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24 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

A generalized sine condition and performance comparison of Wolter type II and Wolter-Schwarzschild extreme ultraviolet telescopes

An equation similar to the Abbe sine condition is derived for a Wolter type II telescope. This equation and the sine condition are then combined to produce a so called generalized sine condition. Using the law of reflection, Fermat's principle, the generalized sine condition, and simple geometry the surface equations for a Wolter type II telescope and an equivalent Wolter-Schwarzschild telescope are calculated. The performances of the telescopes are compared in terms of rms blur circle radius at the Gaussian focal plane and at best focus.

Saha, T. T.↗
NASA NTRS1989

Image defects from surface and alignment errors in grazing incidence telescopes

The rigid body motions and low frequency surface errors of grazing incidence Wolter telescopes are studied. The analysis is based on surface error descriptors proposed by Paul Glenn. In his analysis, the alignment and surface errors are expressed in terms of Legendre-Fourier polynomials. Individual terms in the expression correspond to rigid body motions (decenter and tilt) and low spatial frequency surface errors of mirrors. With the help of the Legendre-Fourier polynomials and the geometry of grazing incidence telescopes, exact and approximated first order equations are derived in this paper for the components of the ray intercepts at the image plane. These equations are then used to calculate the sensitivities of Wolter type I and II telescopes for the rigid body motions and surface deformations. The rms spot diameters calculated from this theory and OSAC ray tracing code agree very well. This theory also provides a tool to predict how rigid body motions and surface errors of the mirrors compensate each other.

Saha, Timo T.↗
NASA NTRS1987

General surface equations for glancing incidence telescopes

A generalized set of equations are derived for two mirror glancing incidence telescopes using Fermat's principle, a differential form of the law of reflection, the generalized sine condition, and a ray propagation equation described in vector form as a theoretical basis. The resulting formulation groups the possible telescope configurations into three distinct classes which are the Wolter, Wolter-Schwarzschild, and higher-order telescopes in which the Hettrick-Bowyer types are a subset. Eight configurations are possible within each class depending on the sign and magnitude of the parameters.

Saha, Timo T.↗
NASA NTRS1988

The equation of state for stellar envelopes. II - Algorithm and selected results

A free-energy-minimization method for computing the dissociation and ionization equilibrium of a multicomponent gas is discussed. The adopted free energy includes terms representing the translational free energy of atoms, ions, and molecules; the internal free energy of particles with excited states; the free energy of a partially degenerate electron gas; and the configurational free energy from shielded Coulomb interactions among charged particles. Internal partition functions are truncated using an occupation probability formalism that accounts for perturbations of bound states by both neutral and charged perturbers. The entire theory is analytical and differentiable to all orders, so it is possible to write explicit analytical formulas for all derivatives required in a Newton-Raphson iteration; these are presented to facilitate future work. Some representative results for both Saha and free-energy-minimization equilibria are presented for a hydrogen-helium plasma with N(He)/N(H) = 0.10. These illustrate nicely the phenomena of pressure dissociation and ionization, and also demonstrate vividly the importance of choosing a reliable cutoff procedure for internal partition functions.

Mihalas, Dimitri↗
NASA NTRS1984

Glancing incidence EUV telescopes - Analysis and comparison

Steps in the derivation of generalized surface equations describing either a Wolter or Wolter-Schwarzschild type II extreme ultraviolet telescope are outlined. These surface equations are incorporated in an optical design program where first-order design parameters are varied to produce a number of different series of type II telescopes. These series are then ray traced to compare and analyze the geometric image quality for different designs in terms of minimum rms angular blur and field curvature. Results of an analysis illustrating the dependence of effective area on first-order design parameters are also presented. The differences and similarities between equivalent Wolter and Wolter-Schwarzschild designs are discussed.

Davila, P. M.↗
NASA NTRS2008

Aberrations for Grazing Incidence Optics

Large number of grazing incidence telescope configurations have been designed and studied. Wolte1 telescopes are commonly used in astronomical applications. Wolter telescopes consist of a paraboloidal primary mirror and a hyperboloidal or an ellipsoidal secondary mirror. There are 8 possible combinations of Wolter telescopes. Out of these possible designs only type 1 and type 2 telescopes are widely used. Type 1 telescope is typically used for x-ray applications and type 2 telescopes are used for EUV applications. Wolter-Schwarzshild (WS) telescopes offer improved image quality over a small field of view. The WS designs are stigmatic and free of third order coma and, therefore, the PSF is significantly better over a small field of view. Typically the image is more symmetric about its centroid. As for the Wolter telescopes there are 8 possible combinations of WS telescopes. These designs have not been widely used because the surface equations are complex parametric equations complicating the analysis and typically the resolution requirements are too low to take full advantage of the WS designs. There are several other design options. Most notable are wide field x-ray telescope designs. Polynomial designs were originally suggested by Burrows4 and hyperboloid-hyperboloid designs for solar physics applications were designed by Harvey5. No general aberration theory exists for grazing incidence telescopes that would cover all the design options. Several authors have studied the aberrations of grazing incidence telescopes. A comprehensive theory of Wolter type 1 and 2 telescopes has been developed. Later this theory was expanded to include all possible combinations of grazing incidence and also normal incidence paraboloid-hyperboloid and paraboloid-ellipsoid telescopes. In this article the aberration theory of Wolter type telescopes is briefly reviewed.

Saha, Timo T.↗