interferometer simulations and FFT analysis

[Eduard Mol]

Hi all, 

The recent discussions here on the listserv on interferometry and sliding window FFT analysis motivated me to explore what the FFT output would look like for different source declinations, interferometer baselines and sliding window size. Yesterday I made a simple model for a 2-element interferometer in python. For the sake of simplicity I assumed that the two elements have simple gaussian beams with a 10-degree beamwidth and are on a perfectly east-west oriented 10 metre baseline. For the FFT analysis I used Acycle instead of painstakingly writing the code myself. Acycle is a timeseries analysis programme originally intended for geological data analysis, but it has many great tools like sliding window FFT and wavelet analysis.

If we assume the antennas are isotropic the interference pattern would look like this:

The sliding window FFT output clearly shows the fringe frequency drift due to the Earth's rotation:

However, if we stick to a 10 degree beamwidth we only sample a small portion of this curve around the peak fringe frequency, and the fringe frequency drift due to earth rotation is very small:. In this case I used an FFT window size matching the HPBW of the single-element beam (40 minutes)

Choosing a larger window, for example 80 units to cover the full extent of the fringes results in a slightly higher frequency (declination) resolution at the cost of a lower resolution in the RA (time) dimension:

[Eduard Mol]

Now to a more practical application of all of this. Let's assume we have two sources at similar RA but slightly different DEC. Because both sources are at the same time in the single-element beam we get source confusion. However, in theory the sources would have slightly different fringe frequencies, so can we separate them by applying FFT analysis?

Here is what the fringes would look like for 2 sources at DEC=0 and DEC=+5. It simply looks like a single source:

The FFT analysis does not resolve the two sources because the difference in fringe frequency is very small close to the celestial equator:

However, at higher declinations the difference in fringe frequency becomes more significant. With 2 sources at +60 and +65 degrees the two sets of fringes at slightly different frequencies create a response that looks like a stronger source flanked by two weaker sources:

However, the FFT analysis shows that it is actually just 2 sources with slightly different fringe frequencies:

[Eduard Mol]

[Mike Otte]

Eduard,

The hope was to resolve some sources that are close together especially at RA 1800 and Dec -10 to -34, basically southern sky. There are 24 sources above 100Jy with 2 stronger ones. 

This technique looks good for visualization but I don't know how the freq axis can be counted as Declination?.

I have some data from this morning.  Would you please plug it in to see what we can see.

I am working on a 3 X 3M dish interferometer  and trying to iron out the bugs.  Last night I changed the cable inputs to the detectors so the baselines were in the same direction.  The baselines are ~ 10M,20M,30M   I am drawing this up to make it easier to explain.  Two of the dishes are portable to explore other baselines and even  N-S besides E-W.

Thanks for the discussion and inputs!  very interesting.

Mike w9ys

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[Eduard Mol]

Hi Mike,

Thanks for the data, I will look at it tomorrow. I’m also curious to see myself what the FFT analysis looks like on some real-world data.

 the fringe frequency is at maximum at the celestial equator and zero at the celestial poles (because the source would not move through the interferometer lobes at all). So the fringe frequency decreases with the cosine of the declination. 

Now I think my fringe frequencies from my model may be off, maybe I forgot a factor 2pi somewhere… anyway, it was more of a conceptual model to get myself (and maybe others) a better grasping all this interferometry stuff. 

Op vr 21 nov 2025 om 15:50 schreef Mike Otte <mike....@gmail.com>

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[Eduard Mol]

Hi Mike, 

As it turns out, deriving the source declination from fringe frequency is not all that complicated. I hope you can follow my notes. 

At a frequency of 1408 MHz (center frequency of the SAWbird HI filters and a baseline of 30.6 metres, the fringe frequency of Taurus A (DEC = 22 degrees) would be 0.583 cycles/ minute. The fringe frequency determined from your interferometer data (baseline 3) using FFT analysis is 0.580 cycles/minute, which would correspond to a declination of 22.7 degrees. Pretty close I would say.

 My simple model gives a fringe frequency of 0.583 cycles/minute as well, so I now have some confidence that it is more or less correct. 

This is what the sliding window FFT analysis looks like on the Taurus A data from baseline 3. The RFI pulses clearly have an effect as well.  The other, shorter baselines look similar, but of course with a lower fringe frequency and a lower resolution in the frequency domain. 

Best regards, 

Eduard

[Eduard Mol]

Forgot to add my notes, here they are!

Best regards, 

Eduard

[Mike Otte]

Yes, I have used Fringe Period before but mostly at baseline 10.6M.

I chose 10.6M to increase detectability.  The amplitude increases with shorter baselines.  (See Jim Abshier's paper in journal)

Also the baseline helps to determine the size of the radio Source. You increase the baseline until the source disappears?.  I am sorry but I am not clear on this point.

So on the other hand, longer baseline increases resolution.   So this is a balance.

Thanks for the analysis!

I will either download Acycle  Or try coding it in python.  

I will reExam the data I gathered over the summer of the RA1800 area.

