holography - university of colorado...

RADIO HOLOGRAPHYOFGMRT DISHESAbhirup Datta�11 Department of Physi s,University of Pune,Pune 411007,India

1E-mail: avirup009�yahoo. o.in

CONTENTS iContents1 Chapter1: Need for Radio-Holography GMRT Dishes 11.1 Overview of GMRT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Design of GMRT Dishes . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Nomen lature of the 30 Antennas . . . . . . . . . . . . . . . . . . . 31.4 Surfa e Error Measurement . . . . . . . . . . . . . . . . . . . . . . . 31.5 Need for Radio-Holography . . . . . . . . . . . . . . . . . . . . . . . 42 Chapter2: Radio-Holography - An Introdu tion 52.1 De�nition in Opti al Wavelength . . . . . . . . . . . . . . . . . . . . 52.2 De�nition- in Radio Wavelength . . . . . . . . . . . . . . . . . . . . 52.3 Di�erent kinds of Radio-Holography . . . . . . . . . . . . . . . . . . 52.3.1 Full-Phase Holography . . . . . . . . . . . . . . . . . . . . . . 62.3.2 Shearing Holography . . . . . . . . . . . . . . . . . . . . . . . . 62.3.3 Phase-Retrieval Holography . . . . . . . . . . . . . . . . . . . 72.3.4 Laser Metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Chapter3: Theory of Radio-Holography 93.1 Aperture-Distribution vs Far Field Pattern . . . . . . . . . . . . . 93.2 Fraunho�er Di�ra tion at Aperture . . . . . . . . . . . . . . . . . 94 Chapter4: Data A quisition Te hnique 114.1 Frequen y of Observation . . . . . . . . . . . . . . . . . . . . . . . . . 114.2 Choi e of the Sour e . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.3 S heme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.4 Nyquist Sampling Theorem . . . . . . . . . . . . . . . . . . . . . . . 134.5 Determination of S an Rates . . . . . . . . . . . . . . . . . . . . . . 145 Chapter5: Data Analysis 155.1 Self-Consisten y Che k . . . . . . . . . . . . . . . . . . . . . . . . . . 155.2 Channel-Collapse and Band-Pass Calibration . . . . . . . . . . . . 155.3 Smoothing the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175.4 Transforming from Far Field to Aperture Field . . . . . . . . . . 196 Chapter6: Results and Measurement of Surfa e Errors 216.1 Measurement of Surfa e Errors - Theory . . . . . . . . . . . . . . . 216.2 Image of Dish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

CONTENTS ii6.3 Self-Consisten y Che ks . . . . . . . . . . . . . . . . . . . . . . . . . . 356.3.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356.3.2 Results for C03 . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 Chapter7: Measurement of Defo us 367.1 Theory for measuring the defo us . . . . . . . . . . . . . . . . . . . 367.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387.3 Results for C03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 Chapter8: Holography at 610 MHz 398.1 S anning Te hnique . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 Chapter9: Se ond Observation at 1280 MHz 439.1 S anning Te hnique . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449.3 Estimate of Coma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4410 Chapter10: Further Development 4911 Chapter11: Codes 5011.1 Fortran Code for S anning Te hnique . . . . . . . . . . . . . . . . . 5011.2 O tave Code for Data Analaysis . . . . . . . . . . . . . . . . . . . . 5411.2.1 Initial Analaysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

CONTENTS iiiA knowledgementThe present report is regarding the Radio-Holography of the GMRT Dishesunder the guidan e of Prof. Rajaram Nityananda, Center Dire tor, NCRA,India. This proje t is a part of my M.S Physi s ourse at Department ofPhysi s, University of Pune and is mandatory for the partial ful�llment of myM.S degree.Working with Prof. Rajaram is a wonderful experien e and an ex ellent op-portunity to me for whi h I am really grateful to him. I should also mentionmy extreme gratitude to Prof. S. Ananthakrishnan , Observatory Dire tor,GMRT. It is due to him I got a han e to work at NCRA. And my proje twith Prof. Rajaram is an out ome of his suggestion.I am also grateful to Prof. A.P.Rao for his valuable suggestions regardingthe development of this proje t. Besides, I am also thankful to all the stu-dents,fa ulties and sta� members of NCRA and GMRT for helping me in myproje t in di�erent aspe ts.

1Chapter 1Need for Radio-Holography GMRTDishes1.1 Overview of GMRTThe Giant MeterWave Radio Teles ope(GMRT) is one of the largest RadioTeles opes in the world. GMRT is a unique fa ility for radio astronomi alresear h using the metrewavelengths range of the radio spe trum,operatingin the frequen y range of about 50 to 1500 MHz . It is lo ated at a siteabout 80 km north of Pune. GMRT onsists of 30 fully steerable giganti paraboli dishes of 45m diameter ea h spread over distan es of upto 25 km.Thenumber and on�guration of the dishes was optimized to meet the prin ipalastrophysi al obje tives whi h require sensitivity at high angular resolution aswell as ability to image radio emission from di�use extended regions. Fourteenof the thirty dishes are lo ated more or less randomly in a ompa t entralarray in a region of about 1 sq km. The remaining sixteen dishes are spreadout along the 3 arms of an approximately `Y'-shaped on�guration over a mu hlarger region, with the longest interferometri baseline of about 25 km.1.2 Design of GMRT DishesThe onstru tion of 30 large dishes at a relatively small ost has been possibledue to an important te hnologi al breakthrough a hieved by Indian S ientistsand Engineers in the design of light-weight, low- ost dishes. The design is basedon what is being alled the `SMART' on ept - for Stret h Mesh Atta hed toRope Trusses. The dish has been made light-weight and of low solidity byrepla ing the onventional ba k-up stru ture by a series of rope trusses (madeof thin stainless steel wire ropes) stret hed between 16 paraboli frames madeof tubular steel. The wire ropes are tensioned suitably to make a mosai ofplane fa ets approximating a paraboli surfa e. A light-weight thin wire mesh(made of 0.55 mm diameter stainless steel wire) with a grid size varying from10 X 10 mm in the entral part of the dish to 20 X 20 mm in the outerparts, stret hed over the rope truss fa ets forms the re e ting surfa e of thedish. The low-solidity design uts down the wind for es by a large fa tor and is

1.2 Design of GMRT Dishes 2

Figure 1.1: Con�guration of GMRT Antennas in the 'Y' shape

1.3 Nomen lature of the 30 Antennas 3parti ularly suited to Indian onditions where there is no snowfall in the plains.The overall windfor es and the resulting torques for a 45-m GMRT dish aresimilar to those for only a 22-m dish of onventional design, thus resultingin substantial savings in ost. The dish is onne ted to a ` radle' whi h issupported by two elevation bearings on a yoke pla ed on a 3.6 m diameterslewing-ring bearing se ured on the top of a 15 metre high on rete tower.The weight of the disk is about 80 tonnes and the ounter-weight is about 40tonnes. The dishes have alt-azimuth mount.1.3 Nomen lature of the AntennasThe antennas at GMRT has been named in order to fa ilitate the observationand data analysis pro edure. The 'Y' shaped array has been formed with 14antennas near the entral region (named Central Square) and the remaining16 are divided into 3 arms whi h form almost a 'Y' shapped �gure.The entral square antennas are named from C00 to C14 (with the ex eption ofC07). So in total there are 14 antennas in the antral square. The 3 arms arenamed East(E), West(W) and South(S). They have antennas named as E02,E03, E04, E05, E06, S01, S02, S03, S04, S06, W01, W02, W03, W04, W05 andW06.1.4 Surfa e Error MeasurementDuring the onstru tion of ea h of these giganti 45m dishes, the whole of itwas not built at the top of the 15m tower. Instead the inner portion was onlybuilt at the top, while the outer part was built at the ground and later �ttedwith the inner portion on the top. So the original paraboloid design of thesurfa e might have got hampered due to these ma hani al �tting reasons. Sothere is a need to measure the surfa e errors of the GMRT dishes in order toestimate the deviation from the ideal paraboli surfa e.There are also other ways in whi h the surfa e may get distorted from itsparaboli nature. It may happen due to gravitational e�e ts, wind for e, un-equal heating of the sun, et .After the onstru tion of ea h dish theodelite measurement has been ondu tedover almost all dishes. But the measurement with theodelite is a very time onsuming pro ess. It took almost 3 - 4 days to measure a single dish. Moreoverthe measurements where taken only pointing the antennas towards the zenith.So the e�e t of gravity on the deformation annot be taken into a ount. Butthe major drawba k of the theodelite measurement has been that it is diÆ ultto make repeated measurements.

