Electromagnetic Wave Propagation in Turbulence, Second

Excerpt

The first edition was published by Springer-Verlag. This edition corrects typographical errors in that edition. The treatment of tilt of uncollimated beams was incorrect in Sections 4.5, and 4.6 because a γ that should have multiplied the diameter was missing. It was pointed out by Jan Herrmann that it was necessary to use the local tilt in these sections.

As pointed out by Byron Zollars, there were some internal inconsistencies with 2π factors in the development of the general formula for variance due to turbulence. This affected some intermediate formulas in Chapters 2 and 3.

Since the propagation of focused beams has become more important, this case has been treated more carefully and extensively.

The derivation of the basic equations for variance and the removal of Zernike terms is developed more carefully.

Many problems can be solved by using the filter functions for variance. For more complicated problems one needs to start with the filter functions for phase or log-amplitude and develop the variance filter functions from these. Several examples on how to do this are illustrated.

Computer algebra programs have become more powerful and many of the integrals can now be solved with these programs. Solving these problems by hand is time consuming and error prone. Having these programs to do this part of the analysis is very helpful.

Typically, one is interested in the Strehl ratio. Analytic solutions are obtained for the variances. The approximations for the Strehl ratio using the phase variance do not give accurate results for many cases of interest. The use of filter functions in the structure function is elaborated in this edition. The problem of finding the Strehl ratio when the structure function is a function of aperture position is addressed. Examples of solving for the Strehl ratio numerically are given.

Chapter 6 of the original book discussed other uses for Mellin transforms. This chapter was not needed for the development of the subsequent chapters. Since I have nothing new to add on this subject, the chapter was eliminated because of the additional topics that were addressed.

I want to thank Ronald Parenti who I have worked with on turbulence problems for over 30 years. Our recent collaboration with Professors Larry Andrews and Ronald Philips has been very productive.

Recent computer code results indicate that the calculation of the scintillation for finite beams based on Rytov theory is in error. The beam wave theory predicts a dip in the scintillation index for Fresnel number around unity. Code results predict a smaller dip. Apparently, the perturbation theory that starts with a diffraction-limited beam on axis is incorrect. In the region of error the tilt can be comparable to the beam diameter. In addition, the focus term caused by turbulence causes a change in beam size, which violates the diffraction-limited assumption. Various authors have corrected the Rytov scintillation by separately including the effects of jitter and beam spreading.

I want to thank Seth Trotz for solving the many problems encountered in converting this document into LATEX2ε. Also, I want to thank Eric P. Magee and his students for pointing out errors in the draft copy of this edition.

Beth Huetter of SPIE helped to correct errors and produce a uniform format.

This work was sponsored by the Department of the Air Force under Air Force Contract FA8721-05-C-0002. Opinions, interpretations, conclusions, and recommendations are those of the author and are not necessarily endorsed by the United States Government.

Richard Sasiela

February, 2007

Lexington, Massachusetts