Find the maximum permissible exposure mpe for the eye at 30

Question

Part -1:

Problem 1) For the purposes of this coursework we shall make some assumptions:

that it is possible to fire the laser at full power when the fibre is not inside the patient, in other words, the light emitted from the fibre could be accessible.

that there is an interlock to prevent the laser from being fired when there is no fibre attached to it.

that the fibre will not be snapped into two pieces with the light emerging from the broken end of the fibre that is connected to the laser. That is to say, we assume that all the light is emitted from the diffuser.

that the laser is CW.

that at distances more than 5 cm from the centre of the diffuser the light can be considered to have a spherical distribution as though it had come from a spherical source.

Using the data in the article, Your working must be shown for all sections of this question. If possible, you should use Excel or something similar to for this coursework with the working shown clearly in comments.

(1) Find the Maximum Permissible Exposure (MPE) for the eye at 30 cm distance from the fibre tip.

(2) Is the irradiance at this distance hazardous if viewed for the same duration as you used in question (1)?

(3) Bearing in mind that somebody might pick up the fibre and look at it without realising that the laser was firing, is eyewear required?

(4) Laser Safety Advisers often like to consider the situation where the fibre gets broken into two pieces during the treatment and somebody picks up the broken end that is connected to the laser and stares into it. Use EN 207 to specify what eyewear should be used to allow for this situation? For the purposes of this question, you may assume that this is a bare tip fibre producing a Gaussian beam with a numerical aperture (NA) of 0.2.

[By the way, I would be very impressed if anybody can explain the sentence "In the Indigo® system, the laser energy is transported from the lasing medium to the laser fiber through semiconductor integrated circuits with relatively low energy loss".].

Extract from The Evolution of Laser Therapy in the Treatment of Benign Prostatic Hyperplasia.

Part -2:

Question 1

A cuvette of thickness d = 5 mm is illuminated by a collimated beam of light at three wavelengths, λ₁, λ₂ and λ₃, giving measurements of absorbance of A(λ₁) = 0.45, A(λ₂) = 0.39 and A(λ₃) = 0.55. The cuvette contains a mixture of three chromophores, absorber 1, absorber 2 and absorber 3, at different concentrations. Given the data in Table 1 below, find the three concentrations in units of molar.

	λ1	λ2	λ3
absorber 1	0.01	0.38	1.31
absorber 2	1.64	0.70	0.50
absorber 3	0.81	1.04	0.14

Table 1. Specific molar absorption coefficients for three absorbers in rim' molar'.

Question 2:

Consider a cylindrical tube (a model of a blood vessel perhaps) with diameter d = 25 μm carrying a fluid with absorption coefficient μ_a = 0.5 mm^-1. The tube is immersed in a highly scattering medium and is illuminated with very wide illumination so it can reasonably be assumed that the fluence rate is constant across the whole tube. Both the scattering medium and the tube have thermal conductivity k = 0.5 Wm^-1K^-1, mass density ρ = 1060 kgm^-3, and specific heat capacity C_p, = 3700 Jkg^-1K^-1.

If the fluence rate in the tube is Φ = 10 Wmm^-2, and the illumination pulse duration t_p = 10 μs, write down and evaluate an expression for the temperature rise AT in the tube Assume no heat diffusion occurs during the pulse.

Write down symbolic expressions for the heat energy stored per unit length of the tube, and the rate at which the tube is losing heat to its surroundings. Clearly state any assumptions that you make. Using these expressions, arrive at a formula for the thermal relaxation time of the tube.

Was the assumption that there was negligible heat diffusion during the optical heating pulse justified?

Question 3:

Throughout this coursework, we will be considering an active medium that consists of atoms with four energy levels. These energy levels are the ground energy level E₀ and three higher energy levels: E₁ < E₂ < E₃. The laser cavity is depicted below:

1. Consider the case where the only radiative decay in this system occurs between levels E₁ and E₀.

a) Imagine that the active medium is optically pumped by a monochromatic source with a frequency ω_pump = (E₁-E₀)/h. Can a laser be produced in this scenario? Explain your answer.

b) Now imagine that the active medium is optically pumped by a white-light flashlamp. Does this system correspond to a three or a four level laser? Explain your answer.

2. Now consider the case where the only radiative decay is between levels E₂ and E₁. The system is optically pumped by a monochromatic source with a frequency given by ω_pump = (E₁-E₀)/h. In this question, you will need the threshold population inversion, which is given by:

[N₂ -N₁] = ω_c²τ²/Π²c²g(ω_c)(γ + 1/2Lln(1/R₁R₂))

where 12 is the spontaneous rate of decay of the upper laser level and u.), is the central frequency of the radiation field.

a) Does this system now correspond to a three or a four level laser? Explain your answer.

b) If the lineshape function is only affected by natural broadening and given that:

ω_c = (E₂ - E₁)/h = 2 x 10¹⁵ rad s^-1

τ₂ = 10 μs
τ₁ = 100 ps

Calculate the value of g(ω_c).

c) Calculate the threshold population inversion given the values above and in Figure 1.

d) Calculate the energy output of the pump source that is required to achieve the threshold population inversion if ω_pump = 4 x 10¹⁵ rad  s^-1 and only 10% of pump photons are absorbed by the active medium. You may assume that atoms in energy level E₃ always decay via E₂ and that the population density of the lower laser level is negligible.