Measurement of Intraocular Optical Distances Using Partially Coherent Laser Light

Abstract

The application of partially coherent laser light to measure intraocular optical distances is discussed. In a first step the optical thickness of the retina at the macula and the optical length of the eye has been measured and a precision of ± 0·03 mm has been obtained. The results of a comparison with the acoustically determined eye length and first fundus profile measurements are presented.     

Fraunhofer Diffraction in Partially Space Coherent Light by Slit Aperture with Amplitude Filters

Fraunhofer diffraction patterns produced by a narrow rectangular aperture having a non-uniform illumination with partially coherent light are presented. Graphs of intensity distributions in the diffraction patterns for three cases of amplitude filters and four forms of the mutual coherence at the slit are given. An increase in the half-width at half-height (H.W.H.H.) and a decrease in the intensity at the centre are observed. Tolerances for the value of the correlation interval in the aperture based on the Strehl intensity criterion have been calculated for various amplitude filters.     

Radiance Functions of Partially Coherent Fields

Abstract

The behaviour of the spectral radiance in fields generated by planar, secondary, quasi-homogeneous sources is investigated. Examples are presented which show how both the spectral intensity and the degree of coherence of the source affect the spatial and the angular distribution of the spectral radiance. These examples clearly show the influence of source coherence on the radiometric behaviour of partially coherent optical fields.     

New Approximation for Partially Coherent Imaging of Straight Edges

Abstract

Partially coherent imaging occurs especially in microscopy and microlithography. The imaging properties of such systems are described by the ‘bilinear transfer function’ (BTF). This paper deals with an approximation of the BTF for conventional microscopy. The approximation allows the analytical calculation of image intensity distributions and the use of a combination of two transfer functions for the amplitude transmission spectrum. Examples of calculations of intensity distributions in the imaging of straight edges are given and compared with exact calculations.     

部分相干成象的模拟计算方法

介绍了一种模拟计算部分相干光成象的实用化方法。根据部分相干理论，推导出数值计算模型，并采用各种方法简化，减少了计算量。     

Radiation Efficiency of Partially Coherent Three-dimensional Sources

Abstract

Radiation efficiency, which is defined as the total power radiated from a source normalized to a maximum value of unity, is investigated theoretically for a partially coherent three-dimensional source. The source model for analysis is assumed to be a primary, homogeneous, isotropic spherical source, and its spatial correlation is characterized by means of properly arranged Bessel functions. A number of representative curves of the radiation efficiency are illustrated as a function of the coherence condition of the source and compared with the curves of the radiation efficiency for the planar source whose spatial coherence is specified by the same functional form of Bessel functions. It is found from such comparison that there exists a kind of reciprocal behaviour in radiation efficiency between the three-dimensional source and the planar one.     

Radiometry of Partially Coherent Fields. I

A formalism is given to generalize the laws of radiometry to include partially coherent fields. This is an alternative formalism to the one proposed by Walther, Marchand, and Wolf. The generalization of radiometry is formulated as a natural extension of the pioneering work due to Wolf in formulating the theory of partial coherence. For the non-coherent case it is shown that the generalized quantities reduce to their counterparts in conventional radiometry.     

Augmented ABCD Matrix for Non-specular Diffraction of Gaussian Beams

Abstract

Optical beams reflected or transmitted by a dielectric interface undergo several non-specular deformations: changes in the beam amplitude, lateral, focal and angular shifts of the beam axis and a magnification of the beam width. In this communication the non-specular interaction of the beam with, in general, multilayered, planar dielectric structure is described in terms of the ray transfer matrix formalism. A relationship between the beam deformations and a 3 × 3 ray transfer matrix of the structure is built. Transfer matrix elements are shown in a simple form dependent on the real deformations.     

Symmetry in Partially Coherent Imaging of Semi-transparent Edges

Abstract

The extended linear approximation [1] is applied to defocused imaging of semi-transparent edges. The approximated intensity distributions are given and the influence of the following parameters are studied: edge transparency and phase shift, coherence parameter and defocusing. For an opaque edge and a phase edge approximated intensity curves are compared to curves obtained by the exact calculation with the ‘bilinear transfer function’. It is shown that characteristic effects of the image intensity can be referred to the two transfer functions of the extended linear approximation and that it is possible to separate the influence of the object and the system, which is the principal advantage of the use of transfer functions.     

The Importance of Phase Information for Constructing Model Partially Coherent Sources

Abstract

An alternative factorisation of the mutual coherence function is presented, given by Γ(r ₁, r ₂, τ) = V(r ₁)V?(r ₂)η(r ₁, r ₂, τ), where V(r) is the time independent part of the coherent analytic signal and η (r ₁, r ₂, τ) is a coherence function. We show how simple coherent model sources, which are composed of sums of plane waves, can be converted into partially coherent model sources. As examples of this we give the most general expressions for the uniform intensity and sinusoidal intensity sources of infinite extent. Modal power coupling calculations also shown to be significantly simplified, for sources with simple sums of plane waves in their coherent limit.     

