Based on the fractal characteristics of turbulence-distorted wavefront, a new algorithm for generating a very long
rectangular turbulent phase screen is proposed. The phase structure function of generated phase screens can be very well
compared to the theoretical one. In comparison to existing approaches, the present algorithm shows obvious advantages.
Multiple phase screen (PS) method is typically used in numerical simulations of light propagation through a turbulent atmosphere and an adaptive optics (AO) system for phase compensation. One of key problems in it is generation of turbulent PS for describing the turbulent atmosphere. The covariance approach is a relatively new approach for generating PS. In this paper, the covariance approach is used to generate turbulent PS and a preliminary numerical simulation investigation on this approach and its generated PS is carried out. We propose to use three methods to evaluate the generated PS in a combining way. It is found that a comparison of the phase structure function of generated PS with the theoretical one is not enough and often inefficient. By contrast, a comparison of open loop and close loop laser propagation results by using generated PS can give a deeper insight. Open loop and close loop results by using PS generated by covariance approach are obtained and compared with those by using PS generated by spectral approach for the first time. It is shown that PS generated by covariance approach includes more abundant frequency components and these components have obvious influences on light propagation through a turbulent media.
In this paper, the theoretical base of the covariance approach for generating random phase screens is analyzed, and corresponding computer program is compiled. Preliminary numerical simulation investigation of this new approach is carried out. We propose to use three methods to evaluate the generated phase screens in a combining way. It is found that a comparison of the phase structure function of generated phase screens with the theoretical one is not enough and often inefficient. Open loop results and close loop results by using phase screens generated by the covariance approach are obtained and compared with those by using phase screens generated by the spectral approach for the first time within our knowledge. It is shown that the phase screens generated by covariance approach include more abundant frequency components than those generated by the spectral approach and these frequency components have obvious influences on the open loop results and the close loop results.
It is well-known that cone effect or focus anisoplanatism is produced by the limited distance of a laser guide star (LGS) which is created within the Earth atmosphere and consequently located at a finite distance from the observer. In this paper, the cone effect of the LGS for different vertical profiles of the refractive index structure constant is numerically investigated by using a revised computer program of atmospheric propagation of optical wave and an adaptive optics (AO) system including dynamic control process. According to the practice, the overall tilt for the tilt-correction mirror is obtained from a natural star and the aberrated wavefront for phase correction of the deformable mirror is obtained from a LGS in our numerical simulation. It is surprisingly found that the effect of altitude of the LGS on the AO phase compensation effectiveness by using the commonly-available vertical profiles of C2n and the lateral wind speed in the atmosphere is relatively weak, and the cone effect for some C2n profiles is even negligible. It is found that the cone effect does not have obvious relationship with the turbulence strength, however, it depends on the vertical distribution profile of apparently. On the other hand, the cone effect depends on the vertical distribution of the lateral wind speed as well. In comparison to a longer wavelength, the cone effect becomes more obvious in the case of a shorter wavelength. In all cases concerned in this paper, an AO system by using a sodium guide star has almost same phase compensation effectiveness as that by using the astronomical target itself as a beacon. Effect of dynamic control process in an AO system on the cone effect is studied in this paper for the first time within our knowledge.
So-called cone effect or focus anisoplanatism is produced by the limited distance of a laser guide star (LGS) which is created within the Earth atmosphere and consequently located at a finite distance from the observer. We believe this is the first time to investigate the cone effect of the LGS by means of a pure numerical simulation. In this paper, the cone effect of the LGS for different vertical profiles of the refractive index structure constant C2n is numerically investigated by using a revised computer program of atmospheric propagation of optical wave and an adaptive optics (AO) system including dynamic control process. It is surprisingly found that the effect of altitudes of the LGS on the AO phase compensation effectiveness by using the commonly-available vertical profiles of C2n and the lateral wind speed in the atmosphere is relatively weak, and the cone effect for some C2n profiles is even negligible. It is found that the cone effect seems not have obvious relationship with the turbulence strength, however, it depends on the vertical distribution profile of C2n apparently. On the other hand, the cone effect depends on the vertical distribution of the lateral wind speed as well. The cone effect becomes more obvious as the zenith angle increases. In comparison to a near infrared wavelength, the cone effect becomes larger in the case of the visible wavelength. In all cases concerned in this paper, an AO system by using a sodium guide star has almost same phase compensation effectiveness as that by using the astronomical target itself as a beacon.
