It should be noted that a manufacturer may identify an add-on telescope as having a magnification M, where in fact the relationship between this and the new FOV will be simply

Φ′ = Φ/M (4.5)

This is equal to the sine of the half angle a ray of light passing through the edge of the aperture stop of a lens makes with the optical axis at the image plane (see Figure 4.4), i.e.,

NA = sin(u) (4.6)

where u is the angle the extreme ray makes with the optical axis. The significance of the NA is that it is the parameter (other than the lens transmission) that determines the relationship between the radiance of an object and the irradiance in the image of that object. The relationship for a lens with a circular aperture is

I = π.W.t.(NA)2 (4.7)

where I is the irradiance (i.e., watts m−2) in the image plane produced by a radiance W (watts m−2 steradian−1) in the object and t is the lens transmission. Note that t will in general vary with wavelength.