\documentclass{kluwer}
\usepackage{epsfig}
\newdisplay{guess}{Conjecture}
\begin{document}
\begin{article}
\begin{opening} 
\title{Solar Soft/Hard X-ray Photometer--Imager aboard the  INTERBALL-Tail Probe}
\author{J. \surname{Sylwester}\thanks{email{ js@cbk.pan.wroc.pl}}}
\institute{Space Research Centre, Polish Academy of Sciences, 51-622, Kopernika~11, Wroc\l aw}
\author{F. \surname{F\'{a}rn\'{\i}k}}
\institute{Astronomical Institute, Academy of Sciences of the Czech Republic, 251 65 Ondrejov}
\author{O. \surname{Likin}}
\institute{Space Research Institute, Russian Academy of Sciences, Profsoyuznaya St. 84/32, Moscow}
\author{Z.~Kordylewski, M.~Siarkowski, S.~Nowak, S.~P\l ocieniak, W.~Trzebi\'{n}ski}
\institute{Space Research Centre, Polish Academy of Sciences, 51-622, Kopernika~11, Wroc\l aw}
\runningauthor{J.~Sylwester {\em et~al.}}
\runningtitle{Soft/Hard X-ray Photometer-Imager}
\begin{abstract}
We describe the RF15-I instrument, comprising a solar photometer and an 
imager, designed for multiband high time resolution measurements of 
integral solar fluxes in the energy range between 2~keV and 240~keV as 
well as for imaging of solar flares in the 2~-~8~keV energy range. The 
instrument was launched in August 1995 aboard the INTERBALL-Tail 
spacecraft. Description of the construction and operations is presented. 
The overall performance and the high sensitivity of the photometer is 
shown on examples. The X-ray tomograph-imager contains a unique 
rotationally modulated collimator. It provides sets of one-dimensional 
scans of flares taken at varying angles due to spinning of the 
satellite. We present principles of the algorithm for imaging from these 
data and show example of reconstructed flare image taken in the  2~-
~4~keV range.  
\end{abstract}
\keywords{solar physics; flares; X-ray photometry; X-ray imaging, instrumentation}
\end{opening}
%%%%%%%%%%%%%%%%%%%%%Section Introduction %%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction} 
The Astronomical Institute of Czech Academy of Sciences has been 
involved in solar X-ray photometry since 1969. Early photometers have 
been placed on board a number of spacecraft including a series of 
Prognoz (5-10) elongated orbit probes. The most recent of these 
photometers is RF15-I (hereafter RF) instrument, which has been included 
as a part of the {\em INTERBALL-Tail} Mission. The instrument has been 
making measurements since August 6, 1995. As a partner in the RF 
experiment, the Solar Physics Division of Polish Space Research Center 
became involved in the programme (in 1986), contributing to the unique 
X-ray Tomograph-Imager (XTI), a novel part of the instrument. Present 
circumstances allow the Polish Team to represent the PI for entire RF 
instrument and took over the responsibility for scientific output of the 
experiment. The present paper describes basic characteristics of the RF 
photometer, imager and presents examples of the data received. In a 
subsequent paper we will present details of data reduction and analysis. 
The photometer and XTI are physically and electronically separate. They 
are however controlled by a common onboard computer PRAM.

The {\em INTERBALL-Tail} is a spin-stabilized satellite placed on a 
highly elongated orbit, presently with $\sim$182000~km apogee and 
$\sim$24000 km perigee. The orbital period is $\sim$96~hours. The 
satellite is directed from IKI (Russia) under the guidance of Prof. 
A.~Galeev and Prof. L.~Zelenyi. It operates within the STEP programme of 
multinational cooperation. Expected orbital life of the satellite 
extends till October 2000. The normal to the satellite instrument plate 
is pointed towards the solar centre within $\pm $10$^{\circ }$ thanks to 
spin-stabilization of the spacecraft. One satellite revolution takes 
$\sim $118~s. Every few days the satellite rotation axis is being 
repointed towards the solar centre as the Sun moves away at the rate of 
$\sim $1$^{\circ }$/day due to Earth motion along the orbit.
% section General
%section{The Photometer} %%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{General}

The RF was developed in order to facilitate high-time resolution 
measurements of integral solar flux in the spectral energy range between 
2~keV and 240~keV and to image solar flares in the bands 2~-~4~keV and 
4~-~8~keV from rotationally modulated data (X-ray Tomograph-Imager, 
XTI). The photograph of RF instrument is shown in Fig.~1. 
%%%%%%%%%%FIGURE 1 General appearance of the RF %%%%%%%%%%%%
\begin{figure}
\centerline{\epsfig{file=fig1.eps,width=12.cm}} 
\vspace{.4cm} 
\caption[]{
General appearance of the RF soft X-ray Photometer-Imager. The 
dimensions of the box shown are 300 $\times 155\times 254~$mm. The box 
which contains both the photometer and the imager is placed atop the 
solar oriented platform of the spacecraft. RF is controlled using  PRAM 
on-board computer placed inside the pressurized section of the satellite 
(not shown).
} 
\end{figure}
%%%%%%END%%FIGURE 1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
The RF is equipped with five detector systems: 
\begin{itemize} 
\vspace{-.27cm}
\item  Proportional gas-filled detector.  
\vspace{-.3cm} 
\item  NaI(Tl) scintillation detector with Al window.
\vspace{-.3cm}
\item  Three silicon detectors sensitive to charged particles (radiation belt detectors).
\vspace{-.3cm}
\item  Proportional detector behind the XTI.
\vspace{-.3cm}
\item  XTI attitude sensor (small optical refractor $\phi=6$\,mm). 
\end{itemize}
Below we describe in more detail both instruments.
%%%%%%%%%%%% Table 1  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table} [bp] 
\caption{
Nominal energy ranges and designations for the lower energy photometer 
channels (formatted into standard, common block of telemetry).
}
\begin{tabular}{ccccc}
\hline
Channel	\#		&  s1  	&  s2 $^{\ast }$ 	&  s3  	&  h1 $^{\ast }$ 	\\ \hline
Energy band [keV]	& $2-3$ 	& $3-5$ 		& $5-8$ 	& $10-15$ 		\\ 
Detector type		& Prop. 	& Prop. 		& Prop. 	& Scint. 		\\ 
\hline
$^{\ast }$recorded in patrol$/$calibration mode 
\end{tabular}
\end{table}
%END Table 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{The Photometer}
In Tables~I~-~IV we present nominal energy ranges and essential 
characteristics of the proportional and scintillation detectors used in 
RF photometer. We split the presentations of detector's properties into 
separate Tables (I and II) according to the way the data are formatted 
and put into the telemetry.

