On the problems of processing wide field images

Transcription

1 On the problems of processing wide field images Irina S. Guseva Pulkovo Observatory, St Petersburg Abstract. A lot of modern instruments for space surveillance provide a large FOV (about several square degrees). High internal precision of the objects detection with CCDs is damaged very often by a large distortion caused by the different deformations of the complicated optical systems of the telescopes that provide such a large FOV. Some ways to take into account these effects are discussed. Another problem arises when observing objects with a wide-field instrument at low altitude. Non-linear deformation of the image caused by the atmospheric refraction cannot be compensated by the use of the common parameters of the astrometric plate reduction, or by the use of the common procedures of the differential refraction account. The approaches to solve this problem are considered. Some problems are discussed concerning the modern reference astrometric and photometric catalogues used for the space monitoring data reduction. Introduction Many problems of data reduction arise when we deal with special telescopes for the fast space surveillance. Such telescopes usually have a large field of view, about several square degrees and need some special efforts for effective image processing. These problems and some ways for their solving are discussed on the bases of our experience in the problem of space surveillance. A short summary of our work on the satellites observations: 1990 first CCD frames with satellites tracks were obtained during the on-ground experiment for the REGATTA-ASTRO space astrometry and photometry project [1,2] numerous attempts to demonstrate the advantages of the CCDs for space surveillance (northern Pulkovo observatory is not a convenient place for the geostationary objects observations) May, start of experimental CCD observations of satellites at Pulkovo, first CCD observations of satellites in the Former USSR [3,4] regular CCD observations of satellites at Pulkovo, St Petersburg, design and improvement of the software for the data processing start of the Pulkovo cooperation of optical observers (PulCON) [5], now ISON [6] (movers Alla Sochilina, Igor Molotov) 2004 start of observations at Ussurijsk Astrophysical Observatory 2005 start of observations at Tarija (Bolivia) 2007 start of observations at Kamchatka We began the satellites observations with a very small CCD telescope only 10 cm diameter. Nevertheless, this instrument proved to be very effective in comparison with former large photographic telescopes. By the way, this is the same instrument that was used for the first professional photo of the first Russian satellite in October, 1957 (Fig.1, 2, 3). Now we use a special automated CCD telescope, RST-220, for the space objects observations that provides us a field of view of 16 square degrees. This instrument allows us to scan the wide band region near the geostationary orbits several times during the night. Unfortunately, we cannot use all the possibilities of such an instrument because of the bad weather conditions at Pulkovo and white nights in the summer. The main problem is that we have to observe the geostationary satellites at the altitude of no more than 22 degree (latitude of Pulkovo ~ 60 deg.), our extreme low observations were at the altitude of 3 deg. Nevertheless, we could obtain more than measurements of satellites positions in 2010.

2 Fig. 1. Double Short-focus Astrograph (AKD) (D=100 mm, F=712 mm) Fig. 2. Dome of AKD (Eastern dome of the Pulkovo observatory main building) Fig. 3. First professional photo of the first satellite made by Tamara Kisseleva with AKD on October, 10, 1957 (with astrometric and photometric measurement)

3 1. Distortion It should be stressed that the creation of astronomical instruments with a large FOV is impossible without a complicated optical system. Modern telescopes with a number of optical and mechanical components are very sensitive to any thermal or mechanical influence on the instrument that can produce deformation and anomalous distortion. Distortion of the complicated systems (versus common astrographs) cannot be expressed by a simple analytical formulae. Even the point spread function (PSF) of such telescopes may be different in different parts of the FOV. The sample of such a system and the PSF variation is shown in Fig. 4, that presents the Modified Richter Slevogt optical system by V.Yu. Terebizh [7]. Such an optical system is similar to that of our telescope, RST-220. Fig. 4. Modified Richer-Slevogt optical system by V. Yu. Terebizh [5] (MRS: D = 350 мм, 2w = 3.5 ) Any disturbance of the alignment of such a system causes a serious problem with anomalous distortions that should be carefully investigated (in common case), and corresponding corrections should be amended for the best astrometric quality. The problem of an anomalous distortion arises very often, when the old design telescopes are supplied with optical correctors to provide the large FOV with a shorter focus. As a sample, the distortion of the ASA N8 telescope (20cm, f/3.6) is shown in Fig. 5 in the form of the residuals of the linear astrometric solution. Two such telescopes were used for the APASS project [8] aimed to create the 5-band global photometric catalogue (the results of this project are included in the last version of the UCAC catalogue UCAC-4 [9]). Usually for the data reduction astronomers use a polynomial relation between the true (ξ i,η i ) and observed (X i, Y i ) coordinates of m reference stars: ξ i = a 0 + a 1 X i + a 2 Y i + a 3 X i 2 + a 4 X i Y i + a 5 Y i 2 + a 6 X i a k Y i n, η i = b 0 + b 1 X i + b 2 Y i + b 3 X i 2 + b 4 X i Y i + b 5 Y i 2 + b 6 Y i b k Y i n, i = 1,..,m (1) The first 3 members in each equation of (1) describe the linear transformation of coordinates, the other ones should describe different kinds of distortions. Solving the system of 2 m equations by the common least-squares procedure gives us (n+1) (n+2) parameters, a 0,, a k, b 0,, b k.. The most usual models of astrometric reduction are the 6 parameters model (the linear or the Turner s model) and the 12 parameters model, accounting for the quadratic members of (1). But in the case of anomalous distortions even the cubic model, with 20 parameters, cannot provide an appropriate result (see Fig. 6), the corners of frame are entirely excluded.

