SR4000 ToF相机深度误差分析与补偿方法

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"Maria Valasia Peppa的硕士论文‘Precision Analysis of 3D Camera’主要探讨了SR4000 Time-of-Flight (ToF)相机的深度误差特性，并提出了潜在的误差补偿模型以减轻其对测量精度的影响。论文首先研究了误差来源、它们的特征以及如何影响深度测量。在实践部分，通过实验对上述分析进行了验证。最后，论文提出了一些简单的方法来减少深度误差，使得ToF相机可以应用于高精度的应用场景。" 这篇论文详细讨论了3D成像技术中的一个重要方面——时间飞行（ToF）相机的精度分析。ToF相机是一种新型的主动传感器，它能够直接获取深度信息，实现三维场景的重建。随着三维映射技术的发展，这类设备如激光扫描仪和立体系统变得越来越受欢迎。作者首先深入剖析了SR4000 ToF相机的深度误差来源。这些误差可能包括信号噪声、环境光干扰、温度变化、光学畸变等多种因素。每种误差源都会影响到相机所获取的深度数据的准确性，从而影响3D重建的质量。作者通过理论分析和实验数据，详细描述了这些误差的特性及其对测量结果的影响。在论文的实验部分，Peppa进行了实际操作，以验证这些误差源对深度测量的具体影响。这些实验可能包括在不同光照、温度和距离条件下拍摄目标，然后分析得到的深度图像，以识别和量化各种误差模式。最后，基于这些分析，作者提出了若干种简单的误差校正方法。这些方法可能包括硬件改进（例如，增强信号处理能力，提高抗干扰能力）、软件算法优化（如，采用滤波技术去除噪声，或利用统计模型估计和纠正误差）等，以降低深度测量的误差，提高ToF相机在高精度应用中的性能。这些方法对于提升3D相机在建筑测量、机器人导航、虚拟现实等领域的应用具有重要意义。总体来说，这篇论文为理解和改善ToF相机的深度测量精度提供了有价值的见解和实用的解决方案，为3D成像技术的发展贡献了重要的一环。

pg. 8

- industrial machine vision (for classifying items)

The ToF cameras are gaining increasing attraction in multiple fields of industry and robotics

because of their simple usage and quick provided results. Furthermore ToF cameras have

become increasingly interesting also in the civil engineering applications. In the literature

authors propose methods to use ToF cameras for structure deformation monitoring [32].

Apparently ToF cameras might replace laser scanners for close range applications in the future.

2.2 Components of a ToF camera

ToF camera consists of a Complementary Metal-oxide Semiconductors (CMOS) chip and an

illumination LED source. Using these main parts the cameras generally convert the incident light

energy into current or charge collector, transfer it to a measurement point and convert it to a

readable signal.

2.2.1 CMOS chip

General background for CMOS technology

The CMOS are part of the active pixel sensors (APS) technology. The CMOS have become a

valuable alternative and are already replacing charge-coupled-device (CCD) sensors in many

applications which have dominated digital imaging since the early 1980s. The more recent APS

technology provides random access to the pixels and allows integrating electronic functionality

or even complete digital processors within the image sensors. Such sensors may be actively

tuned to the application needs leading to a notation “smart sensors” with “smart pixels”.

Horemuž (2006), Kahlmann et al. (2006), May et al. (2009) and Lindner et al. (2010)

In a CMOS image sensor, an individual light-sensing element (photosite) is a photodiode with an

adjacent charge–to-voltage converter, buffer and other preprocessing circuits, depending on

the complexity of the device, such as a local amplifier at each pixel location in active pixel

sensors (APS). These diode photosites are connected in a 2D array, and their voltages are

collected and transferred to the built-in output node by using the row-column addressing

mechanism of random access memory (RAM). CCD chip is a metal-oxide gate that converts

incident photon energy into charge. An individual photosite charge is transported to remote

readout registers through a series of photosite-to-photosite transfers; these readout registers

are masked CCD gates. The serial outputs of the readout registers are then converted into

voltages by the output amplifier and sent to the output node for collection.

