Calculation of zonal power and astigmatism of a freeform gradient index lens with freeform surfaces.

Freeform gradient index (F-GRIN) lenses have been recently shown to enable compact optical design. However, aberration theory is only fully developed for rotationally symmetric distributions with a well-defined optical axis. The F-GRIN has no well-defined optical axis, and rays are continuously perturbed along their trajectory. Optical performance can be understood without abstracting optical function to numerical evaluation. The present work derives freeform power and astigmatism along an axis through a zone of an F-GRIN lens with freeform surfaces. Zonal power and astigmatism can be assessed without tracing any rays, capturing mixed contributions of the F-GRIN and freeform surface. Theory is compared with a commercial design software numerical raytrace evaluation. The comparison shows that the raytrace-free (RTF) calculation represents all raytrace contributions within a margin of error. In one example, it is demonstrated that linear terms of index and surface alone in an F-GRIN corrector can correct the astigmatism of a tilted spherical mirror. Accounting for the induced effects of the spherical mirror, RTF calculation provides the amount of astigmatism correction of the optimized F-GRIN corrector.

Gradient-index Alvarez lenses.

Gradient-index Alvarez lenses (GALs), a new, to the best of our knowledge, type of freeform optical component, are surveyed in this work for their unique properties in generating variable optical power. GALs display similar behavior to conventional surface Alvarez lenses (SALs) by means of a freeform refractive index distribution that has only recently been achievable in fabrication. A first-order framework is described for GALs including analytical expressions for their refractive index distribution and power variation. A useful feature of Alvarez lenses for introducing bias power is also detailed and is helpful for both GALs and SALs. The performance of GALs is studied, and the value of three-dimensional higher-order refractive index terms is demonstrated in an optimized design. Last, a fabricated GAL is demonstrated along with power measurements agreeing closely with the developed first-order theory.

Gradient-index Alvarez lenses: publisher's note.

This publisher's note contains a correction to Appl. Opt.62, 3485 (2023)APOPAI0003-693510.1364/AO.487089.

Multi-material freeform gradient-index spectrometers.

With the advent of 3D printing optical elements, new techniques for manufacturing gradient-index (GRIN) optics have been realized that blend multiple materials in the deposition process. A method to achieve spectral splitting using multi-material GRIN optics is presented. The GRIN is additionally used to generate optical power, allowing for planar entrance and exit surfaces. It is shown that this simultaneous focusing and spectral splitting is not feasible with a two-material GRIN. A comparative design study is then conducted using three and four-material GRIN. A four-material design with optimized materials is also presented to showcase the potential for this new design form.

Achromatization of multi-material gradient-index singlets.

Recent advancements in additive manufacturing have enabled new methods of fabricating gradient-index (GRIN) optics by blending multiple materials in the deposition process. A design study highlighting the advantages of multi-material GRIN optics is presented. It is shown that additional materials in the GRIN allow for higher orders of color correction. A new multi-material refractive index representation, which constrains the GRIN to real materials, is also presented.

Replacing optical surfaces with gradient index functions which preserve ray trajectory.

Laws of reflection and refraction between homogeneous media and gradient index (GRIN) ray behavior are both derived from Fermat's principle. Design methods for GRIN can be difficult to analytically develop. This Letter proposes a foundation for complete replacement of refracting and total internally reflecting optical interfaces in existing designs with GRIN distribution. The proposed method can aid in incorporating GRIN into existing optical designs. Refraction in GRIN is specified to match the ray striking and leaving the optical interface in both position and angle. This result is shown for a collection of similar GRIN functions. One GRIN function is analyzed over a full space of attainable ray bend angles. A local arbitrarily oriented planar interface is replaced with GRIN distribution, and ray behavior is maintained.

Freeform gradient index generalized Coddington's equations.

