2017 Laboratory B: Mie Scattering and Analysis of Focused Beam Propagation

I. Properties of Rayleigh and Mie Scattering

Goal: This portion of the GUI Interaction provides insight into the characteristics of Rayleigh and Mie Scattering.
  1. Launch Mie Simulator (MieSimulator_v1_05R3.exe) GUI tool. This tool calculates Scattering Coefficient, Scattering Cross Section, Reduced Scattering Coefficient, Phase Function, Average Cosine of Phase Function (g), S1 and S2 for a given wavelength range. Number density is given in a volume of 1mm3.
  2. Select "Mono Disperse".
  3. Consider visible and NIR spectral region by entering Start, End, and Step Values of 500, 1200, and 5, respectively in the Wavelength (nm) panel. Unless otherwise stated, use this wavelength range for all simulations.
  4. Enter parameters representative of small cellular organelles: Diameter of 0.1 μm, Volume Fraction of 0.01, Sphere refractive index of 1.4 and Medium refractive index of 1.37.
  5. Click the Run Simulation button.
  6. Examine the plots of Scattering Cross Section, Scattering Coefficient, Reduced Scattering Coefficient and Average Cosine of Phase Function (g) vs wavelength. (Click Display Data button to visualize data values. To zoom plots, use the scroll wheel on your mouse.)
  7. To find fitting parameters fRay and bMie in μs' Power Law Fitting panel (Top right), we use the fitting relationship specified in Steve L. Jacques's review paper ("Optical properties of biological tissues: a review" Phys. Med & Bio. 58(2013) R37-R61); The fitting function is given as A[fRay(λ/λ1000)-4+(1-fRay)(λ/λ1000)-bMie]. Ais μs' at 1000nm and 'λ1000 is 1000nm. Select μs' Power Law Fitting tab and click Best Fit button to find best fitting parameters. You may also use fRay and bMiesliders to fit manually. Take note of A, fRay and bMie values to understand the magnitude and wavelength dependence of μs'.
  8. Repeat the steps 4-7 for parameters representative of a cell nucleus: Diameter of 4.0 μm, Volume Fraction of 0.01, Sphere refractive index of 1.39 and Medium refractive index of 1.37. Note key differences relative to scattering characteristics of small organelles. Understand the relationship between sphere size and bMie. (Hint: Check lecture notes on Rayleigh and Mie scattering).
  9. To understand the relationship between sphere concentration and scattering, move the 5% Range slider to observe the changes in μs and μs'.
  10. Enter Diameter of 0.2 μm, Concentration of 1e9 spheres/mm3, Sphere refractive index of 1.40 and Medium refractive index of 1.33 and Run simulation. Observe Phase Function profiles for Parallel(Para) and Perpendicular(Perp) polarization. Select Ave and visualize the phase function for 500nm and 1200nm. Check the g values for 500nm and 1200nm. Understand the relationship between the Phase Function and Average Cosine of Phase Function. Can you explain why the forward scattering % decreases (or the backward scattering % increases) with the wavelength.
  11. You need to prepare a scattering phantom with 804nm diameter polystyrene spheres in a aqueous medium. Expected reduced scattering coefficient is 0.1mm-1at 632.8nm. Refractive indexes of polystyrene sphere and water are 1.59 and 1.33 respectively. Find the concentration of polystyrene spheres in a 1ml volume. (1ml=1000mm3)
  12. Following table shows three poly disperse Log Normal scatterer distributions in a tissue model (J. Nguyen et al., Biomed. Exp. 4(10) 2013). The distribution 1, 2 and 3 represent small protein complexes, organelles such as lysosomes and mitochondria, and nuclei respectively. Calculate the scattering coefficient of each distribution at 620nm. Select Poly Disperse and set start and end wavelengths to 620nm. Use 51 discrete sphere sizes and apply following parameters. What is the scattering coefficient of all distributions? (Hint: μs All = Σ μs)
 Distribution  Mean Diameter ± Std.Dev.(μm)  Number Density(mm-3)  nScatterer    nMedium
       1             0.06 ± 0.4                  4x1010             1.46       1.33       
       2             0.9 ± 0.3                   5x107              1.40       1.35
       3             9.6 ± 0.1                   5x104              1.39       1.37

