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ISSN 0038 0946, Solar System Research, 2011, Vol. 45, No. 2, pp. 174­181. © Pleiades Publishing, Inc., 2011. Original Russian Text © S.V. Kuzin, S.V. Shestov, S.A. Bogachev, A.A. Pertsov, A.S. Ulyanov, A.A. Reva, 2011, published in Astronomicheskii Vestnik, 2011, Vol. 45, No. 2, pp. 178­ 185.

Processing Method of Images Obtained during the TESIS/CORONAS PHOTON Experiment
S. V. Kuzin, S. V. Shestov, S. A. Bogachev, A. A. Pertsov, A. S. Ulyanov, and A. A. Reva
Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia
Received May 16, 2010

Abstract--In January 2009, the CORONAS PHOTON spacecraft was successfully launched. It includes a set of telescopes and spectroheliometers--TESIS--designed to image the solar corona in soft X ray and EUV spectral ranges. Due to features of the reading system, to obtain physical information from these images, it is necessary to preprocess them, i.e., to remove the background, correct the white field, level, and clean. The paper discusses the algorithms and software developed and used for the preprocessing of images. DOI: 10.1134/S0038094611020122

INTRODUCTION The exploration of the solar corona is extremely important from the standpoint of solving fundamental problems of solar physics and astrophysics. Key issues--the heating of the corona, mechanisms of solar flares, formation and acceleration of solar wind--are still not resolved. In addition, the inter planetary medium is mainly formed by the processes occurring in the solar corona, and therefore their study is important from the practical point of view. Solar flares and the accompanying increased fluxes of ioniz ing radiation and charged particles, emissions of the coronal mass, and the flow of solar wind all cause the space weather near the Earth. To solve these problems, in the early 1990s a research program of solar activity was developed, based on the CORONAS satellites. In 1994, the first satellite of this series, the CORONAS I (Sobelman et al., 1996), was put into orbit, and in 2001 the CORONAS F (Oraevskii, Sobelman, 2002) was, also. On January 30, 2009, the third satellite of the CORONAS program, the CORONAS PHOTON spacecraft (Kotov, 2004), was set into orbit. For the spacecraft, a new set of space telescopes and spectrometers called TESIS was developed at the Lebedev Physical Institute (Kuzin et al., 2010, 2011). In the TESIS, the method of imaging spectroscopy of the Sun is implemented, which was tested on CORONAS satellites of the previous series. This method provides for recording of a complete disk with high spatial, spectral, and temporal resolution. The composition of equipment includes six independent devices (record ing channels) intended for telescopic and spectro scopic observations of the solar corona in soft X ray (SXRR) and extreme ultraviolet (EUV) spectral ranges.

The objectives of the TESIS experiment include the study of the plasma of the Sun (its small scale structure, dynamics, and physical conditions in the plasma, such as temperature and density) and the study of local and global phenomena and structures, i.e., flares, hot clouds, active regions, coronal mass ejections, etc. The TESIS makes it possible to observe the solar corona of different types, i.e., to study small scale structures and dynamics of the plasma with high spatial (up to 1.7) and temporary (up to 1 s) resolu tion, to explore large scale structures at large distances from the Sun's surface (up to three radii), and to con duct observations of separate structures with high spectral resolution (up to 0.01 å) in a broad spectral range, as well as other types of observations. The TESIS management is carried out via pro grams transmitted from the Earth. The management program contains a sequence of commands, i.e., instructions to register the frame in a given recording channel of the TESIS at a given time with a given exposure time. Recorded images are packed into telemetry files and transmitted to the Earth during communication sessions. When the observational data are obtained, telemetry files are decompressed at the Lebedev Physical Institute and images are stored in the TESIS experiment database. Each file contains one image. These files are called zero level files, because they are not subject to any additional treat ment except for decompressing. Preprocessing may include accounting for background in the images, the correction function of white field, the exact definition of solar grid coordinates, etc. The main results of observations from the TESIS are given in the article The TESIS experiment on the CORONAS PHOTON spacecraft of this volume.