Coddington's equations and their generalized forms are useful for lens design and analysis of optical performance. Generalized Coddington's equations (GCE) exist in literature for analysis of decentered systems and freeform surfaces, but not for gradient index (GRIN) lenses. In this work, GCE are presented for the analysis of freeform GRIN lenses with freeform surfaces. Examples are shown where the presented theory converges on Coddington's equations and known paraxial GRIN behavior. The method also correctly shows known afocal behavior proximate to azimuthally directed rays in a cylindrical GRIN. The latter case is one of analytically validated local freeform behavior.

Freeform gradient index progressive addition lens raytrace performance evaluation.

Raytrace evaluation capable of evaluating progressive addition lens (PAL) designs with freeform surface and gradient index (GRIN) contributions is presented. The method is validated on an analytically generated PAL start design and on optimized surface designs. Surface raytrace evaluations are compared with the surface-geometric evaluation commonly presented for freeform surface PAL designs. The evaluation is also tested on analytically generated freeform GRIN PAL designs with spherical and plano surfaces. The raytrace method agrees with the analytic performance and surface-geometric performance near the center of the lens and deviates at the edge of the lens, due to ray obliquity with the surfaces and aggregate contributions of surfaces and/or GRIN. These deviations are expected, as the raytrace model accounts for more physical contributions to optical performance, including pupil diameter and eye position. This raytrace method enables the evaluation of lens performance contributions other than from polished surfaces on homogeneous materials, enabling further exploration of GRIN in PAL designs.

Polychromatic annular folded lenses using freeform gradient-index optics.

The annular folded lens (AFL) is a design form offering large aperture, high-resolution imaging in a very axially compact package. The folded optic can be made monolithic for easier fabrication and alignment, yet the introduction of refractive surfaces with a dispersive optical material gives way to chromatic aberrations. AFL designs using homogeneous media are generally limited to the monochromatic regime, with polychromatic performance greatly reduced. By introducing freeform gradient-index (F-GRIN) media, monolithic AFL designs can achieve higher monochromatic performance as well as provide color correction for diffraction-limited polychromatic imaging. Monochromatic and polychromatic design methodologies are surveyed where the F-GRIN is constrained to remain feasible for fabrication.

Freeform gradient-index media: a new frontier in freeform optics.

Freeform optics enable irregular system geometries and high optical performance by leveraging rotational variance. To this point, for both imaging and illumination, freeform optics has largely been synonymous with freeform surfaces. Here a new frontier in freeform optics is surveyed in the form of freeform gradient-index (F-GRIN) media. F-GRIN leverages arbitrary three-dimensional refractive index distributions to impart unique optical influence. When transversely variant, F-GRIN behaves similarly to freeform surfaces. By introducing a longitudinal refractive index variation as well, F-GRIN optical behavior deviates from that of freeform surfaces due to the effect of volume propagation. F-GRIN is a useful design tool that offers vast degrees of freedom and serves as an important complement to freeform surfaces in the design of advanced optical systems for both imaging and illumination.

Prescribed irradiance distributions with freeform gradient-index optics.

Generating a prescribed irradiance distribution given a source distribution is an inverse problem that sits at the heart of illumination design. The growing prevalence of freeform optics has inspired several design methods for obtaining a prescribed irradiance distribution possessing no symmetry. Up to now, these methods have relied exclusively on freeform optical surfaces for generating freeform irradiances. This paper presents a design method that, for the first time, applies gradient-index (GRIN) optics to solving this inverse problem. Using a piecewise-continuous freeform gradient-index (F-GRIN) profile, a single optic with two planar surfaces can be designed to produce a far-field prescribed irradiance distribution from a point source. The design process is herein presented along with two design examples which demonstrate some of the unique properties of F-GRIN illumination optics.

Efficient representation of freeform gradient-index profiles for non-rotationally symmetric optical design.

