Focal Ratios Research Articles

Optical torque calculations and measurements for DNA torsional studies

The angular optical trap (AOT) is a powerful instrument for measuring the torsional and rotational properties of a biological molecule. Thus far, AOT studies of DNA torsional mechanics have been carried out using a high numerical aperture oil-immersion objective, which permits strong trapping but inevitably introduces spherical aberrations due to the glass-aqueous interface. However, the impact of these aberrations on torque measurements is not fully understood experimentally, partly due to a lack of theoretical guidance. Here, we present a numerical platform based on the finite element method to calculate forces and torques on a trapped quartz cylinder. We have also developed a new experimental method to accurately determine the shift in the trapping position due to the spherical aberrations by using a DNA molecule as a distance ruler. We found that the calculated and measured focal shift ratios are in good agreement. We further determined how the angular trap stiffness depends on the trap height and the cylinder displacement from the trap center and found full agreement between predictions and measurements. As a further verification of the methodology, we showed that DNA torsional properties, which are intrinsic to DNA, could be determined robustly under different trap heights and cylinder displacements. Thus, this work has laid both a theoretical and experimental framework that can be readily extended to investigate the trapping forces and torques exerted on particles with arbitrary shapes and optical properties.

Flat-Focal-Plane Dual-Metasurface Lens for Low Scan Loss and Sidelobe Level of a Metalens Antenna

A flat-focal-plane dual-metasurface lens (dual-metalens) is presented to lower the scan loss and sidelobe level (SLL) of a metalens antenna. The dual-metalens consists of two metasurfaces with different phase shift distributions and focal ratios. This proposed metalens ensures that the focal points of 0° and 30° incident plane waves are on a flat plane, which lowers the beam scan loss and SLLs by reducing the comatic aberration of the metalens. The measurement shows that the proposed antenna achieves a maximum gain of 26.6 dBi at 27.5 GHz with a 10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda _{0}$ </tex-math></inline-formula> -diameter aperture, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda _{0}$ </tex-math></inline-formula> is the wavelength at 28 GHz in free space. The antenna only has a 1.9 dB scan loss with an SLL lower than −14.1 dB at 28 GHz for a scan angle of ±29°. The 3 dB gain frequency range is from 26.8 to 29.3 GHz, which is suitable for the 5G millimeter wave wireless communication.

Optimum telescope focal ratios for microlens-to-fiber coupled integral field spectrographs

We describe the optimum telescope focal ratio for a two-element, three surface, telecentric image-transfer microlens-to-fiber coupled integral field unit within the constraints imposed by micro-optics fabrication and optical aberrations. We create a generalized analytical description of the micro-optics optical parameters from first principals. We find that the optical performance, including all aberrations, of a design constrained by an analytic model considering only spherical aberration and diffraction matches within +/-4% of a design optimized by ray-tracing software such as Zemax. The analytical model does not require any compromise on the available clear aperture; about 90% mechanical aperture of a hexagonal microlens is available for light collection. The optimum telescope f-ratio for a 200{\mu}m core fiber fed at f/3.5 is between f/7 and f/12. We find the optimum telescope focal ratio changes as a function of fiber core diameter and fiber input beam speed. A telescope focal ratio of f/8 would support the largest range of fiber diameters (100 to 500{\mu}m) and fiber injection speeds (between f/3 and f/5). The optimization of telescope and lenslet-coupled fibers is relevant for the design of high-efficiency dedicated survey telescopes, and for retro-fitting existing facilities via introducing focal macro-optics to match the instrument input requirements.

Spatiotemporal Deconvolution of Hydrophone Response for Linear and Nonlinear Beams-Part II: Experimental Validation.

