Instruments of RT-2 Experiment onboard CORONAS-PHOTON and their test and evaluation III: Coded Aperture Mask and Fresnel Zone Plates in RT-2/CZT Payload
Anuj Nandi, S. Palit, D. Debnath, Sandip K. Chakrabarti, T. B. Kotoch, R. Sarkar, Vipin K. Yadav, V. Girish, A. R. Rao, D. Bhattacharya
aa r X i v : . [ a s t r o - ph . I M ] D ec Noname manuscript No. (will be inserted by the editor)
Instruments of RT-2 Experiment onboard CORONAS-PHOTON and their test and evaluation III: CodedAperture Mask and Fresnel Zone Plates in RT-2/CZTPayload
Anuj Nandi · S. Palit · D. Debnath · SandipK. Chakrabarti · T. B. Kotoch · R. Sarkar · Vipin K. Yadav · V. Girish · A. R. Rao · D.Bhattacharya
Received: date / Accepted: date
Abstract
Imaging in hard X-rays of any astrophysical source with high angular resolu-tion is a challenging job. Shadow-casting technique is one of the most viable options forimaging in hard X-rays. We have used two different types of shadow-casters, namely,Coded Aperture Mask (CAM) and Fresnel Zone Plate (FZP) pair and two types ofpixellated solid-state detectors, namely, CZT and CMOS in RT-2/CZT payload, thehard X-ray imaging instrument onboard the CORONAS-PHOTON satellite. In this pa-per, we present the results of simulations with different combinations of coders (CAM
This work was made possible in part from a grant from Indian Space Research Organization(ISRO). Upendra Desai initiated the Zone Plate work and his contribution in the form ofsuggestions and discussions has proved quite valuable for this work. The whole-hearted supportfrom G. Madhavan Nair, Ex-Chairman, ISRO, who initiated the RT-2 project, is gratefullyacknowledged.A. Nandi + , S. Palit, D. Debnath, T. B. Kotoch, R. Sarkar and Vipin K. Yadav + Indian Centre for Space Physics, 43 Chalantika, Garia Station Road, Kolkata 700084Tel.: +91-33-24366003Fax: +91-33-24622153 Ext. 28E-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected] (+: Posted at ICSP by Space Science Division, ISROHead Quarters)Sandip K. ChakrabartiS.N. Bose National Centre for Basic Sciences, JD Block, Salt Lake, Kolkata 700097(Also at Indian Centre for Space Physics, 43 Chalantika, Garia Station Rd., Kolkata 700084)Tel.: +91-33-23355706Fax: +91-33-23353477E-mail: [email protected]. GirishSpace Astronomy and Instrumentation Division, ISAC, Bangalore, 560017E-mail: [email protected]. R. RaoTata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, 400005E-mail: [email protected]. BhattacharyaInter-University Centre for Astronomy and Astrophysics, Ganeshkhind, Pune, 411007E-mail: [email protected] & FZP) and detectors that are employed in the RT-2/CZT payload. We discuss thepossibility of detecting transient Solar flares with good angular resolution for variouscombinations. Simulated results are compared with laboratory experiments to verifythe consistency of the designed configuration.
Keywords
Zone plates · X- and gamma-ray telescopes and instrumentation · Fourieroptics · X-ray imaging
PACS · · · Imaging astrophysical sources in X-rays of electro-magnetic wave band, specially inhard X-rays, is really a challenging and difficult task. X-ray photons do not efficientlyget reflected or refracted because of their ability to penetrate deep into the interactingmaterial. It is, however, possible to image with soft X-ray photons by making themhit a highly polished mirror at a small angle to the reflecting surface. This process,called grazing incidence imaging technique, is effective mainly for soft X-rays (up to ∼
10 keV). For example, in
Chandra and
XMM-Newton missions, soft X-ray imaginghas been done very successfully with this technique. Unfortunately, this direct imagingtechnique is very difficult to implement for hard X-rays and γ -rays.Instead of direct imaging, some indirect imaging techniques have been developedand adopted for imaging in hard X-rays as well as in γ -rays. Shadow casting methodis one such efficient indirect imaging technique (Mertz & Young 1961). This techniqueis based on the total absorption of hard X-rays by the shadow-caster, allowing thegeneration of patterns in the detector plane, which can be deconvolved to get thesource image. There are various types of shadow casting methods depending on thestructure of coder and mask pattern. One such approach is to use a single plane coder,namely Coded Aperture Mask (CAM), which is widely used in different astronomicalobservations (Dicke 1968, Ables 1968, Baker et al., 1983 and Caroli et al., 1987). Inthis approach, mask pattern is basically followed by the individual pixel dimension ofthe detector and therefore, the angular resolution depends on the separation betweenthe coder and the detector plane and the smallest size of the coder element.Another approach (Mertz & Young 1961, Desai et al., 1998, Chakrabarti et al.,2009) to image in hard X-rays with high angular resolution is to use double planecoder of Fresnel Zone Plates (FZPs). The high angular resolution, which is achievableupto a few arc-sec through this method depends on the outermost zone width andseparation between the two coders (pair of FZP) (Palit et al., 2009).RT-2/CZT payload, one of the most important instruments of the RT-2 experi-ment (Debnath et al. 2009, Kotoch et al. 2009, Sarkar et al. 2009, Sreekumar et al.2009) onboard CORONAS-PHOTON mission (Kotov et al. 2008, Nandi et al. 2009),is specially designed to provide high resolution spectral and imaging information ofhard X-ray solar flares at energies above 20 keV. For this, we have employed both theshadow casting methods - the Coded aperture mask (CAM) and dual Fresnel zone plate(FZP) as a coder in RT-2/CZT payload. Detection of hard X-rays requires interactionof photons with denser and heavy material and for imaging, position sensitivity is alsoessential for the detector. We have used two types of solid-state pixellated detectors,namely, Cadmium Zinc Telluride (CZT) and Complementary Metal Oxide Semicon-ductor (CMOS) detectors in RT-2/CZT payload. The solid-state CZT detector has a very good combination of energy resolution, detection efficiency and it is best suitedwith CAM pattern in terms of required spatial resolution. On the other hand, theCMOS detector, with high positional accuracy, is very good for imaging purposes andwith the combination of FZP it can give a few arc-sec of angular resolution.X-ray observation of solar flares must be made from a platform launched abovethe atmosphere. Sending such instrument to near space by