Conventional optical designs with gradient index (GRIN) use rotationally-invariant GRIN profiles described by polynomials with no orthogonality. These GRIN profiles have limited effectiveness at correcting aberrations from tilted/decentered or freeform systems. In this paper, a three-dimensional orthogonal polynomial basis set (the FGRIN basis) is proposed, which enables the design of GRIN profiles with both rotational and axial variations. The FGRIN basis is then demonstrated via the design of a 3D GRIN corrector plate targeted to correct the rotationally-variant aberrations induced from a tilted spherical mirror. A sample corrector is manufactured and tested, showing significant correction of astigmatism. The FGRIN basis opens a new design space of 3D rotational variant GRIN profiles, which has the potential of replacing multiple freeform surfaces and simplifying complex systems.

Mutant SOD1 prevents normal functional recovery through enhanced glial activation and loss of motor neuron innervation after peripheral nerve injury.

BACKGROUND: Amyotrophic lateral sclerosis (ALS) is poorly understood with no effective therapeutics. One long entertained observation is that ALS may be precipitated focally by nerve injury. Many patients with ALS are athletes or veterans, and some have suffered nerve injuries at the site where ALS first presents. Here we explore how a genetic SOD1 mutation alters the inflammatory response and affects functional recovery after an environmental insult in a rat model. METHODS: Unilateral sciatic nerve crush injuries were performed in SOD1 G93A rats prior to disease symptom onset. Functional recovery was compared between injured wild-type littermates and uninjured SOD1 rats. Spinal cord tissues were analyzed quantitatively for SOD1 expression, glial reactivity, and motor neuron synaptic integrity. RESULTS: Injured SOD1 rats failed to recover and showed hastened functional decline with decreased survival. Injury induced extracellular SOD1 expression was associated with heightened, prolonged microglial and astrogial activation in the ventral horn. This inflammatory response spread to uninjured motor neuron pools and was associated with increased motor neuron synaptic loss. DISCUSSION: This study identified a relationship between genetic and environmental contributions to disease onset and progression in ALS. The findings suggest that injury induced SOD1 mutant protein induces a heightened and prolonged inflammatory response resulting in motor neuron degeneration through synaptic loss. Once initiated, this process spreads to adjacent motor neurons leading to contiguous spread of the disease. Treatments that suppress this heightened glial response could slow disease progression in ALS patients with focal sites of disease onset. SIGNIFICANCE STATEMENT: The contribution of environmental factors such as peripheral nerve insults in ALS is not well understood. Here we examined the effect of a single sciatic nerve injury in SOD1 (G93A) rats to explore the contribution of this environmental insult on disease onset and progression. After the injury, SOD1 animals failed to recover and had a more rapid functional decline. Histopathologically, SOD1 animals had heightened SOD1 expression, microglial and astroglial responses, and a reduction of motor neuron innervation. Taken together, these results provide a plausible mechanism of how the SOD1 mutated protein promotes an abnormal response to injury that leads to neurodegenerative changes in an ALS model that is amenable to therapeutic testing.

Simultaneous interferometric measurement of linear coefficient of thermal expansion and temperature-dependent refractive index coefficient of optical materials.

Characterizing the thermal properties of optical materials is necessary for understanding how to design an optical system for changing environmental conditions. A method is presented for simultaneously measuring both the linear coefficient of thermal expansion and the temperature-dependent refractive index coefficient of a sample interferometrically in air. Both the design and fabrication of the interferometer is presented as well as a discussion of the results of measuring both a steel and a CaF2 sample.

Absolute thickness metrology with submicrometer accuracy using a low-coherence distance measuring interferometer.

Absolute physical thickness across the sample aperture is critical in determining the index of a refraction profile from the optical path length profile for gradient index (GRIN) materials, which have a designed inhomogeneous refractive index. Motivated by this application, instrumentation was established to measure the absolute thickness of samples with nominally plane-parallel surfaces up to 50 mm thick. The current system is capable of measuring absolute thickness with 120 nm (1σ) repeatability and submicrometer expanded measurement uncertainty. Beside GRIN materials, this method is also capable of measuring other inhomogeneous and opaque materials.

Engineered bacteria that self-assemble "bioglass" polysilicate coatings display enhanced light focusing.

