On board the T28 aircraft was a Hail Spectrometer and High Volume Particle Spectrometer (HVPS). Both probes output 2D data, and the Hail Spectrometer also output 1D data. The HVPS had an array of 256 diodes, the Hail Spectrometer had 126/64 diodes for 1D/2D data. If image elements were blocked above a certain threshold a particle(s) would be counted. The steps to use these counts to calculate particle concentration (#/m^4) are detailed below.

The counts generated from SODA are saved in a 14xn array where n is the number of x second intervals, where x can be specified when using the SODA gui. x is set to 5 seconds as a default in the gui, and is what has been used in the research so far. An example of these counts is shown below,

{{:atmos:citation:research:count_comparison_header.png?900|}}

{{:atmos:citation:research:count_comparison.png?900|}}

The time interval for 241846 - 241851 is shown. Note that the time intervals count up to 5 seconds forward from the start time. The counts from SODA are in the "SODA" row, and you'll notice that they are much larger than the DISP counts which are the 1D counts. Usually they're larger by factors of 5-10. This will be (partially) resolved later on.

To calculate concentration from counts, the basic forumla is,

    Conc (#/m^4) = Counts / (SA * Airspeed * Binsize change)

where 
  * SA is sample area which is (probe arm length * height)
    * Height is (number of diodes * diode size)
  * Binsize change is the (Max_Size - Min_Size) for each channel.
    * For channel 1 for the Hail Spectrometer, this would be 0.50cm - 0.40cm = 0.10cm

SODA includes extra variables in it's calculations. I can not explain why SODA includes these extra factors, but they are in there, and when included, the resulting concentration is agreeably close to the concentration calculated from the 1D counts. This is why the counts are "(partially) resolved."
  * Counts are multiplied by a correction factor
    * This is the Poisson correction factor.
  * In additions to SA, Airspeed, and Binsize change, SODA also divides by "activetime"
    * "activetime" is the time interval. SODA defaults to 5 seconds for this interval

The new formula is,

    Conc (#/m^4) = (Counts * corr_fac) / (SA * Airspeed * Binsize change * activetime)
    
where for the Hail Spectrometer,
  * Probe arm length: 0.99 m (SODA version)
  * Diode size: 0.009 m
  * Diodes: 64 (SODA version)
  * Airspeed: ~100m/s
  * Binsize change: 0.001, 0.001, 0.001, 0.001, 0.0014, 0.0016, 0.002, 0.0026, 0.003, 0.0031, 0.0044, 0.006, 0.0079, 0.01
  * Corr_fac: ~1.1
  * activetime: 5

When you consider the counts being multiplied by the correction factor and divided by the active time, the 2D counts from SODA better match the 1D counts. In the image below, the 2D counts generated by SODA are much closer to the 1D counts from the DISP file. These "corrected counts" agree pretty well with the 1D counts.

{{:atmos:citation:research:counts_adjustsed_2d.png?900|}}

With the counts from the first image plugged into the second formula, the resulting concentration is, 

{{:atmos:citation:research:conc_compairon_header.png?900|}}

{{:atmos:citation:research:soda_conc_comparison.png?900|}}

The SODA concentrations agree fairly well with the DISP concentrations.

Notes to self on information to include, mention, explore, etc,
  * Counts rounded. Ceiling or round up/down? Which is better representation of data?
  * Time counts forward from time denoted for interval
  * Idk why the counts are 5x higher. Idk why the correction factor. Idk why the divide by active time. Idk
  * Sometimes, although I believe this is fixed in my math now, my calculated 2D concentrations are 1.1x higher. But again, I think this isn't an issue anymore.
  * Sample volumes check out. Airspeed checks out. SODA uses one airspeed for whole time interval. Include a comparison of the numbers
  * Include a comparison of the different probe specs used in 1D and 2D calculation
  * 

to get rid of sec from airspeed, i like to think of it as counts per time interval. so 100 counts per 5 second interval would be 100/5s which gives the seconds on bottom to cancel out the seconds in the airspeed. 10 counts per 1 second likewise gives 10/1s. and all of this normalizes the concentration to one second, which is why the 5 second soda intervals and 1 second disp intervals produce the same looking numbers