Tip-tilt error for extremely large segmented telescopes: detailed theoretical point-spread-function analysis and numerical simulation results

We present an analysis of point-spread functions for segmented mirrors affected by random tip-tilt errors on each segment. In addition to Strehl ratio evaluation, this analysis considers key characteristics such as the intensity and the location of speckles and secondary peaks and the relative energy distribution between these features. We develop a method to describe the shape of a nonaveraged point-spread function and deduce the final expressions for ensemble-averaged characteristics. Based on Keck-type hexagonal segmentation geometry, our study is extended to an arbitrary number of segments, and we describe qualitatively the transition from the case of a mirror with few segments to that of a mirror with several hundred segments--prototype of the next generation of Extremely Large Telescopes.     

Reflection and transmission properties of holographic mirrors and holographic Fabry-Perot filters. I. Holographic mirrors with monochromatic light

The reflection and transmission coefficients of holographic mirrors (HM's) and holographic Fabry-Perot filters (HFPF's) are studied. The diffraction efficiencies, the angular selectivities, and the wavelength sensitivities of HM's and HFPF's and their effects on the spectrum and on the coherence properties of the incident light are investigated. The results show that holographic techniques can indeed be used to construct high-quality reflecting mirrors and Fabry-Perot filters. HM's illuminated by a monochromatic plane wave are investigated in detail. The reflection and transmission coefficients are first studied as functions of frequency (wavelength) of the incident light and also as functions of the angle of incidence. It is shown that HM's can be used as highly reflecting mirrors around their Bragg angle of incidences. Their reflectivity curves have fairly wide angular- and frequency-selectivity ranges.     

Imaging system of wavelet optics described by the Gaussian linear frequency-modulated complex wavelet

The image formation and the point-spread function of an optical system are analyzed by use of the wavelet basis function. The image described by a wavelet is no longer an indivisible whole image. It is, rather, a complex image consisting of many wavelet subimages, which come from the changes of different parameters (scale) a and c, and parameters b and d show the positions of wavelet subimages under different scales. A Gaussian frequency-modulated complex-valued wavelet function is introduced to express the point-spread function of an optical system and used to describe the image formation. The analysis, in allusion to the situation of illumination with a monochromatic plain light wave, shows that using the theory of wavelet optics to describe the image formation of an optical system is feasible.     

Schlieren systems with coherent illumination for quantitative measurements

Schlieren systems with a coherent light source were investigated by the Fourier optics technique. The imaging properties of the systems with various cutoff filters were studied. Systems with a graded piecewise linear filter and a Gaussian step function convolution (graded) filter are considered, demonstrating that the image can be approximated by the geometrical-optics theory of conventional schlieren systems. A nonlinear phase contribution was estimated, allowing for the measurement of strong phase objects. Within the framework of linear approximation the results are described by the phase derivative point-spread function, introduced in this paper as the schlieren point-spread function. In addition, modification of the Lopez cutoff filter is proposed, demonstrating its superiority over the piecewise linear and the Gaussian step convolution filters. Simulations of coherent schlieren imaging as well as phase derivative measurements were performed. Finally, the imaging properties of the schlieren systems with the different filters are compared.     

Narrow-bandpass filters with broad rejection band for single-mode waveguides

Fabry-Perot bandpass filters made of mirrors with both high- and low-Dn (refractive-index modulation) have simultaneously a broad rejection band and a narrow passband. The higher Dn's are obtained with multilayer mirrors and the lower with Bragg gratings (BG's). Implementation of a sampling calculation technique based on the characteristic matrix formalism used for interference coatings allows for simulation of hybrid filters constructed from multilayer mirrors and BG's. The possible defects of hybrid filters are extensively analyzed. Bandpass filters made purely of both high- and low-Dn BG's are also simulated. All these filters are useful for wavelength division multiplexing applications.     

