Methods to measure beam squint at the FEIC

Background

• The NA FEIC has installed a switch that allows both polarizations to be sampled during a 2D scan.
• Q: Can we get reliable squint numbers by setting the horn at 45 deg and taking only one scan? A: No.

Analysis

• Date: Tue, 23 Mar 2010 18:05:16 -0400 (EDT)
• I modified my software that reads the farfield co-pol and cross-pol NSI files to:
1. convert the data to real & imaginary,
3. convert back to phase and amplitude
4. write out a new file (co+cross)
• Here are the images for Pol 0 before and after the addition.
• I can then analyze these co+cross files with the phase center fitter / beam squint calculator program in the same way as the raw copol files. Here are the comparison of squint results for PAI_FE2 data:

 Method Band Freq Tilt copol co+cross scan numbers 3 100 0 4.88% 4.91% 5,6,7,8 6 243 45 11.78% 11.81% 6,8,9,10 7 317 45 22.35% 21.88% 22,23,24,25

This result suggests that scans taken with the probe at 45 deg should yield a good value for the squint. I do not include band 9 here because those squint values were so huge to begin with (the PAI report says 50%, my program gets 125%).

Update (Nov 2010)

• Richard Hills repeated my analysis independently and found disagreement at the level of 2 mm for beam waist location depending on the relative phases of the co and cross scans.
• Investigation of my software found that I used 10log10 for converting from power to amplitude rather than 20log10!
• After fixing that mistake, I confirm the large changes in the phase center vs. phase shift. Using 8 different relative phases, the standard deviations of the results are:
 X Y Z Pol 0 2.1 1.0 5.4 mm Pol 1 3.2 2.2 6.0 mm
• Conclusion is that one would need to employ a grid and take two scans with the probe at 45 deg, one with the grid aligned with Pol 0 and one with it aligned with Pol 1
• Alternatively, we could try to calibrate the displacement that the probe undergoes due to rotation of the stage. Here is a diagram showing the theory of what is happening.

Calibration of probe rotation stage (December 6, 2010)

• Setup band 6 at 243 GHz RF, and set transmitter power to avoid saturation and obtain high dynamic range in nearfield cuts (60 dB)
• Peaked up with an X cut, then a Y cut, then an X cut to locate peak for Pol 0
• Rotated stage by 180 deg, and repeated peak-up procedure. Noted that peak differed by 3 mm in one axis and 0 in the other
• Repeated procedure for Pol 0 where we found the shift to be in the opposite axis, consistent with the axis of rotation being offset from the waveguide axis along one coordinate.
• Scan details:
 Scan EST Peak(dB) Center (m) Pol axis (deg) Fit result 2 11:22:33 -28.78 Y=-0.1682 +45 3 11:25:38 -33.59 Y=-0.1682 +45 4 11:27:43 -26.74 Y=-0.1682 +45 5 11:29:06 -24.85 Y=-0.1682 +45 6 11:30:28 -19.59 Y=-0.1682 +45 7 11:31:42 -15.00 Y=-0.1682 +45 8 11:33:00 -12.33 Y=-0.1682 +45 9 11:34:21 -3.66 Y=-0.1682 +45 10 11:35:35 -4.13 Y=-0.1682 +45 11 11:36:36 -6.80 Y=-0.1682 +45 12 11:37:48 -5.30 Y=-0.1682 +45 13 11:39:49 -0.02 Y=-0.1682 +45 14 11:41:06 +8.43 Y=-0.1682 +45 15 11:42:05 +5.34 Y=-0.1682 +45 16 11:48:07 +5.29 Y=-0.1682 -135 17 12:02:25 +5.26 Y=-0.1682 -135 18 12:03:43 +5.28 X=+0.1602 -135 19 12:05:22 +5.26 X=+0.1602 -135 Y=-0.16654 20 12:06:41 +5.28 Y=-0.1662 -135 X=+0.16051 21 12:10:27 +5.27 Y=-0.1662 +45 22 12:12:22 +5.26 Y=-0.1662 +45 X=+0.16296 23 12:13:31 +5.26 X=+0.1632 +45 Y=-0.16633 Delta X = +2.45 mm, Delay Y = +0.21 mm 24 12:31:01 -21.08 X=+0.1632 -45 25 12:34:17 -20.92 X=+0.1632 -45 26 12:35:30 -23.00 Y=-0.1642 -45 27 12:37:00 -23.05 Y=-0.1642 -45 X= 28 12:38:07 -20.94 X=+0.1622 -45 Y=-0.16533 29 12:39:25 -21.07 X=+0.1622 +135 30 +135 31 +135