4 Fig.5. Residuals of linear plate correction [8] Fig.6. Residuals of cubic plate correction [8].

5 The problem of the model choice is closely connected with the problem of the accuracy of the measured stars positions and the reference stars precision. In the case of the model with a large number of parameters, even a limited number of bad stars can lead to the wrong solution and false results of the astrometric reduction. Especially, it is important if the number of reference stars is comparable with the number of the model parameters, and, additionally, large errors in the star position determinations on the frame may happen (for example, because of a bad CCD pixel or a cosmic ray event). There are many ways to solve the problem of the distortion corrections [10]. Besides the polynomial models it was proposed to use cubic splines, B-splines and other techniques. Some special proposals were made for saving the information on the distortion in the FITS headers. In the case of routine CCD observations of satellites, or other objects, with a wide field instrument, we need a very fast data reduction. Investigation of the distortion for each frame by use of a complicated model takes too much time for the computation and cannot provide a good enough result because of the errors of reference stars position determination. In principle, when observing satellites, we obtain the stars coordinates by using their track images (Fig.7) with worse accuracy than in the case of the common observations of stars (when the telescope follows the stars diurnal motion). Fig.7. A sample of the CCD frame with stars (tracks) and satellite That is why we prefer to use the distortion maps, prepared in advance by the use of a series of frames of the sky fields near the zenith with a lot of stars having precise positions. Unlike the removable photoplates, CCDs are strongly connected with the telescopes and the common distortion of the optics and the CCD is quite stable for a time. The distortion maps may be saved

6 as FITs data for each pixel or for blocks of 10x10 pixels and used for the current CCD frame reduction by keeping in mind like the dark current and flat field correction matrices. In this case the measured X i, Y i for each star on the current frame can be easily (without computations) corrected for the distortion that allows to use the simple and fast 6-parameters solution. Fig. 8 and 9 show the results of the linear solution of the original CCD frames, and after correction for the distortion (it was a bad case of a temporary insufficient alignment of our telescope RST-220). The scale of instrument with the CCD is ~5 arcsec/pixel. Fig. 8. Residuals of linear solution of original frame (narrow band near central line). Fig. 9. Residuals of linear solution after correction for the distortion.

7 2. Differential and chromatic refraction. Our experience of the satellites observations at Pulkovo Observatory (59 46'' N, 30 19'38 E) forced us to pay attention to the problem of the precise refraction correction for image processing. Even on the meridian we could not observe geostationary objects at altitudes higher than 22 degrees, the lowest altitude was about 3º above the horizon. In addition, working with a large FOV (4º x 4º) we have to take into account a strongly nonlinear variation of refraction and the effects of chromatic refraction at low altitudes. The problem is more common than it seems to be, because quite often we have to observe asteroids, comets, and other interesting objects near the horizon. If the frame is obtained off the local meridian, the refraction affects both right ascension and declination (see Fig.10). Fig. 10. Illustration of apparent shift of coordinate grid to zenith The non-linear character of the refraction at low altitudes cannot be compensated by a large number of formal parameters of astrometric reduction. Fig. 11 shows the refraction changes with a step of the zenith distance of 1 degree. It is evident that it is necessary to take into account the non-linear deformation of the frame coordinate grid by refraction in the case of a large FOV at a low altitude, at Z > 70. The best way to solve this problem is to calculate the whole refraction for each star in the FOV instead of a common simplified formula of differential refraction that was used in astrophotography. We use a fast procedure that allows to calculate the refraction for any wavelength and atmospheric parameters for the zenith distances until 85º, with a formal precision of 0.05 arcsec in comparison with the Pulkovo refraction tables, 5 th edition [11]. Certainly, the real atmosphere may differ significantly from the accepted model. If it is necessary to improve the result, the residuals of a common solution may be investigated as a function of tg k Z, and the appropriate corrections may be applied to the measurements. Another problem of wide field astrometry consists in chromatic refraction, the difference of the apparent positions of stars of different spectral classes, if we observe without narrow band photometric filters. Fig. 12 shows the relative dependence of refraction on Z and the wavelength WL of light: graphs present differences between refraction at WL = 600 nm and other samples. Providing observations without filters we should create a procedure to calculate the effective wavelength of the different stars.