New class of axially apodizing filters for confocal scanning microscopy

A new class of axially apodizing continuously transmitting filters is analytically determined and numerically implemented. The longitudinal and lateral properties of the associated point-spread function are displayed both for a single filtered lens and for a combination with a laterally superresolving mask in a confocal configuration. Interesting imaging properties relative to the increase in axial contrast and transverse resolving power for dephasing ring-free pupil filters of moderate losses in luminosity are predicted.     

Image formation and data acquisition in a stage scanning 4Pi confocal fluorescence microscope

We describe the three-dimensional (3-D) image formation and data acquisition in a stage scanning 4Pi confocal fluorescence microscope with the use of two-photon excitation. The 3-D point-spread functions of the 4Pi confocal and regular confocal microscope are measured and compared. Particular emphasis is given to the data acquisition procedure. 4Pi confocal microscopy results in a point-spread function that is 4 times sharper than that of a regular confocal microscope, ultimately leading to superior 3-D imaging of translucent fluorescent specimens. For a two-photon excitation wavelength of approximately 800 nm, we obtain an axial resolution of 140 nm.     

Hubble Space Telescope Faint Object Camera calculated point-spread functions

A set of observed noisy Hubble Space Telescope Faint Object Camera point-spread functions is used to recover the combined Hubble and Faint Object Camera wave-front error. The low-spatial-frequency wave-front error is parameterized in terms of a set of 32 annular Zernike polynomials. The midlevel and higher spatial frequencies are parameterized in terms of set of 891 polar-Fourier polynomials. The parameterized wave-front error is used to generate accurate calculated point-spread functions, both pre- and post-COSTAR (corrective optics space telescope axial replacement), suitable for image restoration at arbitrary wavelengths. We describe the phase-retrieval-based recovery process and the phase parameterization. Resultant calculated precorrection and postcorrection point-spread functions are shown along with an estimate of both pre- and post-COSTAR spherical aberration.     

Imaging performance of telescope mirrors for far-ultraviolet astronomy

We describe image testing, surface metrology, and modeling of telescope mirrors (0.5 m in diameter, f/4.3) for the Far Ultraviolet Spectroscopic Explorer (FUSE) satellite. Laboratory image testing of wavelengths in the visible, vacuum, and midultraviolet validated a theoretical analysis by use of the Optical Surface Analysis Code (OSAC). Our modeling is based on surface metrology, including measurements of figure, midfrequency error, and microroughness. This combination of metrology, out-of-band performance testing, and modeling verified that the mirrors would meet mission requirements. We use OSAC to predict the FUSE telescope's far-ultraviolet (90-120-nm) point-spread function and assess its effect on instrument efficiency. The mirrors have a 90% encircled energy diameter of 1.5 arc sec at lambda = 100 nm. Including the effects of spacecraft pointing error, the mirrors have a predicted average slit transmission at lambda = 100 nm of approximately 87% and 96% for the 1.25- and 4-arc sec-wide spectrograph slits, respectively, where the required transmissions are 50% and 95%.     

A piece-wise spatial invariant model of ultrasonic image formation

A model of ultrasonic image formation has been developed for an electronically focused linear-array transducer. An analytical expression for the point-spread function of the image degradation process is obtained. It consists of two terms: one accounts for the electromechanical properties of the transducer; the other describes the diffraction phenomena associated with the wave propagation. To reduce the computational complexity in image restoration, a piecewise-invariant form for the point-spread function has been suggested. Experimental results prove the validity of the model and the feasibility of the reconstruction process with a few shift-invariant filters.     