This article reports experimental validation for spatiotemporal deconvolution methods and simple empirical formulas to correct pressure and beamwidth measurements for spatial averaging across a hydrophone sensitive element. The method was validated using linear and nonlinear beams transmitted by seven single-element spherically focusing transducers (2-10 MHz; F /#: 1-3) and measured with five hydrophones (sensitive element diameters dg : 85-1000 [Formula: see text]), resulting in 35 transducer/hydrophone combinations. Exponential functions, exp( -αx ), where x = dg /( λ1F /#) and λ1 is the fundamental wavelength, were used to model focal pressure ratios p'/p (where p' is the measured value subjected to spatial averaging and p is the true axial value that would be obtained with a hypothetical point hydrophone). Spatiotemporal deconvolution reduced α (followed by root mean squared difference between data and fit) from 0.29-0.30 (7%) to 0.01 (8%) (linear signals) and from 0.29-0.40 (8%) to 0.04 (14%) (nonlinear signals), indicating successful spatial averaging correction. Linear functions, Cx + 1, were used to model FWHM'/FWHM, where FWHM is full-width half-maximum. Spatiotemporal deconvolution reduced C from 9% (4%) to -0.6% (1%) (linear signals) and from 30% (10%) to 6% (5%) (nonlinear signals), indicating successful spatial averaging correction. Spatiotemporal deconvolution resulted in significant improvement in accuracy even when the hydrophone geometrical sensitive element diameter exceeded the beam FWHM. Responsible reporting of hydrophone-based pressure measurements should always acknowledge spatial averaging considerations.

Hybrid Numerical Methodology for Efficient Design and Optimization of Transmit-Array Antennas, X-Band Application

This paper presents a complete hybrid numerical methodology for the efficient design and optimization of large-scale Transmit-Array (TA) antennas for modern telecommunication applications. There are four main components to the proposed work and methodology: 1) the implementation through Python scripts of a hybrid scheme based on the Friis analytical formula for linking gain and phase of the primary source and elementary cells of the studied transmit-array; 2) the implementation of a Particle Swarm Optimizer (PSO) for efficient characterization of the optimal phase distribution on the in-plane lens maximizing the gain of the antenna and minimizing the side-lobe levels for multiple fed TA antennas; 3) the implementation of a full-wave Finite element and Interconnecting domain decomposition (FETI) for the final analysis of the TA radiating performance; 4) the design, optimization, fabrication and proof of concept of an X band transmit-array including the focal source. This work presents the main functionalities of the hybrid Python/CST tool associated with phase compensation PSO, FETI implementation for transmit-arrays and as an application of this numerical strategy, a new compact unit-cell operating in the X-band (thickness of 3.2 mm) able to easily generate Phase Rotations (PR) necessary for TAs with phase compensation on the aperture. The proposed unit-cell is a completely symmetric design including a metallic via interconnecting two identical square patches (including a circular hole in the center and a microstrip line) by crossing through a ground plane. A particle swarm optimization (PSO) routine is proposed as a way to quickly optimize the phase distribution of the transmit-array unit-cells. The optimization routine is tested through multiple sources and focal ratios, demonstrating a reduction of over 50% of the volume occupied by the antenna, while keeping a high gain (19.5 dBi) and overall good performance.

Photochromic point-diffraction inteferometer

We demonstrate a versatile and fully adaptable point-diffraction interferometer (PDI) for optical testing which is based on a thin photochromic film. Pinholes are optically written in the photochromic layer, and sizes are easily customized to test optics with a wide range of focal ratios. The transparency of the layer can be tuned to optimize the contrast between the pinhole and the surrounding area and maximize the fringe visibility. Accuracy and repeatability of the photochromic PDI are determined; moreover the results are compared with those obtained with a standard Fizeau interferometer.