The proportional detectors consist of two cylindrical compartments with 
steel walls $\sim$1.2 mm thick sharing the same gas. The section exposed 
to the solar radiation is equipped with the Be window in order to select 
the radiation with the energy above $\sim$1~keV. The hidden (twin) 
section is illuminated by the radioactive calibration Fe$^{\rm 55}$ 
source. Corresponding calibration signal is constantly probed in order 
to detect ageing, leaking and other possible effects which may cause 
deterioration of the gas gain. Special electronic feedback 
%%%%%%%%%%%%%Table 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\begin{table} [bp] 
\caption{
Nominal energy ranges and designations for high-energy photometer 
channels recorded (in flare mode) into individual telemetry blocks. The 
measurements are reported every 125 msec.
} 
\begin{tabular}{ccccc} 
\hline 
Channel \# &  h2  	&  h3  	&  h4  	&  h5  \\ 
\hline 
Energy band [keV] 	& $15-30$ 	& $30-60$ 	& $60-120$ & $120-240$ \\ 
Detector type		& Scint. 	& Scint. 	& Scint.
& Scint. 	\\ 
\hline 
\end{tabular} 
\end{table} 
%END Table 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% %TABLE 3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\begin{table}[b] 
\caption{
Essential characteristics of the proportional detector.
} 
\begin{tabular}{lllll} 
\hline 
Aperture 	& Window 	& Gas Filling
& Gas Depth 	& Energy resolution 	\\ \hline 4.5 mm$^{2}$ 	& Be 
150$\mu$m 	& Ar+10\%CO$_{2}$,~350~Torr	& 16~mm 	& 19\% 
at 5.9~keV 	\\ 
\hline 
\end{tabular} 
\end{table} 
%END Table 3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%TABLE 4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\begin{table}[b] 
\caption{Essential characteristics of the scintillation detector.} 
\begin{tabular}{ccccc} 
\hline 
Aperture 	& Window 	& Crystal 
& Diameter/Thickness 	& Energy resolution 	\\ 
\hline 
1452 mm$^{2}$
& Al $94\pm 3\mu $ 	& NaI(Tl) 	& 43/8~mm 		& 22\% 
at 59~keV 	\\ 
\hline 
\end{tabular} 
\end{table}% 
%END Table 4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
system regulates accordingly the high voltage level on both anodes of 
the detector counteracting in this way the effects of gain variations. 
The energy discrimination thresholds are thus kept in place independent 
of the gain variations. However, towards the end of 1997, the activity 
of Fe$^{\rm 55}$ calibration source (7 years from fixing) decreased more 
than 10 times and went outside the limits of self-correction. Details of 
the gain time variations will be presented in a subsequent paper where 
the history of discrimination level positions will be given for entire 
duration of the mission. The average background count rate is $\sim 
$10~cts/s for the proportional detector. 

The scintillation detector contains 8~mm thick NaI(Tl) crystal with the Al filter 
($0.25\pm0.01 \, g/cm^2$ mass thickness) placed in front and a photomultiplier tube. 
This detector has its own calibration source (Am$^{\rm 241}$) but without feedback control. 

In Figure~2, we present efficiencies of the proportional and scintillation detectors 
plotted against the photon energy. The incident solar photon flux is transmitted by 
detector window and absorbed by gas/crystal with the corresponding efficiencies. 
The redistribution over energies according to spectral response function takes place 
afterwards.  
%%%%%%%%%%%%%%%%%%%%%FIGURE 2 Spectral efficiency %%%%%%%%%%
\begin{figure}
%\vspace{2cm}
\centerline{\epsfig{file=fig2.eps,width=12.cm}} 
\caption{
Spectral efficiency of the proportional (left) and scintillation (right) 
detectors as a function of photon energy.
}
\end{figure}
%%%%%%END%%%%%%%%%%%%FIGURE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The proportional detector collects soft X-ray photons in three energy 
bands 2~-~3~keV, 3~-~5~keV and 5~-~8~keV (see Table~1).  The detector 
window is placed slightly below the instrument cover opening. This 
geometry causes the effective aperture to vary by few percent as the 
solar illumination angle changes with the satellite spinning phase. 
Another factor contributing to modulation of the signal is that the 
absorption depth of the photon also depends on the rotation phase. This 
latter effect is especially important for higher energy radiation, for 
which the photon absorption length in the gas is greater than the 
detector depth. 

The scintillation detector measures the hard X-ray flux in five energy 
bands (see Tables~I and II). In flare mode the measurements are made 
every 0.125~s in the four highest energy channels. For these channels, 
the data are allowed to be transmitted to the telemetry provided that 
corresponding rate thresholds (40~cts/s) are exceeded for the four 
consecutive seconds. Otherwise, the data are not written in order to 
secure the telemetry volume. The channel  h1  output is recorded 
differently. It is formatted together with the signal from the 
proportional detectors and sent to telemetry all the time (every 2 or 
8~s) depending on the mode (flare  or  patrol). The adopted mode 
names may however be somewhat misleading, since the most of data have 
been collected in so-called  flare  mode. The reason for this was the 
selection of very low threshold for flare trigger. Actually it has been 
set at the level corresponding to microflare (few cts/s). Switching 
between patrol/flare modes is controlled onboard based on count rates 
recorded in   s2  channel. Early in the mission, the instrument 
operated mostly in the flare mode, for periods up to several hours. 
Later on, following the change in the detector feedback control, the 
frequency of switching between the modes increased, and presently the 
photometer operates preferentially in patrol mode except for flares 
above {\em GOES} class B5~--~B7.

