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NOTES ON A POLARIMETER MODULE FOR SHARC-II

Based on discussions between G. Novak and C.D. Dowell; 2003

[Note added in 2004: This crude 2003 design was based on operation at
alidade platform, but it has since been decided that SHARC-II will move to
Nasmyth focus, so we are now developing a module that can work at
this location.  The Nasmyth design employs curved mirrors, unlike the
alidade design.]
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BASIC IDEA:

"the_idea.jpg" shows the Cass focus, the relay optics, and SHARC-II in a
schematic way.  M5 of the CSO relay optics is shown as a lens.

"the_idea.jpg" illustrates the kind of optical operation that we want
to do.  Imagine if you could somehow split the beam coming from the
primary into two orthogonally polarized beams.  Then "shift" (translate)
one beam a little to the right, and the other a little to the left.  If
you do this shifting at the Cass focus then the two orthogonally polarized
beams will get imaged to opposing ends of the long and skinny SHARC-II
array.  Then SHARC-II becomes equivalent to Hertz in that it detects both
polarization components simultaneously.  All you need to make it into a
polarimeter is to put a half-wave plate near the Cass focus, but displaced
slightly towards the primary.  The nice thing about doing the separation
at the Cass focus is that the mapping between a point in the pupil in
SHARC-II and a point on the primary is essentially unchanged by the
"shift".

FIRST ATTEMPT AT A DESIGN:

"module_concept.jpg" shows a first crude design of a device that could
accomplish the shift.  This device is meant to be placed at the Cass
focus.  This is a scale drawing; the scale is shown at upper left.  The
thin dashed lines are grids with wires perpendicular to the page.  The
thin solid lines are grids with wires parallel to the page.  MM1, MM2,
MM3, MM4, and MM5 are mirrors.  The purpose of MM5 will be described
later.  ("MM" stands for "module mirror". We write "MM" here instead of
"M" as shown in the drawing in order to avoid confusion between our module
mirrors and the CSO mirror nomenclature scheme - where M1 is the primary
and M2 is the secondary, etc.)

Note that the grids nearest to the HWP actually cross.  This kind of
device is called a "crossed-grid".  We can get one of these devices in the
size we need for roughly 6000 pounds sterling.  You can see a picture of
one at:

http://josephson.terahertz.co.uk/QMCI/GRIDS.HTM

We call this a beam combiner because if you imagine the beams from
SHARC-II coming towards the Cass focus you will see that the beam from one
side of the array gets superposed with the beam from the other side of the
array, but in orthogonal polarizations.  There is a "dead-zone" in the
middle of the array that sees the corner where the grids meet.  This could
be covered with absorber.

One also needs to think about the unused polarization.  For each side of
the array, there is an "unused" polarization component that must be
terminated to a cold load.  Thinking again from the point of view of the
beams coming from SHARC-II, the unused polarization goes through the first
grids it meets, and gets reflected by MM5 so that it is now travelling
*out* of the plane of the paper.  Then these beams must travel through
their own set of relay optics to a cold load (perhaps into a 10 degree
Kelvin load cooled by a mechanical cooler).

DETAILS ON BEAM SIZES AND BEAM CLEARANCES:

This first design shown on "module_concept.jpg" assumes that the nominal
Cass focus is at the location of MM5.  It should be possible to focus the
secondary so that the beam waist or actual Cass focus occurs half-way
between MM1 and MM3 (and half-way between MM2 and MM4).  This involves
changing the focus location by 4.5 inches which means moving the secondary
by about (1/600) of this or .007 inches.  If this introduces unacceptable
aberrations, then we could probably move the whole beam combiner thing
closer to the secondary by 4.5 inches.

We need to know the size of the SHARC-II footprint at the Cass focus.  We
assume that we are using two 12x12 sub-arrays as our two orthogonal
polarization arrays.  Then that leaves 8 x 12 pixels in the middle of
SHARC-II unused.  And each polarization then needs to be shifted by 10
pixels, for a relative shift of 20 pixels.  One SHARC-II pixel is 4.6
arcsec that corresponds to 2.76 mm at the Cass focus.  (the Cass focus
plate scale that we use is 1.65 arcsec/mm; from Serabyn's memo.)  A 12x12
footprint on the sky thus corresponds to a (2.76mm x 12 x root-2) = 1.8
inch diameter beam at the Cass focus.  However, the f/12.36 Cass focus
causes the beam to grow to 2.5 inches at the extreme edges of our beam
combiner.  So we have designed for a 3 inch beam throughout.  The shift we
used in the design on page 2 corresponds to 20 pixels, as it should.

This very crude first design "almost" works.  It does have some vignetting
as you can see from the fact that the beams from the relay optics don't
have a full 1.5 inches of clearance on the side where the two grids meet.
Allowing for a grid frame 1 cm in size we find that one row of pixels
vignettes on each side.  So we have a 10 x 12 array, not 12 x 12.  (Also
we neglect for now the problem of having the frames for the two grids
superposed right on top of each other - this can presumably be resolved by
slight shifts of the left and right optical paths.)

Small changes in the design and an adjustment of exactly where we put the
beam waist can probably fix this up so we can recover the full 12x12
footprint.

OTHER ISSUES:

The extra 9 inches of path length that we put in will necessitate
rebuilding M5 so that it is slightly weaker in curvature.  This should not
be too expensive.  [Note added in 2004:  There are some trade-offs
involved here.  In particular, it is impossible by just changing M5 to get
the plate scale, primary image size, and primary-image-to-focus distance
all exactly right.  But we can get close enough so that the penalties are
not large.]

This beam combiner thing will require about 12" x 12" x 12" of space at
the Cass focus.  One of the lateral dimensions could probably be reduced
significantly, at least on one of the sides.  We still need to verify
whether this room exists, but it probably does.  From the Serabyn memos,
it looks like there are no mirrors in the way. 

With SHARC-II at the Nasmyth focus, everything changes.  The Cass focus
becomes much more difficult to access.  [Note added in 2004: We think that
we will be OK at the Nasmyth focus.  Hua-bai's latest design for this is
also posted.]

The paper by 1992 Murray et al. ("High efficiency half-wave plates for
Submillimetre Polarimetry"; IR Physics vol. 33, no. 2, p. 113) shows that
the loss due to using a warm crystal quartz half-wave plate at 350 microns
is 5-10%.

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