Assignment OI Physics_Solutions_WCL

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Florida International University *

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4531

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Mechanical Engineering

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Apr 3, 2024

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BME 4531/5505 Spring 2023 Wei-Chiang Lin, Ph.D. Please answer all the questions below. I recommend you add your answers directly to this document and submit it when completed. Also, the (graduate students only) questions are required for graduate students and optional for undergraduate students. Optical Imaging – Physics Tissue Optics (1) What are the four major optical properties of biological tissues? Absorption, scattering, refractive index and anisotropy factor (2) Please list three major biological absorbers and their corresponding absorption peaks. Absorber Absorption Peaks Source (URL) melanin 335 nm https://www.cl.cam.ac.uk/~jgd1000/melanin.html Deoxy hemoglobin 434 nm, 556 nm https://omlc.org/spectra/hemoglobin/summary.html fat 933 nm https://omlc.org/spectra/fat/fat.txt (3) Why are the scattering coefficient and the anisotropy factor used together to explain a scattering event? The scattering coefficientt will dictate the scattering events that are likely to happen upon interaction with a sample, where the anisotropy factor will dictate the direction of the scattering. (4) What is the first optical window? Why is it important for optical imaging? NIR region of 650–950 nm, since the absorption effect from blood and water are reduced. In addition, the scattering effect of biological tissues in this region is also low. (5) What is the range of g? The anisotropy factor ranges from -1 to 1. (6) Describe the scattering characteristic of the scatterers with the following g values. g Value Scattering Characteristic 1 Backward scattering 0 Isotropic scattering -1 Forward scattering (7) What does a double integrating sphere setup capture in the procedure of optical property measurements? (graduate students only) Diffuse reflectance and total transmittance (8) What is the model typically used to convert the double integrating sphere measurements to optical properties? (graduate students only) Inverse adding-doubling 1

BME 4531/5505 Spring 2023 Wei-Chiang Lin, Ph.D. Reflection and refraction Here c is the speed of light; l wavelength, f frequency. Please complete the table below. Layer 1 Layer 2 Light Speed C1=C/n=C/1.5 C2=C/n = C/2.0 Wavelength (nm) λ1= λ/n1 λ2= λ/n2 Frequency (Hz) f1= f = C1/ λ1 f2= f = C1/ λ2 Frequency of light does not change with n. What is the minimum  i required in order to create total internal reflection between Layer 1 and Layer 2? Total internal reflection can not happen when n1 is smaller than n2. When  i is 0, what is the light power reflected by the front surface of Layer 1? Fresnel Equations for normal incidence, 0.04 Scattering Theory (graduate students only) (1) What is the major assumption of Rayleigh scattering? Particles scattering light are much smaller than the wavelength (2) What is the major assumption of Mie scattering theory? Solid spherical scatterers (3) Use Mie scattering calculator (https://omlc.org/calc/mie_calc.html) to determine the scattering coefficients of the following samples Sphere Diameter (microns) 0.1 1 n_sphere 1.5 1.5 n_medium 1.33 1.33 Wavelength (microns) 0.8 0.8 Concentration (spheres per cubic micron)_ 100 0.01  s (1/cm) 9.98 66 Anisotropy Factor 0.046 0.9106 (4) Which one of these phantoms is a better representation of brain tissue? 2

BME 4531/5505 Spring 2023 Wei-Chiang Lin, Ph.D. Example 2 ( right side), forward scattering nature and similar mus. Photon Migration Theory Beers Law (1) Complete the following table. It=Io*exp(-mua*l) Log10(Io/It)=A Isolating mua using both equations, mua=-ln(1/10 A )/l And then, It=Io*exp(-mua*l) A (absorbance) I t  a (1/cm) 1 0.1 23.03 0.5 0.32 11.51 2 0.01 46.05 Modified Bear’s Law (collimated transmission) (2) Complete the following table. Tc=exp{-(mua+mua)*l}  a (1/cm)  s (1/cm) I t (Collimated Transmission) 1 0 0.905 0.5 0.5 0.905 1 1 0.820 Monte Carlo Simulation (graduate students only) (1) Please illustrate the probability density function of the random number generator used in a Monte Carlo simulation for photon migration. The output of the random number generator = [0,1] The probability for any outcome of the random number generator = 1 3

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BME 4531/5505 Spring 2023 Wei-Chiang Lin, Ph.D. (2) Please complete the table below.  a (1/cm)  s (1/cm) Random Number Step size 1 0 0.1 2.3 0.5 0.5 0.7 0.36 1 1 0.4 0.46 (3) The equation used to complete the table above is: S=-ln(eps)/mut Where s is the photon step size, eps is the random number and mut is the total interaction coefficient (mut +mus) (4) Which phase function is typically used in an MC simulation for photon migration? Henyey Greenstein function (5) Calculate the scattering angle phi if g = 0 and the random number is 0.5. Cos(phi) = 1 – 2ki, ki is the random number 4