1. Introduction
The rapid development of modern optical technologies has driven optical components to play vital roles in diverse fields, including medical imaging, industrial manufacturing, national defense, and consumer electronics. For instance, optical coherence tomography (OCT) is widely employed in retinal imaging [
1], microscopy is indispensable for pathological diagnosis [
2], laser interferometry is used for surface quality evaluation in manufacturing [
3], and high-power laser systems facilitate precision machining [
4]. In defense and space science, advanced telescopes and guidance systems critically rely on high-performance optics [
5,
6], while multi-camera modules and AR/VR optical engines have become central to consumer electronics [
7]. In all these applications, the surface quality of optical components is crucial, as even defects can significantly affect system reliability.
Surface defects such as scratches, pits, voids, and bubbles, despite their small dimensions, disrupt surface continuity and lead to scattering, diffraction, and abnormal absorption of light, thereby degrading imaging quality and sensor accuracy [
8,
9]. Their diverse morphology, irregular distribution, and resemblance to background textures make reliable detection a persistent challenge. Current detection techniques, including optical microscopy, light scattering analysis, and machine vision, have shown promising results. Lou et al. [
10] combined FDTD simulation with dark-field imaging to detect scratches, but the method was constrained by single-view imaging. Liu et al. [
11] proposed a 3D dark-field confocal microscopy system for subsurface defect inspection, and Zheng et al. [
12] developed a real-time deep learning classification system for optical filters, though both approaches remained limited to single-view data. As Ma et al. [
13] emphasized in a recent review, most CNN-based methods still rely on single-angle inputs, failing to capture the complete scattering characteristics. Recent studies have further improved YOLO-based architectures to enhance defect detection accuracy under complex conditions. Ruan et al. [
14] introduced a PyConv and attention-based model for multi-scale surface defect detection, while Tian et al. [
15] enhanced YOLOv5n by modifying its backbone and loss function, achieving notable gains in small target detection. This reveals a key divergence in the field: while some methods emphasize high-resolution local imaging, others prioritize broader scattering measurement, yet both often lack comprehensive angular coverage.
To address these limitations, BRDF (Bidirectional Reflectance Distribution Function), a widely used function for characterizing reflection behavior, has been increasingly applied in multi-angle scattering studies. Meyen et al. [
16] introduced a hemispherical BRDF imaging system with an ellipsoidal mirror and fisheye lens, Ren et al. [
17] proposed a rapid synchronous acquisition method using a parabolic reflector, and Li et al. [
18] developed a four-axis gonioreflectometer for anisotropic materials. More recently, Zou et al. [
19] advanced panoramic multi-angle scattered imaging, significantly improving hemispherical sampling efficiency. To extend BRDF from measurement to defect identification, Li et al. [
20] proposed a Mueller matrix-based method integrating BRDF theory and Rayleigh–Rice scattering for surface and subsurface defect inversion. Sun et al. [
21] further introduced a light scattering peak matrix with Bayesian inference to detect defects under roughness interference, validating its effectiveness through BRDF-FDTD simulation and experiments. Despite these achievements, most research has focused on measurement and modeling rather than on solving the inverse problem of defect recognition.
In this context, the present study proposes a novel defect detection framework that integrates panoramic multi-angle scattered light field acquisition with deep learning-based classification. By employing a hemispherical synchronous imaging system and an improved YOLOv11-based model (SFD-YOLO), we demonstrate robust recognition of typical surface defects through simulated scattering data. The results confirm the effectiveness of combining panoramic scattered light field measurement with advanced neural architectures, offering a reliable pathway toward automated, high-precision optical surface defect detection.
2. Principle of Multi-Angle Scattered Measurement and Defect Identification
2.1. System Overview
To efficiently measure the multi-angle scattered light field induced by surface defects on optical components, a multi-angle scattered light field synchronous measurement system was designed and constructed. The system enables the acquisition of hemispherical scattering information in a single exposure. As shown in
Figure 1, it consists of a collimated laser source, a test platform for the optical specimen, a hemispherical dome, an aspheric reflective mirror, and an imaging system.
