[mmaimcal] comments on Bryan's antenna notes

[John Lugten]

Hi Bryan, imcal group,

I have a few comments on antenna performance requirements.

1. I think our pointing specification has been gradually eroded away from
1/30 beamwidth. 

	For a 12 m antenna at 300 GHz one calculates a primary
beam FWHP = 18.5 arcsec and 1/30 FWHM = .62 arcsec if the dish illumination
is chosen to be that giving best aperture efficiency using the frequency-
independent illumination scheme of Padman et al (1987). At BIMA, we chose 
to underilluminate the dish to increase the primary beam FWHM by about 7%,
which increases the beam solid angle by 14%, and costs only 1% on the
aperture efficiency. This would give 1/30 FWHM = .66 arcsec for the MMA.
I think a strong case can be made for this choice. Another possibility
which apparently is being studied is that of using ``shaped'' optics to
increase the aperture efficiency. I think that would be a poor choice,
but it would result in 1/30 FWHM of less than .6 arcsec -- perhaps 
significantly less.

	Also, unlike the surface accuracy specification where we budget 
about 10 microns for setting error, we make no allowance for measurement
error in the reference pointing position. This measurement error comes
from 2 sources: electrical noise due to finite integration time and
anomalous refraction. I presented these numbers as part of my SPIE talk
in March for a 10 meter aperture, and have updated them for the 12 m
aperture. Following Lucas' memo I calculate for a 200 mJy source (on average
2.1 degrees away), Tsys/freq = .5, 50 antennas, 15 sec integration time on
each point of a 5-point, an electrical noise pointing error of .16 arcsec.
If one is less optimistic on system temperature, taking Tsys(K) = freq(GHz),
then I get a positional accuracy of .32 arcsec. For the anomalous refraction
contribution, using the Holdaway/Woody memo which gives .90 arcsec median
jitter at 50 degrees source elevation, assuming the same 5 x 15 sec total
integration time for our 5-point (and that the atmospheric pattern speed is
about 12 m/s, giving one independent sample of anomalous refraction every
second), I calculate .16 arcsec pointing error. Combining even the more
optimistic system temperature noise contribution with the anomalous 
refraction contribution gives .23 arcsec pointing uncertainty.
 
Combining all this, I would argue that to get 1/30 FWHM performance at
300 GHz, we really need to allow the antenna contractor at most 0.6 
arcsec pointing error in the offset pointing mode. If one believes in
illuminating for best aperture efficiency with unshaped optics, or in 
shaped optics, or is less optimistic about system temperatures, then the
contractor pointing accuracy spec should be more like .5 arcsec.

2. I don't think it makes much difference what scheme one uses for pointing
up, 5-point, 4-point, 3-point or continuous circles. For all cases we
allow minimal time for overhead in moving (i allowed 15 sec to slew to
calibrator and back to source, and all moving between the 5 points, for
a total of 1.5 minutes for each 5-point). Lucas points out that one
gains sensitivity by having 1/5 of all antennas on source during each of the 5 
integrations of a 5-point, which I think argues that one does not save
significant time by skipping the center position as in the OVRO triangle
method.

3. As Harvey says, for fatigue life due to cyclic loading, the lifetime 
is rapidly reduced as the magnitude of the cyclic part of the stress is
increased compared to the endurance stress (which is the allowable stress 
for 10,000,000 cycles for most materials). For our maximum antenna 
acceleration of 24 deg/s/s the edge of the dish accelerates at about 1/4 g, 
which probably does not stress most structural elements close their 
endurance limit since most of the mount structure is designed by stiffness 
requirements, or perhaps by survival wind for the dish itself. However, 
much of the drive train probably will be designed by fatigue lifetime
requirements. 

John