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The diffraction limit sets a hard boundary on how well an optical system, such as a microscope or telescope, can resolve fine details. This limit is determined by the inherent wave properties of light and the unavoidable phenomenon of diffraction when light passes through an aperture. To get the most out of any optical system, it’s crucial to understand what the diffraction limit is, how it works, and why ignoring it can lead to disappointing results.
In any optical system, from microscopes to telescopes, diffraction plays a critical role in setting a resolution ceiling. The diffraction limit is a fundamental restriction caused by the wave-like behavior of light. As light enters an optical system through an aperture, it bends and interferes with itself, producing a pattern known as an Airy disk.
Every optical aperture creates this Airy disk—a small, bright center surrounded by fainter rings of light. The radius of this disk, and thus the smallest point that light can be focused into, is given by the formula:
Ra = 1.22λ/2Na
Where:
This radius defines the minimum spot size, a key factor in how fine an optical system can resolve detail. As the numerical aperture increases, the Airy disk’s size decreases, allowing for finer resolution.
In an ideal world, without optical imperfections, the diffraction limit would be the primary factor in how well a system can resolve details. Each point of light in an image creates its own Airy disk. If these disks don’t overlap, the image is well-resolved. However, when the outer rings of neighboring disks begin to merge, the system becomes diffraction-limited.
At this stage, increasing the aperture size further doesn’t improve resolution because the diffraction cutoff frequencyhas been reached. This is the point where any additional increase in aperture results in negligible gains in resolution, as the overlap of Airy disks makes it impossible to distinguish between finer details.
To calculate the diffraction limit or cutoff frequency, use the following formula:
Diffraction limit = 2Na/λ × (1000 μm/1 mm)
This equation gives us the maximum theoretical resolution based on aperture and wavelength, helping to set clear expectations for optical performance.
Terrestrial telescopes rarely achieve diffraction-limited resolution due to atmospheric disturbances that blur images beyond this theoretical limit. The diffraction limit is a fundamental consequence of light’s wave nature, dictated by the laws of physics, and cannot be surpassed by any conventional optical system. This limit plays a critical role in applications such as microscopy, telescopy, and high-resolution imaging, where precise detail is essential. While everyday photography may be constrained by lens aberrations or sensor quality, advanced optical systems must consider the diffraction limit to capture fine details. In visible light microscopy, the diffraction limit generally falls between 200-250 nanometers, defining the smallest distinguishable features in samples. For telescopes, the diffraction limit is typically expressed in terms of angular resolution, ranging from 0.1 to 1 arc second, depending on the aperture and wavelength used.
Understanding the diffraction limit is vital for anyone working with optical systems, from engineers designing telescopes to scientists using high-powered microscopes. While technological improvements can enhance many aspects of an optical system, the diffraction limit sets a hard boundary on resolution that no amount of engineering can surpass. By accounting for this limit in system design, we can optimize performance and avoid over-promising on what can realistically be achieved.
Recognizing the constraints of diffraction is the first step in mastering the performance potential of any optical setup.
Contact Shanghai Optics today! We’d be more than happy to discuss your projects and how to best bring them to fruition.