A collimated laser illuminates the test sample placed at the center of the hemispherical structure to ensure sufficient energy is received by the relay optical system. The inner wall of the hemisphere is coated with diffuse reflective paint, allowing it to reflect the multi-angle scattered light caused by surface defects. The reflected light is redirected by an aspheric mirror into the imaging system and projected onto a detector, producing a scattered light field image. This image can be analyzed to infer the status and geometry of the defects, as shown in
Figure 1b.
The incident radiant flux
and irradiance
received by the sample surface under a zenith angle
can be expressed as [
22]:
where
is the radius of the incident beam spot.
The total scattered radiant flux over the hemispherical space is denoted as
and the radiance in a given direction is defined as:
In the equation, represents the unit solid angle corresponding to a specific observation direction, while denotes the polar and azimuthal angles of the incident light.
Finally, the radiance captured by the detector through the optical system can be expressed as:
where
is the diffuse reflectance of the hemispherical dome, and
represents the transfer function of the optical imaging system, dependent on aperture, field of view, focal length, and resolution. Since the detector’s grayscale output is proportional to the radiance it receives, the spatial intensity distribution recorded in the image directly reflects the multi-angle scattered behavior of the surface defect, serving as the basis for quantitative analysis and inversion.
2.2. Scattered Measurement Principle of Optical Surface Defects
Surface defects on optical elements—such as scratches, pits, and bubbles—disrupt the ideal surface continuity and alter the reflection behavior of incident light. For an ideal optical surface, reflection characteristics can be described by a combination of specular reflection and Lambertian scattering, both of which follow predictable angular distributions. These characteristics are quantified using the Bidirectional Reflectance Distribution Function (BRDF), defined as:
where
is the reflected radiance in the direction
, and
is the incident irradiance from direction
. BRDF characterizes the reflection capability of a surface under a given incident direction. When surface defects are present, local reflection directions are altered, resulting in enhancement, attenuation, or broadening of radiance in certain angular directions. These changes in the BRDF spatial distribution carry critical information regarding defect type and size, providing a theoretical basis for defect recognition and inversion.
To quantitatively describe the spatial distribution and detection process, the irradiance received on the detector surface is considered equivalent to the image brightness. The image brightness is proportional to the irradiance, with a proportionality constant denoted as
[
23]. Thus, the absolute measurement expression of the multi-angle scattered light field can be derived as follows:
For collimated and stable light source, the incident irradiance
can be regarded as constant
[
24], and the BRDF measurement equation simplifies to:
With the light source, dome scattering coefficient, and measurement optical system fixed, the following definition is given:
Thus, the simplified BRDF formulation becomes:
indicating that the detector output is directly related to the angular reflectance distribution. Consequently, analyzing the spatial intensity distribution allows inversion of defect parameters based on the scattered light field image.
It should be noted that although planar components were adopted in this study for modeling simplicity, optical theory suggests that when scratch dimensions are much smaller than the local radius of curvature, the local scattering behavior can be approximated by that of a plane [
25].
2.3. Inversion Principle of Optical Surface Defects
Different types of surface defects yield distinguishable scattering field intensity distributions, such as variations in brightness concentration, symmetry, and energy dispersion patterns. These features reflect the physical structure of the defect and exhibit high separability, making them a reliable basis for defect recognition and inversion.
Based on this principle, this study proposes a detection pipeline that integrates multi-angle scattered light field measurement with deep learning-based classification. As shown in
Figure 2, the laser irradiates the sample surface, where surface defects induce multi-angle scattering of the reflected light. The hemispherical dome and optical relay system collect this light to generate a 2D scattered light field image. This image is then fed into a neural network, which extracts spatial features and outputs the corresponding defect category, thus completing a full measurement-to-identification pipeline.
The classification model employed in this work is based on the YOLOv11 architecture, modified for end-to-end learning on scattered light field images. It consists of four key modules: the input layer, feature extraction backbone, attention enhancement module (C2PSA), and classification head. The input layer performs normalization, the backbone extracts spatial patterns from the light intensity distribution, the C2PSA module emphasizes discriminative regions, and the classification head predicts defect categories.
Considering the highly structured nature of scattered light field images and the sensitivity of local features to defect categories, we introduce targeted structural enhancements to YOLOv11, constructing an efficient classification network tailored for surface defect recognition. The improved architecture aims to boost both the feature extraction precision and inference efficiency for this domain-specific task.
