The telescopes on some commercial surveillance satellites can resolve objects on

Question

The telescopes on some commercial surveillance satellites can resolve objects on the ground as small as 95 cm across (see Google Earth), and the telescopes on military surveillance satellites reportedly can resolve objects as small as 11 cm across. Assume first that object resolution is determined entirely by Rayleigh's criterion and is not degraded by turbulence in the atmosphere. Also assume that the satellites are at a typical altitude of 415 km and that the wavelength of visible light is 556 nm. What would be the required diameter of the telescope aperture for (a) 95 cm resolution and (b) 11 cm resolution? (c) Now, considering that turbulence is certain to degrade resolution and that the aperture diameter of the Hubble Space Telescope is 2.4 m, what can you say about the answer to (b), i.e. is the military surveillance resolution accomplished?

Explanation / Answer

a) D / L = 1.22 lambda / d

d = 1.22 lambda * L / d = (1.22 * 556 * 10-9 * 415 * 103) / (0.95)

d = 0.296 m

b) d = 1.22 lambda * L / d = (1.22 * 556 * 10-9 * 415 * 103) / (0.11)

d = 2.56 m

c) The military satellites do not use Hubble Telescope-sized apertures

A great deal of very sophisticated optical filtering and digital signal processing techniques go into the final product, for which there is not space for us to describe here

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