Photonic devices are cutting-edge optical materials that produce narrow, intense beams of light, but their synthesis typically requires toxic, complex methodology. Here we employ a synthetic biology approach to produce environmentally-friendly, living microlenses with tunable structural properties. We engineered Escherichia coli bacteria to display the silica biomineralization enzyme silicatein from aquatic sea sponges. Our silicatein-expressing bacteria can self-assemble a shell of polysilicate "bioglass" around themselves. Remarkably, the polysilicate-encapsulated bacteria can focus light into intense nanojets that are nearly an order of magnitude brighter than unmodified bacteria. Polysilicate-encapsulated bacteria are metabolically active for up to four months, potentially allowing them to sense and respond to stimuli over time. Our data demonstrate that engineered bacterial particles have the potential to revolutionize the development of multiple optical and photonic technologies.

Gradient-index materials based on thiol-ene networks.

Gradient-index (GRIN) optics offer spatially varied refractive indexes that can enhance current imaging technologies. Current methods to fabricate GRIN optics are highly complex and costly. Here we report a simple and efficient method that utilizes commercially available reagents to fabricate polymeric GRIN optics with significant refractive index differences (Δn = 0.04). First, two different mixtures of network precursors are layered and time allotted for molecular diffusion in the liquid state, prior to curing. The resulting, partially mixed layers are UV-cured to yield clear, glassy molecular networks with fixed refractive index gradients. The fully cured network resins exhibit smoothly varying composition and refractive index over centimeter length scales, confirmed by spectroscopy and interferometry.

How reliable is the clinical exam in detecting ocular chlamydial infection?

PURPOSE: To describe the relationship between the clinical exam for trachoma and the polymerase chain reaction (PCR) for ocular chlamydia. METHODS: One hundred children in a trachoma-endemic area of Ethiopia were examined three times and swabbed twice for PCR analysis. The assays were compared, and an analysis of the variance between exam and PCR was performed. RESULTS: Inter-examiner agreement was 0.57 (Cohen's kappa), inter-PCR agreement 0.98, and agreement between examiner and PCR, 0.26-0.34. The positive predictive value of the exam in identifying infection was 66%. Inter-examiner variance accounted for 30% of the total variance between the exam and PCR, with the remainder presumably due to an underlying difference in what the exam and PCR measure. CONCLUSIONS: Despite modest inter-grader reliability and correlation with evidence of infection, the clinical exam is widely used due to its convenience and low cost. Efforts to make laboratory tests for ocular Chlamydia trachomatis more affordable would be useful.

Meteors do not break exogenous organic molecules into high yields of diatomics.

Meteoroids that dominate the Earth's extraterrestrial mass influx (50-300 microm size range) may have contributed a unique blend of exogenous organic molecules at the time of the origin of life. Such meteoroids are so large that most of their mass is ablated in the Earth's atmosphere. In the process, organic molecules are decomposed and chemically altered to molecules differently from those delivered to the Earth's surface by smaller (<50 microm) micrometeorites and larger (>10 cm) meteorites. The question addressed here is whether the organic matter in these meteoroids is fully decomposed into atoms or diatomic compounds during ablation. If not, then the ablation products made available for prebiotic organic chemistry, and perhaps early biology, might have retained some memory of their astrophysical nature. To test this hypothesis we searched for CN emission in meteor spectra in an airborne experiment during the 2001 Leonid meteor storm. We found that the meteor's light-emitting air plasma, which included products of meteor ablation, contained less than 1 CN molecule for every 30 meteoric iron atoms. This contrasts sharply with the nitrogen/iron ratio of 1:1.2 in the solid matter of comet 1P/Halley. Unless the nitrogen content or the abundance of complex organic matter in the Leonid parent body, comet 55P/Tempel-Tuttle, differs from that in comet 1P/Halley, it appears that very little of that organic nitrogen decomposes into CN molecules during meteor ablation in the rarefied flow conditions that characterize the atmospheric entry of meteoroids approximately 50 microm-10 cm in size. We propose that the organics of such meteoroids survive instead as larger compounds.