Fractional Bi-Spectrum Analysis for Laser Interferometry Noise Reduction

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Solution Overview

Problem

Laser interferometry on rough surfaces is hindered by speckle noise, which existing noise reduction techniques often address at the cost of blurring details or requiring complex systems, and bi-spectrum analysis is limited in applicability to linear mediums.

Innovation Solution

The introduction of Fractional Bi-Spectrum Analysis (FBSA) and Fractional Cross-Correlation (FCC) using two known wavelengths allows for noise reduction and signal recovery in linear mediums, enhancing the signal-to-noise ratio and enabling accurate thickness measurements and topography analysis.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If conventional noise reduction techniques (median filter, Wiener filter, FFT pass band filters) are applied to reduce speckle noise in laser interferometry, then the signal-to-noise ratio is improved, but the fringe pattern is distorted or details are blurred

Engineering Contradiction:

Improvesignal-to-noise ratioVSAvoidfringe pattern accuracy

Core Design Contradiction:

ReliabilityVSManufacturing precision

Solution Approach 1:

The invention segments the noise reduction process by separating the fringe pattern extraction from the noise filtering. Statistical analysis methods (auto-correlation, cross-correlation, Bi-Spectrum) are applied to the noisy signal to extract statistical properties, and the fringe pattern is then reconstructed from these statistical properties, avoiding direct filtering of the original signal that causes distortion

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The invention introduces statistical parameters (auto-correlation function, cross-correlation function, Bi-Spectrum) as intermediaries between the noisy interferometric signal and the final fringe pattern. These statistical measures serve as mediators that capture the essential signal characteristics while filtering out noise, enabling accurate fringe reconstruction without direct signal manipulation

Inventive Principle:

Principle #24Intermediary (Mediator)

2Reliability

If aperture of the camera is moved to suppress speckle noise through averaging, then the noise effect is reduced, but the system complexity increases

Engineering Contradiction:

Improvespeckle noise suppressionVSAvoidsystem complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The invention replaces the mechanical approach of moving the camera aperture with a computational approach. Instead of physically moving components to achieve noise suppression, statistical analysis methods are applied to the captured image data to suppress speckle noise, eliminating the need for mechanical movement and reducing system complexity

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

3Reliability

If Bi-Spectrum analysis is applied to nonlinear systems for noise reduction, then additive Gaussian noise is eliminated, but the technique is not applicable to linear mediums

Engineering Contradiction:

Improvenoise elimination capabilityVSAvoidapplicability to linear mediums

Core Design Contradiction:

ReliabilityVSAdaptability or versatility

Solution Approach 1:

The invention extends Bi-Spectrum analysis, which was originally designed for nonlinear systems, to work with linear mediums by modifying the analysis approach. The fractional Bi-Spectrum technique is developed to handle both linear and nonlinear systems, making the noise reduction capability universal across different system types

Inventive Principle:

Principle #6Universality (Multi-functionality)

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

FBSA and FCC effectively reduce noise, improve signal recovery, and provide accurate thickness measurements and topography analysis, even on rough and contaminated surfaces, outperforming other techniques like low-pass FFT and auto-correlation at higher noise levels.

Implementation Method 1

illuminating an object to be measured with light at two different wavelengths and an incident angle; capturing an image of the object; detecting a frequency of an interference pattern from the image

Methodology Applied

Scientific EffectInterference: Interference

Data Source

PatentUS10203195B2Noise reduction techniques, fractional bi-spectrum and fractional cross-correlation, and applications

Publication Date: 2019.02.12 JUNIVERSITI OF NORT KAROLINA EHT SHARLOTT

AI summary

A measurement method and system include illuminating an object to be measured with light at two different wavelengths and an incident angle; capturing an image of the object; detecting a frequency of an interference pattern from the image using Fractional Bi-Spectrum Analysis; and calculating a thickness of the object based on the Fractional Bi-Spectrum Analysis. The thickness is calculated based on a relationship between the thickness and the frequency of the interference pattern. The Fractional Bi-Spectrum Analysis is performed on a linear medium with the two different wavelengths being known.