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摘要: 本文提出了一种基于二维线性调频Z变换的衍射光场分布快速计算方法，该方法在不增加运算量的情况下可以显著提高光场分布的图像分辨率，进而能够得到更准确的光束质量β因子值。在算法正确性验证的基础上，本文数值模拟了不同光束波前畸变的均方根RMS值与光束质量β因子的对应关系。仿真结果表明，在像差分布RMS值相同的前提下，几种低阶像差类型中球差类型的像差对光束质量的影响最大。为了模拟不同光斑分布形态，随机Zernike像差组合方式的光束质量β因子的仿真计算结果表明：相同的RMS值情况下，高阶像差占比较高的像差组合方式对应的光束质量β因子较大。Abstract: An algorithm for fast calculation of the field distribution of diffraction based on two-dimension chirp Z transformation is proposed. The proposed algorithm does not increase computation and significantly improves the resolution of the diffraction distribution and obtains a more accurate beam quality β factor. After verifying the correctness of the proposed algorithm, the corresponding relationship between the RMS (Root-Mean-Square) of the beam′s wavefront aberration and β factor is simulated. The simulation results show that with the same RMS value, the effect of a spherical aberration on the β factor is the strongest among the lower order Zernike aberrations. In order to simulate the different distribution of beam spots, the β factors are calculated based on different random Zernike wavefront aberrations. The results indicate that a larger proportion of high-order Zernike aberrations in the cumulative aberrations induces a bigger β factor with an identical RMS value.
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Key words:
- numerical simulation /
- wavefront aberration /
- beam quality /
- chirp Z transformation
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图 2 （a）线性调频Z变换的计算路径和（b）透光孔函数
Figure 2. (a) The calculation path of CZT algorithm and (b) transparent hole function used in the calculation
图 3 （a）探测面上的衍射光强分布及（b）衍射强度曲线
Figure 3. (a) Diffraction intensity distribution at the detection plane and (b) diffraction intensity curve in one dimension
图 4 （a）s-fft算法及（b）CZT算法的衍射强度分布
Figure 4. Diffraction distributions of (a) s-fft algorithm and (b) CZT algorithm
图 5 （a）彗差和（b）球差对应的探测面上的衍射强度分布
Figure 5. Diffraction distributions of (a) coma wavefront aberration and (b) spherical wavefront aberration
图 6 （a）光束质量β因子和（b）桶中功率PIB随波像差RMS值的变化关系
Figure 6. （a）Beam quality β factor and (b) PIB changing with RMS of wavefront aberration
图 7 随机像差对应的光束质量β因子波动（a）和β因子的统计分布（b）
Figure 7. （a）Fluctuation of β factor with random wavefront aberrations and (b) statistical distribution of the β factor
图 9 不同均方根RMS值的随机像差对应的β因子变化情况
Figure 9. Variation in the β factor corresponding to random wavefront aberrations for different RMS values
表 1 光束质量β因子统计结果
Table 1. Statistical results of the β factor
波像差RMS值 β因子统计均值 β因子标准偏差 0.1λ 2.50 0.06 0.2λ 4.42 0.04 0.3λ 6.56 0.07 0.4λ 8.66 0.10 0.5λ 10.81 0.13 0.6λ 12.64 0.16 0.7λ 14.87 0.18 0.8λ 17.11 0.21 0.9λ 18.67 0.22 1.0λ 20.90 0.24 
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