Pupil Effect in a GRIN Lens with Gaussian Illumination

Abstract

Using the propagator method, the quasi-geometric transmittance function and complex amplitude distribution produced by a GRIN lens are evaluated when it is illuminated by a Gaussian beam and the pupil effect is taken into account. The effective pupil is defined and derived by both quasi-geometrical optics and the exact Fresnel diffraction, which it is evaluated in a Rubinowicz representation.     

用点扩展函数确定卫星反射后的脉冲强度

卫星激光测距系统是一个非相干成象光学系统。卫星形状效应是由于卫得上不同位置的反射器对光子反射的时间不同而引起的脉冲强度重新分布的现象。非相干成象系统在等晕区内是空间不变性的光强线性系统。成象光学系统中象强度等于输入物强度与光瞳点扩展函数的卷积。用卫星的点扩展函数描述卫星形状效应,能非常简便地计算出被卫星反射后的脉冲强度分布。讨论了激光测距卫星的点扩展函数的求解方法和表达形式,并分别推导和计算了Lageos卫星和自行设计卫星的点扩展函数以及点扩展函数作用后的脉冲强度分布。     

Generation of a high depth of focus with constant transversal spot size using a phase-only pupil filter

A novel approach is proposed to obtain an extended depth of focus (DoF) in white light with constant transversal spot size within the DoF. It combines a phase-only pupil filter based on multiplexed radial zones with alternating quartic phase functions. The design is first tested via numerical simulations of the point spread function (PSF) based on the scalar diffraction theory. The results for a fourfold gain of the depth of focus are experimentally verified with a phase-only spatial light modulator liquid crystal device combined with a 3D PSF measurement system. A close conformity between the experimental and simulation results proves the effectiveness of the proposed approach.     

Graded-index fiber lens proposed for ultrasmall probes used in biomedical imaging

The quality and parameters of probing optical beams are extremely important in biomedical imaging systems both for image quality and light coupling efficiency considerations. For example, the shape, size, focal position, and focal range of such beams could have a great impact on the lateral resolution, penetration depth, and signal-to-noise ratio of the image in optical coherence tomography. We present a beam profile characterization of different variations of graded-index (GRIN) fiber lenses, which were recently proposed for biomedical imaging probes. Those GRIN lens modules are made of a single mode fiber and a GRIN fiber lens with or without a fiber spacer between them. We discuss theoretical analysis methods, fabrication techniques, and measured performance compared with theory.     

Design of lenses with curved Petzval image surfaces

Abstract

Design strategies have been devoted to simplify and miniaturize optical systems. In this paper, by constraining image surface to coincide with the Petzval surface, we achieve a compact f/2.8 lens system design with a curved Petzval image surface. Arc distortion is proposed to accurately measure the distortion relative to a curved image surface. The optical performance of our curved image surface lens is analysed and compared. Results show that modulation transfer function (MTF) of our curved Petzval design over 69% at 100 cycles/mm for entire fields is achievable with 100-mm effective focal length, 40º full field of view, >92.4% edge relative illumination, <0.5% arc distortion. Comparisons with a traditional lens with a planar image plane demonstrate that a curved Petzval image surface is an excellent strategy to simplify and miniaturize optical systems, compensate field curvature and benefit astigmatism correction, increase off-axis illumination and improve MTF. Furthermore, the lens with a curved Petzval image surface has a more uniform optical power distribution and greater degree of lens symmetry.     

Point-spread function for binary diffractive lenses fabricated with misaligned masks

The influence of mask-alignment errors on the fabrication of four-level binary lenses has been investigated. The pupil function was derived as a function of the amount of misalignment between the two mask patterns based on scalar diffraction theory. It was found that the phase term in the pupil function affects only the location of the point-spread function, whereas the uneven light transmittance degrades the image quality in the direction of the misalignment. The Strehl intensity was found to decrease almost linearly with respect to the amount of error.     

Adaptive model of the gradient index of the human lens. II. Optics of the accommodating aging lens

A simple, parametric model of the gradient refractive index distribution (GRIN) of the human lens with conicoid surfaces able to adapt to individual distributions as well as to the changes of the lens shape and structure with age and accommodation is presented. The first part of this work was published in a companion paper [J. Opt. Soc. Am. A24, 2175 (2007)]. It included the development of the mathematical formulation of the adaptive model; the validation of its customization capability by fitting, sample by sample, a set of in vitro refractive index distributions of lenses of different ages, ranging from 7 to 82 years, from the recent literature; and an average model of the (in vitro) aging crystalline lens. Here we extrapolate that in vitro GRIN model by assuming that the same structural parameters are valid for the living lens. Then, recent data of the changes of the shape of the aging lens with accommodation from the literature are used to build an aging and accommodating lens model. This is straightforward since the GRIN model adapts automatically to the chosen external lens geometry. A strong coupling was found between the adaptive GRIN distributions and the conic constants affecting the refractive power. To account for the lens paradox and the reported changes in lens spherical aberration with age and accommodation, age- and accommodation-dependent functions for the anterior and posterior internal conic constants were derived through optimization.     

轴位移法测定GRIN透镜的折射率分布系数

本文对GRIN透镜的精确光线追迹公式作了推导,介绍了轴位移法对透镜折射率分布的测量方法及相应的数据处理,并对测量误差进行了分析和计算,从而对测定GRIN透镜折射率分布提供了一种精确而且实用的方法。     

3D phase diversity: a myopic deconvolution method for short-exposure images: application to retinal imaging

3D deconvolution is an established technique in microscopy that may be useful for low-cost high-resolution imaging of the retina. We report on a myopic 3D deconvolution method developed in a Bayesian framework. This method uses a 3D imaging model, a noise model that accounts for both photon and detector noises, a regularization term that is appropriate for objects that are a mix of sharp edges and smooth areas, a positivity constraint, and a smart parameterization of the point-spread function (PSF) by the pupil phase. It estimates the object and the PSF jointly. The PSF parameterization through the pupil phase constrains the inversion by dramatically reducing the number of unknowns. The joint deconvolution is further constrained by an additional longitudinal support constraint derived from a 3D interpretation of the phase-diversity technique. This method is validated by simulated retinal images.     