1.5 Need for Radio-Holography 41.5 Need for Radio-HolographyRadio-Holography is very powerful te hnique to measure the surfa e errors ofthe dishes. This pro ess not only an predi t about the surfa e errors butalso predi t about the errors in the feed-positioning, et . It is a mu h fastermethod as ompared to theodelite measurement. The estimated time requiredto omplete the measurement on all 30 dishes is 2 days(approx.) as omparedto about 2-3 months in ase of theodelite measurement. Moreover Radio-Holographi te hnique involves more on software than on me hani al aspe tsso holography does not require the amount of man power required by thetheodelite measurement. And the ost of doing a Holographi measurement ismu h less as ompared to that of a Theodelite measurement.

5Chapter 2Radio-Holography - An Introdu tion2.1 De�nition of Holography in Opti al WavelengthsThe opti al re ording of the obje t wave formed by the resulting interferen epattern of two mutually oherent omponent light beams. In the holographi pro ess, a oherent beam �rst is split into two omponent beams, one of whi hirradiates the obje t, the se ond of whi h irradiates a re ording medium. Thedi�ra tion or s attering of the �rst wave by the obje t forms the obje t wavethat pro eeds to and interferes with the se ond oherent beam, or referen ewave at the medium. The resulting pattern is the three-dimensional re ord(hologram) of the obje t wave.2.2 De�nition- in Radio WavelengthIn radio astronomy, a method for re�ning the feed and panel alignment, thusfor improving the aperture eÆ ien y or antenna gain of a radio teles ope. Bys anning an antenna's beam over a raster around an unresolved radio sour e,and using another antenna pointing at the same sour e as a referen e, infor-mation is obtained about the amplitude and phase distributions of the signalre e ted from the antenna surfa e. These distributions are used to spe ify or-re tions (if needed) for the fo us and alignment of the feeds or of the positionsof individual panels in the re e tor.2.3 Di�erent kinds of Radio-HolographyIn order to a hieve an aperture eÆ ien y of 50 %, a radio teles ope must havea surfa e a ura y of �=16, where � is the observing wavelength. In this se tionwe mention few kinds of Surfa e error measurement te hniques[11℄. Amongthem, ex ept Laser Metrology all other te hniques are based upon the prin iplethat one an derive the shape of an antenna's primary from the amplitudeand phase of its beam pattern on the sky [8℄. The omplete shape requiresmeasuring the beam pattern over the full half-sphere. If the measurement isrestri ted to N beamwidths i.e. an angle of N�=D where D is the diameter ofthe primary, the shape is determined with a spatial resolution of � D=N . The

2.3 Di�erent kinds of Radio-Holography 6beam pattern need not be measured with a mono hromati sour e so long asthe spe tral resolution(�=�� is not so small as to smear the measurements overthe aperture by more than the spatial resolution. Thus the spe tral resolutionshould be larger than N.2.3.1 Full-Phase HolographyFull-Phase Holography is the most mature of the te hniques dis ussed here[9℄.This te hnique requires a transmitter to illuminate the antenna to be measured.The antenna is s anned a ross the transmitter to measure the beam patternof the antenna. A referen e antenna whi h also re eives the transmitter signalis needed in order to provide a phase and amplitude referen e. The outputof the two re eivers when ombined gives both the amplitude and phase ofthe beam pattern of the antenna to be measured. This an be used to derivethe amplitude and relative phase of the radiation re e ted from points on theantenna surfa e when the antenna is pointed dire tly at the transmitter. Anantenna with a perfe t �gure in perfe t fo us would have all these re e tionsin phase with ea h other. The amount that the re e tions are not in phasemeasures the deviations of the surfa e from a perfe t �gure.Atmospheri s intillation e�e ts an indu e an arti� ial phase di�eren e be-tween the referen e antenna and the antenna to be measured. This eefe t onthe measurement will be minimized if the separation between the 2 antennas isminimized. The measurement of the teles ope is best done in the on�gurationthat is normally used for observations.While all the holography te hniques give very a urate results, they do notallow one to measure the fo al length of the teles ope dire tly. Instead theytell one how to optimize the positions of the panels for whatever mean fo allength the panels happen to de�ne. If the fo al length is not what was intendedwhen the panels were fabri ated, one will be led to bend the panels so as toa hieve the erroneous fo al length.2.3.2 Shearing HolographyShearing holography is an alternate method of measuring an antenna's sur-fa e. Instead of measuring the amplitude and phase of the beam pattern onthe sky, it measures these in the fo al plane(whi h is equivalent to measuringthe beam pattern). This fo al pattern of a transmitter or elestial obje t analso be Fourier Transformed to yield the surfa e errors of the teles ope primary[12℄. Instead of measuring the pattern's amplitude and phase dire tly, an inter-ferometer with a beam splitter is used to superimpose the on-axis(referen e)pattern with an o�-axis pattern. The resulting interferen e pattern is fo usedon a single-pixel dete tor. A grid of su h measurements at di�erent o�-axispoints an be used to derive the surfa e error map of the teles ope.

2.3 Di�erent kinds of Radio-Holography 7An advantage of this te hnique over full-phase holography is that it does notrequire a referen e re eiver. And sin e only a modest frequen y resolution(�=��) of about 20 is need and only the power need be measured, the dete -tor an be a bolometer. One an either use a narrow band �lter to a hievethis resolution or, by adding the apability of moving one of the at mir-rors in the interferometer to hange the relative path length of the two armsof the interferometer, the interferometer an be used as a Fourier transformspe trometer. This mirror was s anned at ea h point in the measurement tosynthesize a spe trum.2.3.3 Phase-Retrieval HolographyPhase retrieval holography (also known as out-of-fo us holography) is anotheralternate method of measuring the surfa e errors of a radio teles ope [10℄. Anadvantage of this te hnique is that it is done by simply omparing observa-tions of a point sour e both in fo us and after moving the teles ope out offo us by a known amount. (In pra tise, one obtains more reliable results ifone has observations at several di�erent fo us positions.) Like with ShearingHolography, the point sour e need not be mono hromati . That is, no spe ialholography re eiver or modi� ations to the teles ope are required. Sin e thereare no phase measurements made, the phase must be in e�e t retrieved in theanalysis of the data. One disadvantage is that sin e no phase is measured di-re tly, the problem is non-linear and one annot solve dire tly for the surfa eerror map. Instead, one must propose a model of the surfa e errors and �ndthe best set of model parameters that will �t the data.With both Shearing Holography and Phase-retrieval Holography, one need notuse a transmitter but instead use an an astronomi al ontinuum sour e (solong as it is not too extended). This has the advantage that the shape of theteles ope primary need not be measured with the teles ope pointing near thehorizon as is the ase with a measurement te hnique with a transmitter onthe ground. A disadvantage is that one is limited by the signal to noise ratioone an a hieve on the astronomi al obje t. Even the brightest ontinuumsour es annot a hieve the signal to noise one an obtain with a holographytransmitter. So the size of the resolution element on the teles ope aperture ofthe resulting surfa e error map, s larger than that normally a hieved with atransmitter.2.3.4 Laser MetrologyAnother method of measuring the surfa e of an antenna is laser metrology.Laser rangers are used to measure the distan e of retrore e tors mounted onthe surfa e. A minimum of three laser rangers is needed to de�ne the positionof a retrore e tor in three dimensions but more a urate results are obtainedif there are more than three laser rangers. An advantage of this te hnique isthat it an be done while the teles ope is being used for normal observing.

2.3 Di�erent kinds of Radio-Holography 8A disadvantage is that retrore e tors must be permanently mounted on thesurfa e and their positions measured relative to the panels.The GBT(GreenBank Teles ope) and the LMT(Large Millimeter Teles ope)plan to use this method to measure and orre t the errors in their primariesin real time. Tests of the method for the GBT are promising, but an a -tual measurement of its surfa e via laser rangers has not yet been one. Themeasurement errors are expe ted to be under 100 �m but will probably be onsiderably larger than obtained via holography te hniques.

