Equivalent wavelength compression analysis method and application
By using the equivalent wavelength compression analysis method, the information gain of a multispectral imaging system is quantified, solving the performance evaluation and design problems of the multispectral imaging system, realizing the quantification of information gain and system optimization, and breaking through the Abbe diffraction limit.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHANTOU UNIV
- Filing Date
- 2026-05-07
- Publication Date
- 2026-07-24
Smart Images
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Abstract
Description
Technical Field
[0001] This invention relates to the fields of computational optical imaging and information theory analysis, and in particular to an equivalent wavelength compression analysis method and its application for evaluating the super-resolution performance of multispectral imaging systems. Background Technology
[0002] With the development of computational optics imaging technology, multispectral imaging systems have shown great potential in fields such as super-resolution imaging and 3D measurement. However, how to quantitatively evaluate the information gain brought by multispectral joint encoding and how to determine the theoretical performance limit that the system can achieve have always been problems that need to be solved in this field.
[0003] The existing technology has the following shortcomings: (1) Lack of unified performance evaluation index: Traditional methods usually only focus on the imaging performance of a single spectral channel, such as using Rayleigh criterion or modulation transfer function (MTF) to evaluate resolution, which cannot quantify the information gain brought by multispectral joint coding.
[0004] (2) Information gain is difficult to quantify: Multispectral imaging systems acquire complementary information through multiple wavelength channels, but there is a lack of effective mathematical tools to quantitatively describe the relationship between this information gain and the improvement of system performance.
[0005] (3) Separation of macroscopic and microscopic information: In actual measurements, macroscopic three-dimensional shape priors can often be obtained (such as through stereo vision or white light interference), but existing methods have failed to unify the priors and microscopic spectral coding in the same performance analysis framework.
[0006] (4) Lack of theoretical guidance in system design: When designing a multispectral imaging system, there is a lack of theoretical basis based on information theory for how to select the optimal combination of spectral channels and how to optimize system parameters to maximize information gain.
[0007] While information theory-based analysis methods exist for evaluating imaging system performance, none have yet quantified the information gain of multispectral joint encoding into an intuitive physical index while simultaneously incorporating macroscopic priors. This invention proposes an equivalent wavelength compression analysis method that, by defining the equivalent wavelength as an index, transforms the abstract information gain into an equivalent wavelength with clear physical meaning and establishes a two-factor driven theory, providing a quantitative tool for the theoretical analysis and optimization design of multispectral imaging systems. Summary of the Invention
[0008] The technical problem to be solved by the embodiments of the present invention is to provide an equivalent wavelength compression analysis method and application, which is independent of the specific imaging process and can be used as a theoretical analysis tool.
[0009] To address the aforementioned technical problems, embodiments of the present invention provide an equivalent wavelength compression analysis method, comprising the following steps: S1: Obtain the point spread function of the multispectral imaging system to be analyzed at different wavelengths λ and depths z. ; S2: Construct a spectral-spatial response model based on the obtained point spread function. ,in Image plane coordinates; S3: Construct a three-dimensional position parameter vector based on the spectral-spatial response model regarding the illumination from a point light source above the measured surface. The observational information theory model is derived, and the Fisher information matrix of the multispectral system is calculated. ; S4: Calculate the theoretical axial positioning limit of the multispectral system using the calculated Fisher information matrix of the multispectral system. ; S5: Calculations use only the center wavelength The theoretical axial positioning limit of single-spectral channel fusion macroscopic prior at time:
[0010] in For single-wavelength CRLB without prior knowledge, For macroscopic a priori fields, For macroscopic prior uncertainty, For refractive index, Numerical aperture, Signal-to-noise ratio; S6: Define equivalent wavelength ; S7: Output equivalent wavelength and its relationship with the center wavelength The comparison results; S8: Combining macroscopic prior uncertainty With equivalent wavelength The theoretical axial positioning limit of the prediction system in practical applications: .
[0011] Furthermore, the Fisher information matrix in S3 The calculation formula is:
[0012] in , For the first Each pixel at wavelength The expected number of photons, Intensity of a point light source This is background noise.
[0013] Furthermore, the macroscopic prior uncertainty in S5 Obtained through measurement.
[0014] Furthermore, step S7 also includes calculating the equivalent wavelength compression ratio based on the comparison results:
[0015] Used to quantify the information gain brought about by multispectral joint coding.
