1 Processing of CCD images of star fields without the frame of a flat field by using new software in program shell of MIDAS/ROMAFOT. 1 Andruk V.M., 1Vid’machenko A.P., 2Ivashchenko Yu.M. 1. The main astronomical observatory of the NAS of Ukraine, St. Zabolotnogo, 27, 03680 МСП, Kiev, Ukraine E-mail:
[email protected] 2. Andrushivska astronomical observatory, St. Observatorna 3-7b, Halchyn, Andrushivka, Zhitomir region. E-Mail:
[email protected] Abstract. Results of processing of CCD frames of star fields, obtained by two ways, are analyzed. In the first case (a traditional method) the frame of flat field are used. In the second one the own large-scale flat field it is obtained directly from the processable frames of image. That is we suggest to find the frame of a flat field individually for each frame of the image. Photometric researches of regular errors are carried out for a wide interval of expositions (up to 100 times) for the same celestial objects in zones of overplanning of displaced frames (up to half of the frames size). Comparison of an instrumental photometric scale with a scale of photometric standards shows the absence of photometric field errors and brightness errors. Software procedure of cyclic processing of any quantity of CCD frames of star fields is realized in program shell of MIDAS/ROMAFOT. 1. Introduction. CCD-frame S(i,j) with the image of a star field, contains the information on separate celestial objects and background. Such frame refers to as the “crude” one. For obtaining of the undistorted photometric scale of star magnitudes for all field’s objects on the frame it is necessary to have auxiliary flat field F(i,j) of the frame. Normalized flat field of CCD-frame allows to exclude a photometric error from the “crude” CCD-frame S(i,j) with the image of a star field. The photometric error of a star’s field is caused by instrumental optics and non-uniformity of sensitivity of a working field of a CCD matrix. Transformed CCD-frame, free from a photometric field’s error, we shall name as a pure CCD frame of star field I(i,j). It is necessary to have the CCD frames with corresponding expositions for dark current D(i,j)S and D(i,j)F too. Mainly the frames of dark current D(i,j)S and D(i,j)F have different expositions. So, the pure frame I(i,j) it is possible to write down such as: I(i,j) = {S(i,j) - D(i,j)S} / (1), where matrixes elements (pixels) have current number i and j, and normalized frame is received after division of a difference of the frames {F(i,j)-D(i,j)F} on average value of this difference [2]. In practice (as a rule) the frame of flat field F(i,j) receive by short expositions of the early morning or twilight sky, i.e. the frame of flat field F(i,j) and the “crude” frame of star field S(i,j) are obtained separately and under different conditions. In frame S(i,j) as the registered signal there are two sub signal from celestial objects: actually required value I(i,j) and background from the night sky, i.e., weakened analogue of the F(i,j). Therefore, if all registered objects will be removed (any way) from the “crude” CCD frame of a star field – it will be obtained the own flat fields F(i,j) (for the frame). Thus the “crude” CCD frame image of a star field and frame flat field S(i,j) were obtained under identical physical conditions. Moreover, D(i,j)S and D(i,j)F is identical, i.e. D(i,j)S=D(i,j)F. Means, for reception of the pure CCD frame of star field I(i,j) from crude CCD frame S(i,j) it is enough to have only one auxiliary frame of dark current D(i,j)S. Exposure time for frame S(i,j) and D(i,j)S is identical. Procedure of reception of pure frame I(i,j) according to the formula (1) we shall name “traditional way” (or “the first type”), and similar procedure without using of separately obtained frame of a flat field we shall name “the second way”. In operational shell LINUX/MIDAS/ROMAFOT programs (as MIDAS procedures) of a cyclic processing of finite quantity of CCD frames in *.FITS format are created. For debugging the program observational material obtained on telescope Zeiss-600 of Andrushivska astronomical observatory [1] were used. The images were obtained with using of S1C-017 CCD camera. The sizes of this matrix are 1024 x 1024 pixels, scale is equal to 1 pixel = 0.47 of arc seconds.
2 2. Processing of CCD frames of images of star fields in MIDAS/ROMAFOT. The comparative analysis of two ways of processing of CCD frames. Two different programs on processing of CCD frames of images of star fields with the purpose of definition of rectangular coordinates X, Y and photometric sizes of objects are created. The first type is a processing of the CCD frames by standard way with subtraction of noise from the frame with a flat field and the frame of star fields with the subsequent normalization of the CCD frames of star fields by the CCD frames with a flat field. Procedure of standard processing is in detail described in MIDAS Users Guide (European Southern Observatory - Image Processing Group 1994, MIDAS Users Guide, Volume B, ESO, Garching). In a standard way the normalizing frame with a flat field are in regular intervals lit up to or after observations, i.e. turn out separately. But we have shown that the frame of a flat field it is possible to receive directly from each working frame by removal of objects from the frame. The iterative method of removal of objects and obtaining of the own flat fields from the working frame has been realized as MIDAS-procedure. We shall consider fig. 1. At the left are photometric cuts along X coordinate of the frame with a flat field at different expositions (hot pixels are removed by the frame operation of smoothing with a window of smoothing of some pixels). After subtraction from the frame with a flat field of the frame with noise the kind of photometric cuts is shown on the right.
Fig. 1. Photometric curves for CCD frames with a flat field at different expositions. At the left - for "crude" CCD frames with a flat field; on the right - after subtraction of frames with dark current at the same exposition.
