Normalization in radiometry

When the absolute value X = ?Xmicro(micro).dmicro of incident radiation cannot be obtained from the output V = ?Xmicro(micro) R(x)(micro) dmicroof a selective instrument, with nonuniform responsivity R(x)(micro) = V(micro)(micro)/X(micro)(micro), because the incident distribution X(micro),(micro) is not known, recourse is had to various normalization methods. There is continuing confusion over the significance of a normalized quantity X(n) = V/R(n) and its relationship to the absolute value X. This problem, first discussed for the familiar spectral parameter micro = lambda, is analyzed generally for different normalization methods, in terms of any radiometric quantity X, distributed as Xmicro (micro) identical withdX/dmicro with respect to any radiation parameter a. Peak normalization, most often used, gives conservative, lower-bound values. Bandwidth normalization is also discussed. It is recommended that units for all normalized quantities, such as lumens for photometric quantities, be distinctively designated, e.g., normalized watts or [NW], to emphasize that, without at least the relative incident distribution x(micro) (micro)= X(micro) (micro)/C, they cannot be directly converted to absolute quantities.