I've tried to convert Sharp Rangefiner measurements to distance values. I read http://www.acroname.com/robotics/info/articles/irlinear/irlinear.html but didn't really get it, so, I went my own way. The outcome turns out to be ever so good, so I'll share it with you.
The graph y = 1/x passes (1,1) with a dx/dy of -1 I've assumed that a scaled graph that the rangefinder should conform to could tell something importent at the point on the graph, where dx/dy = -1. I find the point at x,y = (108,113) and plotting the graph y = (108*113)/x ... is almost BULLSEYE ...
Measured points are green Calculated points are red dx/dy are blue
The topmost measuremets are a bit off, so I decided to fiddle a little and changed it to 108 * 113 / (x + 2000 / (x * x)) And my jaw dropped when I saw that the curve turns around at the top point and follows the steep line down to (0,0) .. appearantly showing the all to close points (2-15 cm) conform to the curve too. I cannot download pictured curve to show the amazing fit, and this editor doesn't work properly either, so you'll just have to try it out yourself