http://ebooks.spiedigitallibrary.org.focus.lib.kth.se/content.aspx?bookid=57&sectionid=31562092 (as

last seen on 01/08/2013)

http://ebooks.spiedigitallibrary.org.focus.lib.kth.se/content.aspx?bookid=57&sectionid=31562092 (As

last seen on 01/08/2013)

pg. 9

Figure 2.2: CMOS principle (source: Kahlmann et al. (2006))

CMOS principle in ToF cameras

In the Figure 2.2 the CMOS principle is displayed. Specifically the single emitter of the 3D

camera sends out modulated light, which is reflected by an object partially back to the sensor.

The smart pixels of the CMOS sensors array receive the back scattered light simultaneously in

comparison to the laser scanners. (Shahbazi et al. (2011))The smart pixel itself determines the

correlation between the detected optical signal and the emitted – reference signal which has

been delayed or in other words shifted by the phase offset. (Marvin Lindner et al. (2010)) In

such a way the smart pixels are able to measure the distance (D) of the corresponding points in

space. The measured distances in connection with the geometrical camera relationships can be

afterwards used to compute the 3D coordinates which represent a reconstruction of the imaged

object. (Kahlmann et al. (2006))

2.2.2 Illumination unit - LED

The LEDs in the front part of the ToF sensor emit modulated light waves. The modulation signal

is considered to follow a sinusoidal function. More authors provide formulations for sinusoidal

signals, although other periodic functions can be used (Foix et al. (2011)). The LEDs are covered

by an illumination cover which protects them while allowing light to be transmitted. There is

also the optical filter in the front part which allows only light of wavelengths near that of the

illumination LEDs to pass into the cameras lens. (SR4000 Manual

)

2.3 ToF distance measurement principle

In the ToF systems the time taken for light to travel from an active illumination source to the

objects in the field of view (FOV) and back to the sensor is measured. The distance can be

determined directly from this round trip. (SR4000 Manual) As described by Kahlmann et al.

(2006), the time the light needs to travel from one point to another is proportional to the

distance the light has travelled. The related equation is written in the form as:

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Eq. 2.1

http://www.mesa-imaging.ch/swissranger4000.php

pg. 10

where d represents the distance between the sensor and the object, t the time between

emitting and receiving which indicates how far the light has travelled and c the speed of light

(approximately c=3 x 10

m/s).

In general there are two methods of distance measurement by electro-optical device. The first

one is Pulse Run time method and the second is Phase Shift determination. In the literature the

first one is also referred as pulse modulation and the second as continuous modulation,

Amplitude Modulated Continuous Wave (AMCW) or Intensity modulation approach. (Kahlmann

et al. (2006), Lindner, (2010), Dorrington et al. (2010), Kolb et al. (2009))

Figure 2.3: ToF distance measurement principle, left: Pulse modulation method

–right: Continuous modulation method (source: Kahlmann et al. (2006))

According to the first method the runtime of a single pulse is measured directly as shown in the

Figure 2.3. As Lindner (2010) describes, this implies high demands on the detection accuracy in

order to determine the exact time delay. Kalhman et al. (2006) also add that in order to reach a

distance accuracy of a few millimeters, the clock accuracy has to be as low as a few picoseconds.

In the second method, the phase shift between the emitted signal and its response is measured.

According to Kahlmann et al. (2006) this method avoids high precision clocks and uses more

complex and integrated design. In that sense the system is less demanding, however due to the

periodicity of the emitted signal the non-ambiguity range of the measurements gets limited

(Lindner (2010)).

More specifically the observed scene is illuminated with modulated near infrared (NIR) light.

The modulated signal is assumed to be sinusoidal with modulation frequencies (ω or f

) in the

order of megahertz (MHz), typically in the region of 10 to 100MHz. (Stefan May et al. (2009),

Dorrington et al. (2010))

In the literature the mathematical representation of how the ToF works has been described

thoroughly. According to the sources Kolb et al. (2009), Lindner (2010), May et al. (2009),

Cazorla et al. and Fuchs et al. (2008) the following paragraphs describe the corresponding

mathematical concepts.

