Pointing and Beam-Rotation with an Array-Detector System

Transcription

1 Pointing and Beam-Rotation with an Array-Detector System (Jürgen Stutzki, Version V1.6) Page 1

2 Version Date Author Description Nov JSt initial draft Nov JSt consistent description of beam rotator optic (thanks to input from Urs Graf) and new chapter on implementation in kosma_control Nov JSt include new pixel offset variables Nov JSt include SOFIA l.o.s. rotation, Cassegrain and right Nasmyth port Nov JSt include systematic definition of coordinate systems, numbering of sub-headings Dec JSt clarified distinction between mapping offsets and pixel offset locations, deleted definitions of ~ E, etc. Page 2

3 1 Introduction The purpose of this document is to summarize the issues related to the different coordinates systems on the sky, the telescope, the instrument mounting flange and the instrument focal plane, e.g. in the operation of a Nasmyth-port or Cassegrain-port mounted beam rotator (the former being e.g. used at NANTEN2 with the SMART array receiver, the latter going to be used at SOFIA with the FIFI-LS istrument) and/or the additional l.o.s.-degree of freedom for a 3-axis teslescpe mount like e.g. realized with the spherical oil-bearing mount of SOFIA or in a space telescope. These issues include the nominal beam rotator setting and the related pointing corrections and mapping offsets for indiviudal detector array pixels. Experience has shown, that a trial and error approach, in particular with regard to the many possible signflips in the transformation between the various coordinate systems and the rotation angles involved, does not lead to success: there are too many options and the matter is too complex. Thus, only an ab-initio approach, consistently describing and analyzing these transformations, makes it possible to achieve a proper implementation at the telescope. This document supersedes the technical note Tech_Memo_Beam_Rotator.doc, which was a first attempt to document these issues for the implimentation at NANTEN2. It aims at giving a full documentation of the relevant issues in particular towards their implementation within the kosma_control observing software package, which is in use at NANTEN2 and SOFIA. 1.1 Reference Frames and Coordinate Systems We have to consider 4 reference frames and associated coordinate systems along the line-of-sight from he instrument focal plane to the celestial source, each of which (may) rotate against the others. These are: the sky reference frame, specified by the sky coordinate system in which the celestial source is observed or mapped. Typically this is an offset coordinate systems in either one of Azimuth/Elevation (horizon system), Right Acsension/Declination (equatorial system), or Galactic Longitude/Galactic Latitude relative to the sky reference position. In the following we label this system by the variables conventionally used for RA/Dec, namely ( ; ± ), which in the context of this document therefore may stand for any of the above sky coordinates. the telescope reference frame with its associated telescope coordinate system, which is fixed to the telescope mechanics and optics. In the following, we label these coordinates with ( ; ). For a ground based telescope with a two-axes ( Az=El)-mount, like all radio telescopes and most large modern optical telescopes, a coordinate system attached to ( Az=El) is a natural choice (although not identical to the ( Az; El) coordinates, which refer to the sky, we call the axes the same in the following). For space telescope or the SOFIA telescope, which have three degrees of freedom for rotation, we define the additional angle in the line-of-sight degree of freedom by» l:o:s: in such a way, that at» l:o:s: =0 the ( ; )-coordinates are aligned with ( Az; El) and» l:o:s: gives the counterclockwise rotation angle of the telescope when viewed along its optical axis towards the sky. The origin of the ( ; ) coordinate system is chosen to be the optical axis of the telescope. the instrument mount reference frame, attached to the instrument mount at the telescope, with its associated instrument mount coordinate system, which we specify by coordinates ( u; v) in the following. For a Cassegrain mount, i.e. with fixed orientation lateral position to the telescope, one naturally chooses these coordinates to be aligned with the telescope coordinate system projected into the instrument mounting plane, i.e. possibly flipped in the resp. Az-direction due to a tertiary mirror, like on SOFIA. The origin of the ( u; v) system then is chosen to coincide with the optical axis of the telescope. For a Nasmyth mount, a natural choice is horizontal/vertical, with the horizontal direction pointing to Page 3

