Non-linear relationship between power supplied and perceived brightness in a filament lamp? I was expecting the relationship between these two to be linear, but after conducting an experiment my data fits almost exactly on the curve, $y = 2800.2 x^{2.0173}$, where $y$ is the brightness in Lux and $x$ is the power supplied in Watts. 
Is this due to some property of filament lamps which I have missed, or is my data simply inaccurate?
 A: If you are looking at visual brightness, then you have to fold the wavelength dependent sensitivity of the human eye to the approximate black body spectrum of the filament into the calculation. At low power the filament will emit mostly infrared radiation, which is not visible. Even at the max. temperature of practical filaments the color temperature of the radiation is well below the sensitivity maximum of the human eye, which is in the green part of the spectrum, but as the power goes up, ever more of the emitted light falls into the visual part of the spectrum and the brightness increases more than proportionally with the total power.
A: How did you measure perceived brightness? If you used the visible spectrum, the increasing temperature as the power goes up will shift more of the output into the visible. If you measure total output over the whole spectrum, the relationship should be linear.  The increasing resistance of the bulb should not be a problem if you truly measure power in. It takes more voltage to push a given current, but power in should equal light out as long as you measure all the radiation.  The filament of a light radiates much like a black body The temperature will rise as the fourth root of the power. The wavelength of maximum output will decrease as the inverse temperature.
