A method for measuring the absorption coefficient of germanium optical elements

Abstract

The application discloses a method for measuring absorption coefficient of germanium optical elements, and relates to the technical field of infrared optical material detection, and comprises the following steps: obtaining a sample spectrum record; determining a fringe wave number interval from adjacent transmission maximum wave numbers in the sample spectrum record according to an incident angle to generate an effective geometric path of the incident angle; forming a model input sample from the sample spectrum record, the effective geometric path of the incident angle, a measured transmittance at a target wavelength and a measured specular reflectance; configuring a neural network model, so that an interface reflectance parameter is output according to the incident angle, and an absorption coefficient parameter is output according to a fusion feature of multiple incident angles of the same measuring point; training the neural network model by using the model input sample, a flat plate multiple internal reflection equation and a Beer-Lambert equation to obtain an absorption coefficient inversion model; and inputting a model input sample of a germanium optical element to be measured into the absorption coefficient inversion model to obtain an absorption coefficient of the germanium optical element to be measured. The application is favorable for reducing the influence of interface reflection coupling and optical path errors on absorption coefficient measurement.

Description

Technical Field

[0001] This invention relates to the field of infrared optical material detection technology, and specifically to a method for measuring the absorption coefficient of germanium optical elements. Background Technology

[0002] Germanium optical elements, due to their infrared transmission capability, are often used as transmission components in infrared optical systems. Their absorption coefficient at the operating wavelength directly affects the element's transmission performance and thermal response stability, making it a crucial parameter for material quality evaluation and element fabrication process control. Current absorption coefficient measurements typically rely on establishing an inversion relationship between spectral transmittance and thickness parameters. While this method has some applicability in detecting low-absorption materials, the inversion results are easily affected by interface optical effects and the way optical path values ​​are determined.

[0003] Because germanium has a high refractive index, the reflected component of incident light at the element interface participates in the transmission spectrum response, meaning that transmittance variations simultaneously include the effects of interface reflection and internal material absorption. For planar germanium optical elements with a certain thickness, the propagation path of light within the element also changes with incident conditions, making it difficult to accurately reflect the actual transmission state using nominal thickness to characterize the absorption optical path. These factors make it difficult for absorption coefficient measurements to consistently correspond to the bulk absorption characteristics of the material, affecting the reliability of infrared optical element quality evaluation. Summary of the Invention

[0004] The purpose of this invention is to provide a method for measuring the absorption coefficient of germanium optical elements, so as to solve the problems in the background art mentioned above.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] This invention provides a method for measuring the absorption coefficient of germanium optical elements, comprising:

[0007] The multi-incident angle transmission and specular reflection spectra of multiple measurement points of the sample germanium optical element in the target band containing the target wavelength are obtained to form a sample spectrum record;

[0008] The fringe wavenumber interval is determined by the wavenumber of adjacent transmission maxima in the sample spectral record based on the incident angle, and an effective geometric path for the incident angle is generated.

[0009] The model input sample is formed by the sample spectral record, the effective geometric path of the incident angle, the measured transmittance at the target wavelength, and the measured specular reflectance.

[0010] A neural network model with a physical constraint layer is configured so that the interface reflectivity parameter is output according to the incident angle and the absorption coefficient parameter is output by the fusion feature of multiple incident angles at the same measurement point. The neural network model is trained with the model input samples, the plate multiple internal reflection equation and the Beer-Lamber equation to obtain the absorption coefficient inversion model.

[0011] The absorption coefficient of the germanium optical element under test is obtained by inputting the model of the sample into the absorption coefficient inversion model.

[0012] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0013] This invention acquires the transmission and specular reflection spectra of a sample germanium optical element at multiple measurement points and multiple incident angles, and determines the effective geometric path of the incident angle by the wavenumber of adjacent transmission maxima, thus introducing an optical path constraint corresponding to the actual propagation path into the absorption coefficient inversion process. By configuring a neural network model with a physical constraint layer, the interface reflectivity parameter is output according to the incident angle, and the absorption coefficient parameter is output by the fusion feature of multiple incident angles at the same measurement point. Combined with the multiple internal reflection equation of the flat plate and the Beer-Lambert equation for training, the influence of interface reflection and the bulk absorption of the material can be separated within the same inversion framework. This reduces the errors caused by nominal thickness and single transmittance inversion, making the absorption coefficient of the germanium optical element under test more stably correspond to the bulk absorption characteristics of the material. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0015] Figure 1 A flowchart illustrating a method for measuring the absorption coefficient of a germanium optical element according to an embodiment of the present invention;

[0016] Figure 2 This is a schematic diagram of the structure of a neural network model provided in an embodiment of the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions in the embodiments of this application will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0018] Unless otherwise stated, in the embodiments of this application, "multiple" refers to two or more; "target wavelength neighborhood" refers to a local wavenumber range that includes the wavenumber position corresponding to the target wavelength; "two adjacent maximum wavenumbers within the target wavelength neighborhood" refers to two transmission maximum wavenumbers that are located within the local wavenumber range, are adjacent to each other, and cover or are close to the wavenumber position corresponding to the target wavelength.

[0019] Germanium optical components are commonly used transmission elements in infrared optical systems. The absorption coefficient of germanium material at the operating wavelength directly affects the transmission performance and thermal stability of the component, making it a crucial parameter in evaluating the quality of germanium optical components. The common measurement method involves inverting the absorption coefficient by combining the transmittance at a single wavelength with the nominal thickness of the component. However, on the one hand, germanium has a high refractive index, and interface reflection accounts for a significant proportion of the transmittance. Interface reflection and bulk absorption are coupled in the transmittance, and directly fitting the absorption coefficient from the transmittance easily incorporates the influence of interface reflection into the bulk absorption. On the other hand, there is a discrepancy between the nominal thickness of the component and the actual optical path length of light propagating within the component, and this discrepancy varies with the incident angle. Using the nominal thickness in the inversion introduces optical path error. All of these factors cause the absorption coefficient measurement results to deviate from the bulk absorption characteristics of the material.