[0016] Accordingly, embodiments of the present invention also provide an equivalent wavelength compression analysis system, comprising: The data input module is configured to perform the method described in step S1. The information theory analysis module is configured to perform the methods described in steps S2-S4; The Bayesian fusion module is configured to perform the method described in step S5. An equivalent wavelength calculation module is configured to perform the method described in steps S6-S7; A two-factor prediction module is configured to perform the method described in step S8. The analysis output module is used to output equivalent wavelength, compression ratio, and performance prediction results.
[0017] Accordingly, embodiments of the present invention also provide a method for evaluating the performance of a multispectral imaging system using the above-described equivalent wavelength compression analysis method, comprising: calculating the equivalent wavelength of the system to be evaluated. ,by As a quantitative indicator of system information capacity, The smaller the value, the higher the theoretical resolution of the system; the evaluation method is independent of the imaging process and is used for performance prediction in the system design phase or theoretical analysis of existing systems.
[0018] Accordingly, this invention also provides an application of the above-described equivalent wavelength compression analysis method for the optimal selection of spectral channels in a multispectral imaging system. The method is implemented during the system design phase by calculating the equivalent wavelength for different channel combinations in the candidate spectral channel set. , choose to The smallest channel combination is the optimal encoding scheme.
[0019] Accordingly, embodiments of the present invention also provide a method for optimizing the design of parameters of a multispectral imaging system using the above-described equivalent wavelength compression analysis method, comprising: analyzing the effect of system parameters on equivalent wavelength. The system parameters are adjusted based on the analysis results to achieve the optimal theoretical performance of the system under given constraints; the parameter optimization design method is used to guide the system hardware design.
[0020] Accordingly, embodiments of the present invention also provide a method for combining macroscopic prior uncertainty with the equivalent wavelength compression analysis described above. With equivalent wavelength The two-factor driven formula is used to predict the theoretical axial positioning limit of the system in practical applications; the prediction method includes... As input as known parameters, it does not involve the process of obtaining macroscopic priors.
[0021] Implementing the embodiments of the present invention has the following beneficial effects: Theoretical innovation: The concept of equivalent wavelength is proposed for the first time, quantifying the abstract multispectral information gain into an equivalent wavelength index with clear physical meaning; and a precise expression of the two-factor driven theory is established, unifying the performance scale of macroscopic priors and microscopic coding.
[0022] Independence: The method of this invention does not depend on a specific imaging system or application scenario, and can be independently applied to the theoretical performance analysis and optimization design of any multispectral imaging system.
[0023] Quantifiability: Based on rigorous Fisher information matrix analysis, the calculation of equivalent wavelength has a solid mathematical foundation, and the results are repeatable and verifiable.
[0024] Guiding value: Equivalent wavelength analysis can provide quantitative basis for channel selection and parameter optimization of multispectral imaging systems, avoid blind trial and error, and significantly improve system design efficiency.
[0025] Synergy with macroscopic priors: Two-factor driving theory reduces macroscopic prior uncertainty With equivalent wavelength By incorporating them into the same formula, a unified theoretical framework is provided for the design of multimodal imaging systems, and it can guide the collaborative optimization of macroscopic measurement subsystems and microscopic coding subsystems. Attached Figure Description
[0026] Figure 1 This is a flowchart of the equivalent wavelength compression analysis method in an embodiment of the present invention; Figure 2 This is a schematic diagram comparing the equivalent wavelengths of different spectral channel combinations in an embodiment of the present invention; Figure 3 System parameters in the embodiments of the present invention ( Analysis curves showing the effect of the wavelength on the equivalent wavelength; Figure 4 The axial positioning limit under the dual-factor driving theory in this embodiment of the invention varies with... and A changing 3D surface plot. Detailed Implementation
[0027] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings.
[0028] Example 1: This invention provides an equivalent wavelength compression analysis method, such as... Figure 1 As shown, the following steps are performed.
[0029] Step S1: Obtain the system point spread function response Acquire the multispectral imaging system to be analyzed at different wavelengths and different depths Point spread function The point spread function can be obtained through theoretical simulation calculations (such as diffraction calculations based on optical system parameters) or through experimental measurements (such as axial scanning using a point light source). This method is not dependent on a specific acquisition method and can be independently applied to the system design phase or the analysis of existing systems.
