Grid Parabolic Antenna In Interferometer

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Jim Abshier

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Sep 21, 2021, 1:34:44 PM9/21/21
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A couple of years ago I needed to dismantle one of the two 3 meter
antennas of my 1400 MHz interferometer. This left me without an
interferomer to play with. Recently I decided to obtain a smaller more
portable antenna to use with the remaining 3 meter antenna as an
interferometer. I decided to try using one of those WiFi grid parabolic
antennas that have become popular for hydrogen line detection. The grid
parabolic antenna obtained was for 2.4 GHz, so it was modified using a
dipole feed that was left over from a previous project. The modified
grid parabolic antenna used in conjunction with the 3 meter antenna was
found to work rather well as an interferometer. An image of the modified
grid antenna and an interferogram obtained with this interferometer are
attached.

The interferogram shows Taurus A and 3C157. The lower plot is the raw
data with 10 second integration time, and the upper plot shows the data
with additional low-pass filtering. The rms noise of the raw data was
measured to be about 18 Jy based on 875 Jy for Taurus A. This can be
compared with the approximately 5 Jy sensitivity that I was previously
getting when I had two 3 meter antennas. Overall, I am pleased with the
result.

If you already have a 3 meter antenna, you could build an interferometer
that would produce good results by adding one of those inexpensive WiFi
grid parabolic antennas.

Jim Abshier


Grid Parabolic Antenna.JPG
TauA_3m+GP_Processed_20Sep2021.jpg

Marcus D. Leech

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Sep 21, 2021, 2:38:54 PM9/21/21
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Nice fringes!


Anthony

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Sep 21, 2021, 4:57:28 PM9/21/21
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What hardware and software are you using to create your Inferometer, outside of the antennas. Second question, what is your baseline distance between your antennas?
Thank you!
Your interferogram attachment is very interesting Jim!
 

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Jim Abshier

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Sep 21, 2021, 9:44:44 PM9/21/21
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Anthony,

A diagram of my 1400 MHz interferometer (with two 3 meter antennas) is
attached. It is entirely analog and uses an ICOM R8500 receiver with
external IF amplifiers. Most of the circuitry is "home-brew". The A/D
conversion, post-processing and plotting are done with scripts
(programs) written in octave running on a Linux computer. I didn't
measure the baseline, but it is probably about 8 meters.

Jim Abshier
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Interferometer Diagram cs3.jpeg

Anthony

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Sep 21, 2021, 10:05:32 PM9/21/21
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Yeah, that's what I was afraid of, the program is custom made. 

Thank you, Jim!

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Marcus D. Leech

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Sep 21, 2021, 11:08:25 PM9/21/21
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On 2021-09-21 10:05 p.m., Anthony wrote:
Yeah, that's what I was afraid of, the program is custom made. 

Thank you, Jim!
spectro_radiometer has an interferometer mode, but it does require a dual-channel coherent radio like a LimeSDR.


Anthony

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Sep 21, 2021, 11:19:37 PM9/21/21
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I'm familiar with the LimeSDR, they do require software and programming. Can Python be used? 

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Marcus D. Leech

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Sep 22, 2021, 10:42:28 AM9/22/21
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On 2021-09-21 11:19 p.m., Anthony wrote:
I'm familiar with the LimeSDR, they do require software and programming. Can Python be used?
Well, ANY SDR requires "programming"--that's what makes them SDRs, instead of "designed for a specific purpose" Rs.

LimeSDR works with Gnu Radio, and there are Python bindings for the SoapySDR library that is used to provide
  a hardware-agnosticism layer, so you could use it without Gnu Radio in plain Python.

I'll note that spectro_radiometer will work with LimeSDR radios, but I have to finish the port of spectro_radiometer
  to GR 3.8 so that it "just works" in Ubuntu 20.04 and later.


Anthony

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Sep 22, 2021, 11:00:44 AM9/22/21
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Maybe I'll obtain a LimeSDR later. For right now and still learning GNU/GRC. 

How to get it up and running? GNU is a framework, and the GRC is how you can create the flow diagrams. I'm going thru the GNU online tutorials. 🙂

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Marcus D. Leech

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Sep 22, 2021, 11:03:13 AM9/22/21
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On 2021-09-22 11:00 a.m., Anthony wrote:
Maybe I'll obtain a LimeSDR later. For right now and still learning GNU/GRC. 

