laser beam propagation through random media Chapter2
需积分: 46 82 浏览量
2015-07-03
10:46:16
上传
评论
收藏 181KB PDF 举报
Chapter 2
Random Processes and Random Fields
2.1 Introduction . . ................................................. 36
2.2 Probabilistic Description of Random Process ........................ 37
2.2.1 First- and second-order statistics . ........................... 37
2.2.2 Stationary random process ................................. 38
2.3 Ensemble Averages . . . .......................................... 38
2.3.1 Autocorrelation and autocovariance functions .................. 38
2.3.2 Structure functions ....................................... 40
2.3.3 Basic properties .......................................... 40
2.4 Time Averages and Ergodicity . . .................................. 41
2.5 Power Spectral Density Functions ................................. 42
2.5.1 Riemann-Stieltjes integral .................................. 43
2.6 Random Fields ................................................. 45
2.6.1 Spatial covariance function ................................. 45
2.6.2 One-dimensional spatial power spectrum . . .................... 46
2.6.3 Three-dimensional spatial power spectrum .................... 46
2.6.4 Structure function ........................................ 48
2.7 Summary and Discussion ........................................ 49
2.8 Worked Examples .............................................. 51
Problems ..................................................... 53
References . . . ................................................. 56
Overview: Because the open channel through which we propagate electro-
magnetic radiation is often considered a turbulent medium, we present a
brief review in this chapter of the main ideas associated with a random
field, which in general is a function of a vector spatial variable R and time
t. To begin, however, we start with the somewhat simpler concept of a
random process and then present a parallel treatment for a random field.
Fundamental in the study of random processes is the introduction of
ensemble averages, which are used to formulate mean values, correlation
functions, and covariance functions. The development of these statistics is
greatly simplified for a stationary process, which means that all statistics
only depend on time differences and not the specific time origin. From
a practical point of view, however, we usually consider just the weaker
35
剩余21页未读，继续阅读
资源评论
