This paper presents a new method to model X-ray scattering on random rough surfaces. It combines the approaches we presented in two previous papers – PZ&LVS<sup>1</sup>& PZ.<sup>2</sup> An actual rough surface is (incompletely) described by its Power Spectral Density (PSD). For a given PSD, model surfaces with the same roughness as the actual surface are constructed by preserving the PSD amplitudes and assigning a random phase to each spectral component. Rays representing the incident wave are reflected from the model surface and projected onto a flat plane, which is the first order approximation of the model surface, as outgoing rays and corrected for phase delays. The projected outgoing rays are then corrected for wave densities and redistributed onto an uniform grid where the model surface is constructed. The scattering is then calculated using the Fourier Transform of the resulting distribution. This method provides the exact solutions for scattering in all directions, without small angle approximation. It is generally applicable to any wave scatterings on random rough surfaces and is not limited to small scattering angles. Examples are given for the Chandra X-ray Observatory optics. This method is also useful for the future generation X-ray astronomy missions.
This paper presents a new method to model the transverse scattering from random rough surfaces. It uses the same approach as our 2003 SPIE paper – PZ and LVS,<sup>1</sup> but considers the scattering in the direction perpendicular to the incident plane. For a given Power Spectral Density, a model surface is constructed by assigning a random phase to each spectral component. The incident wave is reflected from the model rough surface and then projected to an outgoing wavefront, which is then redistributed onto an even grid in the transverse direction, with corrections for the wave densities and the phase shifts. Fast Fourier transforms are used to calculate the transverse scattering pattern. This method provides the exact solution to the transverse scattering without small angle approximation. This solution is generally applicable to any transverse wave scatterings on random rough surfaces and is not limited to small scattering angles. This paper together with PZ and LVS<sup>1</sup> provide a complete solution for wave scattering on random rough surfaces in all directions. Examples are given for the Chandra X-ray Observatory optics. This method is also useful for the next generation X-ray astronomy missions.
Chandra X-ray Observatory (CXO) -- the third of NASA's Great
Observatories -- has now been successfully operated for four years and has brought us fruitful scientific results with many exciting
discoveries. The major achievement comparing to previous X-ray
missions lies in the heart of the CXO -- the High Resolution Mirror
Assembly. Its unprecedented spatial resolution and well calibrated
performing characteristics are the keys for its success. We discuss
the effective area of the CXO mirrors, based on the ground calibration measurements made at the X-Ray Calibration Facility in Marshall Space Flight Center before launch. We present the derivations of both on-axis and off-axis effective areas, which are currently used by Chandra observers.
The mirrors flown in the Chandra Observatory are, without doubt, some of the most exquisite optics ever flown on a space mission. Their angular resolution is matched by no other X-ray observatory, existing or planned. The promise of that performance, along with a goal of achieving 1% calibration of the optics' characteristics, led to a decision early in the construction and assembly phase of the mission to develop an accurate and detailed model of the optics and their support structure. This model has served in both engineering and scientific capacities; as a cross-check of the design and a predictor of scientific performance; as a driver of the ground calibration effort; and as a diagnostic of the as-built performance. Finally, it serves, directly and indirectly, as the primary vehicle with which Chandra observers interpret the contribution of the optics' characteristics to their data. We present the underlying concepts in the model, as well the mechanical, engineering and metrology inputs. We discuss its use during ground calibration and as a characterization of on-orbit performance. Finally, we present measures of the model's accuracy, where further improvements may be made, and its applicability to other missions.
