```A little experiment first. Let's see how the Min value of the plot changes with Opacity:

f[x_] := f[x] =
Min[Norm /@ Flatten[ImageData@Rasterize[
ListPlot[theData, AspectRatio -> Automatic, ImageSize -> 200,
PlotStyle -> {Black, Opacity[x]}, Axes -> False]], 1]];
Plot[f[x] , {x, 0, .4}, PlotRange -> Full]

![Mathematica graphics](http://i.stack.imgur.com/rP4Tc.png)

So, it is an exponential.

Let's fit it:

model = a Exp[b x];
fit = FindFit[data, model, {a, b}, x];
modelf = Function[{t}, Evaluate[model /. fit]]
Show[ListPlot@data, Plot[modelf[x], {x, 0, 1}]]

![Mathematica graphics](http://i.stack.imgur.com/vEOEz.png)

Now you are ready to set the min value of the brightness of the plot to whatever you want:

>   opacity = Log[ MinDesiredIntensity / a] / b

Let's use it:

opac = x /. Solve[# == a E^(b x), x] /. fit & /@ {1/2, 1/4, 1/20}

ListPlot[theData, AspectRatio -> Automatic, ImageSize -> 200,
PlotStyle -> {Black, Opacity[#[[1]]]}, Axes -> False] & /@ opac

![Mathematica graphics](http://i.stack.imgur.com/QdGnJ.png)```