# In the light of Polarization

by Antony Escudie

## Introduction

Polarization is a fundamental property of electromagnetic waves, . An electromagnetic wave is composed of two orthogonal oscillating fields, the electric and magnetic ones. The polarization of an electromagnetic wave describes the evolution of the oscillation of the electric and the magnetic fields at a given point in space.

Although almost not directly perceptible by human vision, polarization is well present in our everyday life, and can be put forward through everyday objects. For instance, polarization effect is used for polarized sunglasses to reduce glare from reflecting horizontal surfaces (snow, sea). It is also involved in photography with polarizing filters, for example to darken the sky and to increase contrast, or also to reduce or even eliminate annoying reflections. LCD display technology also uses polarization properties of light, and 3D glasses concept to watch 3D movies is also based on polarization behavior.

Even if human eye is to a large extent only sensible to the intensity and the color of light, the polarization must be considered in Computer Graphics, namely for rendering software. Indeed, polarization is necessary to obtain accurate renders, especially when dealing with scenes containing reflections or outdoor lighting conditions…

Ocean™, developed by Eclat Digital, is natively a polarized renderer, meaning that incoherent generalized polarization ( 3D glasses…) is taken into account. This allows Oceanto provide physically true predictive images and lighting quantification.

## Polarization framework in Ocean

It is a well-known fact that the polarization state of electromagnetic radiation such as light can be described by two formalisms: The Jones and the Stokes formalisms. Ocean™ uses the Stokes formalism, which involves 4 parameters, commonly noted I, Q, U and V, to describe the polarization state:

. I corresponds to the total intensity (equivalent to the radiance)

. Q carries information about horizontal or vertical linear polarization. Q = +1 corresponds to horizontally polarized light and Q = -1 corresponds to vertically polarized light

. U carries information about linear polarization at 45° from horizontal or vertical polarized light

. V carries information about right or left circular polarization. V = +1 corresponds to right circularly polarized light and V = -1 corresponds to left circularly polarized light.

|Figure 1|

Illustration of the Q, U and V parameters and their impact on the polarization state. The red line represents the orientation of the polarization state.

These 4 parameters are generally put into a vector called The Stokes Vector. This Stokes vector paves the entire polarization space, from unpolarized to fully polarized light. Ocean™ being a spectral renderer, the Stokes vector is computed for each wavelength.

As an example, the polarization in Ocean is considered during the treatment of metals, in Ocean™ is considered during the treatment of metals.

## Polarization – Simple illustrations

A light wave can undergo different effects affecting its polarization when interacting with matter. In the following, we consider two cases for which the polarization is affected and illustrate with Ocean™ simulations.

### ABSORPTION/TRANSMISSION

The polarization of light can be changed when the wave passes through an absorbing material. It is often said that the light is filtered. The absorbing material plays the role of a filter, which will let pass the component of the light which is aligned with its filtering properties.

The polarizing filter therefore has a privileged orientation (horizontal, vertical or intermediate angle), which allows the light to pass through. In this way, two polarizers, rotated 90° with respect to each other, will completely filter the light, as shown in Figure 2. A horizontally polarized display is simulated with Ocean (red and blue plan), in front of which we have placed a vertical polarizing filter on its left side (green plan in figure), inducing the complete filtering of the light (black area). By adding a second polarizer (magenta plan), rotated of 45°, between the display and the vertical polarizer, we break the complete filtering. Indeed, the light coming from the display, which is horizontally polarized, becomes 45°-polarized after passing though the rotated filter. The 45°-polarized light is then able to pass through the vertical polarizer and reach the camera.

| Figure 2 |

Illustration of polarizing filters. Left figure shows a sketch of the used setup composed. Right figure presents the rendering of the setup. See text for details.

| Figure 3 |

Illustration of the impact of a polarizer on strong reflection on water surface. Left: Without filter. Right: With filter. Three red balls are placed at the bottom of the pool.

Another example is shown in figure 3. A swimming pool is simulated, in which three red balls are placed at its bottom. The lighting conditions mainly come from the sky. In the left render, strong reflections are observed on the surface of the water, making the bottom of the pool and the two balls on the sides not very visible. In the right render, a polarizer is added to the camera (same principle as the filters used in photography for instance) to remove the reflections on the surface of the water making the bottom and the two balls in question more visible.

### REFLECTION

The reflection of light on a material can also change its polarization. This is what is shown in figure 4, which simulates the principle of an antireflective stack. The assemble of the device is as follows (see figure 4, left), from external layer to internal layer:

. A first polarizer, which is a linear polarizer, rotated of 45° in this simulation (absorption filter, see previous paragraph),

. A second polarizer, with is a quarter-wave plate polarizer and which induces a phase shift of 90° (absorption filter, see previous paragraph),

. A reflective surface, here a piece of glass of 1 mm thickness.

Two light sources are added, one on the top left of the render, to simulate external light coming on the device, and one behind the piece of glass in bottom right of the render, to simulate the emission of the device.

| Figure 4 |

Left: sketch of the setup, top view. It is composed of two polarizers (blue and green lines), one reflective surface (glass foil represented by the black line) and two light sources (small red lines). Right: Ocean simulation, showing the operation of an antireflective filter. For the understanding, the two polarizers and the reflective surface positions are represented by the blue, green and white lines respectively.

Figure 4 right shows the result of the simulation. After passing through the first polarizer, the light is linearly polarizer, rotated of 45°. Passing through the second polarizer, the light experiences a phase shift of π/2 and becomes left circularly polarized. It is then partially transmitted/reflected by the glass foil. The reflection of the light on the glass foil induces a change a its phase (by definition), and the light becomes right circularly polarized. After passing back through the second polarizer, it again becomes linearly polarized, but rotated of -45°. The polarization of the light is now at 90° of the properties of the first polarizer, and will be completely filtered, as shown in the render where no light comes out the first polarizer. At the same time, the light emitted behind the glass foil is well transmitted through all the stack. This is the principle of an antireflective filter.

We have shown through these simple examples that Ocean™ is able to simulate the polarization state of light when it interacts with matter.

Ocean™ can also be used for technical studies on polarization, to test different existing technologies, or to assist in the decision to manufacture new products. Let us now deal with an in-situ example.

## Polarization – In situ illustration

In the automotive industry, one of the lines of study today is to designate new technologies offering greater safety to drivers (commonly described as ADAS for Advanced Driver-Assistance System), such as Head Up Display (HUD) technology. The HUD (its principle is to project an image on the windshield of the vehicle) allows the drivers to have access to information (speed, GPS indications) without taking eyes off the road.

One of the problematic todays is that when a driver wears polarized sunglasses, the HUD image projected on the windshield vanishes. This behavior is well reproduced with Ocean, as shown in figure 5. The left render presents the simulation of a car in a sunny environment, with a camera simulating the point of view of a driver. A grid image is projected onto the windshield and is clearly visible in left render. In this case, the HUD system is composed of a horizontally polarized light display, which is then projected onto the windshield thanks to a mirror. The light arriving on the windshield is perfectly horizontally polarized. Thus, reflected light is horizontally polarized, and detected by the camera.

Remark: unpolarized light (same “amount” of vertical and horizontal polarization) arriving on a glass surface will be partially horizontally polarized when reflected, and partially vertically polarized when refracted (transmission).

Therefore, when driver wears polarized sunglasses, which are vertically polarized, the HUD image vanishes, since its polarization is mostly horizontally oriented (see results in figure 5 right). With Ocean™, it is possible to study different options to solve this problem, for example with a dedicated HUD system, or with specific windshield properties to maximize the reflection of the vertical polarization towards the driver.

The use of virtual prototyping, and therefore of Ocean™, allows in cases such as this one to test a considerable number of configurations, without producing a large number of samples, and is therefore a quick to implement and relatively inexpensive solution.

| Figure 5 |

HUD study example. Left image: classic HUD system, the image is visible. Right: classic HUD system, the image vanished since the driver wears polarized sunglasses.

## Conclusion

We have seen that the polarization properties of the light must be considered for rendering purposes. Eclat Digital took the part of making Ocean™ a rendering software that natively takes into account the polarization state of light. Indeed, it is mandatory to provide physically true predictive images.

Ocean™ uses the Stokes’ formalism to well compute the polarization state of light during the whole simulation, and this is done for all the wavelengths of the spectrum. This feature allows Ocean™ to faithfully reproduce the interaction of light with the objects in a scene, especially with dielectric surfaces such as glass.

In this article, we first illustrated on simple cases the consideration of polarization in Ocean, before continuing on a more complete case, the HUD. Ocean™ can go further, and can be used for display application studies, or for evaluating the appearance of a glazing facade.