4 the left when looking into the telescope's instrument mounting port and the vertical direction pointing up. This choice insures that at an elevation angle of 0, the ( u; v) coordinate system coincides with the ( Az; El) coordinates projected into the instrument mounting plane through the tertiary mirror. The origin of the ( u; v) coordinate system is then chosen to be the point where the beam rotator axis intersects with the instrument mounting plane, i.e. around which the beam rotator rotates the celestial image resp. the focal plane array footprint. the instrument focal plane reference frame, attached to the detector system, with its associated instrument focal plane coordinated system. We designate these coordinates by ( x; y) in the following. For a fix-mounted receiver/detector system, there is no reason to not have these coordinates be chosen such that they are aligned with the ( u; v) direction and the origin to coincide with the optical axis of the telescope; only the offset of the reference detector pixel from the optical axis, usually called the boresight-offset, is relevant then. For an instrument/detector array mounted with a beam rotator, we choose the ( x; y) system such, that it is aligned with ( u; v) at a beam rotator angle of 0. The origin is taken to coincide with that of the ( x; y) system. 1.2 Rotation and Reflections: Coordinate Transformations and Sign- Conventions In the following one carefully has to distinguish between vectors as physical entities (directions and length in space) and their coefficients, i.e. coordinate values in a given reference system. A fully consistent detailed nomenclature would be to elaborate and we are hence somewhat sloppy in often using the same symbols for the same vector even after e.g. the transformation corresponding to the reflection of the image plane on e.g. the tertiary mirror, whereas we distinguish between them in other cases, like the rotation introduced by the beam-rotator. The notation should be clear form the context. We follow the convention that we count angles as positive, which turn counterclockwise when viewed from the instrument along the telescope optical axis towards the sky. Correspondingly, the rotation of a 2-dimensional vector ~r = (x; y) counterclockwise by an angle Á into a new vector ~r 0 = bd(á)~r is done by the rotation matrix bd(á). In any given coordinate system specified by the unit vectors along the coordinate axes, ~e i, the coordinates of ~r are ~r i=x;y = ( x, and the components of the y ) = ( ~r ~e x ) ~r ~e y : µ rotation matrix are bd i;j (Á) = ~e i b cos Á sin Á D(Á)~e j = Note that this latter expression holds sin Á cos Á only for right-handed coordinate systems; for left handed coordinate systems, the signs are inverted: : µ bd i;j;l.h. (Á) = ~e i b cos Á sin Á D(Á)~e j = This is not relevant in the following, because, though sin Á cos Á we use both right- and left-handed coordinate systems, we only calculate coefficients in the right-handed (Az,El) coordinate system. From the above, it also follows that the coordinates of the same vector viewed in two different coordinate system S and S', where S' is rotated relative to S by bd(á), are related by ~r i;s 0 = bd i;j ( Á)~r j;s, as ~r in S' is oriented relative to the coordinate axes in the same way as bd( Á)~r would be relative to the axes of S. Page 4

5 2 Positioning and Focal Plane Orientation 2.1 Pointing the Telescope The telescope is assumed to be mounted in Az/El coordinates, so that the drive and control system allows the telescope to be driven to a specified Az/El position on the sky. The telescope pointing model takes care of all telescope internal misalignments, flexure etc. through appropriate pointing constants and corrections, which include in particular the Az- and El-pointing corrections corresponding to e.g. the misalignment between the optical pointing telescope axis, on which the pointing model is established, and the radio optical axis. These latter two pointing constants, the Az-,El-pointing corrections, ±Az; ±El, are used during observing to quickly correct the telescope pointing, typically on a time-scale of every few hours. All other pointing constants in the elaborate pointing models of modern telescopes are regularly determined by pointing sessions on many objects around the sky (in the case of large radio telescopes, these pointing sources are typically compact and sufficiently bright continuum sources; in the case of small telescopes with limited point source sensitivity, these pointing sessions use optical guide telescopes and optical stars). To determine the Az-,El-pointing corrections, the observers scans across a pointing source (bright planet or the Sun) and determines the Az-,El-offsets, or more precisely: the position offset of the source in Az-,El-coordinates relative to the nominal pointing: Az; El In order to correct the pointing, i.e. to make the telescope point to this particular object, the pointing corrections have to be increased by the values of the Az-,El-offsets: correcting the pointing: ±Az; ±El! ±Az + Az; ±El + El. The Az; El-offsets giving the apparent position of the source in Az,El-coordinates, i.e. the mapping offsets, on the sky, the position offsets of the detector pixel projected on the sky, ( ±a; ±e), has the opposite sign: (±a; ±e) = ( Az; El). 2.2 Horizon System and Source Coordinate System The astronomical observations are typically not done in the horizon coordinate system (Azimuth, Elevation), but in a celestial coordinate system, e.g. equatorial coordinates right ascension (R.A., ) and Figure 1: northern sky, non-circumpolar source, setting declination (Dec, ± ) or Galactic longitude and latitude. The angle between these coordinate systems (which in the following is needed to specify the proper orientation of the beam rotator of the array receiver) is defined as the angle from the second axis of the celestial coordinate system to the second axis of the horizon system (Elevation). We denote this angle by» in the following. The reason for using the Page 5

