Wavefront coding for laser protection of electro-optical imaging systems: a long-distance experimental study

Abstract

Wavefront coding technology employs a phase mask to modulate the phase of incident light, thereby dispersing the laser spot on the detector and achieving laser protection for optical systems. Current research has predominantly concentrated on validating laser damage at a single imaging distance, neglecting the evolution of protective capability across varying distances in the wavefront coding imaging system. To address this limitation, this study establishes a wavefront coding imaging system based on a cubic phase function and experimentally elucidates the variation of laser suppression capacity with transmission distance. Under conditions of pulsed laser-induced point damage in the visible spectrum, a strong correlation is observed between the laser suppression ratio and the laser damage threshold improvement value. Additionally, the NAFNet model is utilized to restore encoded images, resulting in high-fidelity reconstruction. The PSNR for both simulated and experimentally decoded images consistently surpasses 23 dB. Furthermore, under laser irradiation conditions, the model adeptly eliminates laser artifacts and recovers image content. This study possesses considerable practical value for the design and implementation of laser protection mechanisms in optical systems.

Graphical abstract

Keywords

Wavefront coding / Laser suppression / Image restoration

1 Introduction

The advancement of laser technology has made low-cost, miniaturized, high-energy lasers accessible [1–4]. When a laser is misdirected toward electro-optical imaging systems, the high optical gain at the focal plane can easily result in sensor pixel saturation or permanent damage, thereby compromising situational awareness. Instances include laser interference that misleads drone tracking systems [5,6] and attacks on autonomous vehicle sensors that jeopardize their safety [7–9]. Consequently, enhancing the laser protection capabilities of imaging systems to ensure the functionality of photodetectors under high-intensity laser exposure has become a critical research challenge. Laser protection technologies primarily encompass protective materials and computational imaging, with the latter predominantly relying on wavefront coding (WFC) [10] technology driven by phase modulation. The fundamental principle of wavefront coding technology for laser protection is based on wavefront phase modulation, which disrupts the conventional point-to-point correspondence between object and image planes by converting it into a controlled point-to-area relationship. This transformation effectively reduces the energy density reaching the detector surface, thereby mitigating the risk of damage. Ruane et al. [11] first introduced WFC into this field, employing vortex and axicon phase masks to modulate lasers and protect detectors from damage. To further improve protection performance, researchers have investigated various phase types, including cubic, vortex, and axicon lenses [12–17]. Peng et al. [18] adopted a “five half-ring” phase function, which effectively reduced the peak laser irradiance to 10³ times lower than the sensor saturation threshold. Existing studies typically utilize the laser suppression ratio (LSR) to evaluate the level of laser protection during the optimization of phase functions. However, the LSR is determined by examining changes in image grayscale caused by the detector’s linear response to the optical signal before and after phase modulation. This approach enables the evaluation of protective capability without damaging the detector; however, it fails to consider the fact that laser-induced damage generally occurs within the nonlinear response range of the detector. To overcome this limitation, Ye et al. [19] introduced the laser damage threshold (LDT) as a metric to evaluate the protective performance of WFC imaging systems. They performed theoretical simulations and experimental analyses to compare the LDT and damage morphology between conventional and WFC systems. Nevertheless, their study only experimentally validated the protective efficacy of the systems against close-range laser irradiation and did not explore the performance under varying distances of laser irradiation. The vortex phase mask can generate a spiral-shaped PSF, but its PSF changes significantly with defocus, which makes distance-invariant image restoration difficult [20]. An axicon phase mask can generate a Bessel-like beam with extended depth of focus [21]; however, its strong sidelobes introduce multiple zero crossings in the Modulation Transfer Function (MTF), which complicates subsequent image deconvolution. In contrast, the cubic phase plate produces a PSF that is relatively invariant to defocus. This property enables encoded images obtained at different object distances to maintain similar blur characteristics, which is advantageous for image restoration while preserving the laser suppression capability of the system. Meanwhile, the cubic phase plate (CPP) serves as a representative phase element that is easy to fabricate. It offers effective laser protection while exhibiting good aberration tolerance and facilitating efficient chromatic correction in imaging. Consequently, it is frequently employed as a standard for assessing laser protection performance. This study investigates variations in the protective capacity of the CPP concerning distance. In practical applications, laser often originate from distances ranging from hundreds to thousands of meters [22,23]. Comprehending this characteristic provides essential data for the design of optical laser protection systems and is of considerable importance for the practical implementation of WFC systems in laser protection.

