The ASCA Source Position Uncertainties
We would like to determine the accuracy of the source positions measured with ASCA. In performing this calibration, one hopes to understand the various contributions to the error circle with the prospect of reducing their magnitude. While this calibration is particularly useful for source identification, it also serves as an end-to-end check of the attitude solution, calibration files, and aspecting and imaging software. Thus this work forms the basis for improving the pointing accuracy in the ASCA REV2 re-processing and, ultimately, for the ASTRO-E mission. This article summarizes the construction of the ASCA sky coordinate, explains the method used to measure the error circle, and presents the results obtained so far. A method for improving the measured pointing accuracy is outlined. In brief, the current SIS 90% confidence error circle radius (as define herein) is 40 arcsecs; the main uncertainty is introduced by a random error in the absolute pointing between observations. Position measurements with the GIS have additional instrumental and calibration uncertainties, particularly toward the edge of the field-of-view (r > 18 arcmins).
The ASCA sky coordinate system is constructed by applying the attitude solution to the focal plane coordinate of the four instruments on-board ASCA. The attitude solution, based on gyro and star tracker data, gives the inertial orientation of the satellite X-Y-Z axis as a function of time. This is then translated to the focal plane origin of each instrument via a set of alignment matrices (Fujimoto, 1993). Using the ASCA image definition, the sky X-ray image is constructed by interpolating the attitude solution between telemetry frames (~ 0.5 sec), taking into account the annular aberration. The focal plane coordinates are projected onto a standard RA/DEC tangent plane celestial representation (+X=-RA, +Y=+DEC; North towards the top of the image, west to the right), in J2000 coordinates, centered on a selected aspect point (Gotthelf, 1992; see appendix).
The in-orbit performance of the attitude control system (ASC) is found to be close to pre-flight specification (Ninomiya, et al. 1994). However the relative gyro and star tracker solution exhibit a ~ 1 arcminute orbital modulation. The problem is likely related to a temperature dependent flex in the telescope optical bench, as the star trackers and gyros sit on separate spacecraft panels (Kii 1993).
Measuring source positions from the ASCA images is intimately related to the quality of the mirror point spread (response) function (PSF). While no formal in-orbit calibration of the mirror is available, the overall image quality is consistent with ground-based calibration data. The azimuthally average PSF profile is characterized by a sharp core (FWHM ~ 50 arcsecs) and extended wings, which results in a half power diameter of ~ 3 arcmins. However, it is possible to measure the positions of moderately bright (~ 1 count/s) SIS point-like sources to 5 arcsecs accuracy (see Section 2).
This study focuses on the SIS because its image is limited solely by the PSF, as the instrumental (SIS) distortion is negligible; furthermore the focal plane calibration of the SIS is more accurate than that of the GIS. Where as the SIS pixels are physically located on the focal plane, the GIS pixels are reconstructed by removing the pin-cushion instrument image distortions (Gotthelf 1992). In-orbit calibration uncertainties, particularly toward the edge of the field-of-view, compounded by the instrument limited PSF, add to the intrinsic attitude position uncertainty. These uncertainty may be estimated as adding up to ~ 1.0 arcminute positions error at the edge of the GIS FOV.
The procedure for generating the error circle is straight forward - the measured SIS source positions are compared to cataloged values and the ensemble of offsets between the two are plotted and inspected. The error circle is defined as the probability of a measured source laying within a given radius from its cataloged sky position. The 90% confidence radius is deduced from the circle which encloses 90% of the our measured offsets.
Our starting point is to select an unbiased sample of SIS point sources bright enough so that the measured positions are not photon limited. On the other hand, these sources should not be too bright as to suffer from significant pile-up effects or noticeable telemetry saturation. The PV and AO1 ASCA archive was searched for targeted point source with the required SIS count rates and their images examined for suitability (i.e., moderately bright, isolated, point-like sources, etc...). We also eliminated pointings associated with known aspect uncertainties (such as gyro problems).
