Techniques for measuring aberrations in lenses used in photolithography with printed patterns

In optical lithography, it is a serious problem that aberrations in projection lenses reduce the imaging quality. Therefore techniques to measure the aberrations are required that will predict the adverse effects of aberrations on lithographic imagery and reduce them. We present a measurement method that uses a fine grating and its imaging condition to quantify coma, astigmatism, and spherical aberration. With this method, these aberrations can be described with simple expressions from the measured results. Application of this method revealed the coma of Zernike polynomials for our krypton fluoride (KrF) excimer-laser scanner.     

用斑点成像消除光学系统像差的影响

在详细分析用斑点成像消除目标图像中随机扰动影响的基础上,提出了在有像差光学系统中,应用斑点成像消除图像中像差影响的方法。通过在光学系统的光路中引入随机相位屏,采集物的短曝光像,用斑点成像处理,恢复目标图像的功率谱和相位谱,可以得到目标近衍射极限的图像。实验结果表明,这种方法可以消除图像中光学系统像差的影响。     

Aberration measurement of projection optics in lithographic tools based on two-beam interference theory

The degradation of image quality caused by aberrations of projection optics in lithographic tools is a serious problem in optical lithography. We propose what we believe to be a novel technique for measuring aberrations of projection optics based on two-beam interference theory. By utilizing the partial coherent imaging theory, a novel model that accurately characterizes the relative image displacement of a fine grating pattern to a large pattern induced by aberrations is derived. Both even and odd aberrations are extracted independently from the relative image displacements of the printed patterns by two-beam interference imaging of the zeroth and positive first orders. The simulation results show that by using this technique we can measure the aberrations present in the lithographic tool with higher accuracy.     

Variable zoom system with aberration correction capability

We describe experiments conducted with two deformable mirrors (DMs) at fixed locations in an optical microscope imaging system. In this configuration, the DM shapes are controlled to provide 2.5× zoom capability, to allow dynamic focus control and to compensate for aberrations of the fixed optical components. Zoom is achieved by simultaneously adjusting focal lengths of the two DMs, which are inserted between an infinity-corrected microscope objective and a tube lens. Image quality is measured using contrast modulation, and performance of the system is quantified, demonstrating an improved point spread function in the adaptively compensated system.     

High-resolution adaptive optics scanning laser ophthalmoscope with dual deformable mirrors

Adaptive optics scanning laser ophthalmoscopes have been used to produce noninvasive views of the human retina. However, the range of aberration compensation has been limited by the choice of deformable mirror technology. We demonstrate that the use of dual deformable mirrors can effectively compensate large aberrations in the human eye while maintaining the quality of the retinal imagery. We verified experimentally that the use of dual deformable mirrors improved the dynamic range for correction of the wavefront aberrations compared with the use of the micro-electro-mechanical-system mirror alone and improved the quality of the wavefront correction compared with the use of the bimorph mirror alone. We also demonstrated that the large-stroke bimorph deformable mirror improved the capability for axial sectioning with the confocal imaging system by providing an easier way to move the focus axially through different layers of the retina.     

Bispectral Imaging Through Unknown Deterministic Aberrations

Abstract

When the deterministic aberrations are known in an optical system, traditional de-blurring methods are effective. However, when the aberrations are difficult to quantify, such as telescope aberrations or the aberrations in the human eye, other methods are needed. One potential method for de-blurring an image that is formed from a system with unknown aberrations is the bispectral imaging method. It is a promising way to remove the effects of deterministic aberrations when random aberrations are present or artificially introduced into the system. Through computer simulations, we have found the optimal amount of random aberrations to have present in a system containing deterministic aberrations. This amount optimizes the image quality of the reconstruction at high light levels using 100 statistically independent aberrated images of the object. Defocus and several third-order aberrations were considered in the isoplanatic case. The performance of this method was characterized by reconstructing a point source and computing its Strehl ratio. These results are currently being used to incorporate the bispectral imaging method as part of a non-invasive technique to reconstruct high-resolution images of the back of the eye in human subjects.     

Eigenmode super-resolution imaging in arbitrary optical systems

We investigate optical super-resolution by means of eigenmode decomposition in arbitrary imaging systems. This technique is applicable for arbitrary objects but requires a knowledge of the eigenmodes of the imaging system. We outline a reconstruction technique that can be applied even to systems in which the eigenmodes are not orthogonal, and we present numerical simulations of eigenmode super-resolution in systems with resolution limited both by diffraction and by aberrations. Our results indicate that optical super-resolution by direct eigenmode decomposition provides a versatile method of sub-diffraction and distortion-free imaging in arbitrary optical systems.     

