Workflow for modeling of generalized mid-spatial frequency errors in optical systems.

We propose a workflow for modeling generalized mid-spatial frequency (MSF) errors in optical imaging systems. This workflow enables the classification of MSF distributions, filtering of bandlimited signatures, propagation of MSF errors to the exit pupil, and performance predictions that differentiate performance impacts due to the MSF distributions. We demonstrate the workflow by modeling the performance impacts of MSF errors for both transmissive and reflective imaging systems with near-diffraction-limited performance.

Use of pupil-difference moments for predicting optical performance impacts of generalized mid-spatial frequency surface errors.

In this work, we present a methodology for predicting the optical performance impacts of random and structured MSF surface errors using pupil-difference probability distribution (PDPD) moments. In addition, we show that, for random mid-spatial frequency (MSF) surface errors, performance estimates from the PDPD moments converge to performance estimates that assume random statistics. Finally, we apply these methods to several MSF surface errors with different distributions and compare estimated optical performance values to predictions based on earlier methods assuming random error distributions.

Pupil-difference moments for estimating relative modulation from general mid-spatial frequency surface errors.

Standard surface specifications for mid-spatial frequency (MSF) errors do not capture complex surface topography and often lose critical information by making simplifying assumptions about surface distribution and statistics. As a result, it is challenging to link surface specifications with optical performance. In this work, we present use of the pupil-difference probability distribution (PDPD) moments to assess general MSF surface errors and show how the PDPD moments relate to the relative modulation.

Design, fabrication, and characterization of a tunable LED-based illuminator using refractive freeform arrays.

Dynamic illumination using tunable freeform arrays can enable spatial light distributions of variable size with high uniformity from non-uniform sources through relatively small opposing lateral shifts applied to the freeform components. We present the design, manufacturing, and characterization of a tunable LED-based illuminator using custom freeform Alvarez arrays with commercially available optics to shorten the manufacturing cycle. The optomechanical design and manufacturing of the Alvarez lens arrays and mounting parts are presented in detail. The optical performance of the system is evaluated and compared with simulation results using a custom camera-based test station. Experimental results demonstrate and confirm the dynamic illumination concept with good uniformity.

General design method for dynamic freeform optics with variable functionality.

We propose and demonstrate a general design method for refractive two-element systems enabling variable optical performance between two specified boundary conditions. Similar to the Alvarez lens, small, relative lateral shifts in opposite directions are applied to a pair of plano-freeform elements. The surface prescriptions of the boundary lenses and a maximum desired shift between freeform plates are the main design inputs. In contrast to previous approaches, this method is not limited to boundaries with similar optical functions and can enable a wide range of challenging, dynamic functions for both imaging and non-imaging applications. Background theory and design processes are presented both for cases that are conducive to analytical surface descriptions, as well as for non-analytic surfaces that must be described numerically. Multiple examples are presented to demonstrate the flexibility of the proposed method.

Tunable illumination for LED-based systems using refractive freeform arrays.

Tunable illumination with high uniformity can improve functionality for multiple application areas. In lighting applications, dynamic illumination has been achieved by applying axial movement to the source(s) or other optical elements, resulting in poor uniformity, or using a liquid lens that adds design complexity. Advances in high-precision manufacturing methods have facilitated the practical implementation of freeform optical components, enabling new design approaches for illumination systems. This paper explores the use of arrays of varifocal transmissive freeform Alvarez lenses for an LED-based illumination system. The design is initialized using paraxial geometrical optics concepts and then refined for a 1mm-by-1 mm white LED source through a multi-step optimization. Design procedures are discussed, and simulation results are presented for an example illumination system that varies from a small circular spot mode to a large square uniform flood mode through millimeter-scale lateral translation between the Alvarez lens arrays.

Freeform optics for variable extended depth of field imaging.

