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Successful achievements in the research on new imaging techniques are announced time and again – often with the add-on, “Abbe’s resolution limit exceeded!”

Abbe's theory of optical imaging (1873), developed at Carl Zeiss, has lost none of its significance or validity almost 140 years later. Abbe realized that there are three mechanisms at work in optical imaging:

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

The easiest way to see this is on periodic object with regularly recurring structures. This is why microscopes have long been gaged based on whether or not they can resolve the periodical skeleton of a diatom (Pleurosigma Angulatum) – hence the frequently-printed statement “Pleurosigma Angulatum resolved.”

Strictly speaking, Abbe’s resolution limit only applies to the distance between adjacent lines in a grating. If the distance is too short, the diffraction angles are so wide 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. Alongside the wavelength, numerical aperture is the decisive measurement for Abbe’s resolution limit.

Nevertheless, today, resolutions far below Abbe’s resolution limit are being achieved. How is this possible? The explanation lies in what are known as “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 immersion systems from Carl Zeiss result in 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. 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 exceeded,” you can be reasonably sure that the statement refers to a non-linear effect.

October 2, 2012