[mmaimcal] James Lamb's reply to Sri on optics question.

[Al Wootten]

From: "James Lamb" <lamb at ovro.caltech.edu>
To: "S. Srikanth" <ssrikant at nrao.edu>, <carter at iram.fr>
Cc: <akerr at nrao.edu>, "gediss at NRAO.EDU" <gediss at nrao.edu>, <span2 at nrao.edu>,
        <jwebber at nrao.edu>, "John Payne" <jpayne at nrao.edu>
References: <3B38C297.33490FE2 at nrao.edu>
Subject: Re: Band 6 Optics Question.
Date: Tue, 26 Jun 2001 16:13:58 -0700
Organization: Caltech
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Hi Sri,

It's good that you are doing a thorough analysis of the optics
for this band. In answer to your question about the required
edge taper for the ALMA optics, there isn't one. Rather the
system sensitivity has to be maximized. There are trade-offs
among diffraction at the various mirrors, spillover, illumination
efficiency, etc. The resulting edge taper is not necessarily a
good indication of the efficiency.

In the initial design we used 12 dB for the *best-fit Gaussian beam*
(best-fit in the sense of maximum power in the fundamental for a beam
from an *ideal* corrugated feed (J0(r))). The reason for this is that
it gives close to the optimum efficiency for the actual beam from
this ideal horn. The real edge taper from the ideal horn is closer to
10 dB though. Any truncating apertures will produce distortions
which to a first approximation correspond to focusing errors. We
made all the apertures as large as possible to minimize this effect.
If there is significant truncation then the optimum optical
parameters may have to be changed. Another significant non-ideality
is the feed horn which will not produce a perfect J0 amplitude
distribution with a spherical wavefront. This effect can be quite
small for a good horn over the band.

What you should do is to try to calculate the antenna efficiency
and noise, and optimize the G/T. In my analysis I assumed: that
the feed had an ideal spherical J0 aperture field; that the apertures
were all circularly symmetric; and the mirrors could be represented
by thin lenses. I calculated all the way through the system to
estimate the aperture efficiency, allowing for the secondary to be
refocused to remove some of the phase error introduced by the
truncation (this was typically < 1 % in efficiency).

The edge taper depends on how the edge diffraction
rays interfere with the main beam and the value is quite sensitive
to some of these assumptions. (I got -10.5 dB @ 210 GHz, -10.2 dB
@ 243 GHz and -10.1 dB at 275 GHz). However, the integrated efficiency
is less sensitive to these assumptions and the maximum is not
a strong function of the beam size. The only thing that is affected
directly by the edge taper is the secondary mirror diffraction.
The spillover due to this is of order 1 K so this is not a strong
driver.

Sorry this is such a long reply, but I think that in essence if you
need to modify any of the optical parameters it should be done
at least on the basis of aperture efficiency, and preferably on
the basis of G/T. You should have the final feed horn design for
this. In my experience it is very compute-intensive to get efficiencies
at the < 1 % level (i.e. accuracy of the solution of the equations --
even though convergence may be at this level the error relative to
reality may be larger). You need to be quite careful to have
enough points and accuracy.

Please let me know if you have any more questions.

Cheers,

    -James