摘要
结合奇偶函数理论,提出了一种基于两平晶三面干涉测量平晶折射率均匀性的方法。该方法通过两块平晶3个表面之间的组合测量,对折射率均匀性引入的误差进行分部求解,生成4个随机波面作为初始3个表面面形和折射率均匀性误差,对其中的均匀性误差复原,结果与初始值仅相差0.6×10-6,残差与平晶表面面形的低频信息无关,仅取决于折射率均匀性本身的旋转不变项。在100 mm口径Zygo干涉仪上完成了两平晶折射率均匀性检测实验。同时通过三平晶透射法对同一块平晶的折射率均匀性进行检测,将两种方法的测量结果进行对比。结果表明两平晶方法获得的折射率均匀性结果与透射法获得的折射率均匀性波面形状相同,指标结果仅相差0.2×10-6,波面偏差峰谷值相差3 nm。分析了影响评估精度的误差项,旋转角度误差与对准误差的影响在实验精度条件下,均方根偏差均小于1 nm。实验结果表明所提出的两平晶三面互检方法能够有效地对平晶的折射率均匀性进行测量。
Traditionally,the interferometric method has been employed to test the refractive index uniformity of flat optical materials.The method mainly involves two approaches:the overturning method and the transmission method.Both methods require a minimum of three flat samples,including the reference flat,the transmission flat,and the sample flat to be tested.This requirement for multiple flats increases the overall cost of testing.We have proposed a novel method for evaluating the refractive index uniformity of transmission flats,which only requires two flats,offering a significant improvement over existing method.The method is realized by using two surfaces of the transmission flat and one surface of the reference flat,and the sample flat is used as the transmission flat.Based on the even-and-odd functions,we can get the even-odd,oddeven and odd-odd parts of the refractive index uniformity directly.To the even-even part,we resolve it as the even-even-even(eee)and even-even-odd(eeo)part and we can calculate the eeo part by rotate 90°measurement result.Then we resolve the eee part into even-even-even-even(eeee)and even-even-evenodd(eeeo)part and get eeeo part through the rotate 45°measurement result.Finally,by neglecting highorder rotational symmetry terms,we can calculate the refractive index uniformity from the obtained components.This method with its step-by-step decomposition providing an effective and efficient approach to characterize the optical properties of the flat under test.Four random wavefronts are generated as the initial three surface error and the refractive index uniformity errors.The uniformity errors are recovered according to the proposed method.Compared the difference between the recovered results and the initial values,that only 0.6 ppm(10−6)in differ.Additionally,the residual error exhibits rotation invariance,which aligns with theoretical expectations.It is important to note that in the low and middle frequency ranges,the residual error is not affected by the surface error of the flat,but solely determined by the refractive index uniformity itself.The theory is verified the experiment on a 100 mm Zygo interferometer and the refractive index uniformity of the same flat is measured by the three flat transmission method.The test flat is made by quartz.The surface error of the two surfaces are better thanλ/10.The flat has a certain wedge angle.The front and the back surface will not generate interference fringes.The reference flat is a microcrystalline flat,better thanλ/10 as well.The result of the two flat method have the same shape with the three flat transmission method.The refractive index uniformity obtained by the two flats methods is only 0.2 ppm different from that obtained by the transmission method,and the peak-valley value is 3 nm different.To ensure accuracy in the evaluation process,error influence is analyzed considering factors such as rotation angle errors and pix offset errors.By evaluating the influence of error,the experimentally verified results illustrate the effectiveness of this method in accurately evaluating the refractive index uniformity of flat optical materials.The proposed method demonstrates promising potential in the evaluation of refractive index uniformity,reducing resource requirements,and improving cost-effectiveness.
作者
马致遥
郑东晖
陈磊
马骏
MA Zhiyao;ZHENG Donghui;CHEN Lei;MA Jun(Nanjing University of Science and Technology,School of Electronic and Optical Engineering,Nanjing 210094,China)
出处
《光子学报》
EI
CAS
CSCD
北大核心
2024年第2期97-106,共10页
Acta Photonica Sinica
基金
中央高校基本科研业务费专项资金(No.30923010934)
国家自然科学基金(Nos.62005122,61975081)
江苏省自然科学基金(No.BK20200458)。
关键词
物理光学
光干涉测量
奇偶函数法
光学均匀性
绝对检测
Physical optics
Optic interferometry
Odd and even function
Optical uniformity
Absolute test
