First, please get in the habit of labeling your plots, with units. It immensely helps to prevent misunderstandings.

The top one is clearly now a linear plot. The original one, though noisy, is clearly an exponential decay to my eyes. Not entirely sure what is going on in the second one but without plot labels I'm also not really sure what I'm looking at.

EDIT: My guess is that if the second one is 1/OD, then the spikes are artifacts caused by the noise in the original plot (some points accidentally come very close to zero, or even negative values, and taking the inverse of those points results in very large numbers). Typically what I find it useful to do in these cases is do a little data averaging before I process it (combine every 5 points into 1, say). Alternatively you can subject the original data to a simple exponential fit and then do the transform on that.