9Chapter 3Theory of Radio-HolographyRadio-Holography exploits the Fourier-Transform relationship between theAperture-�eld Distribution and the Far-�eld pattern(or the fo al plane dis-tribution)3.1 Aperture-Distribution vs Far Field PatternLet the Far-�eld Pattern be given by :-V (�; �) = v(�; �)exp[�(�; �)℄ (3.1)Let the Aperture-�eld Pattern be given by :-A(x; y) = a(x; y)exp[�(x; y)℄ (3.2)Then the relation between them is given by the Fourier-Transform:A(x; y) = Z Z 1�1 V (�; �)e�j2�(�x+�y)d�d� (3.3)where x, y ) oordinates on the dish�; �) oordinates on the sky-plane.This V (�; �) is ne essarily a omplex voltage ! whi h has to be measured inthe interferometri mode.It is noteworthy here, that equation 3.3 is similar to the expression we en- ounter for Fraunho�er Di�ra tion at the aperture.3.2 Fraunho�er Di�ra tion at ApertureIn ontext to the Fraunho�er di�ra tion �eld let us have an aperture illumi-nated by an ele tromagneti �eld of amplitude E(l,m) where l,m are dire tion osines. If (x,y) plane is in the far �eld of this aperture then the wavefront isplane in the (x,y) plane.

3.2 Fraunho�er Di�ra tion at Aperture 10Let P1 be a point in the (x,y) plane. Then the radiated �eld from the aperturewill have a distribution at P1, when integrated over the entire aperture, as [1℄:~E(x; y) = e�j2��(t�R )R Z ZapertureE(l; m; t� R )e�j2�( x� l+ y�m)dldm (3.4)Now, time dependant �elds are repla ed by their r.m.s �eld amplitudes.~E(x; y) / Z ZapertureE(l; m)e�j2�( x� l+ y�m)dldm (3.5)

11Chapter 4Data A quisition Te hniqueThis hapter deals with the te hnique that was followed while taking theholographi -observation using GMRT. The basi strategy that is adopted hereis in uen ed by the te hnique developed by S ott and Ryle(1957).4.1 Frequen y of ObservationThe frequen y of observation was hosen to be 1280 MHz(L- band) (� = 24.3 m). In this band the primary beam was reported to be 0:4o i.e. 24 ar min.Whereas at other bands it is mu h higher. So in order to redu e the time ofobservation we have hosen L-Band.4.2 Choi e of the Sour eThe sour e to be observed is hosen to be 3C147. It is one of the brightestsour e and one of the ux alibrators that radio-astronomers often use. It isalso a point obje t so it meet our needs of a sour e that will not be resolvedout at longer baselines. The ux of 3C147 is about 22.5 Jyat 20 m. Whereasthe nearest bright sour e at 20 m is 3C286 whi h has a ux density of 15Jy at20 m.4.3 S hemeWe have hosen 2 antennas as referren e ones (C00 and C10),. These referren eantennas will only tra k the sour e throughout the observation. While theremaining 28 antennas will be tra king a ir ular region a ross the sky in thefollowing fashion:All of these 28 tra king antennas will s an over a ir ular region a ross thesky whi h has a radius of 3 beamwidths. This extent of 3 beamwidths is hosen at present to redu e the total duration of observation. If the number ofbeamwidths are in reased we will be able to get a better resolution on the dish.Presently with this total 6 beamwidths s ans we will be able to get a resolution

4.3 S heme 12of about 7.5 m on the dish (sin e the resolution is de�ned as Dn = 7:5m). Thes heme of the observation is also explained in the Fig: 4.1 .

��

��

Circular Region in Sky−PlaneCentered at Source 3C147

Total length of each scan = 144 arcmin

Diameter = 6 Bmwdth

Total 19 cross−scans (scan rate = 18arcmin/min)

Figure 4.1: Illustration of S anning Te hniqueThe tra king antennas will start from the perphery of the ir ular region on skyand then will ross the sour e whi h will be at the enter of the ir ular regionand will go same distan e on the other side of the sour e. The next s an will

4.4 Nyquist Sampling Theorem 13

Figure 4.2: Far-Field Pattern - as observed on the sky-planestart just where the last s an has stopped but with an angular displa ementof 10o on the ir umferen e. This next s an will s an the sour e in the reversedire tion to that of the previous one. And this same pro ess follows untill thes ans overs the full ir ular region and returns with a s an that is just thereverse s an of the �rst s an. So in total we have 19 s ans. Among these 19s ans, the 1st and the 19th are the same s ans taken in the reverse dire tions.This is done just to do some self- onsisten y he ks while analysisng the data.4.4 Nyquist Sampling TheoremA ording to the Nyquist Sampling Theorem [3℄ :- A bandlimited fun tion, on�ned to size of D, an be re onstru ted ompletely if sampled at anglesspa ed by under Nyquist Rate of �D or less.

4.5 Determination of S an Rates 14So following this theorem we �xed the distan e between the su essive s anson the ir umferen e to be 10o whi h less the Nyquist Sampling . Hen e we an now re onstru t the ompletely far-�eld radiation pattern by this numberof s ans, without loosing any information on it.4.5 Determination of S an RatesThe Asimuth-elevation s an-rates for GMRT antenna has been al ulated bythe following formulae: Vasimuth = sign � V � os �n os " (4.1)Velevation = sign � V � sin �n (4.2)wheresign ) alternate s ans are opposite in dire tion w.r.t ea h other.�(n+ 1)� �n =10oV ) resultant s an-rate = 18 ar min per minute ( hosen)") angle of elevation , al ulated from the following formulae [1℄:sin Æ = sinL sin "+ osL os " osA (4.3) os Æ osH = osL sin "� sinL os " osA (4.4) os Æ sinH = � os " sinA (4.5)whereH ) hour-angleÆ) de lination of the sour e , L ) Latitude of GMRT") elevation , A ) asimuth

15Chapter 5Data AnalysisThis hapter deals with the pro edure followed while analysing the data of theobservation mentioned in the previous hapter. This analysis in ludes the at-tempt to build a software for GMRT that will be used in further Holographi measurements. This hapter also attempts to propose a basi formalism thatshould be followed while doing a Holographi Measurement in the Interfero-metri mode.5.1 Self-Consisten y Che kWhile taking the observation 19 total s ans of 6 beamwidths were taken.Among these the 1st and 19th s ans were exa tly the same s an but taken inthe reverse dire tion to ea h other So in order to validate our method of s an-ning these two s ans were used to he k the self- onsisten y( after reversingthe last s an ). The last s an was subtra ted from the �rst and the resultantwas viewed. It gave us a satisfa tory result on�rming that ea h s an a tuallypassed through the sour e in the way the s ans were designed in the previous hapter.5.2 Channel-Collapse and Band-Pass CalibrationIn GMRT we have the data of any observation to be taken a ross a bandwidthof 32 MHz ( with the frequen y of observation as the entral frequen y). Andthis 32 MHz is divided among 256 hannels. This 32 MHz is divided intotwo bands USB(Upper Side Band) and LSB(Lower Side Band), ea h having128 hannels ea h. But we have worked with only one of them. So we haveessentially 128 hannels of data per timestamp.Now inorder to in rease theSignal-to Noise ratio(SNR) the data was ompressed(averaged) over all the128 hannels.But while averaging over all the hannels we annot simply take a mean of thedata a ross the hannels. Sin e there is phase variation a ross the hannels soif we take the simple mean then we will lose the information. Hen e we followa te hnique alled BandPass Calibration inorder to do so.

5.2 Channel-Collapse and Band-Pass Calibration 16BandPass Calibration - Bandpass alibration is ne essary to orre t for om-plex gain variations as a fun tion of frequen y. The shape of the bandpassis determined by the baseband �lters as most other omponents have a atresponse as a fun tion of frequen y. A ross the bandpass, there is almost alinear phase slope of a few degrees per MHz. The hannel-to- hannel ampli-tude variations are of order 0.1-1 per entage. Some antennas show a larger,few per ent, amplitude ripple with an approximate width of 3 MHz

Figure 5.1: Variation of amplitude a ross all hannels at 130The basi pro edure that was followed is as follows :-� Ea h s an ontains a timestamp data whi h is onsour e-data� A polynomial is �tted [4℄a ross the phase part of this onsour e dataover all hannels.

5.3 Smoothing the Data 17

Figure 5.2: Variation of phase a ross all hannels at 130� Then this �t is subtra ted from the a tual onsour e data) ' alibdata'� Now this ' alibdata ' is subtra ted from all the other timestamp datafor ea h individual hannels (in phase only)� Now we simply take the mean of all the hannels for ea h timestamps,where the amplitude part is simply averaged while the phase part isaveraged after the BandPass Calibration has been done5.3 Smoothing the DataAfter averaging the data over all hannels, we have now all 19 s ans having1 data per timestamp. But even after hannel ollapse we observe that the

5.3 Smoothing the Data 18data ontains e�e ts of the RFI and Interplanetary s intillations. So inorderto eliminate these e�e ts we had to smoooth the data.