Integrated photonic building blocks for next-generation astronomical instrumentation I: the multimode waveguide

We report on the fabrication and characterization of composite multimode waveguide structures that consist of a stack of single-mode waveguides fabricated by ultrafast laser inscription. We explore 2 types of composite structures; those that consist of overlapping single-mode waveguides which offer the maximum effective index contrast and non overlapped structures which support multiple modes via strong evanescent coupling. We demonstrate that both types of waveguides have negligible propagation losses (to within experimental uncertainty) for light injected with focal ratios >8, which corresponds to the cutoff of the waveguides. We also show that right below cutoff, there is a narrow region where the injected focal ratio is preserved (to within experimental uncertainty) at the output. Finally, we outline the major application of these highly efficient waveguides; in a device that is used to reformat the light in the focal plane of a telescope to a slit, in order to feed a diffraction-limited spectrograph.

Stereo rectification of uncalibrated and heterogeneous images

In this paper, an algorithm for rectifying heterogeneous and uncalibrated pairs of stereo images is presented. In particular, a pair of images is captured by using a combination of static and dynamic cameras at unequal zoom, thus having different focal lengths and/or image resolutions. The rectification of such pairs of images is made in two steps. In the first step, image shrinking based on focal ratios is performed for compensating the effect of unequal zoom levels followed by a zero padding on the smaller image for making the images of equal size. In the second step, rectification transformations are calculated by solving a nonlinear constrained optimization problem for a given set of pairs of corresponding points (SIFT descriptors) between stereo images. Experiments are performed to evaluate the performance of the proposed method and assess the improvements of the proposed method over direct rectification.

International Ratios Tell a Story—2005

This case provides an opportunity for students to (1) understand the calculation of a number of basic financial ratios, (2) analyze a set of common-size balance sheets and several financial ratio metrics, (3) hypothesize how some basic understanding of an industry should be reflected in certain financial indicators, and (4) present to their classmates a rationale for their pairings and to respond to questions from their classmates. If instructors are so inclined, use of this case also provides an opportunity to (1) discuss an organizing framework for the focal ratios, (2) present the concepts of financial leverage and the DuPont ratio model, and (3) introduce students to some of the published sources for industry metrics.

Photopic Negative Response of Focal Electoretinograms in Glaucomatous Eyes

To determine the clinical importance of the photopic negative response (PhNR) of the focal electoretinogram (fERG) for diagnosing glaucoma. Fifty-nine eyes of 38 patients with open-angle glaucoma (OAG), 12 glaucoma suspects, and 32 eyes of 32 normal controls were studied. The fERGs were elicited by a 15 degrees stimulus spot on the macula region, the supero-temporal, and infero-temporal regions of the macula. The mean of the visual sensitivity was measured by standard automated perimetry (SAP). The optimal cutoff amplitudes of the focal PhNR and ratios of the focal PhNR/b-wave amplitudes that discriminated glaucomatous eyes from normal eyes were obtained from the receiver operating characteristic curves. The amplitudes of the PhNR were significantly smaller in patients with OAG than in normal controls (P < 0.00001). A curvilinear relationship was found between the mean sensitivity (dB, on log scale) and the PhNR amplitude, and between the mean sensitivity and the PhNR/b-wave amplitude ratio. After converting the mean sensitivity from a logarithmic to a linear scale, the amplitude of the PhNR and PhNR/b-wave ratio were linearly correlated with the SAP-determined visual sensitivity in all retinal areas (r = .428-0.544, P < 0.0001). When the optimal cutoff values were used, the sensitivity and specificity of the PhNR/b-wave amplitude ratio were 98.3% and 90.1%, respectively. The reduction of the focal PhNR amplitude was associated with a local decrease in the retinal sensitivity in OAG. The high sensitivity and specificity suggest that the focal PhNR can be used to detect functional loss in OAG.

International Ratios Tell a Story: 2005

This case provides an opportunity for students to (1) understand the calculation of a number of basic financial ratios, (2) analyze a set of common-size balance sheets and several financial ratio metrics, (3) hypothesize how some basic understanding of an industry should be reflected in certain financial indicators, and (4) present to their classmates a rationale for their pairings and to respond to questions from their classmates. If instructors are so inclined, use of this case also provides an opportunity to (1) discuss an organizing framework for the focal ratios, (2) present the concepts of financial leverage and the DuPont ratio model, and (3) introduce students to some of the published sources for industry metrics.

