Distinguishing features of CCD astrometry of faint GEO objects
36th COSPAR Scientific Assembly Beijing, China, July 16-23 2006
Central (Pulkovo) Observatory of the Russian Academy of Sciences
St. Petersburg, Russia
Currently, ground-based optical observations of GEO objects, including space debris, are mostly performed with small (< 1.5m in diameter) telescopes. Despite the loss in limiting magnitude, small telescopes outperform large ones in efficiency of observations of transient events, as well as in survey tasks, which is very important for the GEO monitoring problem.
Still, the limited sensitivity of small telescopes in CCD observations of faint or rapidly moving objects is a significant challenge to observation and image processing techniques. GEO (and close to GEO) objects require observations without sidereal tracking or with the telescope locked on object to achieve maximum sensitivity. Both these techniques turn field stars into trails.
Though CCD photometry of fast-moving objects is also a serious problem (see e.g. Yu.N.Krugly, Sol. Sys. Res. 2004 38,3,241), one of the most important sources of the orbital data uncertainty for GEO objects is the comparatively low positional accuracy of individual observations. First, accurate positions of reference stars are required to obtain the differential astrometry solution. Second, the (also precisely located) target object position needs to be reduced into the same reference frame to compute its final celestial coordinates for the given moment.
Unfortunately, a number of factors contribute to the lower accuracy of reference star positions within a single CCD frame: atmospheric turbulence, wobble of the telescope tube, finite mechanical CCD shutter speed, and low signal-to-noise ratio (SNR). Atmospheric turbulence distorts the shapes of star trails within the image plane and produces peaks and cavities; unlike CCD images acquired with sidereal tracking, these effects are not averaged over the whole exposure time to the Gaussian-like profile. Moreover, atmospheric distortions can differ across the whole frame, especially for large field of view and high zenith angles, making it difficult to account for unambiguously. Swinging of the telescope tube acts in the same direction, though it is the same across the whole field of view. Finite velocity and instability of the CCD shutter leads to uncertainty of positions of the star trail ends; thus for this kind of observations frame transfer CCDs are preferred over the more widespread full-frame CCDs. Finally, comparatively low SNR and the lack of bright reference stars, which is a common problem of observations with small telescopes without sidereal tracking, also contributes to large position errors of reference stars.
Another rarely mentioned problem arises for observations of fast-moving objects without tracking. Even if the image coordinate system could be precisely determined from reference stars, the information about the actual target object location for every moment during exposure is lost. The target object generally has different velocity and direction than reference stars, and atmospheric turbulence thus has the different effect on their trails. Formally speaking, the reference frame associated with stars is not the same as the one for the target object, which results in unpredicted errors during astrometric reduction. These problems altogether increase position error of GEO observations to several times the error achievable for point sources with the same telescope.
From the image processing point of view, there exist the three major methods to determine trail positions in pixel coordinates:
Being the easiest one, the barycenter technique is obviously the most inaccurate of these three. Barycenter positions of trails are heavily distorted by atmospheric turbulence, especially by extinction fluctuations, which can shift measured positions by several pixels, compared to point-like images for which barycenter positions are accurate down to a single pixel. Techniques based on the extraction of trail endpoints by gradient filtering are much more accurate; however they tend to fail at low SNRs and are harder to implement. The most robust and versatile way for obtaining trail positions is a modification of the widely used PSF fitting technique. It has proven to produce reasonable results even for star trails with very low SNR (< 1) or heavily distorted by atmospheric turbulence and is relatively easy to implement and customize for a wide range of telescope parameters and observation conditions. The present paper focuses on the application of the PSF fitting technique to CCD images containing star trails and on the implementation of this technique in Apex II, a software platform for astronomical image processing developed at the Pulkovo observatory.
Application of the PSF fitting technique to trails.
Overview of the Apex II image processing package
Apex II is a general-purpose software platform for astronomical image processing, being developed at Pulkovo observatory. Its architecture and design concepts are similar to those of the major image processing packages including IRAF, MIDAS, and IDL. Like them, Apex II consists of several components:
This structure has proven to be most flexible and versatile. It allows to implement the full range of image processing applications - from interactive command-line driven tools with interactive examination of intermediate processing results to fully automated pipelines for processing large data volumes to standalone GUI applications for specific image reduction tasks.
Unlike the image processing packages mentioned above, Apex II is not based upon a dedicated interpreted programming language, but rather upon the widely-used general-purpose object-oriented scripting language Python. This choice is motivated primarily by the clarity, power, and flexibility of the language, existence of implementations for all major hardware and software platforms, and the extensive standard library for most routine tasks like input/output, data visualization, matrix algebra, curve and surface fitting, n-dimensional image processing etc. Despite the widespread opinion about the low performance of scripting languages, pure Python scripts in Apex II are often faster than similar programs written in conventional compiled programming languages. This is mostly due to the high level of vectorization of mathematical operations and to effective optimization of underlying C/Fortran libraries.
All these advantages currently attract attention of the leading scientific software developers. The evidence for this are Python interfaces to the two major astronomical image processing systems, PyRAF and, recently, PyMIDAS. The standard Apex II library is built primarily on top of the two Python packages, Numerical Python and Scientific Python (NumPy/SciPy). The first of them implements the basic functionality for working with multidimensional arrays, including vectorization and matrix algebra. The second one provides implementation of most of the algorithms commonly used in scientific applications: Fourier transform, integration, solving PDEs, interpolation, optimization and nonlinear regression, signal and image processing, special functions etc. Based on these algorithms, as well as on the built-in Python functions, the Apex II library implements various higher level tasks specific to the field of astronomical image processing, like timescale conversions, calibration and filtering of CCD images, automatic object detection, PSF fitting, astrometric and photo metric reduction, catalog access and so forth.
The graphical subsystem (still under active development) is based on wxWidgets/wxPython, the cross-platform GUI toolkit, and on matplotlib, the scientific data visualization package modeled after MATLAB. These packages can be used to display individual CCD frames or catalog fields, plot various data obtained during image processing, as well as create standalone GUI applications intended for processing of specific kinds of astronomical images.
Thus Apex II is primarily a general-purpose software platform for development of reduction systems for various astronomical data.
The following diagram illustrates the main pipeline for processing of GEO object observations in Apex II. Also, some peculiarities of this kind of astronomical images are highlighted.
Apex II GEO image processing pipeline