For the two-point spherical wave structure function, we propose a modified quadratic approximation, which can be used to investigate the second-order coherence properties (such as the beam spreading, average intensity, cross-spectral density function) of partially coherent beams through the turbulent atmosphere. We prove that the modified quadratic approximation, different from usual one, can be used to study the effects of inner and outer scales of turbulence, and is better than the usual one for a less coherent beam or for a very strong turbulence. A more accurately analytical expression for average intensity of Gaussian-Schell model beams is derived based on the modified quadratic approximation. These results are also illustrated by investigating the average intensity for Gaussian-Schell model beams in turbulence.
The continuous wavelet transform (CWT) introduces an expandable spatial and frequency window which can overcome the inferiority of localization characteristic in Fourier transform and windowed Fourier transform. The CWT method is widely applied in the non-stationary signal analysis field including optical 3D shape reconstruction with remarkable performance. In optical 3D surface measurement, the performance of CWT for optical fringe pattern phase reconstruction usually depends on the choice of wavelet function. A large kind of wavelet functions of CWT, such as Mexican Hat wavelet, Morlet wavelet, DOG wavelet, Gabor wavelet and so on, can be generated from Gauss wavelet function. However, so far, application of the Gauss wavelet transform (GWT) method (i.e. CWT with Gauss wavelet function) in optical profilometry is few reported. In this paper, the method using GWT for optical fringe pattern phase reconstruction is presented first and the comparisons between real and complex GWT methods are discussed in detail. The examples of numerical simulations are also given and analyzed. The results show that both the real GWT method along with a Hilbert transform and the complex GWT method can realize three-dimensional surface reconstruction; and the performance of reconstruction generally depends on the frequency domain appearance of Gauss wavelet functions. For the case of optical fringe pattern of large phase variation with position, the performance of real GWT is better than that of complex one due to complex Gauss series wavelets existing frequency sidelobes. Finally, the experiments are carried out and the experimental results agree well with our theoretical analysis.
Comparison and analysis for several usual types of atmospheric turbulence simulator are first given in this paper. Considering the Tatarskii spectrum and the conditions of laboratory, secondly, the numerical calculations of the <i>M<sup>2</sup></i> factor and the spatial and angular widths of coherent Gaussian beams in turbulence are performed. Finally, a kind of a hot-wind atmospheric turbulence generator is designed and its characteristics are analyzed. The results show that the turbulence generator is very suitable to use in studying the effects of turbulence on the <i>M<sup>2</sup></i> factor of cw laser beams. Also, the values of both the structure constant of refractive index fluctuations C<sub>n</sub><sup>2</sup> and the inner scale of turbulence required by the generator are still in accordance with those of actual atmospheric turbulence.
Conference Committee Involvement (1)
IPTA14-International Conference on Optoelectronic Technology and Application 2014