Is this a realistic design for a kilometer wide telescope?

[RKOwens]

I'm just a bridge engineer and amateur astronomer, so I'm hoping someone here with more advanced expertise in light waves and reflective surfaces can help me. Basically I was wondering how big a space telescope's primary mirror would have to be in order to view an exoplanet 10 or so light years away with the same resolution as the images of Earth taken from the moon. Obviously, it would have to be massive, like a kilometer or so in diameter, which I believe is possible given today's technology but impractical given how much it would cost to lift all of those mirrors into place. So, I came up with an idea that is probably totally absurd, but I'm just going to bounce it off you guys. The idea I have is to create what is basically a kilometer wide primary mirror with 99% or so of it missing. What I mean is, you would have two or four very slender arms (maybe as small as one degree, if you think of a 360 degree circle) where the mirrors are, and in order to generate a complete picture you have to rotate the entire telescope such that the arms "carve out" a complete 360 degree picture. To help illustrate, here's a very rough sketch I drew up showing the primary mirror:

http://s8.postimg.org/47eold9et/telescope.jpg

The purpose, of course, is to cut down on the overall mass and weight of the telescope, such that it would be more affordable to lift into place. The thing I'm wondering though is, is it even physically possible for light to be captured and properly reflected this way? I'm thinking that if such a telescope were to zero in on a distant Earth-like exoplanet and snap one picture, it might look like this:

http://s9.postimg.org/8wps3d9rz/earth.jpg

Then, the telescope (or at least the primary mirror) would be rotated a few degrees, another picture would be taken, rotated again, another picture taken, and the process is repeated until an entire 360 degree picture can be stitched together. But, would light behave in such a way, or would it just be a blurry blob? Does it need a complete 360 degree mirror? I know there would still be other astronomical costs such as a kilometer wide sun shield, and it would require a lot of energy to rotate such massive arms, but right now I'm just wondering if it's physically possible, and whether or not light would behave in such a way.

 

[davenn]

Hi there
welcome to PF

imaging from multiple mirrors some distance apart isn't a new idea :)
Its been done for the best part of a century with radio telescopes and in more recent decades with optical telescopes
eg the 2 x 10 metre Keck twins on Mauna Kea, Hawaii
The digital imaging data from each scope is combined to be able to produce a much higher resolution image

They even do this between the Keck's and the big scopes high in the Andes mountains of South AmericaDave

 

[Doug Huffman]

And the Square Kilometer Array is coming - in radio frequencies.

 

[wabbit]

how big a space telescope's primary mirror would have to be in order to view an exoplanet 10 or so light years away with the same resolution as the images of Earth taken from the moon (...)it would have to be massive, like a kilometer or so in diameter,.

This sounds rather optimistic. For $D=10 ly\simeq 10^{17}m, d=10^3m$ , and $\lambda=500 nm=5\cdot 10^{-7}m$ , I get a resolution of $\sim \lambda\frac{D}{d}\simeq 50,000$ km.
You'd need X-rays at nanometer wavelengths to get the sort of resolution you seek with this geometry.

Regarding the design, you don't need any single big structure - a fleet of spacecraft orbiting in formation somewhere could presumably even have an effective aperture resolution wise of 1,000 km or more (not sure what the limit would be from maintaining exact separation). I believe there are some projects of that kind, don't remember where I saw that though.

Edit : this study seems to be along such lines : http://exep.jpl.nasa.gov/TPF-I/tpf-I_what_is.cfm

(Edit : corrected above, km/m)

 

[Drakkith]

A mirror with 99% of the area missing would be very, very limited in its usefulness. Unlike a radio telescope, which can record data and the combine it later with observations made at different telescopes, optical telescopes cannot directly record the electric field of the incoming light. It simply oscillates too fast for the electronics to respond. Instead, you have to physically combine the light in some manner prior to recording an image, that way the light waves interfere with each other during focusing and end up producing a smaller airy disk. A telescope missing most of the mirror is like blocking out most of the aperture of a regular telescope. With most of the incoming wavefront lost, the remaining portion cannot be focused down to a small spot. Rotating the mirror does nothing because we aren't capturing the values of the electric field, we are just measuring photons.

