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.