本文選題：干涉圖 + 相位測(cè)量��； 參考：《中國科學(xué)院光電技術(shù)研究所》2017年博士論文

【摘要】：隨著現(xiàn)代科技工業(yè)的發(fā)展,各種先進(jìn)設(shè)備都向著光機(jī)電一體化方向發(fā)展。其中,光學(xué)系統(tǒng)是這些復(fù)雜系統(tǒng)的輸入或輸出端口。面形精度是光學(xué)元件的核心技術(shù)指標(biāo),該指標(biāo)能否達(dá)標(biāo)依賴于測(cè)量所能達(dá)到的精度。干涉儀是光學(xué)元件面形檢測(cè)的關(guān)鍵設(shè)備。干涉儀是集光機(jī)電算于一體的現(xiàn)代光學(xué)元件檢測(cè)設(shè)備。參考表面和被測(cè)表面返回的激光光束形成干涉條紋,并通過成像系統(tǒng)轉(zhuǎn)換為數(shù)字信息。在獲取的干涉圖像中,隱含著待測(cè)相位的信息。本文的主要工作就是將探測(cè)器獲取的干涉條紋進(jìn)行解讀,完成直接測(cè)量量(干涉條紋)到最終測(cè)量信息(相位信息)的轉(zhuǎn)化。為提高干涉儀對(duì)環(huán)境影響的適應(yīng)能力,出現(xiàn)了諸如基于隨機(jī)相移技術(shù)、動(dòng)態(tài)干涉技術(shù)、單幀載頻條紋技術(shù)的干涉儀。但這幾類干涉儀都需要從硬件上對(duì)干涉儀設(shè)備進(jìn)行升級(jí)。比如采用多CCD或提高干涉儀大視場(chǎng)成像質(zhì)量等方法。為在現(xiàn)有干涉儀的硬件基礎(chǔ)上,實(shí)現(xiàn)單幀干涉條紋的相位復(fù)原,本文提出了基于單幀干涉條紋數(shù)學(xué)模型的相位復(fù)原技術(shù)。該方法只需要采集單幀干涉條紋,不需要相移器等硬件結(jié)構(gòu)和大傾斜量的特殊要求,即可達(dá)到高精度的相位復(fù)原。這樣就可以實(shí)現(xiàn)低成本、高精度動(dòng)態(tài)相位干涉測(cè)量。本文首先介紹了干涉儀的主要原理和基本的算法理論,研究了干涉圖像濾波技術(shù),特別是提出了多項(xiàng)式擬合濾波技術(shù)。編寫了相位復(fù)原算法中的常用解包裹程序和多項(xiàng)式擬合程序,同時(shí)實(shí)現(xiàn)了移相相位算法的相位復(fù)原,并通過實(shí)驗(yàn)驗(yàn)證了算法的有效性。在對(duì)干涉儀硬件和相關(guān)算法充分調(diào)研之后,建立了單幀條紋的數(shù)學(xué)模型和優(yōu)化目標(biāo)函數(shù)。為了對(duì)條紋模型進(jìn)行優(yōu)化求解,本文中研究了牛頓迭代法和遺傳算法的優(yōu)化原理,分析了兩種優(yōu)化方法對(duì)條紋數(shù)學(xué)模型各自的求解能力,并給出了優(yōu)化過程中參數(shù)邊界的設(shè)置方法。根據(jù)兩種優(yōu)化方法各自的優(yōu)缺點(diǎn),提出了采用遺傳算法和牛頓迭代法混合優(yōu)化的模型求解方法。本文給出了條紋的優(yōu)化仿真結(jié)果,該方法不但可以用于直條紋相位復(fù)原,還可以用于閉合條紋的相位復(fù)原,并通過仿真驗(yàn)證了優(yōu)化方法的有效性。在仿真程序基礎(chǔ)上,將實(shí)測(cè)兩幅干涉圖進(jìn)行了相位的復(fù)原優(yōu)化求解。雖然在實(shí)際的干涉條紋圖中,存在著光強(qiáng)分布的不均勻誤差和相位殘差,但是通過實(shí)驗(yàn)驗(yàn)證了相位求解結(jié)果的對(duì)這類誤差的不敏感性。比較了條紋優(yōu)化算法給出的相位求解結(jié)果與相移方法給出的結(jié)果,兩者具有面形分布和多項(xiàng)式系數(shù)的一致性。為分析殘差對(duì)測(cè)量結(jié)果的影響,將相位擬合殘差引入了優(yōu)化函數(shù)中。仿真分析表明,加入相位殘差后的優(yōu)化迭代求解結(jié)果可以使得優(yōu)化條紋與實(shí)測(cè)條紋光強(qiáng)更加一致,特別是殘差較大的位置效果明顯。由于相位殘差引入能夠提高優(yōu)化精度,提出了基于載頻測(cè)量技術(shù)的相位殘差測(cè)量方法,用來彌補(bǔ)模型求解問題的不足。同時(shí),對(duì)載頻測(cè)量技術(shù)進(jìn)行了原理性的介紹和誤差分析,并實(shí)現(xiàn)了載頻測(cè)量技術(shù)的相位提取算法。通過與相移算法對(duì)比,驗(yàn)證了載頻相位算法的有效性。在驗(yàn)證和分析了基于干涉條紋模型的相位復(fù)原技術(shù)的基礎(chǔ)之上,改進(jìn)了光源的特征參數(shù)。即,考慮了探測(cè)器法向與光軸的夾角問題,在條紋模型中增加3個(gè)未知參數(shù)。模型改進(jìn)后,給出了四種設(shè)置條件下的優(yōu)化求解結(jié)果的對(duì)比分析。最后,為驗(yàn)證本方法最后的可靠性,通過本文提出的復(fù)原技術(shù)對(duì)兩個(gè)具有代表性的實(shí)測(cè)干涉圖進(jìn)行相位復(fù)原,得到了較好的結(jié)果。實(shí)驗(yàn)表明,基于模型的單幀相位復(fù)原算法適用于低階面形誤差較大,中頻誤差較小的光學(xué)表面面形測(cè)量。通過本文的工作,實(shí)現(xiàn)了基于單幀干涉條紋模型的相位復(fù)原技術(shù),其可以用于常用的干涉儀測(cè)量所得的干涉圖相位求解,具有較強(qiáng)的工程應(yīng)用價(jià)值。
[Abstract]:With the development of modern science and technology industry, all kinds of advanced equipment are developing in the direction of light and electrical integration. The optical system is the input or output port of these complex systems. The surface shape accuracy is the core technical index of optical elements, and whether the target can reach the standard depends on the accuracy achieved by the measurement. The key equipment of measurement. Interferometer is a modern optical element detection device which integrates light and electrical calculation. The reference surface and the laser beam returned from the surface are formed to form interference fringes and convert into digital information through the imaging system. In the acquired interference images, the information to be measured is implied. The main work of this article is to make the detector. In order to improve the adaptability of the interferometer to the environmental impact, the interferometer, such as the random phase shift technique, the dynamic interference technique, the single frame carrier stripe technique, has been developed, but these interferometers need to be from the hardware. To upgrade the interferometer equipment, for example, using multiple CCD or improving the image quality of the interferometer large field of view. In order to restore the phase of the single frame interference fringes on the basis of the existing interferometer's hardware, a phase restoration technique based on the single frame interference fringe mathematical model is proposed. The phase recovery of high precision can be achieved without the need of the hardware structure and the special requirement