[0030] Step S2: Construct a spectral-spatial response model Based on the point spread function obtained in step S1, a spectral-spatial response model is constructed to describe the variation of the system's response to a point light source with wavelength and depth. The response model can be expressed as:
[0031] in For image plane coordinates.
[0032] Step S3: Construct an information-theoretic model of the observation data and calculate the Fisher information matrix. Under the illumination of a point light source above the surface being measured, its three-dimensional position parameter vector is defined as follows: ,in The horizontal position For depth. The observation data across multiple wavelength channels follows a Poisson distribution, and its mean can be expressed as:
[0033] in Intensity of a point light source Let be the projection position of the point light source onto the image plane. This is background noise.
[0034] Based on the above observation model, calculate the Fisher information matrix for the three-dimensional position parameter θ. : (1) in For the first Each pixel at wavelength The expected number of photons.
[0035] Step S4: Calculate the theoretical axial positioning limit of the multispectral system (without macroscopic priors) Fisher information matrix based on step S3 Calculate the theoretical axial positioning limit (Crame-Rhodes lower bound, CRLB) for multispectral systems: (2) Step S5: Calculate the theoretical axial positioning limit of the macroscopic prior for single-spectral channel fusion. As a benchmark, calculations were performed using only a single center wavelength. Channels, and integrate macroscopic priors Theoretical axial positioning limit under the given conditions (Bayesian CRLB): (3) in For single-wavelength CRLB without prior knowledge, For macroscopic a priori fields, This represents the macroscopic prior uncertainty (in the dimension of length). For refractive index, Numerical aperture, This refers to the signal-to-noise ratio.
[0036] Step S6: Define the equivalent wavelength Based on the calculation results of steps S4 and S5, the equivalent wavelength is defined. :
[0037] (4) Because multispectral joint encoding provides additional information, it is necessary to have ,therefore This means achieving equivalent wavelength compression.
[0038] Step S7: Output equivalent wavelength compression analysis results Output equivalent wavelength and its relationship with the center wavelength The comparison results, if This indicates that multispectral joint coding achieves an equivalent wavelength compression effect at the information level, and the degree of compression can be determined by the compression ratio. Quantification.
[0039] Step S8: Two-Factor Driven Performance Prediction Combining macroscopic prior uncertainty With equivalent wavelength The theoretical axial positioning limit of the prediction system in practical applications: (5) This formula reveals the "two-factor driven" mechanism in which system performance is jointly determined by macroscopic prior accuracy and microscopic coding efficiency.
[0040] Example 2: This embodiment provides an application of the above method: equivalent wavelength analysis of a tri-color LED lighting multispectral system. This embodiment uses a typical red, green, and blue LED-illuminated microscopic imaging system as an example to apply the method of this invention for equivalent wavelength compression analysis. All calculations are based on system design parameters and do not involve the actual imaging process.
[0041] Step 1: Obtain the system's point spread function response System design parameters: objective lens numerical aperture =1.4, center wavelength =550nm, with red, green, and blue wavelengths of 640nm, 550nm, and 460nm respectively. Based on vector diffraction theory, the point spread function of each wavelength at different depths is simulated and calculated, with a depth range of... 500 nm to +500 nm, step size 20 nm.
[0042] Steps 2-3: Construct an information-theoretic model and calculate the Fisher information matrix. Based on the PSF data obtained from simulation, an observation model is constructed, assuming that the intensity of the point light source corresponds to the signal-to-noise ratio. = 100 (40 dB), background noise is negligible. Calculate the three-dimensional position parameters according to Formula 1. Fisher's information matrix.
[0043] Step 4: Calculate the theoretical axial positioning limit of the multispectral system Using formula (2), the axial positioning limit of the three-channel combination is obtained. =4.9 nm.
[0044] Step 5: Calculate the limit of macroscopic prior for single-spectral channel fusion Take typical macroscopic prior uncertainty =150 nm (achievable using binocular stereo matching + super-resolution technology). First, calculate the single-wavelength CRLB without prior knowledge:
[0045] Then calculate according to formula (3):
[0046] Step 6: Define the equivalent wavelength According to formula 4: =550nm× 420 nm Step 7: Output Analysis Results =420 nm =550 nm, compression ratio C=(1 (420 / 550)×100%=23.6%. The results show that this three-color multispectral system achieves resolution comparable to a monochromatic system operating at 420 nm, realizing a significant equivalent wavelength compression effect. This result also reveals the path to breaking the Abbe diffraction limit.
