Imaging Principles of Lenses

Lens imaging is based on the convex lens imaging principle. Through a combination of lenses, light rays emitted or reflected by an object are projected onto the image plane (aligned with the sensor surface). A combined assembly of convex and concave lenses can effectively correct various optical aberrations, including spherical aberration, off-axis aberration and chromatic aberration, so as to improve image quality.

Introduction to Technical Specifications

1. Focus / Focal Length

When light rays parallel to the optical axis enter a convex lens, an ideal lens converges all rays at a single point before they spread out in a conical shape. This convergence point is defined as the focal point. For a single lens, the focal length refers to the distance from the optical center to the focal point, as shown in Figure 1. For a lens assembly composed of multiple lenses, the focal length refers to the distance from the image principal plane to the focal point, as shown in Figure 2.

2. Aperture 

Inside the lens lies an adjustable polygonal or circular diaphragm with a variable aperture size, known as the aperture. It controls the volume of light passing through the lens, and its size is quantified by the aperture number. The aperture number is the ratio of the lens focal length to the entrance pupil diameter D of the entire lens, denoted as f/#. Calculation formula: f/#=f′/D

A smaller f/# value corresponds to a larger aperture. Standard f/# values increase by a factor of √2, with common grades including F1.4, F2.0, F2.8, F4.0, etc. Within the same unit of time, the light transmission area of one aperture grade is twice that of the next lower grade. For example, adjusting the aperture from f/8 to f/5.6 doubles the light transmission area.

Impact of aperture on image brightness: under identical operating conditions and with the same lens, a larger aperture provides a wider light passage and produces a brighter image.

3. Working Distance

Working Distance: the distance between the target object and the foremost surface of the lens when the lens achieves sharp focus. In practical deployment, a lens cannot focus sharply on targets at all object distances, so its working distance falls within a specific range.

4. Field Angle / Field of View

1. Field AngleIn optical engineering, the field angle is the subtended angle of the lens relative to the image sensor. If y′ represents half the diagonal length of the sensor, the field angle 2θ≈2*arctan(y′/f′).
2. Field of View (FoV)Also referred to as the viewing range, FoV describes the actual observable area captured by the lens. The FoV of the lens and camera resolution jointly determine the detection accuracy achievable by a machine vision system.

With a fixed working distance, a shorter focal length delivers a wider field angle and a larger FoV. With a fixed focal length and constant field angle, a longer working distance results in a larger FoV. 

5. Magnification

Magnification is defined as the ratio of image size to object size.

• When -1＜β ＜0: the object and image are on opposite sides, forming an inverted and reduced real image, as shown by AA′. This is the basic lens imaging principle.
• When β=-1: the object and image are on opposite sides, forming an inverted real image of equal size, as shown by BB′.
• When β＜-1: the object and image are on opposite sides, forming an inverted and magnified real image, as shown by CC′. This is the imaging principle of microscopes.
• When β＞0: the object and image are on the same side, forming an upright and magnified virtual image, as shown by DD′. This is the imaging principle of magnifying glasses.

6. Resolution

Resolution refers to the minimum distinguishable feature size on a target object that an optical system can detect. The smaller the fine details a lens can resolve, the higher its resolution. It is commonly measured as line pairs per millimeter (lp/mm), representing the number of alternating black-and-white line pairs resolvable on the image plane. In practical applications, it is recommended that the lens resolution be no lower than the camera resolution.

7. Depth of Field (DoF)

Depth of Field: the spatial range on the object side where sharp images can be formed on the image plane. In other words, objects within a certain range in front of and behind the focused plane remain sharply imaged without refocusing; this continuous sharp imaging range is the depth of field.

Primary Factors Affecting Depth of Field

1. Lens Aperture A larger aperture reduces depth of field; a smaller aperture increases depth of field.
2. Lens Focal Length A longer focal length reduces depth of field; a shorter focal length increases depth of field.
3. Shooting Distance A longer shooting distance increases depth of field; a shorter shooting distance reduces depth of field.

8. Optical Distortion

Optical distortion: as the magnification of the lens varies across different field angles, the resulting image loses geometric similarity to the original object. Such image deformation is defined as optical distortion. Optical distortion only affects the geometric shape of the image and does not impair sharpness. The two most common types are barrel distortion and pincushion distortion (see figure).

9. TV Distortion

TV distortion measures the visual distortion of an image, with multiple available definitions. The formula for RIAA TV distortion is listed below:

10. Back Focal Length

1. Flange Focal Distance: distance from the lens flange surface to the image plane (sensor).
2. Mechanical Back Focal Length: distance from the rearmost mechanical surface of the lens to the image plane.
3. Optical Back Focal Length: distance from the vertex of the rearmost lens surface inside the lens to the image plane.