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The current largest digital CCD camera is the Vera C. Rubin Observatory, which has a whopping 3.2 gigapixels with a pixel size of 10 micrometers. In contrast, Agfa 10E56 holographic film has a resolution of over 4,000 lines/mm—equivalent to a pixel size of 0.125 micrometers.

It makes me think. Will it be possible to use a chemical image sensor to achieve a nanometer pixel size?

Between 1983 and 2006 the Digitized Sky Survey(DSS2) produced 1.1-gigabyte images (23,040 x 23,040) of 15 micrometers corresponding to 1.0 arcseconds using Photographic-plates. One of their challenges was storage space. They were forced to use a lossy adaptive algorithm to shrink the output size, during which data was lost.

But since 2018, we can produce 7 nanometers chips via the Photolithography process. Can the same technology be used for image sensors? What can we do in 2021?

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    $\begingroup$ What a fascinating question! Extreme Ultraviolet light, phase-shifting masks, absurdly high numerical apertures (greater than unity by definition using immersion) and fancy pattern-doubling processes during etching are what get us to the tens of nanometer and below world. I suppose you could do this with a space telescope using EUV or X-rays. Somewhere in Stack Exchange I remember writing about daguerreotypes and/or making images by projecting images on to a dish of algae, but I can't find any of that right now. $\endgroup$ – uhoh Jan 5 at 16:27
  • $\begingroup$ Even if that film has a resolution of 4,000 lines/mm, that doesn't mean one can generate 4,000 lines/mm in visible light very easily. If you have two counter-propagating 500 nm green laser beams, they will produce a standing wave intensity pattern of that spatial frequency. But that won't happen at the focal plane of a telescope. $\endgroup$ – uhoh Jan 5 at 16:32
  • $\begingroup$ @uhoh can you correct or prevent it? Check out my other question about the theoretical limit of image sensors $\endgroup$ – Ilya Gazman Jan 5 at 17:07
  • $\begingroup$ Correct or prevent what? $\endgroup$ – uhoh Jan 5 at 19:18
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    $\begingroup$ @IlyaGazman your question has inspired me to ask Is it possible to use something besides emulsion to directly record the image of a nighttime object using a telescope? $\endgroup$ – uhoh Jan 21 at 12:50
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Is it possible to use Photolithography for telescope image sensor?

Sure, in the sense that CCDs and similar devices are already made using photolithography, and have been for decades.

But since you then go on to ask:

Will it be possible to use a chemical image sensor to achieve a nanometer pixel size?

it seems that your focus is on the idea that increasing resolution comes from pixels being as physically small as possible -- which is not actually true. There wouldn't actually be any benefit for image sensors in astronomy to have nanometer-sized pixels.

The measurement scale for images of the sky is angular (radians, degrees, arc minutes, arc seconds) and so is the scale for determining limits of resolution. Typically, we talk about this in terms of the point-spread function (PSF), which describes the blurring imposed by the atmosphere and the optics of the telescope and is usually characterized by its full-width at half-maximum (FWHM). The fundamental (diffraction) limit on resolution for a telescope is FHWM in radians $\approx 1.2 \lambda/D$, where $\lambda =$ the wavelength of light and $D =$ the diameter of the telescope's aperture (i.e., the diameter of the main mirror). For a wavelength of 500 nm (green) and a telescope mirror of 10 m, this means FWHM $\sim 0.01$ arc seconds.

If your telescope is on the ground, it will be looking through the atmosphere, which imposes extra blurring, giving you a PSF with a larger FWHM. Even at the best sites, you are very unlikely to do better than FWHM $\sim 0.5$ arc seconds. (Adaptive optics can correct this for small patches of the sky, but then you still have the ultimate diffraction limit from the telescope diameter.)

The second thing to understand is that the actual image of the sky that is formed on the detector can be scaled up or down (magnified or reduced) using the optical design of the camera (separate from the telescope itself). This is what determines the angular scale of the final image (e.g., arcsec/mm); combined with the physical size of the pixels, this determines the angular size of the pixels in the image (e.g., arc seconds/pixel). This in turn determines how big your pixels are relative to the size of the FWHM, so we can talk about pixels/FWHM as a potential measure of resolution.

Now, at this point you might be thinking, "But surely more pixels/FWHM will always be better!" This is, alas, only true up to a point, because of the Nyquist Sampling Theorem. This tells you that in order to recover the maximum possible spatial information in an image, you need pixels small enough that two of them cover the FWHM. But -- and this is key -- you can't gain anything extra with pixels smaller than that size. (There are practical considerations having to do with square pixels sampling round PSFs, so that one can argue that it's slightly better to have, say, 2.5 or 3 or pixels per FWHM. But there's no gain to be had by going from 2 or 3 pixels per FWHM to, say, 10 pixels per FWHM.)

One way to think about it is this: going from $\sim 2$ pixels/FWHM to 10 or 100 pixels/FWHM (e.g., by making really small pixels) is like taking a blurry photograph and enlarging it: you just get bigger blurs (more pixels per FWHM), not better resolution.

So once you have pixels small enough that -- in combination with the camera optics -- you get $\sim 2$ or 3 pixels per FWHM, you're done: you cannot do any better than that. And since we can build cameras (like that for the LSST) using existing CCDs which achieve this, there's no point in trying to make physically smaller pixels for CCDs.

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  • $\begingroup$ Thank you, I have been struggling for weeks now, trying to understand this. I was missing the part that the image on the detector can be optically magnified. $\endgroup$ – Ilya Gazman Jan 21 at 13:28
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The pixel size is not a major constraint on the imaging capabilities of an astronomical telescope. The angular resolution of the image is limited by diffraction at the aperture of the telescope. For a reasonable pixel size, the telescope geometry can then be designed so that each pixel corresponds to a region of sky smaller than that angular resolution, so that making the pixels smaller would gain you very little.

Responding to a comment. A diffraction limited telescope with an aperture of $d$ observing at a wavelength of $\lambda$ has (at best) an angular resolution of $\lambda/d$ radians. So if it has an effective focal length of $l$, the smallest useful pixel size will be around $l\lambda/d$. The effective focal length depends on the whole optical setup and will usually be designed to make this size big enough.

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  • $\begingroup$ Can you please tell me what would be the smallest effective size of a pixel in an x-ray telescope, for example, the XMM-Newton? $\endgroup$ – Ilya Gazman Jan 10 at 20:00
  • $\begingroup$ If by “effective size” you mean physical size, then for XMM-Newton it’s 40 micrometers. $\endgroup$ – Peter Erwin Jan 10 at 23:59
  • $\begingroup$ I don't know much about X-ray telescopes, but their resoution is probably limited by how accurately the X-rays reflect from the surface of the mirror, or by aligment of the multiple mirrors, rather than by diffraction. $\endgroup$ – Steve Linton Jan 11 at 14:20
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    $\begingroup$ Can you please provide a mathematical formula for a reasonable pixel size compared to the wavelength of light and the lens's aperture diameter? $\endgroup$ – Ilya Gazman Jan 14 at 21:03

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