Complete Radio Resolution For Free

Shorter wavelengths yield higher resolution (lower values for r) and visa versa. The greatest resolving power in optical microscopy is realized with near-ultraviolet light, the shortest effective imaging wavelength.

The Rayleigh criterion stated in the equation ?=1.22?D ? = 1.22 ? D gives the smallest possible angle ? between point sources, or the best obtainable resolution. Once this angle is found, the distance between stars can be calculated, since we are given how far away they are.

The factor of 1.22 applies to circular apertures like the pupil of your eye or the apertures in telescopes and cameras. When light passes through an aperture with diameter D, then diffraction limits the resolution to ? = 1.22?/D. If the angular separation of two sources is less than ?, they cannot be resolved.

Rayleigh defended this criterion on sources of equal strength. Considering diffraction through a circular aperture, this translates into: where ? is the angular resolution (radians), ? is the wavelength of light, and D is the diameter of the lens' aperture.

Resolution of a single dish radio telescope: 1.02 ?/D where D = diameter of telescope; therefore, VLA @20 cm: 30' resol. Primary beam (or ?field of view?) for int. = single dish resol.

It's hard to tell exactly what you are asking because if you have followed the derivation then the answer is there: 1.22 is where the Bessel function has the first zero, and the Bessel function arises from the Fourier transform of the aperture function.

The factor of 1.22 applies to circular apertures like the pupil of your eye or the apertures in telescopes and cameras. When light passes through an aperture with diameter D, then diffraction limits the resolution to ? = 1.22?/D. If the angular separation of two sources is less than ?, they cannot be resolved.

This occurs for two point objects separated by the angle ? = 1.22 ? / D, where ? is the wavelength of light (or other electromagnetic radiation) and D is the diameter of the aperture, lens, mirror, etc. This equation also gives the angular spreading of a source of light having a diameter D.

Radio telescopes have much worse angular resolution (cannot see as much detail) than optical telescopes. For example the best optical telescopes have 0.5 arc seconds resolution from the ground and have 10meter mirrors. A radio telescope with 30 meter collecting plate has 0.5 degree resolution.

Radio telescopes have poor resolving power, due to the long wavelengths of radio waves.