Broadband spectral photometry
 

The response of any detector system to energy falling on to it obviously depends on the strength of the radiation received. It also depends on the frequency distribution of the energy and on the spectral sensitivity of the detector. In many instruments, rather than using the full spectral range of the detector, optical elements, such as colour filters, may be applied to select specific spectral zones for measurement. The variation with wavelength of the relative response of the system may be written as S(λ) and may be displayed graphically (see figure 1). The width of the embraced spectrum, Δλ, may be defined as the spectral interval between points on the S(λ) curve where the response is reduced to a half of the maximum value and this is termed the full-width half maximum or FWHM. Each passband can be ascribed an equivalent wavelength, λ₀, defined by

this being the mean wavelength, weighted according to the response curve. To a first order, brightness measurements made using passbands which are narrow in comparison to the broader energy spectrum of a source can be considered as the monochromatic brightness value at the equivalent wavelength.

Figure 1. An example of the relative spectral response of a detector system normalized so that its maximum
equals unity.
Let us suppose that we have been given some equipment and we use it to measure the brightnesses of stars. By defining a standard star, or a set of standard stars (see discussion relating to Pogson’s relationships, a magnitude scale can be set up and by comparing the response of the system to the standard star and all of the stars in turn, each star can be assigned a magnitude. If the same stars now have their brightnesses measured by a second detector system, providing a different passband and different equivalent wavelength, it will be found, in general, that the stars do not appear on this second scale at the identical positions at which they appeared on the first scale. This is a reflection of the fact that each star has an energy envelope defined by its temperature and that the signal from the detector is a function of the amount of energy that falls on it within the spectral range to which it responds. Thus, each detector system has its own magnitude scale.