balloon is an option. Butthe best way is to send it through a satellite orbiting the Earth. Many missions, like GRANAT , HETE , SWIFT etc. had included shadow casting method for imaging inhard X-rays.All of these mission employ CAM and they are for imaging mainly of celestialobjects like AGNs, compact objects and GRBs. RT-2 will be the first of its kind to useboth types of shadow caster (CAM & FZP) for studying hard X-ray solar flares.In this paper, we discuss in detail the coders and detectors employed in the RT-2/CZT payload. We also provide simulation results along with some laboratory testresults to validate these simulations. In the next section, we discuss the principle ofoperation of CAM and FZP as shadow casters and their basic constructions. This in-cludes the theory behind the working principle and the image reconstruction processes.In the same section the specifications of the instruments, viz, detectors and shadowcasters are given. Then in section 3, we discuss the angular resolution (AR) and fieldof view (FOV) of all four combinations of coder and detector used in the payload andmake comparative study of them in terms of these two important characteristics. Insection 4, we present the simulation aspects of each configuration used in this payload.These include shadow formations (eg. Moir´e fringe for FZPs) and source reconstructionfor one or more sources. In section 5, we discuss what we expect in context of solarobservation from the instrument used in this experiment. The results of the labora-tory experiments carried out with the designed instruments are presented in section 6.Finally, in section 7, we make some concluding remarks.
Coded mask imaging is a class of spatial multiplexing technique (Caroli et al., 1987)for imaging of objects in high energy part of the electromagnetic spectrum, speciallyin X-rays & γ -rays. It is a two step process in which data is acquired from somepart of the sky (within FOV of the instrument) and source image is reconstructed bysome computation procedures. A coded mask is a plate consisting of areas which aretransparent and opaque to photons within certain energy ranges. The transparent andopaque areas or mask elements are generally of equal size and are distributed in apredetermined pattern. The mask acts as a shadow caster, viz, shadows of the maskare projected on the detector placed below the mask facing the sky, by the rays comingfrom the sources in the visible part of the sky. The projected shadow on the detectorplane has the same coding information as that of the mask pattern. The informationon the directions of the rays falling on the mask and hence the source positions in thefield of view are encoded in the amounts of shift of all the shadow patterns with respectto the central position and the information on the source intensities are encoded in thestrengths of the patterns. A pinhole camera has the characteristics required for a proper indirect imaging per-formance, but it has poor signal-to-noise ratio. The sensitivity (signal to noise - S/N- ratio) may be increased by increasing the pinhole area but at the same time it willdegrade the angular resolution of the device. A random pinhole camera (Dicke 1968and Ables 1968) can be constructed by placing many pinholes at random in a plate.This increases the open area of the plate, required for better sensitivity and also pre-serves the angular resolution. It is found that ideal patterns for random pinhole camerashould be based on cyclic difference sets (Gunson & Polychronopulos 1976, Fenimore &Cannon 1978). It is also required that every detector pixel is exposed to one full maskpattern. These patterns are also called Uniformly redundant arrays (URA) (Fenimore& Cannon 1978).In RT-2/CZT, CZT detector modules of 256 pixels of size ∼ × areused (see Kotoch et al. 2009 for details). For good hard X-ray spectroscopic observa-tions, it is necessary to have individual pixel calibration and simultaneous backgroundmeasurements. Hence, the individual pixel reading capability of these modules can beeffectively used by incorporating an appropriate coder for the purpose of simultaneousbackground measurement. Further, solar hard X-ray emission (above 20 keV) is ob-servable only during hard X-ray flares which generally are associated with some activeregions. Hence an identification of the active region on the solar surface during solarhard X-ray flares, correct to arc-minute accuracy, would also be a desirable character-istics of the coder. A pseudo noise Hadamard set which is capable of giving maximumpossible transmission (50 %) (Caroli et al., 1987, In’t Zand 1992) is suitable for a maskemploying CZT detector module. For the detector of 256 pixels, we chose 256 maskelements (to maximize the localization accuracy). Since a pseudo noise Hadamard sethas 2 m -1 elements, we chose m = 8 with an extra opaque element in the mask.A pseudo noise Hadamard set is constructed from a shift-register algorithm (Peter-son 1961). The coefficients p j of a m th order primitive polynomial (all the coefficientsare either 1 or 0) can be used as the generating function of a mask pattern of length2 m -1, provided the polynomial is also an irreducible one. The mask elements a i wherei = 0, 2 m -2 can be generated from the coefficients by using the shift register algorithm a i + m = m − X j =0 p j × a i + j ( mod . (1)The above mentioned process for m = 8 gives 16 polynomials from which CAM patternsmay be generated. Out of these 16 options, the following two polynomials were chosenfor the CZT-CAM configurations: x + x + x + x + 1and x + x + x + x + 1 . The choice was made keeping in mind that each individual pixel should get possiblemaximum amount of mechanical support. These were determined by minimizing the mechanical support parameter (MSP) defined as,
MSP = b + 4 c + 8 d, where b corresponds to the number of segments of each pattern held at two or morecorners, c and d corresponds to the number held respectively at ‘one’ and ‘no’ corner.The ‘one’ and ‘no’ corner elements have to be mechanically held to the neighboringclosed elements, slightly reducing the open element area and hence reducing the sen-sitivity. The two patterns generated by the above two polynomials have the minimumMSP. For the 1 st one b = 3 , c = 2 , d = 0 , and for the 2 nd one b = 7 , c = 1 , d = 0 . And each of which gives MSP = 11. The two CAM patterns that are used in thispayload are shown in Figure 4(a) and Figure 6(a).
