What makes optical simulation predictive?
Predictive optical simulation aims to compute how light propagates, interacts with materials, and reaches an observer under well-defined physical conditions. Unlike visualization-oriented rendering, its objective is not visual plausibility but physical correctness: the simulation must remain valid when illumination, material composition, geometry, or observation conditions change.
At the core of this problem lies light transport. Light propagation is governed by wavelength-dependent physical laws that describe reflection, refraction, absorption, scattering, and interference. Any simulation framework that neglects this spectral dependency or replaces it with empirical approximations inevitably loses predictive power.
Geometric optics provides the first-order physical description of light transport by modeling light as energy-carrying rays propagating through space and interacting with interfaces and volumes. While geometric optics alone is not sufficient to describe all optical phenomena, it defines the essential structure upon which spectral radiative transfer, material interaction models, and perception pipelines must be built.
This article establishes geometric optics as the physical foundation of predictive appearance simulation, and the basis for Ocean™ optical simulation software technology.
A supplementary article explores why non-spectral and empirical rendering methods are not predictive and explains how Ocean™’s fully spectral, measurement-driven framework enables physically true simulation of real materials under real lighting conditions.
Geometric optics: The physical basis of light transport
Geometric optics: Rays, light propagation, refraction, and wavelength dependence:
In geometric optics, light is modeled as rays that transport optical energy through space. Rays propagate in homogeneous media and change direction only when interacting with surfaces or material boundaries. These changes are governed by physical laws that depend on the refractive indices of the media involved. Because refractive index varies with wavelength, ray trajectories and energy redistribution are inherently spectral, making wavelength-resolved data essential for predictive optical simulation.
In the real world and in optical simulation, a ray represents the path followed by optical energy. A ray propagates until it encounters:
- a surface boundary,
- an inhomogeneity in the medium,
- or a participating volume such as pigments, particles, fibers, or voids.
At each interaction, physical optics laws determine how the ray’s energy is redistributed between reflection, refraction, absorption, and scattering.
Because energy redistribution occurs at every interaction, light transport must be modeled as a sequence of physically governed events.
Looking at the fish tank as shown, we can see the same fish in two different locations, because light changes directions when it passes from water to air.
In this case, the light can reach the observer by two different paths, and so the fish seems to be in two different places. This bending of light is called refraction and is responsible for many optical phenomena.
Why does light change direction when passing from one material (medium) to another? It is because light changes speed when going from one material to another. The speed of light depends strongly on the type of material, since its interaction with different atoms, crystal lattices, and other substructures varies.
We define the index of refraction n of a material as:
where v is the observed speed of light in the material and it is wavelength dependent. c ≈ 3.00 x 108 m/s -speed of light in a vacuum.
Since the speed of light is always less than c in matter and equals c only in a vacuum, the index of refraction is always greater than or equal to one for visible spectrum.
The refractive index quantifies how fast light propagates in a material compared to vacuum. It is defined as the ratio between the speed of light in vacuum and its phase velocity in the medium.
The refraction of light when it passes from a fast medium to a slow medium bends the light ray toward the normal to the boundary between the two media. The amount of bending depends on the indices of refraction of the two media and is described quantitatively by Snell’s Law.
Why this matters:
Because the refractive index depends on wavelength, refraction is inherently spectral. Dispersion effects cannot be reproduced without wavelength-resolved data.
Because refractive index varies with wavelength, each spectral component of light refracts differently. This phenomenon, known as dispersion, is responsible for:
- chromatic aberration,
- wavelength-dependent caustics,
- angular color shifts in transparent and translucent materials.
Read more in our article: https://eclat-digital.com/spectral-rendering
Common misconception: Dispersion is a secondary effect.
Reality: Dispersion directly follows from the wavelength dependence of refractive index.
Everyday example of geometric optics: Total Internal Reflection in an aquarium:
A simple example can be observed when looking at an aquarium. Depending on the viewing angle, we may clearly see the interior of the tank while the exterior surroundings suddenly disappear, and the surface behaves like a mirror. This effect is not caused by the glass itself, but by a fundamental optical phenomenon governed by geometric optics: total internal reflection at the water–air interface.
