RESEARCH ARTICLE

A novel approach of correlating optical axes of spacecraftto the RF axis of test facility using closerange photogrammetry

C. Koteshwar Rao & Pravesh Mathur &

Swapnil Pathak & Shanmuga Sundaram &

Rajeev Rangrao Badagandi & K. V. Govinda

Received: 29 April 2011 /Accepted: 4 October 2012 /Published online: 9 November 2012# Optical Society of India 2012

Abstract Compact Antenna Test Facility (CATF) isconfigured to carry out antenna characterization and alsofor checkout of the fully integrated spacecraft with an-tenna and other subsystems. The CATF is used for themeasurement of radiation pattern, gain, return loss, crosspolar isolation, precise identification of the bore-sightaxis, EIRP and gain/temperature (G/T ratio) of the anten-na system under the simulated zero-gravity environment.During the test, the spacecraft is positioned on the DeviceUnder Test (DUT) Positioner, which is about 5 m aboveground and the geometric axis of the spacecraft is repre-sented by an optical mirror cube which is correlated withRF (Radio Frequency) axis of the facility in order tomatch the nominal reflector bore-sight with the NominalPlane Wave axis (NPA) of the Facility. Special fixturesare used to simulate the zero-gravity environment. Nov-elty of this paper lies in the development of techniquewhich synergies the optical alignment systems and CloseRange Photogrammetry (CRP) for correlating the opticalaxis of the spacecraft with the RF axis of test facility. Thispaper describes the details of the new technique, generaldescription of the facility and the various alignmentmeasurement systems used for alignment of spacecraftand its subsystems. The paper further claims advantagesof CRP over other methods of measurement in terms of

time & effort saving, real time measurement capability,measurement of critical geometries in inaccessible orien-tations & development of methodology to derive RF &optical axis without the use of physical features as refer-ences on the spacecraft body.

Keywords Optical metrology . Close rangephotogrammetry . Compact Antenna Test Facility

AbbreviationsCATF Compact Antenna Test FacilitySCCS Spacecraft Coordinate SystemNPA Nominal Plane wave AxisDUT Device Under TestEIRP Effective Isotropic Radiated PowerRF Radio FrequencyCRP Close Range PhotogrammetryCMM Coordinates Measuring MachineISAC ISRO Satellite CentreISRO Indian Space Research OrganizationMRC Master Reference CubeFRC Facility Reference CubeECDS Electronic Coordinate Determination System

Introduction

ISRO Satellite Centre (ISAC) is India’s National Sat-ellite Assembly Integration and Test facility. The fa-cilities at ISAC are used for integrating & testing of

J Opt (January–March 2013) 42(1):51–63DOI 10.1007/s12596-012-0096-7

C. K. Rao (*) : P. Mathur : S. Pathak : S. Sundaram :R. R. Badagandi :K. V. GovindaSystems Integration Group, ISRO Satellite Center,Bangalore, Indiae-mail: ckrao3@gmail.com

wide variety of Satellite systems for remote sensingand communication applications and cover a widefrequency range. Communication satellite undergoesvarious payload performance tests to ensure reliableperformance of satellite in orbit.

The satellite antennae measurements for perfor-mance and characterization in transmit and receivebands are carried out in CATF. The measurementincludes 2D/3D radiation pattern, gain, cross polarisolation, bore-sight, etc. The CATF, which replacesextremely long outdoor test ranges, enables to sub-stantially reduce test periods. CATF is closed compactchamber with clean room environment. Absorbers aremounted all around the inside of the facility to isolateexternal signals so as to avoid multipath reflectionsduring measurement. The CATF consists of DUTPositioner, main-reflector, sub-reflector and feed sys-tem. During the test, the spacecraft is placed on theDUT positioner, which is approximately 5 m aboveground. Once the spacecraft is mounted on DUT,alignment measurements are carried out to match thespacecraft antenna bore-sight axis with the nominalplane wave axis (NPA) of the facility.

Optical mirrors, tooling targets, scriber marks etc. areoften used for representing the spacecraft bore-sight axisand NPA of the facility. Alignment measurements in-clude measurement of orientation and 3D position ofthese mirrors and targets which in turn relate spacecraftbore-sight axis and NPA of facility. This is a veryinvolved process and is repeated number of times toensure that the alignment is correct and is within theaccuracy demanded by the CATF measurements.

