This section provides the relation between the count rate on a XDL detector and the intensity of the incident solar radiation. The information in this section is preliminary and is intended only for order-of-magnitude estimates of the count rates.
Consider a single spectral line, and let 
be the intensity of the
spectral line integrated over wavelength (in photons s
cm
sterad
). Consider an area on the detector which has a length 
in
the spatial direction and which is sufficiently wide in the wavelength
direction to encompass the entire spectral line. Let R be the total count
rate in this area (counts per second). Then the relation between 
and R is:
where C
is an efficiency factor (to be discussed below); 
is the
height of the UV telescope mirrors (50 mm); 
is the telescope focal
length (750 mm); r is the heliocentric angle in units of the solar radius
(which can be varied using the mirror mechanism);
is the effective
width of the illuminated portion of the telescope mirror; 
is the length
of the area on the detector (in mm); and 
is the entrance slit
width (variable from about 0.025 to 0.3 mm). The factor 100 converts the
collecting area from mm
to cm
. The width of the illuminated portion
of the mirror is approximately given by
where 
is the distance between the external occulter and the telescope
mirror (1700 mm). (This assumes that the mirror is over-occulted by 1 mm,
and also assumes that the instrument roll axis is pointed at solar disk
center.) V is a factor that accounts for changes in throughput across
the optical surfaces and currently is set equal to 1.0. In order to observe heliocentric positions less than
or near 1.33 R
it is necessary to offset-point the instrument roll axis
relative to the sun-center direction.)
The efficiency factor 
is given by:
where 
is the reflection coefficient of the telescope mirror; 
is the fraction of incident radiation diffracted by the grating into the particular
grating order; and 
is the detector counting efficiency.
In the case of the redundant Ly-
path, an additional factor is the
reflectance of the convex mirror, 
. Estimated values for these
quantities are provided in Tables 11-13 for the Ly-
and O VI channels
and the redundant Ly-
path respectively.
The following are a few examples of count rates
and appropriate integration times for several typical
observations. Consider a measurement of the HI Ly-
profile at 2.5 solar radii with 0.28 
(.05mm)
spectral resolution elements and 14 arcsecond (.05 mm) spatial elements. Using the efficiencies in
Table 11, we find that the count rate (R) is:
Using the coronal hole intensity in Table 3,
we obtain a total count rate of 1.2 
. At this rate
it would take about 2 hours to accumulate 10,000
counts in the line. The streamer intensity
from Table 10 yields a total count rate of 11 
.
At this rate it would take about 14 minutes to
accumulate 10,000 counts in the line. Hence, SOHO should have reasonable count rates for observing
HI Ly-
profiles in coronal holes
up to 2.5 solar radii and beyond.
An OVI 
1032 observation of total line intensity at 2.5 solar radii could
be done, for example, at 1 arcminute (0.2 mm) spatial
and 0.74 
(0.2 mm) spectral elements. Using Table 12, we find that:
Using the Tables 3 and 10, we obtain total
count rates of 0.32 
and 3.6 
in a coronal hole
and in a streamer, respectively. An integration time of
52 min. would be required to accumulate
1000 counts in the hole and 4.6 min. would be
needed for the streamer observation.
Table 11. Efficiencies for the Ly-
Channel
Table 12. Efficiencies for the OVI Channel
Table 13. Efficiencies for the Redundant Ly-
Path
* rough estimate
To measure the spectral line profile of
OVI 
1032 at 1.5 solar radii, a resolution element of
0.0925 
(0.025 mm)
could be tried.
The spatial resolution could be
degraded to about 5 arcmin (1.0 mm). Using Table 12, we find that:
Using Tables 3 and 10, we obtain total count rates of 2.3 
and 68 
for a coronal hole and
a streamer, respectively. Integration times of 1.2 hours and 2.5 min. would be required to accumulate
10,000 counts in the coronal hole and streamer, respectively. It may be desirable to scan the line
across the pixels or use a smaller slit width. This would require additional time, but probably not
an unacceptable amount. Hence, line profile measurements of
minor ions appear to be possible with UVCS/SOHO.
Consider a measurement of electron scattered HI Ly-
at 1.5 solar radii. A slit width of 0.3 mm
(1.7 
) and a spatial height of 1.0 mm (5 arcmin) would be used. Using Table 11, we find:
Using Tables 3 and 10, and scaling with the resonant component to get the streamer intensity, we find
that the streamer intensity of the
electron scattered component is 
. The corresponding
count rates are 0.49 
for the hole and 3.87 
for the streamer. It would take 2 hours to accumulate
3500 counts in the hole profile and 15 minutes to accumulate that number in the streamer. It appears
that the expected count rates are appropriate for measuring electron
scattered Ly-
with UVCS/SOHO.