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This work presents a volumetric calibration method for Scheimpflug plenoptic camera in particle image velocimetry. To establish a prerequisite foundation for the Scheimpflug light-field PIV, the proposed technique makes use of the unique point-like pattern and plenoptic disc feature of particle light-field images to accurately determine affected pixels for a spatial voxel in a measurement volume. With Gaussian optics, an ideal projection model of the Scheimpflug plenoptic camera is derived to provide a basis for the calibration method. By taking lens defects, optical window’s imperfection, inaccurate tilted-angle and other practical application difficulties into account, the calibration method can establish the mapping relationship between a spatial voxel and its affected pixels correctly. The volumetric calibration method was validated by a classic vortex-ring PIV measurement where the correspondence between a voxel and its affected pixels was accurately determined and the volumetric velocity field was successfully acquired.

During the production of a new designed lens system, overweighted assembling and manufacturing errors can cause the degradation of the performance of the whole system. Therefore, optimizations to improve the assembling and manufacturing tolerances sensitivity are greatly required in lens design industry. Following the principle of Gaussian optics, there are some practical implications of the first order derivatives which are of great significance to analyse the sensitivity of a lens system with its structural parameters changing. It is demonstrated that manufacturing errors, such as tilting, decentering and so on, induce the real rays' height shifting on each surface of an imaging system, which subsequently induces the decline of image quality. Thus, we proposed a scheme to use the first order derivatives of the height of a real ray on the image surface in a lens system versus that on the pupil surface, which indicate the height variations of the real ray on the image surface of the lens system caused by the displacement of its corresponding height on the pupil surface, as a merit function to improve the tolerance sensitivity of the whole system. A test program using the ZPL language in Opticstudio has preliminarily confirmed the effectiveness of our proposed methods. And as it is aimed at controlling the real rays of a lens system to reduce its sensitivity according to assembling and manufacturing errors, our scheme is theoretically able to appropriate to all lens design systems.

Aniseikonia as one of the major risk factors for asthenopic problems is mostly overlooked in modern cataract surgery. The purpose of this study was to develop a simple calculation scheme for clinicians to predict the object to image magnification in a pseudophakic eye with biometric data.The calculation scheme for object to image magnification in the pseudophakic eye is based on a vergence calculation of the lens power with theoretical optical formulae. From the biometric data, which are typically derived from both eyes during lens power calculation, the vergences in front of and behind the 3 or 4 refractive surfaces of the pseudophakic eye model are used to predict the magnification for objects at infinity or objects located at a finite measurement distance (e.g. 5 m).With a formula-based lens power calculation a pseudophakic eye model is set up with 3 or 4 refractive surfaces (postoperative spectacle refraction; thick cornea described by anterior surface or thick cornea characterized by anterior and posterior surfaces; intraocular lens). The vergence in front of and behind each refractive surface is derived by means of linear Gaussian optics. The quotient of the product of all vergences in front of the surfaces and the product of all vergences behind the respective surfaces describes the object to image magnification of the eye. A comparison of the object to image magnification of both eyes yields the retinal image size disparity or aniseikonia. This calculation strategy is shown in a step-by-step approach exemplarily for the Haigis and Hoffer‑Q formulae (3 surfaces) and the Castrop formula (4 surfaces).If during planning and lens power calculation biometry is performed for both eyes, ocular magnification of both eyes can be easily derived with this calculation scheme and aniseikonia can be extracted from a comparison of magnification of both eyes. Such a simple prediction should be established as a standard for precataract biometry and lens power calculation for early detection and avoidance of asthenopic complaints after cataract surgery.HINTERGRUND UND ZIELSETZUNG: Die Aniseikonie als mögliche Ursache asthenopischer Beschwerden tritt bei der modernen Kataraktchirurgie oft in den Hintergrund. Ziel der vorliegenden Arbeit ist es, dem Kliniker ein einfaches Berechnungsmodell an die Hand zu geben, mit dem der Abbildungsmaßstab des pseudophaken Auges abgeschätzt werden kann.Das Berechnungsschema für den Abbildungsmaßstab des pseudophaken Auges bezieht sich auf die formelbasierte (vergenzbasierte) Berechnung der Intraokularlinse mit theoretisch-optischen Formeln. Aus den biometrischen Größen, die in der Regel für beide Augen bei der Linsenberechnung vorliegen, kann aus den Vergenzen vor und hinter den 3 oder 4 refraktiven Grenzflächen im pseudophaken Augenmodell der Abbildungsmaßstab für Objekte im Unendlichen oder in einer endlichen Messdistanz ermittelt werden.Bei der formelbasierten Berechnung wird ein pseudophakes Augenmodell mit 3 bzw. 4 refraktiven Grenzflächen (postoperative Brillenrefraktion; dünne Hornhaut, beschrieben durch die Vorderfläche, bzw. dicke Hornhaut, beschrieben durch die Vorder- und Rückfläche; Intraokularlinse) definiert und mit den Methoden der linearen Optik die Vergenz vor und hinter jeder Grenzfläche bestimmt. Der Quotient aus dem Produkt der Vergenzen vor den Grenzflächen und dem Produkt der Vergenzen unmittelbar hinter den Grenzflächen beschreibt direkt den Abbildungsmaßstab des Auges. Aus dem Vergleich des Abbildungsmaßstabs beider Augen kann unmittelbar der retinale Bildgrößenunterschied ermittelt werden. Exemplarisch wird dies anhand der Haigis- und Hoffer-Q-Formel (3 Flächen) und der Castrop-Formel (4 Flächen) gezeigt.Wird bei der Planung der Kataraktoperation die Biometrie und Linsenberechnung an beiden Augen durchgeführt, so kann mit einfachen Mitteln der Abbildungsmaßstab bei beiden Augen und aus dem Vergleich beider Augen die Aniseikonie des pseudophaken Patienten ermittelt werden. Eine derartige Abschätzung sollte fester Bestandteil der Linsenberechnung werden, um mögliche asthenopische Beschwerden nach der Kataraktoperation früh zu erkennen.

