Enter the wavelength and the numerical aperture into the calculator. The calculator will estimate the diffraction-limited resolution (minimum resolvable distance) using the Rayleigh criterion (often mistakenly called “resolving power” when expressed as a distance).
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Diffraction-Limited Resolution Formula (Rayleigh Criterion)
d = 0.61 \frac{\lambda}{NA}Variables:
- d is the diffraction-limited lateral resolution (minimum resolvable distance) (a length, e.g., μm)
- λ is the wavelength of light (same length units as d, e.g., μm)
- NA is the numerical aperture (dimensionless)
To calculate the diffraction-limited resolution (minimum resolvable distance), divide the wavelength by the numerical aperture, then multiply by 0.61. A smaller value of d means better resolving ability.
How to Calculate Resolution (Rayleigh Criterion)?
The following steps outline how to calculate the diffraction-limited resolution (minimum resolvable distance).
- First, determine the wavelength (λ).
- Next, determine the numerical aperture (NA).
- Next, gather the formula from above: d = 0.61 × λ / NA.
- Finally, calculate the resolution (d).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
wavelength (μm) = 0.55
numerical aperture = 0.9
FAQ – Optical Resolution (Rayleigh Criterion)
What is “Resolving Power” here?
This calculator computes the diffraction-limited resolution as a distance (the minimum resolvable separation, d) using the Rayleigh criterion. In many optics contexts, “resolving power” refers to the ability to resolve detail and is often expressed as an inverse quantity (for example, proportional to 1/d) rather than a length.
Why is the numerical aperture important in calculating resolution?
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. A higher NA gives a smaller minimum resolvable distance (better resolution), because d = 0.61λ/NA decreases as NA increases.
How does wavelength affect resolution?
The wavelength of light used in an optical system affects its resolution. Shorter wavelengths produce a smaller minimum resolvable distance than longer wavelengths. This is why ultraviolet light, with its shorter wavelength, is used in some microscopy techniques to achieve higher resolution.
Can resolution be improved by changing the numerical aperture?
Yes, increasing the numerical aperture (NA) of an optical system can improve its resolving ability (reduce the minimum resolvable distance). However, there are practical limits to increasing NA, such as lens design, working distance, and diffraction-related constraints.