8 Fig 11. Increment of refraction by 1 degree step by Z Fig. 12. Atmospheric spectrum at different zenith distances Z. dr difference of refraction at wavelength 600 nm and other: 450,500,550 nm The effective wavelength depends not only on the color of the star (spectral class, or B-V, or other index), but should be calculated with many other parameters: spectral response of the CCD, spectral characteristics of the telescope optics, local atmosphere extinction depending on the wavelength and air mass. Thus, it is individual for each instrument and location.

9 3. Fast background correction When dealing with wide field images we need sometimes to reduce an inconstant sky background, that may be caused, for example, by moonlight, by different density clouds, or any other source of a smooth variation of the background. For the routine observations of satellites such a procedure should be as fast as possible. Stars and satellites may be regarded as point sources on the CCD images and the background variations are rather smoothed, that allows us to propose a quite simple procedure for the fast background correction (FBC). It should be noted that the background correction should be a very delicate procedure and should not change the images of objects that may change their coordinates and photometry (as little as possible). The main idea is to use only 9 points for the background evaluation instead of the whole block of N x N pixels on the CCD frame commonly used in different procedures. N should be larger than the point spread function (PSF), including the valuable pixels at the edge of the star image. Processing of such a block requires a time that usually depends on N 2. Fig. 13. Illustration of the pixel selection for the fast background correction, N = 2n+1 Choosing a grid of 9 points instead of N 2 in a way, that is shown in Fig. 13, we have the same time for the image processing for any N (the PSF is different for different instruments and depends on the optics, CCD, atmosphere, etc). In the case of a quite flat background we can choose as the background value b i,j for a given pixel a i,j, the value of one of the minimal signals of 9 grid points, or some weighted combination of the minimal values. The use of only the minimal signal is not recommended, because the result will be affected by the accidental readout noise of the CCD. Another proposal is to use memory of the result of the previous step b i-1,j (obtained when scanning the CCD by lines or columns) and accept as a current background value some weighted combination of b i,j and b i-1,j. Such a procedure does not work perfectly in the case of strong background gradients. For this reason it is proposed to keep in the memory the value of the gradient in the previous step, and to use some weighted combination of the current b i,j and the saved in memory values of the background and the gradient (the last is corrected also at each step). Such a simple procedure works very fast and effective (see Fig. 14 and 15). By the way, the CCD readout noise goes down after the correction by ~ 10% in our CCD.

10 Fig.13. Fragment of original CCD frame. Fig.14. The same fragment after the background correction.

11 4. Reference astrometric and photometric catalogs Astrometric and photometric observations of any object are based on the precise reference catalogues. Such catalogues should provide a sufficient amount of reference stars on the frame, thus, almost all differential astrometry cannot use the most precise Hipparcos catalogue immediately. The most useful is the Tycho-2 catalog [12], containing a large enough number of stars until 12 th magnitude, to provide astrometric observations with a large FOV. Unfortunately, the precision of the Tycho-2 stars fainter than 12 th V magnitude, is worse than that of the brighter stars. Fig.15. Copy of Table 2 from [12] parameters of the Tycho-2 catalog. For this reason the UCAC catalog based on precise CCD observations, seems to be more useful, especially for the observations of faint objects the difference in the magnitude of object and reference stars should be as little as possible. Unfortunately, the UCAC-3 version of catalog appears to be not as good as was expected. The recently released UCAC3 (Cat. I/315) could not be used because we found plate-dependent distortions in its proper motion system north of - 20 declination [13]. In addition, we have found unexpected errors in the UCAC-3 photometric values B, R, I, included in the UCAC-3 from the SuperCosmos project [14]. The results of the comparison of R with the proper UCAC f-values in the near band were presented at the Russian astronomical conference in 2010 [15], as well as the results of B and I comparison with the corresponding values of the TASS project [16]. Some graphs are shown in Fig. 16 and 17. The new UCAC4 version is a compiled, all-sky star catalog covering mainly the 8 to 16 magnitude range in a single bandpass between V and R. Positional errors are about 15 to 20 mas for stars in the 10 to 14 mag range. Proper motions have been derived for most of the about 113 million stars utilizing about 140 other star catalogs with significant epoch difference to the UCAC CCD observations. These data are supplemented by 2MASS photometric data for about 110 million stars and 5-band (B,V,g,r,i) photometry from the APASS (AAVSO Photometric All- Sky Survey) for over 50 million stars [9]. It seems to be useful to evaluate the UCAC-4 photometry included from the APASS project by a comparison with other catalogues containing photometric data. Unfortunately, there is no all-sky photometric catalog created in a uniform photometric system except the Tycho-2 photometry B and V until magnitude. The most interesting Sloan Digital Sky Survey (SDSS) [17] covers less than square degrees of ~ The SuperCosmos photometry and the USNO series of catalogues are based on different old photographic observations with different instruments and photoplates, that cannot provide the uniformity and high precision of the photometry. The TASS project collects the data on the V, R, I magnitudes for a limited

