Color Calibration / Dimming Curves (MaxM)

I have been working with the BlinkM MaxM for a couple of weeks and with the particular light chians I'm using, the color response is poor - the problem is that the PWM of the MaxM is scaled linearly and the LED output is logarithmic. So when I set the color to (128,128,128) the PWM is at 50% duty and my LED's consume half the measured power but are considerably more than 50% as bright as they would be at (255,255,255). This isn't the fault of the BlinkM hardware of course, but it does make for some odd fading behavior and some non intuitive response when one is trying to achieve a particular color. Also, I'm sure there are other LED's that have a more linear response, so please note that this is only what I am seeing - maybe nobody else is in the same boat.

So what can be done about this? Currently, in my arduino sketch I am transforming my rgb values using an inverse cube function to approximate (term used very liberally) a logarithmic curve. It's not perfect but it's considerably less expensive (CPU and code space) than actual logarithms. Here is the code (red only shown; the same is done for other values):

unsigned long rl = (unsigned long) r * (unsigned long) r
* (unsigned long) r / 65535 + 1;
r = (r == 0 ? 0 : rl);

So this transforms our color values into roughly equivalent "brightness" values -- if using HSB colors you could probably succeed in applying the same transform to only the "B" number and achieve the same thing. Internally the BlinkM is going to transform HSB back to RGB anyway.

The drawbacks with this approach are that at the "dim" end of the color ranges there are not enough steps for smooth dimming though the colors on the whole appear more accurate.

My question is, is there a better way to do this? Can I do anything between the MaxM outputs and the led light chain to achieve a linear to logarithmic transformation? Can the MaxM's internal PWM handling be converted to a higher resolution (4096 bit) and internally use a logarithmic (or other approximate) curve for dimming? Is this even a problem on other LEDs?

I have done a port of cyz_rgb firmware to the MaxM though I have not yet burned it to test. I'm trying to understand more about how the PWM is implemented and might be changed to work better before I begin testing with hardware.

I'm thinking we might not be able to get to 4096 steps of PWM without flickering unless we significantly bump the ATTINY44's clock using an external oscillator. I'm not this deep into the hardware yet --

Thanks for any ideas.