Optical imaging (1873)

© Michael Zoelffel

Did You Know…

…that Non-Linear Effects Influence the Resolution Limit?

Successful achievements in research using new imaging techniques are announced time and again – often with the addendum “Abbe’s resolution limit overcome!”

The theory of optical imaging developed by Ernst Abbe at Carl Zeiss (1873) has lost none of its significance or validity even after nearly 140 years. Abbe recognized that there are three mechanisms at work in optical imaging:

  1. diffraction at the object,
  2. filtering through the imaging optics, and
  3. actual image generation through interference, i.e. the overlapping of the waves that are diffracted and transmitted by the imaging optics.

The easiest way to see this is on periodic objects with regularly recurring structures. Thus, microscopes have long been judged based on whether or not they can resolve the periodic skeleton of a diatom (Pleurosigma Angulatum) hence one frequently saw the headline “Pleurosigma Angulatum resolved” in the past.

Strictly speaking, Abbe’s resolution limit applies only to the distance between adjacent lines in a grating. If the distance is too short, the diffraction angles are so large that the diffracted light exceeds the aperture angle or the numerical aperture of the imaging optics. As a result, the diffraction orders can no longer be transmitted. In addition to the wavelength, numerical aperture is also a critical measurement for Abbe’s resolution limit.

Nevertheless, resolutions are being achieved today that are far below Abbe’s resolution limit. How is this possible? The explanation is supplied by non-linear effects, such as fluorescence or the exposure of photoresist in optical lithography.

Using Abbe’s resolution limit for the distance between two lines, current ZEISS microscopes end up with about one third of the wavelength of the light used, i.e. around 160 nanometers. Thanks to non-linear effects, however, individual fluorophores may be localized at almost any resolution in fluorescence microscopy. The distance between adjacent lines is all that is limited by Abbe’s resolution limit.

So, the next time you read, “Abbe’s resolution limit overcome”, you can be reasonably sure that the statement is referring to a non-linear effect.

2 Oktober 2012