This study explores the evolution of the protective capacity of the WFC system using a CPP related to distance. The LSR and LDT of the system are quantified at various distances to examine their relationship. Additionally, the image restoration network NAFNet [24] is employed to effectively reconstruct the encoded blurred images at different distances and images subjected to laser irradiation, thereby maintaining the superior imaging performance of the optical system while enhancing its laser protection capabilities.

2 Laser damage experiment

In conventional imaging setups, Fig. 1a, the laser concentrates on the detector surface through the focusing mechanism, creating a region of high energy density that poses a risk of damaging the detector. In contrast, the WFC system utilizes a phase mask to manipulate the incident light, dispersing the distribution of laser energy across the detector surface. This dispersion lowers the energy density per pixel, effectively safeguarding the detector against laser-induced damage, as illustrated in Fig. 1b.

2.1 Experimental setup

To quantitatively validate the laser protection performance of the WFC imaging system compared to conventional imaging systems, an experimental test platform, illustrated in Fig. 2, is constructed. A pulsed laser beam is attenuated using an optical attenuator (Thorlabs NEK01) and subsequently directed to a set of reflection mirrors (LBTEX LPM20-532P-HP). After being reflected by the mirrors, the beam passes through an aperture (LBTEX SM2DP25-2B) that controls its diameter before being split by a beam splitter (Thorlabs BP245B1) into two paths. One path is entirely focused by a lens (LBTEX MBCX10307-A) onto an energy meter (Thorlabs PM100D) for energy measurement, while the other path illuminates either the conventional imaging system (Edmund 33306) or the WFC imaging system. The imaging system features an F-number of 1.85, a focal length of 35 mm, and an entrance pupil diameter of 18.91 mm. A CPP with a modulation factor of 200 is fabricated using PMMA plastic as the substrate and is concentrically mounted on the front surface of the imaging system. The pulsed laser source, which generates 532 nm output via a harmonic generation module, delivers a maximum single-pulse energy of 81.1 mJ with a pulse width of 10 ns. Detection is conducted using a monochromatic CMOS sensor (HIK MV-CS060-10UM-PRO) featuring a pixel size of 2.4 μm × 2.4 μm, a resolution of 3072 × 2048, and a fixed exposure time of 24.056 ms. The locations of the two reflectors in the optical path are stationary, while modifying the laser propagation distance Z is accomplished by moving the platform that supports the imaging system. In the optical setup, the two mirrors are fixed in position. The total propagation distance Z of the laser beam is varied by translating the platform that supports the imaging system, which modifies the distance Z₃ between the aperture and the mirror group. The total distance is given by Z = Z₁ + Z₂ + Z₃, where Z₁ and Z₂ are the fixed distances from the laser to the first mirror and between the two mirrors, respectively.

2.2 Results and analysis

The LSR serves as an evaluation metric to gauge the laser protection efficacy of the WFC imaging system. It is calculated as the ratio of the maximum single-pixel received power in a conventional optical imaging system to that in the WFC imaging system. If the maximum single-pixel received energy in the conventional imaging system is denoted as E_con, and for the WFC imaging system is E_cpp, then the LSR can be expressed as LSR = E_con/E_cpp. The power received by the pixel is proportional to the change in grayscale level before the pixel saturates. To investigate the LSR variation with laser propagation distance in the WFC imaging system, experiments are conducted at five distances: 18 m, 35 m, 50 m, 65 m, and 76 m. After acquiring image grayscale distribution data under identical laser parameters, LSR values are calculated for each distance, resulting in corresponding suppression ratios of 5.611, 21.679, 28.541, 28.884, and 30.349, respectively. As shown in Fig. 3, the incident laser forms a high-intensity focal spot on the focal plane in conventional optical systems, increasing the risk of detector damage. In contrast, the WFC system employs a phase mask to modulate the wavefront, dispersing the focused spot into an L-shaped pattern on the imaging plane. This spatial redistribution of energy spreads the concentrated laser power over a larger area, thereby significantly suppressing localized energy intensity.

