# Physical luminance and the CIE XYZ color space

In reading up on the XYZ color space you regularly come across something to the effect that "Y is taken as the luminance" or "relative luminance" whether it be for the XYZ color space or in xyY. I'm struggling to gain any intuition for how this Y value is related to luminance from a photometric perspective. There, the luminence is closely related to the radiance, but weighted as a function of our eye's response. It "contains" all the colors we can see and has actual units. There's seemingly very little connection between the two.

Bottom line: I go out and measure the spectral radiant power reflected off a surface, and calculate the luminance. Then, I take an image that contains that surface. I convert the image to the XYZ color space. How is that Y value related to the calculated luminance? Do the physics/units go completely out the window?

• It's really a similar question as to how luminous different colors should be when converting a color image to black and white. It's like asking whether two different colors have the same brightness. It's somewhat subjective but on average two colors with the same Y value will appear roughly as bright as each other. Have you researched how XYZ were derived? Y is actually defined as Luminance in linear space. – doug Feb 26 at 21:48

Luminance is basically Radiance weighted by the Human Visual System (HVS), i.e. Power per Unit Area per Unit Solid Angle. Whether it is given in relative or absolute units depends on how the values were measured, absolute values require a calibrated reference light source and/or measuring device.

If you have some absolute spectral radiometric measurements and need the corresponding absolute photometric quantity, you need to integrate them to CIE XYZ tristimulus values while using a normalization factor k equal to Km = 683lm.w-1, the maximum spectral luminous efficacy of the HVS. 1 watt of light at 555nm equals to 683 lumens. Y in that context would be an absolute measure of Luminance.

Colorimetry 4th Edition has most of the relevant details, the 3rd edition can be found online and has very similar content.