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175 Controller CCD matrices CCD matrices Focused image Clean image

This article discusses the methods and algorithms developed and used for primary image processing. FEATURES OF OBTAINED IMAGES All images obtained by the TESIS have a number of artifacts, i.e., the dark current, flat field, blurring (related to the feature of input shutters and CCD matrices of the equipment), and frame damage caused by the entry of cosmic particles. In addition, poor accuracy of the spacecraft stabilization leads to the fact that separately taken images of the Sun have a ran dom displacement and rotation relative to the CCD matrix. Many of these shortcomings can be eliminated by the methods of subsequent computer image pro cessing. Let us consider image features in greater detail. The dark current of the matrix is caused by the gen eration of the electron­hole pairs in matrix cells in the absence of the incident radiation. The dark current increases exponentially with increasing temperature of the CCD matrix. Thus, CCD matrices are often cooled while in operation. CCD matrices of the TESIS are equipped Peltier coolers. During the flight tests of the TESIS it was found that on dark images (obtained with a closed input shutter), the signal is well approximated by a linear function, even when Peltier coolers are turned off, and can be easily removed programmatically. The flat field is caused by the response of the CCD matrix on the unit signal, i.e., a beam of light with unit intensity over the section and covering the entire CCD matrix. A nonzero flat field can be caused by a nonuni form sensitivity of the CCD matrix area and uneven ness of deposited filters. To determine the functions of the flat field in the TESIS channels, special observation programs were conducted, which resulted in the appropriate correc tion functions. The blurring in TESIS images is caused by the fea ture of the readout system of images from CCD matri ces and input shutters. The image is recorded to the matrix in the following order: 1) Shutters open. 2) The matrix is cleansed (successive shifts of rows to the output line at the speed of 150 ms/line). 3) The image is exposed. 4) Shutters close. 5) The image is read. Since the cleaning of the matrix occurs when shut ters are opened, it is as though a focused image of the Sun passed over the newly obtained image during this process (see Fig. 1). The effective exposure at such a clean matrix (up to 0.3 s) is usually shorter than the actual exposure (1­10 s). This made it possible to
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Fig. 1. The mechanism of the blurring formation on the images during the cleansing.

develop algorithms to remove the blurring on the working image. The scattered light appears as bright bands at the edges of the CCD matrix. Such illumination is explained by a smaller thickness of focal X ray filters at the edges of the CCD matrix (which is due to technol ogy of the filter application). The manifestation of the scattered light at the edges of the matrix does not make a significant contribution to the signal produced by the radiation of the corona of the Sun. The comparison of the zero level frame and the frame after the primary processing of the 171 å chan nel is shown in Fig. 2. In the upper left of the figure, the original image is depicted (logarithmic scale of intensities, pronounced weak signal). Areas of blurring and dark signal are marked. In the top right of Fig. 2 the same frame is shown with the adjusted dark cur rent, blurring, and flat field. The intensity scale is the same. The dotted line on both images marks the line, the intensity distribution along which is given under the images. METHODS OF IMAGE REGISTRATION During the preparation of the TESIS experiment, two methods of image recording were installed in the flight software, i.e., the recording of a full frame and partial frame. Both options presupposed the use of input shutters of telescopes. Under these conditions, shutters open during recording, the matrix is cleaned and the necessary exposure is conducted, then shutters close and the image is read from the CCD matrix. The main features of a full frame recording are as follows. During the cleaning, the image is shifted upward line by line in the direction of the output string. The newly formed bottom lines do not have useful optical signal (except for the blurring), thus, they are cleared. When reading data from the CCD


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B l ur r in g

KUZIN et al.

Signal, u. ADC 1000 800 600 400 200 0 ­200 0 200 400 600 800 1000 0 coordinate 200 400 600 Blurring

Dark signa l

Signal, u. ADC 1000 800 600 400 200 0 ­200 800 1000 coordinate

Dark signal

Fig. 2. The comparison of the frame of the zero level and the frame after the primary treatment (channel 171 å).