3. Design of the Classification Network for Scattered Light Field Images
To address the challenges of recognizing complex defect patterns in scattered light field images—such as irregular morphology, variable brightness distribution, and ambiguous class boundaries—this study proposes a structurally optimized classification network based on the lightweight YOLOv11 backbone. The improved model is termed SFD-YOLO (Scattered Field Defect YOLO), and its architecture is shown in
Figure 3.
The SFD-YOLO model consists of an input layer, backbone feature extraction module, perceptual enhancement module (PSimam), semantic modeling module (Efficient_Mamba_CSP), attention module (C2PSA), and a classification head. Compared to the original YOLOv11 classification architecture, SFD-YOLO introduces enhancements in both shallow and deep stages: the PSimam module is introduced in the shallow stage to improve perceptual sensitivity to local salient regions, while the Efficient_Mamba_CSP module is incorporated in the deeper layers to strengthen global semantic modeling. These targeted improvements enable more accurate extraction of scattered light field image features without compromising the model’s lightweight efficiency. Specifically, the PSimam module replaces the original CBSs, and the Efficient_Mamba_CSP module replaces the C3K2 structures in the tail.
Shallow Enhancement: Introducing the PSimam Attention Module. In the original YOLOv11 backbone, shallow layers comprise several convolutional blocks (CBSs) for low-level feature extraction. In this work, the last two CBS layers in the shallow stage are replaced by a custom-designed PSimam module, while retaining the first two convolutional layers. The structure of PSimam is illustrated in
Figure 4. It integrates multi-scale convolution paths with the SimAM attention mechanism. The module extracts spatial features in parallel at different scales, fuses them along the channel dimension, and applies the SimAM mechanism to emphasize salient spatial locations in a parameter-free manner. SimAM scores pixel importance based on neuronal activation energy and generates attention weights, allowing the model to focus on key regions and suppress redundant background information [
26].
Deep Enhancement: Introducing the Efficient_Mamba_CSP Module to Replace C3K2. To enhance the ability of deep layers to model long-range dependencies, the two sequential C3K2 modules at the tail of YOLOv11 are replaced with two Efficient_Mamba_CSP modules. These modules are built upon the HSM-SSD (Hidden State Mixer-based State Space Duality) mechanism proposed in EfficientViM [
27]. The core of the module is the Efficient_Mamba_block (shown in
Figure 5), which integrates local and global modeling capabilities.
The Efficient_Mamba_block extracts spatial features using depthwise separable convolution (DWConv) and employs an HSM-SSD unit to project feature sequences into a compressed state space, enabling the modeling of long-range dependencies with linear computational complexity—significantly more efficient than self-attention mechanisms. The module also includes normalization and residual connections to improve feature stability and gradient flow.
Building upon this, the Efficient_Mamba_CSP module (
Figure 6) adopts a CSPNet structure that divides the input into a main path and a residual path. The main path passes through the Efficient_Mamba_block for semantic enhancement, while the residual path directly conveys original features. The outputs are concatenated along the channel dimension to achieve feature fusion. This design balances deep contextual modeling with computational efficiency.
Compared to the original YOLOv11 structure, the proposed SFD-YOLO adopts a localized replacement strategy, inserting the new modules only in key network segments. This preserves the efficiency of the original shallow and mid-level designs while significantly improving the modeling of salient details and long-range context in deep layers. The final architecture strikes a favorable trade-off between classification accuracy and computational cost, making it more robust for identifying optical surface defects from complex scattered light field images.
4. Experiments and Results Analysis
4.1. Generation of the Scattered Light Field Image Dataset for Surface Defects
To evaluate the classification and recognition capability of the proposed method for optical surface defects, it is essential to first construct representative defect models consistent with practical manufacturing scenarios and generate a large-scale dataset of multi-angle scattered field distributions for deep learning. In this study, typical scratch defects—one of the most common types in optical fabrication—are selected as the research target. According to international optical component standards (e.g., ISO 10110-7) [
28], scratch width is a key parameter for defect classification and quality grading and is widely adopted as a standard indicator in surface inspection and quality control. Therefore, accurate inversion of scratch width can not only validate the feasibility of the proposed scattering detection method but also support practical quality evaluation.
