# What prevents digital interferometry in an optical telescope array?

I understand it is common to combine an array of radio telescopes in to a single instrument using interferometry. This has the photon collecting area of the combined radio telescopes but an aperture (and hence resolving power) dependent on the baseline of the devices. There is a nice explanation at the end of this article.

A recent well known application of radio telescope digital interferometry is Event Horizon Telescope's black hole imaging. It demonstrates the additional resolving power of the technique.

For radio telescopes, this interferometry is commonly (now) performed in software, and preceding this, was computed with analgoue signal processing. Individual radio telescopes capture "images" and the signals are jointly processed to build a combined "image" with superior resolution and signal power.

As an example, the proposed square kilometre array has a total receiving surface area equivalent to a single square kilometre radio telescope, but is spread over Africa and Australia, giving it an enormous aperture.

Interferometry is used in optical telescopes too, such as at the Keck Observatory. However, this is achieved with excruciatingly exacting engineering to bring the optical feeds from the telescopes together and combine them.

I speculate that were it was possible to perform digital interferometry on optical telescope images, then this would be pretty neat. I'd like to know why this seems to not be possible.

# Phase

An immediate problem is that the sensor in an optical telescope only captures the magnitude of the signal and does not capture its phase. In contrast, a radio telescope does capture both magnitude and phase, which allows digital interferometry (?).

However – I don't understand why it's not possible to capture the phase of light collected by a telescope by some means. For example, if the captured signal were split in to an image pair and mixed with a "local clock" from a laser source, this seems like it would give a quadrature pair. Phase could be measured provided the rate of phase change remains within the frame rate of the detector.

# Data Sizes

Perhaps this isn't relevant, but consider the total photon count and photon arrival rate in an astronomical image.

A million pixel sensor with 16 bits per pixel is able to capture about 64 billion discrete photons. A big number, but well within the storage capacity of modern commodity computers. If an image is exposed over a minute, then the (average) photon arrival rate would amount to a billion events a second – also processable by modern machines.

Presumably this data estimate is wildly off the mark though, because the source data from the Event Horizon Telescope amounted to 5 petabytes (or half a ton of hard drives in old money). Perhaps sheer data volumes are the reason this approach doesn't work?

# Pretty Cool

Basically, if it were possible, it would transform large telescope construction from a hard and very expensive engineering problem, that only a few people want to solve; in to a demanding computing problem, able to take advantage of the enormous growth in processing power afforded by modern society throwing trillions of dollars in to improving processors.

That would be pretty cool.

• Off hand it must have to do with wavelengths. Radio waves have long wavelengths and the detection of phases is feasible. With the nanometer wavelengths of visible light this if not impossible ( with new nano technology?) must be very exacting and expensive. Mar 4, 2015 at 18:19
• Even if you simple assume you can get the phases, to do the interferometic computation you need to know the relative positions of all the receivers to sub-wavelength precision. Which you can't accomplish at any given time, much less keep track of the steady changes arising from Earth tides, earthquakes and even thermal expansion of the structures. Mar 4, 2015 at 18:24
• @dmckee That sounds like a challenge, definitely! But couldn't you determine that continuously and instantaneously by referring to one (or more) optical beacons jointly visible by the telescopes? Mar 4, 2015 at 18:59
• @annav Well, sure. But if you are building this thing on a single structure then you could also just build a conventional telescope. Mar 4, 2015 at 20:17
• Phase for light is exactly the same as for radio. Both are electromagnetic waves, just at different frequencies. Phase interference effects can be seen with lasers. Measuring the phase is probably part of the problem, if not all of it. Measuring the phase of light directly was not possible in the past (or at least not in a telescope sensor). I don't know if it is now, but if so it is a very new technology. Also digitising is most useful for very long baselines with many telescopes, which would be very expensive. Aug 3, 2017 at 10:31

Radio telescope arrays record the full waveform of the electric field as a function of time, which is possible with fast electronics. For optical frequencies (≈ 500 THz) this is far beyond what's doable today. You could detect only the phase, relative to some reference, which changes on timescales of the coherence time $$\tau_c$$ of the light. According to the Wiener-Khinchin theorem the coherence time is the inverse of the bandwidth $$\Delta \nu$$ of the light. For blackbody radiation from stars $$\Delta \nu$$ is still hundreds of THz. You can filter it to arrive at a lower bandwidth, at the cost of losing most of the intensity and therefore resolution. I'm not aware of any oscilloscope faster than 100 GHz, so if you filter the light down to this bandwidth its intensity is reduced by 3 orders of magnitude.