matrix, the image is shifted to the output string line by line, from where each row is shifted pixel by pixel in the output register, where the signal is digitalized (see Fig. 3a). The rate of the line shift is 150 ms, the time of shifting and reading of 1 pixel is 2 microseconds. The recording of a partial frame [X0 : X1, Y0 : Y1] (see Fig. 3b) is executed, in general, similar to the full frame; the difference lies in the fact that there is no readout from matrix strings with numbers less than Y0 and more than Y1. Since the line by line shift is per formed much faster than the pixel by pixel shift, the readout.] (150 ms in the case of line shift against 150 + 4096 ms when reading the line), the recording of par tial frame usually runs significantly faster than the recording of the full frame due to the rejection of unnecessary lines. In the course of the TESIS experiment, in order to preserve the resource of input shutters, the method of recording the full image in parts was proposed and developed. The image of the Sun is shifted to the far

edge of the matrix relative to the output line by means of the mirror overfocusing (see Fig. 3c). In this config uration, the matrix area adjacent to the output line is almost not illuminated by the solar radiation and can be used as a read buffer. Input shutters of the equip ment are constantly open. When registering a full frame by parts, successive exposures are conducted and parts of the matrix are recorded, indicated in Fig. 3c by rectangles. When reading a single rectangu lar area, at first, it is rapidly shifted upward in the area of temporary storage, and then the image of this region is slowly read (the algorithm is fully consistent with a partial frame). The recorded images are combined after transmission to Earth. The TESIS operated in the mode of recording of full frames by parts since July 2009. For further combination of parts, read areas are superimposed on each other. The mechanism of the blurring formation in such frames differs from full images, which entails the appropriate adaptation of image processing methods (discussed below).
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PROCESSING METHOD OF IMAGES OBTAINED
CCD matrix Output register Output line Workspace of the CCD matrix Area for temporary storage Read areas

177

ADC

Y0 Y1

X0 X () Full frame entirely

1

(b) Partial frame

(c) Full frame by parts

Fig. 3. Methods of image recording of the TESIS.

IMAGE PROCESSING METHODS Image Alignment. Stabilizing system of the CORONAS PHOTON spacecraft provides stabilization of the axis of the satellite at the center of the Sun; the pointing accuracy is 5, sensors of angular rotation limit the rotation of the satellite around this axis within the accuracy of 0.3 ang. min/s. Shifts and rotations of the satellite do not go beyond these ranges, however, they lead to a significant displacement and the rotation of the solar images on the CCD matrices of the TESIS. The problem of linkage of the solar system coordi nates in any given image to the coordinates­pixels of the CCD matrix is solved for each frame separately. For this purpose, the information from TESIS star sensors is used, and the image of the Sun is analyzed. The data from TESIS is subject to this processing after unpacking of the telemetry information. Further information about the rotation and displacement is stored in the headers of image files. Star sensors (OS) are used to keep track of the rota tion angle of the satellite and to determine the rotation angle of the Sun on the images from the TESIS equip ment. Star sensors are two coaxial contradirectional telescopes, installed on a separate platform. The axis of sight of star sensors is perpendicular to the Sun. star sensors record the image of the starry sky, and the angle of the satellite is determined by these frames after the transmission to the Earth. To define the binding of solar system coordinates to the coordinates of the CCD matrix, the position of the solar limb in the image is determined. The concept of solar limb depends on the recording channel, i.e., in the channel 304 å the image is formed mainly by lines
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of cold He II 303.78 å, and the solar disk in it is several times brighter than the surrounding corona. There fore, for the channel 304 å, the limb is determined by a sharp drop in the intensity along the radius. In recording channels 132 å and 171 å, images are formed mainly by the spectral line Fe IX 171.07 å, with the luminescence temperature of 0.8 million K. In this line, the limb is defined by the maximum brightness caused by the doubling of the optical thickness of the corona when ascending over the Sun's surface. The determination of the limb position is con ducted in several steps: (1) rough determination, i.e., through the center of mass of images, and (2) the pre cise determination of the iterative procedure. To this end, several rays are drawn to the center of the Sun from different angles, with respect to the horizontal axis (currently, 1000 rays are used with a step 0.36°); the image is scanned along each ray. On the ray in the area of a presumptive limb, the point of maximum fall of brightness or maximum brightness is defined (depending on the recording channel). The obtained positions of the limb can be approximated by a circle. The acquired radius and center of the circle are used in the next step of iteration. The deviation of the obtained points of the limb from the calculated value is used to determine the area of the alleged search. The iterative procedure is stopped when the deviation of parameters of the circle of nth and (n + 1) steps is within 1 pixel. The obtained information is recorded in the file header. Dark signal recording. The dark signal of the CCD matrix is described well by the plane Sd = Ax + By + C.