Conventionally such measurements were carriedout by developing an optical network of digital Sur-veying Theodolites working on optical principles viz.auto-collimation, cross-collimation and triangulation[1, 2]. These techniques require bulky fixtures andleveled platform to position the network of theodoliteinstruments inside the constrained environment ofCATF. Usage of such techniques at a height of 5 mabove the ground for repeated measurements is atedious and time consuming process.

In the past few decades, a number of portable,hand-held, non-contact 3D measuring systems suchas Laser tracker, Close range Photogrammetry, LaserRadar, etc. have evolved. Advances in the area ofindustrial metrology have generated new technologiesthose are capable of measuring component with com-plex geometry and large dimension. However no

standard or best practice guidelines are available forthe majority of such systems. Therefore these newsystems require appropriate testing and verificationin order for the users to understand their full potentialprior to their deployment in a real manufacturingenvironment. Various case studies are demonstratedin [4, 5] to compare accuracies of CRP, ECDS, andlaser tracker. Further the feasibility of using CRPmethods for spacecraft assembly operations is alsoexplained in [3–5].

Digital Close Range Photogrammetry (CRP) is reg-ularly used as a flexible and highly accurate 3D mea-surement system. CRP’s most common applications liewithin the manufacturing and precision engineering in-dustries. Through the use of triangulation combinedwith specialized targets to mark points of interest, accu-racies exceeding 1:100,000 can be achieved with CRP.

In practical applications, circular targets are used toachieve the highest accuracy. Common types include:retro-reflective targets, which provide a high contrastimage with flash photography, and white targets on ablack background. Accuracy requirements and vary-ing target reflective properties dictate which type oftargeting is most suitable for a particular application.An extensive study on targets used for photogramme-try applications is demonstrated in [6]. However theoptical mirrors and scriber marks, which are used bytheodolite techniques for alignment inside CATF, can-not be measured with CRP technique.

The objective of the developments presented in thispaper is to correlate the optical axis of the spacecraft andbore-sight of the antenna with the NPA/RF axis of thefacility using optical and CRP techniques which furtherclaims improvement in the accuracy and productivity ofthe measurements.

Various reference coordinate systems

Definition of spacecraft reference coordinate system

A typical spacecraft is a cuboid in shape which consistsof a conical ring mounted at the bottom side which getsinterfaced with the adopter of launch vehicle. The phys-ical features of this ring are used to define the referenceframe of spacecraft. There are two techniques which areemployed in defining the coordinate system for thespacecraft. 1st using Autocollimation, where orienta-tion of an optical mirror cube (called as Master

52 J Opt (January–March 2013) 42(1):51–63

Reference Cube) is established with respect to thespacecraft reference frame. 2nd using CRP, where3D coordinates of tooling targets are measuredwith resepect to the spacecraft reference frame.Axis definition of a typical communication space-craft used during this study is explained below. Itwill be referred here onwards as SCCS (i.e. Space-craft Coordinate System) and its axes are repre-sented as Xs,Ys, Zs.

Origin Center of the circular edge of the interface ring.

+ve Yaw: axis(Xs)

From Origin (center of separation plane)towards the top deck & normal to theinterface plane.

+ve Roll : axis(Ys)

Line Joining the centers of two tooling holeprovided on the interface ring.

+ve Pitch: axis(Zs)

From Origin completing the orthogonal righthanded system.

Spacecraft is positioned on a levelled surface tableand the SCCS [Figs. 1 and 2] is established by mea-suring the physical features (i.e. tooling holes & sep-eration plane of spacecraft conical ring) available onthe spacecraft using principle of Auto-Collimation andClose Range Photogrammetry (CRP). The followingsteps are followed for establishing the SCCS referenceand measuring tooling target coordinates and orienta-tion of MRC.

Step1: Place the spacecraft on a levelled surfacetable [Fig. 1].Step2: Mount an optical mirror cube (MRC) onthe top of Spacecraft. Normal of orthogonal facesform a cube coordinate system and its axes arerepresented as Xc, Yc, Zc [Fig. 1]. The specifia-tion of the cube used for this study is as follows:

Material: BK7 Fine annealed GlassSize: 8 mm×8 mm×8 mm +/−0.2 mmFlatness: λ/8 at 632 nm

Faces of the cube are coated with Aluminium withSiO2 Protective layer.

