US-12627307-B2 - Method for enhancing characteristic signals by synthesizing multiple frequency waves

US12627307B2US 12627307 B2US12627307 B2US 12627307B2US-12627307-B2

Abstract

A method for enhancing characteristic signals by synthesizing multiple frequency waves is provided, which includes: obtaining real frequency responses based on the measurement results of spectral signals; selecting complex frequencies to at least partially compensate for spectral line broadening caused by losses; and obtaining complex frequency responses based on multiple real frequency responses and the selected complex frequencies to enhance the characteristic signals.

Inventors

Shuang Zhang
Fuxin GUAN
Kebo ZENG
Qing Dai
Xiangdong Guo

Assignees

THE UNIVERSITY OF HONG KONG
NATIONAL CENTER FOR NANOSCIENCE AND TECHNOLOGY

Dates

Publication Date: 20260512
Application Date: 20240702
Priority Date: 20230704

Claims (12)

1 . A method for enhancing characteristic signals by synthesizing multiple frequency waves, comprising: obtaining a real frequency response based on a measurement result of a spectral signal; selecting a complex frequency to at least partially compensate for spectral line broadening caused by losses; and obtaining a complex frequency response based on the real frequency response and the selected complex frequency to enhance the characteristic signals.
2 . The method for enhancing characteristic signals by synthesizing multiple frequency waves according to claim 1 , wherein the step of obtaining the complex frequency response based on the real frequency response and the complex frequency to enhance the characteristic signals includes calculating the complex frequency response using following formula: F ⁡ ( ω ~ ) ≈ ∑ n F ⁡ ( ω n ) ⁢ 1 i ⁡ ( ω ~ - ω n ) ⁢ e i ( ω ~ - ω n ) ⁢ t 0 ⁢ Δω 2 ⁢ π where F(ω n ) is the real frequency response; F({tilde over (ω)}) is the complex frequency response; ω n is the frequency of the measurement result of the spectral signal, n is a positive integer; {tilde over (ω)} is the complex frequency; t 0 is time; Δω is an interval frequency of ω n .
3 . The method for enhancing characteristic signals by synthesizing multiple frequency waves according to claim 1 , wherein the measurement result of the spectral signal is based on a measurement result of optical detection of molecules, and the complex frequency is selected to at least partially compensate for losses caused by molecular damping vibrations of a molecular layer.
4 . The method for enhancing characteristic signals by synthesizing multiple frequency waves according to claim 3 , wherein the real frequency response approaches zero as the frequency approaches infinity.
5 . The method for enhancing characteristic signals by synthesizing multiple frequency waves according to claim 3 , further comprising: constructing the real frequency response such that the real frequency response approach zero as the frequency approaches infinity before obtaining the real frequency response based on the measurement result of spectral signal, wherein obtaining the complex frequency response based on the real frequency response and the selected complex frequency to enhance the characteristic signals comprises: obtaining an intermediate complex frequency response based on the real frequency response, and obtaining the complex frequency response based on the intermediate complex frequency response.
6 . The method for enhancing characteristic signals by synthesizing multiple frequency waves according to claim 5 , wherein the complex frequency response is an extinction I({tilde over (ω)}), and the real frequency response is an intermediate physical quantity P(ω), P ⁡ ( ω ) = i ⁢ ( 1 t M ( ω ) - 1 ) I ⁡ ( ω ~ ) = 1 - 1 ❘ "\[LeftBracketingBar]" 1 - iP ⁡ ( ω ~ ) ❘ "\[RightBracketingBar]" 2 where t M (ω) is a transmission coefficient, and P({tilde over (ω)}) is the intermediate complex frequency response.
7 . The method for enhancing characteristic signals by synthesizing multiple frequency waves according to claim 3 , wherein the complex frequency is ω ~ = ω - i ⁢ τ 2 , where ω is a current frequency, τ is an attenuation coefficient, and τ is greater than zero and selected to make a dielectric constant of the molecular layer a purely real value.
8 . The method for enhancing characteristic signals by synthesizing multiple frequency waves according to claim 3 , wherein the real frequency responses include amplitude information and phase information.
9 . The method for enhancing characteristic signals by synthesizing multiple frequency waves according to claim 8 , further comprising: calculating the phase information based on the amplitude information using the Kramers-Kronig relations.
10 . The method for enhancing characteristic signals by synthesizing multiple frequency waves according to claim 2 , wherein a length of time to is such that the complex frequency response can enter a quasi-steady-state of complex frequencies.
11 . A computer-readable storage medium comprising a computer program or software, wherein the computer program is executable by a processor to perform the steps of claim 1 .
12 . An electronic device comprising: one or more processors; and a memory for storing one or more executable instructions; wherein the one or more processors are configured to execute the one or more executable instructions to perform the steps of claim 1 .