Figure 5.3: S an data with RFI and s intillationsThe Fast Fourier Transform was used in order to transform the data from thetime domain to the frequen y domain. We know that the radio sour es a rossthe sky has a radiation pattern whi h will mu h slowly varying as ompared tothe RFI(Radio Frequen y Interferen e) or S intillations (mostly Ionospheri ).So after taking the FFT(Fast Fourier Transform) we saw that there is responseat the higher side of the frequen y domain whi h was identi�ed to be due toRFI or s intillations. So we padded the frequen y domain data with zeros onthe higher side of the frequen y domain downto a limit so that we do not lose onthe a tual data. And then the IFFT(Inverse Fourier Transform) of this paddeddata has been taken. The result of this pro ess gave us a mu h smoother datafree from the RFI and S intillations upto an appre iable amount.

5.4 Transforming from Far Field to Aperture Field 19

Figure 5.4: S an-data after smoothing out the RFI and S intillations5.4 Transforming from Far Field to Aperture FieldNow we are left up with the job of assembling all the s ans on the skyplaneand transforming it ba k to the aperture plane.In order to assemble all the s ans together in the sky-plane data for ea h s anis normalised in amplitude with respe t to the onsour e data and the phase ofthe onsour e data is subtra ted from all the other dataThis is done to alibrate all the s ans su h that the value of onsour e datashould be the same in all the s ans(whi h should have been ideally the ase).Dire t Fourier Transform Relation is used in order to get the Aperture-�eld

5.4 Transforming from Far Field to Aperture Field 20Distribution on the dish.~E(x; y) = Z Z E(�x; �y)ei2�(�xx+�yy)d�xd�y (5.1)The form of the above ontinuum relation that is used in the algorithm is [3℄:~E(x; y) =X�x;�y E(�x; �y)ei2�(�xx+�yy) (5.2)where�x and �y are sky-plane oordinates and x, y are oordinates on dish.The orresponding 2 dimensional Dis rete Fourier Transform is given by:A(p; q) =Xm Xn A(m;n)ej2�( pm+qnN ) (5.3)wherex:�� = n:pN and y:�� = q:mN�x:�� = �N

21Chapter 6Results and Measurement of Surfa eErrorsThis hapter deals with the results that are obtained from the observationmentioned in Chapter 4. Here the al ulation of the surfa e errors over thedish is also mentioned.6.1 Measurement of Surfa e Errors - Theory

dθ

θ

Ο

O"

P

R

T

S

θ 2dsinFigure 6.1: Diagram illustrating the e�e t of the distortion of the surfa e of the dishIn order to al ulate the surfa e errors in several antennas we refer to �gure6.1 . In the �gure surfa e ~POR represents the original undistorted surfa e of

6.2 Image of Dish 22any antenna. And the surfa e ~TO"S represents the distorted surfa e. Let ustake the shift in the surfa e i.e. ~OO" to be of the value 'd' whi h is in thedire tion normal to the original surfa e ~POR. Now from the �gure 6.1 we anmake out that the path di�eren e introdu ed due to the surfa e error of 'd' is2d sin � . So we get the phase di�eren e introdu ed a ross the surfa e due tothis deformation of 'd' as given by :�� = 2�� 2d sin � (6.1)Sin e in our ase the frequen y of observation is 1280 MHz, it gives the wave-length � = 23:44 m. And if we onsider � = 90o i.e. for normal in iden e of theradio-waves on the surfa e of the re e tor(whi h o urs for the inner part ofthe dish), then we get approximately the phase hange as :�� = 4�d� (6.2)This result relates that if in the phase ontour of ea h antenna we observe aphase hange of 1 radian then it is related to a surfa e error of 1.87 m.Now it is lear from the Figure 6.1 that if the surfa e of the dish is distorted inthe downward dire tion then the orresponding phase hange will be positive,and when the distortion is upward from the surfa e of the dish, then the orresponding phase hange will be negativeSo in the above ase the phase variation of +1 radians a ross the surfa eindi ates that over that region the surfa e might have been pushed down byan amount of 1.87 m , while a phase hange of -1 radian indi ates that in thatregion there might be a upliftment of the surfa e by an amount of 1.87 m.6.2 Image of DishIn this se tion we present the ontour plots of di�erent antennas in both 130and 175 polarisations. The ontour plots are separate for Phase and Amplitudeparts.Here we digress a bit to explain the meaning of the terms 130 and 175. Thedata that are olle ted at ea h antenna are sent to the Central Ele tronin sBuilding from the Antenna Base through the opti al �bres. Now, the antennas an re ord the data at two di�erent polarisations at ea h frequen ies ( RightCir ular Polarisation and Left Cir ular Polarisation). So the data of both thesepolarisation data are sent simultaneously through the opti al �bres using twodi�erent frequen ies 130 and 175 MHz. Its noteworthy here that at L Bandwe dont have the LCP and RCP but 2 linear polarisations

6.2 Image of Dish 23

Figure 6.2: Amplitude At 130 and 175 for C03 in referen e to C00

Figure 6.3: Amplitude At 130 for C03


Figure 6.4: Phase At 130 and 175 for C03 in referen e to C00

Figure 6.5: Phase At 130 for C03



Figure 6.7: Amplitude At 130 for E03



Figure 6.9: Phase At 130 for E03


Figure 6.14: Amplitude At 130 and 175 for E03 in referen e to C00



Figure 6.16: Phase At 130 and 175 for E03 in referen e to C00



Figure 6.18: Amplitude At 130 and 175 for E05 in referen e to C00



Figure 6.20: Phase At 130 and 175 for E05 in referen e to C00



Figure 6.22: Amplitude At 130 and 175 for S06 in referen e to C00



Figure 6.24: Phase At 130 and 175 for S06 in referen e to C00


6.3 Self-Consisten y Che ks 356.3 Self-Consisten y Che ks6.3.1 TheoryAt this point we have data of ea h target antennas for two referren e antennas.So we an a tually he k the onsisten y between the results of ea h antennawhen orelated with two refern e antennas (for ea h polarisations).We follow a following te hnique to determine the same:Let the aperture �eld distribution of a antenna due to 1st referren e antenna isE(1)(x; y) and that due to the 2nd be E(2)(x; y), then the relation giving per etageof onsisten y is given as: = Rentiredish jE(1)(x; y)� E(2)(x; y)j2dxdyqR jE(1)(x; y)j2dxdy R jE(2)(x; y)j2dxdyX100% (6.3)Now, if we are going to he k for one antenna and the same referren e but theself- onsisten y between polarisation, then E(1)(x; y) and E(2)(x; y) are respe -tively the �elds due to ea h of 130 and 175 polarisations.6.3.2 Results for C03The self- onsisten y between two referren es C10 and C00 at 130 is about 3:4%and that at 175 is 3:5%.The self- onsisten y between two polarisations of C03 with referren e C00 isgiven by 0:39%

36Chapter 7Measurement of Defo us

Defocused Feed

Actual Position of the Feed (Designed)

Fig: Showing Defocus of the FeedFigure 7.1: Diagram depi ting the ondition after the defo us of the feedThis hapter deals with the measurement of the defo us of the feed in separateantennas due to the feed displa ement.7.1 Theory for measuring the defo us

7.1 Theory for measuring the defo us 37F δ θ

θ

θ Fcos δO"

O

P

T RFigure 7.2: Diagram illustrating the e�e t of the defo us of the feedFrom the �gure 7.2 it is ertain that the path di�eren e ÆL introdu ed due tothe defo us of the feed by the extent of Æf is given by:ÆL = Æf(1� os �) (7.1)In the above equation the a tual path di�eren e remains as Æf os �, but andaddition of a onstant term Æf does not hange the information.For small values of � we an approximate the above equation asÆL = Æf �22 (7.2)Now, sin e � = R=f where R =px2 + y2 = distan e of di�erent mesh points onthe dish, and f = fo al length ) ÆL = Æf x2 + y22f 2 (7.3)So the orresponding phase di�eren e Æ�introdu ed on the surfa e of the dishdue to the defo us of the feed is given by :Æ� = Æf x2 + y22f 2 2�� (7.4)

7.2 Analysis 38where � is the wavelength of observation7.2 AnalysisWe have taken the phase part of the holographi data for ea h antenna at both130 and 175 polarisations and has extra ted a quadrati fun tion from it in thefollwing way. R = Xpx2+y2<Rmax(phase(x; y)� �(x2 + y2))2 (7.5)where Rmax denotes the extent (in radius) of the dish to be taken into on-sideration while doing this omputation. Here we have taken Rmax to be 15meters.the array phase(x,y) denotes for ea h of 130 and 175 polarisations. So here wehave al ulated the value of R for 130 and 175 separately.� is the parameter we have used to get the minimum value of R.So by varying the value of � we have obtained the minimum value of R. Thisvalue of � orresponding to the minimum value of R we have ompared withthe above theory to get the value of defo us of the feed for a parti ular antenna.It is important to mention here that the value of � at minimum value of R isalmost same for both 130 and 175.� = 2�Æf2f 2� (7.6)) Æf = ��f 2� (7.7)7.3 Results for C03Taking Fo al Length = 18.54 meters, Wavelength of Observation = 0.23438meters (at 1280 MHz), and value of � from the minimisation pro edure weget the value of the defo us Æf = 0.17951 meters both at 130 as well as 175polarisations. This measure of defo us is about 0.97% of the total fo al length.

