Figure 4.1: Schematic diagram of the
integrating amplifier circuit used in the LWS detectors.
The LWS uses photoconductive detectors in which the radiative input power P
is converted into a photocurrent I. The detectors are used in an integrating
amplifier circuit, shown schematically in figure 4.1,
whereby the photocurrent
is integrated on the gate of an FET. The output voltage 
of the FET
is read non-destructively at a frequency of 88 Hz and the amplifier is
periodically re-set by shorting the gate to earth via switch S1. It is clear
from the diagram that, as the voltage on the gate of the
FET charges, the effective bias 
changes across the detector,
introducing a non-linearity into the response. In the present scheme, this
is taken into account by allowing the responsivity S(t) to vary linearly with
bias:
where 
is the applied bias voltage. The output voltage
- referred for convenience to the input of the FET (i.e. divided by the FET
gain) - then obeys the equation
where 
is the residual charge left on the gate during the re-setting
process, H(t) is the Heaviside function and
being the dark current immediately following a re-set. If equation
4.2
is solved for initial current 
, the power P falling on the detector can
be recovered from the last of equation 4.3, provided
- obtained from
calibration observations - and - obtained from making a
measurement with the detectors blanked off - are known.
The solution to equation 4.2 is
To second order in t, equation 4.4 becomes
where
If a second-order fit is made to the output of the amplifier, the required current Io can be recovered from the first- and second-order coefficients
As stated above, this is the present scheme for extracting the signal falling
on the detectors. It has at least two weaknesses, however. First, the
responsivity S is not linear in the effective bias, as assumed in equation
4.1.
This means that the interpretation of the right-hand side of equation
4.7 as
the initial photocurrent is suspect, particularly for strong fluxes. Secondly,
it is found that the behaviour of the output voltage immediately after re-set
is not as given by equation 3 but is somewhat erratic; in order to deal with
this, about 150 ms the data after are ignored in fitting the second-order
polynomial to the data, thereby sacrificing potential information.
Because of this, improved methods of extracting the signal are being sought.
The favoured scheme at the moment is not to attempt to base the extraction of
the input signal on an understanding of the behaviour of either the detectors
or the circuit. Instead, all the data of an integration ramp are fitted with
a low-order polynomial which is then used to estimate the total change of
output voltage 
in time 
.
The quantity 
is then calibrated
empirically against signals of known strength.