The optics of the growing lungfish eye: Lens shape, focal ratio and pupillary movements inNeoceratodus forsteri(Krefft, 1870)

Lungfish (order Dipnoi) evolved during the Devonian period and are believed to be the closest living relatives to the land vertebrates. Here we describe the previously unknown morphology of the lungfish eye in order to examine ocular adaptations present in early sarcopterygian fish. Unlike many teleosts, the Australian lungfish Neoceratodus forsteri possesses a mobile pupil with a slow pupillary response similar to amphibians. The structure of the eye changes from juvenile to adult, with both eye and lens becoming more elliptical in shape with growth. This change in structure results in a decrease in focal ratio (the distance from lens center to the retina divided by the lens radius) and increased retinal illumination in adult fish. Despite a degree of lenticular correction for spherical aberration, there is considerable variation across the lens. A re-calculation of spatial resolving power using measured focal ratios from cryosectioning reveals a low ability to discriminate fine detail. The dipnoan eye shares more features with amphibian eyes than with most teleost eyes, which may echo the visual needs of this living fossil.

VISPO project: visible image-spectrometer for planetary observations

Satellite instrumentations designed for planetary studies are often open to other interesting applications from ground: not only one can efficiently carry out detailed calibrations before space data become available, but also the prototypes of the satellite instruments can be successfully employed in different fields ranging from astrophysics to cosmology. Both possibilities are opened by coupling these instruments with ground based telescopes having short focal ratios, like those designed for far infrared studies. These possibilities are particularly amazing in view of the long delay usually present between the launch and the collection of the first scientific data (months in case of Mars Express, years in case of Rosetta).We propose in this article to employ immediately this technology, by coupling the developing model of the Image-Spectrometer VIRTIS-M with the ground telescope MITO.This project will allow us to perform a better calibration of the space qualified instrument and observational campaigns, including some important cosmological investigations.

Exact optics - II. Exploration of designs on- and off-axis

The two-mirror telescopes/cameras that have no coma, no spherical aberration and arbitrarily fast focal ratios form a two-parameter (s, K) family of exact optical designs analytically derived earlier. We explore the full range of these designs in the s‐K plane. Here s is the mirror separation/focal length and K is the distance from secondary to focus/focal length. Besides perfect-focus analogues of most well-known telescope designs, there are families of spectrograph cameras, X-ray telescopes and solar furnaces. Systems with s = 2 have minimum astigmatism and have exceptionally good images.

Design and performance considerations of cat's-eye retroreflectors for use in open-path Fourier-transform-infrared spectrometry.

A ray-tracing analysis of cat's-eye retroreflectors for use in active open-path Fourier-transform-infrared (OP/FT-IR) spectrometry and the results of testing f/0.5 and f/1.75 cat's-eye retroreflectors built in our laboratory with a commercial active OP/FT-IR spectrometer are presented. The ray-tracing model is based on the optical characteristics of a commercial single-telescope monostatic OP/FT-IR spectrometer and explores trends in cat's-eye behavior in practical but rigorous field conditions encountered during transportable outdoor use. All mirrors modeled are paraboloids for which the focal ratios of the primary mirror are f/0.5, f/1.75, and f/3. The effect of the focal ratio of the primary mirror, the focal length of the secondary mirror, and the off-axis alignment of the primary and the secondary mirror have been evaluated as a function of path length, including variable input-beam divergence, between the spectrometer and the cat's-eye. The paraboloidal mirrors comprising the primary and secondary of the cat's-eye retroreflectors tested were made in our laboratory by spin casting liquid epoxy-graphite composite mixtures followed by in situ polymerization with no postpolishing.