[0047] Step 8: Two-Factor Driven Performance Prediction Predict the final axial positioning limit after fusing macroscopic priors using formula (5):
[0048] Considering the system efficiency Csys = 0.65 (including spectral efficiency, quantum efficiency, etc.), the actual achievable limit is about 3.2 nm, which is far better than the Abbe diffraction limit of about 200 nm under visible light.
[0049] Example 3: This embodiment demonstrates the application of the above method: spectral channel optimization selection (application in the design phase). This embodiment demonstrates how to apply the method of the present invention to optimize the selection of spectral channel combinations during the system design phase. All analyses are based on theoretical calculations and do not involve actual imaging.
[0050] System settings: Candidate spectral channels include blue (460nm), cyan (500nm), green (550nm), yellow (580nm), and red (640nm). The goal is to select a combination of 2-4 channels from these 5 channels to optimize the system's theoretical performance. The macroscopic prior uncertainty is fixed at [value missing]. =150 nm.
[0051] Analysis process: Combining Figure 2 As shown, the equivalent wavelengths for all possible channel combinations are calculated (according to formulas (1)-(4)), and the results are as follows:
[0052] Optimization conclusion: (1) Among the three-color combinations, blue + green + red (321nm) is better than blue + cyan + green (340nm) and cyan + green + yellow (355nm). (2) The four-color combination of blue + cyan + green + red (315 nm) further compresses the equivalent wavelength, but the gain is relatively limited (from 321 nm to 315 nm, only 1.9% compression). (3) Taking into account system complexity (more channels mean more complex beam splitters or filters) and performance gain, the combination of blue, green and red is the optimal choice.
[0053] Example 4: This embodiment provides an application of the above method: system parameter optimization design (numerical aperture influence). Combination Figure 3 As shown, this embodiment analyzes the influence of the system's numerical aperture on the equivalent wavelength to guide the optimization design of system parameters.
[0054] System settings: Fixed red, green, and blue illumination; signal-to-noise ratio (SNR) = 100; macroscopic prior. =150 nm. Change the numerical aperture NA from 0.8 to 1.4 (in steps of 0.2) and calculate the corresponding equivalent wavelength and axial positioning limit.
[0055] Analysis results:
[0056] Optimization conclusion: (1) Both the equivalent wavelength and the final positioning limit decrease with increasing numerical aperture, while the theoretical performance of the system improves with increasing NA; (2) When NA is increased from 1.2 to 1.4, the equivalent wavelength is compressed from 385 nm to 330 nm, the positioning limit is reduced from 4.3 nm to 3.7 nm, and the gain is significant; (3) If the system cost or working distance limit NA ≤ 1.2, then the theoretical performance upper limit is: ≈385 nm, It is approximately 4.3 nm, which is still far superior to the Abbe diffraction limit of about 200 nm under visible light.
[0057] Example 5: This embodiment provides an application of the above method: performance limit prediction in conjunction with macroscopic priors (two-factor driven, formula (5)). This embodiment demonstrates a method for jointly predicting the actual performance limit of a system using equivalent wavelength and macroscopic prior uncertainty. The macroscopic prior uncertainty in this method... As input as known parameters, it does not involve the process of obtaining prior knowledge.
[0058] This embodiment demonstrates how to use the two-factor driven formula (5) to predict the system performance limit under different macroscopic prior accuracies, such as Figure 4 As shown.
[0059] System settings: Equivalent wavelength of multispectral system =320nm, macroscopic depth prior uncertainty The wavelengths are 50nm, 100nm, and 200nm, respectively. The multispectral system uses red, green, and blue colors, with NA = 0.9, SNR = 100, and equivalent wavelengths... =420 nm (derived from Example 1). Changing the macroscopic prior uncertainty Calculate the corresponding axial positioning limits from 50 nm to 300 nm. .
[0060] Prediction results: Based on the relationship Calculate the theoretical axial positioning limit :
[0061] Results analysis: (1) When (like When =50 nm), Performance is dominated by macroscopic priors; (2) When (like When ≥150 nm, As it approaches saturation, performance is dominated by the limits of micro-coding. (3) Therefore, in practical engineering, the macroscopic a priori accuracy is improved to Most of the benefits can be obtained at approximately 100 nm, further reduction It has limited impact on the final performance of the system.