We discuss the calibration of the wings of the Chandra point spread function. In order to achieve high resolution imaging, the X-ray mirror surfaces must be extremely smooth in order to suppress the effects of scattering from microroughness. In the Chandra program, surfaces with only 1.3-3 Å roughness were achieved over more than 90% of the mirror length. We describe the current state of the calibration of the Chandra PSF wings, incorporating the results of a deep observation of the X-ray source Her X-1. The galactic Hydrogen column density (<i>N<sub>H</sub></i>) to Her X-1 is small, reducing the amplitude of any astrophysical dust scattering halo which would contaminate the mirror scattering wings. The X-ray data clearly show the shadows of the mirror support struts, confirming that the observed halo is predominantly due to mirror scattering. The extreme brightness of the source allows the energy dependence of the PSF wings to be probed with good statistics. The deep observation (heavily piled up in the core) is combined with a zero order
gratings observation (unpiled in the core) to construct an
This paper presents a method for modeling the X-ray scattering from
random rough surfaces. An actual rough surface is (incompletely)
described by its Power Spectral Density (PSD). For a given PSD, model
surfaces with the same roughness as the actual surface are constructed
by preserving the PSD amplitudes and assigning a random phase to each
spectral component. Rays representing the incident wave are reflected
from the model surface and projected onto a flat plane, which
approximates the model surface, as outgoing rays and corrected for
phase delays. The projected outgoing rays are then corrected for wave
densities and redistributed onto an uniform grid where the model
surface is constructed. The scattering is then calculated by taking
the Fast Fourier Transform (FFT) of the resulting distribution. This
method is generally applicable and is not limited to small scattering
angles. It provides the correct asymmetrical scattering profile for
grazing incident radiation. We apply this method to the mirrors of
the Chandra X-ray Observatory and show the results. We also expect
this method to be useful for other X-ray telescope missions.
We present here results of the on-orbit calibration of the point spread function (PSF), comparing it with our predictions. We discuss how the PSF varies with source location in the telescope field of view, as well as with the spectral energy distribution of the source.
The High Resolution Camera (HRC) is one of two focal plane instruments on the NASA Chandra X-ray Observatory which was successfully launched on July 23, 1999. The Chandra X-ray Observatory was designed to perform high resolution spectroscopy and imaging in the X-ray band of 0.07 to 10 keV. The HRC instrument consists of two detectors, HRC-I for imaging and HRC-S for spectroscopy. Each HRC detector consists of a thin aluminized polyimide blocking filter, a chevron pair of microchannel plates and a crossed grid charge readout. The HRC-I is an approximately 100 X 100 mm detector optimized for high resolution imaging and timing, the HRC-S is an approximately 20 X 300 detector optimized to function as the readout for the Low Energy Transmission Grating. In this paper we discuss the in-flight performance of the HRC-S, and present preliminary analysis of flight calibration data and compare it with the results of the ground calibration and pre-flight predictions. In particular we will compare ground data and in-flight data on detector background, quantum efficiency, spatial resolution, pulse height resolution, and point spread response function.
The Chandra X-ray Observatory was launched in July 1999, and is returning exquisite sub-arc second X-ray images of star groups, supernova remnants, galaxies, quasars, and clusters of galaxies. In addition to being the premier X-ray observatory in terms of angular and spectral resolution, Chandra is the best calibrated X-ray facility ever flown. We discuss here the calibration of the on-axis effective area of the High Resolution Mirror Assembly. Because we do not know the absolute X-ray flux density of any celestial source, this must be based primarily on ground measurements and on modeling. We use celestial sources which may be assumed to have smoothly varying spectra, such as the BL Lac object Markarian 421, to verify the continuity of the area calibration as a function of energy across the Ir M-edges. We believe the accuracy of the HRMA area calibration is of order 2%.
In this paper we present and compare flight results with the latest results of the ground calibration for the HRC-I detector. In particular we will compare ground and in flight data on detector background, effective area, quantum efficiency and point spread response function.
The AXAF X-ray mirrors underwent thorough calibration using the X-ray Calibration Facility (XRCF) at the Marshall Space Flight Center in Huntsville, AL from late 1996 to early 1997. The x-ray calibration made novel use of the x-ray continuum from a conventional electron-impact source. Taking advantage of the good spectral resolution of solid-state detectors, continuum measurements proved advantageous in calibration the effective area of AXAF's High-Resolution Mirror Assembly (HRMA) for the entire AXAF energy band. The measurements were made by comparing the spectrum detected by a SSD at the focal plane with the spectrum detected by a beam normalization SSD. The HRMA effective area was calibrated by comparing the measurements with the HRMA raytrace model. The HRMA on-orbit performance predictions are made using the calibration results.
The Advanced X-ray Astrophysics Facility (AXAF) ground calibration program, easily the most extensive in the history of high energy astrophysics, requires careful attention to the verification of its validity for on-orbit operations of the observatory. The purpose of the Flight Contamination Monitor (FCM) is to verify the transfer of the AXAF absolute flux scale calibration from ground to on-orbit operations and to measure or bound any changes in molecular contamination on the AXAF mirrors. This paper reports the current status of the analysis of FCM measurements taken during ground calibration. The FCM measurements during the AXAF activation phase will be the first look at the on-orbit AXAF performance.
