5.5 In-orbit Sensitivity of the LWS - Detector Performance

The sensitivity of the LWS is based on the knowledge of the noise equivalent power (NEP), which is defined for each detector as the noise obtained in dark current measurements with 0.5 s integration time divided by the detector responsivity in A/W.

(5.1)

The noise figures are based on a measurement of the noise under dark conditions taken in revolution 650 (see Section 5.4). To obtain a noise figure 50 minutes of data were taken with the satellite pointing at a dark region of the sky and with a Fabry-Pérot in the beam with its etalons set non-parallel. The noise was estimated from the standard deviation of a Gaussian curve fitted to a histogram of the photocurrent values after deglitching. As most of the LWS observations, they have been performed using 0.5s reset times, which is equivalent to a 1Hz bandwidth.

To avoid making asumptions about the transmission of the telescope and instrument the LWS detector responsivity is not measured directly. Instead the instrument response is derived from the calibration source (Uranus) and its associated model spectrum; it is given as [AcmmW]. We can calculate the Noise Equivalent Spectral Density (NESD) directly from this value:

(5.2)

To convert this to NEP of the detectors requires knowledge of the telescope effective area and the instrument throughput. The instrument throughput was not directly measured on the ground and is complex to calculate. We therefore refer everything to the entrance aperture of the instrument by assuming knowledge of the instrument spectral resolution in grating mode and the effective area of the ISO telescope as a function of wavelength. This effective area has been calculated from an optical model of the ISO telescope and is given for the central wavelength of each detector in Table 5.5. The spectral resolution of the grating is measured from narrow emission line spectra. The calculated instrument NESD and NEFD (noise equivalent flux density) figures and the estimated instrument NEP are given in Table 5.5.

Table 5.5: In-orbit sensitivity of the LWS instrument.

Detector	Centre	Noise for	NESD	Telescope	NEP		cross over
		0.5 s resets	[10Wcm	eff. area	[10		flux
	[m]	[10A]	mHz]	[cm]	WHz]		[Jy]
SW1	46.13	4.17	4.43	2460	3.16	0.0046	260
SW2	56.11	3.83	7.75	2431	5.47	0.0046	1460
SW3	66.03	1.91	3.00	2346	2.04	0.0095	710
SW4	75.61	2.98	5.40	2262	3.55	0.0044	1530
SW5	84.68	2.13	4.28	2205	2.74	0.0044	1330
LW1	102.25	2.68	0.849	1922	0.980	0.0095	360
LW2	122.04	2.26	0.231	1838	0.254	0.0095	42
LW3	141.63	3.19	0.122	1838	0.135	0.0142	28
LW4	160.38	3.83	0.202	1753	0.212	0.0108	80
LW5	177.74	2.21	0.691	1583	0.656	0.0033	360

The instrument NEPs increased by an average of a factor of four compared to pre-launch values. A factor of two increase was expected as 0.5 s amplifier resets were used in-orbit, whereas in the ground testing the NEP was measured using 2 s resets and the noise is proportional to the square root of the reset time for resets up to about 4 s (Shaver et al. 1983, [38]). The increased NEP was also due to the decreased responsivity which many of the detectors exhibited in-orbit, some of which was due to the decrease in detector bias voltage (to reduce spontaneous spiking) and the effects of ionising radiation on the detectors. For further analysis of the detector performance in-orbit compared to that on the ground see Leeks et al. 2001, [25].

If the power falling on the detectors is low enough so that the noise is dominated by the detector read noise, then the signal-to-noise ratio expected in an integration time is given by:

(5.3)

In teh pther extreme, when the power falling on the detectors is high enough such that the noise is dominated by the shot noise in the photon stream, the signal-to-noise is given by:

(5.4)

The power at which the cross over between read noise and photon noise occurs has been derived in a study of the signal-to-noise ratio, performed using internal illuminators measurements (see Swinyard et al. 2000, [41] for more details). They are listed in Table 5.5.