 

[russ_watters]

I'm just a bridge engineer and amateur astronomer, so I'm hoping someone here with more advanced expertise in light waves and reflective surfaces can help me. Basically I was wondering how big a space telescope's primary mirror would have to be in order to view an exoplanet 10 or so light years away with the same resolution as the images of Earth taken from the moon. Obviously, it would have to be massive, like a kilometer or so in diameter, which I believe is possible given today's technology but impractical given how much it would cost to lift all of those mirrors into place.

This is a simple "similar triangles" geometry problem. The easy way to do this is to find the specs of an existing telescope, then mutiply by the ratio of the distances. Unfortunately, you will find that a 1km mirror is orders of magnitude too small to do what you are hoping.

 

[wabbit]

A mirror with 99% of the area missing would be very, very limited in its usefulness.

This doesn't sound right. You have to combine the light, and it wouldn't be a one-piece mirror, but this has been done and while the sensitivity is limited by total collecting area, the resolution is still limited by baseline/diameter. Optical interferometry / aperture synthesis with baselines up to a couple 100 meters (and effective collecting area less than 0.1 % of (baseline)^2 as far as I can tell), are now in use and have produced some impressive images of stellar surfaces (of course exoplanet surface imaging is yet another level of challenge.)

This one of Alderamin (dist. ~ 50 ly) is from the CHARA array:

Cf. http://arxiv.org/abs/0906.22412241- Zhao et al. "Imaging and Modeling Rapidly Rotating Stars: Alpha Cephei and Alpha Ophiuchi", and http://Earth'sky.org/brightest-stars/alderamin-the-kings-brightest-star

 

[Drakkith]

Yes, I was aware of the existence of several different optical interferometers, but I was under the impression that they don't have resolution equal to a full mirror with diameter equal to the baseline, or at least that it takes some very, very careful coaxing and lots of work to even get a usable image. Maybe I was mistaken.

 

[wabbit]

I believe the theoretical limit is the same but in practice it must get very hard to approch that.

Having no idea how close, I just did the folowing a rough check for CHARA :

- announced Limiting resolution 0.15 mas at ~ 500nm. this seems to be more or less what's reached in the image above (eyeballing it I would say that image resolution is somewhere in the .2 or .3 mas, surely less than 0.5)
- max baseline 330m
- theoretical limit for D=baseline. ~ 500nm/330m=2×10^-9=0.4mas
Actually the baseline may be just one arm of the Y I think so this would get closer to the 0.15, and I dropped some factor of order unity somewhere anayway.

But this shows they're at least getting pretty close to the theoretical limit here. Let's say that again. They are getting close to diffraction limited results from a half-kilometer aperture.

Even if this is off by some factor of 2 or so that is seriously impressive.

Edit : actually this shows a big advantage to the "obstructed" design : how would you maintain sub micron alignment in a mirror area of 0.2 square km ? Seems completely undoable. Here they "only" need to keep a total collecting area of a few square meters aligned - hard but feasible, I'd guess world-class but not a first on that metric.

 

[RKOwens]

Thanks for all the information, everyone. I was sure there had to be some reason why it wouldn't work (otherwise someone else would have already done it), I was just more interested in how and why it wouldn't. And wow, I had no clue a mirror would have to be 50,000 km wide to image even a close exoplanet at the resolution mentioned. I remember reading that it's expected that the 6.5 meter wide James Webb Space Telescope will be able to image a nearby exoplanet to about a 1 pixel resolution. I admit I'm no expert on light waves and things like this but can someone please explain how it's possible to achieve 1 pixel resolution with such a small mirror, if the formula used by wabbit comes up with 50,000 km width for something in the vicinity of 1,000,000 pixels? (By the way, the reason I came up with the kilometer wide figure in the original post is that I'd just assumed a mirror 1,000,000 times the collecting area of James Webb would get you 1,000,000 pixel resolution.)

 

[phinds]

What is "one pixel resolution" ?