The transformation from object distribution function in the sky, S(x,y) to the spatialdistribution of the flux in the detector plane, D(x,y) can be mathematically written as(Caroli et al., 1987), D ( x, y ) = C ( x, y ) ∗ S ( x, y ) + B ( x, y ) , (2)where C ( x, y ) is the aperture transmission function, B ( x, y ) is signal independent noiseterm and ∗ is the convolution operator. An estimation of the sky function ( S ′ ( x, y )) canthen be made by filtering the detector flux distribution by a suitable decoding function K ( x, y ) such that K ( x, y ) ∗ C ( x, y ) is a delta function. Therefore, the sky function canbe written as, S ′ ( x, y ) = K ( x, y ) ∗ C ( x, y ) ∗ S ( x, y ) + K ( x, y ) ∗ B ( x, y ) , (3)which is the reconstructed source distribution in the detector plane.There are different types of reconstruction codes for CAMs, out of which suitableones are chosen fulfilling the requirements of source informations. In our reconstructionprocess, all the above mentioned functions are represented as matrices. S is taken as acolumn matrix with number of elements equal to the total number of division i.e howthe observed part of the sky is divided, and the value of each element is the sourcestrength of corresponding divisions of the sky. D is the row matrix with number ofelements equal to the number of detector pixels and each element representing thecounts obtained in the corresponding pixels. Then C is defined as a matrix (a similarapproach is followed by Caroli et al. 1987) whose number of column is equal to thenumber of elements in S and number of rows is equal to the number of elements of D,and C(i,j) is equal to 1 or 0 if the line joining the sky pixel corresponding to the j-thelement of S and detector pixel corresponding to i-th element of D passes respectivelythrough a transparent and opaque region of the CAM. Thus Eqn. 2 can be written as, D = C ∗ S + B, where, B is a matrix which carries the noise information of the detector. Similarly, thesky function can be written in the matrix representation as, S ′ = K ∗ C ∗ S + K ∗ B, Here, we use K as the matrix inverse to the matrix C . The operator ∗ simply denotesthe matrix product. The distribution S ′ with some filtering by point spread function(PSF) gives near exact reconstruction of the object distribution. Object or sourceplanes reconstructed by the above mentioned method from detector flux distributions,is verified with simulations and experimental results for various source distributionsthat are presented in § § A Fresnel Zone Plate (FZP) coder is a dual plate coder, where two zone plates are placedat some distance apart. Fresnel zone plate has the following transmittance function(Barrett & Myers 2004, Chakrabarti et al., 2009) T ( r ) = 1 ± sgn [ sin ( αr )] S ( r ) , (4)where α is a parameter of the zone plate. S(r) is a support function (equals to 1within the outer boundary of the zone plate and zero outside). The sgn function is +1when sin( αr ) > αr ) <
0. Then the transmission function of thecombined zone plates resembles a part of Fourier Transform (Mertz 1965) from sourceplane to detector plane. Zone plates are constructed such that α is related with n th zone radius r n by any one of the following equations, αr n = nπ, (5)or αr n = ( n ±
12 ) π. (6)Taking two zone plates each of which with α satisfying either Eqn. 5 or Eqn. 6 and with+ or - sign in Eqn. 6 (positive and negative zone plate), we can produce transmissionfunction resembling any of the four parts of Fourier transform from source plane todetector plane (Chakrabarti et al., 2009).One of the pair used in this payload (CONFIG-3) is a positive cosine pair, whichimplies that the shadow pattern produced in the detector is the positive cosine part ofthe Fourier transform (Chakrabarti et al., 2009). In this case, the radii of the n th zoneof both the zone plates are given by r n = p ( n ) r , (7)where r is the innermost zone radius and the central zones of the two zone plates aretransparent. The other pair (used in CONFIG-4) is a negative cosine pair. For this pair, theradius of the n th zone of both the zone plates are given by the same equation as thatof the previous one but both the zone plates are negative in nature, i.e, the innermostzones are opaque to X-rays.X-rays passing through two zone plates of a coder produces a shadow in the detec-tor, called Moir´e pattern. The spacing (S) between two adjacent fringes in the Moir´epattern is determined by the orientation of the rays, hence on the source position inthe field of view and is governed by the relation (Desai et al., 1998), S = r D tanθ , (8)where r is the inner zone radius, D is the spacing between two zone plates and θ is theoff axis angle of the source, i.e, the angle made by the source position with the commoncentral axis of the two zone plates. We can find the source position by measuring thefringe separation in the pattern and also the information on intensity can be obtainedfrom the strength of the shadow.In Figure 1(a-b), we present two Moir´e fringe patterns generated by simulationsfor one of our FZP coder configuration (CONFIG-4: FZP2 + CMOS), one of whichis for an on-axis source (Figure 1a) and the other for an off-axis source (Figure 1b).For on-axis source at infinite distance, the rays fall on the front zone plate exactlyface on and two plates are exactly parallel to each other. So the rear zone plate isexactly shadowed by the front one and the fringe pattern resembles exactly a singleFZP pattern (Figure 1a). But in Figure 1b, as the source is at an off-axis position byan offset of 300 arcsec, straight line fringes appear in the pattern. Fig. 1
Moir´e patterns obtained (simulated) with a cosine negative zone plate pair for anon-axis (a) and an off-axis (b) source position.
