For photography enthusiasts or machine vision practitioners, the lens is like a human eye. However, the complex numbers and terms on the lens - focal length, aperture, MTF - often leave people dazzled. These parameters are not just cold numbers, they collectively determine what you ultimately see in the picture. This article will guide you to understand the core parameters of optical lenses and uncover the secrets behind imaging quality.

1, Basic three elements: focal length, aperture, and depth of field

1. Focal length
Focal length, usually represented by f, is the most fundamental identification of a lens. From an optical principle perspective, it refers to the distance (in millimeters) from the optical center of the lens to the focal plane. But from a practical perspective, focal length determines two key effects: viewing angle and magnification.

Short focal length (wide-angle): Small numerical value (such as 16mm), large viewing angle, able to accommodate a wider scene, but distant objects appear smaller. Suitable for shooting landscapes or indoor spaces with limited space.

Long focal length (telephoto): With a large value (such as 200mm) and a narrow viewing angle, it is like a telescope that can zoom in and out of distant objects. Suitable for shooting sports events or wildlife.

It should be noted that the size of the sensor will affect the actual viewing angle. For example, if the same lens is installed on an APS-C format camera, the angle of view will narrow due to the sensor only capturing the central part of the image, which is equivalent to multiplying the focal length by 1.5 times (equivalent focal length).

2. Aperture
Aperture is a hole inside the lens used to control the amount of light entering. Its value is represented by the F-value, such as F1.4, F2.8, F5.6. There is a counterintuitive rule here: the smaller the F-value, the larger the aperture.
Light flux: The smaller the F-value, the more light enters, giving it an advantage in shooting in low light environments and allowing for higher shutter speeds to prevent hand tremors.
Aperture coefficient sequence: The standard F-value sequence (such as 1.4, 2, 2.8, 4, 5.6...) has a difference of twice the amount of incoming light for every two adjacent levels. Because the amount of light passing through is inversely proportional to the square of the F-value.

3. Depth of Field
When you focus on the subject, the range of clear imaging in front and behind the object is the depth of field -1-3. Depth of field is influenced by three factors, which are also powerful tools for photographers to create blurring effects:
Aperture: The larger the aperture (the smaller the F-value), the shallower the depth of field (the more pronounced the background blur); The smaller the aperture (larger F value), the deeper the depth of field (clear front and rear scenes).
Focal length: The longer the focal length, the shallower the depth of field; The shorter the focal length, the deeper the depth of field.
Shooting distance: The closer the lens is to the subject, the shallower the depth of field.

2, Field of view and distortion: field of view angle and distortion

4. Field of view angle
Field of view angle refers to the angle of the scene range that the lens can cover -6 degrees. It is inversely proportional to the focal length and directly proportional to the sensor size.
In machine vision, the horizontal field of view angle (ω H) can be calculated using sensor size (h) and focal length (f): ω H=2 tan ⁻¹ (h/2f) -6. Simply put, if you want to see a larger range at the same distance, you need a shorter focal length or a larger sensor.
5. Distortion
Distortion refers to the degree of distortion of an image, which does not affect clarity, but only affects shape.
Barrel distortion: The image resembles a inflated ball expanding outward and a straight line bending outward. Commonly seen in wide-angle lenss.
Pillow distortion: The image resembles the four corners of a pillow shrinking inward and straight lines bending inward. Commonly seen in telephoto lenss.
High precision measurement systems must use low distortion lenses, otherwise software calibration is required.

3, Core indicators of imaging quality: resolution and MTF

6. Resolution
In the field of lenses, resolution refers to the ability of a lens to distinguish object details, measured in "line pairs per millimeter" (lp/mm), which means how many black and white lines can be distinguished per millimeter distance.
The resolution of the lens needs to match the pixel size of the camera. If the resolution of the lens is too low, even if the camera pixels are high, it cannot present details. According to the Nyquist sampling theorem, the size of the lens line should be approximately 2 times the pixel size.

7. MTF curve
MTF (Modulation Transfer Function) is the most scientific and comprehensive tool for evaluating lens imaging quality. It is not like a single resolution value that only describes the ultimate resolution, but reflects the lens' ability to transmit contrasts.
Horizontal axis: distance from the center of the image (image height).
Vertical axis: Contrast restoration ability (1 for perfect restoration, 0 for complete loss).
Interpretation technique: The higher the curve, the better the contrast and resolution of the lens; The flatter the curve, the better the consistency between the center and edges of the screen.

4, Advanced terminology: It's not just about taking photos

In the field of professional photography or machine vision, there are also some parameters that are crucial:
8. Rear focal length and flange distance
Rear focal length refers to the distance from the surface of the last lens of the lens to the focal point, which is -1. When replacing the lens or using an adapter ring, it is important to pay attention to whether the flange distance (the distance from the mount plane to the focal point) matches. For example, when installing a C-interface lens (with a flange distance of 17.526mm) onto a CS interface camera, it is necessary to install a tier.

9. Main light angle
Chief Ray Angle (CRA) refers to the angle between the principal ray emitted by the lens and the optical axis, which is. In order to ensure that the light can be smoothly received by the "well" of the sensor pixels, the CRA of the lens must be less than or equal to the CRA of the camera, otherwise there will be color cast or darkening at the edges of the image (i.e. Color Shading phenomenon).

10. Telescopic lens
In a regular lens, the closer an object is to the lens, the larger the image. But in precision measurement, this perspective error is not allowed. The telecentric lens is designed with a special optical path to ensure that the imaging magnification remains constant within a certain object distance range, thereby eliminating parallax and making it the preferred choice for high-precision measurements.