In situ optical testing of infrared lenses for high-performance cameras

We propose to evaluate infrared lenses with a dedicated analyzer having the same mechanical interface as the usual cameras. The proposed analysis is based on a wavefront measurement and allows a diagnostic of possible internal defects of the analyzed lens. The infrared lens analyzer described is constituted with a quadriwave lateral shearing interferometer and works with a blackbody light. We describe the response of this interferometer and an innovative method to obtain the wavefront under test. We finally present the experimental analysis of long-wavelength infrared lenses and the particular case of a modified lens that generates a large spherical aberration.     

Systematic comparison of the use of annular and Zernike circle polynomials for annular wavefronts

The theory of wavefront analysis of a noncircular wavefront is given and applied for a systematic comparison of the use of annular and Zernike circle polynomials for the analysis of an annular wavefront. It is shown that, unlike the annular coefficients, the circle coefficients generally change as the number of polynomials used in the expansion changes. Although the wavefront fit with a certain number of circle polynomials is identically the same as that with the corresponding annular polynomials, the piston circle coefficient does not represent the mean value of the aberration function, and the sum of the squares of the other coefficients does not yield its variance. The interferometer setting errors of tip, tilt, and defocus from a four-circle-polynomial expansion are the same as those from the annular-polynomial expansion. However, if these errors are obtained from, say, an 11-circle-polynomial expansion, and are removed from the aberration function, wrong polishing will result by zeroing out the residual aberration function. If the common practice of defining the center of an interferogram and drawing a circle around it is followed, then the circle coefficients of a noncircular interferogram do not yield a correct representation of the aberration function. Moreover, in this case, some of the higher-order coefficients of aberrations that are nonexistent in the aberration function are also nonzero. Finally, the circle coefficients, however obtained, do not represent coefficients of the balanced aberrations for an annular pupil. The various results are illustrated analytically and numerically by considering an annular Seidel aberration function.     

高精度球面检测中调整误差的精确校正

针对高精度球面检测中球面的调整误差影响,分别研究了波前离焦和倾斜所引入的Zernike像差项,并以此为基础,提出了基于Zernike系数的高精度球面调整误差校正方法.利用Zygo干涉仪对大数值孔径的待测球面进行了检测,实验中对待测球面同时引入波前离焦和倾斜误差,再分别运用所提出的校正方法和传统的消倾斜离焦校正方法得到波面数据并进行对比,进而验证了所提出的校正方法的可行性.实验结果表明,利用该方法可有效地校正大数值孔径球面存在调整误差时所引入的球面像差,并且实验中的校正精度达到了0.002λ（λ为检测光波长）.提出的基于Zernike系数的球面调整误差校正方法可降低对于调节机构的精度以及检测人员的经验要求,在高精度球面检测中具有非常高的实际应用价值.     

双平板剪切干涉仪及其干涉图的数值分析

一种用于光学器件及光学成像系统波面差及像质检验的横向剪切干涉仪及其干涉图的数值分析方法,在平行平板横向剪切干涉原理的基础上,分析讨论了改进后的双剪切干涉仪的工作方式及优越性,在对其干涉图的数值分析方法,利用Ｚernike圆正交多项式作为基底函数,对被测光学系统的剪切干涉图进行波面的二维最小二乘拟合,以期重构原始波面,得到被测光学系统的波面差函数,进而不得系统的光学传递函数（ＯＴＦ）,对一组标准镜头进行的测试分析表测量的不确定度＜０．０５。     

Active optics null test system based on a liquid crystal programmable spatial light modulator

We present an active null test system adapted to test lenses and wavefronts with complex shapes and strong local deformations. This system provides greater flexibility than conventional static null tests that match only a precisely positioned, individual wavefront. The system is based on a cylindrical Shack-Hartmann wavefront sensor, a commercial liquid crystal programmable phase modulator (PPM), which acts as the active null corrector, enabling the compensation of large strokes with high fidelity in a single iteration, and a spatial filter to remove unmodulated light when steep phase changes are compensated. We have evaluated the PPM's phase response at 635 nm and checked its performance by measuring its capability to generate different amounts of defocus aberration, finding root mean squared errors below λ/18 for spherical wavefronts with peak-to-valley heights of up to 78.7λ, which stands as the limit from which diffractive artifacts created by the PPM have been found to be critical under no spatial filtering. Results of a null test for a complex lens (an ophthalmic customized progressive addition lens) are presented and discussed.     