Trapped atomic ensembles are convenient systems for quantum information storage in the long-lived sublevels of the electronic ground state and its conversion to propagating optical photons via stimulated Raman processes. Here we investigate a phase-matched emission of photons from a coherently prepared atomic ensemble. We consider an ensemble of cold atoms in an elongated harmonic trap with normal density distribution, and determine the parameters of paraxial optics to match the mode geometry of the emitted radiation and optimally collect it into an optical waveguide.

In the ophthalmic Shack-Hartmann wavefront sensor beacon light originates from various depths within the retina. We model the retina of the human and mouse eyes as formed by two backscattering planes, showing that the use of lenslets with low Fresnel number and/or too small search boxes in the centroiding algorithm will produce artifactual aberrations. We evaluate the impact of these errors for four common beacon illumination strategies: full circular, annular, small circular on-axis and small circular off-axis. We find that artifactual aberrations are larger for annular and off-axis beacon illumination, dominated by defocus plus spherical aberration and defocus plus coma, respectively. These artifactual aberrations can be almost completely eliminated by selecting the minimum centroid search box size based on a simple Gaussian optics model and ocular biometry, provided the lenslet Fresnel number is sufficiently large to introduce minimal cross-talk between images of adjacent lenslets.

We analyze the use of two varifocal lenses, with fixed interlens separation, for achieving tunable magnification at a specific throw. Our discussion extends the Hopkins procedure circumscribed to the determination of fixed optical powers in a multilens system. We illustrate our results by presenting the Gaussian optics design of surgical spectacles, which have tunable magnification while generating virtual images with zero throw. We also report novel formulas describing this type of two-lens zoom system, which works without any mechanical compensation.

An incoherent optical detection sensor (often referred to as energy or direct detection sensor) used for remote detection and ranging purposes is a useful tool. While the accuracy and robustness of an incoherent sensor relative to a coherent sensor may be lacking particularly in cluttered environments, it has a place in the world due to its simplicity and performance. With this, a best design approach is sought to meet requirements in a stochastic fashion. In developing the design approach, motivations are borrowed from decades of research in radar systems. This article provides a sensor- or top-level design approach for an incoherent optical detection sensor based mainly on paths developed in radar.

In Gaussian optics all observers experience the same magnification, the instrument’s angular magnification, when viewing distant objects though a telescope or other afocal instruments. However, ana...

The latest generation of Cassegrain radio astronomy antennas is designed for multiple frequency bands with receivers for individual bands offset from the antenna axis. The offset feed arrangement typically has two focusing elements in the form of ellipsoidal mirrors in the optical path between the feed horn and the antenna focus. This arrangement aligns the beam from the offset feed horn to illuminate the subreflector. The additional focusing elements increase the number of design variables, namely the distances between the horn aperture and the first mirror and that between the two mirrors, and their focal lengths. There are a huge number of possible combinations of these four variables in which the optics system can take on. The design aim is to seek the combination that will give the optimum antenna efficiency, not only at the centre frequency of the particular band but also across its bandwidth. To pick the optimum combination of the variables, it requires working through, by computational mean, a continuum range of variable values at different frequencies which will fit the optics system within the allocated physical space. Physical optics (PO) is a common technique used in optics design. However, due to the repeated iteration of the huge number of computation involved, the use of PO is not feasible. We present a procedure based on using multimode Gaussian optics to pick the optimum design and using PO for final verification of the system performance. The best antenna efficiency is achieved when the beam illuminating the subreflector is truncated with the optimum edge taper. The optimization procedure uses the beam’s edge taper at the subreflector as the iteration target. The band 6 receiver optics design for the Atacama Large Millimetre Array (ALMA) antenna is used to illustrate the optimization procedure.