How to get it up and running? GNU is a framework, and the GRC is how you can create the flow diagrams. I'm going thru the GNU online tutorials. 🙂
Like I said, spectro_radiometer will be ported to GR 3.8 sometime in the coming months.

The baa_seminar flow-graph is perfectly functional for radiometry and spectrometry RIGHT NOW--you attended that seminar :)


Anthony

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Sep 22, 2021, 11:18:25 AM9/22/21
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Anthony

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Sep 22, 2021, 11:19:09 AM9/22/21
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Yes, that was a great seminar!! 

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Marcus D. Leech

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Sep 22, 2021, 11:50:35 AM9/22/21
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On 2021-09-22 11:18 a.m., Anthony wrote:

Yup, CrowdSupply.

My undestanding is that their waiting on a batch to be finished before they can fulfill orders...

Anthony

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Sep 22, 2021, 3:10:52 PM9/22/21
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Have you heard of subtracting off Galaxy spectrum from on galaxy spectrum 

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Marcus D Leech

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Sep 22, 2021, 3:13:40 PM9/22/21
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Sure. That’s pretty much what I do when I do baseline correction. 

Sent from my iPhone

On Sep 22, 2021, at 3:10 PM, Anthony <itpart...@gmail.com> wrote:



Anthony

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Sep 22, 2021, 3:36:13 PM9/22/21
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You mean, it's a different way of just saying, correcting or performing a calibrated background using 50 Ohm termination caps, prior to performing intermediate averaging?

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Anthony

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Sep 22, 2021, 4:03:29 PM9/22/21
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There are several definitions of baseline in astronomy: In radio astronomy, a baseline is a vector connecting two radio telescopes that is used in interferometry to determine the fringe rate of a source at the nominal “phase center” of an observation.

Is this referring to the above article I searched on the internet? or my previous question around calibrated background prior to intermediate averaging?

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Marcus D. Leech

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Sep 22, 2021, 4:07:16 PM9/22/21
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On 2021-09-22 4:03 p.m., Anthony wrote:
There are several definitions of baseline in astronomy: In radio astronomy, a baseline is a vector connecting two radio telescopes that is used in interferometry to determine the fringe rate of a source at the nominal “phase center” of an observation.

Is this referring to the above article I searched on the internet? or my previous question around calibrated background prior to intermediate averaging?
Sorry, different baseline.

I wait for the galactic plane to be well away from my field of view, and use that as the "baseline spectrum" that I subtract from subsequent spectral estimates.
  The spectrum of the sky at 21cm well away from the galactic plane, for a small radio telescope is basically flat, so any "features" in the spectrum are
  necessarily artifacts of the instrumentation/environment itself.

So, yes a "blank" background--like a "dark slide" in optical astronomy.


Anthony

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Sep 22, 2021, 4:17:12 PM9/22/21
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Ok, you're talking calibrated frames, like in optical, Lights, dark, flats, bias, and of course the stacking process. So, isn't just using a calibrated background the same, with the 50 Ohm termination cap? It would remove the curve or waves caused by the LNAs unless you're referring to any background artifacts in respect to the galactic plane when its closes or near the field of view?
 For example, like covering the telescope (refractor) objective and taking a camera shot at your exposure you plan on using for astrophotography and taking into account, the camera temperature, and gain?

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Marcus D. Leech

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Sep 22, 2021, 4:23:08 PM9/22/21
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On 2021-09-22 4:16 p.m., Anthony wrote:
Ok, you're talking calibrated frames, like in optical, Lights, dark, flats, bias, and of course the stacking process. So, isn't just using a calibrated background the same, with the 50 Ohm termination cap? It would remove the curve or waves caused by the LNAs unless you're referring to any background artifacts in respect to the galactic plane when its closes or near the field of view?
 For example, like covering the telescope (refractor) objective and taking a camera shot at your exposure you plan on using for astrophotography and taking into account, the camera temperature, and gain?
Yes, you could just use a 50ohm termination.  A couple of issues:

 (A) It's "brighter" than the average sky, by quite a bit, so you'd have to account for that.
 (B) That approach wont' capture things like low-level spurs from bits of nearby electronics that may be getting in through the side-lobes, etc.

There's no one approach that always produces the results you want...


Anthony

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Sep 22, 2021, 4:24:06 PM9/22/21
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I believe it makes sense, my reason for trying to understand or connect the dots, with this in performing the 50 Ohm termination prior to connecting the LNA to the antenna input. 

