Spectral Separation
Whether it is the XYZ tristimulus values or other colour attributes, they are all derived from the spectrum. Directly measuring the Spectral Power Distribution (SPD) is the most fundamental method of colour measurement. From the spectrum, any required colour attribute can be calculated, offering maximum flexibility.
The core of spectral measurement is spectral separation. Newton used a prism to spatially separate light of different wavelengths, forming a rainbow, which is a method of spectral separation. Principles like prisms and diffraction gratings can both achieve this, with differences in spectral resolution, spectral bandwidth, and spectral range.
After spectral separation, photodetectors such as photodiodes, CCDs, or CMOS sensors are used to capture and process the spatially separated spectrum.
Additionally, depending on whether they have a built-in light source and what specific spectral power distribution (i.e., which radiometric quantity) they measure, spectral measurement instruments can be categorised as spectrophotometers, spectroradiometers, and so on.
Perhaps the most famous spectroradiometer is the Konica Minolta CS-2000, which can measure radiance at 1nm intervals from 380nm to 780nm.
Integration
Sometimes, we only need colour attributes rather than the full spectrum, such as the common CIE XYZ tristimulus values. According to the definition of XYZ:
$$ X = K\int_{380nm}^{780nm} P(\lambda) \cdot \bar{x}(\lambda) d\lambda $$where $P(\lambda)$ is the spectral power distribution, $\bar{x}(\lambda)$ is the colour matching function, and $K$ is a normalisation coefficient.
If there were a colour filter whose transmission spectrum, when multiplied by the detector’s spectral sensitivity function, resulted in an overall spectral sensitivity similar to $\bar{x}(\lambda)$, then the value of $X$ could be obtained by directly reading the output. This method, which is akin to physically integrating the spectrum, is called integration measurement and can directly yield colour attributes.
Attributes that can be measured through integration include: tristimulus values (by integrating with the colour matching functions) and luminance (by integrating with the spectral luminous efficiency function). In short, any attribute obtained by integrating over a spectral sensitivity function can be measured using integration. The accuracy depends on how well the instrument’s spectral characteristics match the target function.
A colorimeter, such as the Datacolor SpyderX, uses integration measurement.
The problem with integration measurement is that the colour matching functions are not constant. For example, they have evolved from the original CIE 1931 colour matching functions to the later CIE 1964, and then to the CIE 2006 versions. Integration measurement methods are not backwards compatible and lack the ability to calculate other spectrum-related metrics. For instance, two light sources measured by an integration device to have identical tristimulus values might have different blue light energy distributions, thus affecting circadian rhythms differently. Furthermore, poorly matched instruments can lead to metamerism, where the output error changes with the spectrum. To some extent, a camera can also be considered a device for the integration measurement of colour, and its spectral sensitivity function is called the SSF (Spectral Sensitivity Function).
Other Aspects of Measurement
Beyond basic spectral measurement, one must also consider the reflectance, gloss, and texture of real objects at different angles. In industrial applications, there is also a need to measure colours across a two-dimensional plane or even in three-dimensional space at once. Specialised instruments and methods exist for these purposes, though they are generally quite expensive.
For example, the EZContrast series from Eldim can measure reflectance or radiance at multiple angles simultaneously, while imaging photometers produced by Topcon can measure the spectrum and colour of multiple points on a two-dimensional plane in a single capture.
A camera, being an imaging device that performs three types of spectral integration, serves as an excellent low-cost tool for two-dimensional colour measurement. However, special attention must be paid to metamerism and device characterisation.
