High Resolution Imaging of Exoplanets Using the Sun as a Lens

We will be able to take megapixel images of exoplanets by putting telescopes in zones that are 600 to 2000 times the distance of the Earth to the Sun. Getting to 600 times as far away from the Sun we can observe exoplanets in other solar systems when we go the exact opposite direction. We look back around the sun and there will be a ultra-high resolution donut image around the sun that is the image of part of the exoplanet.

Gravitational lensing of light is a well-known phenomenon that has been widely used to gather images of distant galaxies and measure the masses of the intervening lensing galaxy clusters. Gravitational lensing has also been used to detect and characterize exoplanets around distant stars, by the study of the transient amplification of light seen at Earth from background stars when the exoplanet and its host star passes directly in front of them. It is perhaps less well-known that the gravitational field of a star like the Sun produces a real image of distant exoplanets that could potentially be measured.

For an Earth-sized exoplanet located between one and ten parsecs away from the Sun and observed at about 1,000 au from the Sun, the image is kilometers in size and cannot be measured all at once by a meter-scale telescope.

The Einstein ring (donut like image) must be wider than the Sun to not be blocked by the Sun’s photosphere. This means getting out beyond 550 au and possibly a further so that the image is beyond the light effects of the sun. We will use coronagraphs to block out the sun, but getting more separation would make it easier to get rid of those light effects.

Creating a megapixel image requires at least one million separate measurements. For a typical photograph, each detector pixel within the camera is performing a separate measurement. This is not the case for exoplanet imaging at the SGL. Only the pixels in the telescope detector that image the Einstein ring are measuring the exoplanet, and the observed Einstein ring contains a blend of light from the entire exoplanet surface, due to the blur of the SGL, along with a large coronal foreground signal. Substantial deconvolution would be required to synthesize the exoplanet image.

Calculating Imaging Time

Consider a simple method to form a megapixel image of the exoplanet:
1. Divide the SGL image plane into a 1000×1000 grid that just contains the exoplanet in the ’directly imaged’ sense.
2. Position the telescope in the center of each pixel for a time T1 and measure the total combined power of the Einstein ring and solar corona.
3. Subtract the independently determined coronal power for each pixel to get the Einstein ring contribution at that pixel.
4. Multiply the vector of image pixels so obtained by a deconvolution matrix describing the SGL blur to obtain a vector of object pixels at the exoplanet

The time required to produce a 1000×1000 pixel image of an exo-Earth at the distance of Proxima Centauri with an SNR of 10 is by this formula the total time of 37 billion seconds, or 1,200 years. An exoplanet twice as far away will take four times as long to image.

Imaging time scales as the NxN image scales. Reducing the resolution to 500×500 reduces the measurement time by a factor of 16 to 75 years.

Reducing the resolution to 250×250 reduces the measurement time by a factor of 16 to 4.68 years.

Reducing the resolution to 125×125 reduces the measurement time by a factor of 16 to 3.5 months.

Reducing the resolution to 62×62 reduces the measurement time by a factor of 16 to 6.6 days.

Sending multiple telescopes reduces the time to form the images.
Ten one-meter telescopes to the same exoplanet image line would reduce the time by ten. This would reduce the 125X125 imaging time to about 10 days.
Twelve hundred one-meter telescopes would reduce the megapixel image time to 1 year.

If one could control the illumination of the exoplanet, a simple method to remove the blur is available. One could illuminate only one pixel on the exoplanet, gather the light for that pixel through the solar corona, and then illuminate the next pixel, and so on, until the whole exoplanet has been imaged. Because all regions contained in pixels other than the one being measured are dark, they cannot contribute light to the pixel of interest, so the blur need not be deconvolved away. The time to collect a megapixel image of an exo-Earth at Proxima Centauri would then
drop from 1,200 years to only 10 hours.