Reflectivity: better than 85 %Perpendicularity: between faces better than10 arc sec

Step3: Establish a network of three digital sur-veying theodolites (in this case ®Lieca’s TM5100Theodolites were used).Step4: Two out of the three theodolites use prin-ciple of autocollimation to measure the normal ofthe two faces of an optical mirror cube. The thirdtheodolite scans the physical feature (such as linejoining the tooling holes on the conical ring of thespacecraft, which represents one of the spacecraftaxes) which is used as azimuth reference for thetwo theodolites. This step provides the three eulerrotations Rx, Ry and Rz of the cube with respect to

Fig. 1 Setup used for Spacecraft Reference Generation

Origin

Fig. 2 Definition of Space-craft Coordinate System

J Opt (January–March 2013) 42(1):51–63 53

Xs,Ys and Zs axis of the SCCS, respectively.Autocollimation procedure for measuring tilt ofthe face of an optical mirror cube is explained asfollows:

Auto-collimation [Fig. 3] is the process of sightingwith a telescope [Fig. 4] focused to infinity to anoptically flat mirror. In order to carry out auto-collimation, the telescope reticule must be illuminatedfrom the eyepiece side. A silhouette of the illuminatedcross hairs is projected onto the mirror and reflectedback to form an image in the plane of cross hairs. If themirror is exactly at 900 to the line of sight the crosshair coincide with their reflected image. The tilt ofmirror is read using the encoders of the theodolitewhich give reading in horizontal and vertical referenceplanes (Fig. 5).

Step5: CRP compatible targets are mounted onthe conical ring of the spacecraft and also a num-ber of tooling targets are mounted on the faces ofthe spacecraft cuboid. The output of CRP mea-surement provides 3D coordinates of centroid ofthese targets. This measured data is used to derivea 3D CAD model wherein a SCCS is created atthe interface ring. The CAD model further relates

the coordinates of centroid of the tooling targetson the faces of spacecraft cuboid to the SCCSdefined at the interface ring. A 3D CAD modelderived using the measured CRP data for a typicalcommunication spacecraft is shown in Fig. 6.Step6: Once the reference coordinate system isestablished, the rotation of Master ReferenceCube(MRC) (about Yaw, Roll & Pitch) and 3Dcoordinates of tooling balls are available withrespect to a common reference frame i.e. SCCS.The measured rotations of MRC & 3D coordi-nates of tooling targets are used for representingspacecraft reference coordinate system and align-ment of various elements (viz. Sensors, actuators,Feed & reflector).

The reference frames of other subsystems like an-tenna, feed etc. are also generated and defined by thephysical/optical features on them. Once the subsystemis assmbled onto the spacecraft, alignment measure-ments are carried out to derive transformation param-eters of the assembly with reference to the SCCSreference frame. The concepts of transformationamong various rigid bodies can be referred from [7,8]. The transformation achieved for one of the subsys-tem with respect to SCCS is explained as follows:

Fig. 3 Theodolites workingprinciple

fl

θ

y

Objective

Mirror

Fig. 4 Auto-collimationPrinciple

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Let us consider spacecraft coordinate system isrepresented as {A} and a subsystem (in this caseantenna coordinate system) is represented by {B}.

The general transformation between these two co-ordinate systems is shown in Fig. 7 which can berepresented as Eq. 1.

Ap ¼ AOB þ AB½R� Bp ð1Þ

Where,

OA denotes the origin of {A}OB denotes the origin of {B}AOB locates OB with respect to OA.AB½R� 3×3 rotation matrix which gives orientaion of

rigid body B in {A}. If AbXB, AbYB and AbZB arereferred as the axes of {B} in terms of axes of{A} then AbXB, AbYB and AbZB represent thecolumns of A

B½R�.

The position vector of the point P, in the rigid bodyB, with reference to the coordinate system {A} or therigid body A is denoted by Ap. Similarly the positionvector of the point P, in the rigid body A, with refer-ence to the coordinate system {B} or the rigid body Bis denoted by Bp.

