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NASA NTRS1990

Formula for the rms blur circle radius of Wolter telescope based on aberration theory

A formula for the rms blur circle for Wolter telescopes has been derived using the transverse ray aberration expressions of Saha (1985), Saha (1984), and Saha (1986). The resulting formula for the rms blur circle radius over an image plane and a formula for the surface of best focus based on third-, fifth-, and seventh-order aberration theory predict results in good agreement with exact ray tracing. It has also been shown that one of the two terms in the empirical formula of VanSpeybroeck and Chase (1972), for the rms blur circle radius of a Wolter I telescope can be justified by the aberration theory results. Numerical results are given comparing the rms blur radius and the surface of best focus vs the half-field angle computed by skew ray tracing and from analytical formulas for grazing incidence Wolter I-II telescopes and a normal incidence Cassegrain telescope.

Shealy, David L.↗

NASA NTRS2006

Phase Sensor for Aligning a Segmented Telescope Mirror

A phase sensor has been developed for use in aligning a segmented telescope mirror to within a fraction of a wavelength in piston. (As used here, piston signifies displacement of a mirror segment along the optical axis of the telescope.) Such precise alignment is necessary in order to realize the full benefit of the large aperture achievable through segmentation. This phase sensor is achromatic. It is based on two-wavelength shearing interferometry, and can be modified to utilize an extended or broad-band (e.g., white) light source. The sensor optics include a ruled diffraction grating and an imaging lens. The sensor can measure the piston shift between segments as well as aberrations of the segments. It can measure the surface error of an individual segment, making it possible to compensate for the error with optimal amount(s) of piston and/or tilt. The precise capture range of the sensor depends partly on the telescope design; the largest relative piston shifts measurable by use of this sensor are of the order of 100 m. The accuracy of the sensor also depends partly on the telescope design; in general, the accuracy is sufficient to enable alignment to within approximately half a wavelength. The interferometric image is digitized and processed by a simple algorithm in real time, and the output of the algorithm can be used to maintain alignment in real time, even in the presence of atmospheric turbulence. The sensor is robust. Through calibration, it can be made insensitive to (and, hence, tolerant of) misalignments and aberrations of its own optics, most aberrations of the telescope as a whole (in contradistinction to aberrations of individual segments), and most aberrations introduced by atmospheric turbulence

Stahl, Philip↗

NASA NTRS1974

Fabrication of optical reflecting diffraction gratings by light-interference phenomenon

Features of technique: major reduction in cost of fabrication; gratings exhibit low stray or scattered radiation, improve signal noise ratio, and eliminate false spectral-lines; gratings can be fabricated free of optical aberrations, with high groove frequencies, and on practically any surface geometry; and fabrication time has been reduced.

Caruso, A. J.↗

NASA NTRS1992

Diffractive optics technology and the NASA Geostationary Earth Observatory (GEO)

Diffractive (or binary) optics offers unique capabilities for the development of large-aperture, high-performance, light-weight optical systems. The Geostationary Earth Observatory (GEO) will consist of a variety of instruments to monitor the environmental conditions of the earth and its atmosphere. The aim of this investigation is to analyze the design of the GEO instrument that is being proposed and to identify the areas in which diffractive (or binary) optics technology can make a significant impact in GEO sensor design. Several potential applications where diffractive optics may indeed serve as a key technology for improving the performance and reducing the weight and cost of the GEO sensors have been identified. Applications include the use of diffractive/refractive hybrid lenses for aft-optic imagers, diffractive telescopes for narrowband imaging, subwavelength structured surfaces for anti-reflection and polarization control, and aberration compensation for reflective imaging systems and grating spectrometers.

Morris, G. Michael↗

NASA NTRS2005

Telescope Wavefront Aberration Compensation with a Deformable Mirror in an Adaptive Optics System

With the goal of reducing the surface wavefront error of low-cost multi-meter-diameter mirrors from about 10 waves peak-to-valley (P-V), at lpm wavelength, to approximately 1-wave or less, we describe a method to compensate for slowly varying wavefront aberrations of telescope mirrors. A deformable mirror is utilized in an active optical compensation system. The kMS wavefront error of a 0.3m telescope improved to 0.05 waves (0.26 waves P-V) from the original value of 1.4 waves RMS (6.5 waves P-V), measured at 633nm, and the Strehl ratio improved to 89% from the original value of 0.08%.

active optics↗

NASA NTRS1979

Effect of mid- and high-spatial frequencies on optical performance

In many of today's telescopes the effects of surface errors on image quality and scattered light are very important. The influence of optical fabrication surface errors on the performance of an optical system is discussed. The methods developed by Hopkins (1957) for aberration tolerancing and Barakat (1972) for random wavefront errors are extended to the examination of mid- and high-spatial frequency surface errors. The discussion covers a review of the basic concepts of image quality, an examination of manufacturing errors as a function of image quality performance, a demonstration of mirror scattering effects in relation to surface errors, and some comments on the nature of the correlation functions. Illustrative examples are included.