Depth Transfer by an Imaging System

In many applications such as three-dimensional (3-D) data acquisition, the scanning of 3-D objects or 3-D display, it is necessary to understand how an imaging system can be used to obtain information on the structure of an object in the direction perpendicular to the image plane, i.e. depth information. In certain cases the formation of a 3-D image can be described by a theory based on optical transfer functions (OTF): the image intensity distribution is given by the 3-D convolution of the object and a 3-D point spread function (PSF); equivalently, in 3-D Fourier space the image spectrum is the product of the object spectrum and a 3-D OTF. This paper investigates the 3-D PSFs and OTFs that are associated with different pupil functions of the imaging system.     

Compensating for nonstationary blurring by further blurring and deconvolution

In many imaging systems, the point spread function (PSF) is nonstationary. Usually, a computation‐intensive iterative algorithm is used to deblur the nonstationary PSF. This article presents a new idea of using a noniterative method to compensate for the spatially variant PSF. This method first further blurs the image with a nonstationary kernel so that the resultant image has a stationary PSF, then deblurs the resultant image using an efficient decovolution technique. The proposed method is illustrated and implemented by single photon emission computed tomography applications. © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 221–226, 2009     

Distorted wave front produced by a high-resolution projection optical system having rotationally symmetric birefringence

The influence of birefringence caused by rotationally symmetric stress distribution in a high-resolution projection optical system is investigated. The general form of the pupil function is derived based on the Jones matrix calculation, expressing the wave front as a combination of the two orthogonal polarization components. Assuming a linearly polarized incident beam, it is found that the main polarization portion of the wave front exiting the projection lens has astigmatic aberration in the Seidel region and shows phase singularity at four pupil points at which the amplitude transmittance becomes zero.     

Birefringence in gradient-index rod lenses: a direct measurement method and interferometric polarization effects

Gradient-index (GRIN) media can contain stress birefringence resulting from the variation in material composition. Anisotropy in a GRIN rod lens affects ray propagation and can degrade image quality. A technique, believed to be new, for measuring birefringence in GRIN rod lenses has been developed. The change in optical path difference (OPD) for orthogonal polarizations is measured directly. With this method, effects on OPD from standard imaging aberrations are excluded. Birefringence measurements for various GRIN rod samples are presented. The data are compared with results obtained previously by use of a Twyman-Green measurement method. Also, the polarization effects on tilt fringes observed with the direct measurement method and the Twyman-Green method are presented and modeled theoretically. Tilt fringes for large birefringence test cases are also modeled.     

Birefringent properties of diametrically loaded gradient-index lenses

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

ABCD matrix of the human lens gradient-index profile: applicability of the calculation methods

The applicability of different approximate methods proposed to determine the paraxial properties of the gradient-index (GRIN) distribution resembling that of the human lens, by means of the system ABCD matrix, is tested. Thus, the parabolic-ray-path approximation has been extended to provide the ABCD matrix of a slab lens comprised of a rotationally GRIN medium. The results show that this method has good numerical stability, and it is also the easiest one in determining the Gaussian constants of the human lens GRIN profile.     

Pupil effect in GRIN material

The effect on the transmittance function in gradient-index material due to a circular pupil is studied, and we characterize this material by its effective transmittance function.     

Theoretical considerations on imaging of micron size electron beam with optical transition radiation

Optical transition radiation (OTR) has been widely used to image electron beam profile. In this paper, we systematically investigated the issues related to imaging of electron beam with OTR. It is found that the point-spread function (PSF) largely depends on the acceptance angle of the lens and is only very weakly dependent on beam energy and the distance from the OTR target to the lens. This excludes the potential obstacles to imaging of high-energy electron beam for which, the photons are emitted in a relatively small cone and the far field condition is hard to fulfill. The image of a whole beam is found by convoluting the real beam distribution with the PSF. It is shown that for micron size beam, the image formed with OTR largely deviates from the real beam distribution. And the real beam distribution could be restored from deconvoluting the image with the PSF. The effectiveness of the restoration is demonstrated, which opens up the possibility of measuring micron size beam profile with OTR.     

Production and Use of a Sine-Wave Test-Object

A distribution of illuminance which is sinusoidal in one direction and uniform in the perpendicular direction is obtained in the image. farmed by a lens the pupil of which is a narrow slit, of a pattern of repeated opaque and clear areas demarcated by sine-curves. The slit acts as a (ilter of spalial frequencies. The image is recorded photographically under conditions of exact tone-reproduction. In this way a test-object with sinusoidal transmittance is obtoined, which is used for meosuring the modulation tronsfer functions of lenses and photographic materiols.     

Single dispersive gradient-index profile for the aging human lens

We provide a single gradient-index (GRIN) profile for the crystalline lens in an updated age-dependent emmetropic-eye model. The parameters defining the GRIN profile include their variation with age and the dispersion of the refractive index in order to account for the increase in the positive-wave spherical aberration, for the constant chromatic difference in the refraction of the human eye, as well as for the decrease in the retinal-image quality with aging. In accounting for these ocular properties, the results show that first, the value of the dispersion parameters are invariant with age. Second, those parameters defining the distribution of the lens index cause the lens-center-index value to decrease slightly, and its position along the lens axis changes with age. Furthermore, these findings are in agreement with the lens paradox.