3 For a quantitative estimation of distinction between the frames we have used factor of curvature “k”, which is equal to the ratio of the maximal value of readout to it average value for all frame. The frame of a flat field with different expositions are received in different days at different brightness, but three top and two bottom ones are received consistently with different expositions. We have obtained that change of factor “k” on 0.01 cause change of a photometric error of a field on 0.01-0.02 star magnitude. On Fig. 2 are shown similar cuts, but here flat fields are received from the frame of images of star fields after removal of all objects. We mark distinction of values of factor “k” for the right parts of both figures.
Fig. 2. Photometric curves for CCD frames with star's fields at different expositions. On the left photometric curves of CCD frames after objects removal from them, on the right - after subtraction of the dark current from the frame at the same exposition.
4 Procedure of the second type of processing of the CCD frames we shall consider by the example of photometric cuts of two frame of the second and third type (frame 1and frame 2, with exposition of 10 and 840 seconds, accordingly). Above on Fig. 3 photometric cuts for the “crude” frame are shown; in the second line - are marked over exposition objects.
Fig. 3. Photometric curves for two CCD frames with an exposition of 10 and 840 seconds. The first frame contains one over exposition object; the second frame contains extensive over exposition site. In the second line of figure over exposition objects are marked with “one”. In the third line the intermediate stage on reduction of the frame to a normal kind is shown. In the bottom line the end result of restoration of over exposition separate objects and extensive over exposition sites of the frame is shown.
5 In the third line - the intermediate stage of restoration of images, and below - a final kind. The kind of photometric cuts after removal of hot pixels is shown on Fig. 4 (above). Change of a kind of photometric cuts during removal of objects from the frame is shown in the second, third and fourth lines. In the bottom line – photometric cuts for the frame after removal of objects, i.e. it is required flat fields which we have received from the image.
Fig. 4. Continuation of fig. 3. Process of objects removing of the frame and finding of the own flat field for two frames is shown.
6 After dividing of the “crude” frame of star field on normalized frame of a flat field -photometric cuts will look like shown on Fig. 5 (above). After removal of hot pixels in the increased kind the photometric cuts are shown on the average line. After photometric correction of over exposition photometric cuts (in the second line of fig. 1) it’s shown in the bottom line of fig. 5.
Fig. 5. Continuation fig. 4. In the top line correction of a flat field (own flat fields are used) for "crude" CCD frame is executed. In the second line results after removing of "hot" pixels are shown. In the bottom line photometric curves after photometric correction for bright over exposition objects are shown.
7 We shall consider the comparison of photometric accuracy of two types of over exposition CCD frames. Observations are made with an exposition of 60 seconds; the average background from the sky is some units. It is an extreme case of applicability of the second type of processing in sense of exception of a photometric mirror of a field. The kind of two sites of the sky after processing in MIDAS/ROMAFOT is shown on fig. 6. The frame are made with overlapping; crosses designate the photo-electric standards in the Vilnius system. Photometric results of processing in ROMAFOT by a standard method are shown on fig. 6 at the left; on the right – are results of processing in ROMAFOT by our method (with a flat field obtained from the frame of the image).
Fig. 6. Errors of determination of star magnitude and objects coordinates from a comparison of two frames are shown.
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Fig. 7. Resulting maps of sky field of IC 4665 after processing of two CCD frames in MIDAS/ROMAFOT. Crosses are photo-electric standards of the Vilnius system. In the top line are differences of star magnitude for two frames depend on distance from the center of the frame; in the second line - values of photometric differences from star magnitude. The differences of star magnitude in a zone of overlapping of two frames are shown in the third and fourth lines. Comparison with photometric standards is shown in last line. Our analysis of the observational data shows, that it is possible to
9 process the CCD frames of star fields without specially obtained frame of a flat field. The frame with own flat field it is possible to receive from the frame of the image of a star field by removal of objects from the frame.
Fig. 8. Results of photometric processing in ROMAFOT are shown: at the left - the standard method of the account of a flat field is applied; on the right - the frame of a flat field were obtained from the frame of the image. In the top line - differences of star magnitudes depending on distance up to the frame center are shown for two consecutive frames; in the second line - photometric differences depending on star magnitude are shown. In the third and fourth lines dependence of differences of star magnitudes in a zone of overlapping of two frames are shown. In last line comparison of our obtained results with photometric standards is shown. Photometric and astrometric accuracy of both methods is practically identical. But time of observations decreases more than twice! 3. The conclusion. The method of processing of the CCD-frames without using of specially obtained frames for flat field is offered, realized and is successfully put into practice. The method is approved in software MIDAS/ROMAFOT. It is shown, that the method does not have photometric field’s error. Programs (such as MIDAS procedures) of cyclic processing of final quantity of CCD frames in *.FITS format are created. Acknowledgements: Work is executed at partial financial support of the Scientific and technological Center in Ukraine (grant NN43) and of the National Space Agency of Ukraine (contract “Astro”). References. 1. Ivashchenko Yu. M., Andruk V.M. Andrushivka astronomical observatory in 2001. In Extension and connection of Reference frames using group based CCD technique // International astronomical conference.-Nikolaev: Atoll.-2001.-P. 224-230. 2. European Southern Observatory - Image Processing Group 1994, MIDAS Users Guide, Volume A, B and C, ESO, Garching.
