The resolution of optical system is influenced by aperture, focal length and detector, but different parameters play a leading role at different levels.
- Theoretical resolution
Mainly determined by the aperture (diffraction limit). According to the Rayleigh Criterion, the theoretical angular resolution of the optical system is determined by the aperture (d), and the formula is:
Where λ is the wavelength of light. The larger the aperture, the smaller the minimum angular distance that can be resolved. For example, the theoretical resolution of a telescope with a diameter of 1 meter for visible light (λ=550nm) is about 0.14 arcseconds. The theoretical resolution of Hubble telescope (2.4m) is about 0.05 arcsec, while that of james webb telescope (6.5m) can reach 0.02 arcsec.
Rayleigh Criterion: In the imaging optical system, the resolving power is the ability to measure the image of two adjacent objects. Due to diffraction, the image formed by the system is no longer an ideal geometric point image, but a spot (airy disk) with a certain size. When two object points are too close and their spots overlap, it may be impossible to distinguish the images of two object points. That is, there is a resolution limit in the optical system, which usually adopts the criterion proposed by Rayleigh: when the center of one airy disk coincides with the first-order dark ring of another airy disk, just two images can be distinguished.
- the focal length and spatial resolution
Convert the angular resolution to the imaging plane, and the focal length (f) converts the angular resolution to the line resolution on the detector (unit: m/pixel):
The longer the focal length, the higher the line resolution corresponding to the same angular resolution. For example, for a system with a focal length of 12 meters, if the angular resolution is 0.1 arcsecond, the linear resolution is about 5.8 microns. However, the focal length does not affect the theoretical angular resolution, but only determines the imaging scale, that is, how many pixels the theoretical resolution in the first section is distributed on. If the pixel size is fixed, the longer the focal length, the more pixels will be occupied by the same object on the detector of the telescope with the same resolution. However, the longer the focal length and the smaller the relative aperture, the less energy the optical system collects from the same object. At this time, the signal-to-noise ratio of the detector needs to be high and integrated for a long time. Therefore, the focal length is also limited by the detector.
- the detector
The pixel size and sampling rate of the "ceiling" detector with actual resolution directly affect the actual achievable resolution. Pixel size limitation: If the pixel size of the detector is larger than the system line resolution, details cannot be distinguished. For example, if the line resolution is 5 microns and the pixel size is 10 microns, the actual resolution is limited by the detector. Nyquist sampling theorem: In order to fully analyze the target, the pixel size should be less than 1/2 of the line resolution.
These are the two frequencies that we often talk about in optical design, one is Nyquist cut-off frequency and the other is optical cut-off frequency.
- Summary
The theoretical limit of resolution is determined by aperture (diffraction limit), but the actual resolution is limited by atmospheric turbulence (ground system), optical aberration, focal length matching and detector performance.
The development of science and technology is inseparable from the progress of scientific research instruments.
