A spectrometer calibration method based on system performance indicators
By analyzing the decrease in axial resolution and sensitivity, and by employing steps such as data acquisition, wavelength calibration, and dispersion compensation, the complexity of spectrometer calibration was solved, achieving efficient spectrometer calibration and high-resolution OCT imaging.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- DALIAN UNIV OF TECH
- Filing Date
- 2023-06-13
- Publication Date
- 2026-08-04
AI Technical Summary
Existing spectrometer calibration methods are complex and cumbersome, requiring the use of standard light sources for calibration, which increases the complexity and time consumption of the calibration process. Furthermore, there is a lack of universally applicable methods for calibration based on system performance indicators such as axial resolution and sensitivity degradation.
By analyzing the decrease in axial resolution and sensitivity, the calibration parameters of the spectrometer were gradually optimized through steps such as data acquisition, wavelength calibration, dispersion compensation, removal of DC term, windowing, zero padding, and Fourier transform, ultimately achieving efficient calibration of the system.
This method enables efficient calibration of the spectrometer, obtains high-resolution OCT tomographic images, ensures high image quality within the imaging range, and reduces the complexity of the calibration process.
Smart Images
Figure CN116858377B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to frequency domain optical coherence tomography (SD-OCT) and spectrometer calibration techniques, and particularly to a spectrometer calibration method based on system performance indicators. Background Technology
[0002] Optical imaging is one of the main methods for examining retinal diseases. It can provide high-precision images of retinal structure, providing a reliable basis for the diagnosis and treatment of various retinal diseases. SD-OCT is a non-contact, non-invasive in vivo biological tissue imaging technology, characterized by real-time display, high resolution, and high scanning depth.
[0003] The spectrometer is a crucial component of SD-OCT, used to decompose interference light into different spectral components and acquire the interference intensity signal after grating dispersion using a linear CCD array. The overall performance of an OCT imaging system depends on the light source and the optical components used. For example, the axial resolution of an SD-OCT system is related to the center wavelength and bandwidth of the light source, while the imaging depth is related to the center wavelength and bandwidth of the light source, as well as the number of pixels in the CCD camera. By rationally designing the structure and parameters of the spectrometer, the system can achieve both high resolution and high imaging depth.
[0004] Among current spectrometer calibration methods, the most common approach is to calibrate the spectrometer using a standard light source with known spectral characteristics (e.g., a mercury lamp). During spectrometer calibration, deviations and nonlinear responses can be detected by comparing the spectrometer's measurements to the standard light source with known standard spectral lines. It's important to note that spectrometer calibration methods may vary depending on the equipment and application. Besides using a standard light source, other methods can be employed, such as using reference samples or standard samples with known spectral characteristics. Different methods can be selected and applied based on specific needs and circumstances.
[0005] In 2021, Du Lili et al. from the Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, proposed a multi-spectral linear fitting algorithm based on atmospheric absorption characteristic spectral lines, specifically targeting the characteristics of the Atmospheric Infrared Ultra-spectral Sounder (AIUS) on the Gaofen-5 satellite, which obtains atmospheric transmittance spectra at different cut heights through occultation observations. This method first selects atmospheric transmittance spectra at appropriate cut heights from the observed spectra and extracts characteristic peaks with distinct features and high signal-to-noise ratios. Simulations and analyses are performed using the HITRAN-2008 spectral library and the SCIATRAN radiative transfer model to determine multiple reference spectral lines and their theoretical wave values across the entire spectral range. Doppler frequency shift correction accurately corrects for spectral drift caused by inherent instrument decay; Gaussian fitting determines the precise data point indices corresponding to the spectral peak positions in the observed spectra. Finally, a univariate linear regression method is used to calculate and obtain the calibration coefficients of the on-orbit spectrum.
[0006] In 2022, Wang Jianwei and colleagues from the Aerospace Information Research Institute of the Chinese Academy of Sciences proposed a wide-bandwidth spectral calibration method based on the assumption that the monochromatic light spectral curve and the spectrometer's spectral response curve are approximately Gaussian functions. By appropriately increasing the bandwidth of the calibration light, the energy entering the hyperspectral imager can be increased, thereby obtaining calibration data with a higher signal-to-noise ratio. This reduces the requirements for calibration equipment while ensuring spectral calibration accuracy.
