Adaptive Optics for Reduction of Thermal Blooming Effects by Phase Compensation

: The use of an AO system for the reduction of thermal blooming effects by phase correction of a 1.064-µm laser was studied. The energy concentration of the beam spot in the far-field increased greatly when the adaptive optics system performed in a closed loop. The phase compensation of the AO system was effective for a Bradley– Hermann distortion number of less than 130. The experimental results were in good agreement with the simulation results. This study provides many physical explanations and important conclusions for using adaptive optics to reduce the thermal blooming effect.


Introduction
Heat-induced changes in the optical parameters of a medium leads to changes in radiation propagation of high energy laser (HEL) beams. This change is referred to as "thermal blooming" [1][2][3][4][5][6]. Thermal blooming causes a negative-lens-like optical effect in the atmosphere that blooms energy out of the beam. This phenomenon can defocus, scatter and distort the optical beam [7]. An adaptive optics (AO) system corrects the effects of thermal blooming by applying a positive-lens-like compensation to the HEL beam. In theory, by focusing the HEL beam, this should override the blooming.
Bradley and Herrmann investigated the use of AO systems to mitigate nonlinear optical effects induced by thermal blooming. They demonstrated an improvement in the system performance with phase compensation of thermal blooming [8]. Since then, several research institutions have studied HEL propagation in the atmosphere and its phase correction, such as MIT Lincoln Laboratory [9][10], Lawrence Livermore National Laboratory [11], and the Air Force Weapons Laboratory [12]. However, there are few experimental reports on the phase compensation of thermal blooming by AO system.
The purpose of this research is to demonstrate the use of an AO system to correct the phase of a collimated Gaussian beam and reduce thermal blooming. The AO system was also used to increase the peak far-field irradiance by correcting the phase of aberrations in the optical system used for the blooming experiments.

Theoretical analysis
The irradiance distribution I (x, y) of a collimated Gaussian beam is expressed as where P is the initial beam power, and D = 2w is the 1/e 2 intensity beam diameter. The phase distortion φB accumulated along the propagation path L and induced by steadystate thermal blooming, which was assumed to be a constant absorption coefficient, α, and a transverse wind speed, V (such as along X-axis positive direction), is given by where nT = dn/dT is the change in refractive index with respect to the temperature of medium at constant pressure, and ρ0, k, and Cp, are the density, wave number and specific heat at constant pressure, respectively [13].
By substituting Eq. (1) into Eq. (2), the blooming phase φGB is obtained as The maximum phase shift is where is the Bradley-Hermann distortion number commonly used as a measure of the strength of thermal blooming [13]. Phase distortion information can be obtained by the Shack-Hartmann wave-front sensor in an open-loop adaptive optics system. Using Eq. (5) to obtain the Bradley-Hermann thermal distortion parameter, ND, of the experiment.

Numerical calculation results and analysis
The thermal blooming effect of laser beams propagating through horizontal atmosphere was studied by performing numerical simulations on Easy-Laser software [14]. In particular, the phase screen simulation method was based on a procedure that replaced a continuous medium of radiation by a sequence of thin screens, simulating distortions acquired by the optical wave through its propagation [15]. Figure 1 shows a simulation of the AO system correcting thermal blooming by applying phase compensations.  For the simulation, we used an AO system that performed phase compensation using a Shack-Hartmann (SH) wave-front sensor (WFS), a tilt mirror (TM), and a deformable mirror (DM) with 127 actuators. Figure 2 shows a schematic of the AO system for phase compensation of the thermal blooming setup. In this scenario, a beacon signal was transmitted from the target plane to the source plane with the effects of current phase screen due to thermal blooming. The phase of the beacon in the source plane was then applied directly to the HEL beam, and the idealized phase compensation process was repeated. Table 1 presents the parameters used in the simulation. In the simulations, the Bradley-Hermann distortion parameter (ND) can be changed by adjusting the laser's power (from 3000 W to 39,000 W). A quantitative assessment of the relative power-in-the-bucket (PIB) was performed to analyze the far-field spot.
The most common metric for gauging the performance of HEL systems is PIB, the power within a circular region in the cross section of the laser beam, which is situated at the laser aimpoint on the target [16].  Then, the magnification of beam quality factor β is used to evaluate the ability of phase compensation of the AO system and reduce the thermal blooming effect. This evaluation method can effectively reduce system aberrations. β is defined as where θREAL-PIB and θIDEAL-PIB are the bucket sizes in far-field with specific powers of real and ideal scenarios, respectively [17]. Since In this equation, βTimes > 1 means that compensation of the AO system influences the thermal blooming effect. The higher the βTimes, the greater the influence.
The different values of βTimes as a function of ND are shown in Fig. 5. atmosphere. The AO system attempts to correct for the increased blooming with even higher positive-lens-like compensation, and the process reinforces itself, ultimately causing failure of the AO system through thermal accumulation.