software analysis commands

• flatgauss -f band6testcut19__NF.txt -v -y 0.1602
• flatgauss -f band6testcut20__NF.txt -v -x -0.1662
• flatgauss -f band6testcut22__NF.txt -v -x -0.1662
• flatgauss -f band6testcut23__NF.txt -v -y 0.1632
• flatgauss -f band6testcut27__NF.txt -v -x -0.1642
• flatgauss -f band6testcut28__NF.txt -v -y 0.1622

2-D scans

Analysis of Band 6 farfield patterns

file angle phase center (-b 6)
Pol0_Band6LO249RF244__NF +45 -4.5094, +0.8589, +276.6949
Pol0_Band6LO249RF24302__NF -135 -7.0489, +1.3125, +256.9539
Pol1_Band6LO249RF24303_neg45__NF -45 -5.2764, +2.0257, +257.9350
Pol1_Band6LO249RF24307_135__NF 135 -5.6144, +0.2388, +259.0191
Pol 0 180 center - Pol 0 0 center = (dX,dY)   -2.539, +0.454
Pol 1 180 center - Pol 1 0 center = (dX1,dY1)   -0.338, -1.787
Pol 0 center - Pol 1 center = (x_diff,y_diff)   +0.767, -1.167
Pol 0 center - Pol 1 180 center = (x_diff1,y_diff1)   +1.105, +0.620
average geometry   major axis = 2.16 mm, minor axis = 0.396, angle=atan(0.396/2.16)= 10 deg
avg correction for rotating from +45 to -45   1.08cos(10)-1.08sin(10), -1.08sin(10)-1.08cos(10) = +0.87, -1.26 mm
avg correction for rotating from +45 to +135   1.08cos(10)+1.08sin(10), +1.08cos(10)-1.08sin(10) = +1.25, +0.876 mm
Pol1_Band6LO249RF24303_neg45__NF avg corrected   -5.2764+0.87, +2.0257-1.26 = (-4.41, +0.7656)
Pol1_Band6LO249RF24307_135__NF avg corrected   -5.6144+1.25, +0.2388+0.876 = (-4.36, +1.115)
squint using scans (1,3) w/avg correction   -4.5094 - -4.41, +0.8589 - +0.7656 = -0.099, +0.093 = (-0.21", +0.20")
squint using scans (1,4) w/avg correction   -4.5095 - -4.36, +0.8589 - +1.115 = -0.149, -0.256 = (-0.32", +0.54)
individual correction from +45 to -45 (from below)   (+1.043,-1.497)
individual correction from +45 to +135 (from below)   (+1.063,+0.724)
Pol1_Band6LO249RF24303_neg45__NF indiv. corrected   -5.2764+1.043, +2.0257-1.497 = (-4.23, +0.53)
Pol1_Band6LO249RF24307_135__NF indiv. corrected   -5.6144+1.063, +0.2388+0.724 = (-4.55, +0.96)
squint using scans (1,3) w/indiv. correction   -4.5094 - -4.23, +0.8589 - +0.53 = -0.28, +0.33 = (-0.59", +0.70")
squint using scans (1,4) w/indiv. correction   -4.5095 - -4.55, +0.8589 - +0.96 = +0.04, -0.10 = (+0.08", -0.21)

Analysis of Band 9 farfield patterns

• uncorrected beam squint = (+1.024,-2.774) mm = (+2.20,-5.96) arcsec = (+0.248,-0.672) beams
file angle phase center (-b 9)
Band9_676GHz45el_p0_20101214_160636__FF_Pol0_Copol.txt 0 -0.2110, -8.3813, -281.3219
Band9_676GHz45el_p1_20101214_171918__FF_Pol1_Copol.txt 90 -1.2355, -5.6073, -274.1291
Band9_676GHz45el_p0_180_20101214_183202__FF_Pol0_Copol.txt 180 -4.4468, -6.5601, -274.5453
Pol 180 center - Pol 0 center = (dX,dY)   -4.2470, +1.8212
Pol 0 center - Pol 1 center = (x_diff,y_diff)   +1.0245, -2.774
geometry   theta = -23 deg
correction for Pol 1 for rotating from 0 to 90 = (x_corr, ycorr)   +1.21, -3.03
Band9_676GHz45el_p1_20101214_171918__FF_Pol1_Copol.txt corrected   -0.0255, -8.637
squint (corrected)   (-0.186,+0.256) mm = (-0.40,+0.55) arcsec = (-0.045,+0.062) beams