基于复小波变换与层间模型的图像去噪

很多小波去噪方法认为小波系数是相互独立的,然而大量实验表明实际图像的小波系数之间是有较强的依赖性。在本文中,我们将利用复小波变换的优势以及小波系数之间的依赖性,提出一种新的图像去噪方法。该方法先确定滤波器系数,再对复小波变换系数建模,并根据MAP准则给出系数的收缩方法进行去噪处理,最后作复小波逆变换。同时在变换的系数抽取之前估计系数的方差,可以使方差估计更准确。     

二元正交小波滤波器的构造

本文提出了一种基于余弦函数的二元紧支撑正交小波滤波器的构造方法。这种构造方法简单易行,能够通过选取不同的参数而设计出不同的小波滤波器。最后,给出了算例。     

On the computation of the nijboer-zernike aberration integrals at arbitrary defocus

Abstract

We present a new computation scheme for the integral expressions describing the contributions of single aberrations to the diffraction integral in the context of an extended Nijboer-Zernike approach. Such a scheme, in the form of a power series involving the defocus parameter with coefficients given explicitly in terms of Bessel functions and binomial coefficients, was presented recently by the authors with satisfactory results for small-to-medium-large defocus values. The new scheme amounts to systemizing the procedure proposed by Nijboer in which the appropriate linearization of products of Zernike polynomials is achieved by using certain results of the modern theory of orthogonal polynomials. It can be used to compute point-spread functions of general optical systems in the presence of arbitrary lens transmission and lens aberration functions and the scheme provides accurate data for any, small or large, defocus value and at any spatial point in one and the same format. The cases with high numerical aperture, requiring a vectorial approach, are equally well handled. The resulting infinite series expressions for these point-spread functions, involving products of Bessel functions, can be shown to be practically immune to loss of digits. In this respect, because of its virtually unlimited defocus range, the scheme is particularly valuable in replacing numerical Fourier transform methods when the defocused pupil functions require intolerably high sampling densities.     

Tolerances For Layer Thicknesses in Dielectric Multilayer Coatings and Interference Filters

A theory is developed for dielectric multilayer coatings in which the layers depart from calculated thickness. The theory is applied to alternating systems of quarter wave layers of ZnS and MgF₂. The effects of thickness errors are: (1) A shift of the wavelength at which maximum reflectance occurs; and (2) a change in phase shift upon reflection. The magnitude of these effects, and also their dependence on various parameters, are determined. Statistical tolerances for layer thicknesses are computed for given tolerances on the multilayer performance. The accuracy required for producing dielectric interference filters is up to about 40 times higher than the accuracy sufficient for the production of dielectric mirrors and beam splitters. Various techniques of experimentally controlling film thicknesses, and their accuracies, are discussed. The production of mirrors and beam splitters deviating from theoretical maximum reflectance by only 1 percent seems to be possible with Dufour’s simple single photocell method of monitoring film thicknesses. With more precise methods, such as those developed by Giacomo and Jacquinot, or Traub, the production of interference filters appears to be possible to within plus or minus one half their half widths.     

Upper and Lower Bounds on Radially Symmetric Optical Transfer Functions

For an optical system under incoherent imaging conditions, the finite aperture and non-negative point-spread function place restrictive bounds on the values of the corresponding optical transfer function. Under the extra condition that the transfer function be radially symmetric, these bounds can be characterized as the eigenvalues of a real symmetric integral operator. In this paper the bounds are calculated first by analytic inequalities that bound the operator norm, then by finding the eigenvalues of a Galerkin approximation to the operator. In contrast to the slit aperture case, the least upper bound and greatest lower bound are found to differ. The pupil functions which achieve these bounds at a given spatial frequency are determined, along with the associated transfer functions.     

Ultrahigh-efficiency, very narrowpassband, tunable optical filter

Recently developed technologies have been uniquely integrated to produce optical filters with unprecedented performance. The precise design and fabrication of narrow-passband and high-efficiency optical filters with a central frequency of 532 nm are reported. Measurements with these filters demonstrate a performance that accurately mirrors the design specification, with one filter having a passband of 70 pm and an efficiency greater than 90% and the second filter having a passband of 7 pm and an efficiency greater than 80%.     

