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4pi PSF


Calculated Point Spread Functions for a Four Pi Microscope changing the Numerical Aperture.

"If the two lens segments were full spherical halves, the focal spot would be a (nearly) spherical spot, too. But since a considerable solid angle is not provided by the lenses, interference typically spawns off 2 axial side-lobes which, if not taken into account, lead to artefactual images". 1


All images are 1 µm height. α is the angular aperture of the 4pi lens (the total angle of the two segments together as measured from the focus).

Image </td><td> Image </td><td> Image </td><td> Image </td><td> Image
α = 194 ° </td><td> α = 212 ° </td><td> α = 252 ° </td><td> α = 288 ° </td><td> α = 352 °


This is a PSF (with some intensity decay in the laterals of the convergent lens due to energy redistribution), not a theoretical 4pi illumination (where intensity would be uniform from all directions of space), but still suggests the real possibility of exciting a central point without noticeable lateral sidelobes.


Microscopic Parameters:

Sample Size: 10 x 10 x 10 nm3 <br>
Pinhole Radius: 100 nm <br>
Lens Refractive Index: 2 <br>
Medium Refractive Index: 2 <br>
Excitation Wavelength: 488 <br>
Emission Wavelength: 520 <br>
Excitation Photons: 1 <br>
Numerical Aperture = Lens Refractive Index * sin(α/4)

1 http://www.mpibpc.gwdg.de/abteilungen/200/4Pi.htm