In a machine vision system, the lens plays a role similar to that of the human eye, as it is responsible for focusing the optical image of the target onto the photosensitive surface of the image sensor (camera). All image data processed by the vision system originates from the lens, and its quality directly impacts the overall performance of the system. Below is a detailed explanation of key technical terms related to industrial lenses used in machine vision.
First, **distortion** refers to the deviation of the image shape from the original object. It can be categorized into pincushion distortion and barrel distortion, as shown in the image below:
Second, **TV distortion** is calculated as the percentage difference between the actual side length of a warped shape and the ideal shape.
Third, **optical magnification** is the ratio of the image size to the object size. This is often represented by the following diagram:
Fourth, **monitor amplification** is the factor by which the image is scaled when displayed on a monitor. The calculation method is as follows:
For example, using a VS-MS1+10x lens with a 1/2†CCD camera to image a 14†monitor, an object of 0.1mm will appear as 44.45mm on the screen. However, this calculation may vary slightly depending on the TV monitor’s scanning status.
Fifth, **resolution** is defined as the smallest distance between two points that can be distinguished, calculated using the formula:
**Resolution = 0.61 × λ / NA**, where λ is the wavelength and NA is the numerical aperture.
This theoretical calculation does not account for distortion.
Note: Wavelength used is typically 550nm.
Sixth, **resolution** can also be expressed as the number of black and white line pairs per millimeter (lp/mm).
Seventh, **MTF (Modulation Transfer Function)** measures how well a lens reproduces contrast across different spatial frequencies. It indicates the imaging quality and the ability of the lens to maintain image contrast.
Eighth, **Working Distance (WD)** is the distance from the front of the lens to the object being imaged.
Ninth, **Object-to-Imager (O-I)** distance is the distance from the object to the image sensor.
Tenth, **imaging circle** refers to the diameter of the image that must fit within the camera's sensor size.
Eleventh, **Camera Mounts** include various types such as C-mount, CS-mount, F-mount, and M72-mount, each with specific dimensions and thread pitches:
- **C-mount**: 1" diameter x 32 TPI, FB: 17.526mm
- **CS-mount**: 1" diameter x 32 TPI, FB: 12.526mm
- **F-mount**: FB: 46.5mm
- **M72-Mount**: FB varies by manufacturer
Twelfth, **Field of View (FOV)** is the area of the object visible through the camera. It is calculated based on the camera's effective area and magnification:
- **Vertical FOV = Effective Vertical Length / Magnification**
- **Horizontal FOV = Effective Horizontal Length / Magnification**
The FOV values are usually derived from standard light source and sensor specifications. The effective pixel size multiplied by the number of pixels gives the actual FOV dimensions.
Thirteenth, **Depth of Field (DOF)** refers to the range of distances over which the image appears acceptably sharp. It is influenced by factors like magnification, f-number, and permissible circle of confusion.
Fourteenth, **Focal Length (f)** is the distance from the rear principal point of the lens to the focal plane.
Fifteenth, **FNO (F-number)** represents the lens brightness and is calculated as **FNO = f / D**, where f is the focal length and D is the diameter of the entrance pupil.
Sixteenth, **Effective F** is the F-number at a specific working distance, given by:
- **Effective F = (1 + Magnification) × F#**
- **Effective F = Magnification / (2 × NA)**
Seventeenth, **NA (Numerical Aperture)** is defined as **NA = sin(u) × n** on the object side and **NA' = sin(u') × n'** on the image side. It is related to magnification by **NA = NA' × Magnification**.
Eighteenth, **Edge Brightness** refers to the contrast between the center and the edges of the image, expressed as a percentage of the central illuminance.
Nineteenth, **Telecentric Lens** is designed so that the chief ray is parallel to the optical axis. There are three types: object-side telecentric, image-side telecentric, and double-side telecentric.
Twentieth, **Telecentricity** refers to the consistency of magnification across the field of view. A higher telecentricity means less magnification error. The chief rays of a telecentric lens are parallel to the optical axis.
Twenty-first, **Depth of Field (DOF)** can be calculated using the formula:
- **DOF = 2 × Permissible COC × Effective F / (Magnification²)**
- **DOF = Permissible Error Value / (NA × Magnification)**
Using a permissible COC of 0.04mm, the DOF is determined accordingly.
Twenty-second, **Airy Disk** is the diffraction pattern formed by a focused point of light. Its radius is calculated as **r = 0.61λ / NA**, and it determines the resolution limit of the lens. For example, with NA = 0.07 and λ = 550nm, r ≈ 4.8μm.
Twenty-third, **MTF and Resolution** are closely related. MTF measures how well a lens preserves contrast at different spatial frequencies. Higher MTF values indicate better image quality. While resolution defines the minimum separable distance, MTF provides a more comprehensive assessment of lens performance.
Figures 2 and 3 illustrate how MTF changes with spatial frequency. The horizontal axis shows the number of cycles per mm, while the vertical axis shows brightness. The contrast between the object and the image is measured, and MTF is derived from the ratio of these values.
Finally, Figure 4 compares the MTF curves of two lenses. One has high contrast but low resolution, while the other has high resolution but lower contrast. This highlights the trade-off between resolution and image quality in lens design.
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