Filament Diameter Measurement via Frequency Domain Analysis
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Solution Overview
Problem
The measurement accuracy of filament diameters using laser diffraction is limited by the number and periodicity of diffraction fringes, especially for high-order fringes, and is affected by noise from CCD cameras, requiring improved algorithms for precise calculations.
Innovation Solution
A method involving repeated scaling and splicing of local fringes, combined with Fourier transform, to analyze and correct errors in fringe period measurements, and processing pseudo-fringes to improve accuracy, with a relative error less than 0.2 μm.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If laser diffraction with Fraunhofer principle is used for measurement, then non-contact measurement is achieved and measurement accuracy is improved, but the number and periodicity of diffraction fringes become limited factors affecting precision
Solution Approach 1:
The patent segments the diffraction fringe pattern into multiple local regions and processes each region separately through Fourier transform. This segmentation allows for more precise local frequency analysis and enables the measurement to overcome the limitation of total fringe number by utilizing distributed frequency information across multiple segments.
Solution Approach 2:
The patent transforms the spatial domain fringe pattern into the frequency domain using Fourier transform, adding a frequency dimension to the analysis. This dimensional transformation converts the problem of limited fringe quantity in spatial domain into frequency domain analysis where periodicity information can be extracted more effectively.
2Quantity of substance
If high-order fringes are used for measurement, then more fringe periods are available, but aperiodicity increases and measurement accuracy deteriorates
Solution Approach 1:
The patent divides the fringe pattern into multiple segments and applies Fourier transform to each segment independently. This segmentation approach allows the system to utilize high-order fringes for increased period count while maintaining periodicity analysis through local frequency domain transformation, preventing the aperiodicity problem from degrading overall measurement accuracy.
Solution Approach 2:
The patent uses the frequency domain information obtained from Fourier transform as feedback to identify and correct periodicity variations. By analyzing the frequency spectrum, the system can detect and compensate for aperiodicity in high-order fringes, maintaining measurement accuracy even when using fringes with varying periodicity.
3Ease of operation
If CCD camera is used to capture diffraction fringes, then non-contact measurement is enabled, but strong light intensity noise is introduced affecting measurement precision
Solution Approach 1:
The patent introduces Fourier transform as an intermediary processing step between the CCD camera capture and the final measurement calculation. This mathematical transformation acts as a mediator that separates the signal (fringe periodicity information) from the noise (light intensity variations), allowing the system to maintain non-contact measurement capability while effectively filtering out light intensity noise through frequency domain analysis.
4Ease of manufacture
If simple Fraunhofer diffractometer is used, then device complexity is reduced and ease of manufacture is improved, but measurement accuracy is limited by fringe period variation
Solution Approach 1:
The patent replaces complex mechanical measurement mechanisms with optical diffraction combined with Fourier transform analysis. Instead of using complex mechanical scanning or contact measurement systems, the invention uses the mathematical properties of Fourier transform to extract precise diameter information from the diffraction pattern, achieving high measurement accuracy with a simple Fraunhofer diffractometer configuration.
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
This approach enhances measurement accuracy to the sub-nanometer level, improving the precision of filament diameter measurements and reducing dependence on experimental devices, while being applicable to other fields analyzing period information.
Implementation Method 1
Laser diffraction based on the Fraunhofer principle has been widely used to precisely measure the diameter of small objects
Implementation Method 2
The diffraction fringes are converged by a convex lens to a CCD at its focal point to obtain the diffraction fringe images
Data Source
AI summary
A method for measuring the diameter of filament diffraction fringes by frequency domain calculation comprising: building a set of diffraction optical path measurement system and capturing diffraction fringe images; determining the starting point of the imaging range; Simulating the electromagnetic field propagation process in Fraunhofer diffraction, and determining the optimal fringe range considering the noise caused by the difference in CCD sensitivity; Finally calculating the filament diameter by Fourier transform for different lengths of fringe. The final value of the calculated filament diameter is obtained by fitting an envelope to the variation of the diameter. The invention is simple in calculation and has little dependence on the experimental device, which means the superiority of using the frequency domain for parameter measurement, and the measurement accuracy is in the sub-nanometer level. In addition, the invention proves the feasibility of extracting the fringe period information in the frequency domain.