Determining the exposure time

 Before starting an observation, one should determine the number of frames that need to be obtained, and thereby the exposure time available per frame. The number of frames required depends upon the science objectives and the mode of observing.

If the observing goal is to obtain spectral line profiles across the entire extent of the target, keep in mind that Nyquist sampling requires that frames be acquired at twice the frequency of the etalon resolution. If using the standard Palomar ET-50 etalon, this corresponds to stepping the etalon gap by intervals of 16 units at H$\alpha$(6563Å) and 12 at [OIII](5007Å). A free spectral range at H$\alpha$ is approximately 42 of these steps. However, because of flexure in the telescope and instrument, it is important to obtain ~110% of a free spectral range, in order to ensure complete coverage, i.e., about 46 steps. If the corners of the field furthest from the optical axis are important, you might even want to obtain ~120% of a free spectral range. This is especially true if a source is observed through transit, where flexure effects are maximized.

In addition to the data frames, an image of a calibration source should be obtained approximately every 20-30 minutes, each time at the same etalon gap setting, in order to monitor the stability of the instrument. These frames should be included in the calculation of the available integration time per object frame, as should the read-out time of the CCD being used.

In general, the way to determine the exposure time and the calibration interval is to first decide how many hours you want to spend on the object. Then use the formula:

T = T_obj + T_cal

T = n * (t_obj + t_ro) + ((n/(d-1)) + 1) * (t_cal + t_ro + t_oh)

where T is the total time in seconds, n is the number of object frames, t_obj is the exposure time in seconds for an object frame, t_ro is the readout time for the CCD, a calibration frame is obtained every d frames, t_cal is the calibration exposure time, and t_oh is the dome rotation overhead for each calibration exposure. If you are using CCD #15 or #16, then the values to be used are approximately n=46, t_ro=40, t_cal=10, and t_oh=60. In this case, you may simply interpolate the exposure time per frame from Table 4.

   

Table 4: The total exposure time for a fully sampled velocity cube using the standard Palomar ET-50 etalon and CCD #15 or #16. A recommended interval for calibration frames is also given.

Exposure time per frame [sec]	Calibration interval [frames]	Total time per cube [hours]
120	8	2.3
180	7	3.1
240	6	3.9
300	5	4.7
400	4	6.1
500	4	7.4
600	3	8.9

To be conservative, you may want to inflate the total time estimate by 10% or so, to allow for weather problems, longer dome moves after calibration frames, and other errors.