PURPOSE Cardinal points are used for ray tracing through Gaussian systems. Anti-principal and anti-nodal points (which we shall refer to as the anti-cardinal points), along with the six familiar cardinal points, belong to a much larger set of special points. The purpose of this paper is to obtain a set of relationships and resulting equalities among the cardinal and anti-cardinal points and to illustrate them using Pascal's ring. METHODS The methodology used relies on Gaussian optics and the transference T. We make use of two equations, obtained via the transference, which give the locations of the six cardinal and four anti-cardinal points with respect to the system. We obtain equalities among the cardinal and anti-cardinal points. We utilise Pascal's ring to illustrate which points depend on frequency and their displacement with change in frequency. RESULTS Pascal described a memory schema in the shape of a hexagon for remembering equalities among the points and illustrating shifts in these points when an aspect of the system changes. We modify and extend Pascal's ring to include the anti-cardinal points. We make use of Pascal's ring extended to illustrate which points are dependent on the frequency of light and the direction of shift of the equalities with change in frequency. For the reduced eye the principal and nodal points are independent of frequency, but the focal points and the anti-cardinal points depend on frequency. For Le Grand's four-surface model eye all six cardinal and four anti-cardinal points depend on frequency. This has implications for definitions, particularly of chromatic aberrations of the eye, that make use of cardinal points and that themselves depend on frequency. CONCLUSIONS Pascal's ring and Pascal's ring extended are novel memory schema for remembering the equalities among the cardinal and anti-cardinal points. The rings are useful for illustrating changes among the equalities and direction of shift of points when an aspect of a system changes. Care should be taken when defining concepts that rely on cardinal points that depend on frequency.

PURPOSE To show that 14-dimensional spaces of augmented point P and angle Q characteristics, matrices obtained from the ray transference, are suitable for quantitative analysis although only the latter define an inner-product space and only on it can one define distances and angles. The paper examines the nature of the spaces and their relationships to other spaces including symmetric dioptric power space. METHODS The paper makes use of linear optics, a three-dimensional generalization of Gaussian optics. Symmetric 2 × 2 dioptric power matrices F define a three-dimensional inner-product space which provides a sound basis for quantitative analysis (calculation of changes, arithmetic means, etc.) of refractive errors and thin systems. For general systems the optical character is defined by the dimensionally-heterogeneous 4 × 4 symplectic matrix S, the transference, or if explicit allowance is made for heterocentricity, the 5 × 5 augmented symplectic matrix T. Ordinary quantitative analysis cannot be performed on them because matrices of neither of these types constitute vector spaces. Suitable transformations have been proposed but because the transforms are dimensionally heterogeneous the spaces are not naturally inner-product spaces. RESULTS The paper obtains 14-dimensional spaces of augmented point P and angle Q characteristics. The 14-dimensional space defined by the augmented angle characteristics Q is dimensionally homogenous and an inner-product space. A 10-dimensional subspace of the space of augmented point characteristics P is also an inner-product space. CONCLUSIONS The spaces are suitable for quantitative analysis of the optical character of eyes and many other systems. Distances and angles can be defined in the inner-product spaces. The optical systems may have multiple separated astigmatic and decentred refracting elements.

The light–energy coupling during femtosecond laser processing of glass is mediated by non-linear ionization mechanisms through the formation of an electron plasma. Its transient optical properties provide information about the density, temperature and scattering rate of the excited electrons. In turn, these properties strongly condition the features and size of the permanent optical modification near the focal volume that are desirable to fabricate photonic devices, such as optical waveguides inside transparent materials. Here, we report on the spectral response of a fs-laser-induced electron plasma inside fused silica by measuring its transient transmission using a broadband probe. We model the interaction of the probe beam with the plasma by combining Drude–Sommerfeld model with Gaussian optics. In this manner, we take into account both the laser–plasma interaction and the influence of the chromatic aberration inherent to a broadband-based system. We find good agreement between experiments at several processing energies and simulations and provide an estimate of the dielectric function of the excited material.