The laser damage resistance of the WFC imaging system is assessed by comparing its laser damage threshold to that of a conventional imaging system at varying distances. Experimental measurements of the point damage thresholds for both systems are conducted at five transmission distances. Point damage is identified by permanent and irreversible changes in pixel response. Under pulsed laser irradiation, once point damage occurs, the affected pixels are driven into a saturated state and appear bright white. Such abnormal pixel response remains unchanged over time and under different imaging conditions, indicating irreversible detector degradation. Laser energy is incrementally increased by decreasing the attenuation of the optical filter, with each energy level applied to an independent test site. To ensure data reliability and minimize random errors, five independent tests are conducted for both imaging systems at every distance. Figure 4a illustrates the morphology of laser-induced damage on the detector at different distances, while Fig. 4b provides an enlarged view of the selected area.

Table 1 displays the laser damage thresholds of the WFC imaging system and the conventional imaging system at different laser transmission distances. The point damage threshold is the incident energy density on the front lens surface when the first point damage occurs on the detector surface, with a laser spot diameter of 22 mm. The transmission distance in the table indicates the distance from the laser output port to the aperture. The second and third columns present the damage threshold values for the conventional imaging system and the WFC imaging system, respectively, while the fourth column illustrates the enhancement in the threshold. The LDT of the conventional imaging system significantly decreases at 35 m in the table. This phenomenon arises because the focused spot at 35 m is smaller than that at 18 m, as demonstrated in Fig. 3. Consequently, the increased concentration of energy on the detector surface necessitates a lower total incident energy to induce point damage. The enhancement of LDT improvement value can be attributed to the relatively stable shape and size of the focused light spot in the WFC system across varying distances. In contrast, the light spot in conventional imaging systems diminishes in size, leading to a decrease in the incident pupil energy when point damage occurs. Figure 5 presents the variation of the LDT improvement value and the LSR with propagation distance. Both metrics increase with distance and gradually approach saturation at longer transmission ranges. The orange shaded area denotes the experimentally measured variation range of the laser damage threshold, and the orange circular markers indicate the average LDT improvement values at each distance. The orange fitted curve corresponds to an exponential saturation model, given by y=34.60-84.31{\mathrm{e}}^{-0.057x}, with a fitting R² value of 0.995 and a Pearson correlation coefficient of 0.905. The light blue shaded area represents the variation range of LSR obtained from repeated measurements, while the blue star markers denote the average LSR values. The blue fitted curve follows an exponential saturation model of y=30.93-78.30{\mathrm{e}}^{-0.063x}, with a fitting R² value of 0.996 and a Pearson correlation coefficient of 0.898. As the propagation distance increases, the LDT improvement value of the WFC imaging system increases from 4.718 to 33.000, and the LSR increases from 5.611 to 30.349. These results demonstrate a strong distance-dependent enhancement in laser protection performance, confirming that the WFC technique becomes increasingly effective at longer transmission distances before reaching a saturation regime.

At all tested distances, the LSR closely correlates with the LDT improvement values consistently falling within the range of the measured LDT improvement. This observation validates a strong association between the LSR and the LDT improvement value under conditions of pulsed laser-induced point damage. Consequently, the LSR proves to be a dependable metric for estimating the laser damage resistance of WFC imaging systems.

Although the LSR and LDT improvement values in the figure show a strong correlation, there is still some deviation between them. Analysis reveals that the LDT measurement is influenced not only by the incident laser’s energy but also by the detector material’s characteristics. It is worth noting that the strong correlation between LSR and LDT improvement values precisely reflects the extremely narrow nonlinear response region to visible light. Typically, the detector’s output signal maintains a linear relationship with the incident laser energy in normal conditions. The strong correlation suggests that when exposed to high-intensity laser irradiation, the nonlinear response region has been compressed to an extremely narrow range. When the laser energy exceeds the linear response region, the detector does not exhibit significant nonlinear characteristics but rapidly transitions from a normal operation to a damaged state.