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Marcus D. Leech

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Sep 22, 2021, 4:25:31 PM9/22/21
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On 2021-09-22 4:23 p.m., Anthony wrote:
I believe it makes sense, my reason for trying to understand or connect the dots, with this in performing the 50 Ohm termination prior to connecting the LNA to the antenna input. 

Yeah, that's always tempting.  But the reality is that system artifacts, particularly small ones, will tend to change and shift with time.  There's no such thing as
 a "calibrate it once and forget about it" in this game...


Paul Oxley

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Sep 22, 2021, 4:27:15 PM9/22/21
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Marcus

Don't forget that the LimeSDR needs a 10 MHz reference to phase lock. I use a Trimble GPS Disciplined Oscillator for this purpose.

 A 10 MHz Crystal would work if it was phase stable.

Without the phase lock, the oscillators would still be free running.

Paul

Marcus D. Leech

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Sep 22, 2021, 4:39:05 PM9/22/21
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On 2021-09-22 4:27 p.m., Paul Oxley wrote:
Marcus

Don't forget that the LimeSDR needs a 10 MHz reference to phase lock. I use a Trimble GPS Disciplined Oscillator for this purpose.

 A 10 MHz Crystal would work if it was phase stable.

Without the phase lock, the oscillators would still be free running.

Paul
Not the LimeSDR-USB.  You only need a common reference when you *GANG* them together.

A single LimeSDR-USB, which has two RX channels is inherently self-coherent, since the two channels
  are derived from a SINGLE synthesizer--you CANNOT tune the two RX channels independently, because
  they *share* a single synthesized LO.

I produced lots of nice fringes a few summers ago with our 610MHz interferometer and a single LimeSDR-USB.

This is very similar to the USRP B210, whose RFFE chip, the AD9361 uses a similar approach--the two RX channels
  share an LO.


 

Anthony

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Sep 22, 2021, 4:40:19 PM9/22/21
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Something like this Paul?


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fasleitung3

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Sep 23, 2021, 4:14:51 AM9/23/21
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Jim, thank you for sharing the results of your nice experiment.
I am presently going through a "interferometer learning curve", using a
3-m dish and a 2.3-m dish. The receiver in my case is a Lime-SDR using
a software-correlator based on Gnu-Radio. Marcus provided me with a GRC
script, thanks Marcus.
I have also used a 1.2-m dish replacing the 3-m dish, which is a bit
along the lines of what you did. Also with this setup one gets nice
fringes. I would assume one could also be successful using two small
dishes, maybe using two of the Wifi grid antennas.
The setup here has a fairly large baseline of 59 meters. Consequently,
the fringe frequency is substantially higher compared to yours. I found
that this has a disadvantage: I need to use a shorter integration time
which makes the signal noisier. I can probably compensate for that by
doing a FFT on the signal and look for the fringe frequency over a
certain time interval.
This brings up one of the questions I am working on: Obviously it is
straightforward to calculate the fringe frequency when the antennas
look due South (or North). Our dishes, however, are fully steerable.
This allows to observe fringes as long as the source is somewhere above
the horizon. The fringe frequency then is lower as the effective
baseline is shorter. However there is an additional effect: The vector
of motion of the source is no longer parallel to the vector of the
antennas baseline. This has an additional impact on the fringe
frequency. Presently I am trying to figure out how to calculate that.
If anyone has some ideas or can direct me to some literature describing
this this would be highly appreciated.
As all this is preliminary work, I have not written things up yet. So I
am attaching just one example from a transit of Cygus.
Just one final comment on the SDRs: As pointed out in this thread, the
most straightforward way is to use a SDR with a dual receiver such as
the Lime-SDR or one of the Ettus devices. I could imagine, though, that
two RTL-SDRs which are modified to accept an external clock are suited
as well. Eventually I will try this out.
Best regards, and have nice fringes,
Wolfgang
> --
cyg_transit_3m-20210824.png

Marcus D. Leech

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Sep 23, 2021, 10:33:33 AM9/23/21
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On 2021-09-23 4:14 a.m., 'fasleitung3' via Society of Amateur Radio
Astronomers wrote:
> As all this is preliminary work, I have not written things up yet. So I
> am attaching just one example from a transit of Cygus.
> Just one final comment on the SDRs: As pointed out in this thread, the
> most straightforward way is to use a SDR with a dual receiver such as
> the Lime-SDR or one of the Ettus devices. I could imagine, though, that
> two RTL-SDRs which are modified to accept an external clock are suited
> as well. Eventually I will try this out.
> Best regards, and have nice fringes,
> Wolfgang
>
With RTL-SDRs, or indeed any other type of "collection of discrete
SDRs", simply providing
  a common clock is necessary, but insufficient.  With RTL-SDR there
are two issues:

  (A) You have to turn off "dither" in the synthesizers
  (B) You still have to compensate for the lack of sample-time
synchronization
  (C) Even with dither turned off, there will be some residual
phase-offset between the synthesizers


For others, (A) may not apply, but (B) will still apply as will (C). 
For some radios, like USRPs, (B) is taken
  care of by the presence of a 1PPS "trigger" input.

