Laser retinal hazard assessment after beam propagation through a turbulent
atmosphere
Supervisor-Professor George Rowlands
The project involves:
● Theoretical analysis
● Generating data by simulation
● Analysis of data
The project could run:
● March – June 2009
● June – September 2009
Introduction
Inadvertent viewing of laser radiation is a well known hazard and can cause serious
retinal injury with permanent loss of visual function. For specified laser power/pulse
energy and beam divergence, laser safety standards (such as ANSI/Z136) permit the
calculation of ocular hazard distances. These calculations are predicated on the
assumption that of Gaussian laser beam profiles. This assumption is adequate for
laboratory based lasers but can be grossly incorrect when a laser beam propagates
through a turbulent atmosphere. Safety standards include corrections to allow for
turbulence but they are empirical and possibly incorrect.
Atmospheric turbulence is a commonly observed phenomenon. Heat haze around
distant objects is often seen on summer days. This image distortion is due to
refraction by index variations in the atmosphere, deflecting light as it travels from the
object to the observer. These refractive anomalies are produced by thermal expansion
which drives convective cells and produces turbulence in the atmosphere. The
turbulent atmosphere contains refractive anomalies on many scales which can be
described either in terms of autocorrelation functions or power spectra (Jakeman and
Ridley 2006).
When coherent light from a laser propagates through the atmosphere the situation is
complicated by interference effects. The aim of this project is to understand how a
laser beam distorts as it propagates through the atmosphere using both phase screen
and statistical approaches and to quantify what implications these distortions have for
the retinal hazard of the laser beam.
Novelty
Propagation through turbulence arises in many branches of physics, including
ionospheric propagation, scattering of radar by rain and the study of Alfven waves in
astrophysics. Phase screen studies have been applied to medical imaging and
ultrasound scans. Work on this topic may have impact in each of these areas but the
primary impact will be to provide grounds to justify or amend current laser exposure
guidelines appropriate to atmospheric turbulence of varying degrees of severity.
Research Objectives
The project can be broken down into several sub-tasks and will depend on the
availability of a PC running Matlab. An FFT propagation routine written using
Matlab is available as are algorithms to estimate the likelihood of laser retinal
damage. Tasks include:
 understanding the origin of turbulence and its description in terms of
power spectra and Cn2;
 the generation of phase screens with known statistics (eg. von Karman or
Kolmogorov distributions);
 using fast Fourier transform techniques;
 propagation of a laser mode through a series of phase screens;
 generating representative far and near field patterns for various levels of
turbulence;
 generating retinal point spread functions;
 ensemble studies - generating intensity distributions and examining how
these quantities vary as the number of phase screens increases;
 examining how the intensity distribution and its statistics vary with
propagation distance.
Some of the incoherent aspects of Gaussian beam propagation can be modelled using
ray optic Monte-Carlo techniques. Here the phase screens can be used to generate
deflection angles which will affect the direction and density of these rays. A
comparison between these incoherent effects with the field propagation results will
help to identify the importance of the coherent properties of the beam. The ray optic
problem could be included or offered as a second mini-project which can run in
parallel.
Techniques Required
● Statistical
analysis-Moments, Gaussian random variables;
● Analytical and numerical solution of PDE's;
● Knowledge of discrete Fourier transforms, aliasing, Nyquist;
● Knowledge of Matlab or similar package;
● Optics/Electromagnetism;
● Understanding of power spectra and autocorrelation functions;
● Some knowledge of the biophysics of laser-retinal tissue interaction.
Exploitation and Spin-off
This work is directly relevant to hazard assessment of laser devices which is being
studied at the Defence science and technology laboratory (Dstl). It is anticipated that
the techniques developed will inform and amend national and international laser safet
standards.
Funding and Resources
The student will require a copy of Matlab and will make use of propagation routines
and algorithms that are already available. Extra supervision is available from Dr
Philip Milsom and Stephen Till, both of Dstl.
Background reading
The techniques described in chapter 14 of Ridley and Jakeman (2006) are directly
relevant to the project. It is anticipated that the student will have read this chapter and
other supporting information prior to the start of the project. The Ridley and Jakeman
book can be borrowed from the Physics department. The latest understanding of
laser-retinal damage and the effects of image distortion are summarised in
publications by Milsom, Till and Rowlands.
References
1. “Modeling fluctuations in scattered waves”, E Jakeman and K D Ridley, Taylor
and Francis, 2006
2. “Lasers”, A E Siegman University Science Books 1986
3. Till et al, “A new model for laser induced damage in the retina”, Bull. Math. Biol.,
65, 731 – 746 (2003)
4. Milsom et al, “The effect of ocular aberrations on retinal laser damage thresholds
in the human eye”, Health Physics, 91, 20 – 28 (2006