Diffractive lenses for chromatic confocal imaging

A diffractive zone plate provides a highly linear wavelength-to-depth coding, allowing for nonmechanical depth scanning in a confocal microscope. This chromatic confocal microscope, constructed with 40x and 60x objectives, achieves axial position changes of 55 and 25 mum, respectively, for a wavelength tuning range of 100 nm. The corresponding longitudinal point-spread functions are measured and shown to possess full-width half-maximums of 2.52 and 2.23 mum, respectively. Two-dimensional profiles of a two-phase-level grating and a four-phase-level diffractive structure are given. The performance of the chromatic confocal microscope is consistent with that of the conventional confocal operation of the microscope.     

Reduced-resolution synthetic-discriminant-function design by multiresolution wavelet analysis

Several approaches to the design of reduced-resolution synthetic discriminant functions (SDF's) using multiresolution wavelet analysis (MWA) techniques are investigated. In the first approach, reducedresolution approximations of a full-resolution SDF are obtained by MWA. In the second approach, reduced-resolution approximations of the training-image Fourier transforms are obtained by MWA, and a reduced-resolution SDF is obtained directly by training on these. For both approaches, reducedresolution MICE-SDF filters were designed with MWA and conventional down-sampling techniques. Simulations showed that filters designed by the second approach with MWA techniques permitted reductions in the number of filter pixels from 128 × 128 to 32 × 32, while still satisfying the design constraints. In comparison, the performances of 32 × 32 filters designed by conventional downsampling techniques were significantly degraded.     

18.2nm正入射显微成像系统滤光片的研究

18．2nm正人射显微成像系统用多层膜可极大地提高18．2nm的反射率，但它对紫外、可见和红外光也产生很高的反射。显微成像系统用的激光等离子体光源会在红外到敦X射线产生大量的辐射，18．2nm正入射显微系统用的胶片对所有光谱都十分敏感。因此，182nm正人射显微成像系统需要用滤光片滤除不需要的光辐射并对18．2nm的软X射线有较大的透射比，这样才能获得18．2nm的软X射线像。本文讨论了18．2nm正入射显微成像系统用滤光片的设计、制作及其特性。为了去除滤光片膜中的应力，用交替蒸镀Al和C多层膜的方法来制备法光片，铝和碳膜是用磁控溅射法制备的。针孔透过率和成像实验表明，所制备的滤光片满足了18．2nm正入射显微成像系统对滤光片的要求，并且为进一步制备其他薄膜滤光片打下了基础。     

Characterization of the Advanced Satellite for Cosmology and Astrophysics x-ray telescope: preflight calibration and ray tracing

The x-ray properties of multinested thin-foil mirror x-ray telescopes (XRT's) on board ASCA, the Advanced Satellite for Cosmology and Astrophysics, were fully evaluated with an x-ray pencil beam.Scanning over the telescope aperture of 35 cm in diameter with an x-ray pencil beam, we found the effective area of a set of XRT's to be 325, 200, and 113 cm(2) at energies of 1.5, 4.5, and 8.0 keV, respectively. We derive the point-spread functions (PSF's) of the XRT's by measuring the image profile at the focal plane with an x-ray CCD. The PSF is found to exhibit a sharp core concentrated within 30 arcsec and a broad wing extended to 3 arcmin in half-power diameter. We also evaluate the contribution of stray light, which is caused by the single reflection of x rays by primary or secondary mirrors and by the backside reflection of the mirrors. To obtain the characteristics of the XRT in the energy region of 0.5-10.0 keV, incorporated with the measurements at discrete energies, we develop a ray-tracing method with the telescope design parameter, the PSF, and optical constants. In particular, we obtain the optical constants around the gold-atom M shell (Au-M) absorption-edge energies by measuring the reflectivity of our mirror sample, with monochromatized x-rays in the energy range of 2.0-3.5 keV from synchrotron radiation. Taking into account the PSF's and optical constants, we find that our ray-tracing program can reproduce all these XRT performances.