The following web page is meant for the exchange of analysis information between MJ Mahoney, Bruce Gary and Richard Denning, who are engaged in understanding the calibration of the MTP/DC8 radiomter system.
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MTP/DC8 Window Effects
Bruce L. Gary
2000 April 29

Introduction

This page reports work done to assess three MTP/DC8 window effects:  losses, reflections and the possibility of a leaky LO standing wave.

Antenna Temperature Equations

Antenna temperature can be written two ways, from the observed quantities and from thermal radiation theory.

    Ta = tB + (CSi - CB)/g
        tB is Base target temperature [K],
        CSi is scky counts for sky location i,
        CB is base counts, and
        g is gain.

    Ta = TB*(1-L-R) +L*tW + R*tR
        TB is sky brightness temperature,
        L is fractional loss due to absorption,
        R is fractional reflectivity of window,
        tW is window temperature [K],
        tR is radiometer region temperature, approximated by tMXR.

Equating these two, and solving for TB, we have

    TB = (tB + (CS-CB)/g - L*tW - R*tR) / (1-L-R)

One can also solve for gain, g, by equating TB to OAT:

    g = (CS-CB) / (OAT*(1-L-R) + L*tW + R*tR - tB)

When gain is derived this way I refer to it as OAT-based system gain.  It is a "system" gain because it involves not only the radiometer but also the window and a finite radome aperture.  Whereas a radiometer gain is referenced to the horn, customarily the horn mounting flange, system gain is referenced to the atmosphere outside the radome window.  The two gains will differ, but hopefully by only a small amount.

Noise Diode Analysis

If the noise diode output [counts] were constant throughout the flight, we could safely state that radiometer gain, referenced to the horn, was constant.  If NDC (the deflection of the noise diode, in counts) varies within a range of 2%, for example, then we could safely state that the radiometer's gain varied within a similar range.  If "system gain" (i.e., referenced to outside the radome window) varies by more than these amounts, we would have to "blame" the window for the extra gain variation.

Figure 1After 40.5 ks, there's a good fit, implying that NDC1 varies lin a linear manner with respect to tMXR.  During the bulk of the flight, between 40 ks and 66 ks, ND-based Channel 1 gain varies within a range of less than 2%.

Figure 2.  Good fit.  NDC2 is linearly related to tMXR.

Figure 3Good fit.  NDC3 is linearly related to tMXR.

From these good fits we may conclude that the radiometer's gain, referenced to the noise diode waveguide coupler, varies by only a few percent during the flight, varies smoothly, and varies linearly with tMXR - with the one small exception of channel 1 during the early part of the flight.
 

Discrediting OAT-Based Gains

Since the ND analysis shows that gains vary by small amounts, and slowly, let us determine the variability of OAT-based gains, and compare with the ND-baed gains.

Figure 4Noise diode based radiometer gain compared with OAT-based system gain, for channel 1.  The red symbols are OAT-based gain, the red trace is an gain equation bassed on a fitting of the OAT-based gain with tMXR and tWIN as independent variables.  Whereas the ND-absed gain varies by less than 2% after 40 ks, the OAT-based system gain varies by 41%!

Figure 5Same, but for Channel 2.

Figure 6Same, but for Channel 3.

Clearly, the OAT-based system gain varies much more than the noise diode based gain, and varies abruptly.  This should cause us to suspect that the AOT-based system gain derivation contains a flawed assumption.  Specifically, we've assumed that window effects are limited to absorbtion and reflection of both the incoming atmospheric radiation and outgoing thermal emission from the instrument area (represented by the mixer temperature).

Could the window be doing something else?  I can think of two additional things the window could be doing:

    1) reflecting a leaking LO signal that comes out the horn, reflects off the window, and re-enters the horn.  As the distance mixer/window/mixer varies slightly, the leaky LO standing wave can change state, shifting between the two extreme states of complete cancelation and complete addition.  This would cause the baseline to shift, or wander, by amounts that could be considerable if the leak is large. 2)

    2) The window clear aperture is limited by the cut-outline of the fairing, and the edge of the fairing will emit microwaves at a temperature comparable to tWIN.  The effect of fairing emission is to increase TB by an amount that depends upon the temperature contrast, tWIN versus OAT, and upon the solid angle of the fairing as illuminated by the horn antenna pattern.  This effect should be limited to a very small fraction of tWIN-OAT, or a small fraction of 30 K, for example.