具任意脱层复合材料梁的模态分析

本文对具任意脱层的复合材料梁进行了模态分析。基于弹性理论建立了考虑剪切变形时复合材料脱层梁的基本方程式。对脱层梁进行了分区处理，方便地描述了脱层长度，脱层位置。利用边界条件，区间位移连续性条件和内力平衡条件建立了梁模态分析的特征方程式。通过实例计算，得出了不同脱层位置和不同脱层长度对脱层梁模态分析的影响。     

Performance of Apodized Apertures under Partially Coherent Illumination

The performance characteristics of optical systems having apodized apertures and employing partially coherent illumination have been investigated. The pupil function has been taken to be of the form f(x y) = 1 m g (x 2 + y 2), where g is the amplitude shading parameter of the filter. The generalized cross-transfer functions for the system have been calculated for different values of the coherence parameter which is the ratio of the numerical aperture of the condenser to that of the objective. The modulations of periodic targets commonly employed, namely, the sine wave, square wave and triangular wave objects, have also been investigated. It has been shown that for the partially coherent and the incoherent illuminations ( S 1) the apodization improves the low frequency response at a cost of the high frequency response of the system. However, for coherent and near coherent illuminations (     

Some Statistical Properties of Random Speckle Patterns in Coherent and Partially Coherent Illumination

The power spectrum of the intensity fluctuations in a random speckle pattern is derived in a simplified manner for coherent illumination. The effect of the power spectrum on the measured signal-to-noise ratio is discussed, and some preliminary measurements of the power spectrum are presented. The power spectrum of the intensity fluctuations for partially coherent illumination is derived for the special case of an aberration-free system, using quadratic filter theory.     

Focal Shift Formula for Focused,Apertured Gaussian Beams

A formula is developed for fast computing focal shift in the diffraction field of a Gaussian beam that is focused by a thin lens filled in a circular aperture of any prescribed radius. This formula is a generalization of two previously known focal shift formulae, one for un-apertured Gaussian beam, another for plane-wave beam.     

Approximate Formulae for Mixed Modulated Coherent and Partially Polarized Chaotic Light

Exact and approximate formulae are obtained for the counting statistics of mixed cosine-modulated coherent and partially polarized chaotic light, particularly with Lorentzian spectrum, for one-photon as well as multiphoton absorption. They are numerically analysed and the accuracy of the approximate formulae is discussed. As a special case chaotic light is investigated. A closer relation to recent papers is outlined.     

Performance of the Optimum Apodizers in Partially Coherent Light

The optimum apodizers have been designed with the tacit assumption that the point-spread functions of the optical instruments that could use them are due to spatially coherent waves. In practice, there is considerable deviation from this ideal condition. In the present paper analytical expressions are given which can be used for a comprehensive study of the performance of the optimum apodizers in partially coherent illumination. The loss of coherence is assumed to be due to atmospheric turbulence. Numerical results concerning the dependence of the encircled energy, the central intensity, the expected resolution etc., for two chosen apodizers show that the performance, in partially coherent illumination, of the optimum apodizers may be contrary to their expected performance. It is therefore very important to take into account the actual state of coherence of the aperture illumination in the designing of apodizers that are to be used under non-ideal conditions.     

有任意脱层复合材料梁的非线性动力稳定性

基于弹性理论建立了有脱层复合材料梁的基本方程式，研究了有任意脱层的考虑横向剪切变形的复合材料梁的非线性动力稳定性，对脱层梁进行分区处理，方便地描述了脱层长度，脱层位置，利用振型函数作为位移函数的形函数，采用增量谐波平衡法对基本方程式进行求解，考虑了不同脱层位置和不同脱层长度对脱层梁的非线性动力稳定性的影响，得出了各种情况下的动力不稳定性区域。     

Modulation of Truncated Periodic Targets in Partially Coherent Light

Formulae have been developed for computing the diffraction images of partially coherent truncated one-dimensional periodic targets. The modulations in the images of these objects are compared with those of an infinite cycle target. The intensity distributions in the limiting case of coherent light imagery are also shown. Both sine-wave and square-wave targets have been considered.     

The Spatial Coherence Properties of Gaussian Schell-model Beams

The transverse and longitudinal spatial coherence properties of the light beams generated by planar gaussian Schell-model sources are discussed. It is found that for all gaussian Schell-model beams the ratio of the transverse coherence length to the beam width remains invariant upon propagation. An examination of the longitudinal coherence for both on-axis and off-axis pairs of points indicates that the longitudinal coherence will not, in general, die out as the separation between the points is increased. Rather, the degree of longitudinal coherence will approach a finite (non-zero) value as long as the source contains a finite coherence area, regardless of how small this area may be. Gaussian quasihomogeneous beams are studied as a limiting case. The relation of the present work to the analysis of speckle size is briefly discussed.