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.