Implications of the grating equation: order overlap
A light source is incident on a grating at a particular angle, α. We observe it at a particular angle, ß. That means that nλ is a constant for fixed geometry. But that does NOT mean that a fixed geometry gives us just one wavelength at a time. Rather, n can be any integer, and so there is a family of wavelengths all of which are transmitted to a detector at once. Suppose we choose d, α, and ß so that nλ = 1.2 µm or 1200 nm. The wavelengths that reach the detector are:
Well, isn't that embarrassing! We get at least 7 different wavelengths playing on our detector. This is called order overlap. ALL gratings suffer from it. There are a number of ways to overcome the problem.
- Use a light source that generates only one of the passed wavelengths.
- Use a filter to block all wavelengths except those desired.
- Use a second grating, such that the wavelengths passed by the second grating and those passed by the first overlap only for one or a few wavelengths (if nλ = 1200 nm for one grating and nλ = 1000 nm for the other, 6th order for the first grating and 5th order for the second overlap, but none of the lower orders both constructively diffract the same wavelength at the chosen angles).
- Cross-disperse with a prism.
- Choose a detector that can only sense the desired wavelength.
- Air absorbs below 200 nm; glass and many plastics absorb below 350 nm. Let these act as filters.