Next, for the edited source list, SIS images were constructed using screened event data from the ASCA (REV1) archive, processed with the latest software and calibration files. The final images were made by merging exposure-corrected and smoothed sky images from both SIS cameras. In order to measure the source position in a model independent way, a bi-quadratic fit is used to characterize the centroid of the peak 7 X 7 pixels (0.1 X 0.1 arcmins pixels) for each source. In this way a consistent set of image maps and positions was produced.
Cataloged coordinates were obtained mostly via HEASARC BROWSE (HIC & PMM) and/or the literature, taking into account proper motion as necessary. Typical errors are ~ 2 arcsecs (optical) and ~ 10 arcsecs (X-ray).
Our final source list contained 48 moderately bright SIS point-like sources. The results of comparing the ASCA and catalog coordinates are summaries in Figs. 1 - 3.
Fig. 1 shows that the offsets in RA and DEC (Delta RA, Delta DEC) are centered on zero and consistent with a random distribution in the RA-DEC plane. There is no significant systematic shifts in Delta RA or Delta DEC in any preferred direction, to within measurement error. The distribution of angular displacements (Fig. 2) yields a mean of ~ 0.4 arcmins, and the 90% confidence error circle is 40 arcsecs. The offsets are not correlate with the day-of-year or show any obvious periodic effect on a year time-scale (Figs. 3a-b). Furthermore, adding and subtracting twice the annual aberration only increases the error circle. These facts suggest that the annual aberration is correctly applied.
Relative sky reconstruction is consistent with the expected pointing stability of the satellite, with its ~ ten arcsecond precision. This is apparent by comparing the reconstructed astronomical image of a point source to ground images acquired during the White Sands telescope calibration of the flight spare mirror and CCD camera. The measurement accuracy is ~ 5 arcsecs as determined from measurements of image fields with multiple sources; the standard deviation of the mean offset of these sources gives the measurement uncertainty. The plate scale is found to be linear over the SIS field-of-view and consistent with expectation, to within measurement errors.
4.1 Contributions to the ASCA error circle
Our results suggest that the SIS mirrors are nominal, i.e., that the plate scale is linear and the point-like X-ray image consistent with the expected PSF. The PSF image itself shows that the pointing is stable during an observation, following a ~ one orbit coarse adjustment at the beginning of most observations. Comparison of the detector and aspected images yields a consistent blur. Thus, the deblur of the attitude solution is equivalent to the blur of the pointing stability. The relative sky reconstruction is within pre-flight specification, to arcsecond precision, as is evident by comparing the reconstruct image of a point source to ground calibration data.
Although there is an apparent arcminute orbital discrepancy in the gyro/star tracker data, there is no additional arcminute blur introduced in the SIS images. This is because the attitude solution relies on the gyro data, which evidently tracks the relative pointing of the boresight with the expected accuracy. The absolute pointing information is transmitted from the star tracker via a damping filter to the gyros. We may conclude that the star tracker information contains the arcminute error; the error circle is thus dominated by a random error in the _absolute_ position, which is otherwise stable over an observation. It should be noted that this error may have propagate into the misalignment matrices during their calibration.
4.2 Orbital variations
The above study was confined to images which where time averaged over many orbits. Some work is underway to study variations in the source positions as a function of the orbital, and other geometric parameters. We considered the effects of day vs. night, and bright vs. dark Earth on the measured positions and find small shifts in the offsets of order 0.1 arcmins, probably due to temperature effects. However the results are not conclusive yet.
4.3 Improving the attitude solution
It may be possible to improve the ASCA error circle by a factor of 2 or 3 because the attitude solution has been shown to track the detailed pointing to ten arcsec precision. The large error circle is likely due to an absolute offset introduced in the attitude solution itself. The on-broad absolute aspect is seen to wander in a sinusoidal manner by ~ one arcminute during an orbit. A false offset in the absolute pointing is generated in the attitude because of this arcminute error. Thus the offset position would depend on the phase of this error when the attitude solution is constructed. Therefore, the absolute offset would be random, as the phase is arbitrary when constructing the solution.
What is needed is a fiducial point to determine the absolute pointing in a reproducible way from observation-to-observation. One way would be to calibrate the offset as a function of appropriate parameters, which depends on the nature of the error, which is not fully understand. This approach requires much study. Another method is to compare the star tracker and gyro data to determine the relative modulation phase, then use the crossing point between the two as a fiducial point (absolute reference). A third, simpler, approach may work - average over the sinusoidal offset from the reconstructed solution during the course of the observation, and use the mean as the fiducial point.
