## Further Reading

Meyer was one of the first researchers to closely investigate spectral
representations in graphics (Meyer and
Greenberg 1980; Meyer et al. 1986). Hall (1989) summarized the state of the art in spectral representations through
1989, and Glassner’s *Principles of Digital Image Synthesis* (1995)
covers the topic through the mid-1990s. Survey articles by Hall (1999), Johnson and Fairchild (1999), and Devlin et al. (2002) are
good resources on this topic.

Borges (1991) analyzed the error introduced from the tristimulus representation when used for spectral computation. Peercy (1993) developed a technique based on choosing basis functions in a scene-dependent manner: by looking at the SPDs of the lights and reflecting objects in the scene, a small number of spectral basis functions that could accurately represent the scene’s SPDs were found using characteristic vector analysis. Rougeron and Péroche (1997) projected all SPDs in the scene onto a hierarchical basis (the Haar wavelets), and showed that this adaptive representation can be used to stay within a desired error bound. Ward and Eydelberg-Vileshin (2002) developed a method for improving the spectral results from a regular RGB-only rendering system by carefully adjusting the color values provided to the system before rendering.

Another approach to spectral representation was investigated by Sun et al. (2001), who partitioned SPDs into a smooth base SPD and a set of spikes. Each part was represented differently, using basis functions that worked well for each of these parts of the distribution. Drew and Finlayson (2003) applied a “sharp” basis, which is adaptive but has the property that computing the product of two functions in the basis doesn’t require a full matrix multiplication as many other basis representations do.

When using a point-sampled representation (like `SampledSpectrum`), it
can be difficult to know how many samples are necessary for accurate
results. Lehtonen et al. (2006) studied this issue and determined that a
5-nm sample spacing was sufficient for real-world SPDs.

Evans and McCool (1999) introduced stratified wavelength clusters for representing SPDs: the idea is that each spectral computation uses a small fixed number of samples at representative wavelengths, chosen according to the spectral distribution of the light source. Subsequent computations use different wavelengths, such that individual computations are relatively efficient (being based on a small number of samples), but, in the aggregate over a large number of computations, the overall range of wavelengths is well covered. Related to this approach is the idea of computing the result for just a single wavelength in each computation and averaging the results together: this was the method used by Walter et al. (1997) and Morley et al. (2006).

Radziszewski et al. (2009) proposed a technique that generates light-carrying paths according to a single wavelength, while tracking their contribution at several additional wavelengths using efficient SIMD instructions. Combining these contributions using multiple importance sampling led to reduced variance when simulating dispersion through rough refractive boundaries. Wilkie et al. (2014) used equally spaced point samples in the wavelength domain and showed how this approach can also be used for photon mapping and rendering of participating media.

Glassner (1989b) has written an article on the underconstrained problem of converting RGB values (e.g., as selected by the user from a display) to an SPD. Smits (1999) developed an improved method that is the one we have implemented in Section 5.2.2. See Meng et al. (2015) for recent work in this area, including thorough discussion of the complexities involved in doing these conversions accurately.

McCluney’s book on radiometry is an excellent introduction to the topic (McCluney 1994). Preisendorfer (1965) also covered radiometry in an accessible manner and delved into the relationship between radiometry and the physics of light. Nicodemus et al. (1977) carefully defined the BRDF, BSSRDF, and various quantities that can be derived from them. See Moon and Spencer (1936, 1948) and Gershun (1939) for classic early introductions to radiometry. Finally, Lambert’s seminal early writings about photometry from the mid-18th century have been translated into English by DiLaura (Lambert 1760).

Correctly implementing radiometric computations can be tricky: one missed cosine term and one is computing a completely different quantity than expected. Debugging these sorts of issues can be quite time-consuming. Ou and Pellacini (2010) showed how to use C++’s type system to associate units with each term of these sorts of computations so that, for example, trying to add a radiance value to another value that represents irradiance would trigger a compile time error.

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