# Diffraction Limit Calculator

## About Diffraction Limit Calculator (Formula)

The Diffraction Limit Calculator is a formula used to determine the smallest resolvable detail or angular resolution of an optical system, such as a telescope or camera, due to the phenomenon of diffraction. It is an important concept in optics and helps to understand the limitations of resolving fine details in images.

The formula for calculating the diffraction limit is:

Angular Resolution (θ) = 1.22 * (λ / D)

Where:

• Angular Resolution (θ) is the smallest resolvable angle in radians.
• λ (Lambda) is the wavelength of light used in the observation.
• D is the diameter of the aperture (opening) of the optical system.

Let’s explain each component of the formula:

1. Angular Resolution (θ): This is the smallest angle between two closely spaced objects or details that can be resolved by the optical system. It is usually expressed in radians or arcseconds.
2. λ (Lambda): The wavelength of light used in the observation. Light of different colors or wavelengths can affect the diffraction limit, with shorter wavelengths providing better resolution.
3. D: The diameter of the aperture, which is the opening that allows light to enter the optical system. In telescopes and cameras, it is often the diameter of the primary lens or mirror.

The concept of the diffraction limit is based on the wave nature of light. When light passes through a small aperture, it diffracts, causing the light waves to bend and interfere with each other, leading to the blurring of fine details in the observed image. The smaller the aperture (larger D value), the less diffraction occurs, resulting in better resolution and a smaller angular resolution.

The value “1.22” in the formula is a constant known as the Rayleigh criterion, which represents the minimum resolvable angle when the central peak of one diffraction pattern coincides with the first minimum of the other pattern.

The Diffraction Limit Calculator is crucial for astronomers, photographers, and optical engineers, as it helps determine the capabilities and limitations of optical instruments. It allows users to choose appropriate equipment or design systems to achieve the desired level of image clarity and resolution, considering the properties of light and the aperture size.