Joseph J. M. Braat

Assessment of an extended Nijboer-Zernike approach for the computation of optical point-spread functions

We assess the validity of an extended Nijboer-Zernike approach [J. Opt. Soc. Am. A 19, 849 (2002)], based on ecently found Bessel-series representations of diffraction integrals comprising an arbitrary aberration and a defocus part, for the computation of optical point-spread functions of circular, aberrated optical systems. These new series representations yield a flexible means to compute optical point-spread functions, both accurately and efficiently, under defocus and aberration conditions that seem to cover almost all cases of practical interest. Because of the analytical nature of the formulas, there are no discretization effects limiting the accuracy, as opposed to the more commonly used numerical packages based on strictly numerical integration methods. Instead, we have an easily managed criterion, expressed in the number of terms to be included in the Bessel-series representations, guaranteeing the desired accuracy. For this reason, the analytical method can also serve as a calibration tool for the numerically based methods. The analysis is not limited to pointlike objects but can also be used for extended objects under various illumination conditions. The calculation schemes are simple and permit one to trace the relative strength of the various interfering complex-amplitude terms that contribute to the final image intensity function.

Extended Nijboer-Zernike representation of the vector field in the focal region of an aberrated high-aperture optical system

Taking the classical Ignatowsky/Richards and Wolf formulas as our starting point, we present expressions for the electric field components in the focal region in the case of a high-numerical-aperture optical system. The transmission function, the aberrations, and the spatially varying state of polarization of the wave exiting the optical system are represented in terms of a Zernike polynomial expansion over the exit pupil of the system; a set of generally complex coefficients is needed for a full description of the field in the exit pupil. The field components in the focal region are obtained by means of the evaluation of a set of basic integrals that all allow an analytic treatment; the expressions for the field components show an explicit dependence on the complex coefficients that characterize the optical system. The electric energy density and the power flow in the aberrated three-dimensional distribution in the focal region are obtained with the expressions for the electric and magnetic field components. Some examples of aberrated focal distributions are presented, and some basic characteristics are discussed.

Calculation of the vectorial field distribution in a stratified focal region of a high numerical aperture imaging system

We present an algorithm for calculating the field distribution in the focal region of stratified media which is fast and easy to implement. Using this algorithm we study the effect on the electric field distribution of an air gap separating a solid immersion lens and a sample, where we analyse the maximum distance for out-of-contact operation. Also, we study how the presence of a metallic substrate affects the field distribution in the focal region; the interference effects of the reflected field could be used as an alternative for 4Pi-microscopy.

Video disk player optics

The optics of a video disk player are described. The bandwidth and the playing time of a disk had been specified at 12 MHz and 30 min, respectively. A readout photodetector signal of high quality can be obtained with a well-corrected objective having a numerical aperture of at least 0.4. Some alternative readout modes and track formats are indicated. Methods for the generation of error signals for the radial and the vertical tracking are briefly discussed.

Assessment of optical systems by means of point-spread functions

Publisher Summary This chapter presents the computation of the point-spread function of optical imaging systems and the characterization of these systems by means of the measured three-dimensional structure of the point-spread function. The point-spread function, accessible in the optical domain only in terms of the energy density or the energy flow, is a nonlinear function of the basic electromagnetic field components in the focal region. That is why the reconstruction of the amplitude and phase of the optical far-field distribution that produced a particular intensity point-spread function is a nonlinear procedure that does not necessarily have a unique solution. Since the 1970s, the quality of optical imaging systems (telescopes, microscope objectives, high-quality projection lenses for optical lithography, space observation cameras) has been pushed to the extreme limits. At this level of perfection, a detailed analysis of the optical point-spread function is necessary to understand the image formation by these instruments, especially when they operate at high numerical aperture. In terms of imaging defects, it allowed to suppose that the wavefront aberration of such instruments is not substantially larger than the wavelength λ of the light. In most cases, the aberration even has to be reduced to a minute fraction of the wavelength of the light to satisfy the extreme specifications of these imaging systems. The past work on point-spread function analysis and its application to the assessment of imaging systems is presented in the chapter. This includes discussions on: the theory of point-spread function formation, energy density and power flow in the focal region, quality assessment by inverse problem solution, and quality assessment using the extended Nijboer–Zernike diffraction theory.

Design of multilayer extreme-ultraviolet mirrors for enhanced reflectivity

We show numerically that the reflectivity of multilayer extreme-UV (EUV) mirrors tuned for the 11-14-nm spectral region, for which the two-component, Mo/Be and Mo/Si multilayer systems with constant layer thickness are commonly used, can be enhanced significantly when we incorporate additional materials within the stack. The reflectivity performance of the quarter-wavelength multilayers can be enhanced further by global optimization procedures with which the layer thicknesses are varied for optimum performance. By incorporating additional materials of differing complex refractive indices-e.g., Rh, Ru, Sr, Pd, and RbCl-in various regions of the stack, we observed peak reflectivity enhancements of as much as ~5% for a single reflector compared with standard unoptimized stacks. We show that, in an EUV optical system with nine near-normal-incidence mirror surfaces, the optical throughput may be increased by a factor as great as 2. We also show that protective capping layers, in addition to protecting the mirrors from environmental attack, may serve to improve the reflectivity characteristics.

Nanometer deep shaping with fluid jet polishing

We describe the theoretical dependence of various important parameters of the fluid jet polishing process on the material removal rate: the processing time, abrasive concentration, abrasive diameter, particle velocity, and the effect of scanning. Some recent experiments are described that prove that it is possible to remove very small amounts of material, less than 1 nm/min, using either short processing times or an appropriate slurry. The removal spot in the stationary case is compared to that in the translational case both theoretically and experimentally. From both a theoretical and an experimental point of view it is shown that the removal is in the ductile regime.

Analytical expressions for the wave-front aberration coefficients of a tilted plane-parallel plate.

An expression is given for the aberration imparted by a tilted plane-parallel plate to a converging or diverging pencil of rays. Analytical expressions for the wave-front aberration coefficients up to the sixth order are derived. These expressions, among others, are of importance when reading an optical disk through its substrate or when using a plane-parallel plate as a beam splitter. Differences with previous expressions from the literature are noted.

General polarized ray-tracing method for inhomogeneous uniaxially anisotropic media

Uniaxial optical anisotropy in the geometrical-optics approach is a classical problem, and most of the theory has been known for at least fifty years. Although the subject appears frequently in the literature, wave propagation through inhomogeneous anisotropic media is rarely addressed. The rapid advances in liquid-crystal lenses call for a good overview of the theory on wave propagation via anisotropic media. Therefore, we present a novel polarized ray-tracing method, which can be applied to anisotropic optical systems that contain inhomogeneous liquid crystals. We describe the propagation of rays in the bulk material of inhomogeneous anisotropic media in three dimensions. In addition, we discuss ray refraction, ray reflection, and energy transfer at, in general, curved anisotropic interfaces with arbitrary orientation and/or arbitrary anisotropic properties. The method presented is a clear outline of how to assess the optical properties of uniaxially anisotropic media.

Holographic simultaneous readout polarization multiplexing based on photoinduced anisotropy in bacteriorhodopsin

Bacteriorhodopsin (bR) is a reversible photochromic protein that can be used as a holographic medium. The dichroic absorption of the bR molecule is polarization dependent, thereby allowing for the recording of polarization holograms. The properties of polarization holograms can be used to multiplex two independent images in a single bR film. A new technique and associated polarization-multiplexing scheme are demonstrated that allow for simultaneous readout of two orthogonally polarized images while achieving a high normalized diffraction efficiency for each of the individual images.