4 ms·

The planet is about 0.05 AU from Proxima Centauri, meaning we need an angular resolution of about 1.9e-7 radians to even distinguish it from its host star. Is

The planet is about 0.05 AU from Proxima Centauri, meaning we need an angular resolution of about 1.9e-7 radians to even distinguish it from its host star. Is that realistic? In theory, an orbiting space telescope has a diffraction-limited resolution of approximately 1.22λ/D (λ = wavelength, D = aperture size). Modern image processing techniques can improve on this somewhat, but it makes a good order-of-magnitude estimate. Anyway, this formula tells us a 4-meter telescope has a maximum angular resolution of about 1.8e-7 radians at a typical visible light wavelength of 600 nm. That would be just good enough... except that we don't actually have a 4 meter orbiting space telescope. Resolving even large features on the planet would require a much larger telescope, probably kilometers or more. For ground based telescopes, the situation is even worse because of atmospheric effects. Despite being 10 meters in aperture, the Keck telescopes in Hawaii are limited to an angular resolution of about 2e-7 radians because of the atmosphere. However, there is reason to hope that the even larger European Extremely Large Telescope will have enough resolution (about 5e-8 radians? hard to tell from their official publications) to image Proxima b directly. https://www.eso.org/sci/meetings/2011/VLTI2011/presentations/Kissler-Patig.pdf https://www.eso.org/sci/meetings/2011/VLTI2011/presentations... Again, this is still not enough to resolve surface features. So, long story short the answer is unfortunately no at present. Maybe space-based manufacturing will let us build a big enough telescope someday?

verandaguy 10y ago
To put things in perspective, what was the angular resolution of Hubble's Ultra Deep Field measurements/photos? (keeping in mind that angular resolution isn't the only challenge here)
- Thorondor 10y ago
  Hubble's angular resolution is about 0.05 arcsec = 2.4e-7 radians. And you're absolutely right that angular resolution isn't the only challenge here - some way of filtering out the extremely bright (relatively) light from the host star is needed as well, for starters.
throwaway_yy2Di 10y ago
The planet is about 0.05 AU from Proxima Centauri, meaning we need an angular resolution of about 1.9e-7 radians to even distinguish it from its host star. Is that realistic? Much more than that; that's the angle for HALF-maximum brightness, but since the star's many orders of magnitude brighter than the planet, you'd need a much larger reduction than 1/2. Unfortunately, the diffraction-limited pattern [0] has fat tails -- it's not Gaussian, the brightness is slow to drop off away from the center (polynomially slow? [1]). I understand you'd need >100 times the FWHM angle in practice, on the order of 1" for JWST for instance [2] This is why coronagraphs will be so useful. [0] https://en.wikipedia.org/wiki/Airy_disk#Mathematical_details https://en.wikipedia.org/wiki/Airy_disk#Mathematical_details [1] a log-log graph shows the envelope is close to inverse-cubic (x^-3) [2] http://nexsci.caltech.edu/workshop/2016/NIRCam_Planets_and_BDs_Sagan2.pdf http://nexsci.caltech.edu/workshop/2016/NIRCam_Planets_and_B...
- Thorondor 10y ago
  Technically, 1.22λ/D is the angle for the first dark circular ring of the Airy disc (first zero of the relevant first-order Bessel function [0]). But you are still right that the host star needs to be blocked out in some way to produce a useful image. I think NASA is working on some ways to do this, see [1]. [0] https://oeis.org/A245461 https://oeis.org/A245461 [1] https://exoplanets.nasa.gov/resources/1015/ https://exoplanets.nasa.gov/resources/1015/
  - throwaway_yy2Di 10y ago
    You're exactly right; good catch.
- throwaway_yy2Di 10y ago
  Here's a better answer on /r/askscience: Can we directly image the planet from earth? 1. "The planet/star contrast is 10^-7 " This basically means for every 10,000,000 photons from the star, we would measure ~ one from the planet. 2. "Current instrumentation using adaptive optics and coronography on 10 m class telescopes (like Sphere on VLT or Gemini Planetary Imager) aims at achieving a contrast of 10^-6 to 10^-7 at an angular resolution of 100-200 mas" 3. "The planet has a separation of 38 mas". 4. Therefore with the best planet imagers we cannot currently directly image the planet. Our best hope is the E-ELT which should have first light in 2024. https://www.reddit.com/r/askscience/comments/4zdkra/askscience_ama_series_we_have_discovered_an/d6v1k6l https://www.reddit.com/r/askscience/comments/4zdkra/askscien...
Tloewald 10y ago
Presumably at some point we'll be able to use several orbiting telescopes as a virtual array.
nkrisc 10y ago
Hm, so clearly we need to remove the atmosphere. It'll be rough for a while, but it's necessary.
semaphoreP 10y ago
To add on to this, adaptive optics systems can be used to correct for atmospheric turbulence. The latest adaptive optics instruments have been able to achieve diffraction-limited imaging (i.e. comparable to if the telescope was in space) with 8 meter telescopes in the near-infrared (1-2 microns), resulting in ~2e-7 radian resolution. Pushing this to larger telescopes and shorter wavelengths will improve this resolution. The bigger problem is actually blocking out the glare of the host star. Especially for a planet this close in angular separation to its host star, blocking out the light from the host star is challenging and requires sophisticated instrumentation (e.g. coronagraphs). The problem with the more sophisticated instrumentation is that you also lose throughput (when trying to block out stellar light, you also end up blocking a lot of light from the planet), meaning we will need a lot of telescope time in addition to sophisticated instrumentation to eventually image this planet.
throwaway_yy2Di 10y ago
However, there is reason to hope that the even larger European Extremely Large Telescope will have enough resolution (about 5e-8 radians? hard to tell from their official publications) 6-12 mas is the advertised figure (0.006" = 3e-8 rad). That's the FWHM for its adaptive-optics imaging camera [0]. If you look at the details [1], it achieves the best resolution (6 mas) in the near-infrared J band, and for Nyquist-sampling reasons the pixel scale is half that (3 mas). [0] https://www.eso.org/public/usa/teles-instr/e-elt/e-elt-instr/micado/ https://www.eso.org/public/usa/teles-instr/e-elt/e-elt-instr... [1] https://www.eso.org/sci/facilities/eelt/fp7-elt-pub/wfi_workshop/pdffile/RFalomo_MAY09.pdf https://www.eso.org/sci/facilities/eelt/fp7-elt-pub/wfi_work...

