Filters

Filters are used in imaging systems to restrict the observed wavelength range. Using multiple filters thus provides color information on the object being studied. Generally, filters are classified as broad band ( $\mathrel{\vcenter{\offinterlineskip \hbox{$>$} \kern 0.3ex \hbox{$\sim$}}}1000$Åwide) medium band (100 $\mathrel{\vcenter{\offinterlineskip \hbox{$<$} \kern 0.3ex \hbox{$\sim$}}}1000$ Å), or narrow band ( $1\mathrel{\vcenter{\offinterlineskip \hbox{$<$} \kern 0.3ex \hbox{$\sim$}}}100$ Å). Broad band filters work by using colored glass, which has pigments which absorb certain wavelengths of light and let others pass. Bandpasses can be constructed by using multiple types of colored glass. These are generally the most inexpensive filters. Narrowband filters, on the other hand, work by the principle of interference, and are often called interference filters. They are made by using two partially reflecting plates separated by a distance $d$ apart. The priciple is fairly simple:

Interference filter diagram When light from the different paths combines constructively, light is transmitted; when it combine destructively, it is not. Simple geometry gives:

$$m\lambda = 2nd \cos \theta$$

It is clear from this expression that the passband of the filter will depend on the angle of incidence. Consequently narrowband filters will have variable bandpasses across the field if they are located in a collimated beam; this can cause great difficulties in interpretation! If the filter is located in a focal plane or a converging beam, however, the mix of incident angles will broaden the filter bandpass. This can be a serious effect in a fast beam.

Since interference filters will pass light at integer multiples of the wavelength, the extra orders often must be blocked. This can be done fairly easily with colored glass.

The width of the bandpass of a narrowband filter is determined by the amount of reflection at each surface. Both the wavelength center and the width can be tuned by using multiple cavities and/or multiple reflecting layers, and most filters in use in astronomy are of this more complex type.

Note filters can introduce aberrations, dust spots, etc.