Ph 343 Lab 4 Calibrating the Radio Telescope II. The ``Temperature'' of the Receiver and the Noise Diode

Due: Thursday, October 31, 2002

Purpose: A blackbody (a perfect thermal emitter) with a known temperature that completely fills the beam of the telescope is our most precise calibration source, since the signal is set by fundamental physics (a temperature measurement with an accuracy of a degree or so is straight-forward). Rutgers has purchased a 12-inch square piece of ECCOSORB SF-1.5 from Emerson & Cuming. This material is a sheet of silicone rubber impregnated with iron compounds whose magnetic and electrical properties produce a medium with a speed of light (well, of radio waves) that is equal to that in a vacuum. This means that radio waves will not reflect off of the surface of the medium. However, the waves are strongly absorbed by the medium. Of course, the match in speeds is not perfect, but more than 99.9% of the incident energy is absorbed at the design frequency of 1.5 GHz. Over 99% of the energy is absorbed between a frequency of 1.425 GHz and 1.575 GHz ($\pm 5$% from the design frequency). This is the claim of the information sheet that came with the product, anyway.

A material that absorbs radio waves will will also emit them well. We will put the ECCOSORB in front of the feed to inject a signal with a known antenna temperature into the system. This determines the receiver temperature and the calcons. A comparison of the signal from the ECCOSORB to that from the noise diode also determines the ``temperature" of the signal injected into the system by the noise diode.

Procedure:
Log onto the computer and start the SRT control window. Work at a frequency of 1430 MHz (1.430 GHz) and take ten samples with zero frequency step. Record your measurements in a file. Turning ``record'' on and off judiciously can help keep the output file from having a large number of extraneous numbers.

Point the telescope to an altitude of 20 degrees to eliminate any signal from the atmosphere.

The manual calibration with the blackbody starts by (gently) placing the sheet of ECCOSORB in front of the feed. One of you may have to hold it there or I may have devised some way to hang the sheet in front of the feed. Write down the temperature of the ECCOSORB (in Centigrade) before and after putting it in front of the feed. Also note the value of calcons (if the calibration is not yet determined, calcons is 1.00). Then push (click on) the ``Vane'' button. The display asks you to insert the calibrator but, since it is already there, push the Vane button again. The computer will take a set of ten measurements and then ask you to remove the calibrator. Go out and remove the ECCOSORB and then click on Vane again. The computer takes another set of ten measurement and then calculates the receiver temperature and the calcons.

With the ECCOSORB removed from in front of the feed, perform a calibration using the noise diode. Make sure that you are recording this calibration, so that you have the actual measured antenna temperatures with the noise diode on.

Perform the manual Vane calibration followed by a noise diode calibration two more times, making sure that the data from all three pairs of calibrations are recorded in your output file.

Analysis:
1. Average the two temperatures of the metal plate backing the ECCOSORB measured before and after each of your three Vane calibrations. Convert your average temperature to the Kelvin scale. This produces $T_{vane}$ for each calibration.

2. For each Vane calibration, average the ten measurements with the ECCOSORB in front of the feed. This is the system temperature with the vane in, $T_{in}$. Similarly, average the ten measurements with no black body in the beam to produce $T_{out}$. Also find the uncertainty in both $T_{in}$ and $T_{out}$.

3. Calculate $T_{rec}$ and calcons for each Vane calibration. Assume $T_{spill} = 20$ K. Your values will differ slightly from those calculated by the control program because it assumes $T_{vane} = 300$ K.

$$T_{rec} = \frac{T_{vane} - (T_{in}/T_{out}) T_{spill}} {(T_{in}/T_{out}) - 1}$$

$$calcons_{new} = \left(\frac{T_{vane}+T_{rec}}{T_{in}}\right) calcons_{old}$$

4. Use the formula for propagation of errors to estimate the uncertainty in a $T_{rec}$ and calcons from a single calibration using your typical measured uncertainties for $T_{in}$ and $T_{out}$. Assume that the uncertainty of $T_{vane}$ is small compared to those for $T_{in}$ and $T_{out}$. Can you state any evidence supporting this assertion? Also assume that there is no uncertainty in $T_{spill}$. How do the uncertainties that you have calculated for $T_{rec}$ and calcons compare to the rms scatter of your three measured values around their means?

5. Average the ten temperatures measured with the noise diode on after the first Vane calibration. These temperatures assume the previous (and slightly incorrect) vane calibration calculated by the control program. Correct for this by multiplying the average temperature by $calcons_{new}/calcons_{prog}$, where $calcons_{new}$ is the value you calculated and $calcons_{prog}$ is the value the control program calculated for the previous vane calibration. This corrected temperature is $T_{diode} + T_{rec} + T_{spill}$. Subtract $T_{spill} = 20$ K and your estimate of $T_{rec}$ to find $T_{diode}$. Repeat the above for your other two calibrations done with the noise diode. Finally, state your best estimate of $T_{diode}$ and its uncertainty.