摘要
光学薄膜作为关键元件，支撑和确保了事实上几乎所有现代光学系统的各种成功应用，其中光学薄膜软件技术发挥过、也必将持续发挥着关键性的作用。论文围绕光学薄膜软件技术中特别具有实用价值的若干前沿或关键方向进行了细致的基础理论和应用技术研究，主要包括决定膜系设计软件计算速度的核心数学算法、面向成品率的鲁棒膜系设计方法、膜材料光学参数表征中测量数据误差处理技术和多层膜反向工程算法开发等内容。这些关键技术的研究，有利于提高国内光学薄膜软件的算法水平和性能指标，有助于软件技术在镀膜生产和薄膜测量中发挥更显著的实用价值，有助于解决工业生产中的成本控制和高端应用中的苛刻光谱质量等突出问题。论文的主要内容和贡献如下：
(1)理论上建立了决定膜系设计软件计算速度和精度的核心数学模型——多层膜膜系光谱系数对膜层参数的一阶及二阶偏导数的解析计算模型，并得到了群延迟和群延迟色散的解析计算表达式。该解析模型，与矩阵法具有一致的物理背景，普遍适用于各向同性的均匀膜系统，形式上简明，数学上严格准确，编程上具有快速算法特性，应用上可用于薄膜光学的各个领域，可以作为薄膜工作者进行膜系分析、设计、表征和反向工程等技术的有力高阶工具。
(2)基于上述膜系光谱系数偏导数解析模型，提出了膜系设计评价函数梯度和Hesse矩阵的准确计算模型和快速实现算法，证明了该解析算法相比于有限差分近似模型在计算精度、计算量和计算时间上的优势，有利于采用二阶最优化方法来加快膜系优化设计的速度，特别是对于提高大膜层数的膜系设计速度有实用价值。
(3)运用上述膜系光谱系数偏导数解析模型，提出了一种新型的三棱锥形玻璃基片光学薄膜超声水听器，在不增加敏感膜膜层数的情况下，其最佳工作点的声光灵敏度较平板玻璃基片光学薄膜超声水听器提高了约一个量级，同时在光路调节、准直及稳定性，无扭曲测量时间和空间平均修正等方面体现了优势。
(4)基于膜系误差灵敏度主动控制思想，提出了新的光学薄膜鲁棒设计方法，研究了其快速实现算法。纵向上与传统膜系设计，横向上与其他鲁棒膜系设计思想，在计算精度和计算时间上进行了对比研究，结果证实了该鲁棒膜系设计方法在计算精度、计算量和时间消耗上的优势。应用上，通过对斜入射消偏振单点减反膜、宽带减反膜、可见—红外双波段减反膜、中性分光膜和线性透射率滤光片等多类光学薄膜的鲁棒设计实验，验证了该鲁棒膜系设计方法的误差控制效果。
(5)针对正交偏振激光器中应用的高性能偏振分光膜，对比研究了不同应用方案的误差响应特性，通过鲁棒设计实验研究，找到了该偏振分光膜膜系误差灵敏度的本质决定因素，提出了一种高鲁棒性的高性能激光偏振分光膜方案，其膜系结构简单，易于实际镀膜，为原方案镀膜过程中的低成品率和光谱质量退化问题提供了一种可能的解决方案。
(6)基于光谱测量系统误差和随机误差的不同特性分析，提出了一种新的膜材料光学参数表征中测量数据误差处理技术。针对难以消除的测量系统误差，利用膜系光谱系数对膜层参数的一阶偏导数的零点位置和符号信息进行有利于反演计算的光谱测量数据筛选，以最小化测量系统误差对薄膜光学参数表征的误差传递作用。针对不可分离的测量随机误差，提出多次在实测光谱数据中人为注入随机噪声的思想，利用统计平均来减小甚至消除实测光谱数据中随机误差对薄膜光学参数表征不确定度的影响。将上述方法分别应用于基于光度法和椭偏法的薄膜表征实验中，以可复现的数值模拟实验探讨了其技术实施细节，以充分的数值实验数据和合理的理论解释支持和验证了这种误差处理技术的可靠性和应用价值。
(7)对比研究了多层膜反向工程中各种局部优化方法在搜索能力、多解性处理、跳出局部极值的可能性、约束条件的影响及其施加策略等方面的性能，通过数值模拟实验给出了反向工程算法中理想的局部优化技术方案。探讨了多层膜反向工程中局部优化算法的有限适用性，提出了一种局部与全局一体化的多层膜反向工程算法，通过对12层锗基红外宽带减反膜、19层规整高反片和29层规整窄带滤光片等薄膜在各种人为模拟的镀膜厚度误差下的反向工程数值模拟实验，以可复现的数据验证了该一体化算法对多层膜反向工程具有良好的可靠性、较局部优化算法的优越性和对各类薄膜的普遍适用性。实验验证上，对15层红光滤光片、31层近红外高反膜、34层高精度激光偏振分光膜和一个未知理论设计结构的美国某高反膜片等已镀薄膜进行了多步骤离线反向工程实验分析，通过复现实测光谱曲线的特征信息（如波峰位置偏移、由系统或随机厚度误差造成的典型光谱特征），得到了多层膜中有物理意义的膜材料折射率色散关系、较可靠的膜系厚度及镀膜误差分布情况，验证了该局部与全局一体化的多层膜反向工程算法的可靠性。
As vital components, thin film optical coatings support or assure the success ofvirtually any modern optical system, among which the optical coating softwaretechnologies had played and will go on to play a critical role. The dissertationinvestigates basic theories and application technologies in details of some front or keyaspects with especially practical significance of optical coating software technologies.The research contents include the core mathematical algorithms determining opticalcoating design software’s calculation speed, the robust design methods of multilayeroptical coatings aiming for high manufacture yield, the spectral measurement data errorstreating techniques of optical parameters characterization of thin film materials, and thereverse engineering algorithm development of multilayer optical coatings. Research onthese key technologies can help to improve the algorithm level and performancespecifications of home-made optical coatings software, and can make the softwaretechnologies play a more prominent role in the manufacture and measurement of opticalcoatings. In a word, they might help to conquer the urgent problems of cost control ofindustrial mass production and spectral quality requirement of high-level applications.The main contents and contributions of this dissertation include:
(1) This dissertation theoretically establishes the core mathematical algorithms ofoptical coating design software, i.e. the analytical computation models of multilayersystem’s spectral coefficients’ first and second order partial derivatives with respect tolayer parameters, which also result in the analytical computation expressions of groupdelay and group delay dispersion. The analytical model of spectral coefficients’ partialderivatives is applicable to any isotropic homogeneous thin film system. And it isconcise in expressions, strict in mathematics, fast in calculation algorithms whileprogramming, and universal in all kinds of application fields of optical coatings. Allthese characteristics enable it to be a powerful research tool for optical coatingengineers to investigate the performance analysis, design, optical characterization andreverse engineering of thin film optical coatings.
(2) Based on the above analytical model of thin film spectral coefficients’ partialderivatives, this dissertation presents accurate calculation model and fast realizationalgorithm of thin film design merit function’s gradients and Hesse matrix with respectto design parameters. Numerical experiments had been conducted to testify theadvantage of the analytical model over the finite differentiating approximation model incalculation amount, accuracy and time of thin film design merit function’s gradients andHesse matrix. And it is best suitable to use second order optimization methods to speedup thin film design process with the established analytical model, where theimprovement in design speed is especially significant when the layer number is large.
(3) Based on the above analytical model of thin film spectral coefficients’ partialderivatives, this dissertation solves the deficiency problem in acoustic-optic sensitivityof an optical multilayer hydrophone with a plate glass substrate. A novel concept opticalmultilayer ultrasonic hydrophone is proposed with the sensing film deposited on atriangular pyramid glass substrate. This dissertation presents reasonable method andadjusting strategy for the optimum working point selection of the ultrasoundmeasurement. Besides of all the other merits of a plate glass substrate optical multilayerhydrophone, the novel hydrophone possesses about8.8-time improved detectionsensitivity without adding the layer number of the sensing film. Moreover, it ischaracterized with more stable optical path alignment and adjustment, longermeasurement time without distortion, and simplified spatial spot area correction, whichcan decrease the difficulty of high frequency signal circuits and will contribute to theaccurate calibration of the hydrophone’s wideband frequency response.
(4) Based on the active control concept of thin film’s sensitivity to layerparameters’ errors, this dissertation presents a novel robust design method of multilayeroptical coatings. And the analytical model and fast calculation algorithm have beenestablished. A thorough comparison in calculation accuracy and time had beenconducted among the presented robust design method, traditional deign method andother robust design thoughts of thin film systems, which demonstrated the advantage ofthe presented robust design method in both aspects. We demonstrated its effectivenessin errors control by applications into a variety of optical coatings, such as broadbandantireflection coating, dual-band antireflection coating, neutral beam splitter and linearramp transmittance filter. It shows that the presented robust design method ownsinherent fast computation characteristic and the designed film is insensitive tomonitored layer parameters’ errors in deposition process, which is of practicalsignificance to improve the mass production yields and repetitive production of highquality optical coatings.