Wavefront aberrations of rotationally symmetric CGHs fabricated by a polar coordinate laser plotter

Computer-generated holograms (CGHs) were fabricated by a polar coordinate laser plotter. The wavefront aberrations of these CGHs caused by fabrication inaccuracies were measured interferometrically. We tested Fresnel zone plates as typical examples of CGHs with focal ratios of ƒ/10 and ƒ/5 with a Fizeau interferometer. The tests comprised both binary phase holograms and binary amplitude holograms. The wavefront aberrations of the CGHs had an rms variation of about λ /50. Two types of aberrations were identified and could be referred to certain writing errors. Their size was deduced from the interferograms.

Spherical primary telescope with aspheric correction at a small internal pupil

The aspheric plate at the center of curvature of a spherical primary is replaced by a small aspheric corrector at a minified pupil located inside a reimaging camera. The correctors are identical for each reimaging camera because the spherical aberration of the primary sphere is identical and symmetrical for all field positions. The magnitude of the field aberrations is evaluated over a range of primary focal ratios and minified pupil diameters. The major term is the increased field angle through the minified aspheric corrector. The field and chromatic aberrations in such a camera are compared with the equivalent full-aperture Schmidt corrector. Field-of-view partitioning enables each subfield to be designed for specific observational requirements, such as multiple-fiber spectrography or CCD imaging. Field partitioning is shown to be a powerful means for the replacement of the large aspheric corrector of a Schmidt telescope by a multiplicity of small reimaging subsystems. The cost to fill the typical wide field of a Schmidt telescope with reimaging modules is approximately 1% the cost of a Schmidt aspheric plate.

Hemodynamic parameters of failing infrainguinal bypass grafts

To assess the relationship of duplex ultrasound hemodynamic parameters in stenotic vein grafts with events such as graft thrombosis or surgical revisions. We studied 35 patent infrainguinal bypass grafts that were observed by means of color duplex graft mapping using a surveillance protocol. During the 11.2 month mean follow-up interval, 10 grafts developed complications. Two stenotic grafts (1 already revised) thrombosed spontaneously, and arteriography was obtained on the basis of either clinical indications or a decreased ankle/brachial index of greater than 0.15 on 9 bypasses, leading to 12 procedures (multiple procedures on 2 grafts). The 14 duplex examinations preceding an event showed these bypasses had increased focal peak systolic velocities that ranged from 250 to 600 cm/s and velocity ratios that ranged from 3.4 to 25.0 at the stenotic segment of the graft, anastomosis, or outflow artery. None of the grafts with a stenotic peak systolic velocity less than 250 cm/s or a velocity ratio less than 3.4 thrombosed spontaneously or required revision. We conclude that stenotic vein grafts with a focal peak systolic velocity of at least 250 cm/s or a velocity ratio of at least 3.4 are at increased risk for thrombosis or need for revision. Asymptomatic stenotic vein grafts with focal peak systolic velocities and ratios less than the above values may be safely observed without immediate risk for thrombosis.

The development and application of a general lateral‐stereo camera model

Abstract A general camera model in a lateral‐stereo setup is developed. In such a model, the image planes do not have to be parallel, the longitudinal planes on which the cameras are placed need not be identical, and the camera parameters are not required to be the same. The developed general model is employed to determine the position and orientation of a box, and the errors resulting from inaccuracy in camera parameters and image preprocessing are very small compared to the traditional parallel model. Sensitivity analyses are done for the deviations in focal lengths, lens centers, image centers, aspect ratios, and image preprocessing. The results show that the proposed model provides a good vehicle toward more stable 3D range acquisition.

Ross null test for conic mirrors

Various refractive null-testing arrangements have been used over the years for testing concave nonspherical mirrors. This paper presents a method for null testing that uses a single plano-convex lens to compensate for the spherical aberration of a concave conic mirror when tested at its center of curvature. This testing method, called the Ross null test, requires a high-quality null lens and a standard Foucault test apparatus. This paper presents graphical and numerical data that provide the necessary parameters for implementing the Ross null test for mirrors with focal ratios ranging from f/3.5 to f/10 and for conic deformations ranging from eccentricities of 0.70-1.50.