6 rotation angle for the second axes rather then the first is, that the convention has the (R.A., Dec.)-system to be left-handed, with R.A. pointing opposite to Az at source transit, so that the first axes have an additional 180 angle between them. Figure 2: northern sky, circumpolar source, setting Figure 3: southern sky, non-circumpolar source, rising Note that in particular for observations in the Horizon-system (Az,El), e.g. for pointing observations on planets, the angle» =0 by definition. Figure 1 to Figure 4 illustrate the typical orientation, sign and magnitude of» for non-circumpolar and circumpolar sources on the northern and southern sky and for the case of (R.A., Dec.)-observations. The values of» in these different cases are summarized in Table 1. Note the singular behavior for sources transiting at zenith as well as when viewed from the equator. Figure 4: southern sky, circumpolar source, rising Page 6

7 hemisphere object location range of» Northern Sky non-circumpolar rising -90 to 0 setting 0 to 90 circumpolar rising 0 to -180 setting 180 to 0 Southern Sky non-circumpolar rising -90 to -180 setting 180 to 90 circumpolar rising -180 to 0 setting 0 to 180 Table 1: Range and sign of angle between source coordinates ; ± and horizon system coordinates Az; El. 2.3 Telescope-Reference Frame: Line-of-Sight Rotation in 3-axes-telescope mounts Some telescopes allow rotation around 3 axes. This is the case for SOFIA, where the telescope floats on its ball bearing, or for space telescopes, which have no mechanical reference frame at all. In this case, the line-of-sight rotation angle of the telescope, i.e. a rotation around an axis aligned along its optical axis, specified by the additional degree of freedom. As defined above, the l.o.s.-angle» l:o:s: is the angle specifying the counterclockwise rotation from the nominal position, i.e. aligned with the ( Az; El)-direction, to the actual orientation of the ( ; )- coordinates. A two-axes ( Az; El)-mounted telescope with the natural choice of the ; coordinates being aligned with ( Az; El ) as discussed above, thus corresponds to the case of =0.» l:o:s: Thus by extending the above definition of» and specifying as» s the angle from the sky reference frame Figure 5: line-of-sight rotation for a three-axes telescope coordinate system to the horizon system as formerly named» without an index, and with» l:o:s: being the angle from the horizon system to the telescope reference frame coordinates, we have the total angle from the sky reference frame coordinates to the telescope reference frame coordinates given by The resulting geometry is illustrated in Figure 5.» =» s +» l:o:s:. Page 7

