Hot-image effect is one of the predominant threats to large-aperture optics in high power laser systems[
High Power Laser Science and Engineering, Volume. 6, Issue 3, 03000e52(2018)
Direct prejudgement of hot images with detected diffraction rings in high power laser system
A direct prejudgement strategy that takes the diffraction ring as the analysis target is put forward to predict hot images induced by defects of tens of microns in the main amplifier section of high power laser systems. Analysis of hot-image formation process shows that the hot image can be precisely calculated with the extracted intensity oscillation of the diffraction ring on the front surface of the nonlinear plate. The gradient direction matching (GDM) method is adopted to detect diffraction rings. Recognition of simulated diffraction rings shows that it is feasible to directly prejudge hot images induced by those closely spaced defects and the defects that are far apart from each other. Image compression and cluster analysis are utilized to optimize the performance of the GDM method in recognizing actually collected diffraction images. Results show that hot images induced by defects of tens of microns can be directly prejudged without redundant information.
1 Introduction
Hot-image effect is one of the predominant threats to large-aperture optics in high power laser systems[
In order to ensure the safe operation of the system, solutions are proposed to circumvent this threat. The spatial filter is a conventional method to suppress hot images in the main amplifier section, which is used to remove those Fourier spectrum components that would experience high gains[
In this paper, formation process of hot images induced by defects of tens of microns is analyzed theoretically and numerically. Results show that the hot image can be precisely calculated with the extracted intensity oscillation of the diffraction ring on the front surface of the nonlinear plate. The gradient direction matching (GDM) method is employed to detect diffraction rings as the gradient direction is the most robust information extracted from the diffraction ring images[
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2 Relationship between diffraction rings and hot images
Hot-image formation process is analyzed theoretically and numerically to investigate the relationship between diffraction rings and hot images. Disk amplifiers are periodically arrayed in the Brewster angle. To simplify analysis, these nonlinear plates are all set perpendicular to the beam propagation direction. Gain and loss characteristics are also ignored in the subsequent analysis, which is shown schematically in Figure
The incident beam is set as the plane wave that propagates along the -axis, where is the amplitude, is the wavelength and is the wavenumber. The beam is modulated by a defect on the scatter plane . Transmittance function of the plane can be described as
The field is composed of two parts: the background wave and the weak perturbation . As damage size is only about tens of microns, amplitude of is much weaker than that of , i.e., . Intensity distribution of the field on the front surface appears as a weak oscillation. What is more, thickness of the nonlinear plate is only about 3–5 cm. It shows that the induced diffraction effect in the plate can be ignored for the final analysis of the hot image. The weak intensity oscillation of the diffraction ring introduces a nonlinear phase on the rear surface. It is proportional to the intensity oscillation , which is given as
Finally, the nonlinear phase on the rear surface induces a focus point on the hot-image plane after another propagation distance () in free space. Field of is given as
Numerical simulation is conducted to verify the approximation in formulas (
Figure
The background intensity is set prior to the full system operation. And the parameters such as , and are also known quantities. What is more, it is feasible to collect diffraction images in a series of low-energy shots prior to the high-energy shot. Therefore, adoption of the pure intensity information of the diffraction ring is a direct and efficient method to prejudge hot images, which is more practical than those conventional methods. Next step is to find an automatic and robust solution to detect these diffraction rings.
3 Detection of diffraction rings with the GDM method
3.1 Recognition of simulated diffraction rings
The GDM method is used to detect diffraction rings, which is known to be more robust than other phase matching methods[
Gradient direction matching is done to calculate the similarity distribution after the extraction of gradient direction fields. Cosine function is used to remove the influence of inversion between some parts of the two direction fields. Fast Fourier transform (FFT) is adopted to remove the limit of template size on the computational efficiency. Similarity threshold is set according to the above matching results. Center of the diffraction ring is finally found out, which corresponds to the local maxima in the similarity distribution. The entire algorithm flow is shown in Figure
In most cases, there may be multiple rings in the collected images, which are induced by multiple defects. Some of them are overlapped with different degrees. Multiple hot images will appear in just one high-energy shot under this condition, which is a serious threat to the system. Therefore, it is of great importance to study the performance of GDM to recognize overlapped diffraction rings. Research in the past years[
A plane wave with wavelength in vacuum is set as the incident beam. Two identical simulated defects are selected to scatter the light with the radius . Amplitude modulation coefficient is 0.8. Phase modulation coefficient is . Area of the beam’s cross-section is also , which is divided into grid points. Diffraction distance in the simulation is 50 cm.
Figures
In a word, the conventional criterion that the overlap ratio should be smaller than 50% is not enough. This result indicates that it is feasible to recognize diffraction rings with the GDM method as long as the regular structure of the central light spot in the diffraction ring is still reserved. Therefore, hot images induced by those closely spaced defects and the defects that are far apart from each other can be directly and automatically prejudged.
However, two kinds of random noises often appear in the actually collected images. One appears like salt & pepper noise, which does not break the regular structure of the central light spot in the diffraction ring but makes the conventional GDM method fail to recognize diffraction rings. Image compression is used to extract the inherent feature of intensity oscillation, which is applied before the extraction of the gradient direction field and is able to solve this problem. The other kind appears as some bright or dark spots near the center of the diffraction ring. It can induce some redundant centers that are very close to the real center, which will greatly limit the efficiency of automatic operation when a lot of images need to be processed in a short time. Cluster analysis based on the minimum distance is adopted to remove these adjacent centers.
3.2 Experimental research with the actually collected images
In order to verify the effect of image compression on optimizing the performance of the GDM method to process actually collected images, the spatial light modulator (SLM) is used to simulate a pure amplitude defect[
Figure
In order to verify the effect of cluster analysis on optimizing the practicability of the GDM method in processing a lot of images in a short time automatically, a damaged plate is used to induce a series of seriously disturbed diffraction images. The plane wave used in the above experiment is still utilized to irradiate the plate. Figure
In a word, the optimized GDM method with image compression and cluster analysis performs well in the actually collected images. It can recognize the diffraction rings that are induced by the defects of tens of microns and provide information for the automatic operation without any redundant messages. Therefore, hot images induced by defects of tens of microns can be directly prejudged.
4 Conclusion
In conclusion, analysis of hot-image formation process shows that the distribution of the hot image can be precisely calculated with the intensity oscillation of the diffraction ring on the front surface of the nonlinear plate. Based on this relationship, a direct prejudgement technique is put forward, which aims to automatically detect diffraction rings. Analysis of recognizing simulated diffraction rings shows that hot images induced by those closely spaced defects and the defects that are far apart from each other can be directly prejudged. The GDM method is optimized with the image compression and cluster analysis to recognize the diffraction rings in the actually collected images. Experimental results show that hot images induced by defects of tens of microns can be directly prejudged without redundant information. As this method can prejudge hot images with the pure intensity information of the diffraction ring, it is more practical than those conventional methods. Next research goal is to further identify those diffraction rings that are currently not recognized.
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Aihua Yang, Zhan Li, Dean Liu, Jie Miao, Jianqiang Zhu. Direct prejudgement of hot images with detected diffraction rings in high power laser system[J]. High Power Laser Science and Engineering, 2018, 6(3): 03000e52
Category: Research Articles
Received: Apr. 11, 2018
Accepted: Aug. 15, 2018
Posted: Aug. 17, 2018
Published Online: Sep. 26, 2018
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