[0020] In view of this, such as Figure 1 As shown, this embodiment discloses a method for measuring the absorption coefficient of a germanium optical element. In the model training phase, the method uses multi-point, multi-incident-angle spectral data of a sample germanium optical element to train an absorption coefficient inversion model. In the model application phase, the model input sample of the germanium optical element to be tested is input into the absorption coefficient inversion model to obtain the absorption coefficient of the germanium optical element to be tested. The sample germanium optical element is used for model training, and the germanium optical element to be tested is used for model application; these two correspond to different processing phases. The specific method is as follows:

[0021] S101: Obtain the multi-incident angle transmission and specular reflection spectra of multiple measurement points of the sample germanium optical element in the target band containing the target wavelength, and form a sample spectrum record;

[0022] S102: Determine the fringe wavenumber interval based on the wavenumber of adjacent transmission maxima in the sample spectral record according to the incident angle, and generate the effective geometric path of the incident angle;

[0023] S103: The model input sample is formed by the sample spectral record, the effective geometric path of the incident angle, the measured transmittance at the target wavelength, and the measured specular reflectance.

[0024] S104: Configure a neural network model with a physical constraint layer so that the interface reflectivity parameter is output according to the incident angle and the absorption coefficient parameter is output by the fusion feature of multiple incident angles at the same measurement point; train the neural network model with model input samples, the plate multiple internal reflection equation and the Beer-Lambert equation to obtain the absorption coefficient inversion model.

[0025] S105: Input the model of the germanium optical element under test into the absorption coefficient inversion model to obtain the absorption coefficient of the germanium optical element under test.

[0026] Specifically, the sample germanium optical element is the same germanium optical element used during the model training phase. To ensure consistency between the training data and the application data, the material type, surface processing state, and target band detection conditions of the sample germanium optical element are matched with the detection conditions of the germanium optical element under test. For example, the sample germanium optical element can be a flat germanium optical element that has been polished on both sides.

[0027] Multiple measurement points are set within the effective light-transmitting area of ​​the sample germanium optical element, with each measurement point corresponding to a local measurement area. These multiple measurement points are used to provide the spectral response at different locations on the sample germanium optical element, allowing the training data to cover the absorption differences of the sample germanium optical element in spatial location. Exemplarily, the multiple measurement points can be arranged in a grid pattern or radially within the effective light-transmitting area; this embodiment does not limit the number or distribution of the measurement points.

[0028] The target wavelength is the operating wavelength at which the absorption coefficient needs to be measured. The target band is a continuous spectral range that includes the target wavelength and covers the spectral range within the neighborhood of the target wavelength where adjacent transmission maxima are located to determine the fringe wavenumber interval; that is, the target band is the spectral interval used to provide conditions for identifying transmission interference fringes. This setting allows the fringe wavenumber interval to be obtained directly from the continuous transmission spectrum, reducing optical path error when inverting the absorption coefficient using single-point transmittance.

[0029] Furthermore, for any measurement point of the sample germanium optical element, the transmission spectrum and specular reflection spectrum within the target wavelength band are acquired according to multiple incident angles. The incident angle is the angle formed by the incident light relative to the normal direction of the incident surface of the sample germanium optical element; each incident angle corresponds to a set of transmission spectra and a set of specular reflection spectra; the transmission spectrum records the spectral data of transmittance varying with wavenumber within the target wavelength band, and the specular reflection spectrum records the spectral data of specular reflectance varying with wavenumber within the target wavelength band; the transmission spectrum and specular reflection spectrum correspond to the same measurement point at the same incident angle. For example, the transmission spectrum and specular reflection spectrum can be acquired by an infrared spectrometer in conjunction with angle-adjustable transmission and specular reflection measurement accessories; multiple incident angles can be set to three or more distinct angles; this embodiment does not limit the number or value of the incident angles.

[0030] Multi-incident angle spectral data at the same measurement point are used to characterize the optical response of interface reflection as the incident angle changes, while the bulk absorption coefficient of the material at the same measurement point and the same target wavelength corresponds to the local region of the same material. Therefore, multi-incident angle transmission and specular reflection spectra provide a data basis for subsequent differentiation of interface reflectivity parameters and absorption coefficient parameters, and can reduce the inversion bias caused by the coupling of interface reflection and material absorption.

[0031] The sample spectral records are organized by measurement point identifiers and incident angle identifiers. Under the same measurement point identifier, multiple incident angle spectral data of the same measurement point are recorded. Under the same incident angle identifier, transmission spectral records and specular reflection spectral records corresponding to the incident angle are recorded. The target band covers the target wavelength and the spectral band where the adjacent transmission maxima are located.

[0032] Specifically, a measurement point identifier is set for each measurement point, and an incident angle identifier is set for each incident angle. Sample spectral records are organized using the measurement point identifier and the incident angle identifier: multiple incident angle spectral data for the same measurement point are stored under the same measurement point identifier; transmission spectral records and specular reflectance spectral records for the corresponding incident angles are stored under the same incident angle identifier. The transmission spectral record includes at least the measurement point identifier, the incident angle identifier, the wavenumber sequence within the target band, and the transmittance sequence corresponding to that wavenumber sequence; the specular reflectance spectral record includes at least the measurement point identifier, the incident angle identifier, the wavenumber sequence within the target band, and the specular reflectance sequence corresponding to that wavenumber sequence.

[0033] As a feasible processing method, when the original spectrum is recorded with wavelength as the independent variable, the wavelength sequence is converted into a wavenumber sequence, and the transmission spectrum and specular reflection spectrum adopt consistent wavenumber coordinates. Let the wavenumber be... , wavelength is Both conditions are met: In the formula, Indicates wave number, This represents the wavelength. This conversion is used to unify the reading reference for adjacent transmission maxima wavenumbers, allowing transmission and specular reflection spectra to participate in subsequent processing under the same wavenumber coordinates. For example, wavenumber... The unit can be .

