Phase Unwrapping via Spectral Differentiation for Noisy Optical Imaging
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Solution Overview
Problem
Existing optical imaging systems face challenges in accurately determining the shape of objects with steep spatial gradients and high noise levels, particularly when phase changes occur rapidly and are corrupted by noise, leading to wrapped phase signals that are difficult to unwrap reliably.
Innovation Solution
A global phase unwrapping methodology using spectral differentiation techniques, which involves spatially-symmetrically extending the wrapped phase-image, modifying it in Fourier space with Laplacian transformations, and adding a phase corrector to produce an unwrapped phase-image that represents the true shape of the object, while denoising and preserving phase gradients.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional optical imaging systems are used to capture phase information, then the imaging process is simple and direct, but the phase signals are wrapped with 2π modulus and corrupted by noise, making reliable shape determination impossible
Solution Approach 1:
The patent segments the phase unwrapping problem into multiple processing stages: (1) spatial extension of the wrapped phase image to create a larger computational domain, (2) Fourier space transformation to convert spatial differentiation into frequency-domain multiplication, (3) spectral differentiation to compute phase gradients, and (4) integration to reconstruct the unwrapped phase. This segmentation allows each stage to be optimized independently, improving overall reliability.
Solution Approach 2:
The patent transitions from spatial domain processing to frequency domain processing by applying Fourier transformation. This dimensionality change allows the use of spectral differentiation, where spatial derivatives become simple multiplications by frequency variables in the Fourier domain, enabling more robust and computationally efficient phase gradient calculation that is less sensitive to noise.
2Measurement precision
If the wrapped phase-image is directly processed without spatial extension, then the computational domain is small and processing is fast, but the phase gradients cannot be accurately determined due to boundary effects and noise
Solution Approach 1:
The patent applies preliminary spatial extension to the wrapped phase image before performing phase unwrapping operations. By extending the image boundaries with replicated or padded data, the method creates a larger computational domain that reduces boundary effects and provides more context for accurate gradient calculation, while the extension itself is a simple preprocessing step that does not significantly increase overall complexity.
Solution Approach 2:
The patent replaces direct spatial differentiation methods with spectral differentiation in the Fourier domain. This substitution transforms the mechanical operation of computing finite differences (which is sensitive to noise and boundary effects) into a frequency-domain multiplication operation, which is more robust and can be efficiently implemented using standard FFT algorithms.
3Ease of manufacture
If traditional phase unwrapping algorithms are used, then the processing steps are simple, but they fail to handle high noise levels and defective fringe patterns
Solution Approach 1:
The patent introduces Fourier transformation as an intermediary step between the wrapped phase image and the final unwrapped result. This intermediary transformation to frequency space allows for more robust processing, where noise and defects are better handled through spectral differentiation and integration operations, before transforming back to the spatial domain to obtain the final phase-unwrapped image.
Data Source
AI summary
Methodology of unwrapping of phase from an optical image in the presence of both noise and unreliable phase fringes configured to tackle both problems simultaneously and, in the most efficient of multiple related implementations, including at least three prongs: i) SD-ROM based denoising procedure, ii) reliable estimation of the gradient of both the wrapped and unwrapped phase with the use of the forward and inverse Laplacian operators; and iii) fringe quality improvement with the use of Fuzzy Logic based Edge Detection. Transformation of optical images with the use of such methodology to provide an image representing visually-perceivable representation of the object's shape. Computer program product configured to implement the same.