# Time-of-Flight Cameras

Time-of-flight cameras are sensors which deliver two types of information for each pixel: the intensity (gray-value) and the distance from the camera (depth). A time-of-flight camera consists of three basic components:

• an active illumination unit,
• a lens, and
• the imaging sensor.

The figure below illustrates the basic working principle: The active illumination unit emits intensity-modulated light in the near-infrared range. Light hitting an object or surface is reflected back to the camera. The reflected light is projected onto the imaging sensor using the lens. By correlating the emitted and received signals it is possible to compute the distance of the illuminated object/scene to the sensor for each pixel.

Time-of-flight principle

From the acquired depth information pretty nice 3-D surface data can be reconstructed in real-time (usually 20-50 fps):

3-D surface reconstruction from time-of-flight data

## Time-of-Flight Cameras in Detail

Conventional imaging sensors, such as in a digital still image camera, consist of multiple photo diodes arranged in a matrix. Normally, these diodes provide a gray-scale or color image of the scene. In contrast to normal cameras, a Photon Mixing Device (PMD) sensor additionally acquires a distance value for each pixel simultaneously to the intensity (gray) value.

Concluding, a time-of-flight (ToF) sensor is a matrix composed of distance sensors. Despite the functional improvement (compared to conventional imaging sensors) a ToF sensor itself is still manufactured in standard CMOS technology. Therefore, imaging and 3-D measurement capabilities can be placed next to system-relevant electronics like analog-digital converters, etc. All ‘intelligence’ of the sensor is incorporated in the chip, including the distance computation for each pixel. Therefore, ToF pixels are sometimes also called ‘smart pixels’.

Recently, applications like gesture recognition or automotive passenger classification use ToF sensors and ToF is about to become a component of consumer electronics. As ToF sensors provide data at rates of more than 30 frames per second, they are suitable for real-time 3-D imaging. We are convinced that ToF technology can contribute to enhance applications within various business fields.

## Working Principle

ToF cameras provide a real-time 2.5-D (only the camera-facing part of the surface can be observed by the ToF camera) representation of an object. The object is actively illuminated by an incoherent light signal. This signal is intensity-modulated with a cosine signal of frequency $f_{mod}$. Usually the emitted light is in the non-visible near infrared range of the spectrum.
The light signal travels with constant speed in the surrounding medium and is reflected by the surface of the object. By estimating the phase-shift $phi_d$ (in rad) between both, the emitted and reflected light signal, the distance $d$ can be computed as:

$d=frac{c}{2f_{mod}}cdotfrac{phi_d}{2pi}$,
where $c$ [m/s] denotes the speed of light, $d$ [m] the distance the light travels, $f_{mod}$ [MHz] the modulation frequency, $phi_d$ [rad] the phase shift.

In addition to depth values, ToF cameras also provide intensity values, representing the amount of light sent back from a specific point.

### Non-ambiguous Range

Due to the periodicity of the cosine-shaped modulation signal, ToF cameras have a non-ambiguous range of $d_n=frac{c}{2f_{mod}}$. Within this range, distances can be computed uniquely. The range depends on the modulation frequency of the camera which defines the wave length of the emitted signal. To compute distances, the camera evaluates the phase shift between a reference (emitted) signal and the received signal. The phase shift $phi_d$ is proportional to the distance $d$. The figure below shows the relation of $phi_d$ and $d$.

Relation of a phase shift to the distance at a fixed modulation frequency of $f_{mod}$=20 MHz.

Currently available ToF cameras operate at a modulation frequency of about 20 MHz. Then, a single wave is of length $2pi$ or 15 m. Thus, the unique range of these ToF cameras is approx. 7.5 m. The range can be altered by adapting the modulation frequency of the active illumination.

## Time-of-Flight Camera Manufacturers

Today, several companies provide time-of-flight cameras. Currently Metrilus supports the following ToF companies:

• Mesa Imaging (Swissranger SR 3000 and SR 4000)
• Fotonic (C-40, C-70)
• PMD (CamCube, CamBoard)
• ifm (O3D-200)

## Literature

This page is based on C. Schaller, ‘Time-of-Flight – A New Modality for Radiotherapy’. Ph.D. Thesis, 2011.

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