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强激光在大气中传输时，尤其在目标静止的时候，大气吸收强激光能量导致的热晕效应会导致光斑的畸变。影响热晕的主要因素是大气对激光的吸收特性和传输光路上的风速分布。参考文献[1]~参考文献[17]中对强激光大气传输的热晕效应开展了各种理论分析、仿真和补偿等研究，形成了较为完善的理论体系。参考文献[18]~参考文献[21]中也开展了激光大气传输和热晕等相关实验研究，但其主要是集中在地面大气和实验室的实验研究，而波长1000nm附近的连续强激光在水面上的大气传输热晕效应实验研究鲜见报道。
本文作者基于理论分析，借鉴热畸变数，通过缩比实验，开展了波长在1000nm左右的连续高能激光水面大气传输热晕效应实验研究，其实验结果为激光水面大气传输规律的深入研究提供了很好的实验依据。
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强激光在大气中传输时，大气吸收强激光能量积累到一定程度产生的热晕效应会导致光斑的畸变。影响热晕的主要因素是大气对激光的吸收特性、系统及目标的运动速度和传输光路上的风速分布。均匀光路上，对于准直传输的光束，热晕的强度可由Bradley-Hermann热畸变数描述：
$ N=\frac{4 \sqrt{2}\left|\frac{\partial n}{\partial T}\right| k \alpha P_{z}}{\rho c_{p} v D} $
(1) 式中，|∂n/∂T| =Cn(λ)P(z)/T2(z)为折射率n温度T梯度，Cn(λ)表示大气折射率结构常数, λ为波长，k为波数，α为大气吸收系数，P为发射功率，z为传输距离，D为发射口径，v为光路上的风速，ρ为大气密度，cp为大气比热容。对于聚焦传输的情况，光斑尺度随传输而变化，可以采用沿光路的积分进行计算。
对于输出波长为1.064μm的固体激光，目前国内尚缺乏对其大气吸收和散射特性的确切研究数据，因此将主要以参考资料数据进行推算。采用Hitran数据库计算表明，美国标准大气模式下，水汽对1.064μm激光的吸收系数为5.2×10-5/km。说明水汽对1.064μm激光的吸收很小。气溶胶的吸收和散射较为复杂，与气溶胶的类型、分布等紧密相关。以此对传输1.2km条件下的热晕效应进行计算，在水面风速为0.2m/s的低风速条件下，采用以上系统参数，热畸变数仅约0.16，不会产生明显的热晕效应，如图 1所示。图中, 功率为10kW，光束质量因子为6.7, 口径为0.45m, 水平传输距离为1.2km, 斜距为2km, 大气透过率为70%。
Figure 1. Thermal blooming under conditions of pure turbulence
依据描述热晕效应的热畸变数公式，可以采用缩比系统的热晕效应定标试验，判断典型系统的热晕效应。
对比计算了S0, S1, S2 3套发射系统在不同参量条件下对水平固定目标聚焦传输的热畸变数及到靶光斑特征。3套系统的参量分别为：口径Ф0=6mm、功率P0=7kW、传输距离z0=1km; 口径Ф1=48mm、功率P1=7kW、传输距离z1=3km; 口径Ф2=66mm、功率P2=70kW、传输距离z2=5km。另外，大气消光系数均为0.15/km，自然风速均为0.2m/s。
图 2中给出了在上述条件下计算得到的热畸变数。发现S0, S1, S2 3套发射系统的热畸变数都很接近。通过对7kW高能固体激光小口径发射传输的聚焦特性的定标分析，可判断较高功率、较大口径发射情况下高能固体激光水面传输的热晕效应。
Figure 2. Thermal aberration number of different system parameters
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根据理论分析，采用56mm口径的发射系统直接发射7kW高能固体激光，照射1km距离上的靶标，根据靶上光斑特性验证高功率高能固体激光水面传输热晕特性。实验光路如图 3所示, 图中还展示了理论分析得到的到靶光斑。实验条件为：距离1km、风速小于2m/s、光源功率7kW、发射口径56mm。图 4为理论仿真结果, r0为大气相干长度。
Figure 3. Schematic diagram of experiments
Figure 4. Simulation results of thermal blooming of 7kW high energy laser with small diameter
图 5和图 6是实验中靶点纤维板上典型光斑，图 7是测试靶上的光斑。如图 5所示，虚线圆中物体是挂在测试靶机架上的一个小挂牌，从其悬挂的形态可以看出此时的风速极低。比较图 4和图 7的理论仿真结果、实验结果，在实验选择的参数情况下，实验与理论分析得到一致的结论，即该功率、发射口径和传输路径条件下，1000nm附近的高能激光水面传输没有明显的热晕效应。
Figure 5. Laser spot on the target board
Figure 6. Laser spot on the target board with successive 3 frames
Figure 7. Laser spot on the focal plane of detector
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实验结果表明，采用56mm口径直接发射7kW高能固体激光，激光水面传输1km后未发现明显的热晕效应。据此实验结果，通过定标分析，可判断较高功率、较大口径发射情况下高能固体激光水面传输的热晕效应。
感谢庞淼等同事给予的实验支持。
近红外激光水面传输热晕效应缩比实验研究
Scaled experiments on thermal blooming of shortwave infrared laser propagation through water surface
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摘要: 为了验证近红外激光在水面大气传输时的热晕效应，采用缩比实验方法，克服了大口径和高功率系统复杂、实验成本高等实际问题，以理论分析为基础设计了高效的实验方案，对1000nm左右的激光水面大气传输热晕效应进行了实验研究，取得了重要的外场实验数据。结果表明，在选择合适的功率和发射口径情况下，1000nm左右的高能激光水面传输热晕效应可忽略。这一结果对大口径和高功率激光系统设计是有帮助的。Abstract: To verify the thermal blooming effect while high energy laser propagates through the atmosphere above the water surface, an innovative method of scaled experiment was applied to overcome the difficult of complexity and expensiveness of high energy laser system with big aperture. One effective experimental method of laser propagation through water surface was designed based on theoretical analysis. The wavelength of laser is about 1000nm. The experimental results show that: The thermal blooming could be ignored while choosing suitable laser power and beam diameter. And the results are also helpful for the design of high energy laser system with big aperture.
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Key words:
- laser technique /
- laser propagation /
- water surface /
- thermal blooming /
- scaled experiments /
- high energy laser
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Figure 4. Simulation results of thermal blooming of 7kW high energy laser with small diameter
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