8 2.4 Instrument Mount Reference Frame Here we have to distinguish between the case of a Nasmyth mount with the corresponding elevation dependent rotation between the telescope focal plane and the instrument mount, or a Cassegrain-mount or Cassegrain-like mount (i.e. with an additional tertiary mirror like on SOFIA), where the telescope focal plane is fixed relative to the instrument mount Nasmyth Mount and Elevation correction We now consider the sky image in a focal plane attached to the Nasmyth port, i.e. a port which is stationary in its horizontal and vertical axis, but rotates with the telescope in azimuth. The tertiary mirror, mounted so that it moves with elevation, rotates the direction of the (Az,El) coordinates with elevation angle. In addition, the reflection on the tertiary inverts the orientation of the (Az/El) coordinates. This reflection also changes the sign of the rotation angle between the 2 nd axis of the source coordinate system (e.g. Dec.) and the direction of the Elevation axis. We choose the Nasmyth focal plane coordinate axes (u,v) in such a way, that their direction coincides with the imaged (Az/El) coordinates at an elevation of 0 ; due to the tertiary reflection, the (u,v) coordinate system thus is left-handed. The resulting geometry is sketched in Figure 6 for the left Nasmyth port. For the right Nasmyth port, the orientation of the rotation with elevation is opposite. Figure 6: Nasmyth port view (left Nasmyth port) In the following, we denote with ~r the position vectors relative to the Nasmyth focal plane, i.e. (u,v)- coordinates; with ~a = (±a; ±e) we denote offset position vectors in the horizon system, i.e. - coordinates. In Figure 6, we have denoted with ~r E = ( u ( Az; El) E ) the position, where the elevation axis hits v E this plane, and with ~r R = ( u R ) the position of a reference point in the (u,v) plane, which for the v R moment can be taken to be the position of a single pixel detector element in a receiver mounted fixed to the Nasmyth port. ~d E is the vector from the (Az,El) reference point, i.e. nominal pointing position, which here is assumed to be at ( Az; El) = (0; 0), to the elevation axis. ~d R;0 is the vector from there to the reference point R in the Nasmyth focal plane, which is a fixed vector in this coordinate system. Figure 6 shows the situation for two different elevations, El (black) and El' (gray), and hence with the Page 8

9 correspondingly different rotation of the ( Az; El) axes viewed from the Nasmyth port. If viewed in the ( Az; El) -coordinate system, the situation is as shown in Figure 7. Note that the reflection on the tertiary mirror changes the sign of the rotation angles. Across the elevation range, the reference position R, i.e. the detector, is located on a circle arc centered at E, which is given by ~d R;0 ~a R (El) = ( ±a R ±e R ) = ~ d E + ~ d R = ~ d E + b D( El ) ~ d R;0 ; where is the vector from the elevation axis to the Nasmyth focal plane reference point R at elevation 0 and we have defined the elevation correction angle El = El. Note the negative sign of the angle in the case of the left Nasmyth port, reflecting the fact that the elevation correction results in a clockwise rotation of ~d R;0 with increasing elevation. For the right Nasmyth port of the telescope, the angle would be the opposite: ½ +El; right Nasmyth El =. El; left Nasmyth With these detector positions in the (ΔAz,ΔEl) plane, the source appears at opposite offsets in an Az/El map, so that, following the above definition of (Az/El)- offsets, we have ( Az. El ) = ( ±a R ) = d ±e ~ E bd( El ) d ~ R;0 R The parameters ~d E and ~d R;0 are measured by fitting a circle to the observed and inverted, i.e. ( Az; El)-offsets of a pointing source, which trace a circle with elevation. Figure 7: Az,El offsets of Nasmyth focal plane reference position at different elevations Note that in the above we have chosen an arbitrary origin of the Nasmyth focal plane coordinate-system (u,v). The resulting equations for the Nasmyth-Elevation pointing correction are, of course, independent of this choice. A convenient choice in practice would be to take the fixed position of the elevation axis as the origin of the (u,v)-coordinate system. Page 9

