A complete analysis of lens imaging principles: from focal length to distortion, understand the secrets of optics in one article

1. Lens Imaging Principle

Lens imaging is based on the principle of convex lens imaging. When light passes through a lens, the lens combination focuses the light reflected or emitted by the object onto the image plane (usually coinciding with the camera sensor). This combination of concave and convex lenses can effectively correct optical defects such as spherical aberration, off-axis aberration, and chromatic aberration, thereby improving image quality.

2. Key parameters of a lens (1) Focus and focal length

Focus: The point where light rays parallel to the optical axis converge after passing through the lens.

Focal length (f'): The distance from the optical center of the lens (or the principal plane of the image side of the lens group) to the focus.

The longer the focal length, the narrower the angle of view, which is suitable for photographing distant objects (such as telephoto lenses).

The shorter the focal length, the wider the angle of view, which is suitable for photographing large scenes (such as wide-angle lenses).

(2) Aperture (f/#) The aperture controls the amount of light that enters the lens. Its size is expressed by the f-number (f/#): f/#=f′Df/#=Df′ The smaller the f/#, the larger the aperture, the more light enters, the brighter the picture, but the shallower the depth of field (the background is more blurred). For every increase in aperture (e.g. f/2.8→f/2.0), the amount of light passing through doubles. The effect of aperture on imaging: Large aperture (f/1.4): Suitable for low-light environments, with strong background blur. Small aperture (f/16): Suitable for landscape photography, with a large depth of field and clear foreground and background.

(3) Working Distance (WD)

Definition: The distance from the target object to the front of the lens when the lens is in sharp focus.

Different lenses have different working distances. For example, a macro lens can focus at very close distances, while a telephoto lens requires a longer working distance.

(4) Field of View (FOV)

Field of View (2θ): The imaging range that the lens can cover. Calculation formula:

2θ≈2×arctan⁡(y′f′)2θ≈2×arctan(f′y′)

y': The half-diagonal length of the sensor.

Field of View (FOV): The physical range that the lens can actually capture.

The shorter the focal length, the larger the field of view (wide-angle lens).

The longer the focal length, the smaller the field of view (telephoto lens).

(5) Magnification (β) Magnification indicates the size ratio of the image to the object: β = -1: Inverted real image of the same size (e.g., 1:1 macro photography). β < -1: Inverted magnified real image (microscope principle). β > 0: Upright magnified virtual image (magnifying glass principle).

(6) Resolution

Definition: The smallest detail that a lens can resolve, unit: lp/mm (line pairs/millimeter).

The lens resolution should be ≥ the camera sensor resolution, otherwise the image clarity will be limited.

(7) Depth of Field (DOF) Depth of field refers to the depth of the object space within which a clear image can be formed on the image plane. Factors affecting depth of field: Aperture: The larger the aperture, the smaller the depth of field (the more blurred the background). Focal length: The longer the focal length, the smaller the depth of field. Shooting distance: The closer the distance, the smaller the depth of field.

(8) Optical distortion

Due to the different magnifications of the lens in different fields of view, the image is distorted, but it does not affect the clarity.

Barrel distortion: The edges of the image expand outward (common with wide-angle lenses).

Pincushion distortion: The edges of the image shrink inward (common with telephoto lenses).

(9) Back focus distance

Flange distance: the distance from the flange surface of the lens to the image plane of the sensor (different for different camera mounts, such as Sony E-mount and Canon EF-mount).

Mechanical back focus distance: the distance from the last mechanical surface of the lens to the image plane.

Optical back focus distance: the distance from the last lens element to the mirror surface.

3. Summary

Lens image quality is influenced by multiple factors, including focal length, aperture, field of view, resolution, depth of field, and distortion. Understanding these parameters can help us better select lenses and optimize our photography. Mastering this knowledge is crucial for both photography enthusiasts and machine vision engineers!

What's your favorite camera? Share your experience in the comments!

(Some images in this article are sourced from the internet and are for reference only.)

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