Lenses come in different types, but even for the same lens type, image quality can vary significantly. This is mainly due to differences in materials, machining accuracy, and lens element structure, which also lead to huge price differences ranging from hundreds to tens of thousands of RMB. Well-known examples include the four-element, three-group Tessar lens and the six-element, four-group double-Gauss lens. For lens designers and manufacturers, the Optical Transfer Function (OTF) is generally used to comprehensively evaluate lens imaging quality. An optical system transmits information about the spatial distribution of brightness. When transmitting scene information, the changes in modulation and phase of sinusoidal signals at various spatial frequencies as they form an actual image are functions of the spatial frequency – this function is called the OTF. OTF typically consists of two parts: the Modulation Transfer Function (MTF) and the Phase Transfer Function (PTF).

Aberrations are a major factor affecting image quality. The six common types of aberrations are as follows:

Spherical Aberration
When a monochromatic conical beam emitted from an object point on the optical axis passes through the optical system and is refracted, if rays at different aperture angles do not converge at the same point on the axis, a diffuse spot (commonly called a circle of confusion) is formed at the ideal image plane on the axis. This imaging error is called spherical aberration.

Coma
For a monochromatic conical beam emitted from an off-axis object point, after refraction through the optical system, if it does not form a sharp point on the ideal image plane but instead forms a comet‑shaped spot with a bright tail, this imaging error is called coma.

Astigmatism
When an oblique monochromatic conical beam from an off‑axis object point is refracted by the optical system and cannot form a clear image point but only a diffuse spot, this imaging error is called astigmatism.

Field Curvature
If the sharp image formed by the optical system of a planar object perpendicular to the optical axis is not on an image plane perpendicular to the optical axis but on a curved surface symmetrical about the optical axis (i.e., the best image surface is curved), this imaging error is called field curvature. When focused so that the center of the frame is sharp, the edges are blurred; when focused for sharp edges, the center becomes blurred.

Chromatic Aberration
When a white object emits a white light beam that passes through the optical system and is refracted, different colors of light fail to converge at a single point, forming a colored spot. This is called chromatic aberration. The cause of chromatic aberration is that the same optical glass has different refractive indices for different wavelengths of light – shorter wavelengths are refracted more strongly, longer wavelengths less so.

Distortion
When a straight line off the axis in the object plane is imaged by the optical system as a curve, this imaging error is called distortion. Distortion affects only the geometric shape of the image, not its sharpness. This is the fundamental difference between distortion and spherical aberration, coma, astigmatism, and field curvature.

When evaluating lens quality, several practical parameters are also used: resolution, acutance, and depth of field.

1. Resolution
Also known as resolving power or definition, resolution refers to the lens’s ability to clearly distinguish fine details of the scene. The limiting factor for lens resolution is the diffraction of light – the diffraction spot (Airy disk). Resolution is measured in line pairs per millimeter (lp/mm).

2. Acutance
Also referred to as contrast, acutance is the contrast between the brightest and darkest parts of an image.

3. Depth of Field (DOF)
In object space, objects within a certain distance in front of and behind the focused object plane can still form relatively sharp images. The longitudinal distance between those objects in front of and behind the focused plane that yield acceptably sharp images – i.e., the depth range in object space that produces relatively sharp images on the actual image plane – is called depth of field.

4. Maximum Relative Aperture and f-number
Relative aperture is the ratio of the entrance pupil diameter (D) to the focal length (f): Relative Aperture = D/f. The reciprocal of the relative aperture is called the f-number (aperture scale), also known as the f-stop or f-number. Most lenses have adjustable relative apertures; the maximum relative aperture or f-number is usually marked on the lens, e.g., 1:1.2 or f/1.2. When shooting in low light or with very short exposure times, a lens with a larger maximum relative aperture should be chosen whenever possible.

Interactions Among Lens Parameters

A good lens performs well in resolution, acutance, depth of field, and aberration correction, but its price may be several times or even hundreds of times higher. By understanding some rules and experience, we can achieve better results even with lenses of the same grade.

1. Effect of Focal Length

• Shorter focal length → greater depth of field

• Shorter focal length → greater distortion

• Shorter focal length → more severe vignetting, reducing illumination at the image edges

2. Effect of Aperture Size

• Larger aperture → brighter image

• Larger aperture → shallower depth of field

• Larger aperture → higher resolution

3. Center vs. Edge of Image Field

• Resolution is generally higher at the center than at the edges

• Illumination (light intensity) is generally higher at the center than at the edges

4. Effect of Light Wavelength

Under the same camera and lens parameters, the shorter the wavelength of the illumination light source, the higher the resolution of the resulting image. Therefore, in vision systems requiring precise dimensional or positional measurements, using short-wavelength monochromatic light as the illumination source greatly improves system accuracy.