Imaging depth of field is shallow in applications with high magnification and high numerical aperture, such as microscopy, resulting in images with in- and out-of-focus regions. Therefore, methods to extend depth of field are of particular interest. Researchers have previously shown the advantages of using freeform components to extend depth of field, with each optical system requiring a specially designed phase plate. In this paper we present a method to enable extended depth-of-field imaging for a range of numerical apertures using freeform phase plates to create variable cubic wavefronts. The concept is similar to an Alvarez lens which creates variable spherical wavefronts through the relative translation of two transmissive elements with XY polynomial surfaces. We discuss design and optimization methods to enable extended depth of field for lenses with different numerical aperture values by considering through-focus variation of the point spread function and compare on- and off-axis performance through multiple metrics.

Simple methods for estimating the performance and specification of optical components with anisotropic mid-spatial frequency surface errors.

Specification and tolerancing of surfaces with mid-spatial frequency (MSF) errors are challenging and require new tools to augment simple surface statistics to better represent the structured characteristics of these errors. A novel surface specification method is developed by considering the structured and anisotropic nature of MSF errors and their impact on the modulation transfer function (MTF). The result is an intuitive plot of bandlimited RMS error values in polar coordinates which contains the surface error anisotropy information and enables an easy to understand acceptance criterion. Methods, application examples, and the connection of this surface specification approach to the MTF are discussed.

The Minimum Modulation Curve as a tool for specifying optical performance: application to surfaces with mid-spatial frequency errors.

There are a variety of common situations in which specification of a one-dimensional modulation transfer function (MTF) or two orthogonal profiles of the 2D MTF are not adequate descriptions of the image quality performance of an optical system. These include systems with an asymmetric on-axis impulse response, systems with off-axis aberrations, systems with surfaces that include mid-spatial frequency errors, and freeform systems. In this paper, we develop the concept of the Minimum Modulation Curve (MMC). Starting with the two-dimensional MTF in polar form, the minimum MTF for any azimuth angle is plotted as a function of the radial spatial frequency. This can be presented in a familiar form similar to an MTF curve and is useful in the context of guaranteeing that a given MTF specification is met for any possible orientation of spatial frequencies in the image. In this way, an MMC may be of value in specifying the required performance of an optical system. We illustrate application of the MMC using profile data for surfaces with mid-spatial frequency errors.

Predictive models for the Strehl ratio of diamond-machined optics.

This paper provides a practical connection between the Strehl ratio as an optical performance metric and manufacturing parameters for diamond-machined optics. The choice of fabrication parameters impacts residual mid-spatial frequency groove structures over the part's surface, which reduce optical performance. Connections between the Strehl ratio and the fabrication parameters are studied using rigorous Rayleigh-Sommerfeld simulations for a sample optical system. The connections are generalized by incorporating the shape of diamond-machined groove structures and the effects of optical path differences for both transmissive and reflective optics. This work validates the analytical representation of the Strehl ratio as a Fourier transform of a probability density that relates to surface errors. The result is a practical tool that can be used to guide the choice of machining parameters to achieve a targeted optical performance.

Design, fabrication, and testing of convex reflective diffraction gratings.

The convex reflective diffraction grating is an essential optical component that lends itself to various applications. In this work, we first outline the design principles of convex diffraction gratings from wavefront quality and efficiency perspectives. We then describe a unique fabrication method that allows for the machining of convex diffraction gratings with variable groove structure, which is extendable to rotationally non-symmetric convex diffraction grating substrates. Finally, we demonstrate two quantitative wavefront measurement methods and respective experimental validation.

Measurement of a multi-layered tear film phantom using optical coherence tomography and statistical decision theory.

