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对于粒径小于50μm吸附于基底表面的干燥颗粒,可近似认为颗粒的吸附力为范德华力。颗粒的吸附力还会使颗粒产生形变,从而导致颗粒与基底表面之间存在接触面,根据Hamaker理论[20],对于上述SiO2球状颗粒,其吸附力可表示为:
$ |F|=\left|F_{1}+F_{2}\right|=\frac{A r}{6 h^{2}}\left(1+\frac{r_{\mathrm{c}}^{2}}{r h}\right) $
(1) 式中,F1, F2分别表示未发生形变的范德华力与形变所引起的范德华力, A为Hamaker常数,r为颗粒的半径,h为颗粒与表面之间的距离,rc为形变导致的颗粒与基底表面的接触半径。根据DERJAGUIN的理论[21],颗粒半径与接触半径之间的关系有:
$ r_{\mathrm{c}}^{3}=\frac{A r^{2}}{8 h^{2}}\left(\frac{1-\sigma_{1}^{2}}{E_{1}}+\frac{1-\sigma_{2}^{2}}{E_{2}}\right) $
(2) 式中,σ1和E1表示颗粒的泊松系数和杨氏模量,σ2和E2表示基底的泊松系数和杨氏模量。
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干式激光清洗的主要原理是利用热膨胀机理,激光直接照射在待清洗物基底和表面颗粒上,光能转换为热能,造成基底热膨胀、颗粒物自身热膨胀或两者同时吸收热膨胀,产生位置变化Δz,从而产生加速度使颗粒脱离基底。这3种方法原理相似,清洗模型基本相同,因此以普适性较强的基底膨胀模型为例,根据能量转换关系以及基底的1维温度场分布可得到:
$ \left(1-R_{\rm s}\right) \int_{0}^{\infty} I\left(t_{1}\right) \mathrm{d} t_{1}=c \rho \int_{0}^{\infty} T(z, t) \mathrm{d} z $
(3) 式中,I(t1)为激光能量,T(z, t)为基底的1维温度场分布,c为基底的比热容,ρ为基底的密度,Rs为表面的反射率,将激光器产生的高斯型脉冲的脉冲形状等参量代入,可得基底的位移的表达式:
$ {z_{\rm{s}}}(t) = \frac{{{\alpha _T}\mathit{\Phi }\left( {1 - {R_{\rm{s}}}} \right)}}{{c\rho }}\left[ {1 - \left( {1 + \frac{t}{\tau }} \right){{\rm{e}}^{ - \frac{1}{\tau }}}} \right] $
(4) 式中,αT为基底材料的热膨胀系数,Φ为激光通量, τ为激光的脉宽, t是时间变量。基于上述公式即可得基底与颗粒的位移速度与加速度。基底的加速度为:
$ a = \frac{{{\alpha _T}\mathit{\Phi }\left( {1 - {R_{\rm{s}}}} \right)}}{{c\rho }}\frac{{{{\rm{e}}^{ - \frac{t}{\tau }}}}}{{{\tau ^2}}}\left( {1 - \frac{t}{\tau }} \right) $
(5) 颗粒的移除条件可表述为在热膨胀很短的时间内,产生的颗粒的动能与弹性势能克服吸附力所做的功,将此过程化简、近似,可得颗粒移除过程的简化式:
$ \frac{4}{3} \pi r^{3} \frac{\rho_{0} v^{2}}{2} \geqslant \frac{A r}{6 h} $
(6) 式中, ρ0为颗粒的密度, v是颗粒的速度。
以实验中所用数据为例进行计算,单发激光清洗未镀膜熔石英光学元件表面粒径为10μm的SiO2颗粒,取激光能量密度为2J/cm2,激光波长为355nm,脉宽为10.7ns,此模型下在激光作用的短时间内,颗粒的瞬间温度最高可达8000K,瞬间加速度可达109m/s2量级,从而使得颗粒能够脱离基底表面。
溶胶-凝胶膜光学表面激光清洗工艺研究
Study on laser cleaning process of sol-gel film optical surface
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摘要: 为了解决光学元件表面的颗粒污染问题,在单发次激光干式清洗的基础上,提出了气流置换系统辅助的激光清洗方法,使用波长为355nm的Nd:YAG激光器,针对镀溶胶-凝胶SiO2薄膜熔石英光学表面粒径为1μm~50μm的典型SiO2颗粒污染物,进行了理论分析和清洗实验,取得了可用于激光清洗的工艺参量。结果表明,对于镀溶胶-凝胶膜熔石英样品的单发激光干式清洗,最佳激光能量密度为2.29J/cm2,与未镀膜石英的激光清洗工艺参量存在一定差异;在最佳工艺参量下,单发次激光清洗对于粒径1μm以上的SiO2颗粒清洗效果明显,移除率可达82.96%;当污染密度过高时会导致清洗效果的减弱及对基底的损伤,而气流置换系统辅助的激光清洗方法可进一步增强对光学表面颗粒污染的去除效果。该研究对大型高功率固体激光装置中的光学元件在线清洗及清洗装备的设计具有重要的研究意义与实用价值。Abstract: In order to solve the problem of particle contamination on the surface of optical elements, on the basis of single laser dry cleaning, laser cleaning assisted by air displacement system was proposed. Nd:YAG laser with 355nm wavelength was used. Typical SiO2 pollutant particulate with optical surface diameter of 1μm~50μm for sol-gel SiO2 thin film fused silica was theoretically analyzed and cleaning experiments were carried out. The process parameters for laser cleaning were obtained. The results show that, for single crystal laser dry cleaning of sol-gel membrane fused silica samples, optimum laser energy density is 2.29J/cm2. The process parameters of laser cleaning are different from those of uncoated quartz. Under the optimum technological parameters, the effect of single laser cleaning on SiO2 particles with particle size more than 1μm is obvious. The removal rate is 82.96%. Excessive contamination density will weaken the cleaning effect and damage the base. Laser cleaning assisted by air displacement system can further enhance the removal effect of particle contamination on optical surface. This research has important research significance and practical value for on-line cleaning of optical components and the design of cleaning equipment in large-scale high-power solid-state laser devices.
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Key words:
- laser technique /
- laser cleaning /
- removal rate /
- fused silica /
- sol-gel film
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