The multiple regression formulas and correlation of ocular components with refractive errors are presented by Gaussian optics. The refractive error changing rate for the cornea and lens power, the axial length, anterior chamber depth (ACD) and vitreous chamber depth (VCD) are calculated, including nonlinear terms for more accurate rate functions than the linear theory. Our theory, consistent with the empirical data, shows that the Pearson correlation coefficients for spherical equivalent (SE) and ocular components are highest for SE with axial length, ACD and VCD and weakest for corneal power, lens power and lens thickness. Moreover, our regression formulas show the asymmetric feature of the correlation that the axial length, ACD and VCD are more strongly correlated (with higher negative regression constants) with refractive errors in eyes with hyperopia than in eyes with myopia, particularly for severe hyperopia.

This work presents a volumetric calibration method for single-camera light-field particle image velocimetry (light-field PIV or LF-PIV). The proposed technique makes use of the unique point-like feature of particle light-field images to accurately determine affected pixels for a spatial voxel over a relative large measurement volume. A calibration model is derived based on Gaussian optics, which relates a spatial point light source with its confusion circle produced on microlens array (MLA), and optical distortions are accounted for by introducing five calibration parameters. By taking lens defects and misalignment between MLA and image sensor into account, the calibration method can calculate weighting coefficient for particle image reconstruction more accurately than the theoretical ray-tracing method, especially for regions further away from focal plane where light ray deflections are significant due to optical distortions. The volumetric calibration method was validated by simulation tests using synthetic light-field images, and has been successfully applied to a classic vortex-ring LF-PIV measurement, where the measurable range in depth direction was successfully extended and the quality of reconstructed volumetric velocity field was greatly improved. MOE (Min. of Education, S’pore) Accepted version

Optrodes are neural probes for delivering light at neurons, at least with an irradiance of 1 mW/mm2. MicroLED (microlight-emitting diode) optrodes with a microlens to collimate the light can improve the irradiance without increasing the microLED power consumption, minimizing the brain overheating. This paper presents FEM (finite element method) simulations of a PDMS (polydimethylsiloxane) microlens capable of collimating the light from a microLED, ensuring an average irradiance of 310 mW/mm2. Based on the simulated microlens, a microlens array was fabricated, using microfabrication processes. One of the PDMS microlens from the fabricated array was experimentally characterized, using AFM (atomic force microscopy) and SEM (scanning electron microscopy). The average surface roughness, base diameter and height of the microlens is 2.3 nm, 80 μm and 55 μm, respectively. It was also possible to determine the microlens focal length (96 μm), numerical aperture (0.42), f-number (1.2) and depth of focus (2.66 μm), using Gaussian optics. The fabrication process was validated, even using PDMS/PDMS demolding without surface treatment of the negative mold., This work is supported by FCT: OpticalBrain, PTDC/CTM-REF/28406/2017 operation code NORTE-01-0145-FEDER- 028406; OCT-RAMAN, PTDC/FIS- OTI/28296/2017 operation code NORTE-01-0145-FEDER-028296; CMEMS-UMinho strategic project UIDB/04436/2020; project of Infrastructures Micro&NanoFabs@PTNORTE- 01-0145-FEDER-022090, PORNorte, Portugal 2020 by FEDER funds through the COMPETE 2020 Programa Operacional Competitividade e Internacionalização (POCI). The work is also supported by RFF Forskningsfond Oslofjordfondet (Project No. 285575 and 296654), National Natural Science Foundation of China (Project No. 61950410621, 61531008 and 11702045). The support from Chongqing Research Program of Basic Research and Frontier Technology (Project No. cstc2016jcyjA0292, cstc2019jcyj-msxmX0776, cstc2017jcyjAX0191, cstc2017jcyjA1842 and cstc2018jcyjA4046), and Chongqing Education Commission – Science and Technology Research Program (Proj. nos. KJZD-K201800802, KJZD-K201900802) are also acknowledged.

Quantifying the microcirculation system is helpful for a more accurate diagnosis of blood flow related diseases. In this work, we report a depth-resolved fractal parameter analysis of human microvasculature obtained with a swept-source optical coherence tomography (SS-OCT) system after depth compensation. In our analysis, the characteristics of Gaussian optics and the attenuation of light intensity with the propagation distance into the tissue were taken into account. To obtain accurate depth-resolved fractal parameter of microvasculature in human skin, a swept-source optical coherence tomography (SS-OCT) system was built. First, three-dimension blood flow datasets were acquired. Then the signals from multiple depth layers of human skin were compensated based on our model, and depth-resolved fractal parameters were extracted finally. The en-face images of the microvasculature of different areas were presented. To the best of our knowledge, for the first time, it was found that the characteristic change of the fractal parameters of the microvasculature of in vivo human skin may be missed due to the light attenuation and the features of Gaussian optics. The depth-resolved fractal analysis of human microvasculature after depth-dependent compensation of imaging signals allows more accurate blood flow related diagnose diseases or monitoring renormalization of the microvasculature after treatment.