[0034] Therefore, the sample spectral records can correspondingly preserve the measurement point source and incident angle source for each set of transmission and specular reflection spectra. This data organization method can reduce the probability of mismatch between data from different incident angles at the same measurement point and ensure that data from different measurement points are accurately incorporated into the feature fusion process of the corresponding measurement points.

[0035] Specifically, the transmission spectrum in the sample spectral record contains transmission interference fringes formed by multiple internal reflections of the plate within the target band, and the interval between adjacent transmission maxima wavenumbers is related to the propagation optical path at the corresponding incident angle. Since changes in the incident angle alter the refraction path of light within the germanium material, the fringe wavenumber intervals are determined separately according to the incident angle, and the effective geometric path at the incident angle is also generated separately according to the incident angle.

[0036] The effective geometric path at the incident angle is the actual one-way geometric path of light at the target wavelength within the sample germanium optical element as it undergoes absorption and attenuation. In this embodiment, the effective geometric path at the incident angle is determined based on measured transmission interference fringes, rather than directly using the nominal thickness of the sample germanium optical element. The optical path information obtained from the measured fringes can reflect the actual propagation path at different incident angles, thereby improving the correspondence between subsequent absorption coefficient parameters and the bulk absorption characteristics of the material.

[0037] Specifically, the process of generating the effective geometric path of the incident angle includes:

[0038] According to the incident angle, the transmission spectrum segment containing the target wavelength is extracted within the target band to obtain the fringe calculation spectrum segment corresponding to each incident angle;

[0039] Specifically, for any measurement point and any incident angle in the sample spectral record, a transmission spectrum segment containing the target wavelength is extracted within the target band. This extracted transmission spectrum segment covers the adjacent transmission maxima used to calculate the fringe wavenumber interval within the neighborhood of the target wavelength. This transmission spectrum segment is then used as the fringe calculation spectral segment corresponding to that incident angle. The above processing is performed on the transmission spectra corresponding to each incident angle to obtain the fringe calculation spectral segment for each incident angle.

[0040] The range of the fringe calculation spectrum segment is determined by the ability to identify adjacent transmission maxima within the target wavelength's neighborhood: if the target wavelength is between two transmission maxima, the fringe calculation spectrum segment includes the wavenumber range containing those two transmission maxima; if the target wavelength is close to a certain transmission maxima, the fringe calculation spectrum segment includes the wavenumber range containing that transmission maxima and its adjacent transmission maxima. Extracting the fringe calculation spectrum segment separately according to the incident angle maintains the correspondence between the transmission interference fringes and the incident angle, avoiding the overlap of fringe information at different incident angles.

[0041] Read the adjacent transmission maxima wavenumbers in the neighborhood of the target wavelength in the fringe calculation spectral band to obtain the fringe wavenumber intervals corresponding to each incident angle;

[0042] Furthermore, for any incident angle corresponding to a fringe calculation spectral segment, transmission maxima in the transmission spectrum are identified along the wavenumber increasing direction; a transmission maxima is the wavenumber position where the transmittance reaches a local peak in the fringe calculation spectral segment. The identified transmission maxima are arranged in the wavenumber increasing direction to form a wavenumber sequence corresponding to that incident angle. Subsequently, two adjacent wavenumber maxima within the target wavelength neighborhood are selected from the wavenumber sequence, and the difference between these two wavenumber maxima is used as the fringe wavenumber interval corresponding to that incident angle.

[0043] The process of obtaining the fringe wavenumber interval includes:

[0044] The transmission maxima in the spectral band are calculated by identifying the fringe along the direction of increasing wavenumber, and the wavenumber sequence of the maxima corresponding to each incident angle is obtained.

[0045] Specifically, for a fringe calculation spectral band corresponding to a certain incident angle, the transmittance sequence is read according to the increasing wavenumber direction. If the transmittance at a certain wavenumber position is greater than the transmittance at the preceding wavenumber position and also greater than the transmittance at the following wavenumber position, then that wavenumber position is determined as the transmission maximum wavenumber. The multiple transmission maximum wavenumbers identified at that incident angle are arranged according to the increasing wavenumber direction to obtain the maximum wavenumber sequence corresponding to that incident angle. Each incident angle forms its corresponding maximum wavenumber sequence according to the same rules.

[0046] As a feasible approach, spectral smoothing and baseline correction can be performed on the calculated fringe bands before identifying transmission maxima. Spectral smoothing and baseline correction reduce the impact of noise and baseline drift on the readings of local peak positions, thus providing a stable data foundation for the maximum wavenumber sequence.

[0047] In the maximum wavenumber sequence, select two adjacent maximum wavenumbers in the neighborhood of the target wavelength, and obtain the fringe wavenumber interval corresponding to each incident angle from the difference between the two maximum wavenumbers.

[0048] Specifically, for a maximum wavenumber sequence corresponding to a certain incident angle, the target wavenumber position is first determined based on the target wavelength. Then, two adjacent maximum wavenumbers are selected in the neighborhood of the target wavenumber position, and the maximum wavenumber with the larger wavenumber is subtracted from the maximum wavenumber with the smaller wavenumber to obtain the fringe wavenumber interval corresponding to that incident angle. The above process is performed for each incident angle to obtain the fringe wavenumber interval corresponding to each incident angle.

[0049] It should be noted that the fringe wavenumber intervals maintain a one-to-one correspondence with the incident angle markers; that is, one incident angle marker corresponds to one fringe wavenumber interval. The fringe wavenumber intervals corresponding to different incident angles are used to generate the effective geometric paths for the corresponding incident angles. This processing preserves the influence of changes in the incident angle on the propagation path within the germanium material.

[0050] Based on the fringe wavenumber interval corresponding to each incident angle, the refractive index of germanium material at the target wavelength, and the corresponding incident angle, the effective geometric path of the incident angle is obtained.