During the patrol mode the calibration of the scintillation detector is 
made approximately every 2~hours (cf. Table~I). For calibration, a 
moving arm equipped with Am$^{\rm{241}}$ radioactive source (half-decay 
time 432.2 years; energy 59.6~keV) is being mechanically inserted into 
the FOV of the detector. The calibration arm partly occults the aperture 
contributing to the signal in  h1. In this way during the calibration 
the recorded signal responds in most cases to the calibration source 
quanta only. The other data reported at the time of calibration 
(s2~fluence)  represent solar signal. The scintillation detector has 
no feedback  control and therefore the ageing effects can be deduced 
only from analysis of time variations of the calibration level readouts. 
This analysis is in progress.

%%%%%%%%%%%Section Example Observations %%%%%%%%%%%%% 
\section{\protect\smallskip Examples of Photometer Observations}
The RF instrument has been collecting data since August 6, 1995. Early 
during the mission, the measurements were made usually in the flare mode 
(i.e. in four channels, cf.~Table~I). Later on, the patrol mode 
measurements prevail. In Figs.~3 and 4, we show examples of data 
collected early during the mission. In Fig.~5 we compare the RF and {\em 
GOES} signals at appropriate channels. The comparison is presented for a 
period when the  quiet  solar X-ray signal has been at the very low 
level. Direct correspondence is observed which allows to relate the {\em 
GOES} flux to the appropriate RF flux and vice versa. The linear 
fit gives the following formula relating the two.
\begin{equation}
F_{GOES}=2.98\,10^{-9}\times (F_{\rm s1}-0.35)\,\,
\end{equation}
where $F_{GOES}$ is the flux in 1~-~8\,\AA\, band (in $W/m^2$) and  $F_{\rm s1}$ 
is the count rate in   s1  RF channel.

The analysis of data scatter indicates, that RF sensitivity is 
approximately equivalent to that of {\em GOES}.
%%%%%%%%%%%%%%FIGURE 3  flare of 20 Oct 95  %%%%%%
\begin{figure}
\centerline{\epsfig{file=fig3.eps,width=11.cm,height=12.cm}} 
\vspace{.3cm}
\caption{
Time variability of solar X-ray emission as recorded in flare mode (every 
2~s) in four lower energy channels: s1,  s2,  s3  and  h1 for 
a selected time interval on 20 October 1995. The measurements cover 
7~hours of uninterrupted observations. The smallest/largest enhancements 
seen correspond (in {\em GOES} X-ray classification) to B1.3 and M1.5 
flares respectively. In channels  s1,  s2 and  h1, the 
 basal  level contains valid solar signal. In channel  s3, the 
basal level represents the detector background only.
}
\end{figure}
%%%%%%END%%%%%%%%%%%%FIGURE 3 %%%%%%%%%%%%%%%%%%%%%%%
%%FIGURE 4 light curves of the 20 October 1995 M1.5%%%
\begin{figure}
\centerline{\epsfig{file=fig4.eps,width=11.cm,height=12.cm}} 
\vspace{.3cm}
\caption{
A portion of Figure~3 showing the light curves for the 20 October 1995 
M1.5 flare in more details. RF light curves are plotted in the upper and 
the fourth panels. Corresponding  {\em GOES} lightcurves are presented 
in between for comparison. The observed  variations in the 
(s2/s1) flux ratio  have been interpreted in terms of an average 
source plasma temperature. Resulting temperature variation plot is 
presented in the lowest panel.
}
\end{figure}
%%%%%%END%%%%FIGURE 4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%FIGURE 5 RF-{\em GOES} Correlation
\begin{figure}
\centerline{\epsfig{file=fig5.eps,width=11.cm,height=9.cm}} 
\vspace{.3cm}
\caption{
Comparison of RF and {\em GOES} records for corresponding energy bands 
of both instruments. Few weak flares have been observed on 8 August 
1995, within the period selected for the comparison. This is illustrated 
in the upper panel where the light curves are plotted. In the bottom 
panel the corresponding correlation diagram is presented with the value 
of correlation coefficient {\em r} given.
}
\end{figure}
%%%%%%END%%%%%%%%%%%%FIGURE 5 %%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%FIGURE 6 {\em BATSE} light curves %%%%%%%%%%%
\begin{figure}
\vspace{0.6cm}
\centerline{\epsfig{file=fig6.ps,width=11.cm,height=12.cm}} 
\vspace{0.5cm}
\caption{
Comparison of higher energy RF records with corresponding {\em Yohkoh} 
HXT  and {\em BATSE} (bottom) light curves for the 1 December 1997 
flare. The rates observed in RF channels shown are not corrected for the 
pile-up and dead-time effects which may lower by up to 20\% the rates 
observed around flare maximum.
}
\end{figure}
%%%%%%END%%%%%%%%%%%%FIGURE 6 %%%%%%%%%%%%%%%%%%%%%%%
One of the noticeable deficiencies of RF photometry is the signal 
modulation due to spacecraft rotation. These observed modulations have 
few percent relative amplitudes and the period around 118~s. In order to 
remove the fluctuations, we have determined appropriate phase modulation 
profiles (for each of the channels separately) using epoch folding 
(details of the procedure will be described in a subsequent paper). 
These folded profiles have been next used in order to remove the 
modulation from the raw data. At present, we are in the process of 
systematic reformatting and regularizing the data. At our web site 
\newline ({\tt www.cbk.pan.wroc.pl/rf15-i$\_$www/RF15-I 
$\_$observations.htm}) we put all the data processed so far along with 
short explanations. On a positive side is that the modulation of the 
signal due to the satellite rotation allows for distinguishing between 
solar X-ray emission and non- solar particle contribution (the last 
being usually not modulated). 