Thank you

Mike w9ys

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Mike Otte W9YS

[Jim Sky]

I added a little fringe rate calculator to my website - http://radiosky.com/FringeCalculator.html - just for meridian transits and EW baselines.

[Mike Otte]

Thanks for the calculator Jim!

For low declinations both positive and negative, Fringe Period is not as useful as it could be.  Zero degrees declination is the lowest Fringe Period.  For both + or -  25 degrees declination you have gained only 20 seconds.   Fringe period is defined as Peak to Peak but to accurately define the peak can be difficult with a slow changing signal.  So i take several peaks and average them but even then it could be seconds off and confidence could be low of which object it is.  So we could use a fast changing signal, the zero crossing.  I have tried but my signals are A/D converter numbers and the first step is  to subtract a number from all the reading to get them near zero. then you can check for zero crossing.  

So my goal was to identify 12 stronger sources in the -9 to -28 declination and 2 of them kind of cover up the other ones.  Fringe period did not help me much.  With the fft frequency representation, I was hoping the source would pop out or at least wiggle the bush.  

Yesterday, I did get fft subroutine working in my interferometer exploring software.  Nothing notable at this point. 

Thanks for adding to the discussion.  This makes it worth pursuing.

73

Mike w9ys

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Mike Otte W9YS

[Eduard Mol]

Mike, can you move (one of) the elements? If so you could do aperture synthesis to narrow down the beam atleast in the RA direction. That would be useful to resolve sources which are at low declination or at almost the same declination but different RA.

Op zo 23 nov 2025 om 17:05 schreef Mike Otte <mike....@gmail.com>

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[Mike Otte]

Yes, actually 2 of the dishes are movable with some difficulty(not daily).  Un hook cable(s) , chose target location, get tractor, unblock, move, block and level, hook up cables. 

 But first I want to explore with them as is and do more tuning ( focus, add choke to 3rd feedhorn,  more shielding on the in observatory lnas). 

Yes, I want to try one dish north of the East dish (Mills Cross) and a couple other configurations , EQ triangle, North of second dish.

Attached is Obs Report  with list of targets.

73

mike

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Mike Otte W9YS

[Jan Lustrup]

Thanks for the online calculator.

The one in Radio-Eyes 1.5.7 works only one way. You input the declination and you get the fringe period fine. But if you input the fringe period to find the declination it does not work.

 

Is there patch or fix for this bug?

Jan Lustrup LA3EQ

Norway

 

From: sara...@googlegroups.com [mailto:sara...@googlegroups.com] On Behalf Of Jim Sky
Sent: søndag 23. november 2025 06:47
To: Society of Amateur Radio Astronomers
Subject: [SARA] Re: interferometer simulations and FFT analysis

 

I added a little fringe rate calculator to my website - http://radiosky.com/FringeCalculator.html - just for meridian transits and EW baselines.

On Friday, November 21, 2025 at 4:43:25 AM UTC-5 Eduard Mol wrote:

Hi all, 

 

The recent discussions here on the listserv on interferometry and sliding window FFT analysis motivated me to explore what the FFT output would look like for different source declinations, interferometer baselines and sliding window size. Yesterday I made a simple model for a 2-element interferometer in python. For the sake of simplicity I assumed that the two elements have simple gaussian beams with a 10-degree beamwidth and are on a perfectly east-west oriented 10 metre baseline. For the FFT analysis I used Acycle instead of painstakingly writing the code myself. Acycle is a timeseries analysis programme originally intended for geological data analysis, but it has many great tools like sliding window FFT and wavelet analysis.

If we assume the antennas are isotropic the interference pattern would look like this:

The sliding window FFT output clearly shows the fringe frequency drift due to the Earth's rotation:

 

However, if we stick to a 10 degree beamwidth we only sample a small portion of this curve around the peak fringe frequency, and the fringe frequency drift due to earth rotation is very small:. In this case I used an FFT window size matching the HPBW of the single-element beam (40 minutes)

 

Choosing a larger window, for example 80 units to cover the full extent of the fringes results in a slightly higher frequency (declination) resolution at the cost of a lower resolution in the RA (time) dimension:

 

[Jim Sky]

Hi Jan,

Yes I am fixing that now.  It should be out soon.

Jim

[James Abshier]

On 11/22/25 09:39, Eduard Mol wrote:
>
> As it turns out, deriving the source declination from fringe frequency
> is not all that complicated. I hope you can follow my notes.
>

For the sliding FFT imaging application, the fringe frequency around
transit does not vary much if the antenna beam is narrow enough. For an
application where you might want to track the source over several hours
to either detect a weak source or get a better estimate of declination,
the fringe frequency can vary substantially. When  this is the case, a
simple FFT is not the best thing to do. For the general case, it is best
to do a reformatting of the fringe data to achieve a single fringe
frequency prior to doing the FFT. The attached write-up illustrates
this. The fringe data were collected using a 400 MHz interferometer a
few years ago. As I recall, the data covers a collection time of about 8
hours. The plots show the improvement in frequency response when
reformatting is done.

Jim Abshier