Intro to Colorimetry: Color measurement basics and how colorimeters work

Color accuracy is critical for modern creative work. It may not be the most glamorous part of the job, but there's a good chance you spend more time in front of a computer editing digital files than you do actually capturing content. And if you're doing that work on a crappy, uncalibrated monitor, you're shooting yourself in the foot.

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That's why a good color management workflow is a must. Pair a high quality monitor with a decent colorimeter and you can ensure the colors you're seeing on the screen are coming out as intended. This is even more important if you want to show off your work in print, since soft proofing requires that your display be as accurately profiled and calibrated as possible.

If you're reading this, you probably already agree. You know that a color-accurate monitor is an important part of your creative workflow, and that this monitor needs to be regularly calibrated if you want to ensure the best possible results. But have you ever stopped to ask how any of this actually works? How do we actually 'measure' color, how do we determine that a color is 'accurate', and how does a colorimeter do it?

That's what we want to cover today.

By the end of this explainer, you should understand the basics of how color is measured and plotted, and how companies like DataColor pack this complicated scientific process into a small plastic puck and a bit of software. Colorimeters like the XRite i1Display product line – which was taken over by a new company called Calibrite to produce the ColorChecker lineup – and DataColor's well-known Spyder product line are staples of every digital photographer's tool chest. And like any tool, it's maximally effective when you, the user, know exactly how it works and what it can (and can't) do.

We won't cover the actual process of display calibration here, but stay tuned because we'll dive deeper into that subject in a second article once we're all starting from the same foundation.

Using a colorimeter to measure the color output of your display allows you to make it more accurate, match it with different displays, and analyze its baseline accuracy.

Colorimetry Basics

At its core, 'colorimetry' is just the science of color measurement, but this is a deceptively simple definition because color vision is a devilishly complicated thing.

Broadly speaking, color scientists quantify color in two ways.

The first and simplest type of color measurement describes the effect that a particular color, be that on a computer screen or printed on a piece of paper, has on the light-detecting cones in your retina. This is like the raw RGB signals coming off of your camera's sensor. The second, far more complicated method adds a bunch of nuance (and math) to describe how you actually perceive color by trying to account for all the processing that happens between that first stage of the visual system and the part of your brain that actually 'sees' what you're looking at. This is like all of the circuitry and processing that sits between your image sensor output and the image that shows up on the rear LCD.

Fortunately, you don't need to understand all of colorimetry to better understand what your colorimeter is doing and how it's doing it. All you really need to know is how color is measured, how color is plotted, and how two colors are compared against one another.

How color is measured

When you place a colorimeter onto your computer monitor and it measures the output of a color patch, it's trying to determine how that light would interact with the color- and luminance-detecting mechanisms in your eye. To do that, it uses something called the CIE 1931 2° standard observer Color Matching Functions (or "CMFs" for short), which I've plotted below:

The 1931 2° standard observer X (red line), Y (green line), and Z (blue line) color matching functions. These functions are the basis for the color space diagram that most of us are familiar with.

The full explanation of how the 1931 CMFs were derived is a bit dense. The oversimplified version is that they're based on three imaginary colored lights, or primaries, that are so saturated a person could 'match' every single color a human can perceive by some positive combination of the three. There's a red primary, labeled X, a green primary, labeled Y, and a blue primary, labeled Z, and the curves tell you how much of each light you would need in order to match every point on the visible spectrum from 380nm (violet) to 730nm (red).

This might seem a little weird and convoluted, but the upshot of this system is that every visible color can be described by a specific combination of X, Y, and Z that is unique to that color.

In other words: we can relate any color back to human vision by determining the combination of X, Y, and Z you would need to use in order to 'match' that color. And because of some neat mathematical tricks that were used when this system was established, the Y value by itself describes a color's luminance and the proportion of X, to Y, to Z describes its color coordinates, or chromaticity.

How color is plotted

Once we have the XYZ values of a color patch, we could just plot the color in a three-dimensional XYZ color space, but this is rarely done in practice. Instead, you're more likely to see a chart that looks like this:

A blank chromaticity diagram. The outer edge represents the pure monochromatic colors of the rainbow, the most saturated colors that humans can perceive.

This is called a chromaticity diagram, and it's a flattened color space based on the XYZ color matching functions that ignores luminance and tells you only about color.

To go back to our image sensor analogy, if the XYZ values are the raw R, G, and B signals coming off of your retina, the xy chromaticity coordinates only tell you about the relative amount of R, G, and B in a particular color. So middle gray with XYZ values of (50, 50, 50) and pure white with XYZ values of (100, 100, 100) are obviously two different "colors," but they will plot at the same point on the chromaticity diagram (0.33, 0.33), also called "equal energy white."

That's a lot of technical jargon, let's look at a real-world example. Say I open up my MacBook Pro 14, switch it into the 'Photography - P3' display mode, and have it show me a patch of pure white. The graph below, captured with a special piece of equipment called a spectroradiometer, measures exactly how much light energy the screen is emitting at every point along the visible spectrum.

In other words: when the screen is showing a white patch, this is the amount of light energy that it's actually sending towards my eyeballs, nanometer by nanometer:

The spectral power distribution of a white patch displayed on the MacBook Pro 14's mini-LED LCD display.