3 Imaging performance

The principle by which wavefront coding technology can be applied to laser protection is based on modulating the incident light field to expand the laser spot, thereby decreasing the energy density on the detector surface. Notably, this modulation unavoidably introduces image blurring, necessitating image reconstruction to enhance image quality. The WFC imaging process is depicted in Fig. 6. However, since the design prioritizes enhancing laser protection performance, the strong modulation emphasis of the phase plate intensifies image blur, thereby complicating the restoration of the encoded images. Leveraging the exceptional performance of existing deep learning-based methods in image restoration, this study employs the advanced restoration network NAFNet to reconstruct the blurred images captured by the system.

3.1 Network structure

NAFNet proposes a simple baseline model for image restoration, whose architecture is illustrated in Fig. 7. The model adopts a symmetric U-Net structure, which utilizes a multi-level encoder-decoder framework, skip connections, and a core module called NAFBlock to progressively extract and integrate multi-scale features, ultimately achieving image deblurring. Detailed operations as well as input and output dimensions for each part of the network are provided in Table 2.

3.2 Loss function and simulation result

The DIV2K [25] and Flickr2K [26] high-resolution public data sets are chosen as the original images. Training data are created by utilizing collected point spread functions (PSFs) based on the imaging model I{}_{\mathrm{W}\mathrm{F}\mathrm{C}}=I{}_{\mathrm{o}\mathrm{r}\mathrm{i}}\ast \mathit{P}\mathit{S}\mathit{F}+n{}_{\mathrm{A}\mathrm{G}\mathrm{W}\mathrm{N}}. An F200A collimator manufactured by Xiaogan Huazhong Precision Instrument Co., Ltd., with a focal length of 200 mm, is employed to calibrate the PSFs. Multiple PSF frames are captured and denoised. Each PSF is subsequently extracted, shifted to the image center, and finally normalized in energy to obtain the PSFs used for subsequent training data generation. A total of 1668 training sets, 166 validation sets, and 166 test sets are constructed. Here, I{}_{\mathrm{W}\mathrm{F}\mathrm{C}} denotes the simulated encoded image; I_{\mathrm{o}\mathrm{r}\mathrm{i}} represents the clear image from the high-resolution data set; * signifies the convolution operation; PSF is the PSF of the WFC system; and n_{AGWN} represents additive white Gaussian noise (AWGN) with a signal-to-noise ratio of 30−40 dB. The PSNRLoss is employed as the loss function, as it facilitates the optimization of network parameters by evaluating the difference in the peak signal-to-noise ratio (PSNR) metric between the decoded image and the clear image. Its calculation formula is:

(1)\mathrm{P}\mathrm{S}\mathrm{N}\mathrm{R}\mathrm{L}\mathrm{o}\mathrm{s}\mathrm{s}=-20{\log }_{10}\left(\frac{MAX}{\sqrt{MSE}}\right),

where MSE is the mean squared error between the decoded image R(i,j) and the clear image O(i,j), which is calculated as:

(2)MSE=\frac{1}{mn}\sum _{i=0}^{m-1}\sum _{j=0}^{n-1}\Vert R(i,j)-O(i,j){\Vert }^2.

Here, m,n denote the dimensions of the image, while MAX represents the maximum pixel value, which is set to 255 in this study. Random flipping and scaling are applied to pairs of sharp and blurred images to enhance data diversity. The model is developed using PyTorch (Python 3.9.21) in the VS Code framework and trained on an NVIDIA GeForce RTX 3090 GPU. Encoded images are randomly cropped to a resolution of 512 × 512 before being input into the network, with an inference time of 49.94 ms per image. Training is conducted with 200,000 iterations, lasting about 11.3 h. The model utilizes the AdamW optimizer with an initial learning rate of 1 × 10⁻³, weight decay of 1 × 10⁻³, and betas of (0.9, 0.99). Additionally, a CosineAnnealingLR scheduler is implemented, with the minimum learning rate set at 1 × 10⁻⁷. Restoration results on a synthetic data set using the Wiener and the NAFNet methods are illustrated in Fig. 8. The encoded images display blurring due to phase-plate modulation; however, both methods successfully recover image details. Quantitative evaluation of 166 test image pairs reveals that the Wiener method achieves an average PSNR of 23.03 dB and an average SSIM of 0.6193, while the NAFNet method attains 24.37 dB in PSNR and 0.7604 in SSIM. These findings indicate that the NAFNet method provides superior image restoration quality.