[0007] Traditional spectrometer calibration methods are generally considered cumbersome and time-consuming, primarily because they require finding a suitable standard light source for calibration. Standard light sources need to possess accurate spectral characteristics, and their use demands certain technical skills and operational experience. These factors increase the complexity and time-consuming nature of the calibration process. Furthermore, there is currently no universally applicable method for calibrating spectrometers based on performance indicators such as axial resolution and sensitivity degradation. Summary of the Invention
[0008] Because previous spectrometer calibration methods were complex and cumbersome, this invention proposes a spectrometer calibration method based on the decrease in axial resolution and sensitivity. This method determines the spectrometer calibration parameters by analyzing the decrease in axial resolution and sensitivity. To calibrate the spectrometer, a set of parameters needs to be found that allows the system to achieve good performance. Through continuous iteration and optimization, the optimal parameters are gradually approached, ultimately completing the spectrometer calibration process.
[0009] The technical solution of this invention is to calibrate a spectrometer based on the decrease in axial resolution and sensitivity, including the following steps:
[0010] 1) Data Acquisition: Unlike actual OCT imaging, in the system setup and wavelength calibration experiments for the spectrometer, the sample in the sample arm of the SD-OCT (Spectral Domain Optical Coherence Tomography) system was replaced with a mirror. The interference fringes formed by the reflections from the two mirrors were imaged by the spectrometer for subsequent calibration and performance analysis. To complete the system's data acquisition, it is essential to ensure the normal operation of the SD-OCT system.
[0011] 2) Wavelength calibration: Wavelength calibration is a process used to determine the relationship between wavelengths and pixels in a spectrometer. By using interference data obtained under different optical path differences, the distribution of wavelengths on the pixels is determined.
[0012] 3) Dispersion compensation: Eliminating the dispersion effect caused by the optical system and determining the corresponding dispersion compensation parameters. Due to the non-uniformity of the refractive index of the medium in the optical system or the difference in the optical path, the propagation speed of the light signal at different wavelengths will be different, resulting in a dispersion effect at the imaging depth.
[0013] 4) Remove DC term: Eliminate the DC component in the interference signal. In order to extract useful reflection information and reduce background noise, it is necessary to remove the DC term from the interference signal.
[0014] 5) Windowing: After removing the DC term, the data is windowed to prevent spectrum leakage.
[0015] 6) Zero padding: Zero padding is a method of interpolating the collected interferometric data, which increases the number of data points to more than twice through interpolation.
[0016] 7) Perform Fourier transform on the data: The Fourier transform converts the time-domain signal into a frequency-domain signal, thereby obtaining the spectral intensity information of the data. By observing the spectral intensity information, we can roughly judge the quality of the selected wavelength calibration parameters and dispersion compensation parameters.
[0017] 8) Observe whether the shape of each peak is sharp. If it is not sharp, repeat steps 2) to 7) or 3) to 7). If the peak is sharp, proceed to the next step.
[0018] 9) Perform Gaussian fitting analysis on each peak to obtain the axial resolution and sensitivity reduction curves of the system.
[0019] 10) If the axial resolution change of the system is sufficiently flat, the requirements are met, and the system calibration is completed; otherwise, the process of steps 2) to 9) or 3) to 9) needs to be repeated.
[0020] Furthermore, step 2) wavelength calibration specifically includes the following steps:
[0021] 2-1) A quadratic polynomial is used to establish a model relating camera pixels to light source wavelength, where λ(n) is the wavelength, n is the number of camera pixels, and β0, β1, and β2 are wavelength calibration parameters. The specific expression is shown below:
[0022] λ(n)=β0+β1n+β2n 2 (1)
[0023] 2-2) The relationship between wavelength λ and wavenumber k can be expressed by the following formula:
[0024] k=2π / λ (2)
[0025] 2-3) By performing a Fourier transform in k-space, information related to the imaging depth z can be obtained.
[0026] Furthermore, step 3) dispersion compensation specifically includes the following steps:
[0027] 3-1) If the system's dispersion is mismatched, there will be a phase difference θ(k) between the reference arm and the sample arm. Let I'(k) be the cross-correlation signal of the real interference spectrum, and its expression is as follows:
[0028]
[0029] Where S(k) represents the power spectral density of the light source, and Δz represents the optical path difference;
[0030] 3-2) Using Taylor expansion, expand the phase difference θ(k) to the third order:
[0031]
[0032] Where k0 represents the center wavenumber;
[0033] 3-3) From equation (4), it can be observed that the second and third terms in the expansion cause dispersion mismatch in the system. Therefore, dispersion compensation can be achieved by setting two parameter values, a2 and a3. The calculation formula for compensation is shown below:
[0034] φ dc (k)=-a2(k-k0) 2 -a3(k-k0) 3 (5).