Noll, R. J.↗

NASA NTRS1982

A new antenna concept for satellite communications

A novel antenna configuration of two reflecting surfaces and a phased array is examined for application to satellite communications and shown to be superior in every respect to earlier designs for service to the continental United States from synchronous orbit. The vignetting that afflicts other two reflector optical systems is eliminated by use of a reflecting field element. The remaining aberrations, predominantly coma, are isolated in the time delay distribution at the surface of the array and can be compensated by ordinary array techniques. The optics exhibits infinite bandwidth and the frequency range is limited only by the design of the array.

Skahill, G.↗

NASA NTRS1994

Designing Aberration-Corrected Solid Unstable Resonators

In improved method of designing solid unstable resonator of laser diode, shapes of mirrors calculated to yield specified mode. Ray tracing used to compute shape of initially unspecified end mirror, given shape of initially specified end mirror and specified output mode. No need to accept aberrations or suboptimal circular shapes, to make iterative design computations in effort to converge on desired mode, or to assume paraxiality of rays: Angles between rays and optical axis large, cross sections of surfaces noncircular, and computed shape of end mirror exact. End mirror corrects for all aberrations.

Lang, Robert J.↗

NASA NTRS1979

Design of stigmatic grazing incidence telescopes with non-parabolic primaries

A two-mirror grazing-incidence telescope having a non-parabolic primary, and designed to be free of spherical aberration has been investigated. A method for determining the second surface equation is described, when the surface equation for one mirror is given. Application to grazing incidence systems such as used in X-ray and planed for EUV astronomy is discussed. Of special interest is the design of a secondary mirror when the hyperboloid of a conventional Wolter type I system is taken as the primary.

Winkler, C. E.↗

NASA NTRS1982

Imaging antenna arrays

Many millimeter and far-infrared imaging systems are limited in sensitivity and speed because they depend on a single scanned element. Because of recent advances in planar detectors such as Schottky diodes, superconducting tunnel junctions, and microbolometers, an attractive approach to this problem is a planar antenna array with integrated detectors. A planar line antenna array and optical system for imaging has been developed. The significant advances are a 'reverse-microscope' optical configuration and a modified bow-tie antenna design. In the 'reverse-microscope' configuration, a lens is attached to the bottom of the substrate containing the antennas. Imaging is done through the substrate. This configuration eliminates the troublesome effects of substrate surface waves. The substrate lens has only a single refracting surface, making possible a virtually aplanatic system, with little spherical aberration or coma. The array is characterized by an optical transfer function that is easily measured. An array with 19 dB crosstalk levels between adjacent antennas has been tested and it was found that the array captured 50 percent of the available power. This imaging system was diffraction limited.

Rutledge, D. B.↗

NASA NTRS1993

Inverting Image Data For Optical Testing And Alignment

Data from images produced by slightly incorrectly figured concave primary mirror in telescope processed into estimate of spherical aberration of mirror, by use of algorithm finding nonlinear least-squares best fit between actual images and synthetic images produced by multiparameter mathematical model of telescope optical system. Estimated spherical aberration, in turn, converted into estimate of deviation of reflector surface from nominal precise shape. Algorithm devised as part of effort to determine error in surface figure of primary mirror of Hubble space telescope, so corrective lens designed. Modified versions of algorithm also used to find optical errors in other components of telescope or of other optical systems, for purposes of testing, alignment, and/or correction.

Shao, Michael↗

NASA NTRS1987

Analytical caustic surfaces

This document discusses the determination of caustic surfaces in terms of rays, reflectors, and wavefronts. Analytical caustics are obtained as a family of lines, a set of points, and several types of equations for geometries encountered in optics and microwave applications. Standard methods of differential geometry are applied under different approaches: directly to reflector surfaces, and alternatively, to wavefronts, to obtain analytical caustics of two sheets or branches. Gauss/Seidel aberrations are introduced into the wavefront approach, forcing the retention of all three coefficients of both the first- and the second-fundamental forms of differential geometry. An existing method for obtaining caustic surfaces through exploitation of the singularities in flux density is examined, and several constant-intensity contour maps are developed using only the intrinsic Gaussian, mean, and normal curvatures of the reflector. Numerous references are provided for extending the material of the present document to the morphologies of caustics and their associated diffraction patterns.

Schmidt, R. F.↗

NASA NTRS2009

Polarization Properties of Rotation Powered Pulsars

Polarization measurements of rotation-powered pulsars and their nebulae have unique diagnostic potential. The polarization position angle of the pulsar wind nebula, as is know for the Crab pulsar, can tell us the orientation of the spin axis. Phase-resolved polarimetry of pulsars has had enormous diagnostic capability at radio and optical wavelengths and could also be a powerful diagnostic in the X-ray range. Measurement of the polarization properties as a function of pulse phase can therefore provide a multidimensional mapping of the pulsar emission. In the 'rotating vector' model, radiation originating near a magnetic pole is expected to show a characteristic S-shaped swing of the position angle vs. pulse phase. In this case it is possible to determine the magnetic inclination and viewing angles. Radiation originating further from the poles or further above the neutron star surface will have a more complex polarization signature, as a result of relativistic effects of aberration and time-of-flight delays and may also cause depolarization of the signal. I will discuss predicted polarization properties of pulsed emission in polar cap models, where radiation originates near the neutron star surface at the magnetic poles, and in slot gap and outer gap models, where radiation originates over a range of altitudes out to the speed-of-light cylinder.