One of the important advantages of RF measurements is that there are 
many periods where the solar signal has been measured every 2~s 
continuously for up to 40 hours in the four energy bands. 

The overall data coverage of the solar X-ray photometry is $\sim 85\%$. 

The physical analysis of data is in progress. In the example shown in 
Figure~4 (bottom panel) we present   derived variations of coronal 
source plasma temperature as determined in the isothermal approximation 
from the ratio of fluxes recorded in the  s1  and  s2  bands. One 
may notice that the scatter in derived temperature is relatively small 
and that the temperatures are within realistic range also for periods 
where no flare in progress has been reported. Details of the physical 
data analysis will be published in a forthcoming paper.

As concerns the data collected in the higher energy channels, reliable 
measurements have been made for hundreds of events (Siarkowski {\em et 
al.}, 1999). Analysis of this data indicates that during strong events, 
pile-up effects might contribute to the flux in higher energy channels, 
as well as the detector dead time effects may become important (as 
pointed up by the Referee). The dead-time for electronics of both 
proportional and scintillation counters is $8\mu$s, larger than 
intrinsic detector's physical dead-times. Therefore, the effects of 
pile-up and dead-time corrections will become important (at 10\% level) 
for count rates above $10^4$~cts/s. A more detailed consideration of 
these problems will be given in the forthcoming paper. 

For the M1.2 flare shown in Fig.~6, RF recorded the fluxes in  h2  and 
 h3  energy channels. This flare has been observed also by {\em 
Yohkoh} HXT and {\em BATSE}. We put corresponding lightcurves in the 
Figure for the comparison. The overall agreement of signals in 
corresponding energy bands is very good (for description of the HXT 
construction see Kosugi et. al., 1991). Detailed  cross-calibration 
between RF, {\em GOES}, HXT and {\em BATSE} measurements is in progress.

The higher energy RF data are also presented and available from our web server.

While crossing van Allen radiation belts the detectors were designed to 
be switched-off. We noticed however that on several occasions the 
particle flux has been low enough not to trigger the in-belt flag. 
Therefore the detectors did not switch-off and recorded signal due to 
particles. This resulted in a characteristic pattern of recordings in 
all channels of RF. Such particle events can be easily recognized 
through their specific inverted/flat energy spectrum. On at least one 
occasion the non-solar hard X-ray event has been detected, originating 
from the SRG1900+14 burst (Sylwester {\em et al.}, 1998). 

We have encountered a number of problems during data reduction and 
prompt analysis. For example, the count rate level from large flares 
(i.e. above M5-M6 {\em GOES} class) exceeds the capacity of counters 
(set at 32000 and 64000 hits per integration time in particular 
channels). This caused counter wrapping, sometimes many-fold.

% section{X-ray Tomograph-Imager}%%%%%%%%%%%%%%%%%%%%
\section{\protect\bigskip  The X-ray Tomograph-Imager}
A concept of imaging modulation collimator is based on reconstruction of 
full two-dimensional images from sets of one-dimensional projections. 
The principles of the (rotating) modulation collimator have been 
described in-depth by Oda {\em et al.} (1976) and Tsuneta (1984). 
Progress in technology and three-axis attitude stabilization of 
satellites resulted in development of the fixed imaging collimators 
(HXIS; van Beek, 1976) and telescopes with the CCD devices ({\em Yohkoh} 
SXT). However, high-energy (above 10~keV) images can  be obtained by 
making use of modulation collimator technique alone (e.g., {\em Yohkoh} 
HXT), in which a concept rotating modulation collimator aboard a spin-
axis stabilized spacecraft may be the simplest form of instrument 
hardware. Presently, the HESSI instument (under development, Lin {\em et 
al.} 1998) also incorporates this concept. One of the best examples of 
the results obtained using rotationally modulated collimators are the 
hard X-ray images of solar flares from the Japanese satellite {\em 
HINOTORI} (Tsuneta, 1984). 

In disigning the X-ray Tomograph-Imager we incorporated a similar, but 
modified concept of the construction of the rotationally modulated 
collimator. In the following we present a description of this instument 
called X-ray Tomograph-Imager (XTI), principles of its operation and a 
brief information on the image reconstruction algorithm. More in-depth 
description of this imager will be given in a separate paper. 

The XTI consists of two units:
\begin{itemize}
\vspace{-.3cm}
\item The X-ray collimator, and
\vspace{-.3cm}
\item The optical solar disk sensor.
\vspace{-.2cm} 
\end{itemize}
The construction of the units is described below.

\subsection{\protect\smallskip  The X-ray Collimator (XRC)}
The purpose of XRC is to modulate and measure the X-ray signal from 
flares and the hottest part of active regions. Since the rotation axis of 
the {\em INTERBALL-Tail} satellite is mostly offset from the X-ray 
source by a few degrees, the recurrent transmission windows of the 
collimator become available for modulation of X-rays, as the phase of 
source relative to the optical plane of the collimator changes. The 
concept of the collimator construction adopted in XTI is presented in 
Figure~7. The essential construction characteristics of the collimator 
are illustrated in Fig.~8 and given in Table~V. The XRC consists of a 
system of three precisely co-aligned grid planes placed in front of the 
double proportional counter operating in the 2~-~4 keV and 4~-~8 keV 
energy ranges. The detector is analogous to that used in the photometer, 
but there are different electronics and discrimination thresholds. The 
feedback control is used to counteract the gain variations, as described 
earlier.

