GOAL: Examine characteristics of the focal field formed by a focused beam in the absence and presence of spherical scatterers

I. Effect of numerical aperture (NA) on focus

Goal: Get familiar with the "Focused Beam Simulation Tool" and understand the effect of NA on the focal volume.

1. Launch the Focused Beam Simulation Tool in MATLAB. (Type FocusedBeamSimulationTool in MATLAB command window).
2. Set Numerical Aperture to 0.25.
3. In the Simulation Options box select No Scatterers.
4. In the Output Selection box select Total field: Ex.
5. In the checkboxes to the right check XY and XZ plane views.
6. Click Run Simulation.
7. Wait until you see Completed! in the Matlab command window.
8. Save GUI as a MATLAB figure (File->Save As...).
9. Repeat steps 1-6 for Numerical Aperture = 0.5 and 1.0.
10. Compare the results for the different numerical apertures.

Questions:

1. Which numerical aperture provides a tighter focal spot?
2. 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.
3. Compare the amplitude of Ex, Ey and Ez components. Which component(s) are dominant and why?

II. Focal field distortions

Goal: Understand the focal field distortion by spherical scatterers

1. Set Numerical Aperture to 0.7
2. In Simulation Options select One Scatterer
3. In Scatterer Info set diameter of Scat. 1 to 1.0 (1μm)
4. Set the location of the scatterer center X:, Y: and Z: to -2, 0, -5 μm, respectively
5. In Output Selection select Scattered field: Ex
6. Check XY and XZ plane views.
7. Click Run Simulation.
8. Observe the amplitude and phase patterns.
9. Save GUI as a MATLAB figure.
10. Repeat the steps II.3-II.10 for Scat. 1, Dia = 2.5 and 5.0 μm.
11. Compare the results for the different sized scatterers.
12. In Simulation Options select Two Scatterers.
13. Set diameter of Scat. 1 to 1.0 μm.
14. Set the location of scatterer 1 center X:, Y: and Z: to -2, 0, -5 μm, respectively.
15. Set diameter of Scat. 2 to 5.0 μm.
16. Set the location of scatterer 2 center X:, Y: and Z: to 2, 0, -5 μm, respectively.
17. Click Run Simulation.
18. Observe results.
19. Change diameter of Scat. 1 to 2.5 μm and click Run Simulation.
20. Observe results.

III. Focal spot displacement

Goal: Understand the focal spot displacement and amplitude change by a single spherical scatterer

1. Set Numerical Aperture to 0.7.
2. In Simulation Options select No Scatterers.
3. In Output Selection set Total field: Ex.
4. Check XY and XZ plane views.
5. Select Linear.
6. Click Run Simulation.
7. Click on MATLAB “Data Cursor” icon (in "Tools" pulldown), find the largest amplitude in the XZ view plot. Record the value of “Index” (amplitude) and “y” (z location).
8. In Simulation Options select One Scatterer.
9. In Scatterer Info set diameter of Scat. 1 to 5.0 μm.
10. Set location of scatterer center X:, Y: and Z: to 0, 0, -2.5 μm, respectively.
11. Click Run simulation.
12. Use “Data cursor” to find the largest amplitude in the XZ view plot. Record the value of “Index” (amplitude) and “y” (z location).
13. Repeat the steps 9-11 for Z = -5, -7.5, -10, -12,5 and -30 μm.
14. Calculate the amplitude change relative to non scattering case at each location.
15. Plot Z vs amplitude change.
16. Plot Z vs displacement of the largest amplitude spot.

Questions:

1. What conclusion do you come from above (B III. 15 and 16) plots?
2. If you repeat above lab (B III) for lower NA, what results do you expect?