39Chapter 8Holography at 610 MHzTill now the results of holographi measurement at 1280 MHz has been men-tioned. Inorder to validate the holographi pro edure followed there have beena need to he k the results at 610 MHz also. Ideally it should give similar re-sults to those obtained at 1280 MHz. As ompared to the L-band feed ( a orrugated horn) of GMRT the 610 feed is a oaxial ylinder having the dualfrequen y mode at 610 MHz and also at 327 Mhz.8.1 S anning Te hniqueThe te hnique is identi al to that mentioned in hapter 4 (in ase of 1280MHz). But primary beamwidth at 610 MHz is 54 min. So to perform theentire observation of 19 s ans(6 beamwidths ea h) in short time the s an ratewas taken to be 36 ar min per min as ompared to 18 ar min per min in aseof 1280 MHz. In this observation the sour e was 3C147 (as in hapter 4).In this observation, di�erent antennas were given di�erent magnitude of feedrotations in either anti lo kwise or lo kwise dire tions. But still some of theantennas (in luding the referen e antennas were kept at pointing only and notbeen given any pointing o�set. This a tion of feed rotation will introdu edeliberately a oma term in the phase distribution a ross the surfa e of thedish.The status of the feed-rotation in ea h antennas used is given as follows:-� C01,C10(Referen e Antennas)! no feed-rotation.� C02,C03,C04,C05,C11,E03,E04,E06 ! no feed-rotation.� S03,S06 ! feed rotated by +200 ounts.� E02,E05 ! feed rotated by -200 ounts.� C09,W03 ! feed rotated by +300 ounts.� S01,W02 ! feed rotated by -300 ounts.

8.2 Results 40� C12,C13 ! feed rotated by +400 ounts.� C08,W01 ! feed rotated by -400 ounts.Here, we should mention that Feeds at GMRT are ontrolled by the FPS(FeedPositioning System) and the onvention used by FPS for rotation is 15360 ounts 270o. And +,- sign resembles the lo kwise and anti lo kwise rotationsrespe tively.8.2 ResultsPresently only one antenna(E03) at 610 MHz has been analyzed in referren eto C01.

8.2 Results 41

Figure 8.1: Amplitude At 130 and 175 for E03 with referen e as C01


8.2 Results 42

Figure 8.3: Phase At 130 and 175 for E03 with referen e as C01


43Chapter 9Se ond Observation at 1280 MHzThere was a need of the se ond observation at 1280 MHz in order to justifythe onsisten y of the results of last observation at 1280 MHz(mentioned inChapter 4.9.1 S anning Te hniqueThe te hnique is exa tly the same as mentioned in hapter 4. But tis time theentire observation of 19 s ans(6 beamwidths ea h) was to be peformed in shorttime, so the s an rate was taken to be 36 ar min per min as ompared to 18ar min per min in hapter 4. In this observation the sour e was 3C286.In this observation, di�erent antennas were given di�erent magnitude of feedrotations in either anti lo kwise or lo kwise dire tions. But still some of theantennas (in luding the referen e antennas were kept at pointing only and notbeen given any pointing o�set. This a tion of feed rotation will introdu edeliberately a oma term in the phase distribution a ross the surfa e of thedish.The status of the feed-rotation in ea h antennas used is given as follows:-� C00,C06,C10(Referen e Antennas)! no feed-rotation.� C01,C02,C03,C04,C05,E03,S04,W06 ! no feed-rotation.� C05,E06,S06 ! feed rotated by +200 ounts.� E05,S03,W04 ! feed rotated by -200 ounts.� E02,E04,W03 ! feed rotated by +300 ounts.� C14,S01,W02 ! feed rotated by -300 ounts.� C12,C13,W01 ! feed rotated by +400 ounts.� C08,C09,C11 ! feed rotated by -400 ounts.

9.2 Results 449.2 ResultsIn the next �gures, we an see the results of C03(with referren e to C00). Theobserved pattern is similar to that obtained hapter 6. In fa t, the onsisten y al ulationas per equation 6.3 gives 4.9% at 130 and 5.1% at 175.9.3 Estimate of ComaThe qualitative behaviour of oma has been observed in the above sets of data.The behaviour is at per with the expe ted as referred in [6℄. We are trying toextra t the quantitative measure of Coma as well.

9.3 Estimate of Coma 45

Figure 9.1: Amplitude At 130 and 175 for C03 with referen e as C00 without feed rotation



Figure 9.3: Phase At 130 and 175 for C03 with referen e as C00 without feed rotation



Figure 9.5: Amplitude At 130 and 175 for E05 with referen e as C00 with feed rotation



Figure 9.7: Phase At 130 and 175 for E05 with referen e as C00 with feed rotation


49Chapter 10S ope of Further DevelopmentThis proje t was aimed to over the basi formalism of Radio-Holographi measurements at GMRT. Even though the basi formalism has been done butstill there remains a plethora of work that an be done to develop the operation.Below some of them are mentioned.� The present resolution on the dish is about 7 meters. It an be redu ed to 1 meter(whi h is appre iable) by taking longer s ans of about 10 beamwidths.� The algorithm that has been developde an be veri�ed by simulating the ode witha given aperture illumination with some known defe ts.� The oma estimation has been started. But that too requires a deep study to �gureout.� To extra t every possible defe ts from the aperture illumination by expansion of the ir ular Zernike Polynomials [6℄� The 610 MHz data has to be analysed for all the antennas.� Holography an also be done by manually moving the feed in the verti al dire tion.� The present software developed is in parts. So the most useful future work will beto merge all the program and reate a single stand alone program that will take theLTA �le as input and will produ e holographi maps(in amplitude and phase) as itsoutput.

50Chapter 11Codes11.1 Fortran Code for S anning Te hnique* Program to evaluate the respe tive Azimuth and elevation S an rate* in different s ans that suffi e the Holography experiment of 14th* De ember 2003, and 22nd April at GMRT.impli it none* all variables are in ar minreal*8 v_alpha,v_beta,theta_n(10000), os_el_n(10000)real*8 theta_in r,s an_rate,start_obs,end_obsreal*8 extent,radius,time_ea h_s an,freqreal*8 NY_spa ing,dead_time,sour e_transitreal*8 rate_el,rate_as, urrent_time,latreal*8 hour_angle(10000),de ,sin_el,breal*8 peak_time,beam_width,verify,res_v,stop_s anreal*8 p,D2Rinteger*4 n,i,j,valueopen(unit=11,file='holo_14=11.out')open(unit=12,file='holo_14=12.out')open(unit=13,file='holo_14=13.out')open(unit=14,file='holo_14=34.out')D2R = ATAN(1.0D0)/45.0D0* Latitude of GMRT(in degree)lat = 19.1* De lination of the sour e : de (in degrees)write(*,*)'Enter beamwidth at frequen y of obs(in deg)'read(*,*)bwrite(11,*)'The primary beamwidth at frequen y of obs(in deg)',bwrite(*,*)'Enter the de lination of the sour e(in degrees)'

