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Sensitivity and Calculation of Observing Times

By measuring with a set of different apertures a curve of growth (i. e. signal vs. aperture size) can be obtained and compared with that of a true point source. Any difference in signal can be attributed to an extended component of the central source. Since circular apertures do not allow for any spatial resolution we treat this extended component as an additional point-source flux contained in the annulus determined by the difference between the smallest and largest apertures used and express it as a percentage of the central point-source flux. The following sensitivity calculation only applies to point-sources, i. e. if the existence of a central point-like source can be assumed, around which the extended component is located. For extended sources the standard sensitivity calculation for photometry of extended sources applies (cf. Sect. 6.4.3).

Since here the S/N ratio refers to the flux of the extended component , the calculations are based on the fraction of the central point-source flux :

 

Then the S/N ratio becomes:

 

where refers to the NEP of the extended component, which is defined below. t is the integration time per aperture.

The power from the extended component incident on the detector is:

 

The sensitivity parameter C1 is given in Tab. 10.

To obtain of the extended component in the annulus the following formula is used:

 

The subscripts have the following meanings:

s - source , b - background, S - small aperture, L - large aperture, det - detector

The individual NEP terms are calculated in the same way as described in Sect. 6.4 on single pointing photometry:

     

The constants C2 and C3 are tabulated in Tab. 10.



Tue Dec 6 17:24:45 MET 1994