Calculate optical resolution using the Rayleigh criterion from wavelength and numerical aperture to find minimum resolvable distance or NA.
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Optical Resolution (Rayleigh) Formula
The Rayleigh criterion estimates the smallest distance between two points that can still be resolved as separate points by an optical system.
d = (0.61*\lambda)/NA
Rearranged to calculate wavelength:
\lambda = (d*NA)/0.61
Rearranged to calculate numerical aperture:
NA = (0.61*\lambda)/d
- d = resolution, or minimum resolvable distance
- λ = wavelength of light
- NA = numerical aperture, a unitless measure of light-gathering ability
- 0.61 = Rayleigh criterion constant for circular apertures
If you enter wavelength and numerical aperture, the calculator finds the minimum resolvable distance. If you enter resolution and numerical aperture, it finds the wavelength. If you enter wavelength and resolution, it finds the numerical aperture needed to reach that resolution.
Common Wavelengths and Resolution Scale
| Light or radiation | Typical wavelength | Same value in micrometers |
|---|---|---|
| Violet visible light | 400 nm | 0.400 μm |
| Green visible light | 550 nm | 0.550 μm |
| Red visible light | 650 nm | 0.650 μm |
| Near infrared | 850 nm | 0.850 μm |
Typical Numerical Aperture Ranges
| Optical system | Typical NA range | Effect on resolution |
|---|---|---|
| Low-power microscope objective | 0.10 to 0.25 | Larger minimum resolvable distance |
| Medium-power objective | 0.40 to 0.75 | Moderate resolution |
| High-NA dry objective | 0.80 to 0.95 | Smaller minimum resolvable distance |
| Oil immersion objective | 1.20 to 1.40 | Very high optical resolution |
Example Problems
Example 1: Calculate resolution
You have a wavelength of 550 nm and a numerical aperture of 1.25.
d = (0.61*550)/1.25
d = 268.4\text{ nm}The minimum resolvable distance is 268.4 nm, or 0.2684 μm.
Example 2: Calculate numerical aperture
You want a resolution of 0.30 μm using light with a wavelength of 0.55 μm.
NA = (0.61*0.55)/0.30
NA = 1.1183
You need a numerical aperture of about 1.12.
FAQ
What does a smaller resolution value mean?
A smaller value of d means better resolution. It means the optical system can distinguish two points that are closer together. For example, 200 nm resolution is better than 500 nm resolution.
How does numerical aperture affect optical resolution?
A higher numerical aperture improves resolution because NA is in the denominator of the Rayleigh formula. When NA increases, the minimum resolvable distance decreases. This is why high-NA microscope objectives can show finer detail.
Do wavelength and resolution need to use the same units?
The formula requires consistent length units. The calculator converts wavelength and resolution units internally, so you can enter wavelength in nm and resolution in μm. If you calculate by hand, convert both length values to the same unit before using the formula.
