The absorption of a photon of wavelength 
(nm) in a superconductor
is followed by a series of fast processes in which the photon energy is
converted into a population of free charge carriers known as
quasiparticles in excess of any thermal population. For typical transition
metal superconductors this conversion process is of order of a few
nanoseconds. At sufficiently low temperatures (typically about an order of
magnitude lower than the superconductor's critical temperature 
) the number density of thermal carriers is very small and the number
of excess carriers N0 created as a result of the absorption of a
photon of wavelength is inversely proportional to the photon
wavelength. In general N0 can be written:
Here the wavelength is in nm and the energy gap is in meV. Thus in a
Tantalum superconductor at a temperature well below the critical
temperature, (
K and 
meV),
the initial number of free charge carriers 
created by
the photoabsorption of an optical photon is of order 
for a photon with 
nm. The fluctuations in the initial
number of quasiparticles N0 depends on the Fano factor F of the
superconductor and is the fundamental limit to the spectral resolution
(Fano 1947). The Fano limited wavelength resolution in Tantalum is 
nm
at nm. For a full description of the photoabsorption
process in a superconductor as well as the spectroscopic capabilities when
related to superconducting tunnel junctions the reader is referred to
Rando et al. (1992) and
Peacock et al. (1997b) respectively.
The quasiparticles produced after photoabsorption in a superconducting thin film can be detected by applying a d.c. potential across two such films separated by a thin insulating barrier; forming a superconducting tunnel junction (STJ). This potential favours the transfer of quasiparticles from one film to the other through quantum-mechanical tunneling across the barrier. The detector signal is therefore represented by the current developed by this tunnel process. After initial tunneling, a quasiparticle can tunnel back, therefore contributing many times to the overall signal (Gray 1978). On average each quasiparticle will contribute <n> times to the signal. Hence the number of effective charge carriers N which appear to have been created is N = <n> N0 . Further experimental details of the characteristics associated with this multiple tunneling, which is equivalent to an internal amplification within the junction, can be found in Poelaert et al. (1996).
The initial fluctuation in the number of charge carriers created in the photoabsorption process combined with the tunnel noise (Goldie 1994), associated with the multiple tunnelling of charge carriers across the barrier, leads to an overall limiting resolution for a perfectly symmetrical junction of the form:
Here the Fano factor F can be assumed to be 
, considered typical
of many of the transition metal elemental superconductors such as tantalum
(Rando et al. 1992). Thus for tantalum based STJ's the tunnel limiting
resolution for the case when 
is 
nm
for nm.
At least two other components due to the readout noise of the analogue
electronics 
) and spatial non-uniformity's
),must also be added to a first approximation in
quadrature,resulting in the measured resolution 
.
The electronics component can be determined from the measured full width
at half maximum 
of an average test charge 
injected into the preamplifier with the STJ in circuit, such that
.