KEYWORDS: Chemical oxygen iodine lasers, Chemical lasers, Oxygen, Iodine, Chemical analysis, Laser resonators, Performance modeling, Energy efficiency, Resonators, Mirrors
A modified simplified rate equation (RE) model of flowing chemical oxygen-iodine laser (COIL), which is adapted to both the condition of homogeneous broadening and inhomogeneous broadening being of importance and the condition of inhomogeneous broadening being predominant, is presented for performance analyses of a COIL. By using the Voigt profile function and the gain-equal-loss approximation, a gain expression has been deduced from the rate equations of upper and lower level laser species. This gain expression is adapted to the conditions of very low gas pressure up to quite high pressure and can deal with the condition of lasing frequency being not equal to the central one of spectral profile. The expressions of output power and extraction efficiency in a flowing COIL can be obtained by solving the coupling equations of the deduced gain expression and the energy equation which expresses the complete transformation of the energy stored in singlet delta state oxygen into laser energy. By using these expressions, the RotoCOIL experiment is simulated, and obtained results agree well with experiment data. Effects of various adjustable parameters on the performances of COIL are also presented.
KEYWORDS: Chemical lasers, Oxygen, Iodine, Chemical oxygen iodine lasers, Performance modeling, Laser resonators, Mirrors, Particles, Data modeling, Gas lasers
The effect of the translational nonequilibrium on performance modeling of flowing chemical oxygen-iodine lasers (COIL) is emphasized in this paper. The spectral line broadening (SLB) model is a basic factor for predicting the performances of flowing COIL. The Voigt profile function is a well-known SLB model and is usually utilized. In the case of gas pressure in laser cavity less than 5 torr, a low pressure limit expression of the Voigt profile function is used. These two SLB models imply that all lasing particles can interact with monochromatic laser radiation. Basically, the inhomogeneous broadening effects are not considered in these two SLB models and they cannot predict the spectral content. The latter requires consideration of finite translational relaxation rate. Unfortunately, it is rather difficult to solve simultaneously the Navier-Stokes (NS) equations and the conservation equations of the number of lasing particles per unit volume and per unit frequency interval. In the operating condition of flowing COIL, it is possible to obtain a perturbational solution of the conservational equations for lasing particles and deduce a new relation between the gain and the optical intensity, i.e., a new gain-saturation relation. By coupling the gain-saturation relation with other governing equations (such as the NS equations, chemical reaction equations and the optical model of gain-equal-loss), we have numerically calculated the performances of flowing COIL. The present results are compared with those obtained by the common rate-equation (RE) model, in which the Voigt profile function and its low pressure limit expression are used. The difference of different model’s results is great. For instance, in the case of lasing frequency coinciding with the central frequency of line profile and very low gas pressure, the gain saturation relation of the present model is quite different with that of the RE model.
It is well known that noise and detection error can affect the performances of an adaptive optics (AO) system. Effects of noise and detection error on the phase compensation effectiveness in a dynamic AO system are investigated by means of a pure numerical simulation in this paper. A theoretical model for numerically simulating effects of noise and detection error in a static AO system and a corresponding computer program were presented in a previous article. A numerical simulation of effects of noise and detection error is combined with our previous numeral simulation of a dynamic AO system in this paper and a corresponding computer program has been compiled. Effects of detection error, readout noise and photon noise are included and investigated by a numerical simulation for finding the preferred working conditions and the best performances in a practical dynamic AO system. An approximate model is presented as well. Under many practical conditions such approximate model is a good alternative to the more accurate one. A simple algorithm which can be used for reducing the effect ofnoise is presented as well. When signal to noise ratio is very low, such method can be used to improve the performances of a dynamic AO system.
Phase compensation effectiveness and long time period working stability are two most important performances of an adaptive optics (AO) system. Effects of reconstruction matrix and controller coefficients on these performances are investigated by means of a pure numerical simulation in this paper. A new modified reconstruction matrix is proposed and compared with other existing matrixes in practical application. It is shown that the recently proposed reconstruction matrix can produce better phase compensation results and much better long time period working stability in an AO system. Different reconstruction matrix can greatly affect the long time period working stability under certain conditions. Under some conditions, an AO system with a reconstruction matrix can work stably in a quite long time period, but a working instability can occur in a super-long time period. It is found that the controller coefficients have even greater effect on the long time period working stability in an AO system. The controller coefficient ?1=1.00 is a marginally stable (sub-stable) condition for an AO system. When ?1<1, the long time period working stability of an AO system is much improved.