[0051] The refractive index of the germanium material at the target wavelength can be determined from the refractive index calibration data of the sample germanium optical element, or from a table of refractive index data of the germanium material at the target wavelength; the corresponding incident angle is the external incident angle when acquiring the transmission spectrum. Based on the refractive index of the germanium material at the target wavelength and the corresponding incident angle, the refraction angle of the light after entering the germanium material can be determined; then, based on the fringe wavenumber interval corresponding to the incident angle, the effective geometric path of the incident angle at that incident angle can be obtained.

[0052] One feasible processing method is as follows. The first... The external incident angle is denoted as The refractive index of germanium material at the target wavelength is denoted as . , will the The angle of refraction within the germanium material at each incident angle is denoted as . According to the law of refraction, Determined by the following formula: In the formula, Indicates the first An external angle of incidence, This represents the refractive index of germanium material at the target wavelength. Indicates the first The internal refraction angle of the germanium material corresponding to each incident angle.

[0053] The first The fringe wavenumber interval corresponding to each incident angle is denoted as . , will the The effective geometric path for each incident angle is denoted as . Then, based on the correspondence between the fringe wavenumber interval and the optical path length of the plate interference, we can obtain: In the formula, Indicates the first The fringe wavenumber interval corresponding to each incident angle Indicates the first Effective geometric path for each incident angle and The meaning is the same as before. In physical terms, it represents the actual geometric distance of a light ray traveling one way through the interior of a germanium optical element.

[0054] It is understandable that for an internal refraction angle of... Plane interference, fringe wavenumber intervals corresponding to adjacent transmission maxima With the local thickness of the component Between satisfy The one-way geometric path of light within germanium material is... Combining the two equations yields the effective geometric path for the aforementioned incident angle. The expression. Therefore, The fringe wavenumber interval can be directly determined from the measured fringe wavenumber without relying on the nominal thickness. For example, when... The unit is hour, The unit is .

[0055] Through the above calculations, a corresponding effective geometric path for each incident angle is obtained, and each effective geometric path is associated and saved with the same measurement point identifier and the corresponding incident angle identifier. This processing provides the data foundation for the formation of subsequent model input samples, including the target band spectrum, actual measurements at the target wavelength, and the effective geometric path of the incident angle. Since the effective geometric path of the incident angle is determined by the measured transmission interference fringes, subsequent model training can distinguish interface reflectivity parameters and absorption coefficient parameters under optical path conditions that more closely approximate the actual propagation path.

[0056] Furthermore, after the aforementioned processing, the sample spectral records already contain transmission and specular reflection spectra within the target band corresponding to multiple measurement points and multiple incident angles, and the effective geometric paths for each incident angle have also been generated. To enable the neural network model to simultaneously use spectral morphology, measured values ​​at the target wavelength, and actual optical path information, the above data needs to be registered according to the measurement points and incident angles to form the model input samples.

[0057] The model input samples are organized based on the measurement point and the incident angle. For any incident angle at the same measurement point, the model input samples include the transmission spectrum within the target band, the specular reflection spectrum within the target band, the effective geometric path of the incident angle, the measured transmittance at the target wavelength, and the measured specular reflectance at the target wavelength. The transmission spectrum and specular reflection spectrum within the target band are used to extract spectral features; the effective geometric path of the incident angle is used for the Beer-Lambert equation in the physical constraint layer; and the measured transmittance and specular reflectance at the target wavelength are used to calculate the deviation from the reconstructed transmittance and reconstructed specular reflectance. All the above data come from the sample spectral records and the effective geometric path of the incident angle, and the data source is unified.

[0058] Specifically, the process of obtaining the model input samples includes:

[0059] The effective geometric path of the incident angle is incorporated into the sample spectrum record according to the measurement point and the incident angle, and the optical path is incorporated into the record.

[0060] Specifically, for any record in the sample spectral record, based on the measurement point identifier and incident angle identifier carried in the record, the effective geometric path of the incident angle corresponding to the same measurement point and the same incident angle is found; after finding the corresponding effective geometric path of the incident angle, the effective geometric path of the incident angle is written into the record, so that the record simultaneously has the transmission spectrum in the target band, the specular reflection spectrum in the target band and the effective geometric path of the incident angle, and the optical path is obtained after writing is completed.

[0061] The optical path incorporation record retains the measurement point identifier and the incident angle identifier: the measurement point identifier indicates the sample measurement point corresponding to the record, and the incident angle identifier indicates the incident angle corresponding to the record. Since the effective geometric path of the incident angle corresponds one-to-one with the incident angle, writing with the same measurement point and the same incident angle can avoid the misuse of the effective optical path under different incident angles, ensuring that each set of spectral data has corresponding optical path information, which helps to reduce the inversion error caused by substituting nominal thickness for actual optical path.

[0062] The transmission spectrum, specular reflection spectrum, effective geometric path of incident angle, measured transmittance and measured specular reflectance at the target wavelength are extracted from the optical path incorporation record to obtain the model input sample.

[0063] Furthermore, for each optical path, the transmission spectrum and specular reflection spectrum within the target wavelength band are extracted. The transmission spectrum within the target wavelength band includes the wavenumber sequence and the corresponding transmittance sequence; the specular reflection spectrum within the target wavelength band includes the wavenumber sequence and the corresponding specular reflectance sequence. Subsequently, the measured transmittance at the target wavelength is read from the transmission spectrum within the target wavelength band, and the measured specular reflectance at the target wavelength is read from the specular reflection spectrum within the target wavelength band. To eliminate local intensity oscillations caused by transmission interference fringes and ensure consistency between the measured values ​​at the target wavelength and the physical response of the incoherent plate multiple internal reflection equation based on intensity superposition in the physical constraint layer, the measured transmittance and measured specular reflectance at the target wavelength are extracted by calculating the envelope mean or performing low-pass smoothing filtering on the interference fringes in the neighborhood of the target wavelength to obtain the corresponding incoherent baseline intensity values. As an feasible processing method, if the target wavelength does not fall on the spectral sampling point, interpolation is performed based on the adjacent sampling points after the target wavelength has undergone the low-pass smoothing filtering or envelope mean calculation to obtain the measured transmittance and measured specular reflectance at the target wavelength.