11.1 Fortran Code for S anning Te hnique 51read(*,*)de write(11,*)'The de lination of the sour e(in degrees) ',de * urrent_time is in minutes urrent_time=0.0d0write(*,*)'Enter the starting time of observation'read(*,*)start_obswrite(11,*)'The starting time of observation',start_obswrite(*,*)'Enter the ending time of observation'read(*,*)end_obswrite(11,*)'The starting time of observation',end_obswrite(*,*)'Enter the dead time between ea h s ans(min)'read(*,*)dead_timewrite(11,*)'The dead time between s ans',dead_timewrite(*,*)'Observing Frequen y(in MHZ) ?'read(*,*)freqwrite(11,*)'Observing frequen y(in MHZ) is ',freqwrite(*,*)'Transit time of sour e(in hours) ?'read(*,*)sour e_transitwrite(11,*)'Transit time(hrs) of sour e ',sour e_transitwrite(*,*)'How many beamwidth u want to go ?'read(*,*)extentwrite(11,*)'NO. of beamwidth u want to go ',extentbeam_width=b*60* Therefore the radius of the ir ular mesh isradius = beam_width*extentwrite(11,*)'Ans'write(11,*)'The radius(in ar -min) of the mesh is' , radiuswrite(*,*)'No. of s ans u want to take'read(*,*)nwrite(11,*)'No. of s ans to be take',nwrite(*,*)'The resultant s an-rate(ar -min/min) u want to take'read(*,*)s an_ratewrite(11,*)'Resultant s an-rate(ar -min/min) u want',s an_rate

11.1 Fortran Code for S anning Te hnique 52time_ea h_s an= 2.*radius/s an_ratewrite(11,*)'Ans'write(11,*)'Tot time(min) reqd for 1 s an',time_ea h_s an* Nyquist Sampling Spa ing = lambda/ D* D = 45 m, diameter of the dish.NY_spa ing= ((300/freq)*(180*60/3.14))/45write(11,*)'Ans'write(11,*)'Nyquist Spa ing(in ar -min) is ',NY_spa ingwrite(11,*)'Ans'write(11,*)'Total S ans predi ted by Nyquist is ',NY_spa ing* tot= (3.14*radius)/NY-spa ingwrite(11,*)'Tot Time(min)for all s ans ',(3.14*radius)*time_ea h_s an/NY_spa ing* tot= (3.14*radius)/NY-spa ingwrite(11,*)'Tot Time(min)for all s ans ',(3.14*radius)*time_ea h_s an/NY_spa ing* theta_in r= (180*60)/ntheta_n(1)=0.write(12,*)'s an_no', 'rate_alpha','rate_beta','res_v ','theta_n 'write(13,*)'s an_no ', 'rate_as ','rate_el','peak_time ','resultant_s an_rate'write(14,*)'s an#' ,'s an_start',' rate_as',' rate_el','s an_stop','peak_time'value = 1do i=1,n+1* Hour Angle at transit of the sour e is 0hour_angle(i)=0.-(sour e_transit-start_obs-(( urrent_time+(time_ea h_s an/2))/60.))1*1.002785515* The last multipli ative fa tor is the ore tion due to the sidereal time.sin_el=(sin(D2R*lat)*sin(D2R*de ))+( os(D2R*lat)* os(D2R*de )* os(hour_angle(i)*D2R*15)) os_el_n(i)=dsqrt(1-(sin_el*sin_el))write(*,*)(theta_n(i)),sin(D2R*theta_n(i)), os(D2R*theta_n(i))v_alpha=value*s an_rate* os(theta_n(i)*D2R)v_beta=value*s an_rate*sin(theta_n(i)*D2R)res_v=dsqrt((v_alpha*v_alpha)+(v_beta*v_beta))write(12,1)i,v_alpha,v_beta,res_v,theta_n(i)1 format(2x,I2,7x,F8.4,5x,F8.4,6x,F8.4,6x,F8.4,2x)

11.1 Fortran Code for S anning Te hnique 53peak_time= urrent_time+(time_ea h_s an/2)rate_el=v_betarate_as=v_alpha/ os_el_n(i)rate_as=v_alpha/ os_el_n(i)verify =dsqrt( (rate_el*rate_el)+(rate_as*rate_as))write(13,2)i,rate_as,rate_el,peak_time,verify2 format(2x,I2,6x,F8.4,6x,F8.4,5x,F8.4,5x,F8.4,2x)stop_s an= urrent_time+time_ea h_s anwrite(14,3)i, urrent_time,rate_as,rate_el,stop_s an,peak_time,sin_el3 format(2x,I2,4x,F6.2,4x,F19.13,4x,F8.4,4x,F6.2,4x,F6.2,2x,F6.2)value=-value urrent_time= urrent_time+(time_ea h_s an+dead_time)* Theta is al ulated in degreetheta_n(i+1)=(180./n)*ienddostopend

11.2 O tave Code for Data Analaysis 5411.2 O tave Code for Data Analaysis11.2.1 Initial Analysis* O tave Code of the program that takes in the input as ea h s an(extra ted from the* LTA file using "./xtra t" program) and gives in the output all the s ans after* Bandpass Calibration, Smoothing, Channel Collapse and well-aligned.%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%fun tion initial_holography l ; lear;% lose;%************* Opening Files *************************New130 = zeros(1,402);New175 = zeros(1,402);pro essed_data_130 = zeros(18,201);pro essed_data_175 = zeros(18,201);filename10 = "130.out";filename11 = "175.out";%*************** alling ea h s an files for storing the skydata in an array ***********for i = 1:1:18i if(i== 1)i filename0 = "14de _0_C00:C03_target_all hannel.out";filename1 = "14de _0_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an0%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);f lose(fp10);f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendif

11.2 O tave Code for Data Analaysis 55if(i== 2)i filename0 = "14de _1_C00:C03_target_all hannel.out";filename1 = "14de _1_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an1%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);f lose(fp10);f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendifif(i == 3)i filename0 = "14de _2_C00:C03_target_all hannel.out";filename1 = "14de _2_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an2%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);f lose(fp10);f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendifif(i== 4)i filename0 = "14de _3_C00:C03_target_all hannel.out";filename1 = "14de _3_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an3

11.2 O tave Code for Data Analaysis 56%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);f lose(fp10);f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendifif(i==5)i filename0 = "14de _4_C00:C03_target_all hannel.out";filename1 = "14de _4_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an4%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);f lose(fp10);f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendifif(i== 6)i filename0 = "14de _5_C00:C03_target_all hannel.out";filename1 = "14de _5_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an5%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);

11.2 O tave Code for Data Analaysis 57f lose(fp10);f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendifif(i==7)i filename0 = "14de _6_C00:C03_target_all hannel.out";filename1 = "14de _6_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an6%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);f lose(fp10);f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendifif(i== 8)i filename0 = "14de _7_C00:C03_target_all hannel.out";filename1 = "14de _7_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an7%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);f lose(fp10);f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;

11.2 O tave Code for Data Analaysis 58k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendifif(i== 9)i filename0 = "14de _8_C00:C03_target_all hannel.out";filename1 = "14de _8_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an8%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);f lose(fp10);f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendifif(i== 10)i filename0 = "14de _9_C00:C03_target_all hannel.out";filename1 = "14de _9_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an9%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);f lose(fp10);f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendif

11.2 O tave Code for Data Analaysis 59if(i== 11)i filename0 = "14de _10_C00:C03_target_all hannel.out";filename1 = "14de _10_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an10%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);f lose(fp10);f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendifif(i== 12)i filename0 = "14de _11_C00:C03_target_all hannel.out";filename1 = "14de _11_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an11%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);f lose(fp10);f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendifif(i== 13)i filename0 = "14de _12_C00:C03_target_all hannel.out";filename1 = "14de _12_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an12

11.2 O tave Code for Data Analaysis 60%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);f lose(fp10);f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendifif(i==14)i filename0 = "14de _13_C00:C03_target_all hannel.out";filename1 = "14de _13_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an13%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);f lose(fp10);f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendifif(i==15)i filename0 = "14de _14_C00:C03_target_all hannel.out";filename1 = "14de _14_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an14%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);f lose(fp10);

11.2 O tave Code for Data Analaysis 61f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendifif(i==16)i filename0 = "14de _15_C00:C03_target_all hannel.out";filename1 = "14de _15_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an15%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);f lose(fp10);f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendifif(i==17)i filename0 = "14de _16_C00:C03_target_all hannel.out";filename1 = "14de _16_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an16%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);f lose(fp10);f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);