Due to rotation of the satellite, the X-rays from a solar source are 
modulated, depending on the actual phase of the rotation. The collimator 
field of view has a radius of $\sim 11^{\circ}$, and the collimator has 
been designed to have a number of narrow transmission windows separated 
by 4.8~arc~min. These selected design characteristics allow to isolate a 
flaring area in the Sun covering thus the entire flare without 
overlapping (provided it has extension smaller than $4.8\times 
4.8$~arc~min). In order to have a simpler pattern of modulation fringes, 
we decided to make grids of circular cross-section wires. A cheap and 
easy solution was to use standard copper wires. Copper has enough atomic 
mass to block the harder part of the radiation if of sufficient radius. 
We selected to use wires of $66.8\,\mu$m diameter on the front and 
bottom grids and $50.0\,\mu$m for the middle grid. The wire orientation 
has been fixed exactly parallel (to within $\pm 1\mu$m) between the 
three grid planes using an interferometric technique. The main 
characteristics of the collimator are given in Table~V and in Fig.~8. 
The grid plane positions, exact wire diameters and the pitch have been 
designed according to the physical requirements. The collimator 
construction allows for slight manufacture errors (8~$\mu$m) in placing 
grids within particular grid plane, without affecting the desired 
transmission pattern of the entire collimator.

%FIGURE 7  The XTI and the collimator %%%%%%%%%%%%%%%%
\begin{figure}
\centerline{\epsfig{file=fig7.eps,width=12.cm}}
\vspace{.2cm}
\caption{
The principle of the operation (left) and the photo of the X-ray 
collimator unit. The solar flare X-rays are illuminating the double 
proportional detector ({\bf d}) through a system of three grids. The 
front grid ({\bf a}) contains three regions i.e.: partly open area, 
occulting bar, and gridded area (shaded). The middle grid ({\bf b}) is 
half open and the bottom one is completely filled with grids. The grids 
are made of the copper wires precisely coaligned. The bottom grid is 
located immediately in front of the double proportional counter detector 
({\bf d}) with a window of 3$\times$\,10 mm size. In the photo (right) 
the entire collimator unit is presented (assembled and disassembled). 
The optical disk sensor is attached outside, parallel to the collimator 
axis.
}
\end{figure}
%%%%%%END%%%%%%%%%%%%FIGURE 7 %%%%%%%%%%%%%%%%%%%%%%%
\begin{table}[tbp] 
\centering
\caption{Essential characteristics of the Collimator (see ~Fig.~8)} 
%\vspace{3mm} 
\begin{tabular}{lccccc}
\hline
Length 	& Fringe	& FWHM 		& Transmission$^{\ast }$ 	& Energy bands 	& Readout	\\ 
 	& separation	& 		&  	in X-rays&  		& rate		\\ 
\hline
160 mm	& 4.8~arc~min 	& 11~arc~sec 	& 0.08 				& 2~-~4 keV	& 1/128 s	\\ 
	&  		&  		& 0.09 				& 4~-~8 keV	& 1/128 s 	\\ 
\hline
\end{tabular}
\vspace{2mm}
$^{\ast }${ratio of transmitted to illuminating fluxes; diffraction effects have been taken into account}
\end{table}

The exact location of the grid planes have been calculated according to 
a novel strategy. The novelty of the solution is the use of semi-
numerical interactive method of placing the grids. In case of the XTI, 
we specified the approximate values for the collimator length, thickness 
of grids, desired resolution and transmission fringe separation and 
found the optimum collimator design as presented in Fig.~8. The 
collimator grid system has been co-aligned by visible light technique 
with diffraction effects taken into account. We measured separately the 
transmission in X-rays. The area averaged rms alignment accuracy has 
been found to be $\pm 1\,\mu$m, and the maximum wire misalignment found 
is $\sim 10\,\mu$m.

As shown in Fig.~8, the front and the middle grid wired sections cover 
only a portion (approximately half) of the planes. The front grid has 
additionally an  occultation strip. The width of this strip is 
selected to be 6.2~mm allowing thus to ensure that the solar disk will 
be fully eclipsed (as seen from the detector window). With the Sun 
crossing the bar, the solar X-rays are totally blocked permitting 
measurements of the  background  signal (cf. Fig.~8). 

%%%%%%%%%%%%%%%%%%%%%FIGURE 8 Details of the Collimator Construction  %%%%%%%%%%
\begin{figure}
\centerline{\epsfig{file=fig8.ps,width=12cm}}
\vspace{.2cm}
\caption{
Details of mechanical construction of the collimator as seen from the 
side along the the wires (left) and from the top (three right circles). 
All dimensions are given in $\mu$m. The wires are of circular cross-
section with diameters $\phi = 66.8\, \mu$m for front and bottom grids 
and $\phi = 50.0\,\mu$m for the middle grid. Pitch is $75.0\, \mu$m in 
each grid plane. The diagram is drawn not to scale. In the right panel, 
the three grid planes are depicted as seen from the front. Preserved are 
the proportions between the grid sizes and gridded/occulted/open areas. 
The position of the detector window aperture ($3 \times 10$\, mm) is 
projected on the lower, fully wired grid.
}
\end{figure}
%%%%%%END%%%%%%%%%%%%FIGURE 8 %%%%%%%%%%%%%%%%%%%

