Memo Review Reply
Memo: 434 - Load Calibration at Millimeter and Submillimeter Wavelengths
Mangum, 2002Sep12
Reviewer: Stephane Guilloteau (unsolicited)
Date Received: 2002Oct04
Reply from: Jeff Mangum
Date Received: 2002Oct09
JGM comments are interspersed in the original SG review, and
are denoted by 'JGM>'.
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.
JGM> Noting that tau_s and tau_i are correlated is a good suggestion,
JGM> but the affect of this change is not nearly as catastrophic as
JGM> Stephane suggests. I have made this modification to the
JGM> analysis, but found that it leads to only a mildly significant
JGM> change to the uncertainties inherent in the single-load
JGM> calibration systems for the case where the opacity if badly
JGM> measured and the frequency is greater than 230 GHz. The total
JGM> uncertainties dropped by about 2-3% at 490 and 650 GHz for the
JGM> badly-measured opacity case.
JGM> More important for the badly-measured submillimeter-observation
JGM> cases is the sign error that I found while investigating
JGM> Stephane's suggested change to the analysis. The second to the
JGM> last term in Equation 19 should have a [1 -...] instead of
JGM> [1 +...] in the bracketed term. This lead to a drop of about 8%
JGM> in the uncertainty inherent in the single-load calibration
JGM> systems at 490 and 650 GHz. For all other cases considered, the
JGM> uncertainties dropped by 0.1-0.3%.
JGM> Overall, only the uncertainty estimates for the badly-measured
JGM> opacity cases have changed significantly, and the conclusions of
JGM> the analysis are unaffected.
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).
JGM> 10% is a good "worst-case" estimate. Stephane eludes to a
JGM> different point, though. Like eta_l, if Jm is known to be stable
JGM> over long periods, its uncertainty really does not belong in an
JGM> analysis of the relative calibration system. It really should be
JGM> associated with the absolute calibration scheme.
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)
JGM> I was encouraged to put definitions in an Appendix, and like this
JGM> style better than sprinkling them throughout the paper.
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.
JGM> It is defined in the Appendix A. It is the fraction of the
JGM> receiver beam filled by a load.
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
JGM> Good suggestion. I have put it in Appendix A.
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.
JGM> See comment above.
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.
JGM> It is...in Appendix A...
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.
JGM> See comment above.
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.
JGM> Not totally erroneous at all. See comment above...
The true "free" parameters to be used Tau_s, and Tau_s-Tau_i which is
in most cases a constant in time.
JGM> Yes, I got it...see comment above...
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".
JGM> You are right. It is the emission from sky from the rear
JGM> hemisphere.