verandaguy 10y ago

To put things in perspective, what was the angular resolution of Hubble's Ultra Deep Field measurements/photos? (keeping in mind that angular resolution isn't the only challenge here)

Thorondor 10y ago
Hubble's angular resolution is about 0.05 arcsec = 2.4e-7 radians. And you're absolutely right that angular resolution isn't the only challenge here - some way of filtering out the extremely bright (relatively) light from the host star is needed as well, for starters.

throwaway_yy2Di 10y ago

The planet is about 0.05 AU from Proxima Centauri, meaning we need an angular resolution of about 1.9e-7 radians to even distinguish it from its host star. Is that realistic? Much more than that; that's the angle for HALF-maximum brightness, but since the star's many orders of magnitude brighter than the planet, you'd need a much larger reduction than 1/2. Unfortunately, the diffraction-limited pattern [0] has fat tails -- it's not Gaussian, the brightness is slow to drop off away from the center (polynomially slow? [1]). I understand you'd need >100 times the FWHM angle in practice, on the order of 1" for JWST for instance [2] This is why coronagraphs will be so useful. [0] https://en.wikipedia.org/wiki/Airy_disk#Mathematical_details https://en.wikipedia.org/wiki/Airy_disk#Mathematical_details [1] a log-log graph shows the envelope is close to inverse-cubic (x^-3) [2] http://nexsci.caltech.edu/workshop/2016/NIRCam_Planets_and_BDs_Sagan2.pdf http://nexsci.caltech.edu/workshop/2016/NIRCam_Planets_and_B...

Thorondor 10y ago
Technically, 1.22λ/D is the angle for the first dark circular ring of the Airy disc (first zero of the relevant first-order Bessel function [0]). But you are still right that the host star needs to be blocked out in some way to produce a useful image. I think NASA is working on some ways to do this, see [1]. [0] https://oeis.org/A245461 https://oeis.org/A245461 [1] https://exoplanets.nasa.gov/resources/1015/ https://exoplanets.nasa.gov/resources/1015/
- throwaway_yy2Di 10y ago
  You're exactly right; good catch.
throwaway_yy2Di 10y ago
Here's a better answer on /r/askscience: Can we directly image the planet from earth? 1. "The planet/star contrast is 10^-7 " This basically means for every 10,000,000 photons from the star, we would measure ~ one from the planet. 2. "Current instrumentation using adaptive optics and coronography on 10 m class telescopes (like Sphere on VLT or Gemini Planetary Imager) aims at achieving a contrast of 10^-6 to 10^-7 at an angular resolution of 100-200 mas" 3. "The planet has a separation of 38 mas". 4. Therefore with the best planet imagers we cannot currently directly image the planet. Our best hope is the E-ELT which should have first light in 2024. https://www.reddit.com/r/askscience/comments/4zdkra/askscience_ama_series_we_have_discovered_an/d6v1k6l https://www.reddit.com/r/askscience/comments/4zdkra/askscien...

Tloewald 10y ago

Presumably at some point we'll be able to use several orbiting telescopes as a virtual array.

nkrisc 10y ago

Hm, so clearly we need to remove the atmosphere. It'll be rough for a while, but it's necessary.

semaphoreP 10y ago

To add on to this, adaptive optics systems can be used to correct for atmospheric turbulence. The latest adaptive optics instruments have been able to achieve diffraction-limited imaging (i.e. comparable to if the telescope was in space) with 8 meter telescopes in the near-infrared (1-2 microns), resulting in ~2e-7 radian resolution. Pushing this to larger telescopes and shorter wavelengths will improve this resolution. The bigger problem is actually blocking out the glare of the host star. Especially for a planet this close in angular separation to its host star, blocking out the light from the host star is challenging and requires sophisticated instrumentation (e.g. coronagraphs). The problem with the more sophisticated instrumentation is that you also lose throughput (when trying to block out stellar light, you also end up blocking a lot of light from the planet), meaning we will need a lot of telescope time in addition to sophisticated instrumentation to eventually image this planet.

throwaway_yy2Di 10y ago

However, there is reason to hope that the even larger European Extremely Large Telescope will have enough resolution (about 5e-8 radians? hard to tell from their official publications) 6-12 mas is the advertised figure (0.006" = 3e-8 rad). That's the FWHM for its adaptive-optics imaging camera [0]. If you look at the details [1], it achieves the best resolution (6 mas) in the near-infrared J band, and for Nyquist-sampling reasons the pixel scale is half that (3 mas). [0] https://www.eso.org/public/usa/teles-instr/e-elt/e-elt-instr/micado/ https://www.eso.org/public/usa/teles-instr/e-elt/e-elt-instr... [1] https://www.eso.org/sci/facilities/eelt/fp7-elt-pub/wfi_workshop/pdffile/RFalomo_MAY09.pdf https://www.eso.org/sci/facilities/eelt/fp7-elt-pub/wfi_work...