[mmaimcal] Band 6 Optics Question

[Al Wootten]

I think -10 to -13 db is pretty good while -8 to -11 is marginal.  I'm not sure we have
set an actual range; just that -12db center of band is the goal.

Comments on this???

Al

Geoff and Sri ask:
ANALYSIS OF ALMA BAND 6 (210-275 GHz) RECEIVER OPTICS

Summary: ALMA Memo 362 gives designs for the receiver optics for each of the ALMA bands. 
The goal appears to have been  to achieve an edge taper of -12 dB at the perimeter of the
subreflector.  Using a physical optics analysis, we find that the Band 6 design actually has an
edge taper of -8 to -11 dB.  A slight modification of the optics gives edge tapers of -10 to -13 dB
across the band. What is the acceptable range of edge tapers? 


The optics scheme for Band 6 is shown in Figure 4 of ALMA Memo 362.  The beam from a
corrugated feed horn is coupled to the subreflector using two offset ellipsoids.  Gaussian Beam
analysis was used in the design.  The horn with an aperture diameter of 7mm and length of 50mm
produces a beam waist 2.181 mm at 243 GHz. The first ellipsoid, at a distance of 59.9mm from
the horn aperture, produces an output waist of 2.42mm at a distance of 69.6 mm.  The second
ellipsoid is 140mm from the first and produces an output waist 7.38mm at a distance of
169.9mm.  The angles of incidence on the first and second reflectors are 15 and 16.1 degrees,
respectively.    The 7.38mm waist gives a -12 dB taper at the edge of the subreflector.  When
higher order modes are included the taper will be about -10 dB.

A  rigorous analysis using the Physical Optics (PO) technique was carried out on this optics
scheme.  The feed pattern for the horn, calculated by mode matching,  was used to illuminate the
first ellipsoid.  The resulting output pattern was used as the illuminating pattern for the second
reflector.  The fields on the ellipsoids were calculated at the actual distances from the source. 
The output pattern of the second ellipsoid was calculated at 3 different frequencies.  The patterns
have tapers of -11.1 dB,  -9.6 dB and -8.1 dB at 210, 243 and 275 GHz, respectively, at the edge
of the subreflector.  

By decreasing the spacing between the 2 reflectors by 2.4 mm and using an ellipsoid of
eccentricity 0.674 for the second reflector (compared with e = 0.63 in Memo 362), a beam waist
of 7.97mm is  obtained from Gaussian Beam analysis.  This gives a taper of -14 dB at 3.6
degrees.  A PO analysis for this case gives tapers of -13.1 dB, -11.6 dB and -10.1 dB at 210, 243
and 275 GHz, respectively.  The output waist in this case is closer to the feed axis by 1.5mm in
the lateral direction compared to the first case.  The waist is also lower by 5.6mm along the feed
axis.

In conclusion:  To obtain a taper of about -12dB at the edge of the subreflector, the design given
in ALMA Memo 362 requires modification: the second reflector is moved closer to the first and
its shape changed slightly.

Question:  What is the required edge taper for ALMA receiver optics?
                                                  
S. Srikanth and G. Ediss
National Radio Astronomy Observatory