Case 3: Check of the Radiative Transfer Implementation, limb looking geometry.

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The aim of this case is to check the implementation correctness of the
radiative transfer algorithm, for a limb looking instrument. 

Pre-calculated absorption coefficients will be used as input. 
For specified calculation procedure and instrumental characteristics, the
participants shall provide both, pencil beam monochromatic spectra and
spectra as recorded by the instrument. No refraction is considered.

A perfect single sideband instrument will be assumed.
Two components of the sensor part will be considered:

Antenna
-------
The purpose of the antenna is to maximize the sensitivity of the radiation in
a narrow angular direction while suppressing radiation from the other
directions. This sensitivity is described by the antenna pattern. The
simulated antenna is  assumed the have a Gaussian function, with a width of 
the main beam (FWHM of the Gaussian function) of 0.07 degrees.

Spectrometer
---------- 
The output of the spectrometer is a weighted mean of the signal around
some discrete frequencies (sensor frequencies), channels, that
together generate a spectrum. 
Each channel is described by a response function. In our simulations all the 
channels were assumed to have the same Gaussian shape (FWHM=20 MHz). 

Input - Output Files
--------------------
 Format:
 ========
  The input files are ASCII files, in ARTS format. 
  They can easily be recognized by the extension 'aa'.
  The file can start with an arbitrary number of comment lines.  
  These lines starts with the hash symbol (#) 
  The first row after the comment lines give the number of matrices 
  in the array. After this follows, for each matrix, a row giving 
  the matrix size followed by the data in row order.

 Input:
 ======
 - Freq_mono_Limb.aa -->> the frequency vector for which the absorption 
   coefficients were calculated.
 - p_z_abs_Limb.aa -->> the pressure (altitude) levels corresponding to 
   pre-calculated absorption coefficients, in ARTS format. Data is a 2 columns
   matrix: column 1 contains the levels in pressure units [Pa],  second 
   column contains the geometric altitudes [m]
 - Limb.abs.aa -->> the file gives the pre-calculated  absorption 
   coefficients, in ARTS format. 
   Each row data gives the absorption coefficients for frequencies given in
   Freq_mono_Limb.aa and for one atmospheric level (given in p_z_abs_Limb.aa).
 - Limb_specifications.txt -->> the file gives the numerical 
   values for the platform altitude and ground specifications (altitude, 
   temperature, emissivity). 
 - za_pencil_Limb.aa -->> zenith angles for the pencil beam calculation.
 - za_sensor_Limb.aa -->> zenith angles as seen by antenna.
 - Antenna_Limb.aa -->>  file in ARTS format giving the antenna pattern:
   column 1 gives the relative zenith angles in degrees, column 2 gives 
   response function. The response function is not normalized.
 - Freq_sensor_Limb.aa -->> the frequencies observed by the 
   sensor (the middle points of the backend channels). 
 - channel_response_Limb.aa -->> the file defining the backend 
   channel response. The response of all channels are assumed to be 
   identical. The channel file  has ARTS format, a 2 column matrix where 
   column 1 is (relative) frequencies and column 2 response values.  

 Output:
 =======  
    
 - the pencil beam monochromatic spectra (brightness temperature) for
   the viewing direction specified in za_pencil_Down.aa.  
 - the spectra seen by instrument (including the effect of the antenna
   and of the spectrometer) for discrete frequencies given in
   Freq_sensor_Limb.aa.
  The output data should have ARTS format: each row gives the spectra
  corresponding to one viewing direction.