[0064] When forming the model input samples, the transmission spectrum within the target band, the specular reflection spectrum within the target band, the effective geometric path of the incident angle, the measured transmittance at the target wavelength, and the measured specular reflectance are all retained in the data items corresponding to the same measurement point and the same incident angle. For multiple incident angles at the same measurement point, multiple data items corresponding to each incident angle are formed, and these are combined into a set of model input samples at the same measurement point. Thus, the multi-incident angle data at the same measurement point can jointly participate in the output of the absorption coefficient parameters in the subsequent feature fusion layer.

[0065] The model input samples unify spectral morphology information, measured values ​​at the target wavelength, and effective optical path at the incident angle into a data structure with the same measurement point and the same incident angle. This processing enables subsequent neural network models to simultaneously utilize spectral morphology information, measured transmission and reflection information, and effective optical path information during the same training process, avoiding inconsistent constraints caused by scattered training data sources.

[0066] Specifically, the neural network model is used to invert the absorption coefficient at the target wavelength from the model input samples. Instead of directly fitting the absorption coefficient with a single transmittance, this neural network model outputs the interface reflectivity parameter and the absorption coefficient parameter separately, and introduces the plate multiple internal reflection equation and the Beer-Lambert equation through a physical constraint layer. Thus, a computable physical constraint relationship is formed between the model output parameters, the effective geometric path of the incident angle, the measured transmittance, and the measured specular reflectance, and the model's trainable parameters are updated under this physical constraint relationship.

[0067] It is understandable that, for the same measuring point, the number of incident angles is set as follows: The actual measurements include the measured transmittance and measured specular reflectance at the target wavelength corresponding to each incident angle. There are 1, and the model output parameters to be determined are 2. Interface reflectivity parameters and A total of absorption coefficient parameters One; when When there are two or more parameters, the number of actual measurements is greater than the number of parameters to be determined, which provides sufficient constraints for distinguishing between interface reflectivity parameters and absorption coefficient parameters.

[0068] The neural network model is a physical information neural network model, comprising:

[0069] The spectral feature extraction layer is used to extract spectral features from the model input samples, distinguished by measurement point and incident angle.

[0070] Specifically, the spectral feature extraction layer receives the transmission spectrum and specular reflection spectrum within the target band from the input sample of the model, and outputs the spectral features of the corresponding measurement points and incident angles. The spectral features characterize the spectral shape changes, fringe distribution, and target wavelength neighborhood response of the transmission and specular reflection spectra within the target band.

[0071] As a feasible structure, the spectral feature extraction layer can employ a one-dimensional convolutional layer, a fully connected layer, or a combination of both. In a preferred embodiment of the invention, such as Figure 2 As shown, the spectral feature extraction layer is specifically configured as an architecture consisting of two cascaded one-dimensional convolutional layers and one fully connected layer. The first one-dimensional convolutional layer has a kernel size of 3 and 16 channels, while the second one-dimensional convolutional layer has a kernel size of 3 and 32 channels. The fully connected layer contains 128 neurons and employs the ReLU activation function. The feature fusion layer uses a single fully connected structure containing 256 neurons. Both the interface reflectance output layer and the absorption coefficient output layer use fully connected layers containing 64 neurons, respectively, and output corresponding parameters using the Sigmoid and Softplus activation functions. The specific number of layers and neurons can be configured through this collaborative optimization based on the number of sampling points in the target band.

[0072] The feature fusion layer is used to fuse the spectral features and effective geometric paths of the incident angles at the same measurement point to obtain multi-incident angle fused features.

[0073] Specifically, the feature fusion layer aggregates the spectral features corresponding to each incident angle at the same measurement point, and incorporates the effective geometric paths of each incident angle into the fusion process to obtain multi-incident angle fused features. These multi-incident angle fused features are used to express the joint spectral response at different incident angles at the same measurement point.

[0074] As an feasible processing method, after determining the specific number of the plurality of incident angles... Subsequently, the feature fusion layer can concatenate the spectral features corresponding to each incident angle at the same measurement point with the corresponding effective geometric path of the incident angle, and then map them into multi-incident angle fused features through a fully connected structure with a fixed input dimension. This processing ensures that the absorption coefficient parameter is jointly determined by multiple incident angles at the same measurement point, avoiding unreasonable changes in the absorption coefficient parameter due to spectral fluctuations at a single incident angle.

[0075] Interface reflectance output layer, used to output interface reflectance parameters corresponding to the incident angle based on spectral characteristics;

[0076] Specifically, the interface reflectivity output layer outputs interface reflectivity parameters corresponding to the incident angles based on the multi-incident angle fusion feature. Since interface reflectivity is related to the incident angle, different incident angles correspond to different interface reflectivity parameters. This setting allows the interface reflectivity parameters to vary with the incident angle, conforming to the optical response characteristics of high-refractive-index interfaces in germanium materials. As an feasible processing method, the output of the interface reflectivity output layer can be processed by an activation function with values ​​ranging between 0 and 1, ensuring that the interface reflectivity parameters fall within a physically reasonable value range.

[0077] The absorption coefficient output layer is used to output absorption coefficient parameters based on the multi-incident angle fusion features;

[0078] Specifically, the absorption coefficient output layer outputs absorption coefficient parameters based on the multi-incident angle fusion characteristics corresponding to the same measurement point. These absorption coefficient parameters characterize the bulk absorption of the material at the measurement point corresponding to the target wavelength. The absorption coefficient output layer reuses the same set of output layer weights for different measurement points, enabling the model to learn a unified absorption coefficient inversion rule, rather than setting a fixed parameter table for each sample measurement point. This structure facilitates the absorption coefficient inversion model in processing the model input samples of the germanium optical element under test during the application phase. As an feasible processing method, the output of the absorption coefficient output layer can be processed by a non-negative activation function to ensure that the absorption coefficient parameter has a non-negative value, consistent with the physical meaning of bulk absorption.

