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摘要
Objective The intensity distribution of the laser far-field focal spot is an essential index for measuring the quality of laser beams. It is also the main parameter that reflects the laser beam' s ability to enter the hole in the inertial confinement fusion system. How to measure the intensity distribution of the laser far-field focal spot with high precision determines the evaluation result of the overall performance of the laser system. It is of great guiding significance in the theoretical design stage, development stage, or final stage of practical operation of the laser device. Direct measurement methods of far-field focal spots include the long-focal-length imaging, array camera, and schlieren methods. The long-focal-length lens imaging method is limited by the linear response range of the detector. The array camera method uses a wedge, which introduces additional optical path difference and wave aberration. The schlieren method measures the main lobe and side lobe of the focal spot separately, which is easily affected by the measured environment and noise. The Shack-Hartmann wavefront measurement is an indirect measurement method and causes the loss of middle and high frequency information due to its frequency response characteristics. To achieve a high-precision measurement of far-field focal spot, this paper proposes a method based on multistep phase retrieval for measuring far-field focal spots. Theoretically, a focal spot reconstruction model based on multistep phase retrieval is derived. Then, the chirp-z transform (CZT) is introduced to solve the problem of under-sampling in calculating focal spots. Compared with the traditional fast Fourier transform (FFT) with zero-padding, using CZT to calculate the focal spot avoids calculation redundancy. The proposed method has a higher measurement accuracy of a focal spot than the traditional long-focal-length lens imaging method. Methods The proposed laser far-field focal spot measurement method based on multistep phase retrieval can be divided into two parts. First, the multistep phase retrieval method is used to obtain the near-field complex amplitude of the object plane. Then, it is substituted into the reconstructed model of the laser far-field focal spot and uses CZT to obtain the intensity distribution of the laser far-field focal spot. Meanwhile, considering that the multistep phase retrieval method will introduce distance errors due to the translation of the detector, the quantum genetic algorithm (QGA) is used to optimize the distance errors. The laser far-field focal spot reconstruction algorithm based on multistep phase retrieval is presented. We use the theoretical simulation to analyze the influence of scanning step size and the number of detection positions on the convergence of the proposed method. Thus, the optimal scanning step size and the number of detection positions are determined. Furthermore, a verification device based on a pure phase liquid crystal spatial light modulator (SLM) is set up experimentally to verify the effectiveness of the proposed method. We also compare the experimental results of the proposed method and traditional long-focal-length lens imaging method. Results and Discussions In the simulation, the laser near-field complex amplitude of the object plane is effectively retrieved. The retrieved and theoretical focal spots have the same distribution of main lobe and side lobe in the focal spot (Fig. 7). Compared with CZT, the focal spot calculated using FFT is under-sampled, and the detailed information in the focal spot is lost (Fig. 7). The power in the bucket (PIB) curves of theoretical and retrieved focal spots are completely coincident in the integral area of the entire bucket radius (Fig. 7). In the experiment, the main lobe distribution between the theoretical and retrieved far-field focal spots is consistent (Fig. 9). However, the optical components introduce small aberrations, and the surfaces of these optical components will interfere with each other, resulting in a small difference between the distribution of side lobes for the theoretical and retrieved far-field focal spots (Fig. 9). In the traditional long-focal-length lens imaging method, the introduction of lens aberrations and insufficient dynamic response range of the CCD lead to larger errors in the main lobe and side lobe of focal spots than those in the theoretical focal spot (Fig. 9). The correlation coefficient between the retrieved focal spot using the proposed method and the theoretical focal spot is 0.9976. However, the correlation coefficient between the measured focal spot using the long-focal-length lens imaging method and the theoretical focal spot is 0. 9477. This also confirms that the measurement accuracy of focal spots using the proposed method is much higher than that of the long-focal-length lens imaging method. Conclusions This paper proposes a laser far-field focal spot measurement method based on multistep phase retrieval. The effectiveness of the method is verified through theoretical simulation and experiments. The theoretical simulation results show that the near-field complex amplitude and far-field focal spot of lasers are effectively retrieved. Additionally, the PIB curves of the theoretical and retrieved focal spots are coincident. Moreover, the experimental results show that the profile of the retrieved phase is consistent with that of the theoretical phase loaded using SLM. Therefore, the retrieved and theoretical focal spots have the same distribution of the main lobe. However, there is a small difference in the side lobes because the optical components introduce small aberrations, and the surfaces of these optical components will interfere with each other. The side lobe information of focal spots using the long-focal-length lens imaging method is lost because of the limited dynamic response range in CCD. Therefore, the proposed method has higher precision of laser far-field focal spot than the traditional long-focal-length lens imaging method. The results show that the proposed method can provide a technical means for the high-precision measurement of laser far-field focal spots.
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