Numerical Aperture
In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light [wikipedia].
Objective N.A.
The numerical aperture of a microscope objective is the measure of its ability to gather light while working at a fixed distance (working distance).
The higher the NA, the finer details the objective can resolve.
NA is usually indicated on the microscope objective after its magnification.
Lenses with larger N.A. should also be able to collect more light and so give a brighter image.
Calculating N.A.
You can calculate numerical aperture with the following formula:
NA = n × sin(θ)Where:
- n is the index of refraction of the medium in which the lens is working
- 1.00 for air
- 1.33 for pure water
- 1.51 for immersion oil (about the same than glass which is 1.5)
- θ is the half-angle of the maximum cone of light that can enter or exit the lens
Relation with W.D.
W.D. (Working distance) refers to the clearance in mm between the front tip of the objective and the surface of the specimen focused.
N.A. and W.D. are not directly related. But most of the time, for lens elements of a similar size, increasing the WD result in a lower NA.
Apochromat objectives
Apochromatic objectives tend to have a higher N.A. than equivalent achromatic ones.
Oil objectives
Oil immersion objectives have a higher N.A. than the equivalent dry ones. This is because the refractive index of immersion oil (1.51) is higher than air (1.0).
The maximum N.A. of dry objectives is 0.95, but values > 1.0 can be achieved with immersion oil.
Apochromat oil immersion objectives can achieve very high N.A. and resolve very fine details, but they have a very short W.D.
The APON100XHOTIRF objective has the world’s highest NA of 1.7, while the UPLAPO60XOHR and UPLAPO100XOHR are the world’s first plan apochromat objectives with a numerical aperture (NA) of 1.5[olympus].
Resolving power
Resolution of the objective depend on it’s N.A. and can be calculated using the Rayleigh resolution limit:
d = 0.61λ / NAHere some examples using the objectives of my Olympus BH2.
Note that the Blue (450nm), Green (500nm) and Red (625nm) wavelength also depend on the bayer pattern of your camera sensor.
| Objective | λ | Abbe limit | Rayleigh limit | |||||
|---|---|---|---|---|---|---|---|---|
| MSPlan 10x/0.30 | 450nm | 0.750 µm | 0.915 µm | |||||
| 500nm | 0.833 µm | 1.017 µm | ||||||
| 625nm | 1.042 µm | 1.271 µm | ||||||
| MSPlan 20x/0.46 | 450nm | 0.489 µm | 0.597 µm | |||||
| 500nm | 0.543 µm | 0.663 µm | ||||||
| 625nm | 0.679 µm | 0.829 µm | ||||||
| MSPlan 50x/0.80 | 450nm | 0.281 µm | 0.343 µm | |||||
| 500nm | 0.312 µm | 0.381 µm | ||||||
| 625nm | 0.391 µm | 0.477 µm | ||||||
| Plan 100x/1.25 | 450nm | 0.180 µm | 0.220 µm | |||||
| 500nm | 0.200 µm | 0.244 µm | ||||||
| 625nm | 0.250 µm | 0.305 µm |
Note: the Plan 100x/1.25 is an oil objective, other ones are dry objectives.