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 imagedistortion is due to refraction by index variations in the atmosphere, deflecting light as ittravels from the object to the observer. These refractive anomalies are produced by thermalexpansion which drives convective cells and produces turbulence in the atmosphere. The turbulentatmosphere contains refractive anomalies on many scales which can bedescribed 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 byinterference effects. The aim of this project is to understand how a laser beam distorts as itpropagates 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 ionosphericpropagation, scattering of radar by rain and the study of Alfven waves in astrophysics. Phasescreen studies have been applied to medical imaging and ultrasound scans. Work on this topicmay 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 PCrunning 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 Kolmogorovdistributions);
- 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 phasescreens 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 opticMonte-Carlo techniques. Here the phase screens can be used to generate deflection angles whichwill affect the direction and density of these rays. A comparison between these incoherent effectswith the field propagation results will help to identify the importance of the coherent properties ofthe beam. The ray optic problem could be included or offered as a second mini-project which canrun 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 scienceand 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 alreadyavailable. 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 theproject. It is anticipated that the student will have read this chapter and other supporting informationprior to the start of the project. The Ridley and Jakeman book can be borrowed from the Physicsdepartment. The latest understanding of laser-retinal damage and the effects of image distortion are summarised in publications by Milsom, Till and Rowlands.
References
- “Modeling fluctuations in scattered waves”, E Jakeman and K D Ridley, Taylor and Francis, 2006
- “Lasers”, A E Siegman University Science Books 1986
- Till et al, “A new model for laser induced damage in the retina”, Bull. Math. Biol., 65, 731 – 746 (2003)
- Milsom et al, “The effect of ocular aberrations on retinal laser damage thresholds in the human eye”, Health Physics, 91, 20 – 28 (2006