[0079] The physical constraint layer is used to receive interface reflectivity parameters, absorption coefficient parameters, effective geometric path of incident angle, measured transmittance at target wavelength, and measured specular reflectivity.

[0080] Specifically, the physical constraint layer receives interface reflectivity parameters, absorption coefficient parameters, and the effective geometric path of the incident angle, and calculates the one-way internal transmittance, reconstructed transmittance, and reconstructed specular reflectance at the target wavelength accordingly. The physical constraint layer also receives the measured transmittance and measured specular reflectance at the target wavelength from the model input samples, used to calculate the loss function. This layer restricts the model output to the physical range corresponding to the multiple internal reflection equations of the flat plate and the Beer-Lambert equation, reducing non-physical fitting results. It is understandable that the physical constraint layer performs calculations based on predetermined physical equations and may not contain trainable parameters itself.

[0081] Specifically, the training process of the neural network model includes:

[0082] By substituting the absorption coefficient parameter and the effective geometric path of the incident angle into the Beer-Lamber equation using the physical constraint layer, the one-way transmittance at the target wavelength is obtained.

[0083] Specifically, for the first measurement point under the same measurement point For each incident angle, the absorption coefficient output layer outputs the absorption coefficient parameter corresponding to that measurement point, denoted as . ;No. The effective geometric path for each incident angle is denoted as . The physical constraint layer calculates the first... The transmittance in one pass at the target wavelength corresponding to each incident angle is denoted as . Its expression is: In the formula, Indicates the first Transmittance in one pass corresponding to each incident angle This represents the absorption coefficient parameter corresponding to the same measuring point. Indicates the first The effective geometric path of the incident angle corresponding to each incident angle. For example, when... The unit is At that time, the absorption coefficient parameter The unit is .

[0084] Therefore, the absorption coefficient parameter is mapped to the single-pass transmittance corresponding to each incident angle through the above equation. This process ensures that the absorption coefficient parameter, together with the actual optical path, satisfies the internal absorption attenuation law of the material, preventing the absorption coefficient parameter from becoming an isolated output without physical constraints.

[0085] It should be noted that the same absorption coefficient parameter is used for all incident angles at the same measuring point. The effective geometric path of the incident angle The variation with the incident angle is consistent with the physical premise that the material absorption at the same measuring point is unique and the propagation path varies with the incident angle.

[0086] By substituting the interface reflectivity parameters and single-pass transmittance into the multiple internal reflection equation of the plate using the physical constraint layer, the reconstructed transmittance and reconstructed specular reflectivity at the target wavelength are obtained.

[0087] Among them, the interface reflectivity output layer outputs the first The interface reflectivity parameter corresponding to each incident angle is denoted as . The physical constraint layer will and Substituting the internal reflection equation of the flat plate, the reconstructed transmittance and reconstructed specular reflectance at the target wavelength are generated respectively. The reconstructed transmittance and reconstructed specular reflectance are the results obtained by calculating the physical equation from the model output parameters, and are used to compare with the measured transmittance and measured specular reflectance at the target wavelength.

[0088] The step of substituting the interface reflectivity parameter and the single-pass transmittance into the multiple internal reflection equation of the flat plate includes:

[0089] Substituting the interface reflectivity parameter and the single-pass transmittance into the multiple internal reflection equation of the plate in the transmission form, the reconstructed transmittance at the target wavelength is obtained.

[0090] Specifically, for the first An incident angle will affect the interface reflectivity parameter. and single-trip transmittance Substituting into the equation for multiple internal reflections of a plate in the transmission form, we obtain the first... The reconstructed transmittance at the target wavelength corresponding to each incident angle is denoted as . .

[0091] One feasible transmission method is as follows:

[0092]

[0093] In the formula, Indicates the first Reconstructed transmittance corresponding to each incident angle Indicates the first Interface reflectivity parameters corresponding to each incident angle Indicates the first The transmittance within a single path corresponds to a given incident angle. This formula represents the energy superposition result of multiple reflections of the beam inside the plate on the transmission side.

[0094] By substituting the same interface reflectivity parameter and the same single-pass transmittance into the multiple internal reflection equation of the plate in the form of specular reflection, the reconstructed specular reflectivity at the target wavelength is obtained.

[0095] Specifically, for the same first At each incident angle, the reflectivity parameter of the same interface is... and the transmittance within the same single journey Substituting the equation for multiple internal reflections of a flat plate in the form of specular reflection, we obtain the first... The reconstructed specular reflectivity at the target wavelength corresponding to each incident angle is denoted as . .

[0096] One feasible form of specular reflection is:

[0097]

[0098] In the formula, Indicates the first The reconstructed specular reflectivity corresponding to each incident angle Indicates the first Interface reflectivity parameters corresponding to each incident angle Indicates the first The transmittance within a single path corresponding to each incident angle. This formula corresponds to the energy superposition result of the first interface reflected beam and the multiple reflected beams inside the plate at the specular reflection side.

[0099] It should be noted that the reconstructed transmittance and reconstructed specular reflectance are generated from the same interface reflectance parameter and the same single-pass transmittance. This process ensures that the transmission-side constraint and the reflection-side constraint use consistent interface parameters and volume absorption parameters, reducing parameter inconsistencies caused by fitting the two types of spectra separately.

[0100] The loss function is calculated based on the reconstructed transmittance, reconstructed specular reflectance, measured transmittance at the target wavelength in the model input sample, and measured specular reflectance at the target wavelength. The model parameters are then updated based on the loss function to obtain the absorption coefficient inversion model.

