Background
I have made a tubular capacitive liquid level sensor (This is a professional one, for example). It outputs a frequency that is inversely proportional to the capacitance.
The problem
I have taken readings and put them into an Excel spreadsheet, along with the depth of water when they were taken. They seem to be logarithmic, but they are not. I have taken the natural logarithm and normalized the values, and plotted this versus the percentage of submersion of the sensor.
This is the graph:
X is percentage submerged, Y is reading. "Log Normalized" is the plot of the normalized logarithm values. "Linear" is the plot of the expected/wanted values. "Diff" is the difference between the "Log Normalized" value and the "Linear" value for each pair of those values.
In the final application, I will have a reading, and will will need to find the depth of the water the sensor is in. So I have a point along "Log Normalized", I know its Y-position, and I want to find its X-position (percentage submerged). If I can identify "Diff", I can use that formula to get "Linear" from "Log Normalized".
This is the spreadsheet: spreadsheet of readings