Optical design with parametrically defined aspheric surfaces

The standard aspheric surface definition has been used successfully to correct aberrations in a wide variety of systems. However, in some current applications a more general surface definition is needed. We present a more general approach that uses parametrically defined optical surfaces for the optical design of imaging and illumination systems.     

Analytical and Numerical Examination of the Quantitative Imaging Properties of Optical Diffraction Tomography

Abstract

The imaging properties of two-dimensional optical diffraction tomography are examined analytically and numerically. Taking into account lens aberrations in the optical system used to image the scattered light, we first derive an expression for the overall coherent transfer function. Then we use computer simulations to examine the influence of lens aberrations by comparing images obtained by a system with lens aberrations with images obtained by an aberration-free system. We also discuss the significance of systematic positioning errors in the set-up.     

Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry

Many authors, dating back to at least the 1950s, have presented mathematical expansions of the wave-front aberration function for optical systems without symmetry, typically based on limiting assumptions and simplifications, with some of the most recent work being done by Howard and Stone [Appl. Opt. 39, 3232 (2000)]. This paper reveals that in fact there are no new aberrations in imaging optical systems with near-circular aperture stops but otherwise without symmetry. What does occur is that the field dependence of an aberration often changes when symmetry is abandoned. Each aberration type develops a characteristic field behavior in a system without symmetry. Specifically, for example, astigmatism, develops a binodal field dependence; e.g., there are typically two points in the field with zero astigmatism, and typically neither point is on axis. This construct, nodal aberration theory, for understanding the aberrations in systems without symmetry becomes a direct extension of an optical designer's knowledge base. Through the use of real ray-based analysis methods, such as Zernike coefficients, it is possible to understand completely the aberrations of optical systems without symmetry in terms of rotationally symmetric aberration theory with the simple addition of the concept of field nodes.     

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.     

Lensless broadband diffractive imaging with improved depth of focus: wavefront modulation by multilevel phase masks

This paper introduces a novel lensless full colour diffractive computational imaging system with a planar Multilevel Phase Mask (MPM) as a diffractive optical element (DOE). The novelty concerns: a methodology of MPM design for improved depth of focus (DoF); design of PSFs for RGB imaging and an inverse imaging algorithm with sparse colour image modelling simultaneous for all RGB channels. MPMs are step-wise invariant. The cubic wavefront coding (WFC) is incorporated in MPMs with optimization of number of levels and width of invariant steps. This design of MPM makes the system robust with respect to defocus (improves DoF) and diminish chromatic aberrations typical for DOEs. Broadband multichannel test-images are exploited for design and testing of the lensless system. We consider two alternative optical setups: Wavelength Multiplexing (WM) and Wavelength Division (WD). In WM, the light beam is broadband multichannel with light sources radiating all wavelengths simultaneously and a CMOS sensor is equipped with a Bayer colour filter array (CFA) for registration of spectral measurements. In this setup, a single MPM is designed for the broadband multichannel light beams. In WD, separate exposures of RGB channels are registered by a broadband grey-scale CCD sensor. Different MPMs are designed for each of the RGB channels. Simulation experiments demonstrate the essentially extended DoF of the designed lensless systems and the advanced accuracy and quality of imaging with respect to the corresponding WM and WD systems with refractive lenses. Due to robustness of the designed lensless system to chromatic aberrations, this advantage has a place even with respect to the lens-system.     

Optimization method for ultra-wide-angle and panoramic optical systems

To an ultra-wide-angle and panoramic optical system, the aberrations of point object at any field angle are separated into two types: the aperture-ray aberrations of off-axis point object and the chief-ray aberrations. A simple form of the triangular formulae of tracing an oblique-incidence ray is derived to calculate the chief-ray parameters and their aberrations; moreover, the aperture-ray aberrations of an off-axis point object are analyzed with the plane-symmetric aberration theory. Based on the two types of aberrations, we present a merit function for ultra-wide-angle and panoramic optical systems; the optimization program with the differential-evolution algorithm is then developed. To validate the optimization method we finally optimize a fish-eye lens and a catadioptric omnidirectional imaging system.     

Reduction of the effect of aberrations in a joint-transform correlator

We report the study of the influence of optical aberrations in a joint-transform correlator: The wave aberration of the optical system is computed from data obtained by ray tracing. Three situations are explored: We consider the aberration only in the first diffraction stage (generation of power spectrum), then only in the second (transformation of the power spectrum into correlation), and finally in both stages simultaneously. The results show that the quality of the correlation is determined mostly by the aberrations of the first diffraction stage and that we can optimize the setup by moving the cameras along the optical axis to a suitable position. The good agreement between the predicted data and the experimental results shows that the method explains well the behavior of optical diffraction systems when aberrations are taken into account.     