TB Analysis Using Gains Based on Noise Diode

Figure 7There's a shift in OATnav at 41 ks, and its return at 44.5 ks that does not show up with TB.  TB is higher than OAT from 49 to 53 ks, then becomes lower from 54 to 57 ks.

Figure 8Same comments, except that ll discrepancies are smaller.  Interesting!

Figure 9TB3 exhibits a good fit to OATnav, especially at 41 and 44.5 ks.

TB Analysis Using Gains Based on tMXR

Since NDC varies linearly with tMXR, we may assume that the gain of the radiometer referenced to the horn waveguide joint also varies linearly with tMXR.  If, in addition, the window losses and reflections are constant throughout a flight, then the system gains would also be linearly related to tMXR.  Since there were slight departures of NDC from a linear relationship on tMXR, perhaps using a tMXR-based gain equation will afford a small improvement.  (It does.)

The following plots are for TB that is based on a simple gain equation that has a linear dependence upon tMXR.  I used:

    G1 = 11.76 - 0.20 * (tMXR - 38 C)
    G1 = 13.80 - 0.21 * (tMXR - 38 C)
    G1 = 15.00 - 0.40 * (tMXR - 38 C)

I've also allowed for window losses and reflections of 0.4% and 0.6%.

Figure 10There's slightly better agreement between OATnav and TB based on a tMXR gain equation ijn the 32 to 38 ks region (the region where NDC1 could not be fit well by a linear relationship).

Figure 11Same as the ND-based TB.
 

Figure 12Same as the ND-based TB.

Standing Wave Versus Time for DC000308

It is tempting to consider the TB discrepancy as a baseline offset produced by changes in the standing wave of a leaking LO that reflects off the window and re-enters the waveguide.  If we assume the window changes distance to the mixer during the flight, then this standing wave baseline level  effect will vary for all three channels, but with different amplitudes, owing to the slightly different number of wavelengths along the mixer/window/mixer path.  Is there evidence for this in the data?  Yes!

Figure 13.  Unexplained discrepancies between TB based on "mixer temperature gain equations" and OATnav.

Notice the similar shapes for the "TB discrepancy" for the 3 channels; and notice the smooth progression of large amplitude for Channel 1 to smallest amplitude for Channel 3.  This accounts for Channel 3's fitting OAT the best.

Lapse Rate Idea

In Fig. 13 it's curious that the amplitude of the variations is approximately proportional to the applicable range for each channel.  For example, at an altitude of 10 km the applicable ranges for Channels 1, 2 and 3 are approximately 2.79, 1.06 and 0.48 km, and the amplitudes for the variation near 43 ks is 3.1, 1.6 and 0.8 K.  These two sets of values are in approximately the same ratio to each other.

Figure 14.  The thick green trace is -dT/dz at flight altitude, and it correlates very well with the TB discrepancy traces.  At 43 ks dT/dz is +5 [K/km].  What elevation pointing offset would be required to produce a -3 K TB error for Channel 1, with an applicable range of about 2.8 km?  The answer is 12.1 degrees, or one scan position!

Oh, Oh!  Did I make a mistake in identifying the horizon view in the counts matrix?

Stay tuned!

Sky Location Mistake Discovered

Yes, I used scan location #5 instead of #6, due to a Y2K bug (ymd$ in D1.BAS checks for yymmdd$ to set scan direction instead of yyyymmdd$; I was using an old version of D1.BAS).  So, after re-reducing the data using scan location #6 for the horizon, I get the following plots of TB(t):

Figure 15.  The corrected version of Fig. 10.  RMS difference between TB and OAT is o.29 K.

Figure 16.  The corrected version of Fig. 11.  RMS difference between TB and OAT is o.34 K.
 

Figure 17.  The corrected version of Fig. 12.  RMS difference between TB and OAT is o.25 K.
 
 




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This site opened:  April 29, 2000.  Last Update: April 30, 2000