12 number of stars until magnitudes. The APASS project is not finished yet, thus, less than half of the UCAC-4 is provided with the 5-band photometry. R UCmag-Rsc (mag) R Ucmag (mag) Fig.16. Difference between the f values of the UCAC project (Ucmag) and the R values introduced from the SuperCosmos project (the Pleiades area) [15] R UCmag-Rsc (mag) Ucmag (mag) R Fig.17. Difference between the f values of the UCAC project and the R values introduced from the SuperCosmos project (North galactic pole area) [15]

13 Evaluation of the UCAC-4/APASS photometry in the B-band may be done with the Tycho-2 B values only. The result of the comparison is shown in Fig. 18. The stars were selected in an arbitrary area around (RA=6h, Dec=0), but the same shape of graph remains for other selections. Fig.18. Difference between B values from the UCAC-4 / APASS and the Tycho-2 Fig.19. Difference between V values from the UCAC-4 / APASS and the Tycho-2

14 Both Fig.18 and Fig.19 show the systematic deviation of B and V values from the different catalogs for all stars brighter than 10 mag. Such a deviation can be explained by the errors in the UCAC-4/APASS photometry only (the reliable range of the APASS photometry is between 10 and 17 mag). It may be confirmed by the comparison of V from the UCAC- 4/APASS with V from the TASS (Fig. 20). One can see the same deviation for the stars brighter than 10 mag while Fig.21 show no systematic difference between V (Tycho-2) and V (TASS). Fig.20. Difference between V values from the UCAC-4 / APASS and the TASS Fig.21. Difference between V values from the Tycho-2 and the TASS.

15 Such systematic errors in the UCAC-4 / APASS photometry for the stars brighter 10 mag should be taken into account. They could cause also a small systematic shift in the range mag between the UCAC-4 / APASS and the TASS. The photometric values in the g, r, i-bands of the UCAC-4/APASS were obtained with the same filters as in the Sloan Digital Sky Survey (SDSS) [17]. Fig.22. Photometric system of the SDSS [18], Thus, the SDSS data are, maybe, the only possible source for the comparison of g, r, i values of the UCAC-4/APASS. The results are shown in the Fig. 23, 24, 25. Such results are very similar for the different parts of the sky where such a comparison may be fulfilled. The systematic difference between g, r, i values in both data sets needs some further investigation. The falling points in the low part of the graphs may be explained by the large accidental errors of the SDSS. For example: RA Dec g r i UCAC-4: SDSS: UCAC-4: SDSS: UCAC-4: SDSS:

16 Fig.23. Difference between g values from the UCAC-4/APASS and the SDSS. Fig.24. Difference between r values from the UCAC-4/APASS and the SDSS.

17 Fig.25. Difference between i values from the UCAC-4/APASS and the SDSS. Except for the bright stars with evident errors in the UCAC-4/APASS, Fig.23 Fig 25 show the evident separation of stars in the range of and mag. The value of the discrepancy varies from ~0.3 mag in g-band to ~ 0.1 mag in r-band. The conclusion of all the fulfilled comparisons may be as follows: - There was no reason to include in the UCAC-4 the APASS photometry for the stars brighter than 10 mag, these data should be discarded. - There are several systematic problems with the photometry in the range mag, that needs further investigation and independent evaluation. - It is worthwhile to verify the SDSS photometric data before their usage for an investigation of an individual star or object. - There is no all-sky multi-bands photometric catalog of all stars until ~ 16 mag, created in a uniform photometric system.

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