Design strategies to simplify and miniaturize imaging systems

We present the range of optical architectures for imaging systems based on a single optical component, an aperture stop, and a detector. Thanks to the formalism of third-order Seidel aberrations, several strategies of simplification and miniaturization of optical systems are examined. Figures of merit are also introduced to assess the basic optical properties and performance capabilities of such systems; by this way, we show the necessary trade-off between simplicity, miniaturization, and optical performance.     

Orthonormal aberration polynomials for anamorphic optical imaging systems with rectangular pupils

The classical aberrations of an anamorphic optical imaging system, representing the terms of a power-series expansion of its aberration function, are separable in the Cartesian coordinates of a point on its pupil. We discuss the balancing of a classical aberration of a certain order with one or more such aberrations of lower order to minimize its variance across a rectangular pupil of such a system. We show that the balanced aberrations are the products of two Legendre polynomials, one for each of the two Cartesian coordinates of the pupil point. The compound Legendre polynomials are orthogonal across a rectangular pupil and, like the classical aberrations, are inherently separable in the Cartesian coordinates of the pupil point. They are different from the balanced aberrations and the corresponding orthogonal polynomials for a system with rotational symmetry but a rectangular pupil.     

Optical transfer function of slit-coupled axial systems

We studied the influence that aberrations and diffraction have on the quality of the image of a generic family of slit-coupled axisymmetric systems when both effects are competitive. We evaluated the modulation optical transfer function of these systems for small amounts of individual third-order aberrations and different widths of the intermediate slit that couples both stages.     

Vector diffraction problem of focusing a category 1 aberrated wavefront through a multilayered lossless medium

Abstract

In optical storage and other imaging applications, a laser beam is focused through a transparent lossless medium of different refractive index. Applications include optical and magneto-optical recording. It is highly likely that, in the near future, conventional magnetic recording will transition to optically/thermally assisted magnetic recording technology. In all these applications, it is necessary to ascertain the quality of the image formed by the focusing apparatus on an imaging surface when in the neighbourhood of the focus, the focused beam of light passes through a stratified lossless medium. This paper examines the vector diffraction problem of focusing radiation through a multilayered medium. The solution is accomplished by first deriving a general solution of the focusing problem in any homogenous medium. This solution is then used to obtain the solution in the multilayered medium by applying continuity of the electric and magnetic fields at the interfaces. The technique used here allows one to calculate the field quantities in the entire image space. Furthermore, the focusing lens may have Seidel aberrations of the fourth order. The salient feature of this method is that the vector diffraction problem is solved only once - for the zeroth layer, immediately next to the exit pupil. In the remaining layers, the results are obtained by solving linear algebraic equations. The solution of the algebraic equations is obtained in closed form.     

Holographic optical elements in the presence of spherical aberration and focus error: Some remarks on imaging quality

Abstract

When aberrations are small, it is possible to use wave aberration variance to obtain the position of the best image plane in both conventional and holographic optical systems. However, when aberrations increase, this measurement is not sufficient and it does not provide the correct plane position for the best image. In this paper, two alternative methods for evaluating image quality in spherically aberrated on-axis holographic lenses are compared. These two methods are the standard deviation of the distribution of light intensity and entropy. Both methods are based on the calculation of the diffraction integral and the subsequent analysis of the distribution of light intensity as a probability density function for each image plane being analysed. Even though the results obtained with both methods are identical when aberrations are small, only entropy provides the best image when the value of these aberrations increases.     

Coating-induced wave-front aberrations: on-axis astigmatism and chromatic aberration in all-reflecting systems

The coatings used on telescope mirrors and other optical interfaces can have a marked effect on an optical system's image quality. We describe the wave-front aberrations, particularly the defocus and on-axis astigmatism, that are induced by the s- and p-phase shifts of coatings. These coating-induced wave-front aberrations are very small, particularly near the design wavelengths of the coatings, but they can under certain circumstances overshadow the geometric wave-front aberrations of the system. The wave-front aberrations that are induced by reflection-enhanced coatings on an à/1.5 Cassegrain telescope are numerically evaluated as an example. A theory of coating-induced on-axis astigmatism and chromatic aberration is presented, and a simple algorithm that uses polarization ray tracing to calculate coating-induced defocus and astigmatism coefficients in radially symmetric systems is provided.