And even with radios like the LimeSDR, where there's a common LO, the
*mixers* use what's called 2XLO
  phase-splitting, which means there's a 180degree phase ambiguity when
the device powers up--either
  the two mixers will be in-phase, or they'll be precisely 180deg
out-of-phase.  This isn't a huge deal for
  a single observing run, but if you're "stacking" interferograms, it
matters.

If you need what I call "brutal phase coherence", the system details
matter a lot, and for radio astronomy
  you need "brutal" phase coherence.  At least if you want to produce
"science grade" results.




bsn...@gmail.com

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Sep 23, 2021, 1:05:14 PM9/23/21
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In can barely get a single antenna system working consistently so have no interest in interferometry.

But, I have been using some of Peter East's software and ran across this:
"Long Baseline Interferometry with Unmatched SDRs" May, 2014

His most recent version of the various tools is 2017 and some of them do seem to adress the problems of using basic SDRs for interferometry.
The above article is somewhere on his web site......bill...

Anthony

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Sep 23, 2021, 1:16:03 PM9/23/21
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Thanks for sharing! I need to check it out. I need to figure how far to move one of my dishes to get an adequate baseline for interferometer. Thank goodness there is quite a bit of resources on the net..

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Marcus D. Leech

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Sep 23, 2021, 1:38:37 PM9/23/21
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On 2021-09-23 1:15 p.m., Anthony wrote:
Thanks for sharing! I need to check it out. I need to figure how far to move one of my dishes to get an adequate baseline for interferometer. Thank goodness there is quite a bit of resources on the net..
How much land do you have in an east-west direction?    Lay out a railway track along that line, make the antennas movable :) :)


Marcus D. Leech

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Sep 23, 2021, 1:40:46 PM9/23/21
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On 2021-09-23 1:05 p.m., bsn...@gmail.com wrote:
In can barely get a single antenna system working consistently so have no interest in interferometry.
Something that is interesting about simple two-element interferometers is that they, like
  the puppy that wants to please its master, "just want to work", so I tend to encourage people
  to at least think about them before making investments in antennas etc.

Anthony

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Sep 23, 2021, 1:52:47 PM9/23/21
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There are articles out there with interferometers that have baselines of 15 or more feet. I have enough room or land to move one dish an extra 25 feet (west), which should be sufficient, bringing the base line to 50 feet. If I decide to do so.



On Thu, Sep 23, 2021, 1:38 PM Marcus D. Leech <patchv...@gmail.com> wrote:
On 2021-09-23 1:15 p.m., Anthony wrote:
Thanks for sharing! I need to check it out. I need to figure how far to move one of my dishes to get an adequate baseline for interferometer. Thank goodness there is quite a bit of resources on the net..


Marcus D Leech

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Sep 23, 2021, 2:04:59 PM9/23/21
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17m should be fine to get decent number of fringes per beam width. 

Sent from my iPhone

On Sep 23, 2021, at 1:52 PM, Anthony <itpart...@gmail.com> wrote:



Marcus D. Leech

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Sep 23, 2021, 2:38:45 PM9/23/21
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On 2021-09-23 1:05 p.m., bsn...@gmail.com wrote:
In can barely get a single antenna system working consistently so have no interest in interferometry.

But, I have been using some of Peter East's software and ran across this:
"Long Baseline Interferometry with Unmatched SDRs" May, 2014

His most recent version of the various tools is 2017 and some of them do seem to adress the problems of using basic SDRs for interferometry.
The above article is somewhere on his web site......bill...
The technique is very similar to the fast-convolution technique that is used in things like the Kerberos SDR to resolve sample-time offsets, except
  that you're doing it continuously to try to estimate both the time and phase offsets. This "works" after a fashion, but requires very bright sources.