To further ensure consistency and reproducibility in the dataset, grooves were employed as simplified representations of scratches in accordance with ISO 10110-7. Such groove-based models allow precise control of geometric parameters (e.g., width, depth, and edge profile), providing a standardized basis for dataset generation. Previous studies have confirmed that grooves with dimensions and orientations similar to scratches exhibit comparable far-field scattering behaviors, including angular intensity distributions and energy patterns [
27].
A parameterized modeling scheme was developed for scratch defects, in which the scratch length was fixed at 6 mm and the depth at 0.1 mm, representing typical minor processing-induced imperfections. It should be noted that while the depth was fixed to isolate the influence of width variation, both depth and width are known to jointly affect scattering intensity patterns, which will be further investigated in extended simulations. The width is sampled uniformly from 0.1 mm to 1.0 mm in 0.1 mm intervals, resulting in 10 categories covering fine to wide scratches. A schematic of the scratch model with a width of 0.2 mm is shown in
Figure 7.
4.1.1. Simulation Parameters
To ensure consistency between simulation and actual fabrication scenarios, the parameters were set based on common optical materials and industrial conditions. The experimental setup includes:
Substrate material: K9 optical glass with surface roughness much smaller than the scratch scale;
Light source: Gaussian beam with wavelength 532 nm, collimated at incident angle 45°, the beam spot diameter is 20 mm;
Dome receiver area: 60 × 60 grid cells with spatial resolution ;
Ray tracing: 2–3 million rays per simulation to maintain peak energy error below 10%.
4.1.2. Dataset Construction
The dataset for training and testing was constructed as follows:
Base data: For each scratch width, 100 sets of scattering distributions were generated at the center by varying the random ray seeds;
Augmented data: For scratch widths from 0.1 mm to 0.9 mm, 10 sets were generated with lateral offset in the −x direction, and 10 more in the +x direction, resulting in 1080 samples;
Wide-width group: For 1.0 mm scratch, 100 center-position samples were generated to serve as contrast.
A summary of the dataset configuration is provided in
Table 1.
The raw scattered images are 2D grid matrices. To enhance training performance, each intensity matrix was normalized and interpolated using bicubic interpolation to 224 × 224 pixels, matching standard input sizes for mainstream CNN architectures.
Figure 8 presents the comparison before and after preprocessing. It is evident that the structural details are well preserved after resizing, while intensity distribution becomes smoother, facilitating stable feature learning.
4.2. Experimental Setup and Evaluation Metrics
The hardware environment used for training is summarized in
Table 2.
The training parameters are as follows:
To ensure a fair evaluation, all models were trained from scratch without pre-trained weights. The following metrics were used:
Top-1 Accuracy (ACC): The percentage of predictions matching the ground truth;
Parameters (Params): Reflecting model size and efficiency (unit: M);
FLOPs: Floating-point operations measuring computational cost (unit: G).
4.3. Ablation Study
To evaluate the effectiveness of the SFD-YOLO architecture, ablation experiments were conducted by progressively integrating the proposed modules. Results are shown in
Table 3.
As observed, integrating the PSimam module alone raises Top-1 ACC by 1.3% with negligible parameter increase and stable computational cost, highlighting its efficacy in enhancing shallow feature representation. Replacing C3K2 with Efficient_Mamba_CSP improves accuracy to 95.1%, reduces parameter count significantly, and maintains a low computational footprint.
Combining both modules yields the best performance (95.6% ACC), with reduced parameters and reasonable FLOPs, validating the architecture’s overall efficiency and robustness.
The accuracy convergence trend of SFD-YOLO during training is illustrated in
Figure 9, where accuracy steadily improves and stabilizes after 160 epochs above 95%, demonstrating the model’s excellent convergence behavior.
Several representative classification results of scattered light field images from the test set are displayed in
Figure 10. For scratch widths of 0.1 mm, 0.2 mm, and 0.4 mm, the prediction accuracy reached 100%, demonstrating that the model could correctly identify all samples. In contrast, the classification accuracy for 1.0 mm width samples was slightly lower at 78%. This performance drop may be attributed to the loss of discriminative scattering variance and smoother edge structures in wider scratches, which is consistent with prior optical scattering studies [
29]. These results indicate that the SFD-YOLO model can generate predictions highly consistent with ground-truth labels across different defect width conditions. In particular, even for samples with similar morphologies or irregular scattering intensity distributions, the model maintained stable classification performance. The slight deviation observed at larger defect widths can be attributed to the increased scattering complexity; however, the model still exhibits robust discriminative capability. This confirms its reliability in handling challenging scenarios where defect categories are highly similar and non-local feature saliency is low.