An exoplanet can only have as little as 10% of its surface illuminated as seen from Earth if its orbital plane is within 18 degrees of edge-on as viewed from Earth, which is relatively rare. Another is that the exoplanet would spend only a relatively small fraction of its orbit in such a crescent phase. If only 10% of the exoplanet’s surface is illuminated (g = 0.1), then the total measurement time is reduced by a factor of 100, or 12 years for the ’exo-Earth at Proxima Centauri’ case.

The observation strategy would be to capture many 15X15, 31X31 and 62X62 using a few dozen telescopes. Multiple observations would be used to understand the illumination phases and other characteristics that would impact how to observe the exoplanet. This could be used to make an observation plan.

SOURCES – Arxiv – Photometric Limits on the High Resolution Imaging of Exoplanets Using the Solar Gravity Lens,Phil A. Willems
Summary Written by Brian Wang, Nextbigfuture.com

28 thoughts on “High Resolution Imaging of Exoplanets Using the Sun as a Lens”

  1. It would be easiest to experiment with using the earth’s atmosphere as a telescope. I wonder if the thick atmosphere of Venus would be even better

  2. I read something similar sometimes ago, just couldn’t remember where. The same concept should work for all the planets and moons with atmosphere. Jupiter is near by and it is the largest planet.

  3. Nuclear fission powered spacecrafts shouldn’t be so hard to build. At least the ones not for human travel. Why? If you use SpaceX to launch it and deliver it to space you remove so much work, potential dangers and so on. Much simpler to design.
    Then you just need to activate the fission reactor powered spacecraft in space and direct it to desired destination.

  4. One option would be to invest much more in fusion. We would reap its benefits and when able to use fusion reactor for space populsion, we could get really far in a relative short amount of time. Another benefit would that telesopes could easily be repositioned and reused.

    Another elagant solution how to get ther fast is by fission rockets, engines. Since SpaceX iswill be able to launch a lot of cargo cheaply in space non working nuclear fission spacecraft, perhaps such as fission fragment rocket could be launched in space by SpaceX(so there won’t be any danger if something goes wrong) and be activated or assembled in moon on seperate space station and launched from there to eliminate the risk because of radioactive material.

    1 m space telescopes are not so hard to build. Nuclear reactors are used in submarines and so on for quite some time. So that is viable option how to get good images of exoplanets in very short ammount of time instead of decades.

    You could also build 2 space stations far from Earth and Mars and launch nuclear fission powered spacecraft between them(obviously you get faster to Mars and back to Earth) and then just use non fission powered rockets for landings and takeoffs to eliminate the risk.

  5. I presume there isn’t much matter per unit volume of space out at 1000AU. But with extremely sensitive instruments and time, might there be enough light backscatter to collect an image focused there by the sun?

    I think you’d probably need to collect imagery from multiple angles to be able to extract a near-planar image via image processing. But maybe not 1000AU off axis.

  6. So, who can do the math for a multiple star system?
    How far out would the inhabitants of say the centauri system have to travel, if they were only content to view those patches of the universe that were briefly lined up with all three stars?

  7. It’s not an issue of resolution in the usual sense. I was talking about concentration of light flux as a function of distance off-axis. Light from a point source passing close to the sun is deflected by 1.75 arc-seconds. Not coincidentally, that’s the angular radius of the sun at the minimum distance required to observe a full Einstein rings for a point source exactly on-axis with the center of the sun. Light flux from any point source within a few arc-seconds of the axis, however, will be concentrated well above its “natural” level in the absence of gravitational lensing. And as long as the mission telescope is within 10 arc-seconds of the focal axis of the target sun, it will be able to image the star as a bright crescent. The size and orientation of that crescent will tell it exactly where it is in relation to the focal axis.

    You’re right, of course, that if the mission telescope were positioned directly on the focal line of the target system’s star, the concentrated light from that star would make it essentially impossible to observe the target exoplanet. Ideally, the mission telescope would be positioned on a focal line roughly centered on the target exoplanet. But it needn’t be exact. The telescope can synthesize a good image of anything within a cone a few thousandths of an arc-second around its focal line. That’s a solid angle tight enough to prevent light from the target system’s star from totally obscuring the light needed for synthesizing an image.

