TPAR_18: Jan 08, 2008

Width of the Focus Curves

Our procedure for determining the best Y-focus for the GBT is to make maps of a bright compact source at 3-5 settings of the Y focus and fit each map to a Gaussian with a free width, peak location, and peak height. The results of these fits (peak amplitude as a function of Y-focus, beam width as a function of Y-focus) are then essentially eyeballed and a focus chosen that gives a big peak and a small beam.

The FWHM of the peak height curves is typically 15-17mm. This is slightly broader than you would expect from naively scaling single-pixel GBT receivers at low frequency. For example, the FWHM of a Y-focus scan at Ka-band (38 GHz) is 30mm. Scaling to 90 GHz we expect a 12-13mm FWHM, 20-40% smaller than we do see. A previously confounding factor in the comparison is that the CCB frequency channel selection in GFM doesn't appear to be working -- based on the width of the beam on the sky, one always gets the 38 GHz channel.

A limited number of optical simulations of subreflector scanning using ZEMAX have been carried out. A point source 1 arcminute off axis in elevation was brought to the center of the array by tilting the subreflector by 0.12 degrees. I am a (not a little) unsure that the tilt was about the right point but with pure tilt it can be seen there is a huge defocus:

I've used a Zemax model of the GBT/MUSTANG to predict beamshapes during a subreflector scan. Beams were calculated for a point source at the center of the scan pattern (zero subreflector tilt), a sources 0.5 and 1 arcminutes from the center (in elevation) (-0.06 and -0.12 degrees of subreflector tilt). Refocusing of the subreflector was allowed at each position (lfcy was allowed to float to whatever value gave the best focus) and vignetting was set to give the correct illumination of the GBT.

• subreflector_1arcmin.pdf: A subreflector scan 1' off axis with refocusing - just so you know with no subreflector tilt every single ray at all points across the array meets at a point. The array is on the right and the secondary focus of the GBT is on the left. In this plot you can clearly see the aberrations created at the secondary focus of the GBT.

• subreflector_scan_beams.pdf: The beamshapes expected in a subreflector scan.

However a simple shift in lcy (I’m fairly sure I have that direction right but I should check) brings the source back in focus. From a geometric optical view this focus is not perfect however initial calculations show that the beam shape is close to diffraction limited.

• subreflector_1arcmin_refocus.pdf: A subreflector scan 1' off axis with refocusing.

More needs to be done here but once I confirm the exact movements of the secondary I'll look into it more. As well as the location/direction of focus offsets I also need the order in which they are applied. In practice the angles on the GBT are small enough that this probably does not matter but I might as well get things right.

The beam quality drops quickly once you are more than 0.5' off axis and by 1'off axis the strehl ratio is approximately 0.5 due to a large astigmatism. I think this means that at 90GHz subreflector scans will have limited use. The situation should not be as bad at lower frequencies but I would be interested in knowing if my predictions match up with what is measured.

SRD-24th Jan 2008

SRD-28th Jan 2008

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However, perhaps this could be the detector thermal time constant?

Expected beam shape during subreflector scans.

A limited number of optical simulations of subreflector scanning using ZEMAX have been carried out. A point source 1 arcminute off axis in elevation was brought to the center of the array by tilting the subreflector by 0.12 degrees. I am a (not a little) unsure that the tilt was about the right point but with pure tilt it can be seen there is a huge defocus:

• subreflector_1arcmin.pdf: A subreflector scan 1' off axis with refocusing - just so you know with no subreflector tilt every single ray at all points across the array meets at a point. The array is on the right and the secondary focus of the GBT is on the left. In this plot you can clearly see the aberrations created at the secondary focus of the GBT.

However a simple shift in lcy (I’m fairly sure I have that direction right but I should check) brings the source back in focus. From a geometric optical view this focus is not perfect however initial calculations show that the beam shape is close to diffraction limited.

• subreflector_1arcmin_refocus.pdf: A subreflector scan 1' off axis with refocusing.

More needs to be done here but once I confirm the exact movements of the secondary I'll look into it more. As well as the location/direction of focus offsets I also need the order in which they are applied. In practice the angles on the GBT are small enough that this probably does not matter but I might as well get things right.

SRD-24th Jan 2008

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TOC: No TOC in "Pennarray.TparAnalys18"

Much of the smearing has been traced to a ~50 ms difference in the MUSTANG and Antenna timestamps. Correcting for that timestamping problem, here is the above map of Mars:

I've used these data to derive per-detector beam offsets. Here they are (on the right) compared with the nominal beam offsets derived from Mars in scans with the SR stationary (on the left):

(BSM 23jan08)

This has been traced to a 50 ms difference in the MUSTANG and Antenna timestamps (BSM 23jan08)

%META:FILEATTACHMENT{name="marsTpar18s82sr2offTfixNewSkyoff.png" attr="" comment="" date="1201102375" path="marsTpar18s82sr2offTfixNewSkyoff.png" size="65128" user="BrianMason" version="1.1"}% %META:FILEATTACHMENT{name="platescaleCompareSr2arcminOffb.png" attr="" comment="" date="1201102449" path="platescaleCompareSr2arcminOffb.png" size="16764" user="BrianMason" version="1.1"}%

However, inspection of a few timestreams during our run showed similar peak heights

However, inspection of a few timestreams during our run showed similar peak heights. Careful photometry gives the same integrated flux for scan 99 (a slow scan) and scan 103 (the fastest scan). You have to choose your sky region carefully though since there's a lot of negative flux in the bowl around the source. The equality of itegrated fluxes is also clear by comparing the peak heights and fitted beam sizes, which are about right.

