Apart from Atmospheric effects there is a fundamental limitation to the resolution: diffraction.
From geometrical optics one would expect that a "point" on the ground is focused by the lens to form a "point" in the imaging plane. This is not true; because of diffraction a "point" is not focused to a "point" but to an "Airy-disk", which has a certain non-zero diameter.
Because of this diffraction, two point-sources that are very close together will be focussed to two overlapping Airy-disks, making it impossible to tell them apart. The minimum distance that points need to be apart in order to see them as two individual points is:
r = lambda * R / D
In which r is the distance the points need to be apart, lambda is the wavelength, R is the distance from the lens to the object (in this case the distance satellite to ground) and D is the diameter of the lens.
An example: assuming visible light (lambda = 550 nm), an orbit height of 400 km and a 1-meter lens, the minimum theoretically resolvable distance of the ground is 22 centimeters. Clearly it isn't of much use to build a lens much larger than this because the atmosperic turbulence would then become the bottleneck.
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Apart from Atmospheric effects there is a fundamental limitation to the resolution: diffraction.
From geometrical optics one would expect that a "point" on the ground is focused by the lens to form a "point" in the imaging plane. This is not true; because of diffraction a "point" is not focused to a "point" but to an "Airy-disk", which has a certain non-zero diameter.
Because of this diffraction, two point-sources that are very close together will be focussed to two overlapping Airy-disks, making it impossible to tell them apart. The minimum distance that points need to be apart in order to see them as two individual points is:
r = lambda * R / D
In which r is the distance the points need to be apart, lambda is the wavelength, R is the distance from the lens to the object (in this case the distance satellite to ground) and D is the diameter of the lens.
An example: assuming visible light (lambda = 550 nm), an orbit height of 400 km and a 1-meter lens, the minimum theoretically resolvable distance of the ground is 22 centimeters. Clearly it isn't of much use to build a lens much larger than this because the atmosperic turbulence would then become the bottleneck.