Diffractive Anaylsis And Metrics For Long-distance Focusing Of Laser Beam

Focusing the high power laser beam on a remote target for a spot with high energy density is functional in the fields of national defense and industry. With the purpose of developing the beam focusing system, many procedures, such as the laser beam transmitter design, the simulation of field propagation and the feedback of the beam focusing quality, has to be finished. In these procedures, there are many tasks about modeling, parameter selection and structure design to deal with. Simulation is a consume-saving method for the problems. Diffractive theory is one of the basic methods to deal with modern optical engineering problem, and it is accurate enough to simulate laser beam propagation through a long distance. In this thesis, an optimized beam propagation algorithm is proposed to simulate laser beam focusing problem. The modal coefficients of the partially coherent laser beam are discussed in detail. Combining with the specific design, the effects caused by the system parameters’ change is analyzed with theory and experiment. Besides, beam quality metrics based on the speckle field scattered from the target are proposed to feedback the focusing spot size accurately. In brief, the thesis constructs a closed loop of simulation by covering the issues of laser transmitting, propagation and feedback metrics. The main works studied in this thesis are illustrated briefly as follows:1. Based on the scalar diffraction theory, laser beam propagation theory and laser beam quality description, beam propagation algorithms, which can manage different field distributions, coherence and propagation conditions, are provided. Firstly, in order to simulate the beam propagation through first-order systems, wide-window angular spectrum(WWAS) method is proposed applying the Collins formula and chirp Fourier transform(CFT). The application of CFT separates the input, spatial frequency and output fields, as a result increasing the size of the computation window would not cause calculation burdens and the SNR decrease simulating long distance propagation is inhibited. Besides, the separation of the three fields makes the sampling process more flexible. The sampling conditions of WWAS algorithm are then given by SNR analysis, and the comparison among different angular spectrum algorithms are discussed in the free space propagation. As a result of this comparison the advantages of the WWAS method in this thesis are pointed out. Secondly, a linear equations method is proposed to calculate the complete modal content of the partially coherent laser beam using only the intensity information. This method could give not only the incoherent expansion coefficients of the modal decomposition but also the cross-correlation expansion coefficients using the intensity profiles in several planes of finite distance along the propagation direction. A simulation is also presented to verify the validity of this theory. Using the modal coefficients distribution, an algorithm for simulating partially coherent beam propagation is proposed, which gives consideration to both the effectiveness of FFT and the simulation accuracy.2. After the discussions about the beam propagation algorithms, the property of long-distance focusing of laser beam is analyzed. The laser beam focusing system is designed using Zemax program, and then the geometry parameters, laser beam parameters, focusing shifts and focusing curve are calculated. The diffraction loss and the energy change of focusing spot are investigated using beam propagation algorithm, and the results are compared with the outcomes assessed by the generalized M2 factor, which shows the function of generalized M2 factor in assessment of the apodized optical systems. The issues concerning tolerance aberration and focusing error are processed by applying Zemax and Matlab simultaneously, which means that Zemax provides the aberration coefficients at the exit pupil plane for the beam propagation algorithm. After getting the simulated focusing field distribution, analysis can be done to show whether the tolerance range is reasonable or not. Then the intensity distribution and spot patterns are measured experimentally, which proves the correctness of the simulation. Besides, laser beam propagation through atmospheric turbulence is discussed theoretically, and the change of M2 factor after propagation is studied. Finally, the balance between beam quality and atmospheric turbulence is concluded when there are no adaptive compensations.3. The study of the beam quality metrics based on the speckle field scattered from a remote target is conducted. For static or slowly moving target, two speckle metrics are proposed to feed back the spot size character: The clipped speckle autocorrelation metric(CSAM) is calculated using the autocorrelation function, which is proved to increase with the spot size. The clipped speckle edge integral(CSEI) metric is the other speckle metric, which is obtained by summing up the edges of the clipped speckle image, and this metric becomes smaller when the spot size increases. The thesis simulates how the receiving system parameters, the target roughness and the finite sample effect affect the metric accuracy, and implements experiments to prove the ability to characterize the focusing spot size of the two speckle metrics. For fast moving target, two detectors cross-correlation method is proposed to assess the spot size on a remote target. In this thesis, the model for the two detectors cross-correlation method is programmed by Matlab to examine its availability, and then the accuracy of this method is simulated from the aspects of two detector distance, sampling number and so on. Finally, the limitations of this method to detect the spot size are demonstrated.