[0035] The beneficial effects of this invention are as follows: This invention proposes a spectrometer calibration method based on the decrease in axial resolution and sensitivity, aiming to reduce the complexity of spectrometer calibration. Using the method of this invention, the spectrometer system was successfully applied to SD-OCT retinal imaging experiments, obtaining high-resolution OCT tomographic images and ensuring high image quality within the imaging range. Attached Figure Description
[0036] Figure 1 Flowchart for Spectrometer System Calibration
[0037] Figure 2 Axial resolution diagram of the system
[0038] Figure 3 Figure showing the decrease in system sensitivity Detailed Implementation
[0039] The calibration of a spectrometer with a wavelength range of 805nm-904nm is listed below. The invention is further illustrated with examples and accompanying drawings, but this should not be construed as limiting the scope of protection of the invention.
[0040] A spectrometer calibration method based on the decrease in axial resolution and sensitivity, the steps of which are as follows:
[0041] 1) Data Acquisition: In this case, a transmission grating G (1200 lines / mm) manufactured by Wasatch Photonics (USA) was selected for beam splitting, and a linear CCD camera (OCTOPLUS 2048, sampling frequency 130kHz) manufactured by e2v (UK) was used for data acquisition. The camera's data acquisition mode was set to internal line trigger mode (maximum exposure time and programmable line period), and the data acquisition rate was set to 100kHz. The width of the data was 2048, and the height was 100. Since the data acquisition required for system calibration does not involve the scanning process, the scanning galvanometer was kept in its original position. On the test platform, the optical path difference range was set to 0 to 2mm, and data acquisition was performed every 0.25mm change, for a total of 9 sets of data.
[0042] 2) Wavelength calibration: For data obtained under different optical path differences, it is first necessary to determine the distribution of wavelengths on the pixels.
[0043] Step 2) Wavelength calibration, as shown, specifically includes the following steps:
[0044] 2-1) This invention uses a quadratic polynomial to establish a model relating camera pixels to light source wavelengths, where λ(n) is the wavelength, n is the number of camera pixels, and β0, β1, and β2 are wavelength calibration parameters. The specific expression is shown below:
[0045] λ(n)=β0+β1n+β2n 2 (6)
[0046] 2-2) The relationship between wavelength λ and wavenumber k can be expressed by the following formula:
[0047] k = 2π / λ (7)
[0048] 2-3) By performing a Fourier transform in k-space, information related to the imaging depth z can be obtained.
[0049] 3) Dispersion compensation: This step aims to eliminate the dispersion effect caused by the optical system and determine the appropriate dispersion compensation parameters.
[0050] Step 3) Dispersion compensation, as shown, specifically includes the following steps:
[0051] 3-1) If the system's dispersion is mismatched, there will be a phase difference θ(k) between the reference arm and the sample arm. Let I'(k) be the cross-correlation signal of the real interference spectrum, and its expression is as follows:
[0052]
[0053] Where S(k) represents the power spectral density of the light source, and Δz represents the optical path difference;
[0054] 3-2) Using Taylor expansion, expand the phase difference θ(k) to the third order:
[0055]
[0056] Where k0 represents the center wavenumber;
[0057] 3-3) As can be observed from the above equation, the second and third terms in the expansion cause dispersion mismatch in the system. Therefore, dispersion compensation can be achieved by setting two parameter values, a2 and a3. The calculation formula for compensation is shown below:
[0058] φ dc (k)=-a2(k-k0) 2 -a3(k-k0) 3 (10)
[0059] 4) DC Term Removal: In this case, the data averaging method is used to eliminate the DC component in the interference signal. The purpose of this step is to remove the DC term from the spectrometer system. The data averaging method is simple and requires no additional steps, thus offering high efficiency. Averaging the nine sets of data yields a result that can be approximated as the DC term of the spectrometer system.
[0060] 5) Windowing: After removing the DC term, the data is windowed to prevent spectral leakage. In this case, a rectangular window is chosen for windowing.
[0061] 6) Zero padding: In this case, the collected interference data is interpolated to double the number of data points.