Fig. 5 Optical mirror cube Rotation measurement using 2theodolites

Camera Network for CRP measurement on a Spacecraft

3D Model of a Spacecraft Derived using CRP

Fig. 6 3D CAD model derived using CRP

Fig. 7 Transformation between two rigid bodies

Fig. 8 Setup - Spacecraft Mounted on DUT Positioner insideCATF

J Opt (January–March 2013) 42(1):51–63 55

In terms of components, each of the unit vectors bXB,bYB and bZB, attached to the rigid body B, can be describedin {A} as Eq. 2

AbXB ¼ r11bXA þ r21bYA þ r31bZAAbYB ¼ r12bXA þ r22bYA þ r32bZAAbZB ¼ r13bXA þ r23bYA þ r32bZA

9=; ð2Þ

Where, rij (i,j being 1,2,3) are the components.The Rotation matrix A

B½R� can also be described as

AB½R� ¼

r11 r12 r13r21 r22 r23r31 r32 r33

24

35 ð3Þ

Setup of Compact Antenna Test Facilityand conventional method of correlating bore-sightaxes of spacecraft to RF axis of test facility

This section provides a brief overview about the setupinside the CATF facility and the limitations of con-ventional procedure being used for aligning bore-sightaxis of spacecraft with that of the RF axis of CATFfacility. The setup of the CATF is as shown in Figs. 8,9 and 10.

The device under test (spacecraft along with anten-nae) is mounted on the DUT Positioner, which is at aheight of about 5 m above the ground. The details ofthe setup inside CATF is shown in Figs. 8 and 10.

The RF signals, emitted by the facility feed,gets reflected via the facility reflectors and reachesto spacecraft reflector. Geometrical relationship be-tween the shape of facility reflectors (Primary andSecondary) and the facility feed is establishedduring the facility establishment (Fig. 9). The re-lation between various coordinate systems (asshown in Fig. 11) are then measured using align-ment measurement techniques.

Scriber marks and optical mirror cubes (such asFRC) are mounted on the rigid places of the CATFfor defining the reference of the facility. A FacilityReference Cube (FRC) is located on the sub reflectorpedestal. The normal of faces of FRC (which definesthe Facility CS) is then related to the geometry of thefacility using a network of theodolites. Figure 12shows a setup of theodolite network inside CATF,the details are as follows:

Six theodolite stations established on stable fixtures(Fig. 13 shows fixtures used for positioning theodo-lites) at height of DUT. The theodolite stations arerepresented by cross mark and named as Ti. Opticalaxis of T1 is set normal to the mirrored face of FRC. T1

provides azimuth reference for T2 & T3.T2 and T3 are set normal to two orthogonal faces of

MRC and hence provide three euler rotations withrespect to local vertical & FRC using the procedureexplained in section Definition of spacecraft referencecoordinate system.

3D coordinates of scriber marks on the facilityreflector & tooling targets of spacecraft reflector ismeasured using Electronic Coordinate Determination

Fig. 9 RF Signals traversalfrom facility to Spacecraftreflector

DUT Positioner

Primary Reflector

Secondary Reflector

RF Absorbers

Fig. 10 Elements of CATF Geometry

56 J Opt (January–March 2013) 42(1):51–63

System (ECDS ®Lieca). In this technique, point coor-dinates are measured via intersection from theodolitesrays (minimum 2). The operators aim two telescopesat a target in space. Digital encoders register the rela-tive angular positions of the two theodolite heads withrespect to a reference coordinate system. A softwarecalled AXYZ (®Lieca) computes the 3D coordinatesof the sighted target and relates mirror cube normals tothe various reference frames defined by respectivetooling targets. The pointing accuracy of such networkdepends on the geometry of intersecting axes of twotheodolites sighting a common target. More number ofstations are required to improve geometry and sight-ability of various tooling targets on the facility andspacecraft. The detailed discussion on proceduresadopted for measurement inside a CATF facility usingtheodolite network is provided in [1].

Setting up the theodolite stations at a height of 5 mis time consuming and sometimes critical geometries/

locations of the target points are impossible to measureusing thedolite station geometries.

In order to overcome the above problem, variousstudies were undertaken and several 3D measurementsystems, including CRP were evaluated. It was con-ceived that CRP has several inherent advantages forspacecraft alignment applications, particularly in termsof speed, accuracy, repeatability, ease of operation andminimizing manpower to complete tasks. The detailsof the case studies are presented in [2]. However CRPcan measure only high contrast targets (such as retro-reflective targets manufactured by ®3 M & HUBBSwere used for this study) and direct measurement ofoptical mirror cubes of spacecraft and CATF facility(i.e. FRC) is not possible using CRP.