A particular consequence of Snell’s law explains why, at certain viewing angles, we can see the interior of an aquarium but not the surroundings beyond the glass wall. This occurs because light travels from a slower medium (water, refractive index ≈ 1.33) to a faster medium (air, refractive index ≈ 1.00), leading to refraction away from the normal.
To determine the limiting case, we calculate the angle for which the refracted ray emerges at 90°, known as the critical angle. Using Snell’s law:
n₁ sin θ₁ = n₂ sin θ₂
With: 1 * sin90 = 1.33 sinθ
Which gives: θ = 48.8°
This value corresponds to the critical angle for the water–air interface. Now what happens if we have the light enter at an angle higher than that? If we attempt to compute the refraction angle:
1 * sinθ = 1.33 sin50
we obtain: sinθ = 1.02.
Since this value lies outside the valid range of the sine function, refraction is no longer possible. Instead, the interface behaves like a reflective boundary, and the light is entirely reflected back into the water. This phenomenon is known as total internal reflection.
Total internal reflection (source: Avantier)
Illustration of total internal reflection effect.
Total internal reflection illustrates how simple laws from geometric optics can produce strong visual effects that depend directly on material properties and viewing geometry. In predictive optical simulation, these ray-based mechanisms must be reproduced accurately, but physically correct appearance also requires modeling how materials redistribute light through interface physics and volumetric interactions using physically grounded optical data.
Interface physics: Fresnel equation and the role of the Complex Refractive Index:
When light reaches a material interface, optical energy is redistributed between reflection and transmission according to wavelength, incidence angle, polarization, and material properties. This redistribution is governed by the Fresnel equations, which require the refractive indices of both media. For absorbing materials, these equations must be extended using a complex refractive index to correctly model phase propagation and energy losses. Because all these quantities are wavelength-dependent, physically correct interface modeling requires fully spectral data. Without it, polarization effects, angular reflectance, absorption, and energy conservation cannot be simulated predictively.
When light falls on the interface, part of it is reflected and the rest is transmitted. The distribution of the light’s energy on the interface between the two media can be calculated with Fresnel equations. That is, they give the reflection and transmission coefficients for waves parallel and perpendicular to the plane of incidence (Figure below). This shows that considering polarization of light in simulation calculation is important for physical accuracy. For a dielectric isotropic medium in Ocean™ Fresnel equations dictate the probability of the light reflection or transmission governing how many rays following these paths resulting in power distribution of the physically true light-material interaction for a ray-tracing algorithm.
The amount of polarization depends on the indices of refraction of the media involved.
Unpolarized light has equal amounts of vertical and horizontal polarization. After interaction with a surface, the vertical components are preferentially absorbed or refracted, leaving the reflected light more horizontally polarized (in 
symbol 
refers to polarization perpendicular to the plane of incidence).
Why this matters:
Because Fresnel coefficients differ for each polarization state, ignoring polarization leads to incorrect energy distribution at interfaces.
Fresnel equations quantify how incident electromagnetic energy is split between reflection and transmission as a function of incidence angle, polarization, and refractive indices.
It defines the reflection coefficients as:
And the transmission coefficients as:
Note that these coefficients are fractional amplitudes, and must be squared to get fractional intensities for reflection and transmission.
Checking out conservation of energy in this situation leads to the relationship:
which applies to both the parallel and perpendicular cases (both polarization states).
The angular dependence of Fresnel reflectance produces characteristic polarization effects.
Typical reflection and transmission curves for external reflection. These curves are the graphical representation of the Fresnel equations. Note that the reflected amplitude for the light polarized parallel to the incident plane is zero for a specific angle called the Brewster angle.
The reflected light is then linearly polarized in a plane perpendicular to the incident plane. This polarization by reflection is exploited in numerous optical devices.
Polarization by reflection.
Polarization by reflection.It can be shown that reflected light is completely polarized at an angle of reflection θb, given by Brewster’s law:
At this angle, the reflected light becomes fully linearly polarized perpendicular to the plane of incidence. This effect is widely exploited in optical devices and must be reproduced accurately in physically based simulations.