Harding Alice K.↗

NASA NTRS1977

Performance analysis of grazing incidence imaging systems

An exact expression relating the coordinates of a point on the incident ray, a point of reflection from an arbitrary surface, and a point on the reflected ray is derived. The exact relation is then specialized for the case of grazing incidence, and first order and third order systematic analyses are carried out for a single reflective surface and then for a combination of two surfaces. The third order treatment yields a complete set of primary aberrations for single element and two element systems. The importance of a judicious choice for a coordinate system in showing field curvature to clearly be the predominant aberration for a two element system is discussed. The validity of the theory is verified through comparisons with the exact ray trace results for the case of the telescope.

Winkler, C. E.↗

NASA NTRSDate not supplied

Uncertainty Estimates for Fitting Zernike Polynomials to Discrete Data

Zernike polynomials are a widely used metric in modern optical analysis. They conveniently represent surfaces as a series of weighted terms corresponding to various optical aberrations. Ideally, each term is independent of others in the series, but Zernike polynomials lose this property when working with sets of discrete data. This gives rise to uncertainty in each polynomial’s actual contribution and affects metrology and simulation estimates of their relative weights. Several factors influencing these estimates are the number and arrangement of sample locations, the method for calculating the weights, and the total number of Zernike terms used in the calculation. Discussed is the uncertainty associated with linear regression using random sampling. Other topics reviewed are complex Zernike polynomials and vector spaces of functions.

Zernike Polynomials↗

NASA NTRS1986

Grazing incidence optics; Proceedings of the Meeting, Orlando, FL, Apr. 3, 4, 1986

Papers are presented on the diffraction-limited performance of grazing incidence optical systems; transverse ray aberrations of Wolter type 1 telescopes; hybrid X-ray telescope systems; surface characterization of grazing incidence optics in the extreme UV and X-ray regions; and the surface roughness properties of synchrotron radiation optics. Topics discussed include the simulation of free-abrasive grinding of grazing incidence mirrors with vertical-honing and flexible blades; mirrors for the Extreme Ultraviolet Explorer; the design and development of conical X-ray imaging mirrors; thermal loading considerations for synchrotron radiation mirrors; and grazing incidence optics for synchrotron radiation insertion-device beams. Consideration is given to the interpretation of glancing incidence scattering measurements; damage processes in short wavelength coated FEL optics; the replication of grain incidence optics; and the assembly and alignment of the Technology Mirror Assembly.

Osantowski, John F.↗

NASA NTRS2002

Diffractive optical elements on non-flat substrates using electron beam lithography

The present disclosure describes a technique for creating diffraction gratings on curved surfaces with electron beam lithography. The curved surface can act as an optical element to produce flat and aberration-free images in imaging spectrometers. In addition, the fabrication technique can modify the power structure of the grating orders so that there is more energy in the first order than for a typical grating. The inventors noticed that by using electron-beam lithography techniques, a variety of convex gratings that are well-suited to the requirements of imaging spectrometers can be manufactured.

Maker, Paul D.↗

NASA NTRS2012

Telescope Alignment From Sparsely Sampled Wavefront Measurements Over Pupil Subapertures

Alignment of two-element telescopes is a classic problem. During recent integration and test of the Space Interferometry Mission s (SIM s) Astrometric Beam Combiner (ABC), the innovators were faced with aligning two such telescope subsystems in the presence of a further complication: only two small subapertures in each telescope s pupil were accessible for measuring the wavefront with a Fizeau interferometer. This meant that the familiar aberrations that might be interpreted to infer system misalignments could be viewed only over small sub-regions of the pupil, making them hard to recognize. Further, there was no contiguous surface of the pupil connecting these two subapertures, so relative phase piston information was lost; the underlying full-aperture aberrations therefore had an additional degree of ambiguity. The solution presented here is to recognize that, in the absence of phase piston, the Zygo measurements primarily provide phase tilt in the subaperture windows of interest. Because these windows are small and situated far from the center of the (inaccessible) unobscured full aperture, any aberrations that are higher-order than tilt will be extremely high-order on the full aperture, and so not necessary or helpful to the alignment. Knowledge of the telescope s optical prescription allows straightforward evaluation of sensitivities (subap mode strength per unit full-aperture aberration), and these can be used in a predictive matrix approach to move with assurance to an aligned state. The technique is novel in every operational way compared to the standard approach of alignment based on full-aperture aberrations or searching for best rms wavefront. This approach is closely grounded in the observable quantities most appropriate to the problem. It is also more intuitive than inverting full phase maps (or subaperture Zernike spectra) with a ray-tracing program, which must certainly work in principle, but in practice met with limited success. Even if such classical alignment techniques became practical, the techniques reported here form a reassuringly transparent and intuitive check on the course of the alignment with very little computational effort.

Bloemhof, Eric E.↗