We compared the measured position of 48 SIS point sources to cataloged values and derive an ASCA error circle of 40 arcsecs radius (90% confidence level), and mean of ~ 0.4 arcmins. The offsets are consistent with a random shift in RA/DEC between pointings.
- Latest REV1 software is OK.
- Annual aberration correctly applied.
- Focal plane calibration OK.
- Boresight-instrument alignment calibration OK (but see Section 4.3).
- Mirrors linearity nominal.
- SIS measurement of point source positions are good to ~ 5 arcsecs.
- The attitude stability in pointing mode is ~ 10 arcsecs.
- The attitude reconstruction during an observation is ~ 10 arcsecs.
- The 90% confidence level error circle is 40 arcsecs radius.
- The error circle is centered on zero offset and is consistent with a random
- Large error circle mean of ~ 0.4 arcmins radius likely due to an absolute
offset in the attitude solution from observation to observation.
Fujimoto, R. 1993, alignment matrix calibration.
Gotthelf, E. V. 1992, computer code "ASCALIN", available in the FTOOL software package.
Gotthelf, E. V. 1992, computer code "CAL_GIS_SPATIAL_PCF2.FOR", produces the GIS gain, image, risetime distortion maps stored in the telescope definition file.
Kii, T. 1994, personal communication.
Ninomiya, K., Hasimoto, T., Kii, T., Muranaka, N., Uo, M., Maeda, K., Saitoh, T., 1994, in "Advances in the Astronautical Sciences" ed. Culp, D. & Rausch, R. (Univelt Corp., San Diego), Guidance and Control (Amer. Astonautical Society), Vol 86.
Description of "ASCALIN" -- ASCA calibration & processing software
C***************************************************************************** C C DESCRIPTION: C C Program to transform from ASCA raw telemetry values to physically C meaningful values. C C The results are written out to the input science file DETX, DETY C (detector coordinates), X, Y (sky coordinates), and PI (spectral C channel) columns. C C ASCALIN reads an input Science file, a Telescope Definition file, C and a Temporal History file. C C The Telescope Definition file is a calibration file which defines the C coordinate transformations for each instrument. C C For the SIS, the detector DETX and DETY are constructed from the RAWX, C RAWY, and CCDID values by placing each chip image in the correct C relative position on the focal plane to define a SIS detector system. C C For the GIS, the non-linear spatial and gain distortions are corrected C for using the spatial and gain response maps given in the Telescope C Definition file. C C The SIS and GIS temporal gain variations are given by the Gain History C files. For the SIS this includes CTI corrections. C C The detector coordinates for all four instruments are reconstructed C using 'look up' convention. This system is parallel to the S/C C coordinate system with the S/C Y-axis flipped. C C The sky X, Y binned R.A. and DEC. coordinates for each event is C determined by calculating the linear pixel offsets relative to a C sky pointing from the linearized detector DETX, DETY coordinates. C C The attitude file contains the reconstructed aspect of the satellite C as a function of time. This information, along with the telescope/ C boresight mis-alignment, is use to transform the detector pixels C onto a tangent plane projection in a linear binned R.A. and DEC. C pixel image coordinates centered on the SIS0 detector center. C C The sky reference point for the aspecting may be selected from either C the science file nominal R.A. and Dec. keywords (KEY), a given input C value (USER), or the file average defined as the Attitude file mean C R.A. and Dec. during the science file stop and start time (ATT). C C The option is available to perform a 'fixed aspect' using a set Euler C angles to calculate the sky X, Y binned R.A. and DEC. coordinates C for each event (FIXEDASP). C C ASCALIN is the re-unification of GISLIN/SISLIN/COORD/FIXEDASP. C C*****************************************************************************
a) offset of measured RA DEC from standard coordinates, b) offset of measured angular displacements from standard coordinates.
a) [[Delta]] RA vs. Day-of-year, b) [[Delta]] DEC vs. Day-of-Year.
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