Resolving power

This article deals with spatial resolution in optics; for other meanings see also temporal resolution .

In optics, the term resolving power refers to the differentiation of fine structures, for example the minimum distance that two point-like objects must have in order to be able to perceive them as separate objects. It can be quantified by specifying an angular distance ( angular resolution ) or by specifying the distance between structures that are barely separable. The contrast transfer function describes the dependence of the resolution on the contrast .

eye

The resolution of the naked eye can vary greatly from person to person. Adults with normal vision can still see things clearly that are moved within about 10 cm of the eye, but only for a short time, as fatigue soon occurs. The accommodation is too strenuous in the long run. Most adults can see an object consistently at a distance of 25 cm. This distance is therefore called the conventional visual range or reference visual range . Here the eye can achieve the best spatial resolution for longer periods of time. At this distance, some people can still distinguish structures at a distance of 0.15 mm. This corresponds to a viewing angle of approximately 2  arc minutes . Other people, on the other hand, only distinguish structures at a distance of 0.3 mm or 4 angular minutes. If the object is held between 25 and 10 cm close to the eye, a correspondingly better spatial resolution can be achieved for short periods of time. With relaxed eyes and greater distances, several meters to infinity, the typical angular resolution of the human eye is 1 angular minute corresponding to a visual acuity of 1.

With weak contrasts and towards the edge of the field of vision , the visual acuity decreases noticeably.

Optical instruments

see also: resolution (photography) and resolution (microscopy) , as well as telescope characterization

Optical devices such as telescopes or microscopes expand the possibilities of the eye - both in terms of its resolution as well as its perception of brightness . The latter is determined exclusively by the aperture (opening of the objective). In the case of visual observations, the magnification of the telescope or microscope can usefully be increased until the angular resolution of the optical device is adapted to that of the human eye. One then speaks of the useful magnification . Too much magnification, however, at which the visual contrast becomes too low, is called dead magnification . In this case, the image only appears larger, but no additional details are visible.

The resolution of optical instruments is limited by diffraction (so-called diffraction limitation , see diffraction disks ). To separate two point sources with a diffraction-limited instrument, the Rayleigh criterion can be used, for example .

The resolving power of microscopes is described in detail here . It depends on the numerical aperture of the objective used and the observation wavelength. For an observation wavelength of 0.55 micrometers (green light), for objectives with a numerical aperture of 0.1, 0.65 and 1.4, for example, a resolution of 2.75, 0.423 and 0.196 micrometers is obtained. It should be noted that a numerical aperture of 1.4 is a maximum for microscope objectives; accordingly, a maximum resolution of approx. 0.2 micrometers can be achieved for green light. To see such small structures with the naked eye, a magnification of approx. 1000 is useful. The magnification can be adjusted in the microscope by combining the objective and eyepiece.

By using non-linear interactions between light and matter, such as saturation of dye transitions in STED microscopy or switching the dyes on / off in photo-activated localization microscopy (PALM), the resolution can be increased further. With the STED method, resolutions of 20 to 30 nanometers are typically achieved. Further improvements led to resolutions of around 1 nanometer in 2016.

The size of the probe in atomic force microscopy (resolutions in the sub-nanometer range) or optical near-field microscopy (resolutions around 20 nanometers) can also determine and further increase the resolution.

In the case of large entrance pupils of optical systems , the resolution is usually not yet limited by diffraction, but rather by aperture errors. These can be reduced by stopping down , so that the critical aperture results in an optimal resolution.

Air turbulence ( seeing ) usually limits the resolution ( angular resolution ) of earth-based telescopes to around 1 ″ . Larger telescopes do not automatically produce a better resolution here. In order for these earth-based telescopes to achieve their maximum resolution, special techniques are required, for example adaptive optics or speckle interferometry . The Hubble space telescope achieves a resolution of around 0.05 ″ at visible wavelengths because the disturbing atmosphere is eliminated, but it collects less light than the largest telescopes on the earth's surface.

Seeing effects can be reduced when observing small but bright objects such as planets or multiple star systems using a video camera connected to the telescope. Even amateur astronomers can map planetary structures with a resolution of less than an arc second by selecting and superimposing dozens to thousands of individual images (" lucky imaging ").

The minimum angle between two objects that can still be distinguished in the telescope, limited by downward diffraction, is given by the following relationship:

${\displaystyle \sin(\delta _{\varphi })=1{,}22{\frac {\lambda }{D}}}$

${\displaystyle \delta _{\varphi }}$ : minimum angle

${\displaystyle \lambda }$ : Wavelength of the observed radiation

${\displaystyle D}$ : Opening diameter

The formula is confirmed by the empirically found relationship by Dawes . By “connecting” several individual telescopes, an image can be calculated using interferometry with the resolution that corresponds to the distance between the telescopes.

Web links

• Resolving power. In: Lexicon of Optics. (Online version by Harry Paul (Ed.): Lexikon der Optik . Spektrum Akademischer Verlag, 2003, ISBN 3-8274-1422-9 .)
• The resolving power in astronomy: point sources, Airy disks and seeing disks
• Thomas Kusserow: Basics of technical optics. 2015/2016 (PDF).
• Video: resolving power . Institute for Scientific Film (IWF) 2004, made available by the Technical Information Library (TIB), doi : 10.3203 / IWF / C-14892 .

Individual evidence

1. ↑ Dieter Gerlach: The light microscope . 2nd Edition. Thieme Verlag, Stuttgart 1985, ISBN 3-13-530302-0 , p. 2 .
2. ↑ Fluorescence microscopy: It doesn't get any sharper , researchers reach ultimate resolution limit in fluorescence microscopy, MPG, 2016.
3. ↑ Ludwig Bergmann , Clemens Schaefer : Textbook of Experimental Physics . Volume 3: Optics . De Gruyter, Berlin / New York 2004, ISBN 3-11-017081-7 , p. 370.