What is interferometry? | Hacker News Reader

What is interferometry?

eso.org

65 pointssohkamyung19 comments

Quite fantastic to be able to image the surface of stars with that principle. Antares here: https://www.eso.org/public/news/eso1726/

I'll have a go at sketching a simple explanation (feel free to correct):

Light has some intrinsic properties, one of those is a repeating quantity called phase. Simply, think of a number going 012301230123...

By sending two identical beams of light out at source A, and reading at sink B then the phase should be identical at B. Since the phase has changed the same number of times for both.

But if one of those beams has travelled further, it will be out of phase,

eg., A1 = 01230123012, A2 = 012301230123

Imagine taking a difference of that last reading: 3 - 2.

That difference is then a measure of how further A2 travelled than A1.

By keeping all conditions equal along the paths of these beams except for one, you can measure the impact of the difference of that one condition.

Eg., with gravity, we take such differences to be a kind of "mapping of space", since it is gravity which causes one to have travelled further, and gravity is really more-or-less just another name for "the geometry of space as determined by mass".

The original experimentalist (Michelson) gave perhaps the best lay mans description in terms of an analogy with a swimmer crossing a fast moving river. Long story short, an interferometer detects the difference between two swimmers in their apparent distance swam (number of strokes they had to make), even though the physical distance traversed was the same for both. In this analogy the swimmers are individual photons of light and the "number of strokes" actually means the peaks / troughs of a given wave of light. Basically, a beam of light is split and then meets up again. If the length of the two paths are different, the peaks and troughs of the light wave will have drifted out of sync when they meet back up, and that will cause the interference pattern of the light wave interfering with itself to shift in proportion to the amount of drift. "Phase" is just the word scientists have settled on to describe this offset effect. Amplitude, wavelength and phase together give a complete description of any wave (light or otherwise). Hope that takes the mystery out of this "intrinsic physical property".

Everything you wrote was accurate. I am merely expanding on the gaps.

Two people walking side by side, in synchronized step, come upon a hill. The left side of the hill is flatter than the right side. By the time them have crossed the hill, the two people are out of step due to the difference in distance walked between them

Wow. Multiple large telescopes interconnected by an optical path through underground tunnels to form a giant interferometer. It's amazing that they got it to work.

It's really hard! Temperature changes the phase of the optical signal.

>"ALMA can combine up to 66 antennas, with 1225 baselines, and a maximum distance of 16 kilometres between the antennas. Thus, ALMA has by far the highest resolution available in radio astronomy, up to ten times better than that achieved, at visible wavelengths, by the NASA/ESA Hubble Space Telescope. [...] In the case of ALMA, radio waves are combined digitally inside a powerful computer called correlator."

Nice!

Compare the concept of interferometry (putting together a signal from multiple parts from multiple receivers) with that of phased-array beamforming (sending a signal by breaking it up into multiple parts and sending those parts via different transmitters...)

These two ideas would seem to be candidates for being conceptual opposites -- at least to a cursory examination...

The most extreme example is the event horizon telescope which produced the first picture of a black hole.

It was using the entire earth as the size of the interferometer, they had telescopes all over the earth and recombined the results later.

Does anyone know a good introduction to the mathematics of it?

Edit: https://space.mit.edu/home/tegmark/omniscope.html mentions

Introduction to Radio Astronomy Interferometry and Synthesis in Radio Astronomy by Thompson, Moran, and Swenson – probably the definitive reference on radio astronomy.

An Introduction to Radio Astronomy by Burke and Graham-Smith – chapters 5 and 6 the most relevant.

Tools of Radio Astronomy by Wilson, Rohlfs, and Huttemeister -- a popular reference.

This might go beyond what you mean by "introduction," but . . .

An Introduction to Optical Stellar Interferometry A. Labeyrie (Author), S. G. Lipson (Author), P. Nisenson (Author)

I recommend learning about the Fourier Transform, and then peeking at how frequency transformations are used to represent everyday images, like the Cosine Transform used in JPEG.

3 blue 1 brown FFT: https://youtu.be/spUNpyF58BY

JPEG components https://en.wikipedia.org/wiki/JPEG#Discrete_cosine_transform

I worked at the Very Large Array radio telescope for a while, and even so the language didn't click for me until I thought about the signal transforms that have become ubiquitous in everyday life.

And a co worker described the telescope as a double-slit experiment, with multiple 2-D holes instead of slits; imagine the interference pattern that you get when you have multiple slits. The elements of an interferometer are the "slits", but they are receiving the light rather than emitting it. The VLA has 27 radio dishes for its elements, so poke 27 holes in a board and shoot a laser through the holes, you get this blurry pattern on the wall. That's the distortion from the shape of your telescope, you're trying to cancel that out...