Optics technology is being increasingly used in mainstream industrial and research domains such as terrestrial telescopes, biomedical imaging and optical communication. One of the most widely used modeling approaches for such systems is Gaussian optics, which describes light as a beam. In this paper, we propose to use higher-order-logic theorem proving for the analysis of Gaussian optical systems. In particular, we present the formalization of Gaussian beams and verify the corresponding properties such as beam transformation, beam waist radius and location. Consequently, we build formal reasoning support for the analysis of quasi-optical systems. In order to demonstrate the effectiveness of our approach, we present a case study about the receiver module of a real-world Atacama Pathfinder Experiment (APEX) telescope.

The way to generalize scalar to wave optics, thus including polarization in the treatment consistent with the Maxwell equations was shown by Mukunda, Simon and Sudarshan for paraxial systems, based on a group theoretical analysis. Here, the Mukunda–Simon–Sudarshan (MSS) theory for the passage from scalar to vector optics is derived by casting the basic formalism in a framework very similar to the Dirac electron theory. The resulting formalism is suitable for extending the MSS-theory beyond the paraxial approximation.

This work deals with a problem of paraxial analysis of optical systems for transformation of Gaussian beams. General equations describing the paraxial parameters of a two-element zoom system for transformation of a Gaussian beam are derived. It is shown that such a zoom lens has different kinematics with respect to classical zoom system designed for homocentric beams, which depends on the parameters of the transformed Gaussian beam.

This paper reports on the discovery of the most unambiguous generalized vectorial laws of reflection and refraction along with the launching of a new world of geometrical optics with a lot of novel interesting physical insights to optical phenomena.

Special Problems in Ray Optics Orbital Angular Momentum: A Ray Optical Interpretation, M. Padgett Wigner Distributions Moments for Beam Characterization, T. Alieva, A. Camara, and M.J. Bastiaans Dynamic Programming Applications in Optics, M.L. Calvo, J. Perez-Rios, and V. Lakshminarayanan Mathematical Formalism in Wave Optics Basis Expansions for Monochromatic Field Propagation in Free Space, M.A. Alonso and N.J. Moore Solutions of Paraxial Equations and Families of Gaussian Beams, E. Abramochkin, T. Alieva, and J.A. Rodrigo The Decomposition Method to Solve Differential Equations: Optical Applications, V. Lakshminarayanan and S. Nandy Plasmonics An Introduction to Mathematics of Transformational Plasmonics, M. Kadic, S. Guenneau, and S. Enoch Plasmonics: Computational Approach, M. Sukharev Applications of Group Theory in Optics Lorentz Group in Ray and Polarization Optics, S. Baskal and Y.S. Kim Paraxial Wave Equation: Lie Algebra-Based Approach, A. Torre Dihedral Polynomials, M. Viana Lie Algebra and Liouville Space Methods in Quantum Optics, M. Ban Quantum Optics Methods From Classical to Quantum Light and Vice Versa: Quantum Phase-Space Methods, A. Luis Coherence Functions in Classical and Quantum Optics, I. Ashraf Zahid and V. Lakshmianrayanan Quantum Memory Channels in Quantum Optics, T. Rybar, M. Zyman, and V. Buzek Computational Optics/Image Processing An Introduction to Super-Resolution Imaging, J.D. Simpkins and R.L. Stevenson The Differential Structure of Images, B.M. ter Haar Romeny Index

A multi-Gaussian beam model uses a superposition of Gaussian beams to simulate the waves radiated from an ultrasonic transducer. It is shown here that propagation and reflection/transmission laws for Gaussian beams in fluids and elastic solids can be written in the form of A, B, C, D matrices that are analogous to the A, B, C, D scalars used in Gaussian optics. This representation leads to simple expressions for a Gaussian beam even after that beam has been transmitted or reflected at multiple curved interfaces and produces a highly modular multi-Gaussian beam model that is also computationally very efficient. Some examples of the use of this model for both planar and curved interfaces will be given.

We present a new method to achieve compactness for zoom lens design with a high zoom ratio. In the method, initial parameters of lens system are solved with Gaussian optics Theory. And then the first-order quantities are assigned to lens modules. After obtaining the lens module zoom system, the real lens groups are successively designed to combine to form lens system. Compared to separately designed lens groups, the approach can give a better starting zoom lens for it has only 9 variables of each group to optimize. Based on the new method, the final design is a four-group zoom system with a focal length range of 10 to 200mm. The system has a variable aperture from 1/2.8 at wide field to 1/5.6 at narrow field. The Modulation Transfer Function(MTF) exceeds 40% at 100lp/mm of all zoom positions, over all fields. Wherefore it has a good imaging performance when used with a 1/3-inch CCD.