However, perhaps this could be the detector thermal time constant?

Detector Time Constant Tests

However, inspection of a few timestreams during our run showed similar peak heights

I also examined the other subreflector encoders (X,Y,Z position and Y tilt) for scan 108 (SR scan) and 107 (regular daisy scan immediately preceeding). The other degrees of freedom of the SR were not doing dramatically different things in the SR scan than in the regular scan -- if anything, they were more stable. plots here

As a zeroth order exercise I have simply made maps with the QD off, and with all 8 possible assignments and signs of (QD-X,QD-Z) to (elevation,cross-elevation). Before applying the QD offsets, the time series were passed through a 10th degree high-pass polynomial filter with a half-power point of around 0.03 Hz, successfully removing long-term drifts but leaving signals at structural frequencies of the GBT. An approach which removes the sag terms but leaves lower frequencies present in the data QD would be desirable -- this could allow scan-synchronous quasi-static distortions to be modelled as well. The MUSTANG maps made from this exercise are shown here.

As a zeroth order exercise I have simply made maps with the QD off, and with all 8 possible assignments and signs of (QD-X,QD-Z) to (elevation,cross-elevation). Before applying the QD offsets, the time series were passed through a high-pass filter with a half-power point of around 0.03 Hz, successfully removing long-term drifts but leaving signals at structural frequencies of the GBT. An approach which removes the sag terms but leaves lower frequencies present in the data QD would be desirable -- this could allow scan-synchronous quasi-static distortions to be modelled as well. The MUSTANG maps made from this exercise are shown here.

The full set of plots from this exercise are shown here

In TPAR_18 we did a suite of tests of different scan patterns and scan speeds, mostly using daisy scans.

A summary of the scans done (with the expected peak velocities and accelerations) is as follows

Some observations from this exercise:

• Daisy scans of moderate size (1-2 arcminutes) are faithfully executed without exciting excessive feedarm vibrations, even with fairly short periods (20 sec). Periods of 10 seconds are not faithfully executed, probably because of the servo bandwidth limit of 0.3 Hz.
• The 5'x5' box scan is also well executed and does not excite excessive vibrations.
• Very slow scans, on the other hand, are not very well executed.
• Our MUSTANG OOF scan excites somewhat more feedarm vibration

The full set of plots from this exercise are shown here, along with some further notes.

As a zeroth order exercise I have simply made maps with the QD off, and with all 8 possible assignments and signs of (QD-X,QD-Z) to (elevation,cross-elevation). Before applying the QD offsets, the time series were passed through a 10th degree high-pass polynomial filter with a half-power point of around 0.03 Hz, successfully removing long-term drifts but leaving signals at structural frequencies of the GBT. An approach which removes the sag terms but leaves lower frequencies present in the data QD would be desirable -- this could allow scan-synchronous quasi-static distortions to be modelled as well.

As a zeroth order exercise I have simply made maps with the QD off, and with all 8 possible assignments and signs of (QD-X,QD-Z) to (elevation,cross-elevation). Before applying the QD offsets, the time series were passed through a 10th degree high-pass polynomial filter with a half-power point of around 0.03 Hz, successfully removing long-term drifts but leaving signals at structural frequencies of the GBT. An approach which removes the sag terms but leaves lower frequencies present in the data QD would be desirable -- this could allow scan-synchronous quasi-static distortions to be modelled as well. The MUSTANG maps made from this exercise are shown here.

The full set of plots from this exercise are shown here

We have been logging quadrant detector data along with our MUSTANG data. I conducted a preliminary investigation into the possibility of improving our pointing/maps with this data. We were lucky to acquire some excellent data to test this, in particular:

The GBT is equipped with a Quadrant Detector (QD) mounted on the elevation bearing which (through a small hole in the primary) measures the deflection of the tip of the feedarm. This allows the potential ability to correct for pointing errors not registered by the telescope encoders, due for instance, to wind gusts, oscillations of the feedarm, or forcible deflections of the feedarm due to sustained accelerations. We have been logging quadrant detector data along with our MUSTANG data. I conducted a preliminary investigation into the possibility of improving our pointing/maps with this data. We were lucky to acquire some excellent data to test this, in particular:

Servo and Structure stability with a Variety of Scan Speeds

• both sources show significant distortion when placed off-center -- see plots below. For the off-center map of 3c279, a Gaussian fit results in widths of 21"x15" (FWHM). By way of comparison we expect 8"x8" based on the telescope and receiver optics, and often achieve 9"-10" in scans with the primary.