We discuss the x-ray measurement of the focus and alignment of the AXAF (Advanced X-ray Astrophysics Facility) x-ray optics. The high resolution mirror assembly (HRMA) consists of four nested Wolter type I x-ray optics. The attainment of the program goals for high resolution imaging requires that the mirror foci be coincident, both axially and laterally; in addition, the relative tilts between optics within each mirror pair must be small. The mirror tilts and the parfocalization were measured at the X-Ray Calibration Facility (XRCF) at the Marshall Space Flight Center in Huntsville, Alabama during a series of tests in the winter/spring of 1996/1997. The x-ray measurements are compared to the optical alignment data obtained by Eastman Kodak using the HRMA Alignment and Test System (HATS) during HRMA assembly. From these data a preliminary model for the relative location and rigid-body orientation of the individual mirror elements is developed; this mirror model is a component of the SAO high fidelity HRMA raytrace model.
We discuss the ring focus measurements for the Advanced X-ray Astrophysics Facility (AXAF) x-ray optics -- the high resolution mirror assembly (HRMA). The HRMA is an assembly of four pairs of nested Wolter Type-I grazing incidence mirrors coated with iridium (Ir). The ring focus measurements are an essential part of the AXAF ground calibration carried out at the X-Ray Calibration Facility (XRCF) at the Marshall Space Flight Center (MSFC) in Huntsville, Alabama. The ring focus measurements reveal aspects of the test system distortions and the mirror surface figures which are difficult or impossible to detect in the focal plane. The measurement results show periodic modulations of the ring width which was caused by gravity and strain in the epoxy bonds that are part of the mechanical support system. The strongest component of the modulation has 12-fold symmetry due to the 12 flexures that support each mirror shell. We discuss the ring focus model and compare it with the test results to understand the test system distortions an the mirror glass imperfection, and to predict the impact for the AXAF mirror on-orbit performance.
The AXAF (Advanced X-ray Astrophysics Facility) high resolution mirror assembly (HRMA) now is complete and has been tested at the NASA Marshall Space Flight Center (MSFC) X-ray Calibration Facility (XRCF). The surface and alignment properties of the mirror were thoroughly measured before the x-ray test, which allowed accurate performance predictions to be performed. The preliminary analysis of the measured x-ray image distributions for all energies tested show excellent agreement with predictions made before the beginning of the test. There is a discrepancy between the measured and predicted effective areas; this typically is less than 5%, and is less than 13% for all energies measured. We present evidence that this discrepancy is due to uncertainties in the calibration of the test instrumentation, and therefore can be expected to be reduced when results from further instrument calibration tests now in progress are incorporated into the analysis. We predict that 65 - 80% (depending upon energy) of the flux from an imaged point source will be contained on a one arc second diameter aperture in flight. We expect the HRMA to more than fulfill the requirements necessary to achieve the AXAF scientific objectives.
The AXAF VETA-I mirror x-ray test results have been cross checked with predictions based upon the HDOS metrology measurements and calculations of the effects of imperfect test system geometry and mirror mount induced distortions. The cross check was done by comparing the VETA-I x-ray test results with a VETA-I model, which is a computer simulation of the VETA-I mirror performance during the x-ray test. The HDOS (Hughes Danbury Optical Systems, Inc., Danbury, Conn.) metrology measurements (with CIDS, PMS, and WYKO) were performed after the VETA-I x-ray test in order to determine the surface figure errors of the mirror pair, including the overall surface map and the surface roughness. Mirror performance was predicted based on the measured surface figure errors and x-ray scattering theory. All the VETA-I x-ray test data (FWHM, encircled energy, effective area, wing scan, and ring focus) were cross checked with the HDOS metrology measurements. The results of this study show reasonably good agreement between the x-ray test data and the metrology data. Similar analysis should be performed for the HRMA mirrors, which is an important step in securing a scientifically successful AXAF mission.
