Hypertelescopes on the Moon Can Have Better than 1 Microarcsecond Resolution

Nextbigfuture commenter, Goat Guy, verified the resolution of very large hypertelescopes and optical interferometers.

The highest angular resolutions for telescopes can be achieved by arrays of telescopes called astronomical interferometers. Hypertelescopes are being worked on that would combine many, many telescopes into very large arrays of tens, hundreds and even space based arrays of one million kilometers.

Hypertelescopes seem very doable with 25 kilometer baselines in thousands of large lunar craters. They could even go up to hundreds of kilometer baseline hypertelescopes on the moon.

Nextbigfuture reader Goat Guy calculated very large interferometer ‘resolution’ slightly higher than the Raleigh’s limit formula. A bit. Using just the numbers BOLD highlighted about the Keck interferometer, 85 m baseline and 2.2×10⁻⁶ m wavelength:

AR = 1.22λ/D
AR = (1.22 × 2.2×10⁻⁶) ÷ 85
AR = 3.16×10⁻⁸ radians
AR = (…) ÷ 2π • ( 360° × 60 min × 60 sec × 1000 milliarcsec/sec )
AR = 6.51 milliarcsec

6.51 being somewhat larger (less resolving) than the quoted 5 mas. Comes more in line if the 85 m baseline is added with the 10 m diameters of each of Keck’s telescopes (comes down to 5.61 mas). Even more likely, is that the ‘resolution’ of interferometers is somewhat better technically than straight optical imaging mirrors. You know, convolution, edge interpolation, all that.

So … it is kind of a relief: the basic physics ‘checks out’, giving confidence that the OTHER projections might also be similarly evaluated. Let’s see.

10,000 m (10 km) dia, 2.2×10⁻⁶ λ = 0.055 mas or 55,000 nanoarcsec
25,000 m (25 km) dia, 2.2×10⁻⁶ λ = 0.022 mas or 22,000 nanoarcsec (22 microarcsecond)

And for that ‘could be hundreds of kilometers’ bit:

250,000 m (250 km) dia, 550×10⁻⁹ λ = 0.000554 mas or 554 nanoarcsec

Note ^^ that I also changed wavelength to 550 nanometers, being the middle of the green part of the optical spectrum. CLEARLY no-where near 100 nano-arcsec. Clearly.

Nextbigfuture notes that it would be better than 1 microarcsecond for a 250 kilometer baseline.
Nextbigfuture believes that the hypertelescope planners are looking at 3000-4000 kilometer baselines for optical scopes dispersed aroundt the moon to achieve 100 nanoarcsecond resolution.

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ONE of the most annoying aspects of all synthetic aperture optical (or even RADAR!!!) systems is that the need to align the little imaging reflectors to within fractions-of-a-wavelength grows, and grows, and grows, the bigger the synthetic aperture itself.

Perspective: Setting aside for the moment the Keck interferometer, and just the actual Keck mirrors (10 m diameter each, consisting of 36 hexagonal 1.6 m sub-mirrors apiece too), The figuring (optical term for ‘precision of shape) of the actual paraboloids was better than ¹⁄₁₀₀th of a wäve. … because, at the actual focal point, wäve errors get multiplied by the square-root of diameter. (This is why small backyard hobbyist telescopes can easily ‘get away with’ quarter wäve optics. Square-root of diameter.)

Projecting to the 10 to 25 kilometer scale, the positioning accuracy would need to exceed ¹⁄₁₀₀₀₀ wäve across the whole synthetic aperture diameter!!! On good old Earth, we have wind, air, seismicity, heating/cooling, tides, position of Moon, and even movement of large equipment that affects the active correction going on at Keck. A lot is done to counteract these effects.

Positioning on the Moon — in a crater — doesn’t exactly alleviate this list.

Sure … no wind per se, precious little atmosphere. Yet, there’s still seismicity, there’s a LOT of heating/cooling at least on a 28.5 day cycle. There actually are ‘tides’ (every action has an equal-and-opposite reaction, so Earth tides are also Lunar tides), yada, yada. More critically on Luna as opposed to Earth, our precious synthetic aperture telescope would be literally bombarded 24–7 by, oh, you know: Solar wind (protons, helium ions), Interstellar particles (“low energy Cosmic rays”), Intergalactic denizens (High energy CRs). And the wavering magnetic field of Old Sol, along with unpredictable blasts of Coronal Mass Ejections. And X-Rays. Lots of X-Rays.

Now, I’m not saying really that it couldn’t be done. But it is pretty glib to project the magnificence of such a beast without trotting out the shortcomings that its developers will face.

Are these shortcomings ‘terminal’? Hmmm… maybe: the aggregate of influences (in my estimate) feel large enough to prevent imaging even a small fraction of the theoretical limit, calculated above. Thus then, what’s the point?

One might argue that ‘the point’ is that with massive light gathering, the very, very dim planets (compared to their overwhelmingly bright stars) still could reasonably imaged in a ‘science sense’. You know, not pretty pictures at the back of the 25 kilometer wide Polaroid camera, but rather, lots of juicy pixels of data, fed through spectrographs, polarizers, and other filters looking for signatures of life, and with sufficient density-of-observation that way more than ‘just a hint’ could be achieved. More like, “well, how about that, Planet Zorcon is TEAMING with critters and forests!”

That’d be something, if even the Polaroid picture ain’t so clear. Moreover, the enormous potential light gathering could in a way RELIEVE those crazy-precise positioning and local influence counteracting requirements. Video, taken at thousands of frames per second, could ‘stop action’ the quivering telescope mirrors, allowing their correction to be computed, frame by frame, mathematically. Solves most of the problem, and likely could deliver pretty Polaroids too. Certainly Astronomy and National Geographic front-cover quality images. After awhile.

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I think I am more fond of sending all this magic imaging stuff to hover in Space, free from planetary body influences. The same solar-wind and heating, and other problems need address. But the whole structure, as Webb has aptly demonstrated, is (un?)surprisingly stabile, drifting about in Space. Oh, sure, needed a humungous heat-shield to deflect Sol’s super-bright hot rays away, but this didn’t exactly break the bank, or the science budget.

⋅-⋅-⋅ Just saying, ⋅-⋅-⋅
⋅-=≡ GoatGuy ✓ ≡=-⋅