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Diffraction

Diffraction is an optical phenomenon that limits the sharpness of a photograph while reducing the relative aperture of the lens. Unlike other optical aberrations, diffraction is fundamentally unremovable, universal and equally common to all photographic lenses without exception, regardless of their quality and cost.

Diffraction can only be seen at 100% magnification. Notice how the image becomes less and less sharp with increasing aperture.
With the passage of light through the aperture, the bulk of the light waves continues to move rectilinearly. However, those waves whose path lies near the very edge of the diaphragm deviate from their original direction, trying to go around the obstacle that has arisen on their way. The smaller the size of the aperture opening, the greater the percentage of rays touching its edge, and the more light is scattered. Due to the diffraction of light waves, the image of a point light source does not take the form of a point (as it would be in an ideal optical system), but of a blurry spot, which is called an Airy disk.

Despite some similarities between the Airy disk and the scattering circle that occurs when the lens is defocused, the Airy disk has three very characteristic features.

Airy Drive
Firstly, the circle of confusion is lit more or less evenly, while the brightness of the Airy disk rapidly decreases with distance from its center.

Secondly, unlike the scattering circle, which is a lonely round spot, the Airy disk is surrounded by a series of concentric rings. These rings arise due to the interference of light waves deviated from the original path with each other, as well as with waves that maintain a rectilinear direction. Together with the Airy disk, the rings form a characteristic diffraction pattern known as the Airy pattern. 85% of the illumination falls on the Airy disk itself, and 15% on the rings surrounding it.

Thirdly, with aperture of the lens, the diameter of the scattering circle decreases, while the diameter of the Airy disk, on the contrary, increases. Accordingly, with a decrease in the relative aperture (i.e., with an increase in the number of aperture), the depth of the sharply depicted space increases, but the overall sharpness of the photograph decreases.

Diffraction and resolution of the camera
According to the Rayleigh criterion, in order for two adjacent Airy disks to be visually distinguishable, their radius should not exceed the distance between the centers of the disks. Otherwise, the disks are perceived as a single point. Since at a constant light wavelength, the radius of the Airy disk depends solely on the aperture value, for any distance between the disks there is a certain maximum aperture value, upon reaching which the disks grow so much that they merge together.

What does this have to do with digital photography? The most immediate. Two theoretical points can be distinguished in the image only if the distance between them is not less than the distance between the centers of two adjacent pixels of the matrix. If two points are Airy disks (but in reality it cannot be otherwise), then at a certain aperture value they will still cease to be distinguishable due to the diffraction effect. Thus, the potential resolution of the system is limited on the one hand by the pixel density of the matrix, and on the other hand, by the value of the relative aperture of the diaphragm.

The aperture value at which the radius of the Airy disk is equal to the pixel size of the matrix of a specific digital camera is called the diffraction-limited aperture value or simply diffraction-limited aperture (tracing paper from the English diffraction limited aperture – DLA). At aperture numbers greater than the diffraction-limited value, image degradation due to diffraction becomes visually distinguishable.

The value of the diffraction-limited aperture for any digital camera can be calculated using the following formula:

Diffraction-limited aperture, where

K – diffraction-limited aperture;

n is the pixel size of the matrix in micrometers (microns);

λ is the wavelength of light in nanometers.

The pixel size n (see “How do I know the matrix pixel size?”) Corresponds to the limiting radius of the Airy disk or, if you want, the diffraction limit of the optical system. I advise taking 540 nm for the wavelength λ, since both the human eye and the digital photomatrix are most sensitive specifically to green. For blue, diffraction will be less pronounced, and for red more.

To save your time, the author was not too lazy to calculate the values ​​of the diffraction-limited aperture for matrices with various parameters and compile an appropriate table. Using these or smaller aperture numbers, you can be sure that your pictures are free from the negative effects of diffraction and that their blur is due to imperfections in the photo equipment.

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