Problem is, as the eye's response to brightness isn't linear, when I
    simply control the LEDs brightness using an 8 bit value (with no
    compensation) they don't appear to dim smoothly. So my thought was to
    take the 8 bit value, use it as an index into a lookup table which
    would give me a higher bit value (ie a 12 or 14 bit).

Do you really need 256 steps?  Why not try something like a 4 bit
lookup into your 8bit pwm table.  That would be easier (IMO) than
implementing a >8bit PWM on an 8 bit controller, and it'd also be
realtively easy to move the values around to make it look the way
you want it to...


    which is essentially the integral of the area under a sine wave

That'd be unlikely, since the integral of a sine wave is another sine wave!

BillW

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