As the shadow pattern is a part of Fourier transform, we can reconstruct the observedpart of the sky by applying Inverse Fourier transform on the photon distribution ar- ray obtained in the detector plane (Mertz 1965). During the image reconstruction, acomputer developed FFT code is used to do the inverse Fourier transform.As a single set of FZP coder gives a part of the Fourier transform, the inverseFourier transform returns extra objects other than the required source (Chakrabartiet al., 2009). These include a pseudo source (ghost image) exactly at the position ofmirror reflection of the actual source, and a central DC-offset. If we use two pairsof zone plates with suitable specifications, we can remove the pseudo-source. By usingfour suitably combined pairs of zone plates, we can also remove the central offset (Palitet al., 2009).For a point source at finite distance, the reconstructed source looks like a darkcircular spot (as can be seen in Figure 15(b) and Figure 16(b)). This spreading, whichdeteriorates the angular resolution of the instrument is due to the divergence of thephoton beam incident on the front FZP plate (Palit et al., 2009). Diverging effect canbe rectified by modifying the zone radii of the second FZP plate (Palit et al., 2009).2.3 Configuration detailsIt is already mentioned that RT-2/CZT payload consists of different types of codersand detectors for imaging in hard X-rays of solar flares. In this section, we presentthe configuration details of the RT-2/CZT payload. The specifications of the detectorsused in the payload are given in Table 1.
Table 1
Detectors
CZT (3 numbers) CMOS (1 number)
Dimension (cm) × × Number of pixels ×
16 512 × Pixel dimension (2.5 × mm (50 × µ Geometric area (4 x 4) cm × × cm We have two different types of shadow-casting devices (coders), namely, CAMs andFZPs. Two different types of CAM pattern are used for two CZT modules, whereastwo pairs of zone plates with different dimensions are used for one CZT module andCMOS detector. The specifications of the coders those are used in RT-2/CZT payloadare given in the Table 2. Table 2
Device (coder)
CAM Dual FZP
Material
Tantalum Tungsten
Thickness(mm)
No. of device
No. of plates in a device
Area of coder plates cm cm for FZP14.52 cm for FZP2 Spacing between plates —— 32 cm for FZP1 & FZP2
Spacing between
40 cm 8 cm coder and detector (lower FZP to detector)
Coder shape
Square Circular zones
No. of coder element ×
16 = 256 151 for FZP1144 for FZP2
Smallest coder size/width mm µ for FZP141 µ for FZP2FZP1 is a ‘positive’ cosine type and FZP2 is ‘negative’ cosine type coder. The frontview of collimator containing all the shadow-casters (coders) is shown in Figure 2. Fig. 2
Front view of the collimator displaying all the coders. One CAM is shielded with 1mm Al sheet (CONFIG-1) and the other one is open to the sky (CONFIG-2). Front plates ofFZP1 (CONFIG-3) and FZP2 (CONFIG-4) are also shown.0
Detectors and coders are placed at the two ends of the collimator of the payload.The collimator is divided into four quadrants with a height of 32 cm . Each quadrantwith coder and detector is an independent configuration and it is termed as CONFIG .Therefore, RT-2/CZT payload has four configurations that are summarized in the Table3. Table 3Configuration Combination Angular resolution FOVCONFIG-1 CAM1 + CZT1 21.5 arc-minute 5.72 degreeCONFIG-2 CAM2 + CZT2 21.5 arc-minute 5.72 degreeCONFIG-3 FZP1 + CZT3 64 arc-sec 409 arcsecCONFIG-4 FZP2 + CMOS 54 arc-sec 4.29 degree
In imaging, angular resolution (AR) and FOV are the crucial aspects which determinethe sensitivity and effectiveness of the instrument. Generally, angular resolution of aninstrument depends on the smallest coder element size and separation between thecoder and the detector. In the RT-2/CZT payload we are using various types of codersand detectors in different configurations and we present the calculation of the AR andFOV of all four configurations. The angular resolution of any coder-detector system canbe calculated using the schematic diagram shown in Figure 3. Let us consider the caseof CAM, where AB is the size of a single CAM element and CD is the size of a detectorpixel. Now, if two sources have to be resolved by the imaging system, the rays comingfrom the two sources to any pixel must pass through different CAM elements. Hencethe separation between the two points where the rays from the two sources (which fallson the same detector pixel) fall on two different CAM pixels must not be less than AB.The angle subtended by this minimum distance on any point of the detector pixel is θ p . In case of FZP coder, the scenario would be a little different. Here, AB and CDwould be the radii of finest zones of the front and rear zone plates. But as every pointof the finest zone is equivalent for imaging purpose, the angular resolution should be θ r rather than θ p (Palit et al., 2009).To calculate the field of view (FOV), we use the same kind of picture as shownin Figure 3. But for different configurations containing CAM and CZT detector, wehave to replace AB and CD by an edge of CAM and the detector respectively and forconfigurations containing FZPs, we have to replace them by the diameters of the zoneplate (FZP1 & FZP2) far from detector and the zone plate (FZP1 & FZP2) nearer tothe detector respectively. Now, the angle subtended by AB at the point O will be theFOV of the different configurations of the instrument.For such coders, there is an inverse relationship between the angular resolutionand the FOV. Since the total height of the coding device is fixed (due to satelliteconstraints), some maneuverability was available for the FZP in terms of the spacingbetween the two FZP coders. If we decrease the spacing between the two zone plates,the FOV will increase but resolution would be poor. In our instruments, we havemaintained a balance between them. Fig. 3
Schematic diagram to compute angular resolution of CAM and FZP coder. In thefigure, AB and CD are the size (width) of one single CAM element (finest zone in FZP) anddetector pixel respectively.