 

[wabbit]

As suggested by phinds, the Webb telescope is not resolving the planet itself, it is detecting it - which is by itself quite a feat, not that the planet itself is very faint - it must be no fainter that stars commonly imaged by that telescope - but because it must be very close to it's star, so :

- First the telescope needs to resolve the planet from the star. With the formula above we get a resolution for 6.5m, of ~10 M km (assuming the planet it's imaging is at ~10ly). Sounds OK for a planet-star distance, if that planet is not orbiting too closely, but you also want a good separation between the images of star and planet, so already this could be close to the limits.

- Then remove the light from the star which might otherwise easily wash out the much fainter planet. Perhaps they might be using a coronograph for that, and they might have issues with stray light too. (I don't know any specifics about this observation, just guessing)

The issues above are as far as I know what makes direct imaging of exoplanets something close to the limit of current telescopes - and by imaging I mean here getting a dot (and presumaby also a spectrum from that dot).

So your project is most likely for a next generation of multi-craft space telescopes flying in formation to get a large baseline, and using interferometry to reconstruct an image. I don't think its unfeasible though, just expensive and technically challenging, but I would still expect to see such an image one day. After all, look at that image of Alderamin already, it's a star yes not a planet, but still - and this is from a terrestrial array, not a space based one.

 

[wabbit]

I had no clue a mirror would have to be 50,000 km wide to image even a close exoplanet at the resolution mentioned.

Not quite - 50,000km was the estimated resolution at 10ly from your 1km telescope. The estimate I gave above for the required baseline was ~1000km (50km resolution, that was actually just a guess at the sort of thing you were aiming for), though 100 km would already produce images with 500km resolution, which personally I'd be quite happy with:)

 

[Drakkith]

Having no idea how close, I just did the folowing a rough check for CHARA :

- announced Limiting resolution 0.15 mas at ~ 500nm. this seems to be more or less what's reached in the image above (eyeballing it I would say that image resolution is somewhere in the .2 or .3 mas, surely less than 0.5)
- max baseline 330m
- theoretical limit for D=baseline. ~ 500nm/330m=2×10^-9=0.4mas
Actually the baseline may be just one arm of the Y I think so this would get closer to the 0.15, and I dropped some factor of order unity somewhere anayway.

But this shows they're at least getting pretty close to the theoretical limit here. Let's say that again. They are getting close to diffraction limited results from a half-kilometer aperture.

Hmmm. Guess I need to brush up on my optics then. I'd like to know how they accomplish all this over multiple measurements.

Edit : actually this shows a big advantage to the "obstructed" design : how would you maintain sub micron alignment in a mirror area of 0.2 square km ? Seems completely undoable. Here they "only" need to keep a total collecting area of a few square meters aligned - hard but feasible, I'd guess world-class but not a first on that metric.

Multiple smaller mirrors put together would do it.

 

[wabbit]

I'd like to know how they accomplish all this over multiple measurements.

The article mentionned above in post#7 (mangled the link though, it is http://arxiv.org/abs/0906.2241) discusses that, or the CHARA site too. My understanding is that they dynamically adjust the light paths lengths to sub-wavelength accuracy by using moving mirrors. This is in essence adaptive optics, only instead of moving parts of one big mirror (They might not need to do that here because their individual collecting mirrors are fairly small, ~50cm or so I think), they move smaller mirrors located in a dedicated area - and deviations must be detected from something like monitoring an interference pattern.

Multiple smaller mirrors put together would do it.

That is the setup used here, only the individual mirrors are spread out over a large area. The issue I was referring to is that synchronizing a large area has a difficulty increasing with the area - so in practice the collecting area must remain small (one or a few square meters for CHARA) while the overall diameter of the system must be large (a few 100 meters for CHARA) to provide the required resolution - so the "effective obstruction" 1-collecting/total must be close to 100% (e.g. 1m^2 vs (100m)^2 gives 99.99% "area obstruction"). The cost and weight of the system would presumably also increase somewhat proportionally with collecting area.

Edit: they have very few mirrors in an Y pattern so that alone would provide good resolution only in three directions. They combine the different orienations resulting from Earth rotation to eventually resolve in more directions. I don't know what algorithms they use to combine the images at different rotation angles, but I believe this can be done without inter-image phase information.