How to use On The Fly time estimator

1. Input Data

   • The observing time calculator uses basic parameters to define an OTF observation. Figure 1 shows a screenshot of the observing time calculator form.
   • Fields (1) and (2) represent the instrument to be used and the frequency. Allowed frequencies are defined exactly in the operative range for each band. In case the user provides a frequency value out of range, it will be replaced by the central frequency of the band. For FLASH+ one has the choice to select different sidebands (LSB or USB) but the default value corresponds to the lowest receiver temperature.
   • Field (3) is the required spectral velocity resolution. The rms or sigma will be calculated adopting this resolution, see Field (9).
   • Fields (4) and (5) are the PWV and source elevation. Both are used to estimate the line-of-sight sky opacity and are the main variables to estimate the system temperature.
   • Fields (6) and (7) define the map size and shape. The most important here is to identify the direction along which the map will be done. Figure 2 shows an example OTF where scanning is done along the X direction; so in this case X and Y are, respectively, the scanning and the orthogonal directions. To make the calculation easier some simplifications are done: Firstly, the dump step used in the estimator is always one third of the beam size. Similarly, the distance between rows (or columns) is also one third of the beam at the selected frequency.
   • Field (8) defines the dump time which is the time spent in each dump. This value is limited between 0.1 and 4 seconds.
   • Field (9) defines the rms or sigma requested by the user (see Field(3)).
     
     

     Figure 1: OTC form.	Figure 2: OTF example.

   
   

2. How is the estimation computed?

   • The total time in On-The-Fly observation depends on a series of parameters: the scanning velocity (which is a function of the dump time, t_dump, provided by the user), the map dimensions, the time spent on the reference position, t_off, and the number of calibrations done during the map, n_cal.
   • The scanning velocity can be obtained like this:
     

     (1)

   • The dump step (∆x) is fixed to one third of the beam size (∆x = beam/3). The total amount of time spent on the source (t_on^total) is just the sum of all dump times in the map (Eq. 9).
   • To determine how often the telescope moves to the off (or reference) position one needs to consider the instrument stability time. It is usually between 30 and 60 second and therefore the time to complete a row should be lower than this time.
   • The noise level reached after spending the total amount of time in a full map is computed with the radiometer equation:
     

     (2)

     where η_eff is the backend efficiency, ∆υ is the frequency resolution and T_sys is the system temperature.
   • We can consider that for OTF maps the off-time (defined as the amount of time spent in the off position) is proportional to the on-time:
     

     (3)

   • At APEX, this proportionality factor α is computed as:
     

     (4)

     where Δx is the dump step, Lx the scanning axis length and n_on2off is the number of rows between two off integrations.
   • As mentioned before, the estimator considers Δx fixed to one-third of the beam size, and if we denote the number of dumps per line as n_dump, the following expressions hold:
     

     (5)

   • This means that α can be expressed only as a function of the number of dumps between off integrations:
     

     (6)

   • Inserting equations (3) and (6) into equation (2) one can see that the noise after one coverage of the map (σ¹) can be expressed as:
     

     (7)

   • To reach the final σ provided by the user we need to cover the map several times. This number is just:
     

     (8)

   • And then, the total on-source time spent in the map is:
     

     (9)

     In general if n_on2off is greater than 1, the number of submaps n_submap is the number of blocks comprised by the full map (a submap is just the number of rows covered between two consecutive off integrations). This is just:
     

     (10)

     where Ly and Δy are, respectively, the length and step in the orthogonal direction. Again Δy is also fixed as one third of the beam size.
   • Finally, the total off-time spent to do the map is:
     

     (11)

   • The calibration time is estimated under the premise that it is done every ten minutes and t_cal is 30 seconds without overheads (with overheads, it is 90s). .
   • When an OTF map is observed at APEX, the noise in such a map is derived by using the CLASS software, and these are the commands that we run (respecting all the default parameters in such functions):

     table NGC3603 new
     xy_map NGC3603
     let name NGC3603
     let type lmv
     lut rainbow3
     go noise
     

   • The σ value computed like that (using the function go noise) should match the estimation done by the observing time calculator. One should consider that CLASS measures the noise in a map which has been resampled with a half beam pixel size grid. This was obtained from a grid with pixel size of one-third of the beam, convolved with a Gaussian kernel also of size equal to one-third of the beam.
   • Taking this in consideration the t_on present in equation (7) should be equal to the time spent in half a beam. Therefore, t_on = n_halfbeam * t_dump (n_halfbeam is the number of dump in a half of beam) and σ¹ would then be:
     

     (12)

   • Figure 3 summarizes the results for more than thousand OTF maps taken with APEX-1 and FLASH345. The plots show the ratio distribution between the observed and estimated time for APEX-1 (left) and FLASH345 (right). The plots show a peak in the distribution around 1.3. This means we need to apply an overhead compensation equal to 1.3 to adjust the ratio to one.
     
     

     Figure 3: Ratio distribution for observer and estimated time with APEX-1 (left) and FLASH345 (right).

   • Finally to estimate the total time spent in an On-The-Fly map we sum the total on-time, the total off-time and the time spent on calibrations. An additional factor of 1.5 is added to compensate for the time spent in pointing, focusing and tuning. Therefore the total time given by the estimator is:
     

     (13)

Last update: May 24th, 2015