Main spectroscope parameters

Spectral resolution power (R)

The resolution (Δλ) of a spectroscope corresponds to the smallest observable details in the spectrum. It’s a quantity expressed in wavelengths (either nanometers or angstroms; 1 nm = 10 Å). Usually, we use Resolution Power (R) instead, which is a dimensionless quantity defined at a given wavelength (λ). In astronomical applications, the Power of Resolution is often given around the Hα line, at 656.3 nm, and is calculated as follows:

R = λ / Δλ

A spectroscope is generally considered to offer low resolution below R = 1000, and high resolution above R = 8000 (these values can vary greatly depending on the context in which you’re working – the figures given here correspond to the amateur environment).

A low-resolution instrument covers a wide range of wavelengths (e.g. the entire visible range), and enables faint objects to be observed; for a given magnitude, exposure times are significantly shorter in low-resolution.

Conversely, a high-resolution instrument will enable us to observe – for example – minute details in the profile of a spectral line, but at the cost of a smaller field of view, and a significantly longer exposure time. Over a full night of observations, you’ll see far fewer objects.

As a general rule, all Doppler shift measurements are almost exclusively high-resolution (only objects with very high radial velocities, such as quasars, are accessible at low resolution).

Slit size

The spectroscope entrance slit is the interface between the telescope and the spectroscope. This slit is (almost) always the object of an essential trade-off: on the one hand, you want to widen it to collect as many photons as possible, and on the other, you want to close it to increase resolution (the slit has a direct effect on the instrument’s resolution).

Ideally, the size of the slit should correspond to the size of the image of a star at the focus of the telescope. This depends on two parameters: the telescope’s focal length and the sky’s seeing at your observation site (seeing characterizes the sky’s turbulence). If you don’t know the seeing of your sky, or if you’re observing in an “ordinary” site, consider a seing of 3″ (arcseconds). In the best observation sites, seeing can be as low as one arcsecond.

The size (T in µm) of the image of the star at the focus of the telescope of focal length F (in mm) for seeing s (in arcseconds) is calculated by the following formula:

T = F . s . π . 1000 / (3600 . 180) = F . 0,00485

For a given telescope and site, we recommend using a slit at least as large as this value.
An example: in the case of an amateur telescope with a focal length of 2 metres and a good observation site (seeing 2.5″), the slit size will be of the order of 25µm (2000 x 2.5 x 0.00485 = 24.25).

The above calculation can only be made if you know the telescope you will be using. If not, you can also use the slot size to estimate the telescope’s maximum diameter.

Aperture (F-ratio)

A telescope (or refractor) is defined by its focal length and diameter, and the ratio between these two values (F-ratio) is often given as its “aperture”. The more open a telescope is, the brighter it is (and the more expensive it generally is, because it’s optically complex to make an open instrument).

A spectroscope also has the same aperture parameter, which indicates its ability to handle a more or less open input light beam.

We will always try to match the aperture of the spectroscope to that of the telescope; for example, if a telescope is F/8, prefer a spectroscope also at F/8. If we deviate from this ideal adjustment, the instrument will function correctly (it will produce quality spectra), but at the cost of a loss of efficiency, either in light (we lose photons) or in resolution (we could do better).

Other parameters

Beyond these three main parameters, there are a few others to consider when choosing your instrumentation. For example, we need to consider mechanical adaptation (draw-in, adapter rings), or sensor sampling. At this stage, however, these can be considered secondary elements. For further details, we recommend reading the “Succesfully Starting in Astronomical Spectroscopy – A Practical Guide”.

Which telescope to choose?

I already have a telescope

If you already have a telescope, it can advise you on the type of spectroscope to install.

1. You can then make a quick calculation of the optimum slot size (see previous paragraph). To put it simply, below 500mm in diameter, we consider ourselves to be in the “small telescope” range, which corresponds to most of Shelyak’s instruments.

200 – 300 mm telescope: Initiation range

2. If the diameter of your telescope is greater than 500mm, it’s useful to make slightly more precise calculations. Depending on your objectives, you’ll certainly have to choose between higher resolution (even if it means losing a little light), or limiting magnitude (at the cost of lower resolution).

Up to 500 mm diameter: Performance range

3. Above this diameter (> 500mm), consider a fiber-optic spectroscope, such as the eShel, or even the Whoppshel. Since, for a given resolution, the size of the spectroscope is proportional to that of the telescope, we quickly arrive at instruments that are bulky and heavy, and therefore subject to mechanical bending. Using an optical fiber between the telescope and the spectroscope separates these two elements, and keeps the spectro stable on a table. The optical fiber is typically 50μm in diameter (compared with most slits closer to 25μm), which is well suited to telescopes of 500mm and above. In the case of the Whoppshel, the fiber can even go up to 105μm in diameter (and thus telescopes in the 1m class and beyond)

Over 500 mm in diameter: eShel & Whoppshel

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I don’t have a telescope

1- Use a mirror telescope for spectroscopy. By design, these telescopes are purely achromatic, meaning they behave exactly the same at all wavelengths. These are the instruments that will best enable you to explore extreme wavelengths (UV and IR). There are currently two types of instrument on the market: Newton telescopes and Ritchey-Chrétien (RC) telescopes.

2 -To observe faint objects (low resolution), prefer an “open” telescope, i.e. with an F/D ratio of less than 5 (this is the case with Newtons, for example). Conversely, for high resolution, prefer a more closed telescope (F/8 or higher – RCs are generally at F/8).

High resolution: bright targets

If you’re interested in radial velocity measurements, or measurements that require you to observe details in a line profile (in emission or absorption), then you need to go for high resolution. Either the spectroscopes : UVEX, LHIRES III and eShel

 

Versatility (for experienced observers) :

If you have several answers to this same question, because you’re aiming for several types of observations (some high-resolution, some low-resolution), then you should go for a versatile instrument, like the UVEX.

There’s clearly a compromise to be found between limit magnitude and resolution. If you need both (high resolution and faint objects), then the only variable is the diameter of the telescope, because you’ll need to collect more light; that’s why cutting-edge research is done with very large-diameter telescopes.