Sid 1 (4) Figure 1: optical fiber with acceptance angle.

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1 UNIVERSITETET I LINKÖPING Dept Biomedical Engineering Examination in TBMT36 Biomedical optics Saturday 10 th January Exam hours: to The exam consists of essay questions that should be answered as good as possible. It is an individually written exam and co-operation is not permitted. Write clear and concise. Educational aids: Calculator, Tefyma, Language dictionaries, Handbook of physics, equations in optics (last page added to exam). Write your identification number on every paper. Reports without id are handled as if they were blank and not taken care of. Only one question should be answered on a single A4. Grading: Not pass <25 F C B 5 >39 A Results are available 10 working days after the exam. Good luck! Göran Salerud

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3 You have to explain all equations and variables you are using. If possible use simple drawings to clarify abstract situations or complex visions. Also write down the delimitations you apply. Do not forget to motivate your answers. 1. Glass prisms are often used to bend light in a given direction as well as to bend it back again (retroreflection). The process of refraction in prisms is understood easily with the use of light rays and Snell s law. When light is transported from one medium to another different physical phenomena appears. Light trajectory or path changes are the most common. White light can be separated into different colours using prisms. a. Describe the working principle of a prism how to achieve a colour spectrum from impinging white light. Necessary equations should be covered (2p) b. Are there special requirements for the impinging white light? (1p) c. A glass of unknown index of refraction is shaped in the form of an isosceles prism with an apex angle of 25. In the laboratory, with the help of a laser beam and a prism table, the minimum angle of deviation for this prism is measured carefully to be What is the refractive index of this glass material? (2p) 2. Optical fibres are frequently used in bio-optical applications for either delivering or collecting fluence of light. Using a distributed light source it could be hard to get enough light into the fibre (see figure 1). Derive the accepted light emitting area of the light source at a distance of 5 cm if the fibre core is 125 mm in diameter and the fibre cladding is 20 mm thick. The refractive indexes are 1.5 (core) and 1.38 (cladding) respectively. (2p) Figure 1: optical fiber with acceptance angle. Sid 1 (4)

4 3. When light/photons interact with biological tissue the main process is loss of photon energy. Depending on the strength of the process it will affect the penetration depth, energy delivered and thereby also photobiology effects. In figure 1 the most common chromophores are visualized (except for lipids and cytochrome C). a. How would you explain and motivate the wavelength range named as the therapeutic or diagnostic window. (1p) b. If figure 2 represents the chromophores of the skin how will they contribute to the absorption and scattering properties (coefficients)? (2p) c. How would changes in anatomical and physiological parameters modify this interpretation? (1p) Figure 2: Chromophores in the skin with depicted therapeutic window. 4. A common interacting process between biological tissue and light is the absorption of photon energy. a. Describe with your own words a classical approach to the absorption process using the bilirubin molecule as an example. The answer should relate to the density, absorption coefficient and the size of the molecule. (2p) b. In the visible and near-infrared region of the optical spectrum there are well-documented absorption peaks for oxygenated and de-oxygenated hemoglobin. Suppose you want to calculate the following three parameters: the concentrations of oxyhemoglobin and deoxyhemoglobin, and the relative oxygenation of the blood. At wavelengths 758, 798, and 898 nm, the extinction coefficients for oxygenated hemoglobin are 0.444, 0.702, and mm -1 cm -1 and for de-oxygenated hemoglobin 1.533, 0.702, and mm -1 cm -1, respectively. The total absorption coefficients at these three wavelengths in the tissue can be measured using a time-resolved system as 0.293, and cm -1 respectively. Measuring through the finger with a thickness of 2 cm, calculate the relative oxygenation of the tissue, assuming negligible influence of the absorption of the tissue itself at these three wavelengths. (3p) Sid 2 (4)