Description

TECHNICAL FIELD OF THE INVENTION The present invention relates to the field of signal detection, particularly to a method for enhancing characteristic signals by synthesizing multiple frequency waves. BACKGROUND OF THE INVENTION Sensors play a crucial role in early disease diagnosis, personalized medicine, and rapid detection of toxic substances, significantly impacting environmental monitoring, food safety, and public health. However, effectively detecting samples with extremely low concentrations of biomolecules remains a major challenge. Surface-enhanced infrared absorption (SEIRA) based on plasmonic nanostructures, especially graphene plasmons, has become an effective method to improve biosensor sensitivity. Although graphene plasmon-based SEIRA offers advantages such as ultra-high sensitivity and active tunability, inherent molecular damping reduces the interaction between vibrational modes and plasmons. As a result, at lower concentrations, the spectra of plasmon-enhanced molecular signals become weaker and broader, ultimately getting masked by noise. To compensate for molecular damping, one method is to add optical gain materials. However, this requires complex setups and may be incompatible with the detection system. Additionally, gain materials often introduce instability and additional noise. Therefore, there is a need for a simple and effective method to compensate for molecular damping to enhance molecular detection. SUMMARY OF THE INVENTION In light of the aforementioned problems in the prior art, the present invention proposes a method for enhancing characteristic signals by synthesizing multiple frequency waves, which includes: obtaining real frequency responses based on the measurement results of spectral signals;selecting complex frequencies to at least partially compensate for spectral line broadening caused by losses; andobtaining complex frequency responses based on multiple real frequency responses and the selected complex frequencies to enhance the characteristic signals. In one embodiment, the step of obtaining complex frequency responses based on multiple real frequency responses and the complex frequencies to enhance the characteristic signals includes calculating the complex frequency response using the following formula: F⁡(ω~)≈∑nF⁡(ωn)⁢1i⁡(ω~-ωn)⁢ei⁡(ω~-ωn)⁢t0⁢Δω2⁢π where F(ωn) is the real frequency response; F({tilde over (ω)}) is the complex frequency response; ωn is the frequency of the spectral signal measurement results, n is a positive integer; {tilde over (ω)} is the complex frequency; t0 is time; Δω is the interval frequency of ωn. In one embodiment, the measurement results of the spectral signals are based on optical detection of molecules, and the complex frequencies are selected to at least partially compensate for losses caused by molecular damping vibrations of the molecular layer. In one embodiment, the real frequency response approaches zero as the frequency approaches infinity. In one embodiment, the method further includes: constructing real frequency responses such that the real frequency responses approach zero as the frequency approaches infinity before obtaining the real frequency responses based on the measurement results of spectral signals; andobtaining an intermediate complex frequency response based on multiple real frequency responses, and obtaining the complex frequency response based on the intermediate complex frequency response. In one embodiment, the complex frequency response is the extinction I({tilde over (ω)}), and the real frequency response is the intermediate physical quantity P(ω), P⁡(ω)=i⁡(1tM(ω)-1)I⁡(ω~)=1-1❘"\[LeftBracketingBar]"1-iP⁡(ω~)❘"\[RightBracketingBar]"2 where tM(ω) is the transmission coefficient, P({tilde over (ω)}) is the intermediate complex frequency response. In one embodiment, the complex frequency ω~=ω-i⁢τ2, ω is the current frequency, τ is the attenuation coefficient, and τ is greater than zero and selected to make the dielectric constant of the molecular layer a purely real value. In one embodiment, the real frequency responses include amplitude information and phase information. In one embodiment, the method further includes: calculating the phase information based on the amplitude information using the Kramers-Kronig relations. In one embodiment, the length of time to is such that the complex frequency response can enter a quasi-steady-state of complex frequencies. The present invention also provides a computer-readable storage medium comprising a computer program, wherein the computer program is executable by a processor to perform the steps of the aforementioned method. The present invention also provides an electronic device, comprising: one or more processors; anda memory for storing one or more executable instructions; wherein the one or more processors are configured to execute the one or more executable instructions to perform the steps of the aforementioned method. The method for enhancing characteristic sign