Lens numerical aperture and resolution

1.What is lens resolution?


When observing an object with magnification, magnification is of course important, but

It is also important to be able to discern fine details.

This ability is called resolution,

It is expressed as “the minimum distance that allows two points that are close to each other to be distinguished.


Resolution = Distance at which two points can be identified


*If you are observing the presence or absence of minute objects, it is possible to check even smaller objects.

Expressed mathematically, resolution = kλ/NA.

k is a coefficient and values ​​of 0.61 and 0.5 are used.

λ is the wavelength of light. For normal visible light, use 0.55μm.

NA is the numerical aperture of the lens. (This value indicates one of the lens’s performance.)

The larger the numerical aperture, the higher the resolution (smaller the numerical value).


(Example) If the lens has a numerical aperture (NA) of 0.9,

Resolution = 0.5×0.55/0.9 = 0.30μm.


If the distance between two points is 0.30μm, two points can be identified.

There is no relationship between resolution and magnification, so no matter how much you increase the magnification with this lens,

The discrimination between two points is 0.30μm.



2. Numerical aperture of lens


This is an important value that determines the performance of the lens.

Numerical aperture (NA) = nsinθ

n is the refractive index of the medium from the object to the lens, and if it is air, n = 1.

θ is the amount of light that enters the lens from the point where the optical axis intersects the object.

This is the outermost angle.




The larger the numerical aperture

This will be a bright lens.

Also, since resolution = kλ/NA, the larger the numerical aperture, the

The resolution will be higher. (The number will be smaller.)


3. Examples of our megapixel compatible telecentric lenses



The numerical aperture is 0.026.

Resolution = (0.61×0.55)/0.026 = 12.9μm. 

This almost matches the resolution (12.7μm) in the table above.



4. Examples of our medium magnification zoom lenses


The numerical aperture of our medium magnification zoom lens (SDS-M) ranges from 0.014 (at the lowest magnification) to 0.036 (at the maximum magnification).

Resolution at lowest magnification = (0.61×0.55)/0.014 = 23.9μm

Resolution at maximum magnification = (0.61×0.55)/0.036 = 9.3μm.