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Is there something like a Moore's law for spectral resolution? Maybe a chart from which one could extrapolate?

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    $\begingroup$ Across a given part of the spectrum, or in general? A century ago people were doing good atomic spectra measurements… $\endgroup$
    – Jon Custer
    Feb 4, 2023 at 23:41
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    $\begingroup$ I'm particularly interested in en.wikipedia.org/wiki/Doppler_spectroscopy, so the improvement in the R-value/radial velocity shift detection sensitivity $\endgroup$
    – 2080
    Feb 5, 2023 at 6:40
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    $\begingroup$ Note that you don't in general get any improvement in Doppler sensitivity once you have resolved the features being used for the measurement. $\endgroup$
    – ProfRob
    Feb 5, 2023 at 11:34
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    $\begingroup$ Edit to say "astronomical spectrographs". If you want to discuss spectrographs in general then I'm not sure Astronomy SE is the right place. However, a different SE is where you might get a more interesting answer since astronomy users are not the ones demanding the highest resolution. $\endgroup$
    – ProfRob
    Feb 5, 2023 at 11:37

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There are probably two aspects to this. First, is there a progression in the technological capability to produce spectrographs that are of higher and higher resolution - almost certainly. Second, is there a progression in the resolving power of spectrographs in use at astronomical observatories. Not really, or not in the last 30 years or so anyway.

The problem with a comparison to Moore's law is that whilst there is an insatiable demand for faster and faster computing there is not so much demand for ever-higher resolution spectroscopy in astronomy. Instead the development has been more towards: extending the wavelength coverage, especially into the infrared; extending the fields of view and multiplexing capabilities - by that I mean the development of multi-object spectrographs and integral-field spectrographs - improving the throughput; and finally, an increase in the stability of spectrographs, driven mainly by the exoplanet boom.

The first proper spectrograph I ever used professionally was the "walk-in" coud'e echelle spectrograph at the Mount Stromlo 1.9-m telescope (sadly burned down) in the 1990s. This had a 222-inch collimator focus and a 130-inch camera focus! It had already been there for many(?) years and had a usable resolving power in excess of 100,000. At the same time, the Anglo Australian Telescope (as it was then) had an Ultra-high resolution facility, capable of a resolving power of $10^6$ over a narrow wavelength range.

Most of the high resolution spectrographs today, used chiefly for detailed chemical abundance analysises and observing exoplanet hosts, have resolving powers in the range 50,000 to 120,000 and indeed the new high-resolution spectrograph for the E-ELT (ANDES) will have a resolving power of 100,000.

The reason why demand for higher resolution is not there for the study of stars is that the intrinsic broadening of the spectral lines of a star is already well-resolved at a resolving power of 100,000. Going to even higher resolutions is not especially useful for most studies and results in narrower wavelength coverage, lower throughput and lower signal to noise ratios.

Where there is an application is in studies of the interstellar medium, where lines can be much narrower, or in spatially resolved studies of the solar photosphere (where one has lots of photons to play with), or for doing transmission spectroscopy through (relatively) cool exoplanet atmospheres. An interesting summary of the state of the art and the different instrumentation options to produce spectrographs with a resolving power of $10^6$ is presented by Zhu et al. (2020), but given that such resolving powers were reachable 30 years ago, I think the principle improvements are in throughput, stability and wavelength coverage and there isn't a (recent) Moore's law that applies to the resolving powers that are used.

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Is there something like a Moore's law for spectral resolution?

This is an interesting question! I'm going give a defense for a qualified "yes" as a partial answer, but it will take some time to track down an actual plot.

Here's a roadmap for someone interested in this topic:

Prisms

Newton (and certainly many others) experimented with dispersion of the colors of sunlight using a prism almost 400 years ago. See for example Did Newton ever use filtered or prism-dispersed colored light to view "Newton's rings" or other thin-film interference effects? Since the Sun is a star and polymath Newton an astronomer among other things, I think we can count this kind of experiment as an early (or first) data point. Exactly where in time and resolution is impossible to pinpoint, so perhaps make it a fuzzy cloud, or choose a first publication.

Once an optical system and a slit is introduced, a prism spectrometer can overcome the angular spread of the Sun's large disk and a higher resolution spectrum can be obtained. Once photographic emulsion is developed, it can be recorded.

Diffraction grating-based spectroscopy

This came next I assume.

This answer to Where does "the grating equation" come from? Does it have a another name? cites

A history of 19th century spectroscopy, Appendix F to his book Group Theory and Physics, Cambridge UP, 1994.

but I don't know when the first spectrum of the Sun, or another star was seen, photographed, or published.

However, this is where it gets more Moore's Law-like. Resolvance of Grating scales as

$$\frac{\lambda}{\Delta \lambda} = mN$$

where $N$ is the total number of grating grooves illuminated and $m$ is the diffraction order used. The resolvance or resolving power might be a few hundred for a low resolution instrument and between 10,000 and 100,000 for a high resolution Echelle gating-based spectrograph.

The reason that grating performance might follow a Moore's Law-like trajectory is that they have to be manufactured using technology that ensures strict periodicity. While high spatial frequency "jitter" in the placement of grooves might add some haze, it's the very low spatial frequency variation in groove placement (and to a lesser extent, depth) that was limiting resolution.

Traditionally blazed gratings were manufactured with a mechanical ruling engine.

H. A. Rowland with his ruling engine for diffraction gratings (Jones 1988)

H. A. Rowland with his ruling engine for diffraction gratings (Jones 1988)

Source: Researchgate, chapter Compliant Manipulators in book: Handbook of Manufacturing Engineering and Technology (pp.1-64) Publisher: Springer Editors: Andrew Nee (2014)

Groove placement was controlled by incrementing a drive screw, and gratings were plagued by spatial variations corresponding to complete rotations of this screw.

So the improvement of grating resolution was, at least during some period of time in the history of spectroscopy, controlled by these drive screws and techniques to overcome periodic variations in groove phase.

Once laser interferometers and quadrature detection and active feedback became available in manipulation and mechanical translation, manufacture of blazed gratings was no longer limited in resolution by the screws that drove the instrument.

Holographic gratings were a parallel technology that did not rely on a mechanical process, but instead "wrote" the entire grating at once using the interference pattern of two beams split from a monochromatic source of light. These of course had their own distortions and low frequency phase noise, and several techniques were developed to flatten them as well.

Etalons

Fabry-Perot etalons have their own timelines and applications.

You will see these primarily used in Fourier transform spectroscopy for longer wavelength applications (microns to millimeters) where grating-based instruments would be too large to be practical.

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  • $\begingroup$ @EdV thanks! I just copied/pasted from the source but I should have caught that. $\endgroup$
    – uhoh
    Feb 5, 2023 at 20:00

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