11.2 O tave Code for Data Analaysis 62pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendifif(i==18)i filename0 = "14de _17_C00:C03_target_all hannel.out";filename1 = "14de _17_C00:C03_a .out";smoothing(filename0,filename1); % alling the fun tion smoothing for s an17%****Sorting the raw-data into a single row matrix*********fp10 = fopen(filename10,"r");fp11 = fopen(filename11,"r");[New130 stop℄ = fs anf(fp10,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp11,"%f",[1,Inf℄);f lose(fp10);f lose(fp11);%**********************************************************for k = 1:1:201k1 = 2*k - 1;k2 = 2*k ;pro essed_data_130(i,k) = New130(1,k1) + j* New130(1,k2);pro essed_data_175(i,k) = New175(1,k1) + j* New175(1,k2);endforendifendfor%*******************************************************************************************Printing to File ****************filename20 = "intial_data_130.hol";filename21 = "initial_data_175.hol";fp20 = fopen(filename20,"w");fp21 = fopen(filename21,"w");for m =1:1:18for n =1:1:201fprintf(fp20,"%f %f \n",real(pro essed_data_130(m,n)),imag(pro essed_data_130(m,n)) );fprintf(fp21,"%f %f \n",real(pro essed_data_175(m,n)),imag(pro essed_data_175(m,n)) );endforendforf lose(fp20);f lose(fp21);%********************************************************************************endfun tionfun tion smoothing(filename0,filename1)****Sorting the raw-data into a single row matrix*********fp0 = fopen(filename0,"r");filename0

11.2 O tave Code for Data Analaysis 63filename1uptostring("#","O",fp0); %rea hing the last har string "#O"upto har("\n", fp0 ); %rea hing the end of the line[rawdata stop℄ = fs anf(fp0,"%f",[1,Inf℄);f lose(fp0);%**********************************************************[M N℄ = size(rawdata) ;data_real_130_0 = zeros(1,128);data_im_130_0 = zeros(1,128);data_real_175_0 = zeros(1,128);data_im_175_0 = zeros(1,128);i = 1;k = 1;for m = 2:2:Nif(m < 258)data_real_130_0(1,i) = rawdata(1,m);data_im_130_0(1,i) = rawdata(1,m+1);i = i + 1;endifif(m >= 258 )data_real_175_0(1,k) = rawdata(1,m);data_im_175_0(1,k) = rawdata(1,m+1);k = k+1;endifendforrawdata =[℄; %killing the rawdata matrix%#############################################################Ant130_0 = data_real_130_0+ j*data_im_130_0;Ant175_0 = data_real_175_0+ j*data_im_175_0;Xaxis = 1:1:128;################# End of File 1 #############################********* Cal ulations ****************************for i =1:1:100 alib_130(i) = arg(Ant130_0(i+10)); alib_175(i) = arg(Ant175_0(i+10));endforres alib_130 = detrend ( alib_130,1);res alib_175 = detrend ( alib_175,1);for i = 1:1:100smooth_130(i) = alib_130(i) - res alib_130 (i);smooth_175(i) = alib_175(i) - res alib_175 (i);endfor

11.2 O tave Code for Data Analaysis 64%************************************************************Xaxis1 = 1:1:100;****************************************************************************************** Beginning the Channel alibration for ea h s ans *************************Sorting the raw-data into a single row matrix*********fp1 = fopen(filename1,"r");uptostring("#","O",fp1); %rea hing the last har string "#O"upto har("\n", fp1 ); %rea hing the end of the line[rawdata stop℄ = fs anf(fp1,"%f",[1,Inf℄);f lose(fp1);**********************************************************Col=401;[M N℄ = size(rawdata) ;Rows =N/Col;i = 1;data = zeros(Rows,Col);for m = 1:1:Rowsfor n = 1:1:Coldata(m,n) = rawdata(1,i);i = i + 1;endforendforrawdata =[℄; %killing the rawdata matrix[M1 N1℄ = size( data ) ;avg_data = zeros(M1,5); al_data = zeros(M1,5);phase_diff = zeros(M1,5);for m = 1:1:M1ir=1;k=1; for n=2:2:N1avg_data(m,1)=data(m,1);if(n <= 201) al_data(m,1) = data(m,n) + j*data(m,n+1);

11.2 O tave Code for Data Analaysis 65phase_diff(m,1) = arg( al_data(m,1)) - smooth_130(ir);nval_real = abs( al_data(m,1))* os(phase_diff(m,1));nval_imag = abs( al_data(m,1))*sin(phase_diff(m,1));avg_data(m,2) = avg_data(m,2) + nval_real;avg_data(m,3) = avg_data(m,3) + nval_imag;ir= ir+1;endifif(n >= 202) al_data(m,2) = data(m,n) + j*data(m,n+1);phase_diff(m,2)= arg( al_data(m,2)) - smooth_175(k);nval_real = abs( al_data(m,1))* os(phase_diff(m,1));nval_imag = abs( al_data(m,1))*sin(phase_diff(m,1));avg_data(m,4) = avg_data(m,4) + nval_real;avg_data(m,5) = avg_data(m,5) + nval_imag;k=k+1;endifendforavg_data(m,2)= avg_data(m,2)/100;avg_data(m,3)=avg_data(m,3)/100;avg_data(m,4)=avg_data(m,4)/100;avg_data(m,5)=avg_data(m,5)/100;endfor*****Sorting the data into time, ant-USB & ant-LSB (re + j im)****TimeStamp = avg_data(:,1)';Ant130 = avg_data(:,2)' + j*avg_data(:,3)';[orig_row orig_ ol℄ = size(Ant130);Ant130 = [zeros(1,250),Ant130,zeros(1,250)℄;Ant175 = avg_data(:,4)' + j*avg_data(:,5)';Ant175 = [zeros(1,250),Ant175,zeros(1,250)℄;****************** Analysis ********************FFT130 = fft(Ant130);

11.2 O tave Code for Data Analaysis 66Mag130 = abs(FFT130);FFT175 = fft(Ant175);Mag175 = abs(FFT175);[M10 N10℄ = size(Mag130);Xaxis2 = 1:1:N10;%[M11 N11℄ = size(Xaxis2)BW = .1;nn = round(N10*BW);ONES = ones(1, nn);kk = N10 - 2*nn;PadMat = [ ONES, zeros(1,kk), ONES ℄;PFFT130 = FFT130.*PadMat;PFFT175 = FFT175.*PadMat;IFFT130 = ifft(PFFT130);IFFT175 = ifft(PFFT175);[M8 N8℄ = size(IFFT130) ;[Max130 ind130℄ = max(IFFT130);[Max175 ind175℄ = max(IFFT175);**********************************************Resizing of the s an arrays and normalisingNew130 = zeros(1,201);New175 = zeros(1,201);Xaxis10 = 1:1:201;k1= 251;for i = 1:1:201if(i <= (101 - ( ind130 - 250)))New130(1,i) = 0;endifif(i > (101 - ( ind130 - 250)))New130(1,i) = IFFT130(k1);k1 = k1+1;endifendfork2= 251;for i = 1:1:201if(i <= (101 - ( ind175 - 250)))

11.2 O tave Code for Data Analaysis 67New175(1,i) = 0;endifif(i > (101 - ( ind175 - 250)))New175(1,i) = IFFT175(k2);k2 = k2+1;endifendfor%New130%New175phase130 = arg(New130(1,101));phase175 = arg(New175(1,101));amp130 = abs(New130(1,101));amp175 = abs(New175(1,101));ind = 102 - ( ind130 - 250) + orig_ ol;for i = (102 - ( ind130 - 250)):1:201if(i <= (102 - ( ind130 - 250) +orig_ ol))phase_ ur130= arg(New130(1,i)) - phase130 ;abs_ ur130 = abs(New130(1,i))/amp130 ;re_ ur130 = abs_ ur130 * os(phase_ ur130);im_ ur130 = abs_ ur130 * sin(phase_ ur130); plx_ ur130 = re_ ur130 + j*im_ ur130;New130(1,i) = plx_ ur130;endifif(i > (102 - ( ind130 - 250) +orig_ ol))New130(1,i) = 0 + 0*j;endifendforfor i = (102 - ( ind175 - 250)):1:201if(i <= (102 - ( ind175 - 250) +orig_ ol))phase_ ur175 = arg(New175(1,i)) - phase175;abs_ ur175 = abs(New175(1,i))/amp175 ;re_ ur175 = abs_ ur175 * os(phase_ ur175);im_ ur175 = abs_ ur175 * sin(phase_ ur175); plx_ ur175 = re_ ur175 + j*im_ ur175;New175(1,i) = plx_ ur175;endifif(i > (102 - ( ind175 - 250) +orig_ ol))New175(1,i) = 0 + 0*j;endif