A deeper analysis suggests that the reduced accuracy for 1.0 mm scratches is mainly due to the loss of discriminative scattering patterns at larger widths. Wider scratches generate stronger but spatially saturated scattering, which decreases angular variance and weakens edge-related features. Similar effects have also been reported in prior studies of wide defects [
29]. To mitigate this limitation, future work will incorporate balanced datasets with wider defect samples and adopt improved attention mechanisms to enhance the recognition of broad scattering structures.
The visual classification outputs of SFD-YOLO for a set of typical scattered light field images are provided in
Figure 11. Each subfigure displays the model’s prediction for a specific image, with the predicted class label shown in the upper-left corner. The color intensity reflects scattering strength—red for high-intensity regions and blue for low-intensity areas. Distinct variations in scattering patterns are observed across different defect widths (e.g., width_0.3, width_0.4, width_0.8, and width_1.0), particularly in brightness concentration, symmetry, and energy dispersion. Among the 16 test samples displayed, despite 14 exhibiting highly similar intensity distributions, the model accurately classified them, demonstrating its ability to differentiate subtle structural cues. This effectiveness is attributed to the integration of deep semantic modeling and shallow attention mechanisms, enabling precise localization of critical features and reliable classification of fine-grained patterns.
In conclusion, the visualization results further validate the SFD-YOLO model in terms of performance stability and application potential for multi-angle scattered light field recognition. Although this work focused on single-type scratch defects, different defect morphologies (e.g., pits or voids) produce distinguishable scattering distributions, suggesting that multi-defect classification remains theoretically feasible. The model demonstrates the capability of accurate automated classification of complex optical defects and scale-level inversion, highlighting its significance in practical optical inspection.
5. Conclusions and Outlook
In response to the need for rapid and efficient detection of surface defects in optical components, this study proposes a novel inspection method that integrates multi-angle scattered field measurement with deep learning-based classification. Leveraging a panoramic imaging-based BRDF measurement system, the method enables the simultaneous acquisition of hemispherical scattered light field images through a single exposure. This significantly improves the efficiency and stability of multi-angle data acquisition and provides high-quality, complete scattering information for subsequent defect identification.
On this basis, a lightweight neural network named SFD-YOLO was developed for the classification of defect-induced scattered light field images. Built upon the YOLOv11 architecture, the network incorporates two custom-designed modules tailored to the characteristics of scattered light field data: a PSimam attention module for enhanced perception of local salient features, and an Efficient_Mamba_CSP module for modeling long-range dependencies and global context. These improvements allow the model to achieve accurate feature extraction and classification while maintaining high inference efficiency.
Experimental validation demonstrates that the proposed method achieves stable and accurate classification of scattered light field images corresponding to typical surface defects. The results confirm its capability for precise defect recognition and establish a solid foundation for future work in defect parameter inversion and quality control. The approach proves to be both practical and valuable for engineering applications in optical surface defect inspection.
In addition to these promising results, several important aspects remain to be further explored. Although planar components were used in this study, optical theory suggests that when the scratch dimensions are much smaller than the local curvature radius, the local scattering behavior can be approximated by that of a plane. Future work will therefore extend simulations to spherical and freeform surfaces to systematically investigate curvature effects. Moreover, our classification results indicate that scattering field images contain sufficient discriminative information for scratch width identification, with accuracies ranging from 78% to 100%. To achieve quantitative inversion of both width and depth, regression modules will be introduced in subsequent studies. In addition, future datasets will incorporate multiple and overlapping defects to verify robustness under complex conditions, and depth–width coupling will be further explored with enhanced multi-scale feature fusion and depth-sensitive attention modules. Finally, while defect localization was not addressed in this work, object detection methods will be integrated to achieve localization and annotation, enabling practical applications such as defect tracing, re-polishing, and repair.
In future work, efforts will also be directed toward implementing this methodology in real-time, in-line inspection systems, thereby enhancing the automation and reliability of optical component quality evaluation in industrial settings.