Experimental results and analysis
It is difficult to setup a full-scale experiment to investigate phase compensation of thermal blooming. Such an experiment would require an HEL system, an AO system robust enough to handle the HEL beam powers needed for thermal blooming, a test range, and a facility large enough to conduct the experiment. Therefore, from the perspective of feasibility, in this experiment, we used CH3CH2OH as the absorption medium and a low-power laser to generate severe thermal blooming. The experimental arrangement is illustrated in Fig. 6. A photograph of the experimental layout is illustrated in Fig. 7 Parameters of the system that were used in the experiment are presented in Table 2. Absorption coefficient of ethanol (cm -1 ) 0.11 [18] The length of the thermal blooming cell (cm) 15 Moving speed of the thermal blooming cell (mm/s) 1-20 Beam diameter in the thermal blooming cell (mm) 8 Layout of deformable mirror with 127 actuators is shown in Fig. 8. It should be noted that the theoretical range of ND that can be generated by a thermal blooming cell in the above scenario is approximately from 37 to 410.
In the experiment, the transverse wind speed, V (from 1mm/s to 20mm/s), was simulated by transversing the platform [19]. A vast difference between the open-and closed-loop operations of the AO system can be observed. Figure 9 shows the results of the experiment with wave-front errors PV/RMS for the AO system's operations for cases where V was 5 mm/s, 10 mm/s and 15 mm/s, respectively.  As shown in Fig. 11, phase compensation of the AO system can greatly increase the energy concentration of the beam spot in the far-field when ND are 82. 18 respectively. Therefore, the effect of phase compensation of an AO system on thermal blooming is significant. Figure 12   When the speed of the mobile platform was low, the thermal blooming effect would generate a large amount of accumulated heat, and the range of phase compensation of the AO system is limited. Therefore, the range of ND generated by the experiments were smaller than those generated by the simulations. Hence, the experimental results are consistent with the simulation results.

Conclusions
In this paper, phase compensation of AO system for thermal blooming reduction is studied through simulation and experiment. In the simulation, the AO system was used to compensate thermal blooming phase distortion by 1.064-μm laser propagating through the horizontal atmosphere. In the experiment, CH3CH2OH was used as the absorption medium instead of horizontal atmosphere, and transverse wind speed was generated by moving the platform carrying CH3CH2OH. Thermal distortion was induced by the low-power laser in the medium. Simulation results show that the closedloop operation of AO can enhance the phase compensation of thermal blooming when ND is approximately 50. When ND is less than 130, the AO system will improve beam quality of the far-field spot. Additionally, experimental results showing beam quality of the far-field was improved, which is consistent with the results obtained numerically.
This research can provide a reference value for engineering applications requiring efficient HEL propagation.

Availability of data and materials
Detail about data has been provided in the manuscript.

Competing interests
The authors declare that they have no competing interests.

Funding
This work was supported by the Chinese Academy of Sciences Innovation Fund [grant number CXJJ-16S022].

Authors' contributions
SYW and XL carried out the theoretical analysis, numerical simulation and participated in the discussion of experimental results. All authors engaged in the idea of the method.
The writing of the manuscript was done by SYW.