Speckle Phenomena in Optics: Theory and Applications |mdf u=
kp!(e0n
Joseph W. Goodman Yt_t>
.b!HEi<F
Contents E@l@f
1 Origins and Manifestations of Speckle 1 Zs;c0T">
1.1 General Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 +# !?+'A
1.2 Intuitive Explanation of the Cause of Speckle . . . . . . . . . . . . . . . . . . . . . . . . . 2 X4Uy3 TV>
1.3 Some Mathematical Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 v}z^M_eFm
2 Random Phasor Sums 7 X'%BS
2.1 First and Second Moments of the Real and Imaginary Parts of the Resultant Phasor . . . . . 8 >}C:EnECy
2.2 Random Walk with a Large Number of Independent Steps . . . . . . . . . . . . . . . . . . 9 muBl~6_mb2
2.3 Random Phasor Sum Plus a Known Phasor . . . . . . . . . . . . . . . . . . . . . . . . . . 12 `r}a:w-
2.4 Sums of Random Phasor Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 .vIRz-S
2.5 Random Phasor Sums with a Finite Number of Equal-Length Components . . . . . . . . . 16 vS:=%@c>ta
2.6 Random Phasor Sums with a Nonuniform Distribution of Phases . . . . . . . . . . . . . . . 17 qC=ZH#
3 First-Order Statistical Properties of Optical Speckle 23 Z^J)]UL/
3.1 Definition of Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 (Hmh b}H
3.2 First-Order Statistics of the Intensity and Phase . . . . . . . . . . . . . . . . . . . . . . . . 24 vDR>
Q&/K
3.2.1 Large Number of Random Phasors . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 W>,D$
3.2.2 Constant Phasor plus a Random Phasor Sum . . . . . . . . . . . . . . . . . . . . . 27 JE@3 UXg
3.2.3 Finite Number of Equal-Length Phasors . . . . . . . . . . . . . . . . . . . . . . . . 31 j xq89x
3.3 Sums of Speckle Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 !wKNYe
3.3.1 Sums on an Amplitude Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 8{7'w|/;.{
3.3.2 Sum of Two Independent Speckle Intensities . . . . . . . . . . . . . . . . . . . . . 34 Fa </
3.3.3 Sum of N Independent Speckle Intensities . . . . . . . . . . . . . . . . . . . . . . 37 JuRWR0@`
3.3.4 Sums of Correlated Speckle Intensities . . . . . . . . . . . . . . . . . . . . . . . . 40 hu}uc&N)iE
3.4 Partially Polarized Speckle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 y.gNjc
3.5 Partially Developed Speckle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 @ kba^z
3.6 Speckled Speckle, or Compound Speckle Statistics . . . . . . . . . . . . . . . . . . . . . . 47 0&Iu+hv
3.6.1 Speckle Driven by a Negative Exponential Intensity Distribution . . . . . . . . . . . 48 eSW}H_3
3.6.2 Speckle Driven by a Gamma Intensity Distribution . . . . . . . . . . . . . . . . . . 50 <K/iX%b?
3.6.3 Sums of Independent Speckle Patterns Driven by a Gamma Intensity Distribution . . 51 9`@}KnvB?
4 Higher-Order Statistical Properties of Optical Speckle 55 &4M,)Q (
4.1 Multivariate Gaussian Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 qA25P<