In Fig.~9 we schematically draw the trajectory of a compact solar source 
(flare) as seen in the coordinate system of the collimator (front grid). 
Provided nutation is negligible, the solar source trajectory is a 
circular path crossing the open area, occultation bar and gridded area. 
Depending on the offset $\delta$ of the source relative to the axis of 
the collimator, a number of modulation patterns are expected:
\begin{itemize}
\vspace{-.3cm}
\item no bar occultation for $\delta < 0.54^{\circ}$
\vspace{-.3cm}
\item single partial bar occultation for $0.54^{\circ} < \delta < 1.55^{\circ}$
\vspace{-.3cm}
\item double partial bar occultation for $1.55^{\circ} < \delta < 2.63^{\circ}$
\vspace{-.3cm}
\item full modulation pattern (as in Fig.~9) for $\delta > 3.64^{\circ}$
\end{itemize}
%%FIGURE 9  Various phases of modulation   %%%%%%%%%%
\begin{figure}
\centerline{\epsfig{file=fig9.eps,width=7.cm}}
\vspace{.2cm}
\caption{
A scheme showing various phases of the modulation of the solar radiation 
passing through the collimator. The Sun is shown as a small circle with 
the X-ray source as a small spot placed inside. Due to rotation of the 
spacecraft the apparent position of the source, as seen from the 
detector window, follows the circular path. For a part of the rotation 
period (phase {\bf a}) no modulation of the signal is observed. At phase 
{\bf b} the source enters the occultation strip which angular width is 
more than the solar diameter and therefore, at phase {\bf c}, the solar 
soft X-ray radiation is totally blocked. In this period the signal 
recorded corresponds to the detector background. At phase {\bf d} the 
source enters the gridded section of the collimator and the signal is 
frequently modulated when the source crosses individual transmission 
windows. At each transmission window, the X-ray source is scanned at 
different angle (changing by $\pi/2$ between phases {\bf d} and {\bf 
f}).
}
\end{figure}
%%%%%%END%%%%%%%%%%%%FIGURE 9 %%%%%%%%%%%%%%%%%%%%%%%
An example of calculated characteristic pattern of the signal modulation 
is shown in Figure~10. 
%%%%%%%%%%%%FIGURE 10 The Pattern of modulation %%%%%%
\begin{figure}
\centerline{\epsfig{file=fig10.eps,width=12.cm}}
\caption{
Numerically simulated noisy pattern of the X-ray signal modulation. The 
individual phases of the depicted pattern correspond directly to the 
passage of the X-ray source through individual sections of the 
collimator (as indicated in Figure~9). The number of peaks in the 
modulated pattern depends on the angular distance $\delta$ of the source 
relative to the satellite spin axis. The profiles within individual 
fringes depend on the distribution of X-ray brightness within the 
localized emitting region.
}
\end{figure}
%%%%%%END%%%%%%%%%%%%FIGURE 10 %%%%%%%%%%%%%%%%%%%%%%

The actual position of the satellite rotation axis relative to the 
 optical  solar disk is monitored by a dedicated optical sensor unit 
described below. 

\subsection{\protect\smallskip  The Optical Solar disk Sensor (SDS)}
The optical solar disk sensor (SDS) was intended to be used in order to 
establish distance between disk center and the X-ray source. This would 
enable for potential identification of the active region contributing to 
the X-ray signal. By incorporating the satellite attitude data, it would 
be possible to determine the rotation phase relative to the celestial 
coordinate system, fixing thus the absolute source position on the disk. 

The SDS unit consists of the optical system which projects images of the 
solar disk on the system of two narrow slits. The optical axis of SDS is 
coaligned with the axis of the X-ray collimator. The slits are adjusted 
to be parallel to the occulting bar. Spinning of the spacecraft causes 
the projected optical solar disk to circle through the double slit 
system presented in Fig.~11. 
%%%%%%%%FIGURE 11 The Pattern of SDS modulation %%%%%%
\begin{figure}
\centerline{\epsfig{file=fig11.eps,width=7cm}}
\caption{
Scheme of the  motion  of the visible image of the solar disk across 
the system of the slits in the SDS unit. At crossing times t$_1$~-
~t$_8$~ the electronic system connected to the photodiode located behind 
the grids issues flags informing that the solar disk enters/leaves 
individual slits. Since the apparent angular width of one of the slits 
is twice the other, the on-board computer is able to recognize the 
direction of the motion and calculate the instant phase of the rotation 
from the slit crossing timing. The scheme is made up to show apparent 
angular scales as concerns slit widths and solar diameter.
}
\end{figure}
%%%%%%END%%%%%%%%%%%%FIGURE 11 %%%%%%%%%%%%%%%%%%%%%%

Behind the slit system, the photodiode monitors the overall optical flux 
passing through the slit system. A dedicated on-board computer routine 
analyzes the slit crossing times and determines corresponding phases of 
rotation and the solar centre offset angle based on the history of slit 
crossing times from the previous rotation. The slit crossing times were 
envisaged to be dumped to the telemetry after every 100 satellite 
rotations. 

It is by misfortune that during the pre-flight preparations immediately 
preceding the launch from the Baikonur, the aperture of the SDS optical 
sensor has not been cleared. As a consequence we are missing the data 
from this sensor. We have fortunately foresighted for such an 
unfortunate situation and pre-programmed a safe-mode activity for the 
XTI in such circumstances.

\subsection{\protect\smallskip  On-board data processing}

The signals incoming from the XTI are being processed in real time by 
the PRAM onboard computer and stored temporarily to the onboard memory 
before being sent to the ground. 

In order to effectively use the memory capacity, we devised an 
elaborated scheme of on-board signal processing, which saves the memory 
and allows to concentrate on flare events occuring between consecutive 
telemetry dumps. In particular, the signal from XTI X-ray detector is 
constantly monitored in order to detect the flare occurence. Flare 
intensity class is being estimated in real time and the decision is made 
on-board when and which observing sequence is to be executed. Even with 
such elaborated scheme, only $\sim 80$ compressed image modulation 
sequences  can be stored in the on-board memory between consecutive 
ground telemetry dumps (say one sequence per hour on average). 

The following XTI operation modes have been preprogrammed: 

\begin{itemize}
\vspace{-.3cm}
\item low activity -- only minimum and maximum X-ray rate values for a 
given S/C spin are stored;
\vspace{-.3cm}
\item high activity -- detailed modulated signal together with extreme 
and averaged values of the background from unmodulated signal are 
preserved. Interfringe  zeros  are discarded.
\vspace{-.3cm}
\end{itemize}
Such organization of the data collection compresses substantially the 
volume of the data to be recorded on-board, but necessarily needs the 
time stamp from the onboard clock to be assigned to each data package. 
In order to shorten the time info byte length, the  local clock  has 
been used giving only the data pack number in a sequence.