5 5. Gustav Mie developed a scattering theory for small water droplets. This theory is also used in the investigation of the scattering properties of living tissue. The fluence decay, due to scattering processes, can be modelled depending on the scattering coefficient, scattering phase function and the anisotropic value. It usually starts with a simplistic model of a single scattering event. The single scattering process/event is often depicted through the scattering phase functions as displayed in figure 3. Figure 3: Scattering phase functions. a. Explain and interpret the phase function for the anisotropy values g=0, g=0.8 and g=0.95, and how they relate to biological structures. Also give examples of their limitations. (3p) b. In a similar way as with the absorption process, try to intuitively describe how intensity is lost in relation to the scattering coefficient, scattering cross section, density and efficiency. (3p) 6. The fluence rate in a cross-section of tissue depends on the optical properties and its concentration. Sketch four different situations (µ a << µ s, µ a < µ s, µ a >> µ s och µ a > µ s and explain and motivate their appereance. As lightsource has been used a pencil beam of coherent light at nm. (4 p) 7. Assume tissue with optical properties µ a and µ s. An optical fibre with an isotropically irradiating distal diffusor tip is inserted in the tissue without causing any bleeding. The power is 100 mw. The light at some distance from the fibre tip is scattered sufficiently many times to be able to be described by diffusion theory. The source S can then be described as a point source with power P [W]: S r, t = δ r P The fluence rate Φ r can be obtained at distance r from the tip utilizing diffusion theory and employing the Green's function times the power of the source. The expression is: Φ r = Pμ!!"" 1 4πμ! Where r = r r e(!!!""!) Sid 3 (4)

6 a. Calculate the fluence rates of the light for two different oxygenation saturation levels at a distance of 3 and 11 mm from the fibre tip, respectively. Use light with a wavelength of 580 nm and 720 nm respectively, see figure 4. Discuss also the two different selections of wavelengths in relation to optical properties. (4p) b. Calculate how much light is absorbed at the same distances from the tip. Provide the units. (1p) Figure 4: Reduced scattering and absorption spectra of tissue for various oxygen saturation. 8. Instead of using diffusion theory, stochastic modelling with Monte Carlo is frequently used to resolve the optical properties in biomedical optics. a. Monte Carlo modelling can use either the forward or inverse light transport modelling. Describe how MC forward and inverse models are used and perform in different situations, depending on the need for prerequisites. (3p) b. Describe the advantages and drawbacks in using Monte Carlo and diffusion theory. (2p) 9. In a tissue where absorption is less dominant and scattering is large the impact of a collimated monochromatic light source give rise to a diffusion process, figure 5, left panel. Light is delivered at an angle θ (45 o ) by a optical fiber (or laser beam). The center of the diffusion process is offset from the point of point of photon entry by Δx. Hence, two measurements (Δx, δ=slope) makes it possible to evaluate µ a, µ s. The resulting reflectance curve along the impact plane is shown in figure 1, right panel. Explain theoretically how absorption, scattering coefficient and diffusion can be obtained in this setup. From the figures calculate the values of µ a and µ s. n=1.33 (5p) Figure 5: Left panel: Fluence image of injected light. Middle panel: schematic diagram. Right Sid 4 (4)

7 panel: resulting reflectance curve in the impact plane (y-axis in log scale). 10. In many biomedical optics applications coherent light sources are used. Michelson interferometer devices can tell the thickness of very thin sheets etc. Coherence and coherent sources are not always easy to understand since one can specify both temporal and spatial coherence. OCT, optical coherence tomography is using intermediate coherence or partial coherent light sources to make cross-sectional scanning of the tissue. a. Explain how it works and why it is not possible to use high coherent light sources in OCT. (2p) b. What are the limiting factors for resolution in OCT imaging and how exactly do they influence the resolution? (1p) c. Calculate the coherence length for a stable laser source operating at nm with a 1.7 GHz line width, which corresponds to a nanometer line width and a superluminescent diode operating at 830 nm with a bandwidth of 25 nm. (1p) 11. Another technique for 3D images of tissue is PhotoAcoustics (PA). a. Describe the PA technique briefly and how it is possible to use both light and mechanical wave properties to image biological tissue? (3p) b. Compare pros and cons between PA and OCT for making a good image. (2p) Sid 5 (4)