  8. 1000 AU is the perfect sweet spot for a Orion/Medusa spacecraft, lot of
    cargo capacity and just a few years of travel time. Data travels
    back to earth in about a week.

  9. We actually do have multiple suns/stars – they just aren’t at convenient locations for imaging planets, and moving them around is ‘difficult’.

  10. Isn’t the “lens” in this case the gravity of the sun?
    So we can make multiple lenses, providing we have multiple suns. Which we don’t.

  11. I guessed that HLLV is Heavy Lift Launch Vehicle or something similar.
    TAU (Thousand Astronomical Units) was a proposed uncrewed space probe that would go to a distance of one thousand astronomical units (1000 AU) from the Earth .
    NEP, nuclear electric propulsion, I guess?
    The Jupiter Icy Moons Orbiter (JIMO)

    As for the black hole, I think that a black hole (or neutron star) will allow you to do a gravitational slingshot at a much higher velocity than a normal planet will.

    I think that if you try a gravitational slingshot on a body, it can only alter your velocity by some fraction of its own escape velocity. So to get a really fast slingshot you need some body with a really high escape velocity. eg. Black hole.
    Unfortunately, you also need the black hole to be moving at high velocity relative to your current velocity. I don’t think that planet 9 would be moving fast relative to any probe that was able to reach it, not compared to the relative velocities you would get from a much closer to the sun body. eg. Jupiter.

  12. Well, that was kind of the point of the 2nd paragraph – if we don’t need to collect the entire ring area to get a full image maybe that would let us reduce the size of the secondaries?

  13. You for sure would want to have very good near-earth space telescopes capable of rough imaging and analysis of exoplanets before committing to send a mission to the solar gravitational lensing axis for any target planet. Such a mission is a faster alternative to sending an interstellar probe to a nearby stellar. The distance is four light days instead of four to four hundred light years, and the telescope could observe the planet closely for an indefinite period. Before committing to the mission, however, you’d want to know that the planet harbored life and was sufficiently “interesting” to warrant a dedicated observation mission.

    Accurate positioning is not a problem. It’s easy for the onboard guidance system to know which way it needs to nudge the vehicle carrying the mission. All it needs to do is to view the target star in the distorting gravitational field of the sun to calculate precise course corrections. I don’t think I want to try to explain that here. Suffice to say that the SGL does not create a real image of the target that requires one to be precisely positioned within the image to see anything. The sun’s gravity field concentrates light from the target in a pattern that has a tall peak — a singularity, actually — at zero degrees off-axis. But the concentration factor is still thousands of times above ambient (what it would be in the absence of any gravity field) at an arc-second or so off-axis.

  14. Even if you could image an exoplanet in 10 days, would you be able to send the image back to Earth that quickly? You’d be looking at lower than dial up speeds at that distance.

  15. Most of the information here about how to do the imaging can be disregarded. It’s possible to do very much better. I was astonished when I read the NIAC report from the group behind this study to see how badly it missed the mark. Their analysis was correct for the system as they proposed it, but what they proposed was really, really stupid.

    Tinfoil hat time: it’s as if a group utterly opposed to humanity building effective SGL (solar gravitational lens) imaging systems for high resolution monitoring of extrasolar planets had set out to preemptively discredit the concept. The people who did the study appear to have the credentials to do a proper job, and there’s a veneer of technical competence that gives weight to their report. But it’s reminiscent of the scholarly papers of the late 19th century that rigorously “proved” that heavier than air flight in powered aircraft was impossible. “See, here’s a hypothetical design for the system, and when we analyze it carefully, we see that it won’t work. Or works so poorly that it’s completely impractical.”

    So fine. Don’t use that design. Step back and look at the fundamentals. The photon density from the extrasolar planet in the vicinity of the SGL turns out to be ample to do high resolution imaging in near real time. You just need to be a bit more clever in how you collect and process those photons to recover the image.

  16. I think the time-to-image calculation ins vastly off. Try this… let’s take the case of a non-tidally-locked planet, helpfully oriented with a rotational axis that is perpendicular to its orbital axis, and all of that star-crossing.  It rotates, again helpfully, once a day.  