10 2.4.2 Cassegrain and Cassegrain-like mounts In this case, the instrument mount reference frame is fixed relative to the telescope and can thus be chosen to be identical to the telescope reference fram coordinates. Thus, there is no elevation dependent rotation of the field-of-view, and correspondingly the elevation correction angle El introduced above, is effectively constant =0. The offset from the elevation axis to the reference point R in the focal plane is then an elevation independent, additive offset: ~a R = ( ±a R ) = d. ±e ~ E + bd( El = 0) d ~ R;0 = d ~ E + d ~ R;0 R It nevertheless makes sense to keep both parameters, ~d E and dr;0 ~, as one is the telescope port-dependent offset of the elevation axis relative to the nominal pointing, the other one the instrument dependent offset from there to the reference point in the ports focal plane. The latter may be either the offset of the (reference) detector pixel for a fix-mounted instrument, or the position of the beam rotator axis for an instrument mounted with a beam rotator. We thus expand the above definition of the elevation correction angle Cassegrain (or Cassegrain-like) port as follows: 8 < +El; right Nasmyth El = El; left Nasmyth : 0 Cassegrain like 2.5 Instrument focal plane and Beam Rotator E to include the case of a Figure 8: Instrument focal plane coordinates Without a beam rotator, i.e. an instrument mounted fixed to the Nasmyth port, the Nasmyth focal plane is identical to the instrument focal plane. With a beam rotator, we have to distinguish the two. In the following, we use (x,y) as the instrument focal plane (IFP) coordinates. For convenience, the intersection of the beam-rotator axis with this plane is chosen as the origin of this coordinate system. The orientation is chosen such that at a beam rotator angle ½=0 the instrument focal plane coordinate system coincides with the Nasmyth focal plane coordinate system, and hence with the (Az; El) coordinate system projected into the Nasmyth focal plane at an elevation of 0. Page 10

11 Figure 9: rotated pixel offsets obtained from intrinsic pixel offsets The purpose of the beam rotator is to rotate the instrument focal plane, so that the orientation of a focal plane array matches the sky/source coordinate system in an appropriate way, defined by the astronomical observations. The array has an internal symmetry, defining an array internal coordinate system (³; ) which is tilted by p and an offset ~c 0 relative to the instrument focal plane system (x,y). An alternative instrument focal plane system (IFP') is the one which is tilted relative to (x,y) by p and is labeled by (x',y') in the following. The N pixels of the focal plane array, labeled by index i = 0; : : : ; N 1, then have position vectors, which are the sum of the vector to the array center, ~c 0 plus the pixel offsets vector from the array center, ~p i. The resulting geometry is as shown in Figure 8. As shown in Figure 9, one can regard the vector ~c0 and ~p0;i as being obtained by rotating the vectors ~C0 and ~P 0;i through an angle of p, so that ~c 0 + ~p 0;i = bd( p ) (~C 0 + ~P 0;i ) where ~C 0 and ~P 0;i are the (back-) rotated offset of the array center and the (symmetric) array-intrinsic pixel offsets. These, together with the tilt-angle p are the array geometry parameters actually fitted to the array-offsets measured by beam-rotator scans on a pointing source (ideally the Sun), as discussed below. We now consider the beam-rotator. As illustrated in Figure 10, the image rotation is achieved through the three reflections on the K-mirror arrangement which effectively results in mirroring the entrance plane along a line through the origin, which is oriented parallel to the K-mirror arrangement and hence rotates with the physical angle of the beam rotator, ½=2. The angular offset from this line of ½=2 for the entrance and exit plane sums up to a relative rotation between the two of an angle ½. In essence, a physical rotation of the K-mirror by ½=2 results in a rotation of the instrument focal plane image by an angle ½ in the Nasmyth focal plane in the same direction. The nominal rotator angle of ½ = El = El for pointing observations in the (Az/El) system (see below) at the left Nasmyth port, i.e. a negative value of the commanded beam rotator angle, corresponds to a clockwise physical rotation of the beam rotator by an angle El=2. Figure 11 shows the same situation, but now leaving out the instrument focal plane and including the Page 11