The AXAF VETA-I mirror ring focus measurements were made with a HRI (microchannel plate) X-ray detector. The ring focus is a sharply focused ring formed by X-rays before they reach the VETA-I focal plane. It is caused by spherical aberrations due to the finite source distance and the despace in the VETA-I test. The ring focus test reveals some aspects of the test system distortions and the mirror surface figure which are difficult or impossible to detect at the focal plane. The test results show periodic modulations of the ring radius and width which could be caused by gravity, thermal, and/or epoxy shrinkage distortions. We expect that a similar test for the finally assembled mirror of AXAF-I will be highly valuable.
Intensity distribution measurements of the X-ray source for the AXAF VETA-I mirror test are reported. During the VETA-I test, microscope pictures were taken for each used anode immediately after it was brought out of the source chamber. The source sizes and the intensity distribution structures are shown. They are compared and shown to agree with the results from pinhole camera measurements. It is demonstrated that under operating conditions characteristic of the VETA-I test, all the source sizes have an FWHM of less than 0.45 mm. For a source of this size at 528 m away, the angular size to VETA is less than 0.17 arcsec, which is small compared to the on-ground VETA angular resolution. These results were crucial for VETA data analysis and for obtaining the on-ground and predicted in-orbit VETA point response function.
Measurements of the VETA encircled energies have been performed at 5 energies within 16 radii ranging from 0.05 to 200 arcseconds. We report here on the analysis of the accuracy of those measurements. A common 'error tree' structure applies, and we present representative numbers for the larger terms. At 0.277, 1.5, and 2.07 keV, and for radii of 3 arcsec and larger, our measurements have estimated 1 sigma errors of 0.6 to 1.5 percent. Effects of measurement statistics and of the VETA test mount limit the accuracy at smaller angles, and modulation by the counter window support structure together with the imperfect position repeatability limit the accuracy for the 0.93 and 2.3 keV energies. We expect to mitigate these limitations when calibrating the complete AXAF flight mirror assembly.
The AXAF VETA-I mirror encircled energy was measured with a series of apertures and two flow gas proportional counters at five X-ray energies ranging from 0.28 to 2.3 keV. The proportional counter has a thin plastic window with an opaque wire mesh supporting grid. Depending on the counter position, this mesh can cause the X-ray transmission to vary as much as +/- 9 percent, which directly translates into an error in the encircled energy. In order to correct this wire mesh effect, window scan measurements were made, in which the counter was scanned in both horizontal (Y) and vertical (Z) directions with the aperture fixed. Post VETA measurement of the VXDS setup were made to determine the exact geometry and position of the mesh grid. Computer models of the window mesh were developed to simulate the X-ray transmission based on this measurement. The window scan data were fitted to such mesh models and corrections were made. After this study, the mesh effect was well understood and the final results of the encircled energy were obtained with an uncertainty of less than 0.8 percent.
The study measures the X-ray reflectivity of the AXAF VETA-I optic and compares it with theoretical predictions. Measurements made at energies of 0.28, 0.9, 1.5, 2.1, and 2.3 keV are compared with predictions based on ray trace calculations. Results on the variation of the reflectivity with energy as well as the absolute value of the reflectivity are presented. A synchrotron reflectivity measurement with a high-energy resolution over the range 0.26 to 1.8 keV on a flat Zerodur sample is also reported. Evidence is found for contamination of the flat by a thin layer of carbon on the surface, and the possibility of alteration of the surface composition of the VETA-I mirror, perhaps by the polishing technique. The overall agreement between the measured and calculated effective area of VETA-I is between 2.6 and 10 percent. Measurements at individual energies deviate from the best-fitting calculation to 0.3 to 0.8 percent, averaging 0.6 percent at energies below the high energy cutoff of the mirror reflectivity, and are as high as 20.7 percent at the cutoff.
We employ the X-ray measurements of the VETA-I taken at the X-Ray Calibration Facility (XRCF) of the Marshall Space Flight Center (MSFC) to extract information about the surface finish quality of the outermost pair of AXAF mirrors. The particular measurements we consider are 1D scans of the core of the point response function (PRF) (FWHM scans), the encircled energy as a function of radius, and 1D scans of the wings of the PRF. We discuss briefly our raytrace model which incorporates the numerous effects present in the VETA-I test, such as the finite source distance, the size and shape of the X-ray source, the residual gravitational distortions of the optic, the despace of the VETA-I, and particulate contamination. We show how the data constrain the amplitude of mirror surface deviations for spatial frequencies greater than about 0.1/mm. Constraints on the average amplitude of circumferential slope errors are derived as well.