All an imaging satellite is, really, is a large, space based optical telescope/camera, not unlike the Hubble Space Telescope.
The resolving power of any telescope can be calculated by the following formula:
θ = 115.8/D
where θ is angular resolution of the objective, expressed in seconds of arc, and D is the diameter of the objective in millimeters.
This is commonly referred to as the Dawes limit of the objective, and is quite a good estimate of the theoretical resolution the objective is capable of.
The Hubble telescope has an objective of 2.4 meters and this is probably pretty close to the maximum diameter that can be launched into space with currently available launch vehicles, so the NRO satellites can't be much bigger than this.
The Dawes limit of a 2.4 meter objective works out to around .05 seconds of arc.
To figure out actual size of an object from its angular size at a given distance use the formula:
For a distance of about 650 kilometers, which is likely a typical operating altitude for imaging satellites, this works out to right around 10 centimeters.
Пусть высота шрифта примерно 3 мм, расстояние до спутника 100 км (100 000 000 мм), расстояние от точки фокусировки до поверхности первой линзы, к примеру, 100 мм. При отображении буквы работает самая большая поверхность линзы размером 3/1000000 мм (0.003 мкм), которая должна иметь настолько правильную форму, чтобы буква отображалось хотя бы, как 10 точек в высоту, для этого остаётся всего 0.00015 мкм на точку. Плюс внутреняя поверхность линзы, а линза не одна -- точность изготовления всех стёкол должна быть на пару порядков выше, чем мои 0.00015 мкм. Длина волны видимого света в среднем - одна полумиллионная метра, то есть всего 0.5 мкм.
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Вот дифракционный предел:
The resolving power of any telescope can be calculated by the following formula:
θ = 115.8/D
where θ is angular resolution of the objective, expressed in seconds of arc, and D is the diameter of the objective in millimeters.
This is commonly referred to as the Dawes limit of the objective, and is quite a good estimate of the theoretical resolution the objective is capable of.
The Hubble telescope has an objective of 2.4 meters and this is probably pretty close to the maximum diameter that can be launched into space with currently available launch vehicles, so the NRO satellites can't be much bigger than this.
The Dawes limit of a 2.4 meter objective works out to around .05 seconds of arc.
To figure out actual size of an object from its angular size at a given distance use the formula:
angular size(in degrees) = 57.3*actual size / distance
For a distance of about 650 kilometers, which is likely a typical operating altitude for imaging satellites, this works out to right around 10 centimeters.
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