The illumination module attached to the camera emits incoherent (NIR) light g(t) which is

expressed mathematically as:

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󰇛󰇜

Eq. 2.2

pg. 11

This reemitted signal is also called reference or original signal. It takes the following form where

the time (t) is continuous:

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󰇜

 󰇛  󰇜

Eq. 2.3

where α is the amplitude of the incident optical signal, b is a constant component results from

the background illumination also referred as correlation bias and the phase shift – phase delay

φ transports the distance information. The phase delay between the original signal g(t) and the

reemitted S(t) is connected via a correlation equation:

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 󰇛 󰇜

Eq. 2.4

where from the reflected sinusoidal light four measurements S(τ0) , S(τ1), S(τ2), S(τ3) at 0, 90,

180 and 270 degrees (deg) of the phase are taken each period T= 1/f

. (May et al. (2009), Figure

2.4) The phase shift, which is proportional to the covered distance, is measured in parallel

within each smart pixel of the CMOS sensor’s array. (May et al. (2009)) At the same time, the

phase shift is propotional to the time of flight of the light reflected by the distant object.

As explicitly described by Fuchs et al. (2008) the reemitted S(t) and emitted signal g(t) are

directly correlated in the solid-state CMOS sensor pixels. The incident photons activate the

semi-conductor to generate electrons that are forced by Sτ(t) to accumulate in two integrational

capacitors where they are sorted and read out by a controller. The difference between these

two integrational capacitors corresponds to the correlation c(τ) which is proportional to the

phase-delay.

Figure 2.4: received sinusoidal modulated input signal (source: May et al. 2009)

As it is shown on the Figure 2.4 signal (b) represents the mean of the total light incident on the

sensor i.e. background that is usually referred as intensity (b

) plus modulated and (α) is the

amplitude of just the modulated signal. The phase shift (φ) is calculated from the four

aforementioned samples to produce the distance measurements. (SR4000 Manual) In the

literature (Foix et al. (2011)) the phase demodulation technique is also mentioned as “four-

bucket” sampling. The phase φi, the amplitude αi and the intensity bias well as the distance

measurement for every n pixel in the image array {di|i=1,…,n} can be calculated as follows:

pg. 12

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Eq. 2.5

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Eq. 2.6

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Eq. 2.7

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Eq. 2.8

where the λm is the wavelength of the modulated signal. (May et al., 2009) As the Eq. 2.8

describes the phase φi has a range of 0 to 2π, hence the maximum operating distance is limited

to half of the wavelength because the light must complete a return trip.The phase shift is

related directly to propagation time which leads to distance for every pixel in the image scene.

This distance measurement function (Eq. 2.8) represents the radial distance values from the

perspective center of the camera to the object for every pixel. (Dorrington et al. (2010))

According to the manual for the ToF camera SR4000 the amplitude can be used as a measure of

quality for the distance measurement and/or to generate a gray-scale image such as a

traditional gray-scale digital photograph (Dorrington et al. (2010)). The amplitude indicates the

amount of modulated light reaching the sensor and disregards external illumination and

incoherent stray light. (Reynolds et al.) It has a similar meaning like the intensity and in cases

where the ToF camera does not provide amplitude values it provides intensity instead.

2.3.1 Characteristics of the ToFSR4000 camera

The used ToF camera in the experiments of the thesis is the SR4000, whose characteristics are

as follow:

Table 2.1: Technical specifications of the SR4000 ToF camera

Pixel array size

176(h) x 144(v)

Field of View (FOV)

43.6° (h) x 34.6° (v)

Detection Range:

0.1-10m

Absolute accuracy

(99% reflectivity over calibrated range)

+/-15mm

Calibrated Range:

0.8-8.0m

Modulated frequency

15MHz

Illumination frequency (LEDs)

850nm

Focus length

10mm

Maximum frame rate

50fps

The SR 4000 camera type has various models of different detection ranges. This model works

for distances until 10m but the range within the manufacturer has calibrated the camera lies

between 0.8m and 8.0 m. For that reason all experiments were performed within that range.

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