Timing Jitter in Time-of-Flight Range Imaging Cameras

✍ Scribed by Gehan Anthonys

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 299
• Category: Library

✦ Synopsis

This book explains how depth measurements from the Time-of-Flight (ToF) range imaging cameras are influenced by the electronic timing-jitter. The author presents jitter extraction and measurement techniques for any type of ToF range imaging cameras. The author mainly focuses on ToF cameras that are based on the amplitude modulated continuous wave (AMCW) lidar techniques that measure the phase difference between the emitted and reflected light signals. The book discusses timing-jitter in the emitted light signal, which is sensible since the light signal of the camera is relatively straightforward to access. The specific types of jitter that present on the light source signal are investigated throughout the book. The book is structured across three main sections: a brief literature review, jitter measurement, and jitter influence in AMCW ToF range imaging.

✦ Table of Contents

Preface
Acknowledgements
Contents
Acronyms
Symbols
Standard Operations
Standard Types of a Variable
Variables and Functions
Constants
1 Introduction
1.1 Time-of-Flight Range Imaging Systems
1.1.1 Continuous Wave Modulation
1.1.2 Pulse-Based Modulation
1.1.3 Pseudo-Noise Modulation ToF Depth Cameras
1.2 Different Depth Measurement Techniques
1.2.1 Stereoscopic Vision
1.2.2 Structured Light
1.2.3 Infrared Thermography
1.3 Applications of ToF Range Imaging Cameras
1.4 Book Overview
1.5 Further Reading
References
Part I ToF Range Imaging Cameras and Measurement Error
2 ToF Range Imaging Cameras
2.1 ToF Depth Camera Components
2.2 Operational Principle in ToF Systems
2.2.1 Shuttered Light Pulse Principle
2.2.2 Direct ToF Principle
2.2.3 Indirect ToF Principle
2.2.3.1 Homodyne Operation
2.2.3.2 Heterodyne Operation
2.3 Aliasing of Signals
2.4 Unambiguous Range
2.5 Commercial ToF Range Imaging Cameras
2.5.1 MESA Imaging SwissRanger 4000
2.5.2 SoftKinetic DepthSense 325
2.6 Chapter Remarks and Further Reading
References
3 Measurement Error in Range Imaging Systems
3.1 Harmonic Cancellation
3.2 Error Sources in Range Measurement
3.2.1 Accuracy and Precision
3.2.2 Noise and Jitter
3.3 Noise Sources in Range Imaging Cameras
3.3.1 Integration Time Related Noise
3.3.2 Temperature Noise
3.3.3 Built-in Pixel-Related Noise
3.3.4 Intensity of Reflected Light
3.3.5 Depth Distortion
3.3.6 Multipath Interference
3.3.7 Motion Blurs
3.3.8 Signal-to-Noise Ratio
3.3.9 Random Noise
3.4 Noise Mitigation Techniques
3.4.1 Temperature Noise
3.4.2 Depth Calibration
3.4.3 Camera Distortion
3.4.4 Built-in Pixel-Related Noise
3.4.5 Light Scattering
3.4.6 Non-linearity and Multipath Interference
3.4.7 Motion Blurs
3.4.8 Signal-to-Noise Ratio
3.5 Chapter Remarks and Further Reading
References
4 Jitter and Measurement of Jitter
4.1 Jitter
4.1.1 Period Jitter
4.1.2 Cycle-to-Cycle Jitter
4.1.3 Time Interval Error Jitter
4.1.4 Phase Jitter
4.2 Types of Jitter in Signals
4.2.1 Random Jitter
4.2.2 Periodic Jitter
4.2.3 Bounded Uncorrelated Jitter
4.2.4 Data Dependent Jitter
4.2.4.1 Duty Cycle Distortion Jitter
4.2.4.2 Inter Symbol Interference Jitter
4.3 Phase of Sinusoidal Signals
4.4 Jitter Sources in Ranging Systems
4.4.1 Sources for Random Jitter
4.4.1.1 Thermal Noise
4.4.1.2 Shot or Poisson Noise
4.4.1.3 Flicker Noise
4.4.2 Sources for Deterministic Jitter
4.4.2.1 Crosstalk
4.4.2.2 Electromagnetic Interference
4.4.2.3 Reflection
4.4.2.4 Data Dependent Phenomena
4.5 Analysis of Jitter in Signals
4.5.1 Graphical Approaches
4.5.1.1 Eye Diagram
4.5.1.2 Histogram
4.5.1.3 Bathtub Curve
4.5.2 Time and Frequency Domains
4.5.3 Statistical and Signal Processing Techniques
4.6 Impact of Jitter on Range Imaging
4.7 Chapter Remarks and Further Readings
References
Part II Jitter Extraction and Measurement
5 Proposed Methodology for Jitter Measurement
5.1 Background
5.2 Proposed Methodology
5.2.1 Signal Smoothing
5.2.1.1 Moving Average
5.2.1.2 Weighted Moving Average
5.2.1.3 Savitzky-Golay
5.2.2 Frequency Estimation for the Reference Signal
5.2.3 Amplitude Estimation for the Reference Signal
5.2.4 Identifying Zero Crossings
5.2.5 Spectral Leakage
5.2.6 Window Functions for Minimizing Spectral Leakage
5.2.6.1 Uniform
5.2.6.2 Hann
5.2.6.3 Hamming
5.2.6.4 Blackman
5.2.7 Window Correction Factors
5.2.7.1 Coherent Gain
