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 GUI tool. This tool calculates Scattering Cross Section, Reduced Scattering Coefficient, Phase Function and g (Average Cosine of Phase Function) for a given wavelength range. We consider a 1mm^3 volume in number density calculation.
2. Select "Mono Disperse".
3. Enter parameters representative of small cellular organelles: Diameter of 0.1 μm, Concentration(Number Density) of 100.0 spheres/μm³, Sphere refractive index of 1.4 and Mediumrefractive index of 1.37.
4. Consider visible and NIR spectral region by entering Start, End, and Step Values of 500, 1000, and 5, respectively in the Wavelength (nm) panel.
5. Click the Run Simulation button.
6. Examine carefully the plots of Scattering Cross Section, Reduced Scattering Coefficient and g (Average Cosine of Phase Function) vs Wavelength. If need to zoom those plots, use the wheel in your mouse.
7. We define A(λ/λ₁₀₀₀)^-b relationship in power law fitting. λ₁₀₀₀ is 1000nm and A is μ_s' at 1000nm. Change b slider next to μ_s' plot to find the "best fit" curve. Take note of A and b values to understand the magnitude and wavelength dependence of μ_s'.
8. Repeat the steps I.4-I.7 for parameters representative of mitochondria: Diameter of 0.7 μm, Concentration of 0.00855 spheres/μm³, Sphere refractive index of 1.42 and Medium refractive index of 1.37. Note key differences relative to scattering characteristics of a small organelle. Specified Concentration maintains the A value obtained in the previous step. Change the Concentration to observe changes in μ_s' and A.
9. Repeat the steps I.4-I.7 for parameters representative of a nuclei: Diameter of 4.0 μm, Concentration of 0.00075 spheres/μm³, Sphere refractive index of 1.39 and Medium refractive index of 1.37. Note key differences relative to scattering characteristics of the small organelles and mitochondria.
10. Select "Poly Disperse" and Log Normal distribution.
11. Enter parameters representative of small cellular organelles: Mean Diameter of 0.1 μm, Std. Deviation of 0.01 μm, Volume Fraction of 0.05236, Sphere refractive index of 1.4 and Medium refractive index of 1.37. Set Discrete sphere sizes to 21. (Note: For mono disperse 1.0μm sphere distribution, the concentration of 100.0 spheres/μm³ is equivalent to the volume fraction of 0.05236.)
12. Click the Run Simulation button.
13. Observe discrete sphere distribution. Use b slider next to μ_s' plot to find the "best fit" curve. Take note of A and b values. Compare results with Mono Disperse case in I-3.
14. Select "Mono Disperse".
15. Enter Diameter of 0.01 μm, Concentration of 1 spheres/μm³, 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.
16. Repeat I-15 for Diameter of 0.2 μm.

Question:

1. You want to prepare a scattering phantom with 804nm diameter polystyrene spheres in a aqueous medium. Expected reduced scattering coefficient is 0.1mm^-1 at 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.

II. Effect of numerical aperture (NA) on focus

Goal: Get familiar with the "FocusedBeamSimulator" GUI tool and understand the effect of NA on the focal volume.

We consider flat "x-polarized" plane wave incident upon an apalantic lens and Cartesian coordinates. The lens is placed 1000μm below the origin to have its nominal focal point at the origin. The XY and XZ detectors are placed parallel to the x-y and x-z planes respectively. The plots in the middle column shows the amplitude and phase obtained from the analytical solution. The plots in the right column shows the results obtained from Huygens-Fresnel approach. 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.

1. Launch the FocusedBeamSimulator GUI tool.
2. Set Numerical Aperture to 0.7.
3. In the Output Detector Plane Selection, select XY plane (Z = 0).
4. Click Run Simulation.
5. Wait until you see HF Inc. Done! in the progress slot in between Run Simulation and Close.
6. Choose different electric field components in the Electric Field Component Selection. Change Plot Scale (Amplitude) to Log10s see details. Observe dominant Ex component for x-polarized plane wave incident.
7. Use the wheel in your mouse to zoom the plot. The theoretical Airy disk radius in microscopy is 0.61 λ / NA. Estimate Airy disk radii from your results and compare them with theoretical values.
8. Repeat steps 3-7 for Numerical Aperture = 1.1. Compare the results for the different numerical apertures.
9. Which numerical aperture provides a tighter focal spot?
10. Set Numerical Aperture to 0.7.
11. In the Output Detector Plane Selection, select XZ plane (Y = 0).
12. Click Run Simulation.
13. Observe amplitude and phase profiles in the focal volume.
14. Repeat steps 11-13 for Numerical Aperture = 1.1. Compare the results for the different numerical apertures.

Question:

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 focal field distortion by spherical scatterers.

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

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 single and two scatterers.
3. In the Output Detector Plane Selection, select XZ plane (Y = 0) and in the Electric Field Component Selection panel, select Ex.
4. Check Scatterer 1 and select the diameter as 2.5 μm.
5. Set the location of the scatterer center X:, Y: and Z: to -2, 0, -4 μm, respectively.
6. In the Huygens-Fresnel Approach panel, select Scattered.
7. Click Run Simulation.
8. Observe amplitude and phase profiles. Note the Max. Amp.
9. Toggle between Incident and Incident+Scattered radio buttons and observe the amplitude and phase changes.
10. Repeat the steps 6-9 for X = -2, 0, 2 and 4 μm.
11. Change the diameter of the Scatterer 1 to 5.0 μm. and repeat steps 5-10.
12. If time permits, select the XY plane (Z = 0) and repeat step 11.
13. Select the XY plane (Z = 0).
14. Check Scatterer 1 and select the diameter as 1.0 μm. Set the location of the scatterer center X:, Y: and Z: to -2, 0, -4 μm, respectively.
15. Check Scatterer 2 and select the diameter as 5.0 μm. Set the location of the scatterer center X:, Y: and Z: to -2, 0, -10 μm, respectively.
16. Click Run Simulation.
17. Select Scattered radio button and note the Max. Amp. and Phase @ Max. Amp..
18. Select Incident+Scattered radio button and note the Max. Amp. and Phase @ Max. Amp..
19. Interchange scatterer locations and repeat steps 16-18.

IV. Amplitude change and focal spot displacement

Goal: Understand the amplitude change by a single spherical scatterer.

1. Set Numerical Aperture to 0.7.
2. In the Output Detector Plane Selection, select XZ plane (Y = 0).
3. in the Electric Field Component Selection panel, select Ex.
4. Select Linear Scale.
5. Click Run Simulation. Record Max. Amp. for non scattering case.
6. Check Scatterer 1 and select the diameter as 5.0 μm.
7. Set location of scatterer center X:, Y: and Z: to 0, 0, -2.51 μm, respectively.
8. Click Run simulation. Record Max. Amp. and Max. Amp. Location.
9. Repeat the steps 9-11 for Z = -5, -7.5, -10, -12,5, -15, -30 and -45 μm.
10. Calculate the amplitude change and focal spot displacement relative to non scattering case at each scatterer location.
11. Plot Z vs amplitude change and Z vs focal spot displacement.