[0062] 7) Perform Fourier transform on the data: The Fourier transform converts the time-domain signal into a frequency-domain signal, thereby obtaining the spectral intensity information of the data. By observing the frequency-domain intensity information, one can roughly judge the quality of the selected wavelength calibration parameters and dispersion compensation parameters.
[0063] 8) Observe whether the shape of each peak is sharp. If it is not sharp, repeat steps 2) to 7) or 3) to 7). If the peak is sharp, proceed to the next step.
[0064] 9) Perform Gaussian fitting analysis on each peak to obtain the axial resolution and sensitivity reduction curves of the system.
[0065] 10) If the system resolution change is sufficiently flat, i.e. the requirements are met, the wavelength calibration of the system is completed; otherwise, the process of steps 2) to 9) or 3) to 9) needs to be repeated.
[0066] After the above calibration steps, the wavelength calibration results are β0 = 967.8389, β1 = -0.092422, and β2 = 1.2 × 10⁻⁶. -8 The dispersion compensation result is a2 = 6.566 × 10 -8 a3 = 3.02 × 10 -11 .
[0067] Figure 2 The system resolution map is shown, with a maximum resolution of 4.14 μm and a minimum of 2.72 μm. Axial resolution remains relatively stable within the imaging range. Figure 3 The graphs show the sensitivity decrease of the system, with a decrease of 20 dB. These two figures clearly demonstrate that the spectrometer calibration method proposed in this invention, based on axial resolution and sensitivity decrease, is feasible and meets the requirements of OCT applications.
Claims
1. A spectrometer calibration method based on system performance indicators, characterized in that, Includes the following steps: 1) Data acquisition: In the experiment of system construction and wavelength calibration of the spectrometer, the sample in the sample arm of the SD-OCT system was replaced by a mirror. The interference fringes formed by the reflection of the two mirrors were imaged by the spectrometer and used for subsequent calibration and performance analysis. 2) Wavelength calibration: Wavelength calibration is a process used to determine the relationship between wavelength and pixels in a spectrometer; by using interference data obtained under different optical path differences, the distribution of wavelengths on the pixels is determined. 3) Dispersion compensation: Eliminate the dispersion effect caused by the optical system and determine the corresponding dispersion compensation parameters; 4) Remove DC term: Eliminate the DC component in the interference signal; 5) Windowing: Used to prevent spectrum leakage; 6) Zero padding: The collected interferometric data is interpolated, which increases the number of data points to more than double through interpolation; 7) Perform Fourier transform on the data: Fourier transform converts the time-domain signal into a frequency-domain signal, thereby obtaining the spectral intensity information of the data. By observing the spectral intensity information, the quality of the selected wavelength calibration parameters and dispersion compensation parameters can be roughly judged. 8) Observe whether the shape of each peak is sharp. If it is not sharp, repeat steps 2) to 7) or 3) to 7). If the peak is sharp, proceed to the next step. 9) Perform Gaussian fitting analysis on each peak to obtain the axial resolution and sensitivity reduction curves of the system; 10) If the axial resolution variation of the system is sufficiently flat, the requirements are met, and the system calibration is complete; otherwise, steps 2) to 9) or 3) to 9) need to be repeated. Step 2), wavelength calibration, specifically includes the following steps: 2-1) A quadratic polynomial is used to establish a model of the relationship between camera pixels and light source wavelength, where... λ ( n () represents the wavelength. n For camera pixels, β 0、 β 1. β 2 represents the wavelength calibration parameter; the specific expression is shown below: （1） 2-2) Wavelength λ and wave number k The relationship between them can be expressed by the following formula: （2） 2-3) By k Performing a Fourier transform on the space yields the image depth. z Relevant information; Step 3), dispersion compensation, specifically includes the following steps: 3-1) If the system's dispersion is mismatched, there will be a phase difference between the reference arm and the sample arm. θ ( k ),set up I ’ ( k The cross-correlation signal of the real interference spectrum is expressed as follows: （3） in, S ( k ) represents the power spectral density of the light source, Δ z Indicates optical path difference; 3-2) Using Taylor expansion, the phase difference is... θ ( k Expanding to the third stage: （4） in, k 0 indicates the center wavenumber; 3-3) It can be observed from equation (4) that the second and third terms in the expansion cause dispersion mismatch in the system; therefore, this can be resolved by setting the values of the two parameters. a 2 and a 3. Dispersion compensation is performed; the calculation formula for compensation is shown below: （5）。