A new approach presented in the preceding sectionprovides a simple method, for determination of rela-tive orientation of geometric axis of the spacecraftdefined by MRC, and the 3D position of reflectors

Fig. 11 Various ReferenceCoordinate Systems (CS)Used inside CATF

Fig. 12 Theodolite Net-work to Relate Antenna Ge-ometry with the FRC ofCATF

J Opt (January–March 2013) 42(1):51–63 57

and feed system with respect to the bore-sight axis ofthe CATF (Fig. 14).

Brief overview of measurement systems used

Digital surveying theodolites

Once levelled and optical axis of the instrument isaligned to the normal of a flat mirror using principleof auto-collimation, this system measures elevation tiltof the normal of the flat mirror with respect to a localgravity and azimuth tilt with respect to any base linereference defined as an azimuth reference. For this

study ®Lieca TM5100 digital theodolites wereused. A detailed description of the working oftheodolites and triangulation for industrial applica-tion is described in [2].

Electronic Coordinate Determination System (ECDS)

In this technique, point coordinates are measured viaintersection of minimum of two rays from theodolites(Fig. 15). Typically, points are identified using physi-cal targets such as tooling balls, crosshairs as featureson the object. The operators aim two telescopes at atarget in space. Digital encoders register the relativeangular positions of the two theodolites heads withrespect to a reference coordinate system. A computeruses AXYZ software & the principle of triangulationto determine the coordinates of target positions.

Close range photogrammetry

Photogrammetry uses the basic principle of triangula-tion (Fig. 16) to produce 3-dimensional point measure-ments. By mathematically intersecting converging linesin space, the precise location of the point can be

Fig. 13 Theodolite Mounted on Bulky Fixtures

Fig. 14 Theodolites work-ing principle (CourtesyWikipedia)

Fig. 15 ECDS uses Triangulation to measure Tooling targets onthe spacecraft

58 J Opt (January–March 2013) 42(1):51–63

determined. However, unlike theodolites, photogram-metry can measure multiple points at a time with virtu-ally no limit on the number of simultaneouslytriangulated points.

In the case of photogrammetry, it is the two-dimensional (x, y) location of the target on the imagethat is measured to produce this line. By taking pic-tures from at least two different locations and measur-ing the same target in each picture, a “line of sight” isdeveloped from each camera location to the target. Ifthe camera location and aiming direction are known,the lines can be mathematically intersected to producethe xyz coordinates of each targeted point.

Photogrammetric reconstruction

This section provides a brief overview of the photo-graphic reconstruction process, which results in apoint cloud of discrete points. The necessary stepsare presented below for a reader to get an overall ideaof photgrammetric reconstruction process. Further

details can be accessed from [9]. GSI’s INCA3a Cam-era (Specification details are as shown Fig. 17) withVSTAR-S software was used for carrying photogram-metric measurements of spacecraft and the facility.

Network design The number of overlapping photosand how the photos are shot are critical to the qualityof the reconstruction. It is vital to capture the objectcompletely and accurately. Failure to plan ahead maylead to difficulties that cannot be corrected withoutgoing back and shooting the site again.

Calibration Onsite Photographing and RectificationCalibration are used to determine the lens distortionand to determine the internal parameters of each cam-era used. On-site photographing is the actual photo-graphing of the site, while rectification removes thelens distortion from the images.

Matching Corresponding points between images needto be matched. The robustness of this step affects the

Fig. 16 Principle of Trian-gulation (courtesy VSTARSmanual)

Fig. 17 V-STARS INCA3System Specifications.(Reproduced from V-STARS INCA3 brochure)

J Opt (January–March 2013) 42(1):51–63 59

quality of the following steps, since the data acquiredhere are used throughout the other steps.

Determining epipolar geometry An essential or fun-damental matrix is calculated using the matched pointsacquired in the previous step.

Relative orientation The camera matrices are estimat-ed using the epipolar geometry. Since it is not possibleto know the size or location of the depicted objects,some of the parameters in the camera matrices will befixed.

Triangulation Calculates the 3D coordinates ofmatched points. Beside the matched points, this alsorequires the camera matrices. Consider two views withone camera matrix and one 3D point for each view andthen the points have been matched to each other.