It is based on the observation that two unsynchronized, but reasonable-quality, oscillators will have both a fast mutual phase-noise component, and
  a slower frequency-drift component.  Frequency drift is the same as phase drift, so if that drift is of the same order of magnitude as your
  fringe rates, it will completely obliterate any fringes.  Once you've compensated for the frequency drift, you're left with the mutual phase-noise
  component, and the SNR of the correlation (fringes) will depend on the "character" and magnitude of the residual mutual phase-noise.  For systems
  with shared LOs or "locked" LOs, the residual phase-noise is quite small.  For independent oscillators, it's quite a bit larger.


Jim Abshier

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Sep 23, 2021, 5:23:50 PM9/23/21
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Wolfgang: Thank you for enlightening us about your interferometer
activities and recent results. On the topic of antennas, the effective
antenna area of an interferometer is the geometric mean of the two
antennas. Even though one of them is much smaller than the other, the
geometric mean can still be fairly large. In my case, the geometric mean
of the 3 meter and WiFi antennas is sqrt(7x0.6) which is about 2 m^2. If
two WiFi antennas were used, the area would be just 0.6 m^2. This would
still work as an interferometer. I have estimated that in that case my
rms noise would be about 60 Jy rather than the 18 Jy I am getting with
the 3 meter and WiFi antennas. Of course the above areas are geometric
areas and actually should be reduced by the efficiency factor, which I
usually assume is about 0.5.

With a baseline of 56 meters and an SDR capable of 60 MHz bandwidth, I
think you need to consider the possibility of bandwidth decorrelation.
Even if you are only recording fringes at transit as the source
traverses the antenna beam, bandwidth decorrelation could be an issue.
Fortunately with the SDR you have the capability to correct for delays
due to changing geometry. Delay tracking will also solve the fringe
frequency problem and allow you to track the source down to the horizon.
It seems that as amateur radio astronomers acquire more of the equipment
that enables them to do what professional observatories do, they also
encounter the same problems that those observatories have to deal with.

On the topic of figuring out fringe frequencies for arbitrary
geometries, I recommend that you look at Interferometry and Synthesis in
Radio Astronomy by Thompson, Moran and Swenson. I think that this is now
available free on line. You mention motion of the source and its
relationship to the baseline. In aperture synthesis imaging, it is the
baseline motion that is considered. The source is considered fixed in a
celestial inertial space.

Good luck in your interferometry program. I would be very interested in
hearing about how it is progressing and seeing its results.

Jim Abshier

On 9/23/21 4:14 AM, 'fasleitung3' via Society of Amateur Radio

Hamish Barker

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Sep 23, 2021, 7:22:20 PM9/23/21
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for those starting the interferometry route (or RA in general), I enjoyed and got a lot out of watching Rick Perley and others great presentations at the 

16th Synthesis Imaging Workshop at NRAO.

several reviewings may be necessary to grok sufficiently. As rick says, in interferometry the concepts are simple but if you don't get it or feel stupid it's because they are unfamiliar.

pdfs here:

videos (very very good, mostly split screen with presenter and the slides):



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Anthony

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Sep 23, 2021, 7:38:47 PM9/23/21
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Thanks Harnish for sharing! 

Always great to hear from you and your input to the group!

fasleitung3

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Sep 24, 2021, 1:06:04 PM9/24/21
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Thank you Marcus, for pointing out the issues encountered when using
RTL-SDRs. I will stick with the Lime for the time being. The fact that
I may encounter a 180° phase shift at different start up times is also
new to me and something to be considered.
Cheers,
Wolfgang
> --

Peter East

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Sep 24, 2021, 2:43:31 PM9/24/21
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A rough measure for an interferometer angle between fringe peaks is  = wavelength/( d x cos(el) x cos(az)) radians, where 'el' and 'az' are elevation and azimuth angles of the source relative to the interferometer baseline 'd'.
Peter

fasleitung3

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Sep 24, 2021, 4:26:02 PM9/24/21
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Thank you, Jim, for your comments. When I started learning about radio
astronomy I more or less skipped the sections about interferometry. So
I am at the beginning here and your comments demonstrate that there is
a lot of new things to be learned. And this is really the fun: Learning
about new things and then try to apply what one has learned.

