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How to Determine Parameters

Determining Parameters and Sensitivities

You can determine observation parameters and estimate sensitivities in the following way. See Fig. 1-1 in "Introduction" to understand meanings of variables to appear below.

#Derivation of equations is shown in "Miscellaneous Information".

At first you should set fundamental parameters listed below:

  1. The dimension of the mapping area l1 ["] \times l2 ["] (l1 along the scan, l2 across the scan).
  2. Time to be taken in a scan row (on-source) tscan [s] : scan speed on the celestial sphere then becomes vscan ["/s] = l1/tscan .
    • tscan should be chosen so that the antenna does not move more than 1/3 or 1/4 of HPBW during the data dump (integration) time tdump [s], 0.1 (ACG) or 0.2 (WHSF) sec.
    • See Hints on Choosing Parameters.
  3. Set the number of on-source scans per one OFF NscanSEQ; separation between the scan rows {\mit\Delta}l ["]; and the grid spacing of a map to be made d ["] \times d ["]. Now the number of scan rows is written as Nrow = l2/{\mit\Delta} l  +1 .

Using these values, parameters and the sensitivity are determined as follows. You can calculate them using a tool (otfaste.pl).

  1. An overhead time per one scan row tOH [s] is written as tOH = 6 + 8/NscanSEQ .
  2. Determine an optimal OFF-point integration time tOFF [s] as
    t_{\rm OFF} = \sqrt{\left(t_{\rm scan}+t_{\rm OH} \right) \frac{\eta N_{\rm scan}^{\rm SEQ} d t_{\rm scan}}{l_1}} .
    Here \eta=4.3 (It depends on the type and parameters of convolution function. With the default parameters, it becomes 4.3 for Bessel*Gauss, 1.2 for Sinc*Gauss, 6.3 for Gauss, 1.0 for Pillbox, 10.2 for Spheroidal. See Miscellaneous Information: Derivation of Observation Parameters and Sensitivity).
  3. The total time spent to run a observe table including OFF, R-SKY, antenna slew, etc. is estimated to be
    t_{\rm OBStot} = N_{\rm row} \left(t_{\rm scan} + t_{\rm OH} + \frac{t_{\rm OFF}}{N_{\rm scan}^{\rm SEQ}} \right) f_{\rm cal} .
    Here fcal is an overhead to obtain R-SKY calibration data (if you use 1 minute at every 15 minutes, fcal=16/15).
    • If tOBStot becomes larger than the interval between pointing observations, you have to reduce tOBStot by, e.g., divide the mapping area into multiple observation tables.
  4. The total on-source time is
    t_{\rm ONtot} = N_{\rm row}t_{\rm scan} \simeq \frac{l_1 l_2}{{\mit\Delta}l \cdot v_{\rm scan}} .
  5. The effective integration times of ON and OFF for a map grid are written as, respectively,
    t_{\rm cell}^{\rm ON} = \eta \times \left( t_{\rm ONtot} \frac{d^2}{l_1 l_2} \right)
    and
    t_{\rm cell}^{\rm OFF} = t_{\rm OFF} \left( 1+\frac{d-{\mit\Delta}l}{N_{\rm scan}^{\rm SEQ}{\mit\Delta}l} \right) .
  6. Using the system noise temperature Tsys [K] and the frequency resolution of the map to be made B [Hz], the rms noise temperature of the map is estimated as
    {\mit\Delta}T_{\rm A}^* = \frac{T_{\rm sys}}{\eta_{\rm q}\sqrt{B}}\sqrt{\frac{1}{t_{\rm cell}^{\rm ON}}+\frac{1}{t_{\rm cell}^{\rm OFF}}} .
    Here \etaq is the quantization efficiency of the spectrometer: it is 0.88 for the MAC (ACG), 0.60 for the WHSF.

Compared with the common position-switch ("step-and-integrate") observations, higher observing efficiency is expected to be acheived in OTF observations due to the following facts:

See Miscellaneous Information: FAQ section: an example of comparison between OTF and position-switch is shown. In case of the limit of dead time -> 0, the efficiency in time can get 4 times higher than the position-switch observations.

Hints on Choosing Parameters

An Example of Parameters

Assuming to use the MAC (ACG) with parameters l1=l2=300 ["], tscan=30 [s], {\mit\Delta}l=7.5 ["], d=7.5 ["], Tsys(SSB)=500 [K], and B=1 [MHz]

% perl otfaste.pl.txt
### OTF sensitivity estimation for ASTE ###
backend type                            (1:MAC, 2:WHSF): 1
length of mapping area (along the scans)    l1 [arcsec]: 300
length of mapping area (perp. to the scans) l2 [arcsec]: 300
time for scan                                 tscan [s]: 30
number of ONs per OFF                        Nscan(SEQ): 1
separation between scans              (delta)l [arcsec]: 7.5
map grid                                     d [arcsec]: 7.5
system noise temperature                       Tsys [K]: 500
resolution bandwidth                            B [kHz]: 1000
--- Summary of parameters of your observation ---
Backend type                                           : MAC
Length of mapping area (along the scans)    l1 [arcsec]: 300.00
Length of mapping area (perp. to the scans) l2 [arcsec]: 300.00
Time for scan                                 tscan [s]: 30.00
Number of ONs per OFF                        Nscan(SEQ): 1
Separation between scans              (delta)l [arcsec]: 7.50
Map grid                                     d [arcsec]: 7.50
System noise temperature                       Tsys [K]: 500.00
Resolution bandwidth                            B [kHz]: 1000.000
Scan speed (1.0" per 0.1s sample)               ["/sec]: 10.0
Effective integrtion time of ON                   [sec]: 3.31
Effective integrtion time of OFF                  [sec]: 12.00
Overhead time per one scan                        [sec]: 14.0
Total on-souce time                               [min]: 20.5
Total time per one map                            [min]: 40.8
Observing efficiency eta(ON/OBS)                       : 0.50
Optimal OFF-point integration time                [sec]: 12.0 -> 12
Rms noise temperature of one map                    [K]: 0.353

The optimal OFF-integration is 12 seconds. This table will take about 40 minutes to run and {\mit\Delta}TA*=0.35 [K] is obtained. Effective spatial resolution becomes 24" (see Miscellaneous Information: Convolution in "Make Map").

#FYI: Redirection of the standard input to a file (sample) may make recalculation much easier: e.g., perl otfaste.pl.txt < otfaste_input.txt. If you execute this script as perl otfaste.pl.txt tex, you can see an example of results of sensitivity estimation.

last update: 2015-02-20