Standing waves measured by moving the platform with the tiedowns.

    On 04jan05 data was taken to measure these standing waves. The measurements started at 15:42.

The setup and processing:

• lband wide in linear polarization mode
• 3 contiguous 50 Mhz bands centered at 1400,1450, and 1500 Mhz. Each 50 MHz band had 2048 channels.
• Data was dumped once a second using the interim correlator.
• 60 seconds of data was taken before the tiedowns were moved. This was used as the bandpass correction.
• The tiedowns were then moved from 12.42 inches to 16.42 inches in 243 seconds (.016 tdinches/second). They were then moved back down to the starting position. An increasing tiedown position causes the platform to move lower so the platform was lowered and then raised. The entire motion took about 20 minutes.

• Compute the median bandpass for the 60 seconds before the tiedowns were moved. Divide this into each of the 1 second spectra during the move.
• For moving up and moving down average channels 1100 thru 1500 and then use these 243 numbers to flatten each spectra (i should have subtracted the values rather then dividing....).
• combine the 3 50 Mhz spectra into a contiguous 150 Mhz spectra.
• clip the spectra to +/- .02 Tsys. This is to get rid of the galaxy and the bandpass edges.
• 0 extend and then compute the fft of each of these 150 Mhz spectra. This is the Acf.
• compute the  magnitude  abs(acf) and and phase atan(float(acf),imaginary(acf)).

   The bandpass correction was taken from the tiedown starting position and was used for the entire 20 minutes.  Any ripples present in the spectra near this tiedown reference position should be canceled by the bandpass correction (assuming they are stable in time). When we move away from the reference position the ripples should shift in phase and no longer cancel.

    The acf will have a spike if the same radiation takes two paths into the horn. The lag for the time delay of  the path difference will show increased correlation because the same signal is in the immediate and delayed elements of the multiplier. For a peak to move from 1 acf channel to the next, the signal path must increase by c*acfShiftLen. For150 Mhz bandwidth this is about 1 meter. If you have a complex acf, then the phase at each lag will shift through 2pi radians when the extra path length changes by 1 wavelength (21 cm).

---

Images of ripple strength versus tiedown offset

• Ripple amplitude vs delay. polA,B separate (.gif):
• The top two plots are polA, polB when the platform was moving down (td extension increasing). You see no ripples until  1 inch of td offset. Ripples then appear with the strongest at 1.04 usecs. This happens in both polA and polB.
• The bottom two plots are when the platform is moving up (td extension decreasing). The ripples remain visible g until 1 tiedown inch before the starting position.
The ripples are repeatable when moving up and down, and between polA and polB.
• Ripple amplitude vs delay  averaging polA and B (.gif):   This has the same data as the above plot but polA and polB have been averaged to increase the signal to noise.

---

Plotting the amplitude and change of phase:

• Fig 1 Avg strength of ripples vs delay (polA,B separate). The top plot is platform moving down, the bottom plot is platform moving up. Red (polA) and blue (polB) are the average of 100 seconds when the platform was farthest from the reference position. Green is 30 seconds closest to the reference position. The vertical scale is in units of Tsys )an offset has been added for display purposes). The width of the spike at 1.04 usecs is not resolved. With 150 Mhz bw the distance resolution is 1.  meter. The center of the polB 1.04 usec peak is offset from the polA peak by a fraction of a channel.
• Fig 2 Avg strength of ripples vs delay (avg pols and motion).
• Top plot has averaged the polarization's. Blue is platform moving down, red is platform moving up. Green is when we are close to the reference position.
• Bottom plot averages pols and directions: The black line is the average of the directions and the polarization's when far from the reference position. The green line is the average when close to the reference position. The 8 largest peaks have been flagged (in red) and the delay and strength of each of them is listed in the table on the right. The 1.04 Usec peak has a strength of .00089 Tsys. The processing divided by a reference spectrum. Below we will see that we moved the platform by  6 cm which would shift the sine wave in the spectra by 30%.  Dividing a sine wave by one shifted by 30% would increase the amplitude by about 50% .  The averaged data covered a 15% to 30% shift in the sine wave so the  .001 Tsys may be a little higher than the  ripple value without the bandpass correction
• Fig 3 change of phase of 1.04 usec peak: To move between channels of the acf the distance must change by 1 meter. Smaller changes will cause the ripple in the spectra to shift in frequency. This can be measured by creating a complex acf and watching the phase of the 1.04 usec delay move. A distance of 1 lambda will move  the phase 2*pi radians. For the phase to be defined, the amplitude must be non zero. Close the the starting platform position the bandpass correction cancels the ripples so the amplitude is close to zero. As we move farther away, the amplitude becomes non zero and the phase is defined.
• Top plot 1.04Usec phase vs td motion (rawDat): The phase for polA, polB, moving Up, and moving Down are all plotted separately. This is the raw data before fixing phase jumps of 2pi radians. All 4 of the measurements track each other.
• Bottom plot 1.04Usec phase vs tdmotion (avgPol): PolA and polB have been averaged and the phase jumps of 2pi were removed. The vertical scale was switched from radians to cm. Black has the platform moving up, red is platform moving down. Both directions track each other. The blue line is a  linear fit to platform motion versus tiedown motion. The fit gave .642 platform motion/tiedown motion (or 1.56 tiedown motion/platform motion). The slope is not unity because the tiedown/main cables stretch a little and the tiedown boom rotates.   The value of 1.56 is a little smaller than what was measured (1.73)  fitting a years worth of data  (tiedown motion and platform motion from the distomats).  This was all done at a of ten degrees (where the cos(10) = .09).
• Fig 4 Phase versus tdmotion for 8 largest peaks: If a peak in the acf comes from a reflection that goes down to the dish and back, then the phase of the peak should change as we move the platform. This was seen in the 1.04 Usec peak. The  phase for the 8 largest peaks (see figure 2 bottom plot) were plotted versus tiedown motion to see if they depended on the distance between the platform and the dish. The top plot has the platform moving up, the bottom plot shows when the platform was moving down. Each color is a different peak (the delays are printed on the left .. .65,.79,.81... usecs). Linear fits were done to each plot.
• Fig 5 Slope of phase vs td motion for the 8 peaks: The slope of the fits from figure 4 are plotted versus delay (peak location). Black is moving up and red is moving down.  Seeing a  slope equal to the 1.04 usec delay means that the peak goes between the dish and the bowl.  0 slope  says the the path length is not changing with the platform/bowl distance (or the amplitude is so small that the phase is not well defined). Since all peaks are present after dividing by the reference, they must be changing. They all go back to 0 when we return to the reference so the change is related to motion rather than time.
• .79 usec, .95usec, 1.04 usec, 1.17 usec peaks are probably reflecting between the bowl and the platform.
• .9 usec, 1.25 usec peaks change with platform motion but with a different slope.
• .65 usec and .81 usec don't seem to change phase with platform motion.

---

Some distances:

    These distance show that the 1.04 usec peak is between the horn and the reflector.
german's plot of the distances (.pdf):

---

Summary:

• Standing waves were seen that changed their strength as we moved the platform. The strongest peaks were at:
• 1.04 , .79, .91, 1.25, .81, .65, .95, 1.17 usecs (ordered strongest to weakest).
When we returned to the same platform position (20 minutes later) they returned to their original values (the bandpass correction canceled them).
• The 1.04 usec delay  corresponds to the distance between the horn and the dish. The amplitude was about .001 Tsys.  It showed a change of phase with tiedown motion of 1.56 tdMotion/platform motion. This comes from the stretching of the tiedown/main cables and the rotation of the td cable boom.
• The delays at  .79 , .95, and  1.17 usecs moved with the same rate of  phase as the 1.04 usec peak. They are probably bouncing between the bowl and the platform.
• The delays at .91 and 1.25 usecs change phase with a different rate so than the 1.04 usec peak. They are reflecting off of the platform and something else.
• The delays at .65 and .81 usecs do not change phase as we move the platform.
• The standing wave at 1.04 usecs was not resolved with 150 Mhz bw (1 meter resolution).
• The 1.04 usec standing wave is shifted a bit in polA and polB (by a fraction of a channel).
• For total power on off observing: If the tiedowns move appreciably between a position switch on and position switch off, then this could introduce standing waves. This might happen when we move from raining (distomats not working) to no  rain (distomats starting to work). It might also happen when the dome is at high za and passes in front of a tower causing the tiedown cables to lose tension.

 home_~phil