In the RT-2/CZT payload, there are four configurations in which two differentCAMs are used with two identical CZT detector modules, whereas for other two con-figurations dual FZPs are used with CZT and CMOS detectors respectively. The con-figuration details are given in Table 3.CONFIG-1 contains CAM1 as the coder and CZT1 as detector. Smallest coderelement size (AB) is of 0 . cm and spacing between CAM1 and CZT1 is 40 cm . Sothe angular resolution comes out to be 21 . arcmin and FOV is 5.72 ◦ .CONFIG-2 also contain a CAM (CAM2) and a CZT detector (CZT2). In this case,as the parameters are the same as that of previous one the angular resolution and FOVhave the same value as the previous configuration (CONFIG-1).In CONFIG-3, the coder is dual FZP (FZP1) with diameter 3 . cm and the finestzone width is 0 . cm . The spacing between the two zone plates is 32 cm . The angularresolution comes out to be 64 arcsec . Unlike the other cases, in FZP configurations, theFOV is not determined by the diameter and spacing only. Finite size of the detectorpixel actually put limitation on the FOV (Chakrabarti et al., 2009 & Palit et al., 2009).As fringe separation decreases with an increase in the off-axis angle of the source, thedetector pixel can not differentiate two adjacent fringes if the separation between themgoes below the detector pixel size for any large off-axis source. Hence, reconstructionof those sources is not possible. Detector pixel limited FOV for this configuration(CONFIG-3) is found to be 409 arcsec wide.CONFIG-4 is designed with dual FZP (FZP2) as shadow-caster of diameter 2 . cm and a high spatial resolution CMOS as a detector. The width of outermost zone is0 . cm and the spacing between two FZP is 32 cm . The maximum achievableangular resolution is around 54 arcsec and FOV is 4.29 ◦ .In the present configuration, the FZP coders have superior angular resolution com-pared to CAM. In the case of FZP with CZT detector (CONFIG-3) configuration, theFOV is limited by large pixel size of detector to a very small value. The configuration of CMOS detector with FZP is the most viable option to image the hard X-ray solarflares. All the shadow casters along with the detectors, when placed in orbit to grab imagesof the source, receive parallel rays of radiation as the sources are effectively at infinitedistance. In general, it is difficult during laboratory experiments to have a source whichis at an infinite distance so that the shadow caster can receive parallel beam of X-rays.For experimental arrangements however large the X-ray source distance is made, theeffect of divergence of the beam appears in the reconstructed source figures as can beseen in the laboratory results corresponding to the FZP coders (see § × , while considering a single source. Fordouble or multiple sources with varying intensity, photon numbers for the brightestsource remains the same and photon numbers for relatively lower intensity sources arementioned in respective sections. This number is sufficient for hundred second (on-board accumulation time for each frame) data accumulation by the imager (4 differentconfiguration for imaging in RT-2/CZT payload) from a C class flare (and above) thatoccur on the surface of the Sun.Simulation results are interpreted based on the 2D and 3D representations of thereconstructed source position and relative strength of the peaks. Source intensity vari-ation in reconstructed image plane is plotted in arbitrary units. Detailed simulationresults for all four configurations are presented in the following sections.4.1 CONFIG-1: CAM1 + CZT1CONFIG-1 consists of a single coder CAM (CAM1) and a CZT (CZT1) module andboth are placed 40 cm apart in the first quadrant of the collimator. CAM pattern forthis configuration is shown in Figure 4(a) (top left). The CAM pattern is generatedfrom the first polynomial given in section 2.1.1. A source position is generated at aposition of θ = 42 ◦ and φ =1 ◦ ′ . The angle θ is measured taking positive horizontalaxis as polar x coordinate ( θ =0 ◦ ) and φ is the angle from the vertical axis. The shadowof CAM due to this source on detector plane is shown in Figure 4(b) (top right). Theshift of shadow pattern of the CAM from central position has coded the informationon the position of source with respect to the central point in FOV. Reconstruction ofthe image (source position) from the CAM pattern is done according to the method discussed in section 2.1.2. In Figure 4(c)(bottom left) and Figure 4(d) (bottom right),we have shown the 2D and 3D view of the reconstructed source (image). In both thefigures of the reconstructed sky plane, the FOV is 5.72 ◦ wide along each sides. Thereconstructed source position as we evaluated from Figure 4(c), matches with the actualsource position assigned during simulation. From Figure 4(d), we also get a measureof the actual intensity of the source. Fig. 4 (a) Simulated picture of CAM1 pattern, where opaque elements are coded by blackcolor. (b) Shadow pattern obtained in the CZT detector for CONFIG-1 for a single source. (c)Two dimensional view of reconstructed sky plane. (d) Three dimensional picture of the sourceplane obtained by reconstruction.
In Figure 5(a-c), we present the simulation results to verify the accuracy of themathematically obtained angular resolution of the configuration containing CAM1 andCZT1. For this, we have placed two sources at an angular separation of 21.5 arc-minutefrom each other. The number of photons falling on the CAM from the brighter sourceis 5 × and that from the fainter one is 2.5 × . In Figure 5(a), we have shown theshadow pattern obtained for two sources which are placed very close to each other.The reconstructed source (image) in 2D and 3D view of both the sources are shown inFigure 5(b)(top right) and 5(c)(bottom). It can be seen from the figures that the twosources are separated by one pixel between them. So the sources can be said to be justresolved. Fig. 5 (a) Shadow pattern obtained for two sources placed very close to each other (21.5 arc-min) with CAM1 and CZT1 (top left) configuration. (b) 2D view of reconstructed sky plane(top right). (c) 3D view of the source intensities obtained by reconstruction (bottom).