Purpose: To evaluate a new method of calculation of total corneal astigmatism based on Gaussian optics and the power design of a spherocylindrical lens (C) in the healthy eye and to compare it with keratometric (K) and power vector (PV) methods. Methods: A total of 92 healthy eyes of 92 patients (age, 17–65 years) were enrolled. Corneal astigmatism was calculated in all cases using K, PV, and our new approach C that considers the contribution of corneal thickness. An evaluation of the interchangeability of our new approach with the other 2 methods was performed using Bland–Altman analysis. Results: Statistically significant differences between methods were found in the magnitude of astigmatism (P < 0.001), with the highest values provided by K. These differences in the magnitude of astigmatism were clinically relevant when K and C were compared [limits of agreement (LoA), −0.40 to 0.62 D), but not for the comparison between PV and C (LoA, −0.03 to 0.01 D). Differences in the axis of astigmatism between methods did not reach statistical significance (P = 0.408). However, they were clinically relevant when comparing K and C (LoA, −5.48 to 15.68 degrees) but not for the comparison between PV and C (LoA, −1.68 to 1.42 degrees). Conclusions: The use of our new approach for the calculation of total corneal astigmatism provides astigmatic results comparable to the PV method, which suggests that the effect of pachymetry on total corneal astigmatism is minimal in healthy eyes.

Objective lenses are conventionally operated at high magnification, and to a good approximation it may be assume that the image is formed at infinity. In microscope objective lenses a different set of cardinal elements must be used. The chapter reviews whether fields exist for which fixed real cardinal elements can be defined for a range of object positions. This leads to the concept of Newtonian imaging fields. Newtonian concept states that the family of ray that emerge parallel to the axis intersect the latter at some point F 1 o , which is called the real object focus; a family of rays emerging from the lens parallel to one another but not parallel to the axis intersect in the focal plane, the plane through F 1 o perpendicular to the axis.

Introduction to Optics is now available in a re-issued edition from Cambridge University Press. Designed to offer a comprehensive and engaging introduction to intermediate and upper level undergraduate physics and engineering students, this text also allows instructors to select specialized content to suit individual curricular needs and goals. Specific features of the text, in terms of coverage beyond traditional areas, include extensive use of matrices in dealing with ray tracing, polarization, and multiple thin-film interference; three chapters devoted to lasers; a separate chapter on the optics of the eye; and individual chapters on holography, coherence, fiber optics, interferometry, Fourier optics, nonlinear optics, and Fresnel equations.

In this article, an approach for the design and construction of a refractive 2.5× Galilean beam expander–focuser system which incorporates a two-axis galvanometer for coupling non-collinear laser beams into a 5×4200 μm core diameter fiber-optic array is discussed. M 2 Gaussian beam waist and beam waist location computations using the ABCD ray matrix and Zemax ® paraxial Gaussian optics methods are given. Using the described optical system a 532 nm and 637 nm laser beams are coupled noncollinearly into 200 μm core diameter fiber array by focusing down the laser beams to 71.26 ± 3.18 m and 90.32 ± 4.28 μm diameter spots, respectively. Furthermore, an experimental validation for the focused beam size calculations using a knife-edge profilemeter is provided. The measured average transmission for the fibers in the fiber-optic array is 92.54 ± 3.78% (maximum FCE (fiber coupling efficiency): 99%; minimum FCE: 82%). Whereas the Zemax ® calculated geometric ray-optics fiber coupling efficiency for the beam expander-focuser into a 200 μm core diameter fiber using uncoated lenses and without accounting for Fresnel reflections and bulk absorption effects is 100%. Geometric ray-optics calculations indicate that Fresnel reflections and bulk absorption effects account for 7% of the 100% FCE value. The described optical switching scheme which incorporates a galvanometer is used for exciting asynchronously 20 PCR (Polymerase Chain Reaction) vessels in high throughput DNA/RNA amplification systems.

The Gaussian sphere has been widely used as a model to study light scattering by irregular particles; and, despite extensive numerical studies, the optical properties are not thoroughly understood. Based on Gaussian spheres and using a combination of the invariant imbedding T-matrix method and an improved geometric-optics method, the single-scattering properties (namely, the 4×4 phase matrix, extinction cross section, single-scattering albedo, and asymmetry factor) are computed in the Rayleigh to geometric optics regimes. The simulations are performed with various degrees of irregularity, and the effects of particle irregularities are investigated over a wide range of particle sizes. Furthermore, the theoretical simulations based on Gaussian spheres are used to fit the measured optical properties of feldspar particles from the well-known Amsterdam–Granada light scattering database. A mixture of several shapes is shown to closely reproduce the measured phase matrices. The results may be potentially useful for remote-sensing and radiative-transfer applications involving dust aerosol.

