Apodization Function Segmentation for Spectrometry Resolution

Solution Overview

Problem

Standard apodization functions in spectrometry fail to effectively remove low and medium frequency instrument background and artifact signals, leading to interference in auto-referenced spectra and difficulty in chemical analysis, especially for low concentration components and gas analysis.

Innovation Solution

An improved apodization function with multiple segments, where the first segment applies a uniform weight and the second segment has a decaying weight profile, is applied to both sample and reference interferograms to generate apodized waveforms that reduce low and medium frequency signals while retaining high frequency signals, enhancing spectral analysis.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Object-affected harmful factors

If a standard apodization function with continuously decaying weight profile is applied to reduce Gibbs phenomenon ringing, then truncation error and artifact ringing are reduced, but resolution between neighboring peaks deteriorates

Engineering Contradiction:

ImproveringingVSAvoidresolution

Core Design Contradiction:

Object-affected harmful factorsVSMeasurement precision

Solution Approach 1:

The apodization function is divided into multiple segments with different weight profiles. The first segment uses a uniform weight profile to maintain resolution, while subsequent segments use decaying weight profiles to reduce ringing. This segmentation allows the system to achieve both high resolution and reduced ringing simultaneously, resolving the trade-off between these two parameters.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Different portions of the interferogram are assigned different weight profiles according to their specific requirements. Early portions (first segment) receive uniform weighting for resolution, while later portions (subsequent segments) receive decaying weighting for ringing reduction. This local differentiation optimizes both resolution and ringing reduction in their respective regions.

Inventive Principle:

Principle #3Local quality

2Measurement precision

If the interferogram oscillation is allowed to continue to increase resolution, then resolution between neighboring peaks is improved, but truncation error and artifact ringing increase

Engineering Contradiction:

ImproveresolutionVSAvoidringing

Core Design Contradiction:

Measurement precisionVSObject-affected harmful factors

Solution Approach 1:

The apodization function is divided into multiple segments with different weight profiles. The first segment uses a uniform weight profile to maintain resolution, while subsequent segments use decaying weight profiles to reduce ringing. This segmentation allows the system to achieve both high resolution and reduced ringing simultaneously, resolving the trade-off between these two parameters.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Different portions of the interferogram are assigned different weight profiles according to their specific requirements. Early portions (first segment) receive uniform weighting for resolution, while later portions (subsequent segments) receive decaying weighting for ringing reduction. This local differentiation optimizes both resolution and ringing reduction in their respective regions.

Inventive Principle:

Principle #3Local quality

3Measurement precision

If low and medium frequency instrument background signals are removed through apodization, then spectral analysis accuracy is improved, but high frequency signal retention deteriorates

Engineering Contradiction:

Improvespectral analysis accuracyVSAvoidhigh frequency signal retention

Core Design Contradiction:

Measurement precisionVSLoss of information

Solution Approach 1:

The apodization function is divided into multiple segments where the first segment maintains uniform weighting to preserve high frequency signals, while subsequent segments apply decaying weights to remove low and medium frequency instrument background. This segmentation enables selective filtering that removes unwanted background while retaining useful high frequency signal information.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Different portions of the interferogram are assigned different weight profiles according to their specific requirements. Early portions (first segment) receive uniform weighting for resolution, while later portions (subsequent segments) receive decaying weighting for ringing reduction. This local differentiation optimizes both resolution and ringing reduction in their respective regions.

Inventive Principle:

Principle #3Local quality

Data Source

PatentUS7546208B2Method and apparatus of signal processing for use in spectrometry using an improved apodization function

Publication Date: 2009.06.09 MKS INSTR INC

AI summary

A method and apparatus is disclosed for signal spectrometry using an improved apodization function. Such method and apparatus involve (i) obtaining sample and reference time domain waveforms; (ii) applying sample and reference apodization waveforms to the sample and reference time domain waveforms, such that substantially same weight is applied to corresponding substantially coextensive regions of the sample and reference time domain waveforms, (iii) transforming the sample and reference apodized waveforms from the time domain into the frequency domain; and (iv) generating referenced spectral analysis waveform for signal analysis from a ratio of the transformed sample and reference frequency spectra, the spectral analysis waveform substantially excluding frequencies associated with the corresponding substantially coextensive regions of the apodized sample and reference time domain waveforms.