Multi-Wavelength Phase Unwrapping for Noise-Robust Distance Estimation
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Solution Overview
Problem
Existing phase unwrapping methods in imaging systems require low noise levels, necessitating higher power signals to achieve accurate distance estimation, which is inefficient and undesirable.
Innovation Solution
A method using multiple wavelengths with a processor configured to determine phase values, compute a 2N-dimensional vector, and solve a Closed Vector Point problem to estimate distance on a flat torus, employing a torus decoder and sphere decoding algorithm to minimize noise sensitivity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing phase unwrapping methods are used, then distance estimation accuracy is maintained, but noise levels must be kept low requiring higher power signals
Solution Approach 1:
The patent changes the parameter space by mapping phase values to a 2N-dimensional vector and performing computations on a flat torus manifold. This transformation allows the system to operate effectively at higher noise levels by fundamentally changing how phase unwrapping is computed, rather than simply increasing signal power to overcome noise.
Solution Approach 2:
The patent introduces additional dimensions by mapping N phase values to a 2N-dimensional vector space and utilizing the flat torus manifold structure. This dimensional expansion provides new computational pathways that are more robust to noise, allowing accurate distance estimation without requiring high-power signals.
2Measurement precision
If higher power signals are used to overcome noise, then distance estimation accuracy is maintained, but energy consumption increases
Solution Approach 1:
The patent transforms the computational parameters from traditional phase unwrapping methods to operations on a flat torus manifold in 2N-dimensional space. This parameter transformation enables the system to achieve the same measurement precision with lower energy consumption by exploiting the geometric structure of the torus to naturally handle noise.
Solution Approach 2:
The patent replaces the physical approach of increasing signal power (mechanical/electrical solution) with a computational/mathematical approach using flat torus geometry. Instead of fighting noise with more power, the system uses geometric transformations and sphere decoding to achieve noise robustness computationally.
3Reliability
If traditional phase unwrapping methods are used, then computational complexity is low, but noise sensitivity is high
Solution Approach 1:
The patent moves the computation from traditional 1D phase space to a 2N-dimensional flat torus manifold. While this increases dimensional complexity, it provides a geometric framework that naturally handles the periodicity and ambiguity of phase measurements, making the solution more reliable in noisy environments.
Solution Approach 2:
The patent introduces the flat torus manifold as an intermediary mathematical structure between the raw phase measurements and the final distance estimate. This intermediary structure provides a natural framework for handling phase unwrapping ambiguities and noise, facilitating a more robust computation path.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Enables accurate distance estimation at higher noise levels using lower-powered electromagnetic signals, reducing computational complexity and maintaining accuracy in noisy environments.
Implementation Method 1
a signal receiver configured to receive a reflected electromagnetic signal from an imaged object
Implementation Method 2
a signal source configured to emit an electromagnetic signal
Data Source
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Figure 2
Figure 3A
AI summary
Example imaging systems are disclosed. One example includes a signal source and a signal receiver configured to receive a reflected electromagnetic signal from an imaged object. The imaging system further includes a processor configured to, for each of N wavelengths, determine a phase value of a reflected component of the reflected electromagnetic signal having that wavelength. The processor may compute an estimated distance to the imaged object at least in part by mapping the plurality of phase values to a 2N-dimensional vector, and computing a plurality of zeroes of a trigonometric polynomial. For each of the plurality of zeroes, computing the estimated distance may further include computing a respective geodesic distance between the 2N-dimensional vector and a point along the curve evaluated at that zero, and selecting and outputting a shortest geodesic distance multiplied by a least common multiple of the wavelengths.