To extend our understanding of tear film dynamics for the management of dry eye disease, we propose a method to optically sense the tear film and estimate simultaneously the thicknesses of the lipid and aqueous layers. The proposed method, SDT-OCT, combines ultra-high axial resolution optical coherence tomography (OCT) and a robust estimator based on statistical decision theory (SDT) to achieve thickness measurements at the nanometer scale. Unlike conventional Fourier-domain OCT where peak detection of layers occurs in Fourier space, in SDT-OCT thickness is estimated using statistical decision theory directly on the raw spectra acquired with the OCT system. In this paper, we demonstrate in simulation that a customized OCT system tailored to ~1 µm axial point spread function (FWHM) in the corneal tissue, combined with the maximum-likelihood estimator, can estimate thicknesses of the nanometer-scale lipid and micron-scale aqueous layers of the tear film, simultaneously, with nanometer precision. This capability was validated in experiments using a physical phantom that consists of two layers of optical coatings that mimic the lipid and aqueous layers of the tear film.

Fabrication and characterization of a biomimetic polarization selective lens.

Incorporating optical structures on curved lens surfaces can improve performance, consolidate functions, and create novel, miniaturized devices. Although commonly found in biological systems, patterning of micro- and nano-optical structures on curved surfaces is challenging for conventional methods. Previous works have demonstrated the ability to pattern curved surfaces but have done little to create functioning devices. In this Letter, we describe a novel spray-coating technique coupled with interferometric exposure and dry etching to create near-IR wire-grid polarizers on convex lens surfaces. Experimental measurements show extinction ratios of >40:1 and transmission values of >80%, which are comparable to modeled results of similar polarizers on flat surfaces.

Variable-diameter refractive beam shaping with freeform optical surfaces.

We propose a refractive two-element system that converts the gaussian irradiance of an incident laser beam into a nominally flat-top output spot at a given distance with the capability to vary the spot diameter. The elements are high-order freeform surfaces that, when laterally translated, form a variable composite beam shaper. The general approach for determining the required freeform surfaces is discussed, and example design results are presented.

Performance of conformal guided mode resonance filters.

Guided mode resonance (GMR) filters are highly functional micro-optics capable of narrowband spectral filtering. GMR devices have previously been demonstrated on flat substrates using a wide range of materials and configurations. In this Letter, we apply a soft lithographic technique followed by the deposition of dielectric layers to generate GMR filters on a concave lens surface. Resonances of the resulting conformal GMR filters are experimentally measured and characterized, and the results are compared to the performance of similar GMR filters fabricated on flat surfaces.

Effective medium approximations for modeling optical reflectance from gratings with rough edges.

Line edge roughness (LER) has been identified as a potential source of uncertainty in optical scatterometry measurements. Characterizing the effect of LER on optical scatterometry signals is required to assess the uncertainty of the measurement. However, rigorous approaches to modeling the structures that are needed to simulate LER can be computationally expensive. In this work, we compare the effect of LER on scatterometry signals computed using an effective medium approximation (EMA) to those computed with realizations of rough interfaces. We find that for correlation lengths much less than the wavelength but greater than the rms roughness, an anisotropic EMA provides a satisfactory approximation in the cases studied.

Design of Talbot array illuminators for three-dimensional intensity distributions.

The self-imaging phenomenon is investigated as the basis for designing diffractive optical elements to generate three-dimensional diffraction patterns. The phase-only diffractive element is related to the intensity distribution at a finite and discrete set of Fresnel diffraction planes by use of the matrix formalism of the fractional Talbot effect. This description provides a framework to determine the degrees of freedom which can be exploited for design. It also helps to identify inherent symmetries of periodic wavefronts, which limit the set of intensity patterns that can be implemented. A simulated annealing algorithm is used to exploit the design freedom. Our discussion includes an example to illustrate observations.

Fabrication of micro optics on coreless fiber segments.

Fabrication of micro optics for fiber optics applications is a challenge due to their size and the issues associated with alignment of the optics to single-mode fibers. This study summarizes a method for fabricating diffractive optical elements on the ends of coreless fiber segments for passive alignment to single-mode fibers. Results are presented for passively aligned diffractive lens elements used for both collimation and beam shaping.