11.2 O tave Code for Data Analaysis 68endfor%New130***************Printing to File ****************filename10="130.out";filename11="175.out";fp10 = fopen(filename10,"w");fp11 = fopen(filename11,"w");for m =1:1:201fprintf(fp10,"%f %f \n",real(New130(1,m)),imag(New130(1,m)) );fprintf(fp11,"%f %f \n",real(New175(1,m)),imag(New175(1,m)) );endforf lose(fp10);f lose(fp11);endfun tion#################################################################fun tion upto har( last har, fp1 )tmp har = '';while ( tmp har != last har )tmp har = fgets(fp1,1);endwhileendfun tion#################################################################fun tion uptostring( 1, 2, fp2 )tt = 0;while(tt == 0 )upto har( 1, fp2 );tmp har = fgets( fp2, 1);if (tmp har == 2 )tt = 1;endifendwhileendfun tion####################################################################\subse tion[\large{Final Analaysis}℄{\large{\textbf{Final Analysis}}}* O tave ode that takes the output of initinal_holography* and then omputes the aperture distribution by using the* dire t Fourier Transformfun tion final_holographyfilename20 = "intial_data_130.hol";

11.2 O tave Code for Data Analaysis 69filename21 = "initial_data_175.hol";pro essed_data_130=zeros(18,201);pro essed_data_175=zeros(18,201);%****Sorting the raw-data into a single row matrix*********fp20 = fopen(filename20,"r");fp21 = fopen(filename21,"r");[New130 stop℄ = fs anf(fp20,"%f",[1,Inf℄);[New175 stop℄ = fs anf(fp21,"%f",[1,Inf℄);f lose(fp20);f lose(fp21);%**********************************************************n=1for k=1:1:18for i=1:1:201pro essed_data_130(k,i) = New130(1,n)+j*New130(1,n+1);pro essed_data_175(k,i) = New175(1,n)+j*New175(1,n+1);n=n+2;endforendfor% reating the mesh of the dish with 1 m a ura y.xgrid_dish = zeros(1,61);ygrid_dish = zeros(1,61);delta =1;% distan e in metersdeltaxgrid_dish(1,1) = -(30*delta);ygrid_dish(1,1) = -(30*delta);for i = 2:1:61k = i - 1;xgrid_dish(1,i) = xgrid_dish(1,k) + delta ;ygrid_dish(1,i) = ygrid_dish(1,k) + delta ;endfor120000xgrid_dishygrid_dishzgrid_dish_130 = zeros(61,61); % reating the grid onsisting the field-valuezgrid_dish_175 = zeros(61,61);%**********************----------------------%******* Dire t Fourier transform ***********fa tor = 0.;Lambda = 0.23438; % wavelength of observation in metersFT_Tot_130 = 0.;FT_S an_130 = 0.;FT_Tot_175 = 0.;

11.2 O tave Code for Data Analaysis 70FT_S an_175 = 0.;rad = pi/(180*60);rad1 = pi/180;delta_theta = 252./100; % tot. ar min overage / total points in a s anNs an = 18; % total no. of s ans takendelta_alpha = 180./Ns an;for px = 1:1:61%xgrid_dish(1,px)for py = 1:1:61FT_Tot_130 = 0.;FT_Tot_175 = 0.;% ygrid_dish(1,py)sign = -1;alpha = 0.;for k = 1:1:Ns anFT_S an_130 = 0.;FT_S an_175 = 0.;k;theta = sign.*delta_theta.*50;wx =1;for i=1:2:201i;theta;theta_x = theta* os(alpha*rad1);theta_y = theta*sin(alpha*rad1);weightage=abs(delta_alpha*(theta*delta_theta)* (rad1*rad*rad));if(i==101)weightage = abs((pi./4)*delta_theta*delta_theta*(rad*rad)/Ns an);endifw(1,wx) = weightage;fa tor = exp(j*(2*pi)*((xgrid_dish(1,px).*theta_x*rad)+(ygrid_dish(1,py).*theta_y*rad))/Lambda);FT_S an_130 = FT_S an_130+(pro essed_data_130(k,i).*weightage*fa tor);FT_S an_175 = FT_S an_175+(pro essed_data_175(k,i).*weightage*fa tor);theta = theta - sign*delta_theta;wx = wx +1;endforalpha = alpha + delta_alpha;% differen e in alpha for ea h s an than the previoussign = - sign; % hanging of sign due to the s anning te hnique

11.2 O tave Code for Data Analaysis 71FT_Tot_130 = FT_Tot_130 + FT_S an_130;FT_Tot_175 = FT_Tot_175 + FT_S an_175;endforzgrid_dish_130(px,py) = FT_Tot_130;zgrid_dish_175(px,py) = FT_Tot_175;endforendforzgrid_dish_130;wXaxis=1:1:16;figure(1); ontour(xgrid_dish,ygrid_dish,abs(zgrid_dish_130));figure(2);mesh(xgrid_dish,ygrid_dish,abs(zgrid_dish_130));IFF130=ifft2(zgrid_dish_130);IF130=fftshift(IFF130);figure(10);mesh(xgrid_dish,ygrid_dish,abs(IF130));figure(3); ontour(xgrid_dish,ygrid_dish,abs(zgrid_dish_175));figure(4);mesh(xgrid_dish,ygrid_dish,abs(zgrid_dish_175));figure(5); ontour(xgrid_dish,ygrid_dish,arg(zgrid_dish_130));figure(6);mesh(xgrid_dish,ygrid_dish,arg(zgrid_dish_130));figure(7); ontour(xgrid_dish,ygrid_dish,arg(zgrid_dish_175));figure(8);mesh(xgrid_dish,ygrid_dish,arg(zgrid_dish_175));figure(5)%plot(Xaxis,abs(zgrid_dish_130(1,:)),'r',abs(zgrid_dish_175(1,:)),'b');%figure(6)%plot(Xaxis,arg(zgrid_dish_130(1,:)),'r',arg(zgrid_dish_175(1,:)),'b');figure(11);plot(w);%endfun tion%***************Printing to File ****************

11.2 O tave Code for Data Analaysis 72filename20 = "final_data_130+175_C00:C03.hol";fp20 = fopen(filename20,"w");for m =1:1:61for n =1:1:61fprintf(fp20,"%f %f %f %f \n",real(zgrid_dish_130(m,n)), imag(zgrid_dish_130(m,n)),real(zgrid_dish_175(m,n)), imag(zgrid_dish_175(m,n)) );endforendforf lose(fp20);endfun tion%********************************************************************************

BIBLIOGRAPHY 73Bibliography[1℄ A.Ri hard Thompson, James M.Moran and George W.Swenson Jr: Interferometryand Synthesis in Radio Astronomy, John Wiley Sons. In , 2nd Edition(2001).[2℄ K.Rohlfs and T.L.Wilson: Tools of Radio Astronomy, Springer-Verlag, 2nd Edi-tion(1996).[3℄ Ronald N.Bra ewell: The Fourier Transform and its Appli ations Ma Graw-Hill BookCompany, 2nd Edition(1986).[4℄ Philip R.Bewington:Data Redu tion and Error Analysis for the Physi al S ien es,Ma Graw-Hill Book Company(1969).[5℄ C.A. Balanis: Antenna Theory - Analysis and Design, John Wiley Sons (Asia) PteLTD.[6℄ Max Born and Emil Wolf: Prin iples of Opti s, 6th Edition, Cambridge UniversityPress(1980).[7℄ John D.Kraus: Radio Astronomy, 2nd Edition, Cygnus-Quasar Books(1986).[8℄ P.F.S ott and M.Ryle: A rapid method for measuring the �gure of a radio teles opere e tor, Monthly Noti es of Royal Astronomi al So iety(1977) Vol-178, Pages: 539-545.[9℄ J.C.Bennett, A.P.Anderson, Peter A.M Innes and A.J.T.Whitaker: Mi rowave Holo-graphi Metrology of Large Re e tor Antennas, IEEE Trans. Ant. Prop.(1976) Vol-AP-24, No-3 Pages- 295-303.[10℄ D.Morris: Phase Retrieval in the Radio Holography of Re e tor Antennas and RadioTeles opes, IEEE Trans. Ant. Prop.(1985),Vol- AP-33 pages 749-755.[11℄ William L.Peters Surfa e Measurements of Large Antennas At High A ura y,hawk.iszf.irk.ru/URSI2002/GAabstra ts/papers/p0964.pdf[12℄ E.Serabyn, T.G.Philips and C.R.Mason: Surfa e Figure Measurements of Radio Tele-s opes with a Shearing Interferometer ' Applied Opti s(1991), vol. 30, pages 1227-1241.

holography - university of colorado...

Documents