12 Figure 10: Beam-rotator rotation: the K-mirror arrangement effectively mirrors the entrance plane along a line through the origin oriented along the K-mirror plane and rotating with it. Shown are the mirror images for a rotator angle of 0 (bottom right), and the mirrored image obtained at an angle of ½=2, effectively resulting in a rotation by ½ relative to the ½=0 image. astronomically relevant source/sky coordinates projected into the Nasmyth focal plane. Viewed on the sky, i.e. in the ( Az; El) plane, the tertiary mirror reflection flips the orientation of the Az-axis and changes the signs of the rotation angles ½ and p, so that the geometry looks like shown in Figure 12. In order to calculate the location of a particular pixel of the array receiver (no. 3 in the Figure) in the ( Az; El) -plane, we now have to take for ~d R;0, i.e. the offset from the elevation axis to the reference point, the sum of the offsets from the elevation axis to the beam rotator axis, and from thereon to the array pixel, the latter being the offset at rotator angle 0 rotated by the angle ½ (in the ( Az; El) plane), i.e. ~d R;0! d ~ R;0 + ~c + ~p i = d ~ R;0 + bd( ½)(~c 0 + ~p 0;i ) = d ~. R;0 + bd( ½) bd( p )( ~C 0 + ~P 0;i ) = d ~ R;0 + bd( ½ p )( ~C 0 + ~P 0;i ) Page 12

13 The location of the reference pixel i in the ( Az; El) -plane is thus, as a function of Elevation and rotator-angle, given by ±a(el; ½) ~a i (El; ½) = ( ±e(el; ½) ) = d ~ h E + bd( El ) ~dr;0 + bd( ½ p )( ~C 0 + ~P 0;i )i = ~ d E + b D( El ) ~ d R;0 + b D( El ) b D( ½ p )( ~ C 0 + ~ P 0;i ) = ~ d E + bd( El ) ~ d R;0 + bd( El ½ p )( ~C 0 + ~P 0;i ) Figure 11: Nasmyth focal plane geometry with beam rotator and array receiver Thus, we get for the mapping offsets of pixel i ( Az i El i ) = ( ±a i ±e i ) = ~ d E bd( El ) ~ d R;0 bd( El ½ p )( ~C 0 + ~P 0 ) The parameters ~C 0 and ~P 0;i, as well as the angle p are determined by mapping of a pointing source (favorably the Sun) repeatedly at a fixed elevation (i.e. fast in time and/or close to transit) with different rotator angles and fitting the resulting circles against a model of the array geometry (the offsets ~C 0 and, ~P 0;i as well as p, are set to zero for this measurement). With the rotator angle ½ tracking with elevation, i.e. setting the rotator angle to its nominal value (see below) for mapping in the horizon system, namely ½ = El p, and the above determined constants ~C 0 and ~P 0;i now activated, the beam rotator axis Page 13

14 offset from the elevation axis, ~d R;0, and the elevation axis offset de ~ can then be determined by following a pointing source over a large range in elevation, similar to what has been already discussed above for the case of a single pixel receiver without beam rotator. Alternatively, a full half day pointing session with the sun elevation covering the range from close to horizon to culmination (morning) or vice-versa (afternoon), all corrections set to 0, and cycling the beam rotator angle through a set of e.g. five fixed settings, gives a full set of measurements against which all corrections can be fitted simultaneously. Figure 12: Array setting projected back into Az,El coordinates Page 14

15 Figure 13: Nominal beam rotator setting with the array aligned with Az,El 2.6 Nominal beam rotator setting In order to rotate the array so that its pixels are oriented along the axes of a given source coordinate system (or have a specified rotation against these axes ½ source ), one can read from Figure 13, that the angle has to be set such that ½ = (» El) + ½ source + p for the left Nasmyth mount, where El = El, i.e. the nominal rotator angle setting is ½ nom = El +» ½ source p. = El +» s +» l:o:s: ½ source p If the actual setting is ½ = ½ nom + ½ (i.e. ½ specifies the offset between the actual and nominal setting, ½ = ½ ½ nom ) one has Page 15