The telemetry storage threshold flag level is being determined on-board 
by comparing the X-ray signal with the dynamically changing remaining 
telemetry quota. This telemetry quota depends on a recent history of 
solar flare activity. If no flares have been observed towards the time 
of the following telemetry dump, the modulation patterns are forced to 
be recorded independent of the solar activity level, in order to fill 
the telemetry allocated. If a flare is being detected, the program seeks 
for the period of flare maximum to occur. When found, the modulation 
sequence is stored. Around the flare maximum phase, when the time 
variability of the signal is small, we expect the morphological changes 
in the flare structure to be slow enough to allow (ideally) for 
realistic image reconstruction from the data taken within a half of the 
modulated portion of the rotation lasting $\sim30$~s).

\subsection{\protect\smallskip Example Observations from XTI}

In Figure~12, an example of the XTI modulated signal for the 20 October 
1995 flare is shown. There are hundreds of periods identified already 
where the imaging sequences have been executed. We will present detailed 
analysis of these periods in one of a subsequent publications.
%%%%%%%%%%%%%%%%%%%%%FIGURE 12  Example observations from XTI %%%%%%%%%%%
\begin{figure}
\centerline{\epsfig{file=fig12.eps,width=12cm}}
\caption{
The observed modulation of the X-ray signal in the 2 - 4~keV band of the 
X-ray Tomograph-Imager (XTI) for 20 October 1995 flare. In the bottom 
panel, initial small portion of the recorded signal is enlarged in order 
to present more details of the record shown above. On the horizontal 
axis the time elapsed  from the start of this particular modulation 
sequence is indicated.
}
\end{figure}
%%%%%%END%%%%%%%%%%%%FIGURE 12 %%%%%%%%%%%%%%%%%%%%%%

\subsection{Deconvolution of XTI images}

The solar X-ray source (flare) is scanned at various angles (directions) 
due to spinning motion of the satellite. The detector signal in any of 
the transmission fringes represents one-dimensional projection of the 
two-dimensional source brightness distribution. As the phase of the 
rotation changes views from many projection angles are recorded. A 
resulting set of multiple one-dimensional scans constitutes the input 
for the numerical image reconstruction algorithm. Below, we briefly 
introduce the basics of this image reconstruction algorithm.

In Fig.~13 we present definitions used when formulating the problem of 
image reconstruction. In this representation $f(k,l)$ is the X-ray 
brightness of the investigated source.
%%%%%%%%%%%%%%%%%%%%%FIGURE 13 Definition of image space%%%%%%%%%%
\begin{figure}
\centerline{\epsfig{file=fig13.eps,width=12.cm}}
%\vspace{2cm}
\caption{
Basic formulation of image reconstruction problem. See the text for details.
}
\end{figure}
%%%%%%END%%%%%%%%%%%%FIGURE 13 %%%%%%%%%%%%%%%%%%%%%%%
Fixed coordinate system $(k,l)$ is used. During the scan, the value of 
the measured signal in each position (time bin represented as column $m$ 
perpendicular to the scan direction) represents a result of convolution 
of the collimator transmission function $g$ and the source intensity 
integrated along this perpendicular direction. Thus, the flux measured 
in bin number $j$ can be expressed as:
\begin{equation}
I(j)=\sum_{m}^{ }f(m)g(j-m)
\end{equation}
For the purpose of image reconstruction we have assumed the collimator 
transmission function to consist of a number of triangular profiles 
(windows) with FWHM~=~$b$~=~11~arcsec. The consecutive transmission 
windows are separated by the angular distance $p~=288$~arcsec. In the 
assumed coordinate system, the transmission $g$ in bin $j$ is:
\begin{equation}
g(j)=\left\{ 
\begin{array}{lcr}
1-\frac{|jd-np|}{b} & , & {\rm when} \,\, |jd-np\,|\le b \\ 
0 & , & {\rm when} \,\, |jd-np\,| > b 
\end{array}
\right.
\end{equation}
where $d$ is the bin width and $n$\,=\,0, 1, 2, ... is the index of 
particular transmission window. In case of scan taken at the position 
angle $\varphi_i$, the value of $m$ in Eq.~(2) is $k~cos~\varphi_i + 
l~sin~\varphi_i$, so the signal measured in bin $j$ can be expressed as:
\begin{equation}
I(j,~\varphi_i) =  \sum_{k,l}^{ }f(k,~l)\,g(j - k~cos~\varphi_i -
l~sin~\varphi_i)
\end{equation}
For compact sources with spatial extension smaller than the separation 
between transmission fringes, only a single transmission FOV contributes 
to the signal. By rotating the collimator relative to the source, its 
brightness distribution $f_{kl}$ is recorded in a set of intensity 
vectors $I_{ij}$ (corresponding to individual scans). This 
transformation is handled  by a transmission tensor $g_{ijkl}$.
\begin{equation}
I_{ij} =  \sum_{k,l}^{ }f_{kl}~g_{ijkl}
\end{equation}
The purpose of image restoration process is to solve the inverse problem 
i.e. to determine $f(k,l)$ from measured $I_{ij}$. We have developed an 
elaborated maximum likelihood iterative procedure to solve this inverse 
problem. Within the algorithm, we assume a uniform brightness 
distribution as an initial approximation ($f_{kl}= const$). The 
subsequent (improved, $n+1$) approximation for $f^{n+1}_{kl}$ 
distribution is obtained by multiplying the preceding result by the 
appropriate correction matrix. This correction matrix represents the 
ratio of the observed $(O)$ and calculated $(C)$ flux in each bin, 
weighted by the collimator transmission function:
\begin{equation}
f^{n+1}_{kl}=f^{n}_{kl}
\frac{\sum\limits_{i,j}\,\frac{I^{O}_{ij}}{I^{C}_{ij}}~g_{ijkl}}
{\sum\limits_{i,j}\,~g_{ijkl}} \,\,.
\end{equation}
For instance, if the observed flux at bin $j$ is greater the calculated 
one, we increase the brightness in each of the pixels $(k,l)$ which 
contribute to this bin (in proportion to the corresponding individual 
weights of the collimator transmission function). 