[0101] Specifically, in the model input sample, the first... The measured transmittance at the target wavelength corresponding to each incident angle is denoted as . The measured specular reflectivity at the target wavelength is denoted as . The physical constraint layer is based on , , and Calculate the loss function. The loss function includes transmittance deviation, specular reflectance deviation, and total transmittance and reflectance deviation: transmittance deviation constrains the reconstructed transmittance to be consistent with the measured transmittance; specular reflectance deviation constrains the reconstructed specular reflectance to be consistent with the measured specular reflectance; and total transmittance and reflectance deviation constrains the overall energy distribution between transmission and specular reflection.

[0102] The loss function is calculated as follows:

[0103]

[0104] In the formula, Represents the loss function. This indicates the number of incident angles corresponding to the same measuring point. Indicates the first An angle of incidence, Indicates the first Reconstructed transmittance corresponding to each incident angle Indicates the first Measured transmittance at the target wavelength corresponding to each incident angle Indicates the first The reconstructed specular reflectivity corresponding to each incident angle Indicates the first Measured specular reflectivity at the target wavelength corresponding to each incident angle.

[0105] The above loss function adopts The three types of deviations are normalized to ensure that the errors under different incident angles have a consistent comparison benchmark. The third term is the total transmission and reflection deviation term, which is used to constrain the total transmission and reflection output corresponding to the model to be consistent with the measured total transmission and reflection, and to limit the model to only fit the transmission side or only fit the reflection side.

[0106] It should be noted that the loss function described above is calculated for the same measurement point. When the sample germanium optical element contains multiple measurement points, the loss function can be calculated separately for each measurement point using the above formula, and the average or weighted sum of the loss functions for each measurement point can be used as the total loss function for training, so that the update of the model parameters takes into account the data of each measurement point.

[0107] During training, the model parameters are iteratively updated based on the loss function. The model parameters include trainable parameters from the spectral feature extraction layer, feature fusion layer, interface reflectance output layer, and absorption coefficient output layer. In each iteration, the input sample enters the neural network model, and after processing by each layer, the interface reflectance parameters and absorption coefficient parameters are obtained. Then, the physical constraint layer obtains the reconstructed transmittance, reconstructed specular reflectance, and loss function. Subsequently, the model parameters are updated based on the loss function until the training stopping condition is met, resulting in the absorption coefficient inversion model. As a feasible approach, gradient descent-type optimization algorithms can be used to update the model parameters. The training stopping condition can be that the loss function converges to a preset range, or the number of iterations reaches a preset number. The preset range and preset number of iterations can be determined based on the actual training situation.

[0108] Through the above training, the neural network model develops the ability to invert absorption coefficients under the joint constraints of spectral data and physical equations. This absorption coefficient inversion model can distinguish between interface reflectivity parameters and absorption coefficient parameters based on multi-incident angle transmission and specular reflection spectra, reducing the influence of interface reflection coupling on absorption coefficient measurement results.

[0109] Specifically, the germanium optical element under test is only introduced during the model application stage. The model input sample of the germanium optical element under test is formed according to the same data items as the model input sample of the sample germanium optical element. Specifically, the multi-incident angle transmission spectrum and specular reflection spectrum of the germanium optical element under test at the same measurement point in the target band containing the target wavelength are obtained; the effective geometric path of the incident angle corresponding to the germanium optical element under test is determined according to the incident angle; the measured transmittance and measured specular reflectance at the target wavelength are extracted; and then the model input sample of the germanium optical element under test is formed from the transmission spectrum, specular reflection spectrum, effective geometric path of the incident angle, measured transmittance, and measured specular reflectance at the target wavelength in the target band. It can be understood that the effective geometric path of the incident angle of the germanium optical element under test can be determined by the measured transmission interference fringes of the germanium optical element under test in the same way as in step S102.

[0110] The model of the germanium optical element under test is input into the absorption coefficient inversion model. The spectral feature extraction layer in the absorption coefficient inversion model extracts the multi-incident angle spectral features of the germanium optical element under test. The feature fusion layer fuses the spectral features corresponding to each incident angle at the same test point and the effective geometric path of the incident angle. The absorption coefficient output layer outputs the absorption coefficient of the germanium optical element under test based on the fusion result. It should be noted that the model parameters of the absorption coefficient inversion model are not changed during the model application stage.

[0111] Since the model input samples of the germanium optical element under test have the same data items and the same data organization method as the model input samples used in the model training phase, the model input samples of the germanium optical element under test can match the input structure of the absorption coefficient inversion model. The absorption coefficient of the germanium optical element under test output by the model is the absorption coefficient at the target wavelength; when multiple test points are set for the germanium optical element under test, the absorption coefficient at the target wavelength of the corresponding test point can be obtained separately for each test point.

[0112] By applying the absorption coefficient inversion model, the multi-incident angle transmission and specular reflection spectra, effective geometric path of the incident angle, and actual measurements at the target wavelength of the germanium optical element under test are unified for the absorption coefficient output. This processing allows the measurement results to simultaneously consider the coupling relationship between the effective geometric path of the incident angle, interface reflection, and bulk absorption of the material, thereby improving the correspondence between the absorption coefficient measurement results at the target wavelength and the bulk absorption characteristics of the material.

[0113] In summary, the method for measuring the absorption coefficient of germanium optical elements provided in this embodiment provides a data foundation for decoupling interface reflection and bulk material absorption through multi-point, multi-incident angle transmission and specular reflection spectrum acquisition. It reduces optical path error by determining the effective geometric path of the incident angle from measured transmission interference fringes and replacing the nominal thickness in the inversion process. By configuring a neural network model with a physical constraint layer, the interface reflectivity parameter is output according to the incident angle, and the absorption coefficient parameter is output from the fused features of multiple incident angles at the same measurement point. The training process is constrained by the multiple internal reflection equation of a flat plate and the Beer-Lambert equation, ensuring that the model output conforms to the physical laws of flat plate optical transmission. Furthermore, the consistency between transmission-side and reflection-side constraints is guaranteed by a loss function that simultaneously includes transmittance deviation, specular reflectivity deviation, and total transmittance / reflection deviation. Therefore, the measurement results of the absorption coefficient of the germanium optical element under test can better correspond to the bulk absorption characteristics of the material.

