The Diffraction Limit Calculator helps determine the smallest angular resolution that an optical system can achieve due to the wave nature of light. This is crucial in fields such as astronomy, microscopy, and photography, where resolving fine details is essential. By inputting the wavelength of light and the aperture diameter of the optical system, users can calculate the diffraction limit and understand the fundamental resolution constraints.
Formula of Diffraction Limit Calculator
The diffraction limit is calculated using the following equation:
θ = 1.22 × (λ / D)
其中：
θ is the diffraction limit in radians λ is the wavelength of the light, typically measured in nanometers or meters D is the aperture diameter of the optical system, usually in meters
This formula defines the smallest angle that can be resolved by an optical system. Smaller values of θ indicate better resolving power.
Diffraction Limit Reference Table
This table provides common diffraction limits for different wavelengths and aperture diameters to help users make quick estimations.
| 波长（nm） | Aperture Diameter (m) | Diffraction Limit (arcseconds) |
|---|---|---|
| 500 | 0.1 | 2.44 |
| 500 | 1.0 | 0.24 |
| 500 | 10.0 | 0.024 |
| 650 | 0.1 | 3.17 |
| 650 | 1.0 | 0.32 |
| 650 | 10.0 | 0.032 |
These values illustrate how increasing the aperture size improves resolution, while longer wavelengths result in lower resolving power.
Example of Diffraction Limit Calculator
An astronomer is using a telescope with a 2-meter aperture to observe stars using a 600 nm wavelength filter. To determine the diffraction limit:
θ = 1.22 × (600 × 10⁻⁹ / 2)
θ = 3.66 × 10⁻⁷ radians
Converting to arcseconds:
θ × (206265) = 0.075 arcseconds
This means the telescope can resolve details as small as 0.075 arcseconds under ideal conditions.
最常见的常见问题解答
The diffraction limit is the smallest angular separation that an optical system can resolve, determined by the wavelength of light and the aperture diameter.
Larger apertures result in a smaller diffraction limit, meaning better resolving power and the ability to see finer details.
Longer wavelengths result in a higher diffraction limit, reducing resolution. Shorter wavelengths allow for finer detail resolution.