The quality of the iterative convergence is judged in terms of $\chi^2$ statistics. 
The process of image reconstruction is terminated when the value of reduced $\chi^2$ 
approaches unity. 

The inversion technique used here is a straightforward extension of one-
and two-dimensional maximum likelihood iterative inversion methods 
commonly used for solar X-ray data analysis (Sylwester, Schrijver and 
Mewe, 1980; ~Svestka {\em et al.}, 1983, Sylwester and Sylwester, 1998, 
1999). It is analogous of the computer tomography image reconstruction 
procedure used in medical applications, where scans from many directions 
are used to generate two--dimensional picture of (slices) of the body 
internal structure.

The method used is inherently positively constrained since it uses 
multiplicative corrections based on observed to calculated (weighted) 
flux ratios. Within the present method it is possible to vary the pixel 
size in the reconstructed image, independently of the size or the number 
of modulation scans used for image reconstruction. At present, we 
perform deconvolution using 10~arcsec $\times 10$~arcsec pixel size in 
the deconvolved image. We will look for the solutions with finer mesh in 
the future. In Fig.~14 we present an example of the reconstructed image 
for the 20 October 1995 flare observed around 06:14 UT. The lightcurves 
of this flare are shown in Fig.~4. The flare took place on the disk (S09 
W55).
%%%%%%%%%%%% FIGURE 14 Reconstructed image %%%%%%%%%%
\begin{figure}
\centerline{\epsfig{file=fig14.eps,width=9.cm}}
%\vspace{2cm}
\caption{
Example of reconstructed flare image (at  06:14 UT), close to the 
maximum phase of 20 October 1995 M1.5 flare. The event took place on a 
disk,  close to the South-West solar limb.
}
\end{figure}
%END%%%%%%%%%%%%FIGURE 14 %%%%%%%%%%%%%%%%%%%%%%%%%%%% 
The limiting spatial resolution  on the reconstructed image depends on 
many factors such as the signal/noise ratio of the modulated signal, the 
amplitude of nutation of the spacecraft rotation axis and the time 
variations of brightness within the flaring structure during the 
modulation period (we assume the latter not to change during this time). 
There are hundreds of identified modulation sequencies available for the 
image reconstruction. We will perform their analysis in the near future.

%%%%%%%%%%%%%%%% Conclusions %%%%%%%%%%%%%%%%%%%%%%%%
\section{\protect\bigskip Conclusions}
We present the RF15-I soft/hard X-ray photometer/imager presently aboard 
the {\em INTERBALL-Tail} Probe. The RF appears to be one of the most 
sensitive solar photometers in the 10~-~15~keV band and the only X-ray 
instrument measuring presently integral solar flux in the entire energy 
range 2~-~240~keV. By observing the Sun since September 1995 this 
photometer has supplied  complementary data to {\em GOES}, {\em BATSE} 
and HXT~{\em Yohkoh} measurements. In particular till the end of 1997, 
150 flares have been observed for which H$\alpha$ observations have been 
reported and no {\em GOES} class have been assigned. Many flares have 
been detected with the hard X-ray emission extending up to 30~keV~-
~60~keV which have fallen into times of the {\em BATSE}  and/or {\em 
Yohkoh} nights and hence have not been reported by those Teams. A number 
of weak ({\em GOES} class~B) flare events have been observed to 
pronounce exceptionally hard X-ray spectra extending up to $\sim$120~keV 
energy (Siarkowski {\em et al.}, 1999). Collected data constitute a 
viable source for investigations of X-ray solar global oscillations, 
flare energetics and weak events statistics. Future data analysis will 
hopefully reveal more details on the coronal and flare heating and 
particle acceleration processes. We envisage that the data can also be 
usefull in studies of processes responsible for formation of 
magnetospheric X-rays within the auroral regions, since there are 
indications that such an emission has also been observed by the RF 
detectors.

The X-ray tomograph-imager, a unique rotationally modulated collimator, 
provides sets of one-dimensional scans of flares taken at varying 
angles. We present principles of the algorithm of the numerical analysis 
of these data used to reconstruct images of solar flares in the range 
2~-~4~-~8~keV. Comparison of these reconstructed images with those 
obtained from {\em Yohkoh} HXT advanced imager is in progress. The 
results of such comparison will possibly allow to develop next 
generation rotationally modulated hard X-ray imagers.

\section{Acknowledgements} 
The construction of RF has been possible thanks to enthusiasm of many 
people including Jiri Ullrich  and Miroslav Halik from Czech Republic, 
and J. B\c{a}ka\l a, E. Sta\'{n}czyk and $\fbox{R.~Zawerbny}$ from 
Poland. We would especially thank J. B\c{a}ka\l a and S. Gburek for 
preparing some figures included in this paper. In the present 
contribution we have presented data obtained through the CGRO {\em 
BATSE} Solar Flare Data Archive maintained by the Solar Data Analysis 
Center at NASA-Goddard Space Flight Center and provided by the {\em 
BATSE} team headed by Dr.~G.~Fishman. {\em GOES} X-ray data have been 
taken from SEC NOAA. {\em Yohkoh} HXT data have been analysed using the 
software developed by the Japanese Team.

Our final special thanks are to the Referee of this paper, Professor 
Takeo Kosugi (PI for HXT) for his kind critical comments and corrections 
which definitely lead to the improvement of this paper content, 
organisation and presentation. 

This contribution has been supported by  grant 2.P03C.006.13 of Polish 
State Committee for Scientific Research (KBN).

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\end{article}
\end{document}