    A single telescope at 800 AU would be able to image, what … 1 pixel?  Dunno.  No.  I rather than that a cheap 100 × 100 pixel telescope might be more realistic. Film Fresnel light gathering ‘lens’, with a single pixel (or maybe … a grating and a spectrograph of several thousand ‘pixels’ of photodiodes) at each Fresnel focal point. All gathering in parallel. Exposure time of a few minutes per pointed-to location, they ‘traveling’ past the 100 × 100 array at the rotational rate of the planet.  

    Well, if nothing else, the mutual rotation frame guarantees that every point imaged will be imaged 100 times, as passing past the 100×100 array. Cool! Moreover, as the planet revolves around its star, more pictures of the surface accumulate every exo-planetary day.  

    It seems to me that not even a fraction of an Earth month could ‘image’ the whole of the planet multiple times. A 100 pixel wide stripe, with a little joggling could image 1000 or more pixels of a stripe, wide. And the exoplanet delivers the 6000+ pixels of stripe-length to image the whole visible face.  

    I may be a simple goat, but I don’t really see the problem.
    ⋅-=≡ GoatGuy ✓ ≡=-⋅

  17. I believe what we need is some practice in constructing composite telescopes in space out of free flying components without any physical connections. That will enable us to build really big telescopes that can be improved incrementally, with mass production lowering the cost of the individual elements.

  18. Yes, we really do need to get past at least 650 AU, ideally 1000. Otherwise your secondary optics need to be absolutely enormous.

  19. You should be able to derive an accurate rotational period for an exoplanet fairly quickly, even from one pixel, and once you have that, all you need to do is loiter at least one such period at each pixel.

    Granted, short term weather patterns would be averaged out, but you’d still see geographic features.

  20. Do we really need to go to 1000AU? I.e. you can shorten focal length by using multiple lenses.
    So what if one used a lot of big mirrors at maybe 100AU, and tried to focused those back to maybe 5AU (a bit past Jupiter’s orbit I believe)?

    And maybe those mirrors don’t need to image light from the whole ring? With normal lenses, one doesn’t need the whole surface area of the lens to get an image. More lens surface just gives you more light – which of course is important, but we’re considering trade-offs here.

  21. Why would planet 9 have to be a black hole in order for it to be usable for a gravity assist?

    I don’t know what to think about the first part of your post, because I don’t recognize those acronyms, and Google gives obviously not correct meanings for some of them.

  22. HLLVs can shove an atomic Hubble with a detachable NEP bud similar to the TAU concept. That is as doable as JIMO I would think. Now, my choice of target would be the galactic core black hole. It doesn’t move too much and may itself act as a lens when it passes between us and other galaxies. Also, if planet nine is a small black hole, it can be used to sling shot things outward.

  23. Frankly, the important information is actually the spectroscopic decomposition of the surface so we get atmospheric components, presence of tholins, and other markers of biosuitability, if not actual biology.

  24. I don’t see the purpose of attempting to get an image with a large number of pixels using the gravitational lens, as described here.

    The target exoplanet will be constantly rotating, and so will be in a different position at the time the light is captured from each pixel. So it seems that the image so formed will not depict the actual appearance of the exoplanet. Is there a way to convert such a mess into an accurate depiction of the exoplanet?

    If not, is there any benefit to sending an instrument to the gravitational lens focus?

  25. I’d change that to only worth it when we have done what you say.

    First we build better space telescopes at or near Earth in space, the kind that can be aimed towards any target, then we start looking for legit Earth-like exoplanets around nearby stars (we’ll know they are good candidates even with pixel sized images).

    Then we plan to send SGL exoplanet telescopes specifically for the best star systems.

    In that way the ROI is assured and we will have the next best data and pictures of those places before going there (which can take a long while to happen, if ever).

  26. Not worth it. A very large virtual telescope make up of a large array of free flying space telescopes would give us what we need to know and that is are there earth like planets out there.

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