16 El ½ p = El (½ nom + ½) p = El ( El +» ½ source p + ½) p =» + ½ source ½ and the offsets between pixel j and i in ( Az, El)-coordinates are ~a j ~a i = ( ±a j ) ( ±a i ) = bd(» + ½. ±e j ±e source ½)( ~P O;j ~P 0;i ) i The ( AZ; El) coordinate system is rotated by bd(») against the ( ; ±) coordinate system, and vice-versa the ( ; ±) -coordinate system is rotated by bd(») against ( Az; El). In addition, the sign of the R.A.-coordinate is flipped. Thus the pixel offset coordinates ( ±p ; ±p ± ) in the ( ; ± ) -coordinate system are obtained by the inverse rotation from the ( Az; El) -offsets, namely µ µ µ µ ±p ;j ±p ;i ( ) = D(»)( ±p ±;j ±p b ±aj ±ai ) ±;i ±e j ±e i, = D(») b D(» b + ½ source ½)( P ~ 0;j P ~ 0;i ) = b D(½ source ½)( ~ P 0;j ~ P 0;i ) i.e. they are the pixel offsets rotated by the angle ½ source ½, and flipped for the R.A.-coordinate. In particular, if ½ source = 0 as well as ½ = 0, the ( ; ±) offsets are aligned with the array internal pixel offsets. Page 16

17 3 Implementation in the kosma_control environment Within the kosma_control-environment all parameters are stored and exchanged as KOSMA_file_iovariables in the corresponding KOSMA_file_io-files. The following table summarized, which of the parameters used above correspond to which of the KOSMA_file_io-variables. parameter KOSMA_file_io-variable KOSMA_file_io-file comments general control-parameters obs_coord_sys_on KOSMA_obs2tel coordinate system for source reference position. Possible values are: B1950, B2000, GALACTIC, HORIZON obs_coord_sys_del KOSMA_obs2tel source mapping coordinate system, possible values: see above obs_coord_sys_focal_plane KOSMA_obs2tel type of instrument mounting flange coordinate system; possible values are: HORIZON, i.e. horizontal/vertical Nasmyth mount coordinate system TELESCOPE, i.e. telescope fixed (e.g. SOFIA) instr_beam_rotator[ninstr] Rx_hardware.set instrument has beam rotator [Y/N] instr_tertiary_mirror[ninstr] TEL_hardware.set instrument port has tertiary mirror [Y/N] rx_instr_name master_parameters instrument name (for info and identification) rx_port port.set left or right Nasmyth port [LEFT/RIGHT] ninstr parameters for the rotator angle» s» l:o:s:» =» s +» l:o:s: total number of instruments available tel_angle_focal_plane KOSMA_tel2obs.set angle from 2 nd coordinate axis of source mapping coordinate system to El-axis, calculated by the telescope system tel_los_act KOSMA_tel2obs.set actual l.o.s. angle of telescope rotation angle from 2 nd coordinate axis of source mapping coordinates to 2 nd coordinate of telescope focal Page 17

18 parameter KOSMA_file_io-variable KOSMA_file_io-file comments El ½ source p ½ nom ½ ½ plane system ) tel_elv_act KOSMA_tel2obs.set actual elevation of the telescope (not encoder readings) rot_source_angle KOSMA_angle_fp.set additional beam rotator angle counterclockwise from mapping coordinates (user specified) instr_focal_plane_rotation [instr_nr] TEL_hardware.status value of the array tilt angle, transferred to TEL_hardware.status from the Rx_hardware.status file for the reference pixel by 'setpoint -p i' Rx_tilt_1, Rx_tilt_2 Rx_hardware.status angle to compensate for tilt of array footprint, determined from beam-rotator pointing measurement session fp_angle KOSMA_track_fp.set commanded rotator angle rotator_angle KOSMA_rotator.status actual rotator angle - fp_angle_diff KOSMA_track_fp.set difference between commanded and actual rotator angle (minus sign kept for consistency with old data sets). parameters relevant for pixel offsets ~C 0, ~P 0;i instr_reference_pos_x,y[nins TEL_hardware.status tr]= ~C 0 + ~P 0;refpixel ~d R;0 Rx_cx_1, Rx_cy_1, Rx_cx_2, Rx_cy_2, Rx_gridsize_1, Rx_gridsize_2, Rx_px[i], Rx_px[i], Rx_last_pix_1, Rx_last_pix_2 instr_rotator_axis_x,y[ninstr ], instr_boresight_offset_x,y[ni nstr] Rx_hardware.status TEL_hardware.status values calculated from variables Rx_cx,y[i] and Rx_px,y[i] for reference pixel, transferred to TEL_hardware.status by 'setpoint -p i' parameters to calculate pixel offset in [mm] in focal plane for first and second sub-array, determined from beam-rotator pointing measurement session. offset from elevation axis to rotator axis, resp. single pixel boresight (additive) determined from Nasmyth pointing measurement session tel_plate_scale KOSMA_tel2obs.set used to convert mm-offsets in focal-plane to offsets in arc secs instr_focal_length_correctio rx-specific correction to focal Page 18