We want to find the 3D position of the point seenin both views. The back projection of an imagepoint is a line going through both the camera focalpoint and the image plane. The back-projection ofeach view’s point will result in two lines. Byestimating the intersection of these two lines, a3D coordinate can be found. If the measurementsin the views contain errors, the rays will mostlikely not intersect. There are two approaches tosolve this problem, either by minimizing theobject-space error or image space error.

Registration Combine the triangulated coordinates toa common coordinate system.

Error minimization Minimize the combined error ofall the 3D coordinates, this is usually referred to asbundle adjustment.

Fig. 18 Setup used for thenew approach

Fig. 19 Setup used for thenew approach

60 J Opt (January–March 2013) 42(1):51–63

Absolute orientation Use control points with knowncoordinates to transform the Euclidean reconstructionto an external coordinate system.

Details of the newly developed approach

The objective of this measurement is to correlate var-ious coordinate systems (as shown in Fig. 18) insideCATF. Following are the details of Coordinate Sys-tems (CS) referred in Figs. 18 and 19:

a. Spacecraft CS: represented by CRP compatibletooling targets and MRC (the detailed proce-dure of reference established is explained insection Definition of spacecraft reference coor-dinate system.

b. Antenna CS: The relation between shape ofspacecraft antenna and CRP compatible targets isestablished using CMM. The tooling targets rep-resent Antenna CS.

c. Facility CS: An optical mirror cube is mounted atthe base of facility reflector during establishmentof CATF is referred as Facility reference Cube(FRC). The normal of the faces of FRC representfacility coordinate system.

d. Surface Table CS: Normal to surface table planedefines Y-axis and normal to leveling mirror planedefines Z-axis and X-axis completes the righthanded coordinate system on surface table.

Since CRP cannot measure optical mirror cubedirectly, the major challenge of this development wasto relate the CRP compatible tooling targets to theoptical mirror cube which represents the facility CSand Spacecraft CS. The following is the setup detailsused to meet the objective:

& A surface table (size 1 m2) with surface finishbetter than 0.005 mm is setup near the base ofthe DUT positioner. Normal of the leveled surfacetable is parallel to local gravity vector and thesame gravity vector is also the reference for atheodolite to measure the elevation angle of anyoptical mirror.

& A leveling mirror (200×200) mm2 is placed on theleveled surface table and plane of the mirror ismade perpendicular to the plane of surface table.The specifications of the leveling mirror are asfollows:

Material: BK7 Fine annealed GlassSize: 200 mm×200 mm×20 mm +/−0.2 mmFlatness: λ/8 at 632 nm

Faces of the cube are coated with Aluminium withSiO2 Protective layer.

Reflectivity: better than 85 %

& Two digital theodolites (Lieca-TM5100A) T1 &T2

are established on stable fixtures. T1 is set normalFRC which provides azimuth reference to T2 & T2

is set normal to leveling mirror.& Once the rotations of FRC and leveling mirrors are

measured, the relation between Facility CS andSurface table CS can be established using Eq. 1–3described in section Brief overview of measurementsystems used.

& To derive the Surface Table CS using CRP thefollowing steps are followed:

1. 12 numbers of CRP compatible targets arestuck on the surface of the surface table andthe plane of the leveling mirror to define nor-mal of the surfaces.

2. A standard Scale, auto-bar and coded targetsare also placed near the setup which is used forderiving the exterior orientation of the cameraand scaling the photographs.

3. Photography is carried out from different loca-tions using a hand held metric cameraINCA3®GSI and the processing is carried outusing VSTARS®GSI software to derive the 3D

Table 2 Scan window used for conducting raster scan

Axis Start of Scan End of Scan Step Size

Azimuth -5 deg +5 deg 0.2 deg

Elevation -3.5 deg +3.5 deg 0.2 deg

Table 1 Comparison of readings obtained using conventionaland new appraoch

Rotationabout Yaw

Rotationabout Roll

Rotationabout Pitch

MRC readingsConventionalApproach

+1.2794° -0.7197° +0.5566°

MRC readings NewApproach

+1.2750° -0.7166° +0.5538°

Difference 0.0044° 0.0031° 0.0028°

J Opt (January–March 2013) 42(1):51–63 61

coordinates of the targets of surface table andleveling mirror along with the tooling targets(which defines the reference frames of reflector,feed and bore-sight axis of the facility). VSATRSsoftware automates the steps described in sectionBrief Overview of Measurement Systems usedfor photogrammetric reconstruction to generate3D coordinates of the target points.

