Correcting for non-linear brightness in LEDs when using PWM

When driving an LED with PWM, the brightness (as I perceive it) does not scale linearly with duty cycle. The brightness is slow to ramp up, then increases exponentially with duty cycle.

Can anyone suggest a rule of thumb to use as a correction factor, or other workaround?

Answer

For 16 levels it's easy to do a simple look-up table "by hand" and convert the 4 bit value in an 8 bit value to pass to PWM controller: this is the component i've used in my FPGA led array driver. For an 8 bit level controller, you'll need at least 11-12 bit output from the look-up table.

library IEEE;
use IEEE.Std_logic_1164.all;

entity Linearize is
port ( reqlev : in std_logic_vector (3 downto 0) ;

    pwmdrive : out std_logic_vector (7 downto 0) );
    end Linearize;

architecture LUT of Linearize is
    begin
    with reqlev select
        pwmdrive <= "00000000" when "0000",
                    "00000010" when "0001",
                    "00000100" when "0010",
                    "00000111" when "0011",

                    "00001011" when "0100",
                    "00010010" when "0101",
                    "00011110" when "0110",
                    "00101000" when "0111",
                    "00110010" when "1000",
                    "01000001" when "1001",
                    "01010000" when "1010",
                    "01100100" when "1011",
                    "01111101" when "1100",
                    "10100000" when "1101",

                    "11001000" when "1110",
                    "11111111" when "1111",
                    "00000000" when others;
    end LUT;