Grating To Sensor Calculator

Courtesy of Tom Field at Field Tested Systems

Use the calculator on this page to help you determine the optimal setup for your Star Analyser grating.

The first thing is: don't worry about getting your setup exactly right. The tolerances in spectroscopy with the Star Analyser are very forgiving. Use the calculator here to come up with approximate settings, and then go out and have fun capturing spectra!

The default values in the Input section of the calculator shown below are sample values for the Star Analyser 100 (SA100) grating used with a typical 8" SCT and a small video camera. To use the calculator, replace the sample values with values that describe your own equipment. (We recommend the default value of 3 arcseconds in the Seeing field, unless you know that your local conditions specifically call for a different value.)

If your Input values are out of range for satisfactory performance, a red message offers advice on how to modify your setup. To eliminate a red message, change your setup to modify one or more of your input values. For instance, you might shorten or lengthen your camera's nosepiece (if any), or add our 10mm spacer, to change the Grating to Sensor value. Or you could use a focal reducer to change the Telescope Focal Ratio.

NOTE: Using the Star Analyser as an "objective grating" on the front of a DSLR camera lens is a special case. Click here to scroll to an objective grating discussion at the bottom of this page.

If there is no red message, you can capture good spectra with your setup. You might see other messages that make optional suggestions for getting even better results. The fine tuning described in the optional messages is not required, but it is worth thinking about. Often these messages point out a simple change which can significantly improve the quality of your spectra.

The Output section of the calculator describes the performance you can expect. The key Output fields show you how the grating performs with your Input values:

In some applications it can be difficult to achieve optimum spacing using the SA100. In these cases the Star Analyser 200 (SA200) is often helpful. The SA200 generates the same spectrum length at half the spacing.

Where optimum spacing is feasible with the SA100, it should be chosen for best performance. However, there are two cases where the SA200 is particularly useful:

If you have questions, please don't hesitate to post them to the Star Analyser Yahoo group

The video below shows an example of the calculator in use.


Input
mm
f
arcsec
mm
um
pixels
Output
mm
pixels FWHM
Angstroms/pixel
Angstroms
.

How can the calculator improve your setup?

If your Input values result in all three messages showing a green OK, you have optimized your settings. If not, you can try out various changes in the calculator before actually making changes in your equipment. You might add one or more spacers. Or change the focal ratio. Once you achieve settings that satisfy you, you can adjust your equipment accordingly.

Consider the sample Input values. (If you have already changed those values, click Reset to see them again.) They result in a Dispersion value of 14.0 Angstrongs/pixel. No red messages appear, so the setup is satisfactory for capturing good spectra.

And yet the Dispersion field shows the message "Resolution could be improved..." This is not a critical problem which prevents you from using the grating. However, it explains changes you could make to get better results. For instance, you might add a 10mm spacer. To see the effects of doing that, change the Grating to Sensor Distance (field 5) from 40 to 50. Increasing this distance optimizes the resolution by spreading out the spectrum. You can see this in the Dispersion value (field 10), which changes from 14.0 to 11.2.

Now the "Resolution could be improved..." message is gone, replaced by the green OK. But the message next to the Spectrum Coverage (field 11) is no longer the green OK. The new message, "Difficult to fit..." is not red, so this setup too would be satisfactory for capturing good spectra. However, you could still improve on it. Instead of adding a spacer, you might try changing the Telescope Focal Ratio (field 2). To do this, click Reset (to undo the spacer) and then change field 2 from 10 to 6.3.

Now all three messages are a green OK. You have found an optimum setup for use with this equipment.

You could, of course, go even further, but that is not always a good idea. As we mentioned above, useful values for Dispersion (field 10) are typically in the range of 7-20 Angstroms/pixel. The smaller this value, the more spread out your spectra. To make this value smaller, you can increase the Grating to Sensor Distance (field 5) or use a Grating (field 4) with more lines/mm.

It's tempting to make this value smaller and smaller, in order to spread the spectra farther and farther. However, just as when you add more and more magnification to your telescope, there is a point beyond which the image degrades due to optical limitations and merely gets dimmer and dimmer. Even before that, it is important to remember that the more you spread out a spectrum, the fainter it gets, requiring more exposure time. The optimum value depends on your particular setup. The calculator warns you if you might be using too much dispersion.

Where should you start?

We recommend that you start by capturing the spectrum of a midrange "easy" star: a type A star such as Vega. The spectra of these stars have very clear Hydrogen Balmer lines, which makes calibration easy. Once you have calibrated a type A star, you can easily calibrate spectra of more difficult stars that don't have such clearly identifiable lines. To do this, use the zero order star image in a one-point calibration procedure. For a video example of this procedure, using RSpec software, click here.

What kind of resolution can you expect?

The best possible resolution is twice the dispersion, according to the Nyquist sampling theorem. So in theory, the best resolution you could get with a dispersion of 10 Angstroms/pixel is in the range of 20 Angstroms. However, there are other factors that affect the resolution before reaching this theoretical limit.

First of all, the resolution of any grating in a converging beam setup (or any other slitless system) is limited by star size. And once you apply enough dispersion to overcome the star-size limit, the resolution is limited by aberrations because the beam is not parallel through the grating. Increasing the dispersion further does not overcome these aberrations. It only magnifies the effect and makes the spectrum fainter.

In practice, the maximum resolution you can get when using a grating as described here, regardless of dispersion, is about R ~100-200. For instance, at 6000 Angstroms, this yields a resolution of 30-60 Angstroms. This maximum is independent of the number of lines/mm in the grating; that is, you cannot improve the resolution by switching from the SA100 to the SA200.

Doug West provides a more theoretical treatment of this topic, available here.

Objective Gratings

For an objective grating setup, such as mounting the grating on the face of a DSLR camera lens, set the Grating To Sensor Distance (field 5) to the focal length of the lens, and ignore any messages about the focal ratio (field 2). In this setup, the distance between the grating and the lens has no effect on the spectrum. However, it is usually best to mount the grating as close to the lens as possible, to minimize vignetting. The SA200 is optimised for the typical short  focal length zoom lenses found as standard on most DSLR. The SA100 however needs a telephoto lens to take full advantage of the additional resolution.  The optimum focal length for the SA200 is in the range 35-100 mm and for the SA100   70-200mm  (note these are the actual lens focal lengths not the 35mm camera equivalents).

The advantage of an objective grating setup is that, because the light in the beam from a distant star is parallel, the spectra produced are significantly sharper than those achieved with the grating between a telescope and a camera. In this setup you can gain resolution by lengthening the spectrum. Zooming your DSLR lens can achieve values as low as 3 Angstroms/pixel. (Here you can ignore the high-dispersion warning in the calculator.)

The disadvantage of an objective grating setup is that, because a DSLR's aperture is considerably smaller than that of most telescopes, it is suitable only for use with bright stars.

For a more in depth look at particular equipment configurations please visit threehillsobservatory.

© Copyright 2014 Field Tested Systems, LLC. Used with permission. (Version 1.02)