[0062] Application value: This method can be used to evaluate the accuracy requirements of macroscopic measurement subsystems and guide how to balance macroscopic measurement inputs with microscopic coding inputs during system design to achieve synergistic optimization.
[0063] The above description is merely a preferred embodiment of the present invention and should not be construed as limiting the scope of the invention. Therefore, any equivalent variations made in accordance with the claims of the present invention are still within the scope of the present invention.
Claims
1. An equivalent wavelength compression analysis method, characterized in that, Includes the following steps: S1: Obtain the point spread function of the multispectral imaging system to be analyzed at different wavelengths λ and depths z. ; S2: Construct a spectral-spatial response model based on the obtained point spread function. ,in Image plane coordinates; S3: Construct a three-dimensional position parameter vector based on the spectral-spatial response model regarding the illumination from a point light source above the measured surface. The observational information theory model is derived, and the Fisher information matrix of the multispectral system is calculated. ; S4: Calculate the theoretical axial positioning limit of the multispectral system using the calculated Fisher information matrix of the multispectral system. ; S5: Calculations use only the center wavelength The theoretical axial positioning limit of single-spectral channel fusion macroscopic prior at time: in For single-wavelength CRLB without prior knowledge, For macroscopic a priori fields, For macroscopic prior uncertainty, For refractive index, Numerical aperture, Signal-to-noise ratio; S6: Define equivalent wavelength ; S7: Output equivalent wavelength and its relationship with the center wavelength The comparison results; S8: Combining macroscopic prior uncertainty With equivalent wavelength The theoretical axial positioning limit of the prediction system in practical applications: 。 2. The equivalent wavelength compression analysis method according to claim 1, characterized in that, The Fisher information matrix in S3 The calculation formula is: in , For the first Each pixel at wavelength The expected number of photons, Intensity of a point light source This is background noise.
3. The equivalent wavelength compression analysis method according to claim 1, characterized in that, The macroscopic prior uncertainty in S5 Obtained through measurement.
4. The equivalent wavelength compression analysis method according to claim 1, characterized in that, S7 also includes a step of calculating the equivalent wavelength compression ratio based on the comparison results: Used to quantify the information gain brought about by multispectral joint coding.
5. An equivalent wavelength compression analysis system, characterized in that, include: The data input module is configured to perform the method of step S1 as described in any one of claims 1-4; An information theory analysis module is configured to perform the method of steps S2-S4 as described in any one of claims 1-4; The Bayesian fusion module is configured to perform the method of step S5 as described in any one of claims 1-4; An equivalent wavelength calculation module is configured to perform the method of steps S6-S7 as described in any one of claims 1-4; A two-factor prediction module is configured to perform the method of step S8 as described in any one of claims 1-4; The analysis output module is used to output equivalent wavelength, compression ratio, and performance prediction results.
6. A method for evaluating the performance of a multispectral imaging system using the equivalent wavelength compression analysis method according to any one of claims 1-4, characterized in that, include: Calculate the equivalent wavelength of the system to be evaluated. ,by As a quantitative indicator of system information capacity, The smaller the value, the higher the theoretical resolution of the system; the evaluation method is independent of the imaging process and is used for performance prediction in the system design phase or theoretical analysis of existing systems.
7. An application of the equivalent wavelength compression analysis method according to any one of claims 1-4 for the optimal selection of spectral channels in a multispectral imaging system, characterized in that, The method implemented during the system design phase is as follows: For different channel combinations in the candidate spectral channel set, their equivalent wavelengths are calculated separately. , choose to The smallest channel combination is the optimal encoding scheme.
8. A method for optimizing the parameters of a multispectral imaging system using the equivalent wavelength compression analysis method according to any one of claims 1-4, characterized in that, include: Analyze the system parameters for the equivalent wavelength The system parameters are adjusted based on the analysis results to achieve the optimal theoretical performance of the system under given constraints; the parameter optimization design method is used to guide the system hardware design.
9. An equivalent wavelength compression analysis method according to any one of claims 1-4 for incorporating macroscopic prior uncertainty. With equivalent wavelength The two-factor driven formula is used to predict the theoretical axial positioning limit of the system in practical applications; the prediction method includes... As input as known parameters, it does not involve the process of obtaining macroscopic priors.