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Subtracting the first equation from the second, we obtain

S
or

i, k + 1

-S

i, k

= (S 0)

i, k + 1

- (1 -)(S 0 )i, k ,

Fig. 4. The frame of the 171 å channel (on the left), regis tered as a whole, and the calculated blur (on the right).

(S 0 )i, k + 1 = (1 -)(S 0 )i, k + (Si, k + 1 - S i, k ). The last relation is a recurrence formula relating the intensity S0 at (k + 1) line to the intensity at k. The resulting formula can be used to successively restore the signal on the entire matrix. When registering the full frame by parts, the blur ring is also influenced by all the points of the column S
i, k

In the first approximation, constants A, B, and C were determined by averaging carried out over a series of frames processed manually. For a more accurate accounting of the dark signal, the dark signal of the first approximation is subtracted from the image, pix els with intensity above the threshold are clipped, and the remaining approximation is carried out according
' to the formula S d = A ' x + B ' y + C ' . Obtained coeffi cients give the compensation for the second approxi mation.

= (S 0 )

i, k

+

k' = 1



N

(S 0 )

i, k '

= (S 0 )

i, k

+ Ci .

Thus, to eliminate the blurring effect, it is neces sary to calculate the constants i for each column i. Summing up all the lines of the image, we obtain

k' = 1



N

S

i, k '

=

k' = 1



N

(S 0)

i, k '

+ NCi = (N + )Ci,

-1

from which it follows

In the case of processing of a full frame, registered by parts, the following method is used. The top (not illuminated) part of the image contains only the dark signal and blurring. Since the dark signal depends mainly on the x coordinate of the CCD matrix (this feature was determined by the processing of frames received in one part), to compensate for the dark sig nal it is necessary to subtract the top of the frame from the rest. The same operation removes the blurring (see below). The blurring recording. An example of blurring for the frame of the 171 å channel, registered in one part, is shown in Fig. 4. Consider the deletion algorithm. If there are no other effects, let the signal on the CCD matrix be determined by the two dimensional array Si, k , and undistorted by blurring signal be determined by (S0)i, k. Then, because of the blurring, intensities of all points, lying below, influence the resulting signal for each point ( i, k):
k -1

Ci = (

k' = 1



N

S

i, k '

) N +

(

-1

).

S

i, k

= (S 0)

i, k

+

k' = 1



(S 0 )

i, k '

, where = t 2 t1, t1 is

the exposure time, and t2 is the one line time shift. We write a similar equation for the (k + 1) line

S

i, k + 1

= (S 0 )

i, k + 1

+

k' = 1



k

(S 0 )

i, k '

.

The blurring compensation is made by the rowwise subtraction of Ci from the original image. Blurring compensation methods are inapplicable in the case when there are filled regions in the frame (which arise, for example, when registering flares). In these cases, the use of these algorithms leads to the for mation of artifacts in the regions lying above the filled area. By combining images, taken with different expo sure times, we can achieve the expansion of the dynamic range and eliminate the appearance of filled regions in the images. The use of these images to subtract the blur ring excludes the manifestation of such artifacts. Note that since the top of the image is not covered by the Sun during the recording of the full frame by parts and, therefore, it does not contain filled areas, then by calculating the coefficients Ci on the part of the image (for example, by averaging several lines), it is also possible to bypass the computational errors. The recording of the flat field. It is easier to measure the function of the flat field during the flight (Kuhn et al., 1991; Moses et al., 1997). This requires a special program of observations with the recording of a series of frames, shifted relative to each other. Consider the general approach to the determina tion of the flat field function. Let the flat field (which in our case is determined by the transmission of the CCD matrix filter) at the point r = (x, y) of the CCD matrix be given by the function f ( r ) . For the ideal fil
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179

ter f ( r ) = 1 . Due to uneven transmission of the real filter f (r ) = 1 + g(r ). We assume that the defects in the filter are uniformly distributed over the entire area of the CCD matrix and their sizes are small. In the absence of other effects, the signal on the matrix S (r ' ) at the point r ' = r + d will be determined by the fol lowing formula