3.3 Experiment result

A total of 800 image pairs, each comprising a sharp image and its blurred counterpart, were captured by the WFC camera. These images are randomly cropped to 512 × 512 pixels for input. The network is subsequently fine-tuned over 10,000 iterations, with a total training time of 2.7 h, to adapt to the detector’s actual noise and response characteristics. For evaluating the model’s decoding performance, 31 sets of clear and blurred images taken at distances spanning 2 to 300 m are utilized for testing, with results displayed in Fig. 9. The Wiener method produces an average PSNR of 22.26 dB and an average SSIM of 0.6823, while the NAFNet achieves an average PSNR of 23.86 dB and an average SSIM of 0.8090. The encoded images exhibit blurring, but the decoding algorithm substantially enhances image clarity and effectively restores details. Compared to traditional Wiener filtering, NAFNet demonstrates improved artifact suppression and noise reduction, leading to an overall enhancement in restored image quality. Furthermore, the decoded images consistently maintain high restoration quality at varying object distances, highlighting the model’s efficacy in recovering encoded images across different ranges.

3.4 Imaging performance under laser irradiation

To assess the imaging performance of the system under laser irradiation, we acquire 800 sets of data employing a WFC camera, each comprising a sharp image and its corresponding blurred image captured during laser irradiation. The incident laser energy is varied to create blurred images at different energy levels, ensuring the network’s adaptability. Laser spot regions are cropped into a resolution of 512 × 512, then subjected to positional shifts to disperse the spots across various areas of the images. A total of 3,200 samples are generated, which are then divided into training, validation, and test sets in a 10:1:1 ratio. Continuing from the fine-tuned weights for deblurring blurred images, the network is further trained following the same configuration, with training lasting 200,000 iterations over approximately 28 h. Evaluation of the WFC system’s imaging performance under laser irradiation is conducted by testing on 266 sets of data, resulting in restored images as depicted in Fig. 10. Figure 10a shows the original images, while Figs. 10c and e exhibit the restored blurred images shown in Figs. 10b and d, respectively.

The comparison between Figs. 10c and e illustrates that the algorithm effectively restores the blurred regions outside the laser spot while preserving intricate textural details, thereby indicating robust imaging performance. Although the area of the laser spot experiences pixel saturation, which obscures the underlying scene information and leads to partial data loss, the restored image recovers numerous details and preserves a natural overall tone. Details such as the textures near wall tiles, clothing buttons, and the shapes of text are well restored. To quantitatively evaluate the restored images, 266 test data sets with a resolution of 512 × 512 are analyzed without laser irradiation. The average PSNR is 24.4866 dB, and the average SSIM is 0.7456. Conversely, with laser irradiation, the restored images exhibit an average PSNR of 24.2807 dB and an average SSIM of 0.7397. These metrics suggest that, even with laser irradiation, the restored images maintain quality only slightly inferior to those without exposure. This implies that while the irradiated area may saturate and lose specific details, the model can generate realistic details by considering the neighboring pixel distribution, effectively preserving the overall image quality.

To compare the computational efficiency of the restoration algorithms, images are processed using the pre-trained network and the wiener method, respectively. The corresponding inference times are presented in Fig. 11.

4 Conclusion

This study experimentally reveals the evolution of laser protection effectiveness of the WFC system with the transmission distance, indicating an improvement in protection capability with increasing distance. By measuring the LSR and the LDT, a significant correlation is observed between the LSR and the LDT improvement values under pulsed laser-induced point damage conditions, indicating that LSR can be used as an effective indicator for evaluating the laser protection capability of the WFC imaging system. To evaluate the system’s imaging performance, this research utilizes NAFNet to learn the mapping relationship between encoded and clear images. The experimental findings demonstrate the efficacy of the proposed approach in restoring encoded images across various distances, notably reducing artifacts and texture distortion. Despite laser exposure, the method eliminates the laser spot, retrieves partial information from saturated areas, and thereby upholds the image fidelity. Subsequent research will concentrate on optimizing system parameters to enhance both protection performance and imaging quality concurrently, while expanding the protective wavelength range to the infrared spectrum.

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