  We examine the mathematical and physical significance of the spectral density
sigma(w) introduced by Ford in Phys. Rev. D38, 528 (1988), defining the
contribution of each frequency to the renormalised energy density of a quantum
field. Firstly, by considering a simple example, we argue that sigma(w) is well
defined, in the sense of being regulator independent, despite an apparently
regulator dependent definition. We then suggest that sigma(w) is a spectral
distribution, rather than a function, which only produces physically meaningful
results when integrated over a sufficiently large range of frequencies and with
a high energy smooth enough regulator. Moreover, sigma(w) is seen to be simply
the difference between the bare spectral density and the spectral density of
the reference background. This interpretation yields a simple `rule of thumb'
to writing down a (formal) expression for sigma(w) as shown in an explicit
example. Finally, by considering an example in which the sign of the Casimir
force varies, we show that the spectrum carries no manifest information about
this sign; it can only be inferred by integrating sigma(w).