The CONFIG-1 and CONFIG-2 are identical as both configurations use CAM andCZT except the CAM patterns are different in CAM1 and CAM2. Therefore, the FOVand angular resolution in both configuration are mathematically the same.4.2 CONFIG-2: CAM2 + CZT2The CAM used in this configuration is different from the CAM pattern of CONFIG-1.The CAM2 pattern is generated from the second polynomial given in section 2.1.1 andis shown in Figure 6a (top left). Simulation results for CONFIG-2 (CAM2 and CZT2)are shown in Figure 6(b,c,d). In this case, we have considered two sources in the fieldof view of the collimator with position θ = 227 ◦ ′ , φ =3 ◦ ′ and θ = 90 ◦ ′ , φ =00 ◦ ′ respectively. Number of X-ray photons falling on CAM2 from the two sources arethe same (5 × counts). In Figure 6b (top right), we have presented the combinedshadow pattern of the CAM (CAM2) generated by the two sources. Fig. 6
Simulated picture (opaque elements of the pattern are coded by black color) of CAMused in CONFIG-2 (top left). (b) Shadow pattern obtained for two sources (top right). (c)2D view of reconstructed sky plane (bottom left). (d) 3D picture of the sources obtained byreconstruction (bottom right). See text for details.
The shifts of individual shadows produced by each source is compatible with theirpositions as can be seen from the Figure 6. In Figure 6c (bottom left), we have presentedthe 2D picture of the reconstructed object plane. From this figure, we get the exactinformation about the positions of the two sources. These positions agree with theassigned positions of the sources during simulation. From Figure 6d (bottom right),which is the 3D view of the reconstructed source plane, we get the information on therelative brightnesses of the sources. The two peaks correspond to the two reconstructedsources and they are found to be of the same height (intensity). It is clearly seen fromthis simulation that the relative brightnesses of the sources in reconstructed planeare exactly replicated irrespective of their relative positions whereas in case of manyother imaging devices there may be position dependencies of relative intensities of thereconstructed sources.In the next simulation step, we place two sources at extreme right and left endsof the collimator wall to verify mathematically calculated FOV. Sources are placed at θ = 0 ◦ and θ = 180 ◦ with common φ angle of value 2.86 ◦ . It is clearly seen from thereconstructed images that the sources are really placed at the two extreme edges of thecollimator and their separation is the measured value of FOV. In Figure 7(b, c), 2Dand 3D view of the reconstructed images of the sky plane with two sources are shown. Fig. 7 (a) Shadow pattern of CAM2 for two sources placed at two extreme ends of FOV (topleft), (b) 2D view of reconstructed sky plane (top right).(d) 3D view of the sources obtainedby reconstruction. n th zoneradius for each of the zone plates is equal to √ n times the inner radius and the centralzones are transparent to X-rays. CZT detector consists of 256 pixels having dimensionof 0.25 cm × θ =116 ◦ and φ = 170 ′′ . We have chopped out the central DC-offset(Chakrabarti et al. 2009) to get the prominent source picture, while plotting the re-constructed images. A pseudo source apart from the original source position is seen inthe reconstructed image. Combination of cosine and sine FZPs can remove the effectof ghost image (pseudo source). The finite size of the detector pixel restricts the fieldof view to 409 ′′ . Fig. 8 (a) Fringes obtained on CZT3 detector with FZP1 as coder (top left). Two sourcesappear in the reconstructed 2D (b) and 3D (c) image plane, one of which is the pseudo sourceof the actual source. The central DC-offset is chopped out.
FOV calculated for this configuration can be verified from the simulation too. Forthe simulation, we have considered a single source placed at θ = 0 ◦ and φ = 204 ′′ .In Figure 9(a-c), we have plotted the fringe pattern along with 2D and 3D recon-structed source in the detector plane. It is seen that the reconstructed source (also thepseudo source) is at extreme edge of the reconstructed array. This confirms that theFOV of the instrument is actually twice the angle of φ , i.e, 409 ′′ .We have also carried out simulation to verify the angular resolution achievableby this configuration. According to the design specifications, the calculated angularresolution is around 64 ′′ (see section 3). In Figures 10(a-c), we have presented thecombined fringes and reconstructed 2D and 3D views of reconstructed sky plane oftwo closely placed sources. The sources are placed at roughly 64 arc-sec apart. Fromthe 2D (top right) and 3D (bottom) images of the reconstructed sources, we find thattwo sources are just resolved. Hence we can conclude that the mathematically foundangular resolution is well supported by simulations. Fig. 9 (a) Fringes obtained on a CZT detector combined with a FZP coder (top left). Thesource is at extreme right edge of the reconstructed sky array shown in the reconstructed 2D(top right) and 3D (bottom) view. φ = 2.145 ◦ and θ = 0 ◦ .The Moir´e fringe pattern for the source with offset φ = 2.145 ◦ is shown in Figure11(a). In Figure 11(b), 3D view of the reconstructed source plane is shown along with Fig. 10 (a) Fringes for two closely placed sources in the limited FOV of CONFIG-3 (top left).(b) Sources appear to be very close and just resolved in the reconstructed 2D (top right) and3D (bottom) images. Sources at right side of central point in reconstructed plane representthe actual sources. Pseudo source (ghost image) is also seen in the reconstructed image planealong with the background noise. the pseudo source (ghost source). Reconstructed source plane shows that the source isat extreme end of the FOV of the collimator, which confirms that the FOV is actually4.29 ◦ (twice the φ value).The most important aspect of this configuration is the best possible angular res-olution which could be around 54 ′′ . To verify the mathematically calculated angularresolution value, we simulate with two sources placed 54 ′′ apart and less than that.From simulation, it is found that the sources which are placed less than 54 ′′ apartare not resolvable at all. In Figure 12(a,b), we have shown the fringe pattern and re-constructed sky plane of two sources which are separated by 54 ′′ . The double pseudo Fig. 11 (a) Fringes obtained on a CMOS detector with a pair of zone plates as coded aperture(left). (b) 3D picture of the reconstructed source along with pseudo source which also appearsin the reconstructed source plane. The central DC offset is chopped out.
