimental approach and a numerical simulation. Specifically, refractive index variations inside molded glass lenses were evaluated by measuring optical wavefront variations with a Shack-Hartmann sensor system. The measured refractive index variations of the molded glass lenses were compared with the numerical simulation as a validation of the modeling approach.     

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.     

Particular solution for geodesic lenses

On the basis of the analytical method of designing aspherical optical waveguide geodesic lenses [J. Opt. Soc. Am. 69, 1248 (1979)], a particular solution for geodesic lenses without any curvature singularity was obtained.     

Extensions to a lens design program for the ray-optical design of waveguide lenses and prism couplers

Abstract

The design of integrated optical lens systems requires special software because such systems contain both three-dimensional and twodimensional elements (e.g. bulk prisms and planar waveguide lenses), and the waveguides are often anisotropic. We extended the popular optical computer-aided design program OSLO SIX so that it can evaluate and optimize systems that contain coupling prisms and planar waveguide lenses. We describe our software extensions and through examples we demonstrate their usage and benefits. We confirm our computations by measurement results. Finally, we present a ray-optical interpretation of transverse image line inclination and a method for its elimination.     

Mechanical modeling of fluid-driven polymer lenses

A finite-element model (FEM) is employed to study the pressure response of deformable elastic membranes used as tunable optical elements. The model is capable of determining in situ both the modulus and the prestrain from a measurement of peak deflection versus pressure. Given accurate values for modulus and prestrain, it is shown that the two parameters of a standard optical shape function (radius of curvature and conic constant) can be accurately predicted. The effects of prestrain in polydimethylsiloxane (PDMS) membranes are investigated in detail. It was found that prestrain reduces the sensitivity of the membrane shape to the details of the edge clamping. It also reduces the variation of the conic constant with changes in curvature. Thus the ability to control the prestrain as well as thickness and modulus is important to developing robust optical designs based on fluid-driven polymer lenses.     

Three-dimensional Imaging in Confocal Fluorescent Microscopy with Annular Lenses

Abstract

Three-dimensional imaging properties in confocal fluorescent microscope systems with annular lenses are investigated in terms of the three-dimensional optical transfer function (OTF). Starting from the OTF, we also consider the optical sectioning property. The dependence of the OTF and the optical sectioning strength on the radius of the central obstruction of the lens is revealed. For the case of a finite-sized circular pinhole in front of the detector, both the OTF and the optical sectioning strength, together with the signal level, are calculated as a function of the radius of the pinhole. Investigations show that for a given finite size of the pinhole, the optical sectioning strength can be increased by altering the radius of the central obstruction of the lens to an optimum value, and that a higher signal level may be maintained by using an annular objective only.     

Optical element for generation of accelerating Airy beams

We demonstrate an optical element for generation of accelerating Airy beams. The element is conveniently constructed by combination of positive and negative cylindrical lenses of matching radii of curvature. With proper choice of lens curvatures, the resulting surface profile closely follows a cubic polynomial. Passing a gaussian beam through this element and performing optical Fourier transform yields beam profiles close to the Airy function. Our experiments demonstrate parabolic propagation, or acceleration, of the resulting focal spots.     

Lens Systems with Frontal Aperture Stops

The requirements for the aberration correction in lenses with frontal aperture stops (FASs) are determined. The theory of distortion and field curvature correction is examined in such asymmetrical optical configurations. Computed results for an orthoscopic telecentric objective of the OR-3 type are given. A design for an f/1·6 photographic lens with field 65° is given. Some conclusions for the trends in FAS system development are drawn. The theoretical results of the synthesis and aberration correction for this type of lens system are given.     

Minimal optical decomposition of ray transfer matrices

The properties of first-order optical systems are described paraxially by a ray transfer matrix, also called the ABCD matrix. Here we consider the inverse problem: an ABCD matrix is given, and we look for the minimal optical system that consists of only lenses and pieces of free-space propagation. Similar decompositions have been studied before but without the restriction to these two element types or without an attempt at minimalization. As the main results of this paper, we found that general lossless one-dimensional optical systems can be synthesized with a maximum of four elements and two-dimensional optical systems can be synthesized with six elements at most.     

