Coherent use of opposing lenses for axial resolution increase in fluorescence microscopy. I. Comparative study of concepts.

We study the use of coherent counterpropagating interfering waves to increase threefold to sevenfold the optical bandwidth and the resolution of fluorescence microscopy along the optic axis. Systematic comparison of the point-spread function and the optical transfer function (OTF) for the standing-wave microscope (SWM), the incoherent illumination interference image interference microscope (I5M), and the 4Pi confocal microscope reveals essential differences among their resolution capabilities. It is shown that the OTF's of these microscopes differ strongly in contiguity and amplitude within the enlarged range of transferred frequencies, and therefore they also differ in their ability to provide data from which interference artifacts can be removed. We demonstrate that for practical aperture angles the production of an interference pattern is insufficient for improving the axial resolution by the expected factor of 3-7. Conditions of the OTF for unambiguous improvement of axial resolution of arbitrary objects are fulfilled not at all in the SWM, partially in the I5M, and fully in the two-photon 4Pi confocal microscope.

Coherent use of opposing lenses for axial resolution increase. II. Power and limitation of nonlinear image restoration.

We analyze the ability of nonlinear image restoration to remove interference artifacts in microscopes that enlarge the axial optical bandwidth through coherent counterpropagating waves. We calculate the images of an elaborate test object as produced by confocal, standing-wave, incoherent illumination interference image interference, and 4Pi confocal microscopes, and we subsequently investigate the extent to which the initial object can be restored by the information allowed by their optical transfer function. We find that nonlinear restoration is successful only if the transfer function is sufficiently contiguous and has amplitudes well above the noise level, as is mostly the case in a two-photon excitation 4Pi confocal microscope.

Dual-color 4Pi-confocal microscopy with 3D-resolution in the 100 nm range.

We report the development of simultaneous two-color channel recording in 4Pi-confocal microscopy. A marked increase of spatial resolution over confocal microscopy becomes manifested in 4Pi-confocal three-dimensional (3D) data stacks of dual-labeled objects. The fundamentally improved resolution is verified both with densely labeled fluorescence beads as well as with membrane labeled fixed Escherichia coli. The synergistic combination of dual-color 4Pi-confocal recording with image restoration results in dual-color imaging with a 3D resolution in the 100 nm range.

4Pi-confocal microscopy provides three-dimensional images of the microtubule network with 100- to 150-nm resolution.

We show the applicability of 4Pi-confocal microscopy to three-dimensional imaging of the microtubule network in a fixed mouse fibroblast cell. Comparison with two-photon confocal resolution reveals a fourfold better axial resolution in the 4Pi-confocal case. By combining 4Pi-confocal microscopy with Richardson-Lucy image restoration a further resolution increase is achieved. Featuring a three-dimensional resolution in the range 100-150 nm, the 4Pi-confocal (restored) images are intrinsically more detailed than their confocal counterparts. Our images constitute what to our knowledge are the best-resolved three-dimensional images of entangled cellular microtubules obtained with light to date.

4Pi confocal microscopy with alternate interference.

We introduce 4Pi confocal microscopy with destructive interference of converging waves. Linear lobe deconvolution as well as nonlinear restoration of 4Pi confocal raw data with their point-spread functions (PSF's) leads to almost-identical images, irrespective of whether the 4Pi confocal PSF relies on constructive or destructive interference. Three-dimensional imaging of microtubules of a mouse fibroblast cell yielded an axial resolution near 100-nm in both cases. Moreover, restoration of 4Pi confocal images of the same object with alternate phases is introduced as a powerful test for (nonlinear) image restoration.