ПулКОН ::: Apex II ::: Distinguishing features of CCD astrometry of faint GEO objects

Distinguishing features of CCD astrometry of faint GEO objects

36th COSPAR Scientific Assembly Beijing, China, July 16-23 2006

Vladimir Kouprianov

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:

barycenter positions;
PSF fitting;
gradient filtering.

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.


Construction of model "PSF"
	1. Start from the pure gaussian (or Lorentz, Moffat etc.) PSF
	2. Move halves apart
	3. Assume constant intensity along the trail
Fitting model PSF to trail
	Intensity distribution along the trail is approximated by the model profile constructed as described above. The plot demonstrates residual intensity after PSF fitting.

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:

core - high-level interpreted dynamic (scripting) programming language;
standard library of general-purpose utility functions and algorithms specific to the area of astronomical image processing;
object-oriented graphical user interface (GUI) subsystem for interactive image examination and plotting data, built on top of the core language and library;
a set of user functions and scripts which utilize the above components to perform particular image processing tasks.

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

1. Input image

target
object

This sample frame was obtained on Zeiss-600 (D=600mm F=7200mm Cassegrain, 12x12 arcmin FOV) at the Maidanak observatory, one of those participating in PulCOO (see Molotov I. Pulkovo cooperation of optical observers. Programme & Abstracts of Fourth European Conference on Space Debris, ESOC, Darmstadt, Germany, 18-20 April, 2005, ESA Publication Division, p. 173).

The image represents rather uncommon situation of many bright reference stars (field in the Milky Way). Probably, a shorter exposure time should be chosen to reduce overlapping of star trails.

2. Imagecalibration (optional)

This includes the conventional bias/dark/flat correction and elimination of column defects. Indeed, unless precise photometry is required, this step can be skipped as it has little influence on the astrometric accuracy. Only severe column defects should be removed, while substantial background inhomogeneities can be easily dealt with at the next step.

3. Sky background estimation and subtraction (optional)

Required for automatic object detection using the global thresholding technique if the image background is highly non-uniform (usually due to light pollution, Moon, thin clouds etc.). In Apex II, the image background map can be estimated using the two main algorithms:

a) median filtering with large kernel

Advantages:

simple
preserves faint objects
preserves noise distribution

Disadvantages:

leaves small-scale background
slow

b) multipass sigma-clipped smoothing of an undersized image

Advantages:

eliminates also small-scale variations
fast

Disadvantages:

eats objects with very low SNR
introduces additional noise

4. Image filtering (optional)

Unfortunately, conventional image enhancement and restoration techniques (e.g. PSF convolution, Lucy-Richardson etc.) fail for images with trail-like stars. The only promising method seems to be shifting and combining a series of individual frames to increase SNR of either reference stars or the target object. This method yet reduces the temporal accuracy of measurements and thus is more applicable to surveys and search of new space debris objects than to precise astrometry and orbit improvement.

5. Thresholding

For better automatic threshold estimation, Apex II fits a noise model to the image histogram. Due to the usual lack of reference stars, the common threshold level value is rather low, about 2.5-3 sigma.

Looking to the initial, unfiltered bit mask just after thresholding, one can see many faint stars being split into separate unconnected chains of pixels and numerous overlapping startrails.

6. Bit mask (logical) filtering

Immediately after thresholding, due to the low detection level, the bit mask (even for a previously filtered image) is crowded with a vast number of noise streaks. To reduce the probability of false detections and, on the other hand, to improve detectability of objects with low SNRs, Apex II performs logical filtering of the bit mask. It is somewhat similar to conventional filtering of a grayscale image, though proves to be more robust and less noisy.

Two logical filters for processing of GEO object images are implemented in Apex II. Figures below demonstrate their effect on the bit mask.

a) symmetric filter
Advantages:
has the same effect on the target object and on reference star trails cannot handle trail fragmentation
Disadvantages:
cannot handle trail fragmentation

Circumstances:
faint target object

sufficient bright reference stars

b) filter with a trail-shaped kernel
Advantages:
virtually eliminates star trail
Disadvantages:
wipes out faint target object

Circumstances:
bright slow target object

lack of bright reference stars

7. Segmentation

Based upon the connectivity properties of pixel groups. Another implementation utilizes the wave propagation method, widely used in geosciences.

8. Deblending (optional)

Conventional deblending involving multiple thresholds usually does not work for star trails, splitting them back into separate fragments. An adequate deblending algorithm for the case of trail-shaped object images is still a major problem.

9. Isophotal analisis

This step produces initial guess to trail parameters - centroid position, length, width, orientation, and amplitude.

10. PSF fitting

This step is crucial to the overall accuracy of the target object coordinates. Among many other possible issues that may arise during PSF fitting, we can mention the following two:

PSF fitter may fail for heavily overlapping trails;
fitting to objects with very low SNRs or surrounded by rapidly changing background may produce some strangely-looking artifacts.

Below is a plot of the model object profiles produced by PSF fitting (left), and the corresponding residual frame (input image minus model profiles). One can see that the fitter failed for two kinds of objects: overlapped star trails and very faint stars (actually, with SNR below 1).

artifact

target
object

11. Rejection of false detections

Because of the too low detection level, the image is usually contaminated by numerous artifacts coming from noise streaks, frarments of faint star trails etc.; cosmic rays should be also rejected. Finally, only reference stars of acceptable quality are left.

12. Reference catalog matching

Apex II exploits a number of cross-identification algorithms involving only posi tional information. Flux data has proven to be helpful only for rough selection of subsets of objects of similar brightness, but not as one of the matching criteria.

13. Differential astrometry

During this stage, Apex II obtains the LSPC solution; different plate models can be used. The only important distinction in comparison with point-like objects is that the target object position needs to be reduced into the same reference frame as field stars. To achieve this, either of the trail ends or its geometric center may be used as reference points.

14. Photometric catalog matching and reduction

This step is completely identical to the same process for point-like sources. Either aperture or PSF fluxes, as well as optimal photometry, can be utilized to compute the estimate of the target object magnitude.

Размещен 26 октября 2006.