Dynamic eye model for adaptive optics testing

An artificial dynamic eye model is proposed. The prototype enabled us to introduce temporal variations in defocus and spherical aberration, resembling those typically found in the human eye. The eye model consisted of a meniscus lens together with a modal liquid crystal lens with controllable focus. A diffuser placed at a fixed distance from the lenses acted as the artificial retina. Developed software allowed the user to precisely control the dynamic generation of aberrations. In addition, different refractive errors could simultaneously be emulated by varying the distance between the components of the model. The artificial eye was first used as a dynamic generator of both spherical aberration and defocus, imitating the behavior of a real eye. The artificial eye was implemented in an adaptive optics system designed for the human eye. The system incorporated an electrostatic deformable mirror and a Hartmann-Shack wavefront sensor. Results with and without real time closed-loop aberration correction were obtained. The use of the dynamic artificial eye could be quite useful for testing and evaluating adaptive optics instruments for ophthalmic applications.     

Optical aberrations of intraocular lenses measured in vivo and in vitro

Corneal and ocular aberrations were measured in a group of eyes before and after cataract surgery with spherical intraocular lens (IOL) implantation by use of well-tested techniques developed in our laboratory. By subtraction of corneal from total aberration maps, we also estimated the optical quality of the intraocular lens in vivo. We found that aberrations in pseudophakic eyes are not significantly different from aberrations in eyes before cataract surgery or from previously reported aberrations in healthy eyes of the same age. However, aberrations in pseudophakic eyes are significantly higher than in young eyes. We found a slight increase of corneal aberrations after surgery. The aberrations of the IOL and the lack of balance of the corneal spherical aberrations by the spherical aberrations of the intraocular lens also degraded the optical quality in pseudophakic eyes. We also measured the aberrations of the IOL in vitro, using an eye cell model, and simulated the aberrations of the IOL on the basis of the IOL's physical parameters. We found a good agreement among in vivo, in vitro, and simulated measures of spherical aberration: Unlike the spherical aberration of the young crystalline lens, which tends to be negative, the spherical aberration of the IOL is positive and increases with lens power. Computer simulations and in vitro measurements show that tilts and decentrations might be contributors to the increased third-order aberrations in vivo in comparison with in vitro measurements.     

Combinational system of a truncated ball lens and a hyperbolic lens for collimating a highly divergent source

We propose the use of a truncated ball lens in a collimating system to transform a spherical wave from a highly divergent source into a plane wave. The proposed scheme, which incorporates a hyperbolic lens, is discussed, and the overall system is found to have a large acceptance angle and to be free of spherical aberration. Diffraction and polarization effects are neglected, as well as skew rays.     

High tolerance to spherical aberrations and defects of focus with a birefringent lens

We report a systematic investigation of the imaging behavior of an optical system consisting of a lens from a uniaxial birefringent crystal sandwiched between two linear polarizers into which primary spherical aberration has been introduced. The proposed system has higher tolerance to primary spherical aberration and has a larger depth of focus than an imaging system found with an isotropic lens. Some specific cases are computed and illustrated graphically.     

Holography-based wavefront sensing

We describe a modal wavefront sensing technique of using multiplexed holographic optical elements (HOEs). The phase pattern of a set of aberrations is angle multiplexed in a HOE, and the correlated information is obtained with a position sensing detector. The recorded aberration pattern is based on an orthogonal basis set, the Zernike polynomials, and a spherical reference wave. We show that only two recorded holographic patterns for any particular aberration type are sufficient to allow interpolated readout of aberrations to lambda/50. In this paper, we demonstrate the capability of detecting errors between +/-2lambda PV for each orthogonal set at rates limited only by the speeds of the detection electronics, which could be up to 1 MHz. We show how we take advantage of the unavoidable intermodal and intramodal cross talks in determining the type, amplitude, and orientation of the wavefront aberrations.     