Fig. 12 (a) Fringes obtained (left) with a pair of sources at angular distance from each otherequal to the calculated angular resolution (54 ′′ ) of the FZP2-CMOS combination. (b) 3Dview of the reconstructed sources. To get a closer view, the part of the reconstructed planecontaining the sources is zoomed, so that out of 600 hundred pixels along each side only 200pixels are shown. source (ghost image) is also seen in the 3D view. Separation between the two closelyplaced sources are found to be equal to one detector pixel dimension.So far, we have considered a point source to do the simulation. In principle, it is alsopossible to do simulation for extended sources. Simulation is done for the same config-uration (CONFIG-4) with large number of point sources, which can be convenientlytaken as an extended source. The fringe pattern along with 2D and 3D views of recon-structed sources are given in Figures 13(a-c). Amplitudes of individual reconstructedsource give their relative intensities in the extended source distribution. Fig. 13 (a) Fringes obtained with a pairs of zone plates on CMOS detector for multiplesources (extended source) (top left). (b) 2D view of the reconstructed sources (top right). (c)3D view of reconstructed sources of the sky plane.
The prime objective of RT-2 Experiment onboard CORONAS-PHOTON satellite isto study the solar hard X-ray emission associated with solar flares. Solar flares arethe most powerful explosions on the Sun, when the stored energy in twisted magneticfield is suddenly released. Solar flares are generally classified according to their X-raybrightness in the wavelength range of 1 to 8 ˚A. Intensity of the classified flares (eg. A,B, C, M and X class) are measured based on the peak flux (in unit of
W/m ) which ismeasured on the GOES satellite. X-class flares are the most intense having peak fluxof 10 − W/m , while A-class flares are weakest of having peak flux of 10 − W/m .The peak flux of each class is 10 times greater than the preceding one with a lineardivision of 9 within each class. Therefore, a C4.0 class flare is 11 times more powerfulthan a B3.0 class flare.The spectral and temporal characteristics of solar hard X-ray flare are diverse,ranging from relatively soft, thermal (kT ≈
10 keV) spectra, to hard, power law spectra,and from strong micro-flares with duration of seconds to events lasting 30 minutes ormore. Therefore, the evolution of hard X-ray emission regions with time is an important aspect for better understanding of physics involved in the emission process. To pin-point the emission regions, it is essential to have high angular resolution instruments.The RT-2/CZT payload which is designed with four different configurations (in termsof AR and FOV) will serve the main purpose to image the solar flares with high angularresolution.Normally, the Sun is quiet to the level of being invisible in the hard X-ray and γ -ray energy band. The hard X-ray and γ -ray detection of Sun is necessarily a studyof energetic solar flares of flare strength not less than B3.0.We have considered that the maximum number of photons hitting the coder surfaceis around 5 × (at least for one source), while performing the simulations for all fourconfigurations. In a realistic situation, like a solar flare of X4.8 type, which occurredon 2002 July 23, (during the previous solar cycle), we have estimated the response ofthe particular flare for all four configurations. The spectrum of the giant flare duringimpulsive phase is double power-law like nature (Lin et al. 2003) with indices γ L ≈ . γ H ≈ . × photons/sec/cm /keV at 20 keV. Using the above spectral information, wehave calculated the number of photons impinging on each coders (four configurations)for 100 sec accumulation (onboard accumulation time of each image frame) at differentenergy bands. Apart from the real observation, we have also calculated the numberof photons impinging on each coder surface for a typical flare of C3.5 type, which ischaracterized by a spectrum of single power law of index γ ≈ . photons/sec/cm /keV at 20 keV. The estimated photon counts whichimpinges on all four configurations for both the flares, are given in the Table 4.Table 4 Class Energy CONFIG-1 CONFIG-2 CONFIG-3 CONFIG-4 (keV) Counts Counts Counts Counts(20-50) 1.22 × × × —X4.8 (50-100) 2.12 × × × —(20-100) 1.43 × × × × (20-50) 6.24 × × × —C3.5 (50-100) 3.70 × × × —(20-100) 6.61 × × × × It is evident from the estimations given in Table 4, that we could detect clearand prominent fringes for flares like X4.8 and as low as C3.5 type flare with all fourconfigurations. For less intense flares as low as B type flares, though there may not beimages with prominent fringes in the detectors but after proper reconstruction it couldstill be possible to reproduce the sources in the field of view.The FOV (5.72 ◦ ) of CAM and CZT detector (CONFIG-1 and CONFIG-2) isenough to accommodate the whole Sun. Due to poor angular resolution (21 . ′ ), it ishardly possible to observe and distinguish more than one flare, simultaneously. Imagingof a single flare with CONFIG-3 is more critical as the FOV in this configuration isvery small (409 ′′ ). Therefore, a highly pointed observation (within 409 ′′ ) of flare withthis configuration is possible to image with moderate angular resolution (64 ′′ ). Onthe other hand, the imaging of full Sun with hard X-ray solar flares is nicely possiblewith the CONFIG-4, as the FOV (4.57 ◦ ) and angular resolution (54 ′′ ) are superiorcompared to any other configuration. Tests with CONFIG-2 (CONFIG-1) set up were carried out at laboratory of VSSC,Thiruvananthapuram, India. The set up consists of single plane coder (CAM2) andCZT (CZT2) detector. The CAM is shined with a strong radio-active source placedon top of the collimator at position of θ =150 ◦ (approx) and φ =1.04 ◦ . In Figure 14a(top left), the shadow pattern of the CAM obtained in the CZT detector is shown.In Figures 14b (top right) and 14(c, d) (bottom-left: source with background noise,bottom-right: background noise is averaged out), we have shown the 2D and 3D viewof the reconstructed source plane. The source in the reconstructed plane (detectorplane) is nearly exact reproduction (in terms of position and intensity) of the originalsource. The source, though actually a point source, is spread over two pixels of thereconstructed image plane. It is due to the divergent nature of rays from the radio-active source, which impinges on the coder (CAM2), placed at 132 cm away from thedetector plane. Fig. 14 (a) Shadow pattern obtained during tests with a CAM on a CZT detector for asingle source (top-left). (b) 2D picture of the reconstructed source (top-right). (c) 3D pictureof reconstructed source with background noise. (d) 3D view of the reconstructed source aftersmoothing the background noise.