II. Effect of numerical aperture (NA) on focus beam propagation

Goal: (i) Get familiar with the "FocusedBeamSimulator" GUI tool. (ii) Compare analytical solution and Huygens-Fresnel approach. (iii) Understand the effect of NA on Airy disk formation.
  1. Launch the Focused Beam Simulator (FocusedBeamSimulator.exe) GUI tool. We consider flat "x-polarized" plane wave incident upon an apalantic lens. The lens is placed 1000μm below the origin to have its nominal focal point at the origin. You can observe the electric field components (Ex, Ey and Ez) in the X-Y plane or in the X-Z plane by selecting detector plane as XY plane (Z = 0) or XZ plane (Y = 0). The plots in the left column shows the amplitude and phase obtained from the analytical solution (Richard and Wolf, Proc. Royal Soc. Lond. A 253 (1959)). The analytical solution only provides the focal fields for non scattering medium and it is used as a reference in this lab exercise. The plots in the right column shows the results obtained from Huygens-Fresnel approach. The Huygens-Fresnel method can provide results for both scattering and non scattering medium.
  2. Set Numerical Aperture to 0.4.
  3. In the Output Detector Plane Selection, Select XY plane (Z = 0). You may increase the detector resolution by sliding Detector Resolution slider to improve image quality. Note that each increment approximately doubles the simulation time. We recommend setting Detector Resolution to Medium for following exercises. In the Electric Field Component Selection panel, select Ex. Change Plot Scale to Linear.
  4. Click Run Simulation.
  5. Wait until you see HF Inc. Done! in the progress slot in between Run Simulation and Close.
  6. Change Plot Scale (Amplitude) to Log10 see details. Choose different electric field components in the Electric Field Component Selection. Observe dominant Excomponent for x-polarized plane wave incident.
  7. Airy disk radius = 0.61 λ / NA. Estimate Airy disk radius (the distance between the central maximum and the first minimum) from your results and compare it with the theoretical value. Use the scroll wheel on your mouse to zoom the plot.
  8. Repeat steps 3-7 for Numerical Aperture = 1.1. Compare your results for the different numerical apertures.
  9. Set Numerical Aperture to 0.4.
  10. In the Output Detector Plane Selection, select XZ plane (Y = 0).
  11. Click Run Simulation.
  12. Observe amplitude and phase profiles in the focal volume.
  13. Repeat steps 10-12 for Numerical Aperture = 1.1. Compare the results for the different numerical apertures.
  14. Which numerical aperture provides the tightest focal spot?
  1. This GUI tool is designed for 'flat' x-polarized incident. Laser sources are producing 'Gaussian' beams and you are asked to modify the model for Gaussian x-polarized incident. What additional information do you need? How do you implement it?

III. Focal field distortions

Goal: Understand the effect of scatterer size and location on focal field distortions.

This GUI tool finds the maximum amplitude (Max. Amplitude) in the amplitude plot and displays it above the plot. The phase at the nominal focal point (Phase @ (0,0):) is shown above the phase plot as a reference.

  1. Set Numerical Aperture to 0.7
  2. Click Load Mie Data button to load three pre-computed Mie data tables to study the distortion by one or two scatterers.
  3. In the Output Detector Plane Selection, select XY plane (Z = 0) and in the Electric Field Component Selection panel, select Ex. Change Plot Scale to Linear.
  4. Check Scatterer 1 and select the diameter as 2.5 μm. Set the X:, Y: and Z: coordinates of the scatterer to 0, 0, -3 μm, respectively.
  5. Click Run Simulation.
  6. Select Incident+Scattered radio button and note Max. Amplitude. Calculate the amplitude change relative to the non scattering case.
  7. Uncheck Scatterer 1. Check Scatterer 2 and select the diameter as 5 μm. Set the X:, Y: and Z: coordinates of the scatterer to 0, 0, -10 μm, respectively.
  8. Click Run Simulation.
  9. Observe changes in amplitude and note Max. Amplitude. Calculate the amplitude change relative to the non scattering case.
  10. Check Scatterer 1 and Scatterer 2. Use previous locations (0, 0, -10 μm and 0, 0, -3 μm respectively)
  11. Click Run Simulation.
  12. Observe changes in amplitude and note Max. Amplitude. Calculate the amplitude change relative to the non scattering case.
  13. In the Output Detector Plane Selection, select XZ plane (Y = 0).
  14. Click Run Simulation.
  15. Visualize the changes in the focal volume. Find the location of Max Amplitude.