Then there's the time domain, because the Earth is rotating, so your telescope is sweeping a pattern across the sky. It can seem like a hopeless mess, but it's actually the case that for most observations, that sweep gives you even more coverage of the image. It can be a good thing.

But you have to keep track of one wavefront across all of those moving elements. The correlator is a computer doing those FFTs to find where the signal matches enough between the elements to start extracting finer detail.

I think some insight into how that's possible is around the 8-minute mark of this video:

https://youtu.be/nmgFG7PUHfo?t=8m

I have to admit that I'm still thinking about it all, and it's been 20 years. But JPEG is about at my level.

That's at the 22-minute mark of the same Vertiserum video:

https://youtu.be/nmgFG7PUHfo?t=22m

One traditional university introduction happens to be written by Goodman ("good" man): Introduction to Fourier Optics.

Intro to Radio Astro Interferometry by Thompson and Intro to Radio Astro by Burke and Graham-Smith are strong recommendations. Those were the ones I used in my Radio Astro special topic in Uni.

For some more background info, Essential Radio Astronomy open notes hosted by the National Radio Astronomy Observatory [0] are a great resource as well. This was used as an extra resource in my Radio Astro course. The ERA notes were also later extended into a textbook [1], which I haven't used but have heard it's well done.

[0]: https://science.nrao.edu/opportunities/courses/era/ [1]: https://press.princeton.edu/books/hardcover/9780691137797/es...

After reading an article[1] last week, I fell into a rabbit hole about interferometry and ending at trying to understand special and general relativity. I spent hours stuck in it.

Reminds me of the meme, “Parents, talk to your kids about interferometry or someone else will.”

1- https://arstechnica.com/science/2022/11/what-the-image-of-th...

Related, this is the true reason why stars appear to twinkle, and why planets don't: interference in your eyes [1]

1. https://photonreport.com/2017/06/19/stars-dont-twinkle-in-sp...

Can this technique be applied on a smaller scale for multi-lens arrays for visible light?

They use it for calibration of machine tools, cmms, etc:

https://www.renishaw.com/en/xl-80-laser-system--8268

I am not entirely sure what you are asking, but yes, it can be used at any scale. You might be interested in Aperture masking interferometry[1] which is a method to deal with atmospheric "seeing" and achieve true diffraction limited imaging by sacrificing sensitivity (capturing fewer photons).

[1] https://en.wikipedia.org/wiki/Aperture_masking_interferometr...

Unfortunately a little bit light on how exactly this works. You have the ground pork and casing, and the pork goes in the casing to become a sausage, but I didn't see anything about how you get the pork in the casing.

Anyway, apparently it's called aperture synthesis. I don't find the Wikipedia article on it helpful either, but this lab designed as a toy experiment for undergrads seems to explain enough for me to be satisfied.[0]

Two antennae (I guess you can have more, but simple case here) facing a light source or two. Move them apart and measure the power collected by the antennae. Observe the decline in power for a single source as the distance between the antennae increases, although the shape of that graph depends on the size of the source.

For two sources, you see the power collected by your antennae rise and fall with some periodicity as you move the antennae apart; this is caused by the interference of the light between the two sources (I wonder if the single source case has self-interference since it isn't a point source?).

Presumably from this you can obtain the amplitudes and phases and Fourier transform to get what the source(s) look(s) like. Exercise left to the reader.

Anyway, it is interesting on how many scales interference shows up in physics. Every physics student learns of Michelson-Morley, which was supposed to use the interference of light with itself to measure the difference in distance traveled by light in different directions since light should have been moving at different velocities on Earth as the planet orbits around the Sun... alas, not so, they did not observe the expected interference.

LIGO built upon the same principle (from my understanding, at least), the expansion and contraction of space caused by gravitational waves resulting in difference in distance traveled by light, resulting in interference.

But you need not restrict yourself to light, as you can probe crystals with electrons and neutrons. The amplitudes of where they scatter depend on what angle you hit the crystal at - hit it at a certain angle, and the possible paths traveled differ by an integer-and-a-half number of wavelengths, and you see nothing. This provides you information about the distance between atoms in the crystalline structure, the angles between them, etc. (I may be oversimplifying here as I hardly remember how this works)

[0]: https://vc.bridgew.edu/cgi/viewcontent.cgi?article=1019&cont...

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