19 parameter KOSMA_file_io-variable KOSMA_file_io-file comments ~d E ±a; ±e n[ninstr] pointing corrections instr_elevation_axis_x,y[nin str] fp_offset_x,y obs_x,y_focal_plane TEL_hardware.status KOSMA_track_fp.set KOSMA_obs2tel.set length offsets of elevation axis from nominal pointing (may be different for instruments on different telescope ports) positional offsets of reference pixel projected onto the sky in Az, El, transferred to control_tel via KOSMA_track_fp.set, and from thereon to the telescope via the KOSMA_obs2tel.set-file. The resulting pointing correction (in true angles), to be applied by the telescope task, is the negative of these values ±Az, ±El track_azpoi, track_elpoi KOSMA_track_point.set Az, El. pointing correction (true angles) 3.1 Calculating and setting the beam-rotator angle The task focalplane handles all issues related to the beam-rotator. This includes the calculation of the nominal rotator-angle, setting the beam-rotator to this angle, if a beam-rotator is available, getting the actual beam-rotator angle and calculating the difference between nominal and actual. focalplane relies on the angle» to be calculated by the telescope astronomical drive software. 3.2 Calculating and setting the focalplane offsets for the reference pixel The second issue for focalplane is to derive the proper Az; El-offsets and feed them to the telescope for proper pointing correction. The latter is done through the KOSMA_file_io-file KOSMA_track_fp.set, which the kosma-control telescope control interface routine control_tel uses to convert to the proper telescope-drive control parameters, handled to the telescope through KOSMA_obs2tel.set. This includes the Elevation-dependent Nasmyth-pointing correction as well as the beam-rotator rotated pixel offsets 3.3 Calculating the map offsets from the raw-data during conversion to CLASS-files The parameters derived by focalplane and used by control_tel to command the telescope are also written to the raw-data headers in FITS format. The calibration task kalibrate then uses them to figure out the appropriate map -offsets for the calibrated data in CLASS format; the code for this in buffers.c. Page 19

20 3.4 Fitting the Nasmyth-, rotator- and array-pixel-parameters from pointing observations One important step in commissioning the SMART array receiver is the determination of the pixel offsets and the rotator-/elevation-axis offsets. Traditionally, these are done as two separate steps. The pixel offsets form the beam-rotator axis are measured by fast sun-scans with different rotator angles at an almost constant elevation near transit. These measurements are done with the pixel offsets and the tiltangle set to 0. The analysis (fitting of edge-spikes to the differentiated sun scans) gives the ( Az, El)-offsets of the pixels as a function of beam rotator angle. The task rotfit_smart fits the pixel offsets and the tilt angle to the set of ( Az; El) as a function of rotator angle (at approximately constant elevation). The offsets are actually derived by determining the offset to the array center ~C 0 plus the pixel offsets ~P 0:i. These latter ones are determined by fitting the grid spacing, taken the array geometry as given. As the grid spacing is within 2-3 arc secs within 80, the grid spacing is typically set fixed to this 80, making easier to handle map offsets for the observing. rotfit_smart also fits the tilt angle of the array. In a second step, the Nasmyth correction constants are determined by following a source (the Sun) across a large elevation range, with the Nasmyth correction constants set to 0, the pixel offsets and tilt angle activated and the rotator tracking at the nominal angle so that the pixel offsets are rotated into elevationindependent pointing offsets. A fit to the resulting (±a; ±e) = ( Az; El) offsets versus elevation then allows to determine the offset of the rotator axis from the elevation axis The new approach (still to be fully tested) is to combine these two steps and follow the sun across a large range in elevation with different rotator setting, and then fit both the pixel offsets and array tilt as well as the elevation-/rotator-axis offset in a single fit process. Page 20