Thread by @markmccaughrean

As the start of the last major #JWST deployment approaches, the starboard primary mirror wing, it's time for a thread about what that helps enable – excellent spatial resolution.

It's #SharpnessSaturday (yes, the hashtag symbol also denotes a "sharp" in music 🙂)

So what do we mean by "spatial resolution"?

It's a way of quantifying the sharpness of an image scene, the amount of detail visible at small scales, or at some rather fundamental level, how close two things can be in a scene & still be separated.

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For astronomers, that's often simplified to saying "how close can two stars of equal brightness be on the sky & still separable or resolvable?"

That's not to say the stars need actually be close in space, but just how they appear on the sky.

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The fundamental limit to the resolution of an optical system like a telescope or a microscope comes from diffraction, linked to the wave nature of light.

The essential theory was developed by Ernst Karl Abbe, director of the Jena Observatory.

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en.wikipedia.org/wiki/Ernst_Abbe

As a side note, I was once offered a professorship at the Jena Observatory or the Astrophysical Institute & University Observatory Jena as it is more properly known.

There are many branching points in life & that's a road I did not take.

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Anyway, what Abbe showed, in essence, is that the spatial resolution of a system depends on the size of the entrance aperture & the wavelength of light.

The bigger the aperture, the sharper the resolution.

The longer the wavelength, the poorer the resolution.

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And the relation is linear: if you double the size of your telescope, your resolution improves by a factor of two, & if you double the wavelength, the resolution gets worse by a factor of two.

But this is the case if you are "diffraction limited".

That's not always true.

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In particular, for ground-based telescopes, the atmosphere plays an important role & "blurring" due to turbulence limits most optical-IR telescopes to a resolution considerably worse than Abbe would predict.

Let's put some numbers on this.

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There are many details here including things like the Rayleigh Criterion, where the resolution is defined as the separation at which the peak of one star coincides with the first null in the diffraction pattern of an adjacent equally bright star.

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hyperphysics.phy-astr.gsu.edu/hbase/phyopt/R…

But for present purposes, it's perfectly reasonable to approximate the diffraction-limited resolution of a telescope as λ/D, where λ is the wavelength you're observing at & D is the diameter of your (roughly 😉) circular primary mirror.

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If you give both of those numbers in the same units, say metres, then the answer will be in radians (resolution is an angular thing – how close in angle on the sky can things be & still resolvable?)

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Radians are less common than degrees, & are linked to the geometry of a circle – an arc on the circumference of a circle equal in length to the radius of the circle subtends an angle of 1 radian.

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That means there are 2π radians in a circle or in 360º, so 1 radian = 360/2π = 57.3º.

Astronomers often work in very small angles called arcseconds. There are 60 arcseconds in an arcminute & 60 arcminutes in a degree, so 3600º arcseconds in a degree.

Yep 😳

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Don't shoot the messenger – blame the Sumerians & Babylonians 🤷‍♂️

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en.wikipedia.org/wiki/Sexagesim…

Which brings us to one of the more famous numbers in observational astronomy, namely that there are 206265 arcseconds in a radian (~3600 x 57.3).

Phew – let's get back to those calculations.

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So, let's work out the diffraction limited resolution for a fairly small 1 metre diameter telescope at 500 nanometres, in the mid-visible.

Applying λ/D, getting the units right, & multiplying by 206265 gives us a theoretical resolution of 0.1 arcseconds.

Which is nice.

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Except that for ground-based telescopes, the atmosphere tends to blur things out to around 1 arcsecond, 10 x worse.

We call this "the seeing".

At sea level, it's often more & even on the best mountain top observatories, the seeing is rarely better than 0.3 arcseconds.

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[Note – in Tweet 13, I wrote "3600º arcseconds" & clearly the º is a typo – mentally delete it please. Mea culpa. HT @tc1415]

Now you can beat the resolution down & beat atmospheric turbulence down using (say) adaptive optics and/or laser guide stars, & such technologies are amazing.

Then again, not perfect, but that's something for another thread.

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Now if you put a telescope in space, you remove that obstacle & can reach Abbe's diffraction limit.

For the 2.4m diameter Hubble Space Telescope at 500nm then, that yields ~0.04 arcseconds or 40 milliarcseconds.

So far more detail than most ground-based telescopes.

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What about #JWST then, assuming that it successfully spreads its second primary wing today & becomes a 6.5 metre diameter (kind of) telescope?

Well, in the near-IR at 2 microns (or 2000nm), that will yield 0.063 arcseconds or 63 milliarcsec.

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So despite have a primary mirror that is 2.7 x larger in diameter than HST's, the longer wavelengths that JWST will be operating at means its resolution will be slightly poorer.

And at 20 microns, JWST's resolution will be 0.63 arcseconds, so almost "ground-like".

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FWIW, JWST is capable of detecting photons down to 0.6 microns or 600nm, but its mirrors haven't been polished to work perfectly there, so things will be a bit funky: it will be diffraction-limited at all wavelengths beyond 2 microns.

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Broadly, you can expect Hubble-like resolution in near-IR (1-5 microns) images from JWST, rolling off to ~ground-based resolution at 10–30 microns in the mid-IR.

Indeed, combining images spanning a wide wavelength range & thus resolution is going to be interesting 😳

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That's only part of the story, of course: the collecting area of JWST is ~2.7 x 2.7 = 7.3 x larger than HST, so will be able to detect much fainter objects.

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And because it's a super-cold telescope, the background will be extremely low in the thermal-IR, making it far more powerful than HST or any ground-based telescope at wavelengths beyond ~2.5 microns, which is exactly where much of #JWST's science is.

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Plus JWST has some stunningly sophisticated instruments with large detectors & many filters to yield spectacular images, & allow the detailed analysis of chemistry, physics, & dynamics via spectroscopy.

Combining great resolution, sensitivity, & instruments – that's JWST.

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Today's thread has gone on long enough, but one topic I will return to later is the JWST "point spread function", i.e. the shape that the telescope imprints on unresolved objects like stars through diffraction, as Abbe described.

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With its round primary mirror, HST yields quite a clean & radially symmetric point spread function, with a classical cross due to the simple cross-shaped secondary mirror support structure.

esahubble.org/images/potw102…

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(Question for historians: when did cross-shaped stars start to enter art & the public consciousness? After the invention of telescopes with cross-shaped secondary supports or before? 🧐]

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But #JWST with its hexagonal, jaggy, segmented primary, & tripod secondary mirror, is going to have a far funkier snowflakey point spread function.

That won't affect its ability to do science, but it'll bring a whole new aesthetic to space images.

jwst-docs.stsci.edu/jwst-near-infr…

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As a closing example, here's a simulation I made quite some years ago, showing a star cluster at 8kpc in three JWST wavelengths (1.2, 1.6, & 2.2 microns).

The dynamic range has been compressed so you can see the faint wings of the stars, but still, quite interesting 🙂

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To be clear, that's just a small 820x820 pixel sub-section of a much larger 4096x4096 pixel simulated NIRCam short-wavelength image, & there is no nebulosity or background in there.

Personally, I think JWST images will be spectacular, but they are going to be different.

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Anyway, enough said for today – the final major deployment of #JWST has taken place in the meantime (hooray), so we now have a full telescope to enable all that spatial resolution & funky PSF goodness.

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