Keywords: point

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## Parameter List

Let dX and dY be the offsets on the sky parallel to the Azimuth axis and Elevation axis respectively, produced by a pointing error. The standard pointing model for the Plateau de Bure antennas has the following parameters:

    IAZ      azimuth encoder zero
             dX = IAZ*cos(El)               dY = 0
    IEL      elevation encoder zero
             dX = 0                         dY = IEL
    COH      telescope azimuth collimation
             dX = cos(El)*asin(COH/cos(El)) dY = -asin(sin(El)/sqrt(1-COH**2))
             for COH << cos(El), equivalent to
             dX = COH                       dY = 0,
    COV      telescope vertical collimation
             dX = 0                         dY = COV
    MVE      Azimuth axis tilt towards East
             dX =  MVE*cos(Az)*sin(El)      dY = -MVE*sin(Az)
    MVN      Azimuth axis tilt towards North
             dX = -MVN*sin(Az)*sin(El)      dY = -MVN*cos(Az)
    NPE      Elevation axis tilt (axis non perpendicularity)
             dX = -NPE*sin(El)              dY = 0
             (assuming small NPE and COH in practice.)
    REF0     First order refraction coefficient
             dX = 0                         dY = -REF0/tan(El)
    REF1     Second order refraction coefficient
             dX = 0                         dY = -REF1/tan(El)**3
    ELES     gravity+eccentricity of Elevation encoder
             dX = 0                         dY =  ELES*sin(El)
    ELEC     gravity+eccentricity of Elevation encoder
             dX = 0                         dY =  ELEC*cos(El)
    AZES     eccentricity of Azimuth encoder
             dX = AZES*sin(Az)*cos(El)      dY = 0
    AZEC     eccentricity of Azimuth encoder
             dX = AZEC*cos(Az)*cos(El)      dY = 0
    HEL      Homology elevation bending (cos(El))
             dX = 0                         dY = -HEL*cos(El)

The total pointing correction is thus, in the small COH approximation

        dX = IAZ.cos(El) + COH + sin(El) * (MVE*cos(Az)-MVN*sin(Az)-NPE)
              + cos(El) * (AZES*sin(Az)+AZEC*cos(Az))
        dY = IEL+COV - (MVE*sin(Az)+MVN*cos(Az))
              + (ELES*sin(El)+(ELEC-HEL)*cos(El))
              - REF0/tan(El) - REF1/tan(El)**3 - REF2/tan(El)**5

Since each antenna is equipped with an off-axis optical telescope, there are two sets of `(COH,COV)` values, one for the radio axis and one for the optical axis. As only `IEL+COV` is meaningful, the radio `COV` is set to zero, fixing the `IEL` value.

Five terms dominate the pointing model : `IAZ, IEL+COV, COH, MVE` and `MVN`. In principle `COH, IEL,` and `COV` depend only on the antenna, `MVE` and `MVN` depend on the station and antenna (azimuth bearing), and `IAZ` depends on the antenna (encoder), the station (footpad positions) and the positioning of the antenna on the station (repeatability 1 mm).

The refraction coefficients are weather dependant. Accordingly, the parameters are computed in real time, using temperature, pressure and humidity. REF0 and REF1 are thus fixed to zero in the pointing fit.

Among the other terms, all of which depend on the antenna, just two have been found to be of some importance for some antennas: `ELEC` which enters only in combination with `HEL` in radio (small values on all antennas), and possibly `NPE` (Antenna 3). These are marginally different from zero, however, and confirmation will be required. The other parameters can be set to zero.

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