Improved resolution with interferometer, versus single parabolic antenna

[Henri NICOT]

Greetings and happy New Year to all of you,

Among the many issues that are not too complicated and that I would like to understand in radio astronomy, stands the improved resolution of an interferometer. There is obviously something I missed or I misunderstood which prevents me from practically grasping and quantifying the improvement in resolution between a 2-antenna interferometer and a single parabolic antenna. Let me take the very clear presentation "Modeling a 3-Element Interferometer" by Dr Richard Russel as a background reference.

I think I understand the following drift scan of a single object in front of:

• a single antenna in blue color,
• a double antenna interferometer in orange color.

Let me now consider a double object transiting in front of the same two pieces of equipment:

1. A small single antenna with very poor or no-resolution-at-all would exhibit a single bell shape transit curve, unable to reveal the existence of two separate objects.

2. A single but larger-diameter antenna with "not good enough resolution" would tend to display a drift scan similar to that of M87/M89 as I exhibited in my email to SARA blog, dated November 11th. You can guess two objects but nothing between them.

3. A single but large-diameter antenna will have a good resolution. The two objects could appear quite separated with steep climbing signals. There is a quiet base signal before, after and in-between objects to report presence of details if any.

4. Now let us consider the middle case, the "not good enough resolution". It can be improved by increasing the diameter of the antenna, we moved towards the third case where peak widths and quiet base widths can be measured and expressed in degrees or minutes.

5. If we consider the drift of the two objects in front of the interferometer, are we likely to obtain the following transit curve?

In that case, how does this 4th transit curve show an improvement of the resolution that we need on the 2nd one?

Does it really compare to the result achieved by the 3rd one?

Does the distance between the two objects change the picture and make a fringe pattern different than that attempted in 5. ?

If you understand what I did not, please let me know where I am wrong.

Henri Nicot

[Marko Cebokli]

When the two sources will be separated in  the same plane as your antenna spacing (or at least not orthogonal to it), the result will be the sum of two fringe sets with slightly different fringe frequencies, because the projected baseline of the the two sources will be different. You will have two peaks in the fringe spectrum. The frequency difference will increase with baseline length, allowing separation of closer sources, etc.

In detail, it is not so simple, because the fringe frequencies will not be constant, etc, but the basic principle is this.

Marko Cebokli

2025-01-02 16:39, je Henri NICOT napisal

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[Mario]

Interferometry is not that simple. The signal you get out of the interferometer would not look as you drew it, with high frequency fringe inside the envelope of signal intensity.

What you would do is this - let's say that you are doing a drift scan of the object and that you are recording that signal every minute.

If your interferometer work correctly you would get interference fringes. You need to extract "visibility" from those fringes, which is pretty much the "contrast" of the fringes. Meaning, "visibility" depends on darkest and lightest level of the fringes. Absolutely dark minimum and very bright maximum means that "visibility" is 1.

You do that until the object gets out of your telescope field of view and you chart those visibilities. That's not the image of the object. To get the image, you need to do inverse Fourier transform of those visibilities.

Notice that what you did just now gets you increased resolution in only one direction! The direction of straight line connecting your 2 interferometers (called a baseline), and projecting that line on the sky.

So, all of the above is really just 1D case.

To get a real photo, a 2D case, you would need to do this with many interferometer antennas, positioned all over the terrain, to get as many differently oriented baselines as possible.

[Alex P]

Re-Post

by : Baris Altunkaynak

It is possible to make images with a radio telescope. As Alex mentioned, a radio telescope is a single pixel camera. The brightness of each pixel is the convolution of the sky brightness with your radio telescope's beam profile. You can scan the sky pixel by pixel and form images this way. The problem is, due to the much longer wavelengths than the visible wavelengths, you will generate images that have ridiculously low resolutions. The angular resolution is proportional to the wavelength. Comparing for example 500 nm to 20 cm, you get a factor of 20 cm / 500 nm = 400,000. So your radio telescope needs to be 400 thousand times bigger than an optical telescope to achieve the same angular resolution of the optical telescope. It's impractical to build such large steerable radio telescopes.

Instead radio interferometers with very long baselines are used to make images using earth rotation synthesis. You point many radio telescopes at the same spot in the sky and calculate visibilities which are correlations between the signals recorded by each pair of antennas or a baseline. This gives you a single Fourier mode of the sky brightness distribution. Then by using earth rotation synthesis, you sample the Fourier space with as many points as you can. Then you perform an inverse Fourier transform to construct the image. The problem is you can't sample with infinitely many points so the image will contain artifacts. There are algorithms to clear up these artifacts. That's how big facilities like the VLA or ALMA produce images.

To do this yourself, you will need as many antennas as you can get and have relatively long baselines. You won't get a good sample of the Fourier space by just having a few antennas. Or alternatively you can move your antennas around, recalibrate them and try to sample the Fourier space over many days. I'm not sure if anyone is doing this in the amateur radio astronomy community.

[James Abshier]

Draft copy of amateur aperture synthesis article attached.

Jim Abshier

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[Bruce Rout]

Thank you Baris,

I'm planning a half-mile-wide interferometer in the spring, and I'm sure I'll run into many fun problems. Is the north-south axis of the antennae for vertical resolution?

Yours,

Bruce

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