Increasing Brightness Linearly

I understand that LED brightness seems to be logarithmic as a function of duty cycle. In other words, perceived brightness = log(duty cycle) or that as the duty cycle becomes higher, the perceived differences in brightness become more imperceptible.

A person on the AVR Freaks forum posted this thread on how to use the formula "brightness = log(10^(duty cycle)) = x" to cancel out the log using a lookup table or linear interpolation.

Is there a name for this kind of "linearizing using the inverse"? I searched wikipedia and found "Inverse problem" but it got complicated really quickly with matrices and I couldn't follow.

what is the colour of the LED as IIRC these formulas depend on the colour too.

If you want to implement a lookup table check multimap() - -

My particular LEDs were green and white.

The logarithmic curve is only a relatively coarse approximation. More accurate is the CIE LAB correction:

This post on the forum explains how to calculate a lookup table:,147810.0.html

You may want to check out “progmem”:

Just to leave as reference in google searches, here’s a little code that reasonably compensates our vision tendency and makes it seem like a linear brightness increase.

double LightLevel = 0; 
double Base = 0.0039215;

    while (LightLevel < 255) {  // 1020 increments up to 255  
    analogWrite(LightLevelPin, LightLevel);
    LightLevel = pow(Base, 4) ;
    Base = Base + 0.0039215;

It’s not a problem of the leds, it’s a “problem” with our eyes. Double the duty the brightness does double. But our eyes don’t see it as doubling.

What you want is gamma correction. I would not do it on the fly because the calculation is a bit heavy (not impossible but not easy for an 8-bit chip). In my library I use gamma correction as well :slight_smile: