A Time-of-Flight imaging system emits pulses of IR light and measures how long the light reflected from the objects in the scene takes to come back to the system.

The polarization state of monochromatic light is often described with a Jones vector, having complex electric field amplitudes for <$x$> and <$y$> direction, if propagation occurs in <$z$> direction. That Jones vector may be constant over some area across the beam, or it may vary, for example for a radially polarized beam (see above). The effect of optical elements such as waveplates, polarizers and Faraday rotators can be described with Jones matrices, with which the Jones vectors can be transformed by multiplication. (One assumes a linear relationship between input and output amplitudes.) A whole sequence of such optical elements can be described with a single Jones matrix, which is obtained as the product of the matrices corresponding to the components.

Time-of-Flight is also the best candidate for applications where you have fast moving scenes and need reliable real-time decisions at several distance ranges (including long distances). With ToF systems, no heavy computation is required that may lead to latency and less detection accuracy of a non-determined scene. Our ToF systems provide real time image information with fast response times and no motion blur. They are also robust, compact and cost effective since they are a solid-state design, which uses less power and requires less computation.

Your first plot shows the magnetic and electric field in phase – which is wrong. The magnetic field is made from the changing electric field. The two fields swap energy back and forth. Hence the magnetic field is at a maximum when the electric field has the largest rate of change, that is, at zero E field. The magnetic field zeros in strength when the electric field rate of change is zero, at it's peak. These are a simple consequence of Maxwell's Equations and is covered in most any text on E&M. The worst error I have found in years of use of your marvelous resource!

I would have been glad to finally remove a serious mistake, but I believe my equations are correct. They agree with those in various textbooks and e.g. also in Wikipedia. Your argument concerning energy swapping back and forth between electric and magnetic fields looks somewhat plausible but is not accurate.

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In the previous cases, the direction of the electric field vector was assumed to be constant over the full beam profile. However, there are light beams where that is not the case. For example, there are beams with radial polarization, where the polarization at any point on the beam profile is oriented in the radial direction, i.e., away from the beam axis.

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One distinguishes left and right circular polarization (see Figure 2). For example, left circular polarization means that the electric (and magnetic) field vector rotates in the left direction, seen in the direction of propagation. For an observer looking against the beam, the rotation of course has the opposite direction.

In the case of an indirect ToF imaging system, the system measures the distance by calculating the phase differences of the light waves when they are emitted to the object and when they bounce back. This allows the system to build a 3D map. ToF systems provide users with a greater amount of information in a wide range of challenging conditions for a variety of applications.

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On the other hand, the polarization state of the laser output can be disturbed e.g. by random (and temperature-dependent) birefringence, such as occurs e.g. in optical fibers (if they are not polarization-maintaining or single-polarization fibers) and also in laser crystals or glasses as a result of thermal effects (→ depolarization loss). If the laser gain is not polarization-dependent, small drifts of the birefringence may lead to large changes of the polarization state, and also a significant variation in the polarization state across the beam profile.

In the simplest case, a light beam is linearly polarized, which means that the electric field oscillates in a certain linear direction perpendicular to the beam axis, and the magnetic field oscillates in a direction which is perpendicular both to the propagation axis and the electric field direction. The direction of polarization is taken to be the direction of the electric field oscillations (i.e., not the magnetic ones). For example, a laser beam propagating in <$z$> direction may have the electric field oscillations in the vertical (<$y$>) direction and the magnetic field oscillations in the horizontal (<$x$>) direction (see Figure 1); it can be called vertically polarized or <$y$>-polarized. In a different perspective, this is also shown in the second part of Figure 2.

Of course, the polarization can have any other direction perpendicular to the beam axis. Note that a rotation of the polarization by 180° does not lead to a physically distinct state.

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ToF is intrinsically a very high dynamic range application and increases with the square of the distance, and linearly with the reflectivity range. When long distances are combined with a wide reflectivity range, it can easily lead to applications needing to manage more than 80dB of linear dynamic range. Our sensors are unique in providing on-chip features to handle this, enabling unparallel trade-offs between key ToF application parameters such as distance & reflectivity range, precision and FoV, etc., and minimizing motion blur, enabling you to go to mid/long range distances and to adapt in real-time to operation conditions.

It contains the schematics of the PCB and the source code of the Evaluation Kit including FPGA and embedded software. It has been designed to be a working reference to support your system development, enabling you to save valuable time and resources and significantly improve your time to market.

Further, we have many interesting case studies on the same page, with topics mostly in fiber optics. Concrete examples cases, investigated quantatively, often give you much more insight!

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Compared to the other 3D techniques, Time-of-Flight (ToF) is the most suitable for applications that need flexibility in operation. For example, a ToF system can be mounted on a moving robot or used for measuring changing distances using its factory calibration (depending on the setup). The system can also be adapted to any operational setup making a ToF system well suited for use in complex environments and conditions.

Jones vectors can be used only for fully defined polarization states, not for unpolarized or partially polarized beams (see below) having a stochastic nature.

Because of our multiple tap per pixel innovation technology, our sensors can minimize motion artefacts and optimally use light power.

A circular polarization state can mathematically be obtained as a superposition of electric field oscillations in the vertical and horizontal direction, both with equal strength but a relative phase change of 90°. Effectively, this leads to a rapid rotation of the electric field vector – once per optical cycle – which maintains a constant magnitude.

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We have developed a Time-of-Flight model which, based on your inputs, simulates for your specific conditions the precision vs. the distance, the average and peak like power to obtain a certain precision, the achievable frame rate, and the eye-safety, etc. It precisely matches real measurements and is helpful to support application-level assessment, system-level dimensioning and sensor and system level customization, both for existing or custom sensors.

There are also azimuthally polarized beams, where the electric field direction at any point is tangential, i.e., perpendicular to a line through the point and the beam axis.

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At our Grenoble site, we have developed a laboratory specifically dedicated to 3D Time-of-Flight sensors and systems. This is a fully compliant laser safe 100m² dark room which is coated to avoid reflection in NIR & visible light. Among other key elements, it’s equipped with a software controlled 10m motorized bench, a set of calibrated targets, and a specific illumination source to emulate operation under direct sunlight. The 3D Innovation Lab is used to perform live demos for customers and to characterize and calibrate our 3D Time-of-Flight sensors and systems. It is also essential to emulating application-level test cases, so we can effectively validate our customers’ requirements as well as developing and contributing to the standardization of distance measurements based on ToF techniques.

The degree of linear polarization is often quantified with the polarization extinction ratio (PER), defined as the ratio of optical powers in the two polarization directions. It is often specified in decibels, and measured by recording the orientation-dependent power transmission of a polarizer. Of course, the extinction ratio of the polarizer itself must be higher than that of the laser beam.

A light beam is called unpolarized when the analysis with a polarizer results in 50% of the power to be in each polarization state, regardless of the rotational orientation. Microscopically, this usually means that the polarization state is randomly fluctuating, so that on average no polarization is detected. Note that such fluctuations are not possible for strictly monochromatic light.

The polarization state of light often matters when light hits an optical surface under some angle. A linear polarization state is then denoted as p polarization when the polarization direction lies in the plane spanned by the incoming beam and the reflected beam. The polarization with a direction perpendicular to that is called s polarization. These indications have a German origin: s = senkrecht = perpendicular, p = parallel.

Half-waveplateJones matrix

In many respects, light can be described as a wave phenomenon (→ wave optics). More specifically, light waves are recognized as electromagnetic transverse waves, i.e., with transverse oscillations of the electric and magnetic field.

A radially polarized laser beam may be generated from a linearly polarized beam with some optical element, but it is also possible to obtain radially polarized emission directly from a laser. The advantage of this approach, applied in a solid-state bulk laser, is that depolarization loss may be avoided [4]. Furthermore, there are applications benefiting from radially polarized light.

Note that a very small gain or loss difference for the two polarization directions can be sufficient for obtaining a stable linear polarization, provided that there is no significant coupling of polarization modes within the laser resonator.

Innovative multi-system management is also embedded on-chip to avoid interferences between ToF systems working simultaneously.

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While optical activity usually results from the presence of chiral molecules, with a concentration difference between the two possible enantiometers, it can also be induced by a magnetic field in a substance which is not naturally optically active. That is called the Faraday effect, and is exploited in Faraday rotators and Faraday isolators.

Note that radial or azimuthal polarization state requires a zero electric field strength and thus also a vanishing optical intensity on the beam axis; it is not compatible with a Gaussian beam, for example. Radially polarized beams frequently exhibit a kind of donut profile.

There are cases where polychromatic light can be described with a single Jones vector, since all its frequency components have essentially the same polarization state. However, the polarization state is substantially frequency-dependent in other cases.

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Linearly polarized light can be depolarized (made unpolarized) with a polarization scrambler, which applies the mentioned random polarization changes, or at least quasi-random changes.

Our offer is focused on professional markets where application requirements are challenging and difficult to solve with the commodity Time-of-Flight sensors that are available on the consumer market. Our products have been specifically designed to address the current Time-of-Flight challenges including:

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As explained above, a waveplate or other birefringent optical element may rotate the direction of linear polarization, but more generally one will obtain an elliptical polarization state after such an element. True polarization rotation, where a linear polarization state is always maintained (just with variable direction), can occur in the form of optical activity. Some optically active substances such as ordinary sugar (saccharose) can produce substantial rotation angles already within e.g. a few millimeters of propagation length. Optical activity can be accurately measured with polarimeters.

There are also partially polarized states of light. These can be described with Stokes vectors (but not with Jones vectors). Further, one can define a degree of polarization which can be calculated from the Stokes vector and can vary between 0 (unpolarized) and 1 (fully polarized).

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If the oscillations of the horizontal and vertical electric field vector do not have the same strengths, one has the case of an elliptical polarization, where the electric field vector, projected to a plane perpendicular to the propagation direction, moves along an ellipse.

Fully polarized states can be associated with points on the so-called Poincaré sphere. Partially polarized states correspond to points inside that sphere; unpolarized light is represented by the point at its center.

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With over 10 years of Time-of-Flight experience, Teledyne provides customers with technology solutions ranging from: CMOS image sensors and customised camera modules, right up to full system integration support. This includes a reference design of our evaluation platform, all system-level dimensioning, light & optics assessment, eye safety consideration, modelisation and simulations, algorithms and calibrations. This helps customers to shorten their time-to-market and get the best ToF system to fit their application requirements.

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A camera module with a near infrared light source and optics aimed at showing the sensors ability to perform distance measurements based on pulsed Time-of-Flight technology from short to mid-range distances. It has been designed to be highly flexible so you can evaluate the sensor in multiple configurations and operational cases.