## Introduction

In the previous post about my monitor, I used five colors: red, green, blue, white, and a pale purple. For each of them, I began by specifying RGB values… I used Digital color meter to find their XYZ values… and I demonstrated that the relationship was nonlinear when applied to the purple color.

The relationship was…

XYZ = M (RGB)^1.801

where M, however, is linear (a matrix).

I found the nonlinear part of the relationship from the following graph out of my ColorSync utility…

## introduction & setup

I want to play with five colors. Four of them are perfectly straight-forward: red, green, blue, and white. The fifth color, looking purple to me, is close to one of the colors on the Gretag Macbeth color checker; we’ll be seeing this color again in a subsequent post.

I have two software tools which came with my Mac: the DigitalColor Meter and the ColorSync Utility. If you are not on a Mac, perhaps you have, or can get, something similar.

I want to know the relationship between RGB and XYZ on my monitor. First I will establish that the relationship is not linear; then I will show how what it is and how I found it.

Let’s try finding a linear relationship by looking at the relationship between RGB and XYZ for my five chosen colors, but especially for red, green, and blue.

Here is a red disk, defined by RGB = (1,0,0). If you’re new to my blog, the following commands are Mathematica®.