Since any color visible by humans (including this white patch) can be described by some combination of our imaginary X (red), Y (green), and Z (blue) primaries, we can identify this color's unique location in human color space by calculating how much X, Y, and Z you would need to use in order to match this white light. To do that we multiply the energy values in the graph above, point-by-point, with the X, Y, and Z color matching functions, sum up the results, and multiply by a special photometric constant.

The output of this calculation is a single number for X, a single number for Y, and a single number for Z. For the white patch on my MacBook Pro 14 when it's set to the Photography - P3 mode with the brightness locked, those numbers are:

• X = 150.16
• Y = 156.69
• Z = 180.11.

The Y value is 156.69, which means that my display is current emitting 156.69 candelas per square meter (or "nits") of luminance. And the ratio of X, to Y, to Z is 30.8% X to 32.2% Y to 37% Z, which puts my MacBook's white point at (0.308, 0.322) in xy chromaticity space:

If I then do the same measurement and calculation for a pure red patch, a pure green patch, and a pure blue patch, I get the numbers below, which I can add to the graph to show the full color gamut of my MacBook Pro's display.

	X	Y	Z	x	y
Red	76.40	35.67	0.28	0.680	0.317
Green	40.86	108.04	6.34	0.263	0.696
Blue	33.07	13.00	175.43	0.149	0.059

The resulting triangle represents the most saturated colors that my MacBook Pro can possibly create, and the dot in the center is the white point: the color produced when my display's red, green, and blue primaries are all turned up to maximum. In reality, there's a third dimension to this graph, the capital 'Y' or luminance value, where white is 'brighter' than green, which is brighter than red, which is brighter than blue. But a chromaticity diagram ignores this dimension:

The color gamut of my MacBook Pro 14 display, based on the manually calculated XYZ tristimulus values of the white point and the red, green, and blue primaries.

So the XYZ values allow us to relate all color – no matter how its made – back to human vision, and the chromaticity diagram flattens these values down to a plane that ignores luminance and tells us only about the color itself. But neither of these values accurately describes what a color actually looks like, they can only tell us if two colors match, hence 'color matching functions.'

To go back to the sensor analogy one more time, the raw RGB values coming off of your sensor don't tell you precisely what that pixel will look like on your rear LCD, because those values are just the input to a complicated set of image processing steps. But those values can tell you whether or not two colors match, because if your sensor sends out the exact same RGB values at the start, it doesn't matter what the processor is doing, the two outputs will come out the same.

Of course, when it comes to display calibration, we do care what a color actually looks like. One of the most important measurements used in calibration is Delta E, which is a measurement of how different two colors appear. So if we want to move beyond 'do these two things match' into 'how different are they' we need to move beyond XYZ. That's where the CIELAB color system comes in.

How we compare two colors

CIELAB was created to fulfill the need for a uniform color-difference space: a color space where the distance between two points is correlated to how different those two colors appear when you look at them side-by-side. Written L*a*b*, the L* stands for "Lightness," which tries to mimic our perception of how light or dark a color appears, while the a* and b* are color coordinates that describe a combination of hue and saturation.

CIELAB does two very important things that ultimately allows us to compare how similar colors appear:

1. It scales the XYZ values around a reference white, which partially accounts for the built-in 'white balance' system in human vision. This is critical because the visual system quickly adapts to your surroundings so that a white wall still 'looks white' whether you're under very warm tungsten light or very cold fluorescent light.
2. It generates separate values for how we perceive the achromatic and chromatic properties of color and then plots those together in a (mostly) perceptually uniform color space where the distance between two points in this three dimensional space is roughly equivalent to how different those two colors actually appear when you look at them side-by-side.

If I plot the MacBook Pro 14's white point and RGB primaries in the standard L*a*b* color space, using Illuminant D50 as a reference white, this is what comes out:

MacBook Pro 14 primaries and white point plotted in the rectangular L*a*b* color space, using D50 as the reference white.

3D L*a*b* coordinates like these are the basis for the Delta E 'color distance' metric that's used to compare two colors. All three versions of the Delta E are based on comparing two pairs of L*a*b* coordinates, with the newer versions making a few adjustments to improve accuracy.

Since the distance between points in CIELAB is roughly equivalent to how different those two colors appear, we can experimentally determine the smallest distance that's still noticeable to the average person, what we call a 'just noticeable difference.' For Delta E, that number is somewhere around 2.3, which is why companies advertise monitors with an average Delta E of less than 2.0 across a pre-defined set of gray values and color patches.

How colorimeters work

Hopefully by now it's obvious that the color matching functions are the jumping off point for everything that your colorimeter is trying to do. If you can measure accurate XYZ values, you can plot those values in a chromaticity space and compare them against established standards like AdobeRGB (gamut coverage), you can check how stable your gray values are as you ramp up the brightness (gray balance), and you can convert those values to L*a*b* to calculate how accurately your display can recreate a set of known test colors (Delta E).

But how does a colorimeter actually measure these values?