Y

S(r + d ) = f (r + d )S0(r ),
where S0 is the undistorted image of the Sun, and d = (d x, d y ) is the image shift relative to the origin (see Fig. 5). For the N series of images with shifts di :

r

r' =

r+

d

i

Si

di X

Si (r ) = S(r + di ) = f (r + di )S0(r ).
Summing over i

S0
Fig. 5. The determination of the function of the flat field on a series of images, displaced relative to each other.

i =1



N

S i (r ) = S 0(r )

i =1



N

f (r + di )

= S 0(r )N (1 + [

i =1



N

g(r + d i ) ] N ).

number of images must be sufficient (we used a series of 50 images). --Each frame is processed, the background and blurring are removed. --Relative shifts of images di . --Images of the Sun are brought to the center of the frame and averaged. --Every single image is divided by the average. Thus, separate pieces of the function of the white field f i are calculated. --The functions f i are linked. flat field masks, using this algorithm, of the field for the different channels are shown in Fig. 7. To correct the flat field, the selected image is divided by the corresponding mask (or its part, in the case of recording of a partial frame). Its results are pre sented in Figs. 8 and 9 for channels 171 å and 304 å, respectively. The exact combination of images. At various stages of image processing (e.g., in determining the flat field, or composing the full frame from frames recorded in parts) you need to know the relative shift between images. In these cases, pixel accuracy is not enough. Let us describe an original algorithm for finding the shift between the images with an accuracy of down to a pixel. Denote the selected images by S1(r ), S 2(r ) , r = (x, y). The shift, at which images S1(r ) and S 2(r ) are combined, is determined from the maximum cor relation coefficient

With increasing N: [ g ( r + d i ) ] N g , while g does not depend on the coordinates on the CCD matrix. We assume g = 0. Then we obtain the follow ing approximation for S 0( r ):


N

S 0(r ) = [

i =1



S i (r )] N .

(1)

Thus, having a series of images, shifted relative to each other, we can eliminate the effect of the flat field by the usual averaging. Then, the function of the flat field can be obtained as follows

fi (r ) = f (r + di ) = Si (r ) S0(r ),

(2)

where the function S 0(r ) is defined by (1). The equation (2) holds for the points, whose inten sity is greater than the background level and less than the level of the filling of the image. Given that the image of the Sun occupies a limited area on the CCD matrix, the formula (2) defines values of the function of the f i flat field only in this region. The function of the flat field for all points of the matrix can be obtained by the linkage of independent functions fi . The shift di should be chosen so that images of the Sun S i together covered the entire matrix. Thus, the algorithm of calibration of the flat field is composed of the following steps. --A special series of images (see Fig. 6) is com posed, which are shifted relative to each other and completely covers the entire area of the matrix. The
SOLAR SYSTEM RESEARCH Vol. 45 No. 2 2011

R(d ) =



S1(r )S 2(r - d ),

d = (d x , d y ) .

The search for maximum requires enumeration of all the possible values of d, which is expensive (in terms of computer time). The method, based on the Fourier


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Fig. 6. An example of a series of images of the 171 å channel, obtained during the observational program to determine the flat field. A complete series consists of 50 images recorded sequentially in 30 s each.

1.2 1.0 0.8 0 500 1000 1500

1.4 1.0 0.6 2000 0

500

1000

1500

1.4 1.0 0.6 2000 0

500

1000

1500

2000

Channel 132 å

Channel 171 å

Channel 304 å

Fig. 7. Functions of the flat field for different channels of the TESIS equipment. On top of the image there is the intensity profile along the central line.

transformation, allows us to determine correlation coefficient values for significantly less time. If we transform functions S1(r ), S 2(r ) so that they satisfy the periodic boundary conditions
Si (x + H x , y) = S i (x, y), Si (x, y + H y ) = S i (x, y), i = 1, 2 , ...; where H x and H y are horizontal and ver tical image dimensions, then from the Wiener­ Khinchin theorem it follows that

R = Re F (F (S1)F (S 2 )) ,

(

-1

)

