Photorefractive shearing interferometer

A novel method of obtaining shearing interferogram by slightly moving the crystal in a photorefractive interferometer is proposed. This method can measure the phase of an object itself instead of its diffraction field, and it is easy to realize continuously changeable shearing distance in any lateral direction and introduce carrier fringes at the same time. Both the theoretical analysis and experimental verification are given.     

Geometrical aberrations of self-imaged line gratings

We analyze the properties of a self-imaging system from the point of view of aberration theory. We examine analytically and numerically the geometrical aberrations that are observed in the self-image of a parallel-line grating. We first derive the raytracing equations for determining the optical path of a self-imaging ray with the order of diffraction l. We then obtain the third- and fifth-order contributions to ray aberrations which arise from the difference between the optical paths of a self-imaging ray and of an actual ray. We show that the overall ray aberrations are entirely undercorrected. The ray aberrations approach zero as the ratio of the grating constant to the wavelength of light becomes large enough. In a case of unit magnification, no curvatures are observed in the self-imaged lines. If the magnification is bigger than unity, the light rays passing through the point in a positive or negative domain of the aperture variable contribute to the formation of the curved images. The image evaluation technique discussed here can be useful in the various applications related to the self-image formation of a parallel-line grating and it can also provide insight into the self-imaging of other periodic objects.     

Numerical simulation of the trajectory of a light ray propagating through an optic system with non-centered spherical diopters and broken optic axis

The present paper is devoted to the elaboration of a strategy for the design of some practical focusing devices for the radiation emitted by a high-power laser used in thermal treatment processes. Usually, technological solutions employ spherical mirrors. Because spherical mirrors introduce a certain astigmatism, it is necessary to get an energetically efficient configuration which reduces as much as possible the astigmatic difference, thus concentrating the laser radiation energy which is distributed within the area between the sagital and meridional foci.     

Resonant trapping of scattered light in a degenerate resonator

We demonstrate and discuss the formation of an intriguing interference fringe pattern that is visible in stable resonators at resonator lengths corresponding to a higher-order frequency-degeneracy. The optical trajectories that form these fringes are described for arbitrary degeneracy; the fringes can be used to visualize and quantify imaging aberrations of the cavity relative to a cavity consisting of ideal mirrors.     

Analysis of the common characteristics of the Hartmann,Ronchi, and Shack–Hartmann tests

An overview of the settings of the planes for the filters and observed patterns in the Hartmann and Ronchi tests is presented. Also a new set of filters for both test were developed. In a similar way, it is easy to extend this analysis to the Shack–Hartmann test, and to propose a new Null Shack–Hartmann filter.     

Coma measurement using a PSM and transmission image sensor

As feature size decreases, especially with the use of resolution enhancement technique, requirements for the coma aberrations in the projection lenses of the lithographic tools have become extremely severe. So, fast and accurate in situ measurement of coma is necessary. In the present paper, we present a new method for characterizing the coma aberrations in the projection lens using a phase-shifting mask and a transmission image sensor. By measuring the image positions at multiple NA and partial coherence settings, we are able to extract the coma aberration. The simulation results show that the accuracy of coma measurement increases approximately 20% compared to the previous straightforward measurement technique.     

Aberrations of self-imaged patterns with two-dimensional periodicity

We develop a geometrical theory of aberration in the self-imaged patterns with two-dimensional periodicity. The patterns are considered to be a crossed-line grating or a periodic array of finite apertures. We first derive the raytracing equations for determining the optical path of a self-imaging ray. We then find the third- and fifth-order contributions to the wavefront aberration which arise from the difference between the optical paths of a self-imaging ray and of an actual ray. We also derive the expression of the ray aberration from the wavefront aberration. The ray aberration is classified into five distinct types by analogy with the cases in a refracting lens system. We show that the overall ray aberration is entirely undercorrected and the aberrated image patch is decentered from an ideal image point in the direction parallel to the direction tangent vector of a chief ray. The image evaluation technique discussed here will be useful in various applications related to self-image formation of two-dimensionally periodic patterns.     

偏心光学系统的中心点亮度的计算

本文讨论了偏心光学系统的中心点亮度计算中所必须考虑的离焦、波差展开式、数值计算等几个主要问题。     

Optimum deformable mirror modes for sensorless adaptive optics

Wavefront sensorless adaptive optics schemes rely upon the accurate generation of aberration modes by the adaptive element, usually a deformable mirror. Analytic functions are often used for representation of the aberrations in these systems. Such functions cannot be perfectly reproduced by deformable mirrors and the approximation errors can affect the aberration correction procedure. We derive alternative modal basis sets directly from the actuator influence functions, thus avoiding the approximation errors. We investigate how the choice of aberration modes affects the performance of a sensorless adaptive imaging system. The new modes are found to be most advantageous for deformable mirrors with a small number of actuators.     

Aberrations of plane-symmetric multi-element optical systems

Based on a recently developed aberration theory of plane-symmetric grating systems, its aberration coefficients are firstly extended to be applicable to the plane-symmetric refractive optical surface. To justify the linear approximation of aperture ray in a multi-element system, the ray aberrations of double-element systems with the third-order accuracy of aperture ray are derived and expressed as the form of wave aberrations. The numerical comparisons are then made between the ray tracing, the aberration expressions with the linear and with third-order accuracy of the aperture ray. Moreover, the modifications of the wave and ray aberrations are discussed in the paper when the position of the principal ray changes.