of the large tilt. In this way, the low cost and high precision dynamic phase interferometry can be realized. In this paper, the main principle and basic algorithm theory of the interferometer are introduced, and the filtering technique of the dry image is studied, especially the polynomial of the polynomial. The common unwrapping program and polynomial fitting program in the phase restoration algorithm are compiled, and phase restoration of phase shift phase algorithm is realized, and the effectiveness of the algorithm is verified by experiments. The mathematical model of single frame stripe and the optimization target function are built after the thorough investigation of the interferometer hardware and related algorithms. In order to optimize the model of the stripes, this paper studies the optimization principle of Newton's iterative method and genetic algorithm, analyses the solving ability of the two optimization methods to the mathematical model of the stripes, and gives the setting method of the parameter boundary in the optimization process. According to the advantages and disadvantages of the two optimization methods, the heredity is put forward. The optimization simulation results of the fringe are given in this paper. This method not only can be used for the restoration of the straight stripe phase, but also can be used for the phase restoration of the closed stripe, and the effectiveness of the optimization method is verified by simulation. On the basis of the imitation truth program, the measured two interferograms are carried out. In the actual interference fringe pattern, there is an inhomogeneous error and phase residual of the intensity distribution, but the insensitivity to this kind of error is verified by the experiment. The results of the phase solution and the phase shift method given by the fringe optimization algorithm are compared. In order to analyze the consistency between the surface shape distribution and the polynomial coefficient, in order to analyze the influence of the residual on the measurement results, the phase fitting residuals are introduced into the optimization function. The simulation analysis shows that the optimized iterative solution after the addition of the phase residual can make the optimized stripe and the measured stripe light intensity more effective, especially the larger residual position effect is obvious. Due to the introduction of phase residual to improve the optimization precision, a phase residual measurement method based on carrier frequency measurement technology is proposed to make up for the shortage of the model solving problem. At the same time, the principle of carrier frequency measurement technology is introduced and the error analysis is carried out, and the phase extraction algorithm of carrier frequency measurement technology is realized. The validity of the carrier frequency phase algorithm is verified. Based on the verification and analysis of the phase restoration technology based on the interference fringe model, the characteristic parameters of the light source are improved. That is, considering the angle problem between the detector normal and the optical axis, 3 unknown parameters are added to the fringe model. After the model is improved, the four setting conditions are given. Finally, in order to verify the final reliability of the method, two representative measured interferograms are restored by the proposed restoration technique, and the results are better. The experiment shows that the single frame phase restoration algorithm based on the model is suitable for the lower order error and the intermediate frequency error. Small optical surface profile measurement. Through the work of this paper, the phase restoration technology based on the single frame interference fringe model is realized. It can be used to solve the interferogram phase analysis obtained by the commonly used interferometer. It has strong engineering application value.
【學(xué)位授予單位】：中國科學(xué)院光電技術(shù)研究所
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP391.41

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