# Phase

The heterodyning method you described works well to compare the phase of the incoming light with the phase of a local oscillator. But for interferometry you need to compare the phase of the light relative to the phase at all the other detectors. This is only possible if the all the local oscillators have the same phase.

But how can you synchronize their phase? You could try to build very stable lasers which can be tuned to an exact absolute frequency (the center frequency of the light you filtered out). If you want to measure for 1000 s the lasers need to have the same frequency with an uncertainty well below 1 mHz. Moreover, they must be at this very frequency for the whole measurement duration – usually the frequency stabilities of lasers are given on timescales of a few milliseconds. The best stabilization I know of achieves $$10^{-16}$$ accuracy over a timescale of seconds. [1]

Alternatively you could use one global oscillator as phase reference, i.e. the output of one single laser distributed to all heterodyne setups. Here you basically shift the problem from building a phase-stable interferometer for the starlight to building a phase-stable pathway to distribute the light of the global reference light. In this case you don't suffer so much from intensity losses in the fiber, but still any phase shift will ruin the synchronization. And there are many ways to mess up the phase, like temperature changes or strain.

In both scenarios, if the detectors are on earth they have to look through the atmosphere, which is yet another opportunity to mess up the phase. The refractive index of air depends on its density and composition, which varies spatially and teporally. This phenomenon is called seeing.

# Data Sizes

Although I don't think this is a limiting factor, let me say a few words about the amount of data recorded in this kind of measurements. Firstly, there is no point in using a detector with spatial resolution, like a CCD chip. The resolution of the telescope array comes from the distance of the individual detectors, not from the resolution power of an individual detector. Instead one would have a single heterodyne detection setup without any spatial resolution in each telescope. And instead of recording one datapoint with an integration time of 1 minute you need to constantly measure the phase, which is changing very fast, as mentioned in the beginning. The Keysight UXR1104A Infiniium measures 256 GS/s with 10 bit resolution. This data rate can be easily transferred through a single optical fiber. I don't know how to store it, but people at LHC probably solved this problem as well.

One can make use of the intensity fluctuations in thermal light as it was done by Hanbury Brown and Twiss[2] These measurements don't require to measure the phase of the light itself, but on the random interference of light from different parts of the source. Therefore it is not affected by atmospheric turbulences. The intensity varies on timescales of the coherence time $$\tau_c$$, and this is the level of synchronization one needs. 100 GHz synchronization is much easier than 500 THz as required for phase synchronization.

(Disclaimer: a lot of this answer rests on a paper from 2011, and I imagine the field has advanced.)

In graduate school I studied a paper, "`Longer-Baseline Telescopes Using Quantum Repeaters" that touched on this question. To perform interferometry in the IR and optical, one must actually bring together the photons that are received and interfere them to detect the phase difference. This is possible using fiber-optics, however, fiber tends to lose photons pretty quickly. As a result, one can't build such interferometric arrays very far. For a classical signal, one can afford to lose photons and then insert a repeater, but this won't preserve the phase information we need for interferometry.

Gottesman et al. propose using a technology (thus far largely theoretical or limited to small lab-scale demonstrations) known as a quantum repeater, which would allow a long-distance transport of a photon complete with phase information. This would allow one to build much larger optical interferometric arrays with corresponding increase in angular resolution.

I'm not sure how much work has been done on this concept since the paper was written in 2011, but it's a neat application of quantum information to astronomy.

Something very much like what you envision has been proposed for future astronomical observations, using an array of telescopes in space "flying in formation" - called "Distributed Spacecraft Technology".

It is possible to do interferometry between widely separated telescopes, even on the Earth's surface. The challenge is, as others point out, to track the positions and orientations of all the telescopes down to sub-wavelength accuracy. It's possible to do that, using a coherent reference beacon: a laser light source located in space somewhere close to the line of sight of the telescope array. Sensors at the telescopes can use the light from the reference beacon to determine their positions and orientation to the necessary accuracy. Even if the telescopes are on the ground and light from the beacon and the observed astronomical object needs to pass through Earth's turbulent atmosphere, the effects of turbulence and ground motion can be tracked via the reference light. Since the beacon's light will be affected the same way as starlight that follows nearly the same path, digitally un-doing the distortions of the beacon's light will also digitally un-do distortions of the starlight.

The Breakthrough Starshot project is nearly the same problem in reverse: synchronizing the phase of the emitted light of all of the lasers in a large (10 km) array.