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Change due to uncollimated light

Utilising the filter in uncollimated (i.e. convergent or divergent) light involves slightly more complex considerations. Here, light enters the filter at a range of angles, so that different rays undergo unequal wavelength shifts. This results in not only a central wavelength shift, but a broadening of the bandwidth and lower peak transmission.

As a rough approximation, relatively uniform beams (with full cone angles less than 20) will undergo peak shifts of aproximately one half of that which would be predicted for a collimated beam at the maximum angle of incidence of the cone.

The filters were specified for a focal ratio of 4.5, having a maximum angle of incidence of the cone of , and of effective refractive index 1.6 (see F.6).

Substituting these values in the equation,

The focal ratio of the INT prime focus is 3.29, which gives a maximum angle of incidence of the cone of , so, substituting again into the equation,

Therefore, at the INT prime focus, the central wavelength (i.e. the wavelength of peak transmission) is shifted towards shorter wavelengths by 0.06% from the specified central wavelengths. For example, for an filter with specified central wavelength 6560Å, the effective central wavelength will be 6556.1Å.