For photometry of point-sources the power on the detector is decribed by:
is the flux of the point source in 
at the
selected wavelength;
is the fraction of the point spread function which passes
through the aperture and can be found in Table 2 and 4 of the IOM3.1.
C1 is a wavelength dependent parameter and is tabulated in Tab. 2.
The following parameters are represented by the factor C1:
For extended sources the total power depends on the surface brightness
of the source and the solid angle 
of the aperture, thus:
where 
is the flux density of the extended source in
, e is the obscuration factor by the secondary
mirror of the ISO telescope, where 
, and
is the solid angle of the aperture or array projected on the sky.
The values for can be found in Table 1.
The total noise is described by the following equation:
This includes an additional measurement for background subtraction so that the background and read-out terms are counted twice.
is the photon noise
for a point source:
Table 1:
Solid angles for PHT-P and PHT-S apertures and for individual
pixels of the PHT-C arrays. For PHT-C detectors the individual pixel sizes
are given in parentheses.
| PHT-P apertures | | PHT-S aperture | | |
[  ] |  | |||
| 5'' | 0.00461 | 24  24'' | 0.1354 | |
| 7.6'' | 0.01066 | |||
| 10'' | 0.01846 | |||
| 13.8'' | 0.03515 | |||
| 18'' | 0.05980 | |||
| 23'' | 0.09764 | |||
|
20 32'' | 0.14840 | |||
| 52'' | 0.49907 | |||
| 79'' | 1.15189 | |||
| 99'' | 1.80896 | PHT-C arrays | ||
| 120'' | 2.65779 | (per pixel) | ||
|
127 127'' | 3.73997 | C100 (43.5''x43.5'') | 0.44468 | |
| 180'' | 5.98002 | C200 (89.4''x89.4'') | 1.87820 | |
For extended sources the photon noise is:
The noise induced by the background 
is described by the same
formula, except that becomes the flux density of the
background:
is the detector noise and can be represented by a constant for
each detector:
Table 2: PHT-P and PHT-C In-flight sensitivity characteristics. The sensitivity parameters C1, C2 and C3 are defined in the equations given in this section.
| filter | C1 | C2 | C3 |
[  ] | [  ] | [  ] | |
| P1 | |||
| 3.29 | 1.5 | 1.7 |  |
| 3.6 | 7.1 | 3.8 | |
| 4.85 | 7.3 | 3.8 | |
| 7.3 | 9.8 | 4.5 | |
| 7.7 | 2.0 | 2.0 | |
| 10 | 2.3 | 2.2 | |
| 11.3 | 0.79 | 1.3 | |
| 11.5 | 4.7 | 3.1 | |
| 12.8 | 1.6 | 1.8 | |
| 16 | 0.80 | 1.3 | |
| P2 | |||
| 20 | 5.1 | 3.4 |  |
| 25 | 4.6 | 3.2 | |
| P3 | |||
| 60 | 0.60 | 0.70 |  |
| 100 | 0.88 | 0.85 | |
| C-100 | |||
| 50 | 0.51 | 0.12 |  |
| 60 | 0.66 | 0.13 | |
| 70 | 0.73 | 0.14 | |
| 90 | 1.53 | 0.20 | |
| 100 | 0.96 | 0.16 | |
| 105 | 0.61 | 0.13 | |
| C200 | |||
| 120 | 0.31 | 0.29 |  |
| 135 | 0.72 | 0.44 | |
| 160 | 1.05 | 0.53 | |
| 180 | 0.55 | 0.38 | |
| 200 | 0.23 | 0.25 | |
Now the integration time can be calculated from Eqn. 2. The
constants C1, C2, and C3 are tabulated in Table 2.
The constants C1 and C2 have been determined from a signal and noise analysis
of relatively long staring measurements of calibration stars ( 
sec).
C3 is normally determined from a noise analysis of dark measurements. For
consistency with IOM3.1 we include in this term uncertainties the observer
will face with faint source measurements, like flat-field accuracy, signal
drifts, and also partly sky structure, when subtracting the considerably
brighter background.
These have been obtained from dedicated faint source measurements.
Scaling sensitivity limits from longer measurement times to shorter ones
(of less than 128 sec) does not always follow Eqn. 2, see
Section 5 for more detail.