Probability of Failure of Sylgard-Mounted Optical Lenses in Head-Up Display During Thermal Cycle Testing

Lenses made from optical glass do not have a single characteristic strength. The strength of any optical glass is highly dependent on the area under stress and its surface finish. The nominal design strength of manufactured glass is typically in the 6.9–70 MPa range. This study presents an analysis of measured strain data and an approach to quantify the failure probability of optical lenses that are used in head-up display systems for aircraft applications when these lenses are subjected to accelerated thermal cycling. The thermal cycling produces thermal stress within the elastomerically mounted optical lens of the head-up display. We used a combination of experimental methods and finite element modeling to determine the thermal strain in the optical lens. The thermal strain values that were obtained using these methods were validated and were found to be in a cumulative distribution. This cumulative strain provides a quantitative estimate of the effects of thermal stress in the optical lens. We then determined the failure probability using Weibull parameters.     

The Diffraction Theory of the Aberrations of Stigmatic Orthomorphic Optical or Electron Optical Systems Containing Toric Lenses or Quadrupoles

The diffraction theory of the aberrations of optical systems with an axis of rotational symmetry is now thoroughly established, and the extension to kindred electron optical systems is straightforward. In electron optics, however, certain types of systems containing quadrupoles are of importance, and such systems suffer from aberrations which affect only very oblique rays in axially symmetrical systems. The distortions of the wave surface which correspond to these new aberrations are listed in the present note, and Nijboer's expressions for the consequent disturbances in the image plane of a rotationally symmetrical system are supplemented accordingly. Only the special case—which is, nevertheless, an important one—of stigmatic systems, producing an image free of first-order distortion?, is considered. The analysis is applicable to electron optical orthogonal systems containing quadrupoles and optical systems containing parallel toric lenses alike.     

Birefringent properties of diametrically loaded gradient-index lenses

Gradient-index (GRIN) lenses have been widely used as collimators in various fiber-optic sensors and as optical coupling devices in components designed for optical communication systems. However, relatively little attention has been paid to the birefringent properties of GRIN lenses and the potential for using them as photoelastic sensing elements in optical transducers. Analytical and experimental results are described that were obtained for the intensity distribution produced by studying a GRIN lens by using a polariscope. The residual birefringence inherent in an unloaded lens is initially studied. The lens is then assumed to be diametrically loaded and the superposition is studied by the method of ray tracing. When the results obtained from the simulation for a Selfoc, 0.25-pitch lens are compared with experimental data, an excellent agreement is obtained. Intensity increases monotonically with load, confirming that the lens would be a good choice for the sensing element of an optical transducer designed as part of a strain or acceleration measurement system. The numerical simulation is then used to study the influence of residual stress on sensitivity.     

Gradient-index rod lens with a high acceptance angle for color use by Na(+) for Li(+) exchange

The relationship between the characteristics of gradient-index rod lenses obtained by ion exchange and their mother glass compositions is studied. It is observed that Li(2)O content, R(2)O (Li(2)O + Na(2)O) content, and the Li(2)O/Na(2)O ratio are important factors in attaining a high acceptance angle and a small field curvature. Thus the gradient-index lens array is fabricated by the use of a newly developed glass composition and its optical performance; the modulation transfer function, luminous intensity, and chromatic aberration are precisely evaluated. The array is found to have a sufficiently high performance to be applicable for color use.     

Thin infrared imaging systems through multichannel sampling

The size of infrared camera systems can be reduced by collecting low-resolution images in parallel with multiple narrow-aperture lenses rather than collecting a single high-resolution image with one wide-aperture lens. We describe an infrared imaging system that uses a three-by-three lenslet array with an optical system length of 2.3 mm and achieves Rayleigh criteria resolution comparable with a conventional single-lens system with an optical system length of 26 mm. The high-resolution final image generated by this system is reconstructed from the low-resolution images gathered by each lenslet. This is accomplished using superresolution reconstruction algorithms based on linear and nonlinear interpolation algorithms. Two implementations of the ultrathin camera are demonstrated and their performances are compared with that of a conventional infrared camera.     

The Influence of Inaccuracy of Construction Parameters on the Calculated Optical Transfer Function

The influence of the construction parameters of an optical system such as radii of curvature, refractive indices, thicknesses, and distances of lenses on the optical transfer function (O.T.F.) is discussed with the example of variation of radii. To find out the critical or uncritical parameters of a compound system, the Seidel coefficients (first aberration) are generally sufficient. Then the exact coefficients of wave aberrations are varied by given amounts and the corresponding O.T.F. is calculated and tabulated. The permissible variation of the coefficients for a given tolerance of O.T.F. in a limited spatial frequency range can be seen from the table. The presented technique is demonstrated for a lens of nine surfaces.