Tests with FZP set up were carried out at the X-ray laboratory of ICSP, Kolkata,India which is equipped with an X-ray source generator of operating voltage 5 Voltto 50 Volt. As it is difficult to produce parallel X-ray beam at laboratory, we have generated quasi-parallel (diverging) X-ray beam with 45 feet collimator made of leadshielded aluminum pipe. The detector system (collimator having FZPs and detector)is kept at one end of the 45 feet long pipe opposite to the X-ray source.In the first set of experiment, we have taken dual zone plates of negative in natureand the n-th zone radius for each is √ n times the inner zone radius. The inner zoneradius is 0.1 cm and number of zones in each zone plate is 144 with finest zone width of0.0041 cm. The separation between the zone plates is 32 cm. Highly position sensitiveCMOS detector is used with smallest pixels size of 0.005 cm. Fig. 15 (a) Fringes obtained with a pair of negative cosine FZP on CMOS detector for aslightly off-axis source (top left). (b) 2D view of the reconstructed source (top right) and (c)3D view of reconstructed source are seen in image plane along with pseudo source (bottom).
The X-ray source is positioned at a little off-axis with the central line of beam.The Moir´e fringe pattern observed in the detector plane (CMOS) is shown in Figure15(a). In Figure 15(b,c), we have plotted the 2D and 3D view of the reconstructedpoint source in the detector plane. The pseudo source (ghost image) and central DCoffset both appear in the experimental results. As the central DC-offset is incomparably bigger than the reconstructed source and its pseudo part, we have to chop it out toget the source prominently. Measurement gives the off-axis angle of the source ( φ )as 32 ′ ′′ and θ as 93 ◦ . This is consistent with the priorly specified actual sourceposition. The divergence of the projected X-ray photon beam has caused broadeningof reconstructed source and makes it look like a circular spot.In another experimental set up, different coder (FZP1) along with CMOS detectoris used. The coder is cosine type and positive in nature. The inner zone radius of each ofthe zone plate is 0.122 cm and number of zones is 151 with finest zone width 0.0050 cm.The observed Moir´e fringe pattern on the detector plane is shown in Figure 16(a). Thereconstructed 2D and 3D images in detector plane is shown in Figure 16(b,c). Actualsource (right side) along with the pseudo source (ghost image) is seen in the image.The source is offset by an amount φ =21 ′ ′′ and at θ =50 ◦ ′ . The reconstructed 2D(top right) and 3D pictures (bottom left) represent exact replica of the source plane. Fig. 16 (a) Fringe obtained experimentally with a pair of zone plates (FZP1) on CMOSdetector for a source (top left) at offset 21 ′ ′′ . (b) 2D view of the reconstructed source (topright) and (c) 3D view of reconstructed source are seen along with pseudo source.6 The RT-2/CZT payload onboard CORONAS-PHOTON mission is a unique instrumentfor imaging in hard X-rays. It uses four different kinds of configurations with whichvarious combinations of angular resolutions (AR) and FOVs are achievable for imaginga single source at a time. This instrument also uses FZP coder as a shadow castingdevice for imaging in hard X-rays in space flight, for the first time. Two different typesof coders (CAM and FZP) along with two different types of detectors (CZT and CMOS)are used to achieve variable angular resolutions. As far as imaging is concerned, thismission is first of its kind as it makes use of CAM and FZP coder together as shadowcaster for the first time in space based imaging.The FZP coders, used in the CONFIG-4 along with high position sensitive CMOSdetector (50 µ ), have angular resolution which is much better than those of the config-urations consisting CAMs and CZTs. The best geometric resolution of this instrumentis around 54 ′′ . The hard X-ray imaging devices rely on the number of photons de-tected, and hence the centroiding accuracy for point sources can be much better thanthis, and can reach upto a few arc-seconds for very bright sources. For example, theRHESSI satellite uses another alternative approach to image in hard X-rays with Rota-tion Modulation Collimator (RMC) technique and, depending on the source intensity,source localization accuracy ranged from 2 ′′ to 180 ′′ .It is also possible to achieve good spatial resolution with CAM-CMOS configura-tion. For that one has to design the CAM elements size comparable to those of CMOSpixels to maintain the consistency of spatial resolution with that of the detector. Thisis a much more complex effort in terms of fabrication and alignment.In this paper, we have presented simulation results along with direct reconstructionof images to quantify the AR and FOV of the various configurations used in the payload.Some of the simulation results are verified with laboratory measurements. Since all the4 detectors would be simultaneously imaging the same event (viz., solar flares), it shouldbe possible to make a simultaneous fit to all the four images with a few assumed sourcepositions and hence to accurately measure the source positions and intensity. This willmitigate some of the problems in the direct reconstruction like ghost images in theFZP images and noise patterns in the CAM images.On 30th January, 2009, the CORONAS-PHOTON was launched successfully andall the RT-2 instruments are working to our satisfaction. However, so far, in the 24thcycle, the solar activity has been weak and we are awaiting stronger flares for directimaging. The on-board data quality and results would be discussed elsewhere. Acknowledgements
SP and DD thank CSIR/NET scholarships and RS and TBK thankRT-2/SRF fellowship (ISRO) which supported their research work. The authors are thank-ful to scientists, engineers and technical staffs from TIFR/ICSP/VSSC/ISRO-HQ for varioussupports during RT-2 related experiments.