For the time being I am using only 3 or 4 MHz of bandwidth to avoid
decorrelation. I am hoping to report more details soon.
Best regards and thanks for your comments,
Wolfgang
> --

Marcus D. Leech

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Sep 24, 2021, 4:48:33 PM9/24/21
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On 2021-09-24 4:25 p.m., 'fasleitung3' via Society of Amateur Radio
Astronomers wrote:
> Thank you, Jim, for your comments. When I started learning about radio
> astronomy I more or less skipped the sections about interferometry. So
> I am at the beginning here and your comments demonstrate that there is
> a lot of new things to be learned. And this is really the fun: Learning
> about new things and then try to apply what one has learned.
>
> For the time being I am using only 3 or 4 MHz of bandwidth to avoid
> decorrelation. I am hoping to report more details soon.
> Best regards and thanks for your comments,
> Wolfgang
You could probably go to 20Mhz without suffering significant
decorrelation loss.

Anthony

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Sep 24, 2021, 7:59:38 PM9/24/21
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Can you capture H1 emissions from the Andromeda galaxy without using an interferometer, but only a wave guide? No satellite dish, just a feedhorn and waveguide, is it plausible?

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Marcus D. Leech

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Sep 24, 2021, 8:29:06 PM9/24/21
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On 2021-09-24 7:58 p.m., Anthony wrote:
> Can you capture H1 emissions from the Andromeda galaxy without using
> an interferometer, but only a wave guide? No satellite dish, just a
> feedhorn and waveguide, is it plausible?
>
I'd want to use a fairly large-aperture horn, and "stack" many many
transits, and subtract out the spectral response from before and after
transit.

M31 is moving towards us at about -110km/sec, so expect to see a "hump"
(a tiny one) at around 1421MHz, although that doesn't account for
  other motions, which is left as an exercise for the reader.

I think someone one here has done something similar, I just cannot for
the life of me remember who it was :) :)


Anthony

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Sep 24, 2021, 8:44:45 PM9/24/21
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Thanks Marcus!! 

Was it Job, I'm wondering.


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Marcus D. Leech

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Sep 24, 2021, 8:45:56 PM9/24/21
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On 2021-09-24 8:44 p.m., Anthony wrote:
Thanks Marcus!! 

Was it Job, I'm wondering.
Might have been.  I'm sure he'll speak up if so...


Anthony

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Sep 24, 2021, 8:49:48 PM9/24/21
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😉

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eddiem...@gmail.com

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Sep 25, 2021, 3:15:14 AM9/25/21
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Hi Anthony and all,

Last summer I have tried to detect HI from Andromeda with only driftscans. I was using a 3 metre dish, and with 5 driftscans (about 1.5 hours of integration time) I was able to get decent results. 
I do not think this is possible with only a small feedhorn, because the feedhorn has such a small aperture compared to a 3 metre dish. 

Op 25 sep. 2021 om 02:49 heeft Anthony <itpart...@gmail.com> het volgende geschreven:



Anthony

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Sep 25, 2021, 8:17:09 AM9/25/21
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Hi,
Is that 1.5 hours integration time total or per drift scans? Can you share what the results look like?

Thank you!


eddiem...@gmail.com

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Sep 25, 2021, 9:32:57 AM9/25/21
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Hi Anthony 

It was 1.5 hours in total (approximately 20 minutes per driftscan)

I have posted my results on the SARA forum a few months back, you can find them in this thread: https://groups.google.com/g/sara-list/c/8HtrJ7lExCs

Best regards,

Eduard

Op 25 sep. 2021 om 14:17 heeft Anthony <itpart...@gmail.com> het volgende geschreven:



Anthony

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Sep 25, 2021, 9:45:26 AM9/25/21
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This is great, thank you Eduard!

Anthony

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Sep 29, 2021, 10:25:40 PM9/29/21
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Ah, I'm reading so much I didn't recognize an article you wrote some time ago Jim!

I even mentioned it on one of these SARA group posts! Nice work, even though I'm in the learning stages of RAS. 

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Jim Abshier

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Sep 30, 2021, 12:37:55 PM9/30/21
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Anthony (and others)

I feel that I must apologize for the quality of this article. The
article was written for members of an optical astronomy club. The person
in charge of editing the article really messed up the interferometer
figure. Also, the format of the equations ended up much larger than my
original format. Microsoft Word may have been partly responsible for
that. This article is probably the only one of mine that ever made it to
the Internet. The fact that this article has been referenced several
times is somewhat of an embarrassment. Most of my articles have been
published in the SARA Journal. Editors of the SARA Journal do a much
better job.

Jim Abshier
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Anthony

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Sep 30, 2021, 2:22:43 PM9/30/21
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Thanks Jim!
No worries!! 😊

If that hasn't happened to any one of us before, let that person cast the first SDR!


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