This section describes how to mathematically reconstruct the Model function, which is calculated internally by CLEANest. The reconstruction is available when using the Auto search capability of the CLEANest Workbench.


At the end of the Auto-search for multiple periods section of this Tutorial, we ended up with the below CLEANest Workbench table. 





  1. We expand the CLEANest Workbench table by enabling Detailed info, which results in:




  2. The Model function magnitude can be calculated using the equation: 

    Calculated Model function (t) =


where:


 = Corrected* average magnitude of all data points. In our example: 11.478

n      = Fourier Index (n=1 for first row, n=2 for second row, ...) 

NoP = CLEANest Auto Search Number of Periods. In our example: 2

 = Semi-Amplitude of the nth term. Value is given by Workbench Ampl. column 

  = Frequency of the nth term. Value is given by the Workbench Freq(c/d) column

     = Time ( JD )

  = Corrected* average time of measurement of all data points. In our example: 2448493.0060

 =Phase of the nth term. Value is given by Workbench Phase column 


(* CLEANest makes small corrections/ adjustments to the average magnitude of all data points to determine A0 and to the average time of measurement of all data points to determine T0)



  1. This calculated model function will closely match the exported model function values from previous section. Let's illustrate this with an example. We will compute the Model function magnitude for the second observation in our ObsWin, using the above identified two periods. This observation has JD = 2435670.9.

  2. The formula thus becomes: 

Calculated Model function mag (2435670.9) = 

11.478  + [0.1088 * cos (2 * 3.14159 * (0.0147 * (2435670.9 - 2448493.006) + 0.9397))] 
           + [0.1021 * cos (2 * 3.14159 * (0.0071 * (2435670.9 - 2448493.006) + 0.9429))]

 
      = 11.478 + [0.1088 * cos (2 * 3.14159 * (0.0147 * -12822.106 + 0.9397))]
                   + [0.1021 * cos (2 * 3.14159 * (0.0071 * -12822.106 + 0.9429))]

      = 11.478 + [0.1088 * cos (2 * 3.14159 * -187.54526)] + [0.1021 * cos (2 * 3.14159 * -90.09405)]

      = 11.478 + [0.1088 * -0.9598] + [0.1021 * 0.8304]

      = 11.478 - 0.1044 + 0.0849

      = 11.458

  1. To compute the Model function magnitude for a large set of observations, it is recommended to use an Excel spreadsheet to implement the above formula, or to write a small program.