For the example above, we used a special piece of equipment called a spectroradiometer to measure the light energy directly, and then multiplied that energy output by each of the color matching functions in turn to get the XYZ values for that color. That approach is super precise, but as you might have already guessed it's also slow and expensive. The Konica Minolta CS-2000a used for this testing is a $40,000 piece of lab equipment. Big yikes.

Colorimeters use a clever shortcut to simplify this process. Instead of measuring the precise light energy at every wavelength across the whole visible spectrum, a standard trichromatic colorimeter uses color filters or special optics to mimic the CMFs as closely as possible. By placing these filters and/or optics in front of a specially calibrated sensor, they can measure XYZ values directly, cutting out the additional measurements and math required to do it the way we did.

Because of this, colorimeters are much faster and more efficient at measuring the tens or hundreds of color patches necessary in order to properly profile and calibrate a display. And when they're designed and calibrated appropriately, they can provide all of the data you need to evaluate color accuracy without charging you an arm and a leg.

Challenges and limitations

You may have already guessed this, but the downside to using a fast, efficient, and relatively inexpensive color measuring device is accuracy.

It's difficult and expensive to make precise color filters that match the CMFs exactly, and even slight imperfections in the output can significantly throw off your results. This limitation has gotten worse as displays have gotten better. An ultra-wide-gamut display that can cover 99% of DCI-P3 or AdobeRGB will use saturated RGB primaries that plot as very narrow curves on a spectral power diagram, and since they're so narrow, they'll highlight any small imperfections in the filters and/or optics used to estimate the CMFs.

Say the transmission spectra of your XYZ filters look like the solid lines on this graph, compared to the dotted lines which are the actual CMFs you're trying to replicate:

These made-up XYZ filters are still quite accurate at parts of the curve, but some parts like the peak of the peaks of each filter, and most of the trailing end of the Y (green) filter would produce significant inaccuracies that have to be accounted for.

The Z (blue) filter will under-report at its peak, the Y (green) filter has a bump around 490nm but is weak through most of its trailing end, and the X (red) filter is weak at its short wavelength peak and lets through too much light at its long wavelength peak. If you have very wide primaries these imperfections might smooth themselves out, but with narrow saturated primaries your X, Y, and/or Z values might be based on a small part of each curve that doesn't line up properly.

Colorimeter makers are always trying to find more accurate ways to measure these values. Still, for both technical and economic reasons, the methods they use aren't perfect. So in order to bridge this gap between filters and reality, the software that comes with your colorimeter will use mathematical transformations to correct for the specific errors that the colorimeter will make when it's measuring different types of displays.

This is why your colorimeter software has you choose a 'display technology' or 'backlight technology' before you profile and calibrate the monitor, and this is why you should never ignore that option. Your selection tells the software what kind of spectral output to expect, and it calculates a correction matrix that accounts for the specific errors that the colorimeter will produce when measuring this kind of display.

In the screenshot below, you can see that DataColor gives me five different options for the Spyder X2 Ultra: Wide LED, Standard LED, General, GB LED, and High Brightness. If I measure the same display five times over, using each of these settings in turn, I will get five slightly different results:

Never ignore the "Display Technology" panel. It corrects for imperfections in your colorimeter's measurements, ensuring accurate calibration.

Professional-grade $5,000+ colorimeter from companies like Colorimetry Research cost so much because they guarantee a very high level of accuracy. The quality of their filters is guaranteed within stringent limits, they use more complex mathematical corrections, and they're explicitly designed to be quickly and easily calibrated using a spectroradiometer. This makes them more accurate out of the box, and they can be easily calibrated to 100% accuracy with any display if you've got the time, money, and expertise.

By comparison, a $150-$300 colorimeter from DataColor or Calibrite will only give you 5 or 6 generic display technologies to choose from. If you pick wrong, your calibration could be way off. If you pick right, but your display is a little wonky compared to the generic 'average' the software is using for its corrections, your results will be a little bit off. And even if you have the resources to rent a spectroradiometer and create a custom correction for every display in your studio, the software the comes with these colorimeters doesn't generally support this.

"For most people and most displays most of the time, a modern consumer-grade colorimeter will be very accurate. But it's worth knowing their limitations so you can try to compensate for them."

For most people and most displays most of the time, a modern consumer-grade colorimeter will be very accurate. But it's worth knowing the limitations so you can try to compensate for them. We'll have a lot more to say about that in an upcoming article.

Conclusion

The science of color measurement is fascinating and complex. We only scratched the surface here, ignoring or glossing over some concepts in favor of explaining the basics of how color is measured, plotted and compared. Our goal was to give you a better understanding of the most common color terms you're likely to run across, and how the standard colorimeter measures these things.

In an upcoming article, we'll dive into the actual process of calibrating your display at home, using this basic overview of colorimetry as a foundation. In the near future, we also hope to review the most popular colorimeters from both DataColor and Calibrite, to see how accurate they are with different types of displays, what their latest software will (and won't) let you do, and why we would (or would not) recommend you buy them.

In the meantime, if you have any questions or you want us to dive even deeper, let us know in the comments! The science of light and color is infinitely applicable to photography and video editing, and there is a lot more ground to cover in more technical detail if that's something you're interested in hearing about.

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