5.2.7.2 Incoherent Gain
5.3 Jitter Extraction Using the Spectrum
5.3.1 Calculation of the Jitter Components
5.3.2 Curve Fitting Analysis for the Spectrum
5.4 Chapter Remarks and Further Readings
References
6 Evaluation of the Proposed Methodology
6.1 Introduction
6.2 Simulation Setup
6.3 Results and Discussion
6.3.1 Simulation with Sinusoidal Signals
6.3.2 Simulation with Triangular Signals
6.3.3 Simulation with Rectangular Signals
6.4 Conclusion
6.5 Chapter Remarks
Reference
7 Jitter Extraction in ToF Cameras
7.1 Introduction
7.2 MESA Imaging SwissRanger 4000
7.2.1 Experimental Setup for SR4000
7.2.2 Results and Discussion
7.3 SoftKinetic DepthSense 325
7.3.1 Experimental Setup for DS325
7.3.2 Results and Discussion
7.4 Chapter Remarks
References
8 Software-Defined Radio Technology for Jitter Extraction
8.1 Background
8.2 Commercial SDR Devices
8.3 Operational Principle of the SDR Receiver
8.3.1 SDR Hardware
8.3.2 SDR Software
8.4 Experiment with MESA SR4000
8.5 Results and Discussion
8.6 Experiment with SoftKinetic DS325
8.7 Chapter Remarks
References
Part III Jitter Influence on Range Measurements
9 Influence of Periodic Jitter
9.1 Background
9.2 Notation and Definitions
9.2.1 Mathematical Functions
9.2.1.1 Definitions
9.2.1.2 Relationships
9.2.2 Fourier Transform and Inverse Fourier Transform
9.2.2.1 Definitions
9.2.2.2 Identities
9.2.2.3 Fourier and Its Inverse Transforms of Some Functions
9.3 Correlation Model with Periodic Jitter
9.3.1 Numerical Approaches
9.3.1.1 Trapezoidal Integration
9.3.1.2 Romberg Integration
9.3.2 Analytical Approach
9.3.2.1 Solution of the Amplitude Portion
9.3.2.2 Solution of the Background Portion
9.3.2.3 Long Integration Period
9.3.2.4 Jitter Frequency Is a Non-factor of Modulation Frequency
9.3.2.5 Jitter Frequency Is a Factor of Modulation Frequency
9.3.2.6 Correlation Model in Homodyne Operation
9.3.3 The Phase Error Due to the Periodic Jitter
9.4 Correlation Model Without Periodic Jitter
9.5 Simulation Setup
9.6 Results and Discussion
9.6.1 Jitter Frequency Is a Non-factor of Modulation Frequency
9.6.2 Jitter Frequency Is a Factor of Modulation Frequency
9.6.3 Comparison of the Numerical and AnalyticalApproaches
9.7 Execution Time for the Simulation
9.8 Chapter Remarks
References
10 Influence of Random Jitter
10.1 Background
10.1.1 Mean and Variance of a Continuous Random Variable
10.1.2 Mean and Variance of a Linear Combination of Random Variables
10.1.3 Gaussian (Normal) Probability Distribution
10.1.4 Central Limit Theorem
10.1.5 Monte Carlo Method
10.1.6 Non-parametric Density Estimates
10.1.6.1 Histogram Estimation
10.1.6.2 Kernel Density Estimation
10.2 Random Jitter in the Correlation Model
10.2.1 An Estimator for the Phase Error Due to the Random Jitter
10.2.2 Calculation of Sufficient Number of Samples
10.2.3 Simulation Setup
10.3 Results and Discussion
10.3.1 Phase Error Due to the Random Jitter
10.3.2 Range Error Due to the Random Jitter
10.3.3 Uncertainty Analysis of the Phase Errors
10.4 Execution Time for the Simulation
10.5 Chapter Remarks
References
11 Conclusions and Outlook
11.1 Summary of Findings
11.2 Future Investigations
A Mathematical Derivations
A.1 Bessel Function
A.2 Error Function
A.3 Monotonic Functions
References
B Statistical Theorems
B.1 Definitions
B.1.1 Law of the Unconscious Statistician
B.1.2 Cumulative Distribution Function of a RandomVariable
B.1.3 Gaussian (Normal) Distribution
B.2 Proofs
B.2.1 LOTUS Theorem
B.2.2 Gaussian Integral
B.2.3 Means and Variances of Some Parameters
B.2.3.1 A Continuous Random Variable
B.2.3.2 A Linear Combination of Random Variables
B.2.3.3 The Gaussian Distribution
Reference
C Specific Matlab Scripts
C.1 Jitter Measurements on Simulated Data
C.1.1 Generating Simulation Data: genSG10to50.m
C.1.2 Extracting the Jitter: rstSG10to50.m
C.2 Capturing Multiple Sets of Data from Two Oscilloscopes
C.2.1 DSOS604A High Definition, 6GHz and 20 GSa/s
C.2.2 HP Infiniium 54846B, 2.25GHz and 8 GSa/s
C.3 Romberg Integration Algorithm
C.4 Monte Carlo Simulation
C.4.1 Generating Data with MCS: genMCsRJ.m
C.4.2 Results with Uncertainty: rstMCsRJ.m
References
D Maple Computations
D.1 Correlation Model with Periodic Jitter
D.2 Correlation Model without Periodic Jitter
D.3 Verification of the Analytical Models
Reference
E Units and Uncertainty
E.1 Units of Measurement
Examples
E.2 Uncertainty of Measurement
References
Index