Fluorescence : brighten your renderings

Introduction

We do not need to get into the bright details to uncover this fact: fluorescent colours look amazing. Whether we are looking at a white t-shirt under black light or finding the ink of a highlighter un-naturally bright, we wonder what makes these colours stand out from the rest.
Fluorescence is simply the light that molecules give off when they have been excited. At least in principle, it has been known for quite a while how to handle fluorescent substances, i.e. materials which are capable of shifting the wavelength of light that interacts with them, in the context of computer graphics computations.

But due to technical difficulties with integrating wavelength shifting into modern rendering engines, the feature is still absent from all modern production rendering systems. The absence of this feature is an increasingly unsatisfactory situation, as the effect does play quite a role in the appearance of a number of common materials, such as paper and textiles (both via optical brighteners that are present in a large number of them), and fluorescent warning paint, e.g. on emergency vehicles.

Ocean™ 2021 can give the user a starting point for a physically based spectral rendering model to simulate surface fluorescence. We will show hereafter how fluorescence works and how it can be applied in Ocean™.

Basic principles

Generation of luminescence through excitation of a molecule by ultraviolet or visible light photons is a phenomenon termed photoluminescence, which is formally divided into two categories, fluorescence, and phosphorescence, depending upon the electronic configuration of the excited state and the emission pathway. Fluorescence is the property of some atoms and molecules to absorb light at a particular wavelength and to subsequently emit light of longer wavelength almost instantaneously (10^-9-10^-7 seconds), named the fluorescence lifetime. The process of phosphorescence occurs in a manner like fluorescence, but with a much longer excited state lifetime (10^-3-10² seconds).

1. Excitation

An external source lights the fluorescent material, also called fluorophore, at the excitation wavelength λ_EXC. Each photon from the light will create an excited electronic singlet state (S₁‘).

2. Excited state lifetime

The excited state lasts for a few nanoseconds. During this time, the fluorophore undergoes conformational changes and is also subject to a multitude of possible interactions with its molecular environment. These changes and interactions have two consequences:

The energy of S₁‘ is partially dissipated and a relaxed singlet excited state (S₁) is created. The fluorescence emission comes from the S₁ state.
Not all the molecules initially excited by absorption (Step 1) return to the ground state (S₀) by fluorescence emission. There are many other processes (collisional quenching, intersystem crossing…) may also depopulate the S₁ state.

The fluorescence quantum yield, which is the ratio of the number of fluorescence photons emitted to the number of photons absorbed, is a measure of the relative extent to which these processes occur:

Q = Number of photons emitted / Number of photons absorbed

3. Fluorescence emission

The fluorescence emission consists in emitting at the emission wavelength λ_EMI. Due to energy dissipation during the excited-state lifetime, the energy of this photon is lower, and therefore of longer wavelength, than the excitation photon at λ_EXC.

Fluorescence spectra

Absorption spectrum

A fluorescence excitation spectrum is when the emission wavelength is fixed (usually the wavelength of maximum emission intensity) and the excitation monochromator wavelength is scanned.
Excitation is equivalent to absorption since upon absorption, the molecule reaches the excited state. For a pure product and in the absence of any interference with other molecules in the solution, the excitation and the absorption spectra of a fluorophore should be identical.

Emission spectrum

A fluorescence emission spectrum is when the excitation wavelength is fixed, and the emission wavelength is scanned to get a plot of intensity vs. emission wavelength. For example, following Figure 2, if we fix the excitation spectrum at wavelength C (500 nm) and we scan the emission spectrum between 550 and 720 nm, we will get the emission spectrum corresponding to the letter C.

It is important to remember that although illumination at the excitation maximum of the fluorophore produces the greatest fluorescence output, illumination at lower or higher wavelengths affects only the intensity of the emitted light—the range and overall shape of the emission profile are unchanged.

A new way to render materials

A BSDF, or Bidirectional Scattering Distribution Function, is a general representation of the reflective and transmissive optical properties of surfaces. As previously described, we have seen our fluorescent BSDF model has specific parameters to:

Fluorescent absorption spectrum
Fluorescent emission Spectrum
Quantum yield (Q): fraction of emitted energy to absorbed energy

In addition, other parameters are mandatory:

Non-fluorescent diffusion spectrum
Concentration parameter (C): fraction of fluorescence in the material that can be interpreted as a surface’s relative amount of fluorescent molecules

Examples

In this example, we will render a box containing two balls. The left ball is a control sample with a simple diffusion model (no fluorescence) and the right ball will be the fluorophore. Its associated spectra can be seen in Figure 3.

It must be noted that this fluorophore does not exist and has been created for the purpose of this demonstration. The fluorescent BSDF is however compatible with any measured data.

As seen previously, we allow users to change the concentration parameter (C) and the quantum yield (Q). These two parameters will adjust the behaviour of the fluorescent process and, thus, change the rendering of your material.

Figure 3 – Example scene. A box containing two objects: a control sample (left) and the test object. Both control sample and fluorophore have a green diffuse spectrum green following the graph on the right. The fluorophore has the associated fluorescent absorption and emission spectra.

In figure 4, we can observe that under UV light (bottom left), the fluorescent object emits light at 460 nm (the actual fluorescent spectra are the same than the optical brightener called quinine). Using the concentration parameter, we will weight the re-emission light and add the fluorescent contribution to the diffusion spectrum. Thus, we obtain two different materials (bottom middle and bottom right) even though their spectrum is identical, but their concentration parameter is different (respectively 0.5 and 1).

Figure 5 shows that fluorescent surfaces can convert light from the visible and the ultraviolet range to visible wavelengths, and how Q and C influence the appearance of our BSDF given its spectra.

Figure 5 – Q increasing from left to right, C increasing from top to bottom, varying from 0 to 1

Applications

Now we have seen how our fluorescent model behaves, we can approach the applications of this technology within Ocean. We are now able to render real brightening agents such as displayed in Figure 6: respectively Quinine (flavour component of tonic water), Envy Green, Rhodamine, and Texas Red (dyes).

Figure 6 – our Fluorescent BSDF parametrized with existing optical brighteners: Quinine, Envy Green, Rhodamine and Texas Red

But in what way representing brightening agents can enhance the rendering of material? We have seen previously that these agents are present in many objects, from clothes to plastics, to increase the brightness. In Figure 7, we can see the differences between a tennis ball when there is no fluorescence and when the phenomenon is considered.

Figure 7 – Example of the impact of surface fluorescence on a tennis ball rendering

Conclusion

The development of the surface fluorescence is a major addition to Ocean™ since, to our knowledge, this is the only case of rendering software implementing a physically based fluorescence model. Virtual prototyping can go one step further toward realism by considering more physical reactions.

For now, our rendering engine handles a purely diffuse fluorescent surface. We are currently working on volumetric fluorescence to complete the fluorescence model within Ocean™.

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