The design specifications for the MMA call for an antenna with as
little as 2% loss to rear spillover, blockage, and ohmic heating
(
). This leads to quite small spillover noise. Furthermore, the
sites being examined have very low precipitable water vapor and high
transparencies. Atmospheric and antenna spillover noise are thus
lower for the MMA than for many existing mm/submm telescopes.
Consequently, the suppression of image noise is less important at the
lower frequencies and under the best skies. On the other hand, if the
image separating mixer scheme is successful, the effective termination
temperature of the image is quite low and can still lead to a noise
advantage for SSB systems.
For our calculations, we have used these parameters:
= 0.98
= 0.73 (divides out in Tsys ratios)
= -5 C
= 0.95
= 0.95
= 4.2 K
Atmospheric opacities were produced by the Grossman (1989) model. When using these calculated atmospheric opacities, we have ignored any differences between the atmospheric opacities in the signal and image sidebands. Note that near the atmospheric band edges, this assumption will break down.
Figure 1 shows 
, 
, and
(the DSB penalty) as a function of 
for two sets of image termination conditions. The
first termination condition is a traditional cold-load termination
such as is achieved in current quasi-optical rejection schemes which
give 
30 K. The second condition is appropriate to a
sideband separating mixer system for which = 4.2 K.
For < 0.1, and = 30 K, the DSB system
temperature is less than than the SSB system temperature (i.e.,
is negative). For = 4.2 K, is
never less than , pointing to the importance of
achieving low termination temperatures.
We also show in Figure 1 the sky
temperature 
and the two dominant terms which contribute to
(
and 
; 
is always less than
0.2 K at this frequency). A significant contribution to the system
temperature is that due to rear spillover noise, which points to the
importance of designing antenna structures and optics to minimize rear
spillover and blockage losses. Finally, in Figure 1
we show a comparison between the quantities 
(Equation
17) and 
(Equation
22). If receiver temperatures are below this break-even
point, sky noise dominates and SSB observations are always more
efficient even if astronomical measurements can be collected from both
sidebands.
Figure 1: Representative receiver and system temperatures as a function
of 
at 230 GHz. An image termination noise temperature of 30 K
is representative of the traditional cold load termination technique
used at the 12m. An image termination noise temperature of 4.2 K
represents that expected from the image separating mixer at a physical
temperature of 4.2 K.
Figure 2 shows the Chilean MMA site atmospheric opacity as a function of frequency calculated using the Grossman (1989) atmospheric model. Figure 3 shows the differences between single and double sideband system temperatures as a function of frequency for typical atmospheric conditions at the proposed Chilean MMA site. We have assumed the telescope parameters listed above and an image termination temperature of 4.2 K.
Figure 2: as a function of frequency for the Chilean MMA site.
Calculated using the Grossman (1989) atmospheric model.
Figure 3: Single and double sideband system temperatures (
scale) as a function of frequency for the Chilean MMA site and the
conditions shown in the lower right.
Figure 4 shows the squared ratio of the DSB and SSB system temperatures and thus gives the observing speed ratio for the two options. In the high-transparency 200-300 GHz window, the observing time advantage of SSB is only 25-30%. At higher frequencies for which transparency diminishes and noise climbs, the SSB advantage grows. For the submillimeter windows above 400 GHz, the SSB advantage is over a factor of 2. This implies that one could do two SSB observations faster than one DSB observations even if the lines of interest could have been observed simultaneously in opposite sidebands.
Figure 4: System temperature ratio as a function of frequency for the
Chilean MMA site and the indicated conditions.
These results are for good observing conditions (PWV = 1 mm) and
assumes that the high rear spillover efficiency ( = 0.98) can be
realized. As the weather deteriorates, the SSB advantage grows.
Similarly, if is less than assumed, the SSB advantage grows.
Figure 5 shows how the squared ratio of the DSB
and SSB system temperatures depends on at 230 GHz. The squared
Tsys ratio is a rather steep function of opacity at low values of
. Thus, as the weather becomes marginal or if you are
observing at low elevation angles, SSB-mode observing will offer
significant sensitivity advantages over DSB-mode observing.
Figure 5: System temperature ratio as a function of for the
indicated conditions.
Figure 6 shows the dependence of
(Equation 22) with frequency for
the conditions shown. The Grossman (1989) atmospheric model was used
to calculate the atmospheric contributions to . Shown with
is the ultimate DSB receiver temperature,
. Note that at all frequencies
for the conditions shown, using n=2. Below 400 GHz, an acceptable
receiver temperature (within a factor of 2 of the theoretical limit in
integration time), is about 2 times the quantum limit. At higher
frequencies, it is 3-4 times the quantum limit owing to the greater
sky noise.
Figure 6: as a function of frequency for the
Chilean MMA site and the indicated conditions. The
ultimate receiver performance
is also shown.
