MHO\_StationDelayCorrection
=============================

Purpose
-------

This operator applies a station-specific delay correction to visibility data by
phase-rotating each visibility according to the frequency offset from the
reference frequency. It is used to compensate for timing offsets
(e.g., PC-clock delay) between the two stations in a baseline, typically arising
from hardware or clock synchronization differences.

Control File Trigger
--------------------

This operator is triggered by the ``station_delay`` keyword in the control file.
It belongs to the calibration category with priority 3.5. The parameter is a
real value representing the delay offset in nanoseconds.

Input Data
----------

The operator works in-place on a ``visibility_type`` container. The visibility
must carry metadata tags identifying the reference and remote stations
(Mark4 IDs or station codes) so the operator can determine which station the
correction applies to.

Algorithm
---------

The operator loops over the two stations (reference at index 0, remote at index 1) and checks applicability for each via ``IsApplicable()``. Station matching supports both single-character Mark4 IDs and two-character station codes (case-insensitive). A wildcard identifier (``?`` for Mark4 ID, ``??`` for station code) matches any station.

For an applicable station, the operator iterates over every polarization product and channel, computing a phase-correction phasor:

.. math::

   p = e^{j\theta}

with the rotation angle given by:

.. math::

   \theta = 2\pi \cdot \Delta f \cdot \Delta t

.. math::

   \Delta f = 10^6 \cdot (f_{\rm chan} - f_{\rm ref})

.. math::

   \Delta t = \tau_{\rm ns} \cdot 10^{-9}


where :math:`f_{\rm chan}` is the channel center frequency in MHz, :math:`f_{\rm ref}` is the reference frequency in MHz, :math:`\tau_{\rm ns}` is the delay offset in nanoseconds, and :math:`j` is the imaginary unit.

The phasor is conjugated under two conditions:

1. **Lower sideband (LSB)** data: the phasor is conjugated because LSB has inverted frequency ordering relative to the IF.
2. **Reference station** (index 0): the phasor is conjugated because the reference station's delay correction has the opposite sign convention.

Note that if both conditions apply (reference station + LSB), the two conjugations cancel, yielding the original phasor.

Effect on Data
--------------

This operator modifies the input visibility container in-place. Each visibility
sample for the matched station is multiplied by a complex
phasor :math:`e^{j\theta}` (or its conjugate, depending on
sideband and station role). The phase rotation shifts the
apparent delay of the signal, effectively compensating for a station
clock or hardware delay offset. The axis labels and metadata tags are unchanged.