Subject: Photometric Modulation

From: Alan Watson

Submitted: Sat, 15 Mar 1997 15:01:00 -0700

Message number: 133 (previous: 132, next: 134 up: Index)

It is well known that the oblique reflection off the tertiary mirror
of the 3.5m induces a photometric modulation in observations of
polarized sources. What is possibly less well known is that the
internal oblique refections in DIS and GRIM can induce similar
photometric modulation even in observations of unpolarized sources.
This happens because the tertiary induces polarization, the
instruments also induce polarization, and, under normal circumstances,
the instruments rotate with respect to the tertiary.

The peak-to-peak amplitude of the photometric modulation of an
unpolarized source is 2 * P_t * P_i, where P_t is the induced
polarization from the tertiary and P_i is the induced polarization
from the instrument.

If each mirror induces a polarization P_m and the instrument has n
mirrors in the same orientation, then P_t = P_m and P_i = n * P_m to
first order in P_m. GRIM in f/5 mode has one mirror; GRIM in f/10 and
f/20 modes have two mirrors; DIS has three mirrors (I assume that
reflection off a blazed grating is similar to reflection off a mirror
and I ignore any polarization from transmission through the dichroic).

P_m can be written in terms of the optical constants of the reflecting
material (see Born and Wolf), but unfortunately the constants given
for Al in the standard references are for clean, bulk Al and not for
oxidized Al coatings. Ken Nordsieck tells me that he measured a value
of 10% in the visible for one astronomical mirror using his
spectropolarimeter.

Adopting this value, we find peak-to-peak modulations of:

    2%  GRIM f/5
    4%  GRIM f/10 and f/20
    6%  DIS

The RMS modulations are roughly 0.7%, 1.4%, and 2.1%.

Whether this is of concern to you depends on how accurately you wish
to perform photometry. The modulation for unpolarized sources can be
eliminated by fixing the instrument with respect to the tertiary
(i.e., fixing the rotation of the instrument with respect to the
horizon).

You can perform similar calculations for polarized sources, which
suffer both a modulation as the tertiary rotates on the sky and an
offset because of instrumental polarization. The `direct' instruments
(DSC and SPICAM) have no instrumental polarization (P_i = 0) and will
not suffer a modulation for unpolarized sources. They will, however,
suffer a modulation for polarized sources because of the tertiary.

Alan Watson
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