(3)

where F and F­1 are direct and inverse Fourier trans form. The calculation of correlation coefficients by the formula (3) is carried out using the algorithm of fast Fourier transform (FFT). The use of the FFT signifi cantly reduces computer time costs and does not

require an explicit conversion of functions Si (r ) to a periodic form. In this case, correlation coefficient val ues are calculated simultaneously for all values of the shift d . The accuracy of determining the shift using this method is 1 pixel. To achieve higher recording precision, the maximum correlation coefficient should be searched with subpixel accuracy using inter polation. For interpolation, we applied the approxi mation method using a surface with the minimal cur vature. The shift of the image on the resulting distance was performed using the standard rot function from the IDL (Interactive Data Language). CONCLUSIONS In 2009, as a part of the TESIS experiment onboard the CORONAS PHOTON spacecraft, a huge number of images and spectroheliograms of the Sun were taken
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Fig. 8. An example of the flat field effect on the image of the 171 å channel. On the left, the flat field is not adjusted; on the right it is corrected.

Fig. 9. An example of the effect of the flat field on the image of the 304 å channel. On the left, the flat field is not adjusted; on the right it is corrected.

in SXR and EUV spectral ranges. The TESIS image database of the zero level represents a set of FITS files. Currently, the database contains about 300 thousand images from different channels, most of which are telescopic channels. To process files of the zero level (both primary and subsequent scientific processing) we used a high level programming language, IDL. For the initial treatment on the basis of the above algorithms, a software pack age TES_PREP was developed. To date, the majority of frames passed the primary treatment (solar coordinates were defined, the back ground and blurring were removed, the flat field was corrected, sewn footage was recorded by parts). The database of processed images contain about 50 000 files. Currently, we are working on opening this image database to free Internet access.

no. 218816 (SOTERIA project, www.soteria.eu) of the Seventh Framework Programme of the European Union (FP07/2007 2013). REFERENCES
Kotov, Yu.D., Satellite Project "CORONAS­PHOTON" for Study of Solar Hard Radiation, 35th COSPAR Sci. Assem., Paris, Jul. 18­25 2004, p. 1283. Kuhn, J.R., Lin, H., and Loranz, D., Gain Calibration Nonuniform Image­Array Data Using Only Image Data, Publ. Astron. Soc. Pacific, 1991, vol. 103, p. 1097. Kuzin, S.V., Bogachev, S.A., Zhitnik, I.A., et al., The TESIS Solar Imaging Spectroscopy Experiment on Board the CORONAS­Photon Satellite, Izv. Akad. Nauk, Ser. Fiz., 2010, vol. 74, no. 1, pp. 39­43 [Bull. Russ. Acad. Sci. Phys. (Engl. Transl.), 2010, vol. 74, no. 1, p. 33]. Kuzin, S.V., Zhitnik, I.A., Shestov, S.V., et al., THESIS Experiment for CORONAS­FOTON Spacecraft, Astron. Vestn., 2011, vol. 45, no. 2. Moses, D., Clette, F., Delaboudinire, J. P., et al., EIT Observations of the Extreme Ultraviolet Sun, Sol. Phys., 1997, vol. 175, pp. 571­599. Oraevskii, V.N. and Sobel'man, I.I., Comprehensive Stud ies of Solar Activity on the CORONAS­F Satellite, Pis'ma Astron. Zh., 2002, vol. 28, p. 457 [Astron. Lett. (Engl. Transl.), 2002, vol. 28, no. 6, p. 401]. Sobel'man, I.I., Zhitnik, I.A., Ignat'ev, A.P., et al., Solar X­ray Spectroscopy in 0.8­30.4 nm Range during TEREK and RES Experiments at CORONAS­I Satel lite, Pis'ma Astron. Zh., 1996, vol. 22, p. 605.

ACKNOWLEDGMENTS This work was partially supported by the Russian Foundation for Basic Research, project no. 08 02 01301 a and 08 02 13633 ofi_ts, by the Basic Research Program of the Presidium of the Russian Academy of Sciences (Program 16, Part 3, Basic Research Program of the Department of Physical Sci ence of the Russian Academy of Sciences "Plasma Processes in the Solar System"), and project
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