# Camera Resolution

A key factor when choosing the correct camera for your microscopy application is matching the camera's resolving ability to that of the objective lens used. To do this, you will need to know the objective lens' magnification and numerical aperture, and the pixel-size of the camera's image-sensor.

Ernst Abbe devised a formula for calculating the resolution of an objective lens:

r = λ/2NA

where r (resolution) is equal to λ (wavelength of light) divided by double the NA (numerical aperture) of the objective lens. So a 4X objective lens with a NA of 0.1, would have a resolution of 2.75µm when using an average light-wavelength of 550nm.

2.75µm = 0.55µm/2*0.1

## Compare Magnified Resolution to Pixels

A camera's ability to resolve to fine detail depends on its sensor's pixel-size, since the pixels are the building-blocks of the image; for film cameras, the grain of the film would be the determining factor. Because the image produced by the objective lens is magnified, the lens' resolution needs to be multiplied by its magnification-power to determine the necessary pixel-size to render an equally-detailed image.

p = ro * mo

11µm = 2.75µm * 4

It is arguable that a 1:1 ratio is sufficient to resolve the image, but a 1:2 ratio would be preferable. This means that the pixel-size should be no larger than half the magnified-resolution.

p = (ro * mo)/2

5.5µm = (2.75µm * 4)/2

Objective Magnification NA Resolution λ=550nm Maximum Pixel Size Ideal Pixel Size
4X 0.10 2.75µm 11µm 5.5µm
10X 0.25 1.1µm 11µm 5.5µm
20X 0.40 0.69µm 13.8µm 6.9µm
40X 0.65 0.42µm 16.8µm 8.4µm
60X 0.80 0.34µm 20.4µm 10.2µm
100X 1.25 0.22µm 22µm 11µm

## Don't Forget the Reduction Lens

One more factor to include is the magnification of a reduction lens, when used. If a 0.5X lens is used to "squeeze" more image onto a camera's sensor, then the ideal pixel-size is cut in half.

p = (ro * mo * mr)/2

2.75µm = (2.75µm * 4 * 0.5)/2

## Check the Camera's Pixel-Size When looking at a camera's specifications, look for the pixel-size. If it is not listed, you can estimate the pixel-size by dividing the image-sensor's width by the maximum image-size's width (in pixels).

4.8mm/1280px = .00375mm/px