Enter any 2 values into the calculator. The calculator will evaluate the diffraction-limited resolution (minimum resolvable distance) using the Abbe equation.

Abbe Equation (Resolution) Calculator

Enter any 2 values to calculate the missing variable

Related Calculators

Abbe Equation Formula

d = \lambda/(2\cdot NA)

Variables:

  • d is the diffraction-limited lateral resolution (minimum resolvable distance)
  • λ is the wavelength of light
  • NA is the numerical aperture (unitless)

How to Calculate Abbe Equation?

The following steps outline how to calculate the Abbe diffraction-limited resolution using the Abbe equation.

  1. First, determine the wavelength (λ) of the light used.
  2. Next, determine the numerical aperture (NA) of the optical system.
  3. Next, gather the formula from above: d = λ/(2·NA).
  4. Finally, calculate the resolution (d).
  5. 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 (λ) = 550 nm

numerical aperture (NA) = 1.40

resolution (d) = 550 nm / (2 × 1.40) ≈ 196 nm

FAQs

What is the significance of the numerical aperture in optical systems?

Numerical aperture (NA) is a critical parameter in optical systems that describes a lens’s ability to gather light and resolve fine specimen detail. A higher NA generally enables finer (smaller) diffraction-limited resolution.

How does wavelength affect the resolution of an optical system?

Wavelength plays a crucial role in diffraction-limited resolution. According to the Abbe equation, shorter wavelengths lead to a smaller minimum resolvable distance (better resolution), allowing the system to distinguish finer details.

Can the resolution be improved without changing the numerical aperture or wavelength?

For the Abbe diffraction limit itself, improving resolution generally requires changing the effective numerical aperture or the wavelength. For example, using an immersion medium can increase the effective NA. In some cases, advanced methods (for example, structured illumination microscopy or other super-resolution techniques) can improve effective resolution under specific conditions.

Why is the Abbe equation important in microscopy?

The Abbe equation is fundamental in microscopy because it quantifies the relationship between the diffraction-limited resolution of an optical system, the wavelength of light used, and the numerical aperture of the system. This helps in understanding and designing optical systems for optimal resolution.