Procedure for correcting the phase centers prior to squint calculation

 Pol 1 angle x_corr y_corr +90 (-dX-dY)/2 (dX-dY)/2 -90 (-dX+dY)/2 (-dX-dY)/2
• Apply the corrections to the second polarization's phase center fit and take the difference (as usual) with the 0 degree first polarization's phase center fit in order to compute the corrected squint.

Examples from data taken on Dec 7 and 14, 2010

• Band 6 1st pair:
• dX=-2.539, dY=+0.454, x_diff=+0.767, y_diff=-1.167, abs_diff=2.085
• x_diff>0, y_diff<0, abs_diff>0 --> +90
• x_corr=(2.539-0.454)/2=+1.0425, y_corr=(-2.539-0.454)/2=-1.497 --> (+1.043,-1.497)
• Band 6 2nd pair:
• dX=-0.338, dY=-1.787, x_diff=+1.105, y_diff=+0.620, abs_diff=-1.449
• x_diff>0, y_diff>0, abs_diff<0 --> +90
• x_corr=(0.338+1.787)/2=+1.0625, y_corr=(-0.338+1.787)/2=+0.724 --> (+1.063,+0.724)
• Band 9:
• dX=-4.2470, dY=+1.8212, x_diff=+1.0245, y_diff=-2.774, abs_diff=2.426
• x_diff>0, y_diff<0, abs_diff>0 --> +90
• x_corr=(4.247-1.8212)/2=+1.2129, y_corr=(-4.247-1.8212)/2=-3.0341 --> (+1.213,-3.034)
• Band 7:
• Band7_317GHz45el_p0_20101216_093306__FF_Pol0_Copol.txt: -8.6922, +0.7414, +295.2779
• Band7_317GHz45el_p1_20101216_103353__FF_Pol1_Copol.txt: -5.8354, -0.9150, +299.5873
• Band7_317GHz45el_p1_180_20101216_113440__FF_Pol1_Copol.txt: -10.9059, -2.0975, +300.1474
• dX=-10.9059--5.8354=-5.075, dY=-2.0975--0.9150=-1.1825, x_diff=-5.8354--8.6922=+2.8568, y_diff=-0.9150-0.7414=-1.6564, abs_diff=10.9059-1.1825=9.723
• x_diff>0, y_diff<0, abs_diff>0 --> +90
• x_corr=(5.075+1.1825)/2 = +3.12875, y_corr=(-5.075--1.1825)/2=-1.946
• uncorrected squint = (-2.787,+1.723) mm = (-5.99,+3.70) arcsec = (-0.317,+0.196) beams, in percentage = (+31.69,-19.58) total = 37.25
• corrected squint = (-0.341,+0.223) mm = (-0.73,+0.48) arcsec = (-0.039,+0.025) beams, in percentage = (-3.88,+2.54) total = 4.64

-- ToddHunter - 2010-03-24

Topic attachments
I Attachment Action Size Date Who Comment
pdf 2257_001.pdf manage 80 K 2010-12-20 - 10:51 ToddHunter theoretical cause of large squint measurements, confirmed by these tests
png plotfit19.png manage 31 K 2010-12-06 - 17:27 ToddHunter
png plotfit20.png manage 29 K 2010-12-06 - 17:27 ToddHunter
png plotfit22.png manage 29 K 2010-12-06 - 17:28 ToddHunter
png plotfit23.png manage 31 K 2010-12-06 - 17:28 ToddHunter
png plotfit28.png manage 31 K 2010-12-06 - 17:32 ToddHunter
png pol0_co_vs_copluscross.png manage 165 K 2010-03-24 - 15:50 ToddHunter
pdf squintCorrection-rotated.pdf manage 146 K 2010-12-17 - 09:56 ToddHunter notes showing the correction formula for each quadrant
Topic revision: r14 - 2010-12-20, ToddHunter

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