Memo Review

Memo: 434 - Load Calibration at Millimeter and Submillimeter Wavelengths
      Mangum, 2002Sep12

Reviewer: Stephane Guilloteau  (unsolicited)

Date Received: 2002Oct04


Review:

This paper presents a derivation of the expected accuracy of the 
calibration systems.  However, it contains a major error for the 
one-load case which leads to extremely significant overestimates of the 
errors in that system. The author assumes tau_s and tau_i to be 
independent variables, which is not true. In fact tau_s and tau_i are
essentially 100 % correlated. In general, at frequency nu,
	tau_s (t) = tau_i(t) + Delta_tau(nu)
where Delta_tau(nu) is essentially a constant in time because it mostly 
depends on Oxygen. There are frequencies where the relationship between 
tau_s and tau_i is not that simple, but the high correlation remains 
(e.g. around the 183 GHz water vapor line).

So Eq.19 is erroneous, and all results for one-load (and 
semi-transparent) vane based on the opacity are wrong. 

Moreover, the estimated variation of Jm of up to 10 % is not justified. 
In fact, simple atmospheric models show that Jm should not vary this 
much. The effect of variations in Jm will depend on whether ABSOLUTE 
calibration is desired or only RELATIVE calibration (i.e. stable as 
function of time).


Further comments:
-----------------

I realized that most quantities are defined only in the Appendix. This 
is rather inconvenient for the most important ones (e.g. f, R_i) 

Page 3: In Eq.2, there is a parameter called "f" which is not defined, 
and does not seem to correspond to anything real.  If I take the 
definition from the appendix, then Eq.2 is incorrect since part of the 
beam remains coupled to other terms.

Page 3: Eq.3 corresponds to the Single-Dish case. There is a slightly 
different equation for an interferometer, which actually makes the 
system temperature appear explicitely later on.

Page 3-4: It would be good to remind people that G_s = 1/(1+R_i) and 
G_i = R_i/(1+R_i) if R_i is the image to signal gain ratio

Page 5: Section 4.1. R_i appears in Eq.13 but is defined nowhere (well, 
only in Appendix)

Page 5: Section 4.2. It is written f_1 = f_2 = f, but what is f?
That $f$ appears in Eq.14, and does not seem to correspond to any 
physical quantity.

Page 6: Section 4.3. Here we can understand from f_1 = f and f_2 = 1-f 
that f is the vane transmission, but it would be good to write it 
explicitely.

Section 5.1:  Js and Ji are not independent variables. They are 100 % 
correlated.  Eq.17 actually does not use them as free variables. The 
free variables are Tload(1,2) n_l, R_i, tau_s, f1, f2 as used in Eq.17. 

Section 5.2:  As above, plus tau^s and tau^i which are also not 
independent variables.  However, here Eq.18 erroneously assumes tau_s 
and tau_i to be independent. This is wrong.  In most cases, 
tau_s = tau_i + Cte, so they are 100 % correlated. In fact, in the low
opacity case, it is easy to see that tau_s and tau_i appear with 
opposite signs in Eq.15.  Taking them as independent leads to a totally 
erroneous conclusion. In the homogeneous temperature case 
(Jm = Jspill = Jload), the derivative of Eq.15 vis a vis tau is zero.

The true "free" parameters to be used Tau_s, and Tau_s-Tau_i which is 
in most cases a constant in time.

Page 14: Why does Jsky_hot depend on Jm, if it is "emission which 
terminates to ground"?  I would assume it is "emission which terminates 
to SKY".