You will have to make the assumption that it is possible to capture a nominal set of measurements for the sensor over the operating range that is repeatable. This is the characteristic that you need to fit to. Additionally it may be necessary to appply some temperature compensation but that can be worked out by locating a temperature sensor near the detector and making separate readings for that.

Fitting to the characteristic curve of the detector may be done in many ways. Have you considered just putting the known data points for the sensor into a table and then preforming a linear interpolation between the table entries when a sensor reading falls between two table entries?? This method can be made as accurate as necessary by increasing the number of known data points accordingly. A spreadsheet similar to the one you linked could be used to evaluate this technique.

Michael Karas