扇形子孔径布局H-S传感器对圆域的探测性能研究

通过Zernike模式波前重构算法进行计算机仿真计算,对扇形子孔径布局的Hartmann-Shack波前传感器探测性能进行仿真研究,对比分析了方形子孔径布局Hartmann-Shack波前传感器的探测性能.结果表明,扇形子孔径布局是一种有效的Hartmann-Shack波前传感器的布局方式,在低子孔径密度且径数目差异不多的条件下,比方形孔径布局探测精度更高.     

Interferometric measurement of near-cylindrical surfaces with high amplitude resolution

Subaperture interferometric measurements of highly curved surfaces with a shape close to a cylinder have been performed in a normal-incident setup that consists of a Fizeau interferometer in combination with a plano-concave cylindrical lens. Since the field of view in the circumferential direction is limited by spherical aberration, the optical components were designed to minimize spherical aberration. For reference measurements a second plano-convex cylindrical lens was used. The subaperture setup leads to three-dimensional surface maps of the objects under test. To eliminate the influence of residual geometric aberrations, rectangular polynomials have been fitted and subtracted from the raw data. For deformations with spatial wavelengths below 30 mm, a rms amplitude resolution of 1 nm and a rms amplitude accuracy of 3 nm were achieved. Measurements on Wolter-type-I mirror shells are discussed in detail.     

Misalignment aberrations calibration in testing of high-numerical-aperture spherical surfaces

The calibration of misalignment aberrations is a key issue in the testing of high-numerical-aperture spherical surfaces, and it is hard to separate the high-order aberrations introduced by misalignment from the measured data. The traditional calibration method is still applicable in the case of only wavefront tilt, but no longer effective in the existence of defocus. A calibration technique based on the wavefront difference is proposed to calibrate the misalignment aberrations in the presence of wavefront defocus, and it can be carried out without foreknowledge of the spherical surface under test. With the wavefront difference method, the calibration needs two separate measurements to separate the high-order aberrations. Both the computer simulation and experiments with the ZYGO interferometer have been carried out to validate the proposed calibration technique, with the accuracies better than 0.0005λ RMS and 0.0010λ RMS achieved, respectively. The proposed calibration method provides a feasible way to lower the requirement on the adjustment in the measurement, while retaining good accuracy.     

Normalized parameter relating the spherical aberration of a thin lens to the diffraction limit and fiber coupling efficiency

In this paper, we calculate the transverse spherical aberration TA of a thin lens and defines a normalized aberration Y equal to TA divided by the theoretical resolution limit. As a rule of thumb, (a) a thin lens that suffers only from spherical aberration may be considered effectively diffraction-limited as long as Y < 1.6. Similarly, (b) the coupling efficiency of a Gaussian beam to a single-mode fiber may be high even when Y > 1.6, and, specifically, (c) the lens need be diffraction-limited only over a radius approximately equal to the radius (to the 1/e-point) of the Gaussian beam.     

Adaptive control in an adaptive optics experiment

This paper presents results from an adaptive optics experiment in which an adaptive control loop augments a classical adaptive optics feedback loop. Closed-loop wavefront errors measured by a self-referencing interferometer are fed back to the control loops, which drive a membrane deformable mirror to correct the wavefront. The paper introduces new frequency-weighted deformable mirror modes used as the control channels and new wavefront sensor modes for analyzing the performance of the control loops. The corrected laser beam also is imaged by a diagnostic target camera. The experimental results show reduced closed-loop wavefront errors and correspondingly sharper diagnostic target images produced by the adaptive control loop as compared with the classical AO loop.     

