Calculating Resolution of Space Camera for Imaging Earth

[Vanush]

If I have a camera orbiting in space way above the Earth, and it has a diffraction limited resolution of 4.1*10^-7 m (diameter of airy disc), then how can I find out the corresponding value if the lens is supposed to take images of the Earth?

 

[mgb_phys]

What do you mean by "corresponding value"?
Presumably by the 4.1*10^-7 m you mean the resolution limit at the image plane.
If you knowthe focal length and orbital height you can work out the resolutionsize on the Earth's surface

 

[Vanush]

What do you mean by "corresponding value"?
Presumably by the 4.1*10^-7 m you mean the resolution limit at the image plane.
If you knowthe focal length and orbital height you can work out the resolutionsize on the Earth's surface

Yeah, how do I figure out the res on the Earth? I know the Focal length and orbital height. I was thinking you could just multiply the airy disk size by 100000 for 100km

 

[Redbelly98]

Note that multiplying (airy disc diameter) x (orbital height) gives incorrect units of m^2, when we're looking for an answer in meters.

Hint: what is the camera's magnification factor?

 

[Vanush]

So I'm looking for a dimensionless number? Not sure what it could be, I'm only given lens diamater, focal length and wavelength.

 

[Redbelly98]

Resolution at the Earth's surface will have units of meters.

Eg.: the camera can distinguish objects on Earth that are ___ meters apart.

 

[Vanush]

yeah, I'm having trouble figuring out how I can get that very small airy disc size to correspond to resolution on the Earth's surface, 100km's away. I tried using this

where di is distance to the image from the lens, and do is distance to the object. But, then I get a very small number and if i multiply this number with the airy disc size I don't get a realistic resolution on the Earth's surface.

 

[Redbelly98]

Which of these seems more reasonable to you:

(object) x (magnification) = (image)
or
(image) x (magnification) = (object)

?

 

[Vanush]

Which of these seems more reasonable to you:

(object) x (magnification) = (image)
or
(image) x (magnification) = (object)

?

First one.

 

[Redbelly98]

Good.

Does the 4.1*10^-7 m Airy disk correspond to an object or image?

 

[Vanush]

Good.

Does the 4.1*10^-7 m Airy disk correspond to an object or image?

image

 

[Redbelly98]

Sounds like you can use the 1st equation in post #8 to solve the problem now.