[0114] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for measuring the absorption coefficient of a germanium optical element, characterized in that, include: The multi-incident angle transmission and specular reflection spectra of multiple measurement points of the sample germanium optical element in the target band containing the target wavelength are obtained to form a sample spectrum record; The fringe wavenumber interval is determined by the wavenumber of adjacent transmission maxima in the sample spectral record based on the incident angle, and an effective geometric path for the incident angle is generated. include: According to the incident angle, the transmission spectrum segment containing the target wavelength is extracted within the target band to obtain the fringe calculation spectrum segment corresponding to each incident angle; Read the adjacent transmission maxima wavenumbers in the neighborhood of the target wavelength in the fringe calculation spectral band to obtain the fringe wavenumber intervals corresponding to each incident angle; Based on the fringe wavenumber interval corresponding to each incident angle, the refractive index of germanium material at the target wavelength, and the corresponding incident angle, the effective geometric path of the incident angle is obtained; The model input sample is formed by the sample spectral record, the effective geometric path of the incident angle, the measured transmittance at the target wavelength, and the measured specular reflectance. A neural network model with a physical constraint layer is configured so that the interface reflectivity parameter is output according to the incident angle, and the absorption coefficient parameter is output by the fusion feature of multiple incident angles at the same measurement point; the neural network model is trained with model input samples, the plate multiple internal reflection equation, and the Beer-Lambert equation to obtain the absorption coefficient inversion model; including: By substituting the absorption coefficient parameter and the effective geometric path of the incident angle into the Beer-Lamber equation using the physical constraint layer, the one-way transmittance at the target wavelength is obtained. By substituting the interface reflectivity parameters and single-pass transmittance into the multiple internal reflection equation of the plate using the physical constraint layer, the reconstructed transmittance and reconstructed specular reflectivity at the target wavelength are obtained. The loss function is calculated based on the reconstructed transmittance, reconstructed specular reflectance, measured transmittance at the target wavelength in the model input sample, and measured specular reflectance at the target wavelength. The model parameters are then updated based on the loss function to obtain the absorption coefficient inversion model. The absorption coefficient of the germanium optical element under test is obtained by inputting the model of the sample into the absorption coefficient inversion model.

2. The method according to claim 1, characterized in that, The sample spectral records are organized by measurement point identifiers and incident angle identifiers. Under the same measurement point identifier, multiple incident angle spectral data of the same measurement point are recorded. Under the same incident angle identifier, the transmission spectral record items and specular reflection spectral record items corresponding to the incident angle are recorded. The target band covers the target wavelength and the spectral band where the adjacent transmission maximum value is located.

3. The method according to claim 1, characterized in that, The process of obtaining the fringe wavenumber interval includes: The transmission maxima in the spectral band are calculated by identifying the fringe along the direction of increasing wavenumber, and the wavenumber sequence of the maxima corresponding to each incident angle is obtained. In the maximum wavenumber sequence, select two adjacent maximum wavenumbers in the neighborhood of the target wavelength, and obtain the fringe wavenumber interval corresponding to each incident angle from the difference between the two maximum wavenumbers.

4. The method according to claim 1, characterized in that, The process of obtaining the model input samples includes: The effective geometric path of the incident angle is incorporated into the sample spectrum record according to the measurement point and the incident angle, and the optical path is incorporated into the record. The transmission spectrum, specular reflection spectrum, effective geometric path of incident angle, measured transmittance at target wavelength, and measured specular reflectance at target wavelength are extracted from the optical path incorporation record to obtain the model input sample.

5. The method according to claim 1, characterized in that, The neural network model is a physical information neural network model, including: The spectral feature extraction layer is used to extract spectral features from the model input samples, distinguished by measurement point and incident angle. The feature fusion layer is used to fuse the spectral features and effective geometric paths of the incident angles at the same measurement point to obtain multi-incident angle fused features. Interface reflectance output layer, used to output interface reflectance parameters corresponding to the incident angle based on spectral characteristics; The absorption coefficient output layer is used to output absorption coefficient parameters based on the multi-incident angle fusion features; The physical constraint layer is used to receive interface reflectivity parameters, absorption coefficient parameters, effective geometric path of incident angle, measured transmittance at target wavelength, and measured specular reflectivity.

6. The method according to claim 5, characterized in that, The feature fusion layer has an input terminal that aggregates spectral features and effective geometric paths based on the incident angle at each measurement point. The interface reflectivity output layer has an independent output node corresponding to the incident angle. The absorption coefficient output layer has a shared output node that reuses the same set of output layer weights for different measurement points.

7. The method according to claim 1, characterized in that, The step of substituting the interface reflectivity parameter and the single-pass transmittance into the multiple internal reflection equation of the flat plate includes: Substituting the interface reflectivity parameter and the single-pass transmittance into the multiple internal reflection equation of the plate in the transmission form, the reconstructed transmittance at the target wavelength is obtained. By substituting the same interface reflectivity parameter and the same single-pass transmittance into the multiple internal reflection equation of the plate in the form of specular reflection, the reconstructed specular reflectivity at the target wavelength is obtained.

8. The method according to claim 1, characterized in that, The loss function is calculated as follows: ； In the formula, Represents the loss function. This indicates the number of incident angles corresponding to the same measuring point. Indicates the first An angle of incidence, Indicates the first Reconstructed transmittance corresponding to each incident angle Indicates the first Measured transmittance at the target wavelength corresponding to each incident angle Indicates the first The reconstructed specular reflectivity corresponding to each incident angle Indicates the first Measured specular reflectivity at the target wavelength corresponding to each incident angle.

Images