Angular resolution

Angular resolution or spatial resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object. It is a measure of the angle between two distinguishable objects that are close together in the field of view of the instrument. The term is used in various fields such as astronomy, photography, microscopy, and remote sensing.

The angular resolution is determined by the diameter of the aperture of the instrument and the wavelength of the light being observed. In general, the larger the aperture or the shorter the wavelength, the better the resolution. This relationship is quantified by the Rayleigh criterion, which states that two point sources are considered resolvable when the principal diffraction maximum of one image coincides with the first minimum of the other. According to the Rayleigh criterion, the angular resolution \(\theta\) can be calculated using the formula:

\[ \theta = 1.22 \frac{\lambda}{D} \]

where \(\lambda\) is the wavelength of the light, and \(D\) is the diameter of the aperture.

In astronomy, angular resolution is critical for observing distant celestial objects. The Hubble Space Telescope, for example, has a much higher angular resolution than ground-based telescopes because it operates above the Earth's atmosphere, which can blur images. In microscopy, achieving high angular resolution can mean the difference between seeing a cell in detail or not. Techniques such as electron microscopy have much shorter wavelengths than visible light and thus can achieve much higher resolutions.

Improvements in angular resolution can be achieved through various methods, including increasing the aperture size, using shorter wavelengths, and employing techniques such as adaptive optics in astronomy, which compensates for the blurring effects of the Earth's atmosphere.