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 Image Image Image Image
&alpha; = 194 &deg; </td><td> &alpha; = 212 &deg; </td><td> &alpha; = 252 &deg; </td><td> &alpha; = 288 &deg; </td><td> &alpha; = 352 &deg;

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
Pinhole Radius: 100 nm
Lens Refractive Index: 2
Medium Refractive Index: 2
Excitation Wavelength: 488
Emission Wavelength: 520
Excitation Photons: 1
Numerical Aperture = Lens Refractive Index * sin(&alpha;/4)

1. For more information see https://nanobiophotonics.mpibpc.mpg.de/popular-reading