Is Optical VLBI theoretically feasible? If not why not?

Question

There are plenty of optical interferometers in use with baselines of up to maybe 1km. As far as I can find out, they all work by directly collecting the light at all the telescopes, using mirrors to bring them together and then actually interfering them and observing the fringes with photodetectors.

Meanwhile, radio astronomers do interferometry over distances of thousands of km, but they do it quite differently. Essentially, they record the baseband electromagnetic waveform at each telescope, with an accurate timestamp, transport them all to a central location and combine them computationally.

So my question is whether in principle you could use the radio astronomers methods with an optical (or near IR) signal. Obviously the engineering and computational challenges would be formidable -- you would need to record data at speeds close to 1 Pb/s, timestamp it with femtosecond accuracy and do a ludicrously huge computation to recover an image, but that's not my question here.

On the one hand, it seems like the answer should be "yes" -- electromagnetic waves are electromagnetic waves. On the other hand, why should the phase of a photon observed in one telescope have anything to do with the phase of one observed in another? If you are digitising the data at each telescope, you are ruling out interference fringes on a quantum level, just as happens if you find a way to measure which slit a photon went through in the double-slit interferometer. This suggests that the answer should be "no".

If the answer is "no" then what wavelength does the cutoff happen at? We have radio-style VLBI at 1mm now and optical-style interferometry at 1 $\small\mathsf{\mu m}$, what is possible in between?

Answer 1

This question amounts to: is optical interferometry possible when detecting photons? The answer to this is yes. Many experiments have been done using interferometers where one photon at a time is passed through the apparatus and still reveals an interference pattern when detected on the other side.

The problems with optical interferometry are manifold: optical interferometry at the moment relies on bringing the signals together in hardware; there is an immediate problem with applying the radio interferometry technique of "taping" the data and doing the correlation offline, which is simply that the bit rate of the higher frequency optical light is far too high to do this at the moment. I have to admit ignorance as to whether this will be possible in the forseeable future. There is an obvious issue in recording the time of arrival of photons more accurately than the uncertainty principle allows for even the fastest optical transitions of $\sim 10^{-8}$ s, which is well below the resolution needed to sample frequencies of $\sim 10^{15}$ Hz. (Edit: the fastest detectors don't use transitions in atoms and can achieve timing of $10^{-10}$ s; still too slow by orders of magnitude.)

However, even if you could "tape" the data, there are many other problems to be overcome. These difficulties mostly relate to the coherence length and coherence time of phase changes introduced in the atmosphere above each telescope and the inability to use phase-reference sources as a result; and the inability to use phase-closure techniques unless the sources are very bright. These difficulties are explained in more detail in https://astronomy.stackexchange.com/a/35215/2531

To summarise, telescopes in different places observe the same object through different atmosphere. This introduces phase errors. These can be calibrated out in radio observations by using a nearby reference source. This is because the phase errors persist over a reasonably long time and are similar over a reasonably large ("isoplanatic") patch of the sky. For optical observations, the isoplanatic patch may only be a few arcseconds across, so there is rarely a bright reference source, and the atmosphere changes in any case on timescales of tens of ms.

Optical interferometers get round this by using phase closure techniques. The phase error can be eliminated by comparing the phase differences from at least three stations. But again, you have to do this on very short timescales and this means optical interferometry is limited to bright objects in order to get enough signal.

Where is the cut-off? Well certainly beyond the near-infrared, because those interferometers also use similar techniques (delay lines, phase closure) in their techniques.

Answer 2

In principle yes this should work. Optical telescopes separated by 1000 km would "see" the same photon. Why would this be any difference for radio waves with a few cm to few mm wavelength compared to optical wavelengths (ie radio telescopes are already separated by millions of wavelengths, so clearly the phase of the photon CAN be measured by widely separated telescopes. For the following, I will assume an arbitrary definition of VLBI to mean telescopes are separated enough to require independent clocks and some sort of "recording" medium.

At higher frequencies (roughly 10 GHz with current technology) radio astronomy depends on "heterodyne" receivers (https://en.wikipedia.org/wiki/Heterodyne), which allow the sky signal to be mixed with a reference to bring the signal down to a frequency which can be sampled with digital electronics. I know of no heterodyne techniques which work at optical frequencies.

As mentioned above, having clocks with stable enough frequency stability would be technically challenging (not it is frequency/phase stability you really care about not timing precision). And atmospheric phase stability is likely to be challenging. With short separations, the telescopes see roughly the same atmosphere, so you only need to calibrate out the differential atmosphere. As the separation increases the amount of correlated atmosphere decreases. Note in the case of radio astronomy, once you are a couple of 100 km separated the atmosphere is no longer correlated so does not get any worse.

Finally you need an object which is compact and bright enough to actually detect. With radio VLBI, for example, the fast majority of the universe is un-detectable. Specifically you need some sort of physics which can generate high enough "brightness temperature" (https://en.wikipedia.org/wiki/Brightness_temperature). Normal "thermal" processes age generally not visible with radio VLBI.

Another big difference between radio and optical is optical is "photon limited". To get interference pattern between 3 telescopes optically, the signal must be split, reducing the signal to noise. With radio receivers, the signal can be amplified before splitting with minimal loss in SNR.