The dynamic control process in an adaptive optics (AO) system is the third important factor to affect the performances of the AO system. A numerical simulation of the dynamic control process in an AO system is carried out for the first time to complete a comprehensive numerical simulation of an AO system. By means of the numerical simulation the long-exposure Strehl ratio and other useful metrics for evaluating the performances of an AO system can be obtained. In comparison to the theoretical analyses of automatic control theory, a numerical simulation of the dynamic control process in an AO system is advantageous. The frequency response characteristics are closely related to the dynamic control performance of an AO system. The bandwidth, phase margin and gain margin which are very important parameters for experimenters can be obtained conveniently from a numerical simulation of the frequency response characteristics. A numerical simulation of the frequency response characteristics in an AO system is presented in this paper for the first time. The numerical simulation results agree with the experimental data excellently. The simulation computational results of frequency response by using composite input of multiple frequencies compare to the single-frequency simulation results very well and can be used to determine the practical parameters of bandwidth and margins. The performances of an AO system can be effectively investigated by means of a combination of a numerical simulation of frequency response characteristics with that of the dynamic control process.
In an adaptive optics (AO) system, noise and detection error can produce errors in the slope measurement of a Hartmann-Shack (HS) wavefront sensor and have further effects on the performance of the AO System. The noise in an AO system can be divided into the readout noise and the photon noise. The detection error in an AO system results from the discrete sampling by using number-limited CCD pixels in the HS sensor and the deadspace between the CCD pixels. A theoretical model for numerically simulating the effects of noise and detection error is presented and a corresponding computer program has been compiled, which is combined with our existing program of numerical simulation of the laser propagation in a turbulent media and an AO system in a stationary state. Taking the long-exposure Strehl ratio and the percentage relative error of the centroid slopes for each subaperture as two evaluation parameters, numerical simulation investigations of the effects of detection error (including the limited sampling density and the deadspace), readout noise and photon noise on a practical AO system have been carried out. Statistics method and formulation method are used to evaluate the effects of readout noise and photon noise in the numerical simulation. It is shown that there is no significant difference between results by using these two methods when the signal to noise ratio (SNR) is larger. However, as SNR gets smaller, the formulation method becomes less accurate than the statistics method. The numerical results are very useful for the design of a practical AO system.
A comprehensive model of laser propagation in atmosphere and all portions of an adaptive optics (AO) system for phase compensation is presented and the corresponding computer program is coupled. By using the direct wavefront gradient control method to reconstruct the wavefront phase and utilizing the long-exposure Strehl ratio as the evaluation parameter, the numerical simulation of an AO system in static state with atmospheric propagation of laser beam is carried out. It is found that on certain conditions the phase-screen which describes turbulence in the atmosphere might not be isotropic. The numerical experiments show that the computational results in imaging of lenses by means of the fast Fourier transform (FFT) method agree excellently with those by means of integration method. However, the computer time of FFT method is one order of magnitude less than that of integration method. We present `phase tailoring' of the calculated phase to solve the problem that variance of the calculated residual phase does not correspond to the correction effectiveness of an AO system. It is found for the first time that for a constant delay time of the AO system, when the lateral wind speed exceeds a threshold, the compensation effectiveness of an AO system is better than that of complete phase conjugation. It indicates that a better compensation capability of an AO system does not mean a better correction effectiveness.
Considering time-delay and finite spatial bandwidth of an adaptive optics system, which is used in astronomical observation, the influence of transverse wind along the light propagation path on the performance of the system has been analyzed in this article, and the related analytical expressions have been obtained. The results have been compared with those obtained under open-loop operation, and those obtained when there is an ideal adaptive optics system, i.e., its spatial bandwidth is infinite. It is shown that the transverse wind has serious influence on a system with large diameter when the time delay is long and its spatial bandwidth is high. In some conditions, the performance of a system with higher spatial bandwidth is worse than that of a system with lower spatial bandwidth. This phenomenon has been analyzed. Its possible cause also has been presented in this article.
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