Analysis of influence of diffraction effect of microlens array on Shack-Hartmann wavefront sensor
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摘要:
微透镜阵列的衍射效应会影响夏克—哈特曼波前探测器的探测精度。本文根据惠更斯-菲涅耳衍射理论建立二维微透镜阵列衍射模型，模拟分析使用理想平行光入射微透镜阵列时在焦平面产生的二维衍射光斑阵列。然后，通过计算衍射光斑偏移一个像素的过程中质心的误差，确定最大质心计算误差。接着，利用模式法进行波前重构，获得波前探测误差。仿真结果显示：在偏移0.21和0.79个像素，即波面偏转0.03°和0.13°时，衍射导致的波前误差最大为0.125
λ 。最后，实验验证了该误差计算方法的有效性。该研究结果可为夏克一哈特曼波前探测器的设计提供理论依据。Abstract:The diffraction effect of microlens array will affect the detection accuracy of Shack-Hartmann wavefront sensor. Based on Huygens-Fresnel diffraction theory, a two-dimensional microlens array diffraction model is established to simulate and analyze the two-dimensional diffraction spot array generated in the focal plane when the ideal parallel light is incident on the microlens array. First, the maximum centroid calculation error is determined by calculating the centroid error in the process of diffraction spot shifting by one pixel. Then the wavefront is reconstructed by using the modal method to obtain the wavefront detection error. The simulation results show that the maximum wavefront error caused by diffraction is 0.125
λ at 0.21 and 0.79 pixels offset, that is, when the wavefront deflection is 0.03° and 0.13°. Finally, an experiment is performed to verify the effectiveness of the error calculation method. This work provides a theoretical basis for the design of shack-Hartmann wavefront detector. -
图 1 单个子孔径光斑质心计算示意图
Figure 1. Schematic diagram of single subaperture spot centroid calculation
图 4 (a)任一有衍射光斑中心及 (b) 任一无衍射光斑中心光强分布
Figure 4. Central intensity distribution of (a) any diffraction spot and (b) any non diffraction spot
图 6 (a) 无衍射和 (b) 有衍射的光斑偏移1个像素过程中的质心计算误差； (c) 衍射效应造成的质心计算误差
Figure 6. Centroid calculation error in the process of (a) diffraction free and (b) diffraction spot shifting by 1 pixel; (c) calculation error of centroid caused by diffraction effect
图 7 (a)无衍射的光斑偏移0.79 像素的重构波前；(b) 有衍射的光斑偏移0.79 像素的重构波前；(c) 最大误差波前
Figure 7. (a) Reconstructed wavefront with diffraction free spot offset of 0.79 pixels; (b) reconstructed wavefront with diffraction spot offset of 0.79 pixels; (c) maximum error wavefront
图 8 (a) 无衍射的光斑偏移1个像素过程中的波前倾斜误差；(b) 有衍射的光斑偏移1个像素过程中的波前倾斜误差；(c)衍射效应造成的波前倾斜误差
Figure 8. (a)Wavefront tilt error in the process of diffraction free spot shifting by 1 pixel; (b) wavefront tilt error in the process of diffraction spot shifting by 1 pixel; (c) wavefront tilt error caused by diffraction effect
图 10 哈特曼波前探测实验装置图
Figure 10. Experimental diagram of Hartmann wavefront detection device
图 11 (a) 实验光斑图；(b)初始波前；(c)倾斜波前
Figure 11. (a) Experimental spot diagram; (b) initial warefront (c) inclined wavefront
图 12 (a) 实际波前倾斜量与旋转角度的关系曲线；(b) 仿真波前倾斜量与旋转角度关系曲线；(c) 实验波前倾斜量与旋转角度关系曲线；(d) 波前倾斜误差曲线
Figure 12. (a) Relation curve between actual wavefront tilt and rotation angle; (b) relationship curve between simulated wavefront tilt and rotation angle; (c) relation curve between experimental wavefront tilt and rotation angle; (d) wavefront tilt error curve
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