As a solution to provide a small-size and low-cost 100-Gb/s optical module, direct optical coupling between a lens-integrated surface-emitting DFB laser (LISEL) array and a single-mode fiber (SMF) array is demonstrated. A very-small far-field angle ( $\sim 2$ °) was obtained by monolithic integration of an InP lens with a laser chip. As a result, each channel of the LISEL array can directly couple to an SMF without any additional external optical components. The measured misalignment tolerance between the LISEL array and an SMF array was sufficiently large, namely, $\pm 5.5~\mu \text{m}$ , at excess loss of 1 dB over all four channels with the maximum coupling efficiency of 8.4 dB. These measurement results are in good agreement with a theoretical calculation based on Gaussian optics. These results demonstrate that high coupling efficiency (−3 dB) can be achieved while large misalignment tolerance ( $\pm 4.5~\mu \text{m}$ ) at excess loss of only 1 dB is maintained.

Quasihorizontally oriented ice crystals of cirrus clouds became an object of active study in recent times. Experimental observations are made with the use of multiwavelength and polarization lidars; their signals are interpreted on the basis of solutions obtained in the approximation of physical or geometrical optics. In this work, we compare these approximations for solution of the problem of light backscattering by quasihorizontally oriented hexagonal ice plates. Special attention is paid to the limits to applicability of geometrical optics approach to solution of such problems.

In this paper, we present a condition of optical systems to form images independent of frequency. The condition independent of frequency in case of a single Gaussian beam on an optical axis has been known, but that in case of a beam propagated off the axis or tilted beam, which appears in a wide field-of-view (FOV) telescope, has not been known. We first show relations between an arbitrary electric field on an object plane and an induced one on an image plane after passing through a lens with calculating Fresnel diffraction integrals. If the lens formula is met, there is a one-to-one correspondence between points on the object and image plane. This result enables to use geometrical optical methods. The condition and relations derived here are confirmed by simulations. We also applied them to a wide-FOV telescope.

AIM: To analyze the clinical factors influencing the human vision corrections via the changing of ocular components of human eye in various applications; and to analyze refractive state via a new effective axial length. METHODS: An effective eye model was introduced by the ocular components of human eye including refractive indexes, surface radius (r1, r2, R1, R2) and thickness (t, T) of the cornea and lens, the anterior chamber depth (S1) and the vitreous length (S2). Gaussian optics was used to calculate the change rate of refractive error per unit amount of ocular components of a human eye (the rate function M). A new criterion of myopia was presented via an effective axial length. RESULTS: For typical corneal and lens power of 42 and 21.9 diopters, the rate function Mj (j=1 to 6) were calculated for a 1% change of r1, r2, R1, R2, t, T (in diopters) M1=+0.485, M2=-0.063, M3=+0.053, M4=+0.091, M5=+0.012, and M6=-0.021 diopters. For 1.0 mm increase of S1 and S2, the rate functions were M7=+1.35, and M8=-2.67 diopter/mm, respectively. These rate functions were used to analyze the clinical outcomes in various applications including laser in situ keratomileusis surgery, corneal cross linking procedure, femtosecond laser surgery and scleral ablation for accommodation. CONCLUSION: Using Gaussian optics, analytic formulas are presented for the change of refractive power due to various ocular parameter changes. These formulas provide useful clinical guidance in refractive surgery and other related procedures.

The recent technological development in the MEMS technology lead to the production of curved micromirror with full three-dimensional control. Understanding how the optical beams are transformed on curved micromirrors is yet to be fully understood in such a scale, where the optical beam spot size is comparable to the micromirror radius of curvature. A numerical study of Gaussian beam distortion upon reflection on micro-curved surface is carried out in this work in the near-infrared spectral regime. The physical-optics approach is used as a benchmark for the Gaussian-optics approach. For the case of 45-degree incidence on a spherical micromirror with a 500-µm radius of curvature, the Gaussian-optics approach shows good accuracy for beam minimum waist radius of 5 µm located in the focal plane of the mirror, while for a minimum waist radius of 1.5 µm the Gaussian optics approach fails to predict the reflected beam profile and divergence angle. The accuracy of prediction for the 5-µm waist radius case is reduced, when the incident beam waist is located farther from the mirror.

Full control of the dark ray structure of an optical beam requires an adequate mathematical framework to describe its properties. In this presentation we will provide a new set of mathematical tools whose ultimate goal is to complete a full mathematical representation of dark ray optics. Using this mathematical representation we will discuss the different possibilities to achieve full control of the dark rays trajectories using standard optical elements in an analogous way to the manipulation of ordinary bright rays in geometrical optics.

