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### Time/Sensitivity estimation

This paragraph describes the algorithm to do a time/sensitivity estimation for a position-switched On-The-Fly observation.

Step #1: Computation of and

is just computed as the ratio . Using Eqs.  and , we obtain
 (37)

Using this equation, we start to compute for and . We want to enforce the integer character of in a way which decreases the product . To do this, we use
 (38)

Eq.  ensures that . The value of must be decreased so that Eq.  is enforced.
Step #2: Computation of or
We use the following equations in descending order to compute the elapsed telescope time and in ascending order to compute the rms noise level:
 (39) (40) (41)

Step #3: Computation of derived quantities

 (42) (43) (44) (45)

Step #4: Is an integer number?
The interpretation of the above equation to compute has two cases.
1. . This means that either the user tries to cover a too large sky area in the given telescope elasped time (sensitivity estimation) or the telescope need a minimum time to cover at the maximum velocity possible with the telescope and this minimum time implies a more sensitive observation than requested by the user (time estimation).
2. . will generally not be an integer, we can think to decrease from to obtain an integer value. However, this must be done at constant . Decreasing thus implies increasing . It is not clear that this is possible because of the constraint . Another way to deal with this is to keep to its maximum value and to adjust (sensitivity estimation) or and thus (time estimation) to obtain an integer value of . However, this implies a change in the wishes of the user. The program can not make such a decision alone and we will only warn the user. Indeed, the worst case is when is changing from 1 to 2 because this can decrease the sensitivity by a factor 1.4 (sensitivity estimation) or double the elapsed telescope time (time estimation). The larger the value of the less harm it is to enforce the integer character of .

Next: Comparison Up: Position switched Previous: Relation between and   Contents
Gildas manager 2014-07-01