光学学报, 2011, 31 (8): 0812002, 网络出版: 2011-07-21
微小孔偏差对远场波前质量影响分析
Analysis of Effect of Tiny Pinhole Deviation on Far-Field Wave-Front Quality
光学检测 点衍射干涉仪 瑞利索末菲衍射 小孔边缘粗糙度 椭圆小孔 波前质量 optical testing point diffraction interferometer Rayleigh-Sommerfeld diffraction pinhole edge roughness elliptical pinhole wave-front quality
摘要
点衍射干涉仪(PDI)中小孔质量影响参考球面波的质量,加工和装调误差使实际小孔与理想圆孔之间产生了偏差。利用瑞利索末菲衍射公式,对因小孔加工和装调误差产生的边缘粗糙小孔和椭圆小孔的远场衍射波前质量作了详细的分析。小孔边缘的粗糙度主要在衍射波前中引入了三叶形像差,小孔的椭圆度在衍射波前中引入了小量的像散。对于直径在0.4~1.0 μm的小孔,当小孔半径的均方根(RMS)偏差分别为0,15和30 nm时,衍射波前的RMS偏差分别达到10-8λ,10-4λ和10-3λ量级。研究结果表明,小孔边缘的粗糙度对衍射波前偏差的影响十分明显,但基本不影响强度分布;小孔的椭圆度对衍射波前的偏差影响很小,但对强度分布影响较大。实际加工或装调误差产生的椭圆小孔,其椭圆度很小,可以忽略其对衍射波前质量的影响。
Abstract
The quality of the reference wave front in point-diffraction interferometer (PDI) is constrained by the quality of the pinhole, and the deviation between an actual pinhole and a perfect one is caused by machining errors and the misalignment. The quality of the far-field wave front diffracted by a rough-edge circular pinhole and an elliptical pinhole is analyzed in detail based on Rayleigh-Sommerfeld diffraction formula. Pinhole edge roughness mainly causes the trefoil aberration in diffracted wave front, and the ellipticity of a pinhole will lead to a small amount of astigmatism in diffracted wave front. For pinholes with diameters from 0.4 to 1.0 μm, when the radius root mean square (RMS) deviations are 0, 15 and 30 nm, the RMS deviations of the diffracted wave fronts are in the order of 10-8λ, 10-4λ and 10-3λ, respectively. The results show that pinhole edge roughness has a significant influence on wave front deviation, while it has little to do with the intensity distribution in the diffracted wave front. The ellipticity of the pinhole has very small effect on wave front deviation, but affects the wave front intensity distribution in far-field wave front. Usually, the ellipticity of an elliptical pinhole resulting from machining errors or the misalignment is small, and its effect on far-field wave front quality can be neglected.
卢增雄, 金春水, 马冬梅, 张海涛. 微小孔偏差对远场波前质量影响分析[J]. 光学学报, 2011, 31(8): 0812002. Lu Zengxiong, Jin Chunshui, Ma Dongmei, Zhang Haitao. Analysis of Effect of Tiny Pinhole Deviation on Far-Field Wave-Front Quality[J]. Acta Optica Sinica, 2011, 31(8): 0812002.