4. Further processing on the 3D coordinates oftarget points is carried out using VSATRS soft-ware as follows:

a. Best fit plane-a is derived using targetpoints on surface table points.

b. Best fit plane-b is derived using targetpoints on the plane of mirror.

c. Normal of plane-a and normal of plane-brepresent two orthogonal axis of surface tablecoordinate system which is identical to thecoordinate system derived using a networkof theodolites.

d. Spacecraft coordinate system and Antennacoordinate system are derived using thetooling target data measured during referencegeneration stage (detailed procedure isexplained in section Definition of spacecraftreference coordinate system).

e. Once all the coordinate systems (viz. SCCS,Antenna CS, Surface Table CS and FacilityCS) are derived and the 3D coordinates of thetooling targets are measured in their respec-tive coordinate systems (say local coordinatesystems), transformation among all the coor-dinate system can be done using the Eqs. 1–3explained in section Definition of spacecraftreference coordinate system.

f. MRC and tooling targets on the spacecraftrepresent a common coordinate system i.e.SCCS. Hence the above step can be used toderive orientation of MRC with respect toFacility CS.

5. Two different case studies were carried out to val-idate the results obtained using the new procedure.

The observations during both the measurements arediscussed in the preceding section.

Results & discussion

Case study-1

Measurements were carried out on MRC usingconventional procedure and new procedure. MRC

-3

-3

-3

-3

-3

-3

-3

-3

FT

0.00 2.00 4.00 6.00 8.00

Theta*cos(phi) in Degrees

0.00

2.00

4.00

6.00

Th

eta

*sin(p

hi) in

De

gre

es

Fig. 20 RF Pattern mea-sured using two Differentapproaches (Red-Old Ap-proach, Blue-NewApproach)

62 J Opt (January–March 2013) 42(1):51–63

orientations were calculated using conventional ap-proach and new approach. Table 1 shows the compari-son between MRC orientations measured using themethod as described in the section Setup of CompactAntenna Test Facility and conventional method ofcorrelating bore-sight axes of spacecraft to RF axis oftest facility and the new approach as described insection Details of the newly developed approach insideCATF.

Obsrevations

& The comparison shows the values obtained by thenew approach lie within 0.005 deg.

& It becomes a very tedious and time consuming jobusing ECDS to perform measurements at a heightof 5mts from the ground and also the time requiredfor carrying out the measurement took more than16 h. Whereas with the new approach this jobbecame very simple and the measurements werecompleted within about 2 h.

Case study-II

To further validate the new procedure RF pattern mea-surement, a 0.6 m C-band antenna to be flown in ageostationary spacecraft was tested with the two differentphilosophies (i.e. ECDS using Theodolites networkingand New approach Using CRP) of orienting the antennawith respect to the bore-sight axis of the RF facility.

Measurements in both the cases were performed byconducting raster scan (Performing Azimuth cut mea-surement at difference elevation angles) in the scanwindow given in Table 2.

Data acquisition was carried out using AdvancedAntenna Measurement Software (AAMS) [10]. Con-tour plots with respect to beam peak were generatedfor -3 dB points. Red color shown in figure plotsgenerated for old approach & Blue color shows theplots generated in the case of new approach. Misalign-ment in the reflector (if any) will be directly reflectedin the plots and will be seen in the form of beam shiftbetween the two plots.

Observations

& The contour plots in red and Blue show a completeoverlap, which proves that there is no beam shift

and hence the antenna alignment inside CATF usingold and new approach provide the same results.

& The results show a close match between the twopatterns (Fig. 20).

& This test validates the new procedure and provesthat the RF axis of the facility is parallel to thebore-sight axis of the antenna positioned andaligned on DUT using new procedure.

Conclusions

A new approach for correlating the optical axis to RFaxis of the facility using Close Range Photgrammetryis proposed and demonstrated. The newly developedmethod offers advantages in terms of saving of man-hours and effort. Also measurement of critical geom-etries at elevated height becomes very simple whichseems to be tedious and sometime impossible for theconventional techniques. Preliminary investigations(as explained in Case-1 & Case-2) reveal that withthe specific experimental parameters considered, therange of measurement accuracy lie within 0.005 deg.

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