Angular resolution

The term resolution refers to the distinctness of fine structures, eg the smallest yet perceptible distance between two point-like objects. By specifying an angular distance, or an indication of the distance barely separable structures it can be quantified. The dependence of the resolution on the contrast describes the contrast transfer function.

Eye

The resolving power of the naked eye under ideal conditions is about 0.5 ' to 1 ' (corresponding to 1 mm to 3-6 meters). It is determined similarly to the optical instrument (see below) by the size of the pupil. The spacing of the photoreceptors in the fovea, the site of sharpest vision is adapted to the resolution of the eye. The distance is about 0.3 '.

In average conditions, two points are separated noticeable when their angular distance is 2 '. With weak objects and the edge of the field of view toward the visual acuity but degrades significantly.

In contrast, the visibility of fine structures is higher. They may, for example, in lines with good contrast reach 0.3 ', which is achieved by a kind of image processing in the brain.

Optical instruments

Optical devices such as a telescope or microscope expand the possibilities of the eye - both in regard to its resolution of its brightness perception. For visual observations the magnification of the telescope or microscope can be usefully as far increased until the angular resolution of the optical device is adapted to the human eye. This is called the useful magnification.

The resolution of optical instruments is limited by diffraction (see the Airy disk ). With telescopes one speaks of the Rayleigh criterion that indicates a limit of approximately half the wavelength of illumination light. In microscopes are differentiated according to the structure between the resolution according to Helmholtz and Abbe's resolution limit. When resolution of U according to Helmholtz is assumed self-luminous objects. This results in the smallest possible distance between two self-luminous points which can still be resolved: the wavelength of light, the refractive index of the medium between the object and the lens (which may be air, but also be a liquid ) and the half- opening angle of the lens. The Helmholtz arrangement corresponds to the Fresnel diffraction ( diverging point radiation source). In contrast to Helmholtz, Ernst Abbe is not self-luminous, but of coherently illuminated objects (for example, an illuminated with parallel light optical lattice ), this corresponds to the Fraunhofer diffraction ( parallel light rays as the radiation source ). This structure can be resolved by Abbe, if still contributes the first secondary maximum ( ± 1st order ) for image formation in the microscope of the diffraction image of the structure except the 0th order ( main peak ). According to Abbe, the resolving power of a microscope gives to, in which case the smallest possible line spacing ( lattice constant ) corresponds to the grid.

Taking advantage of nonlinear interactions between light and matter, such as saturation of dye transitions in STED microscopy or switching the dyes in the photoactivated localization microscopy ( PALM), the resolution can be further increased strongly. Also by the size of the probe in atomic force microscopy or optical near-field microscopy, the resolution can be determined and further increased.

For large entrance pupil of the optical system, the resolution is usually limited not by diffraction but by opening errors. This can be reduced by stopping down, so that there is an optimal resolution at the critical aperture.

Mostly limit air turbulence ( seeing ) the resolution ( angular resolution ) ground-based telescopes to about 1 ". Larger telescopes cause here is not automatically better resolution. In order for these ground-based telescopes reach their maximum resolution, it requires special techniques, such as adaptive optics or speckle interferometry. The Hubble Space Telescope achieved due to the elimination of the disturbing atmosphere of a resolution of about 0.05 " at visible wavelengths, but it collects less light than telescopes on the earth's surface.

Seeing effects can be reduced by a device connected to the telescopic video camera for the observation of small but bright objects such as planets or multiple star systems. Even amateur astronomers can reproduce so by choice and superposition of tens to thousands of individual images planetary structures that are far " less than 1 ( " Lucky Imaging ").

The downward limited by diffraction, minimum angle between two telescope still objects of determination is given by the following relationship:

The formula is confirmed by the empirically found relationship between Dawes. By " interconnection " of several individual telescopes can be calculated by interferometry an image with the resolution that corresponds to the maximum distance between the telescopes.