Lens design for a white-light cosine-transform achromat

We describe the lens design for a twin-imaging white-light interferometer in which the interference pattern at the exit-pupil plane is the cosine transform of the spatial-intensity distribution of the object. The achromatic condition in terms of optical power is derived. The analysis of the transform aberration shows that the even aberrations, e.g., spherical aberration and field curvature, do not degrade the cosine transform and need not be corrected. This significant simplification permits us to design systems with good performance and uncomplicated lens structures. We present a lens design with three elements and a length of 320 mm. The system is capable of resolving more than 10(6) pixels with an operating spectral bandwidth of 100 nm. The results of an experiment with an early four-element design are also presented.     

Parabolic liquid mirrors in optical shop testing

A parabolic liquid mirror obtained by the rotation of a mercury bath around a vertical axis has been built and its optical surface characteristics measured to demonstrate that it can be used in optical shop testing as a reference surface. A linear Hartmann test allowed us to check that the focal length is well related to the rotation velocity, following the theory, and that no spherical aberration is present, as assumed by previous authors. The spherical aberration has been found to be smaller than λ/50 at 633 nm. An interferometric test of the mirror compared with a null lens gave information about the quality of the optical surface for which the rms wave-front error, when the random errors are averaged, is ~λ/25. Because modifying the mirror diameter is cheap and fast and adjusting its focal length within a large range is straightforward, the parabolic liquid mirror can become a highly adaptable tool in optical metrology. In particular, it can be used in optical shop testing as a reference surface to test null correctors, to check any system developed to control the shape of large parabolic or quasiparabolic top-quality solid-state mirrors, or to make holographic references of such surfaces.     

Generalized data reduction approach for aspheric testing in a non-null interferometer

Data reduction in non-null tests is difficult due to the presence of retrace error. We propose a simple yet effective data reduction approach for aspheric testing in a non-null interferometer. The new approach gives figure error of the aspheric by just subtracting the theoretical wavefront and first-order errors from the real wavefront obtained in the non-null interferometer. Precise prediction of the theoretical wavefront can be achieved by accurate calibration of the partial compensation system. The approach can be considered a generalization of the traditional data processing method in null tests, and errors that may affect its accuracy are discussed. A set of experiments have been carried out to demonstrate its validity and feasibility.     

Testing the effect of computer-generated hologram fabrication error in a cylindrical interferometry system

This paper presents a method of testing the effect of computer-generated hologram (CGH) fabrication error in a cylindrical interferometry system. An experimental system is developed for calibrating the effect of this error. In the calibrating system, a mirror with high surface accuracy is placed at the focal axis of the cylindrical wave. After transmitting through the CGH, the reflected cylindrical wave can be transformed into a plane wave again, and then the plane wave interferes with the reference plane wave. Finally, the double-pass transmitted wavefront of the CGH, representing the effect of the CGH fabrication error in the experimental system, is obtained by analyzing the interferogram. The mathematical model of misalignment aberration removal in the calibration system is described, and the feasibility is demonstrated via the simulation system established in Zemax. With the mathematical polynomial, most of the possible misalignment errors can be estimated with the least-squares fitting algorithm, and then the double-pass transmitted wavefront of the CGH can be obtained by subtracting the misalignment errors from the result extracted from the real experimental system. Compared to the standard double-pass transmitted wavefront given by Diffraction International Ltd., which manufactured the CGH used in the experimental system, the result is desirable. We conclude that the proposed method is effective in calibrating the effect of the CGH error in the cylindrical interferometry system for the measurement of cylindricity error.     

Multiple-beam lateral shear interferometry for optical testing

Lateral shear interferometry is used to obtain the lateral aberrations of a lens. The zeroth-order fringe in an interferogram obtained from a wedge-plate lateral shear interferometer, however, directly displays the lateral aberration curve of a test lens. Nevertheless, the intensity distribution, is cosinusoidal. Multiple-beam interferometry results in sharpened fringes; hence the multiple-beam wedge-plate shear interferometer displays the lateral aberration curve of a lens sharply, provided the shear is small. For large shear, some new artifacts appear in the interferogram, which are also explained.