(5) Based on the above robust design method of multilayer systems, the spectralcharacteristic responses to layer parameters’ errors were researched comparativelyamong three different application solutions of a high-performance thin-film polarizingbeam splitter (PBS) used in a novel orthogonal polarized dual-frequency laser. Theinherent factor of laser PBS’s errors sensitivity had been found by elaborately arrangednumerical robust design experiments. A robust thin film structure had been designed forthe high-performance laser PBS with moderate layer number and easy-manufacturablelayer thicknesses. This PBS design solution is very suitable for mass production at lowcost and high yield, which will play a positive role in the development, engineering andapplication of the orthogonal polarized dual-frequency laser.
(6) Based on the different characteristic analysis of systematic and random errorsin spectral measurement data, this dissertation presents a novel errors treating technique of optical parameters characterization of single-layer thin film materials. In order tominimize the characterization deviations of thin film optical parameters from real valuescaused by systematic errors hard to eliminate, it is advised to select measurement dataused in optical characterization from spectral bands characterized with opposite signs orsingle zero of first-order spectral coefficients’ partial derivatives with respect to layerthickness and refractive index for most measurement incident angles, and to excludespectral bands characterized with the same signs or both zeros of spectral coefficients’first-order partial derivatives for all measurement incident angles. The essence of thistechnique is to minimize the errors transfer effect of spectral measurement data on thinfilm optical parameters characterization through spectral measurement band selectionby first-order partial derivatives analysis. In order to minimize the characterizationuncertainties of thin film optical parameters from real values caused by random errorsimpossible to exclude, it is creatively presented to inject independent random noise withthe same distribution law and magnitudes into actual measurement data, which areutilized for many times as target spectral coefficients of the investigated film in theprocess of optical characterization. The statistics mean values of all fit opticalparameters obtained each time by the characterization algorithm are then chosen asestimates of the real optical parameters of the investigated film, whose uncertainiesdecrease to one of square root of characterization times equal parts of the initial valueswithout random errors injection. Numerical simulations had been comparably conductedwith both photometric and ellipsometric data to research the applicability and selectionskills of the range of measurement incident angles. The reliability of this technique issupported by resumable numerical experiments’ results and reasonable theoreticalexplanations. It shows this novel errors treating technique might play a practicalsignificance in in-situ characterization and thickness monitoring of thin films.
(7) Different local optimization algorithms in the reverse engineering of multilayeroptical coatings have been compared with characteristics of search ability, multiplesolutions treatment, escaping possibility of local extremum and influence of therestriction condition settings. Numerical experiments show that there is a reasonablelocal optimization method based on the Levenberg-Marquardt algorithm which is bestsuitable for reverse engineering algorithm development of multilayer optical coatings.And the limited applicability of the local optimization algorithm is investigated in termsof reverse engineering quality by numerical simulated experiments. A hybrid reverseengineering algorithm is presented based on genetic algorithm with elite selectionstrategy and nonlinear least-squares method with Levenberg-Marquardt algorithm. Thegood reliability, superiority and universality of the hybrid reverse engineering algorithmis tested and supported by resumable numerical reverse engineering experiments’ resultsof a12-layer infrared antireflection coating, a19-layer quarter-wave mirror and a29-layer quarter-wave narrow band filter under intentionally simulated layer thicknesses errors. As for actual reverse engineering experiments, four multilayer optical coatings,including a15-layer red band-pass filter, a31-layer infrared mirror, a34-layerpolarizing beam splitter and a unknown mirror made in America, were used to prove thereliability and significance of the presented hybrid reverse engineering algorithm withphotometric measurement data by Lambda950spectrometer. Physically sensibledispersion relations of thin-film material’s refractive indices in multilayer coatings arefirstly determined according to the wavelength positions deviations of extremum in themeasured spectral curves. And reliable thicknesses information is secondly determinedby tying to recur the special characteristics in the measured spectral curves which aretypically caused by systematic or random thickness errors. The closeness of fitted modelspectral curves to measured curves and the recurrence of special characteristics inmeasured curves both indicate that the reverse engineered results are reliable both frommathematical and physical point of view.
引文
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