Fresnel equations can also be applied to absorbing media, including metals. In that case, a complex refractive index needs to be used [Read Complex Fresnel interface law in Ocean™ documentation]
A complex refractive index is used to quantify not only the phase change per unit length (ratio of the phase velocity of the wave to the speed of light) but also (via its imaginary part) propagation losses (e.g. caused by absorption and scattering). [Read Complex dielectric function in Ocean™ documentation]
Where:
- n0 is the “standard” refractive index
- κ is the optical extinction coefficient
- and both are wavelength dependent.
The optical extinction coefficient “indicates the amount of attenuation when the electromagnetic wave propagates through the material”. The larger the value, the more light is absorbed and scattered by the material. This characteristic is dimensionless. It is related to the absorption coefficient 
through
This value quantifies how much light is absorbed per unit distance as it propagates through the material and has a dimension 
.
Because absorption accumulates along optical paths, interface physics and volumetric attenuation cannot be decoupled.
As light propagates through an absorbing medium, its intensity decreases exponentially with distance according to the Bouguer–Lambert law.
In the figure below, the absorption along a path (x0; x) is ruled by the Bouguer-Lambertian law, giving the resulting intensity after a distance d:
All above described values are wavelength dependent so the spectral information about incident light and its interaction with the media are strongly dependent on spectral data.
All quantities involved, refractive indices, extinction coefficients, Fresnel terms, and absorption, are wavelength dependent. As a result, interface appearance is inherently spectral.
In Ocean™, this relation is applied directly, meaning that absorption and propagation losses are derived from the same physical equations used in classical optics and electromagnetic theory.
Volumetric interaction: Scattering in participating media:
In many real materials, light does not only interact at surfaces but also within volumes. Volumetric interactions such as scattering and absorption govern the appearance of translucent, turbid, or particulate media. These effects depend on particle size, concentration, and wavelength, and must be modeled using physically based phase functions.
Participating media contain particles or structures that interact with light throughout the volume. Examples include:
- pigmented polymers,
- hazy glass,
- coatings with fillers or flakes,
- biological tissues,
- atmospheric media.
In such real-world materials, light undergoes multiple scattering events before exiting the medium, that have an impact on the appearance of the final object.
When particle sizes are comparable to the wavelength of light, scattering behavior is accurately described by Mie theory. The angular distribution of scattered light depends strongly on:
- particle diameter,
- refractive index contrast,
- wavelength.
This leads to effects such as forward scattering, haze, and reduced contrast. [Read more about Mie medium in Ocean™ documentation]
To efficiently model volumetric scattering in complex scenes, phase functions are used to describe the angular redistribution of light after a scattering event.
A commonly used model is the Henyey–Greenstein phase function, which allows continuous control over scattering anisotropy and can be applied spectrally.
Because scattering directionality affects path length and energy loss, volumetric models directly influence color build-up and brightness.
Ocean™ computes spectral phase functions to simulate Mie scattering based on particle size distributions. The Henyey–Greenstein spectral scattering model is used for applications ranging from atmospheric simulations (dust clouds) to life sciences (biological tissue) and material appearance studies.
A physically grounded pipeline for predictive appearance simulation
Geometric optics defines the structural framework of light transport. Interface physics governs energy redistribution at boundaries. Volumetric scattering controls color build-up and brightness within materials. All these mechanisms are inherently wavelength-dependent.
Predictive optical simulation therefore requires spectral light transport and physically grounded material modeling. Without spectral resolution, dispersion, polarization, absorption, and scattering cannot be reproduced reliably when conditions change.
Understanding these foundations clarifies a critical question: why do many rendering systems fail to produce predictive results?
This is what we explore in the article “How to ensure predictive material appearance in real-world conditions?”, where we analyze the practical limitations of traditional rendering workflows and the structural requirements of a physically true appearance simulation pipeline.
Predictive appearance simulation requires a complete physical chain. Ocean™ integrates geometric optics, spectral radiative transport, measurement-driven material data, real-world lighting models, and human vision modeling into a unified engineering framework.
The result is not optimized visual output, but physically true digital prototypes whose behavior can be analyzed, compared, and validated against real-world observations under any relevant lighting condition.
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