email from vfish, sep3 2021:

> The equations for how the field rotation angles affect circular
> polarization products are given on page 722 of Roberts, Wardle,
> & Brown (1994).  Here's a direct link to a scan of that page:
> http://articles.adsabs.harvard.edu//full/1994ApJ...427..718R/0000722.000.html

> You can ignore any term with a "D" in it, since those apply to
> polarization leakage and we're not (yet) contemplating D-term
> correction in HOPS.  So, basically each polarization product
> (e.g., RR) acquires a phase from the field rotation angle (phi)
> at each telescope, with conjugation for the remote station
> (as usual in correlated products). The equations give you the
> signs of these corrections.

> So what is the field rotation angle?  That depends on the mount type:
>     # mount types with field rotation angle (fr) equations
>     #   CASSEGRAIN:    fr = parallactic angle
>     #   NASMYTHLEFT:   fr = parallactic angle - elevation
>     #   NASMYTHRIGHT:  fr = parallactic angle + elevation

> Basically, the elevation term is needed if the receiver is bolted
> to the floor and therefore doesn't rotate with the telescope.
> To use a common point of reference, the SMT 230 GHz is considered
> Nasmyth right.  (If you recall, when you're standing behind
> the telescope, the 230 GHz receiver is on the right side.)
> If/when you need them, I can give you mount locations for
> all(?) of the current EHT telescopes.

> urfit has ready access to the elevation and parallactic angles
> of each telescope.  They appear on the left of the penultimate
> line in a fourfit plot.

Notes:

fourfit doesn't compute elevation until after it finds a fringe
(see fill_202.c).

param->par_angle is computed only at the first time (see organize_data.c)
So really, par_angle and elev need to be computed from the model for every AP,
once at the outset of every fringe.

neglecting D terms, and suppressing gains,

(alphbetically sorted to align with fourfit usage)

(14) L1.L2* = ...I12 exp[ i( + phi1 - phi2 ) ]
(13) R1.R2* = ...I12 exp[ i( - phi1 + phi2 ) ]
(16) L1.R2* = ...P21 exp[ i( + phi1 + phi2 ) ]
(15) R1.L2* = ...P12 exp[ i( - phi1 - phi2 ) ]
                             polcof

phi is fr, I believe, depending on parallactic angle and elevation.
and 1 and 2 are really 0 and 1 subscripts

the cblock would need to note the mount type on a ref/rem station basis
would want to set up to interpolate the parallactic angle and elevation
to the AP (to do this right).  Otherwise the variation of each over the
course of the scan will not be properly tracked.

splined values are generally computed in compute_model which is called
from fill_208.c

if station ... : mount_type = no_mount|cassegrain|nasmythleft|nasmythright

>     #   CASSEGRAIN:    fr = parallactic angle
>     #   NASMYTHLEFT:   fr = parallactic angle - elevation
>     #   NASMYTHRIGHT:  fr = parallactic angle + elevation

SO if station_pol_mode == CIRC_MODE and mount_type(s) are both defined
then (double) polcof becomes != 1. according to the above formulae

NO: spectral data (DiFX) is inherently complex, so polcof needs to
NO: become type hops_complex.... float complex cexpf(float complex z);
NO: and likewise the normalization factor.

We just want equal weighting when we add them.

for vhelp:

mount_type 'no_mount' or 'cassegrain' or 'nasmythleft' or 'nasmythright'

Anyway, here are mount types for the 230 GHz receivers.
  ALMA,CARMA,GLT,JCMT,KP,SPT: Cassegrain ("alt-az")
  LMT,PV,SMA: Nasmyth left
  SMT: Nasmyth right
  APEX: Nasmyth right, but old receiver was Nasmyth left(*)

(*) i.e., the default should be Nasmyth right, but the user should be
able to override this in the control file

Locations of 345 GHz receivers may be different!  For instance, the 345
GHz receiver at the SMT used to be (still is?) on the opposite side of
the recceiver room for the 230 GHz one.

I believe that all the receivers on the VLBA antennas have field rotation
angles consistent with Cassegrain (i.e., no elevation term).

Note that the underlying type_303 structures store coefficients for values
in degrees, so a time-variable correction requires a different interface.

Note that the equations (13-16) express what would be seen in terms of the
model.  To make a correction, one must use the negative of the phase. (D'oh).

eof