This paper investigates the aperture-averaged angle-of-arrival variance for a Gaussian wave propagating through the weak anisotropic non-Kolmogorov atmospheric turbulence along a horizontal path. A heuristic model is deduced from the results of plane and spherical waves under the geometrical optics approximation. The mathematical expression include the spectral power law value, the anisotropic factor and other essential optical parameters of a Gaussian wave.

Optical coherence microscopy (OCM) has unique advantages of non-invasive 3D imaging without the need of exogenous labels for studying biological samples. However, the imaging depth of this technique is limited by the tradeoff between the depth of focus (DOF) and high lateral resolution in Gaussian optics. To overcome this limitation, we have developed an extended-focus OCM (xf-OCM) imaging system using quasi-Bessel beam illumination to extend the DOF to ∼100 μm, about 3-fold greater than standard OCM. High lateral resolution of 1.6 μm ensured detailed identification of structures within live animal samples. The insensitivity to spherical aberrations strengthened the capability of our xf-OCM system in 3D biological imaging.

Porous material has been considered from the point of view of stereology (geometrical statistics), as a two-phase random mixture of solid material and air. Considered are the materials having the refractive index with the real part that differs notably from unit and the imaginary part much less than unit. Light scattering in such materials has been described using geometrical optics. These two – the geometrical optics laws and the stereological approach – allow one to obtain the inherent optical properties of such a porous material, which are basic in the radiative transfer theory: the photon survival probability, the scattering phase function, and the polarization properties (Mueller matrix). In this work these characteristics are expressed through the refractive index of the material and the random chord length distribution. The obtained results are compared with the traditional approach, modeling the porous material as a pack of particles of different shapes.

A novel wavefront-based algorithm for the beam simulation of both reflective and refractive optics in a complicated quasi-optical system is proposed. The algorithm can be regarded as the extension to the conventional Physical Optics algorithm to handle dielectrics. Internal reflections are modeled in an accurate fashion, and coating and flossy materials can be treated in a straightforward manner. A parallel implementation of the algorithm has been developed and numerical examples show that the algorithm yields sufficient accuracy by comparing with experimental results, while the computational complexity is much less than the full-wave methods. The algorithm offers an alternative approach to the modeling of quasi-optical systems in addition to the Geometrical Optics modeling and full-wave methods.

We demonstrate cloaking with four lenses of different focal lengths. To achieve this, we compute the separation distances between lenses such that the effective ABCD matrix is equal to just a propagation in free space. Previously, calculations using this method are restricted to 2 pairs of lenses with equal focal lengths. Our computations, on the other hand, had no such restrictions: we generalize even with an asymmetric case. We derive expressions that show the dependence of the distances on the lenses and their focal lengths. Furthermore, we propose a way to minimize the length of this cloak. Our equations reduce to the Rochester cloak when its restriction is imposed. A general paraxial cloak could be useful in advanced undergraduate experiments in optics because: 1) the limit imposed by the focal length has been lifted; and 2) there is a pedagogical benefit of doing experiments with lenses beyond the usual imaging experiments such as reinforcing concepts in Gaussian optics., Comment: 10 pages, 4 figures

It was reported in Nature and the Wall Street Journal on June 20th, 2012 that scientists at Duke university have developed a gigapixel camera, capable of over 1,000 times the resolution of a normal camera. According to the reports, this super-resolution camera was motivated by the need of US military authorities to surveil ground and sky. We notice the ripple effect of this technology has spread into the area of national defense and industry, so that this research has started to realize the super-resolution camera as a frontier research topic. As a result, we can understand the optical structure of a super-resolution camera’s lens system to be composed of a front, monocentric objective of a single lens plus 98 rear, multiscale camera lenses. We can also obtain the numerical ranges of specification factors related to the optical structure, such as the diameter of the aperture, and the focal length.Keywords: Gigapixel camera, Multiscale, Monocentric objective, Microcamera lensOCIS codes: (080.0080) Geometric optics; (080.2468) First-order optics; (080.2740) Geometric optical design; (080.3620) Lens system design

Basic features of the modified theory of physical optics (MTPO) are discussed on the example of scattering at perfectly reflecting half-planes and wedges. It is shown that violations of the geometrical optics (GO), introduced in this technique, result in the MTPO solutions which do not satisfy the Helmholtz equation. They are incorrect at a finite distance from a scattering object; however it can be considered as sort of approximations for the field at a large distance from an edge and away from the GO boundaries. IEEE Antennas and Propagation Society