• both sources show significant distortion when placed off-center -- see plots below. For the off-center map of 3c279, a Gaussian fit results in widths of 21"x15" (FWHM). By way of comparison we expect 8"x8" based on the telescope and receiver optics, and regularly achieve 9"-10" in scans with the primary.

To investigate whether perhaps the distortion is due not to gross beam distortions or pointing errors, but to a distortion of the plate scale with subreflector tilt (and corresponding shifting of the individual beam offsets) I fit individual detector beams to the Mars 2' offset data. The resulting beams appear scattered somewhat randomly over a large area, and the map that's made with these offsets is quite poor. Given this and the poor on-axis image quality obtained with subreflector scans it seems likely that the pointing is not reliable to the needed level when scanning the subreflector.

Quadrant Detector Data

We have been logging quadrant detector data along with our MUSTANG data. I conducted a preliminary investigation into the possibility of improving our pointing/maps with this data. We were lucky to acquire some excellent data to test this, in particular:

• TPAR_17, scan 60 -- a continuous OOF raster scan on 3c279 taken under windy conditions (peak gust ~ 25 mph!)
• TPAR_18, scans 105-108 -- r=11' daisy scans at a sequence of increasing speeds, the final one peaking at nearly 7'/sec.

A visual inspection of the QD data (I use samplers X_axis and Z_axis, which according to this MR purport to be estimates of the pointing deflection along the X and Z optical axes in arcseconds) suggests that the X channel corresponds to elevation and the Z channel to cross-elevation. Large systematic changes in X are visible over most scans, presumably corresponding to feedarm sag with elevation which is already modelled by the existing pointing model.

Here is a plot of a typical QD X-channel pointing deflection estimate:

(Note: I might have thought on the basis of the SR Tilt scalings that I was given that Z would be elevation -- it seems likely that some label is swapped somewhere)

As a zeroth order exercise I have simply made maps with the QD off, and with all 8 possible assignments and signs of (QD-X,QD-Z) to (elevation,cross-elevation). Before applying the QD offsets, the time series were passed through a 10th degree high-pass polynomial filter with a half-power point of around 0.03 Hz, successfully removing long-term drifts but leaving signals at structural frequencies of the GBT. An approach which removes the sag terms but leaves lower frequencies present in the data QD would be desirable -- this could allow scan-synchronous quasi-static distortions to be modelled as well.

%META:FILEATTACHMENT{name="tpar18s60qdX.png" attr="" comment="" date="1199984209" path="tpar18s60qdX.png" size="8378" user="BrianMason" version="1.1"}%

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Subreflector Scanning

I evaluated scans 81 (SR daisy on Mars, source on-center), 82 (SR daisy on Mars, source 2' off-center in cross-elevation), 108 (SR daisy on 3c279, source on-center), and 109 (SR daisy on 3c279, source 2' off-center in cross-elevation). Winds were under 1.0 m/s for all scans.

Main findings:

• sources significantly broadened on-center, eg, when I fit a Gaussian to 3c279 in scan 108 I get a FWHM of 16". 3c279 should be a point source, so this broadening corresponds roughly to a 14" RMS pointing offset in each dimension.
• both sources show significant distortion when placed off-center -- see plots below. For the off-center map of 3c279, a Gaussian fit results in widths of 21"x15" (FWHM). By way of comparison we expect 8"x8" based on the telescope and receiver optics, and often achieve 9"-10" in scans with the primary.

Here is a map of Mars collected with the subreflector executing a "daisy" scan with a radius of 4' on the sky. This data was collected at a low elevation (25 degrees) where microphonics (probably due to other GBT receivers) are known to affect our data, resulting in significant glitchy striping in the map. The primary was traking the map center.

Here is a map of 3c279 collected with the subreflector executing a 4' radius daisy pattern. The primary was tracking the map center.

Notes on the analysis procedure:

• Maps are in units of the cal (~38 Jy)
• For each map, the nearest cal was used to estimate the detector gains, and the nearest blank scan was used to estimate per-detector noise weights.
• An integration-by-integration common mode across the array was subtracted from the data (subcommon2)

Effect of the Existing Zernike Model on the MUSTANG Beam

We collected OOF maps with MUSTANG with the current OOF-derived set of Zernike polynomial corrections to the primary on, and with them off.

OOF Map of 3c279, in-focus, with the zernike model on:

The best-fit Gaussian to the in-focus, zernike-On map yields FWHM of 8.1"x10.6", elongated in the cross-elevation (scan) direction. This map was collected at an elevation of 66 degrees.

OOF Map of 3c279, in-focus, with the zernike model off:

The best-fit Gaussian to the in-focus, zernike-Off map yields FWHM of 17.9"x9.4" (elongation in the elevation direction). Note that the peak amplitude of the source response is reduced by a factor of ~2 from the zernike-on map. This map was collected at an elevation of 64 degrees.

-- BrianMason - 09 Jan 2008

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