Calculation relationship between working distance, resolution and field of view angle

The calculation relationship between working distance, resolution, and field of view angle is fundamental in imaging systems, particularly in applications such as camera design, microscopy, and surveillance. These parameters are interrelated and understanding their relationships helps in optimizing the performance of imaging systems.

📐 Working Distance and Field of View Angle

• Working Distance Impact on Field of View: The working distance (WD) is the distance from the lens to the object being imaged. The field of view (FOV) is determined by the focal length (f) and the size of the sensor or target. The relationship can be expressed as $ \text{FOV} = \text{WD} \times \frac{\text{CCD target size}}{\text{focal length}} $. This means that for a fixed focal length, increasing the working distance will increase the field of view, capturing a larger area but at a reduced resolution. 13

• Adjusting Focal Length for Different Working Distances: Fixed focal length lenses maintain a constant field of view angle (AFOV), but adjusting the focal length allows for different sizes of field of view at various working distances. For instance, if you choose a 25mm focal length, you would need approximately 1140mm working distance to achieve a specific field of view. 4

🖼️ Resolution and Field of View Angle

• Resolution and Image Space: Resolution is a measure of how finely detailed an image can be captured. In imaging systems, the resolution is influenced by both the sensor's pixel count and the magnification factor. The relationship between object space resolution and image space resolution is given by $ \text{Object space resolution (lp/mm)} = \text{Image space resolution (lp/mm)} \times X $, where $ X $ is the magnification factor. Higher magnification leads to higher resolution but a smaller field of view. 7

• Impact of Magnification on Field of View: Optical magnification affects the field of view significantly. For example, a higher magnification reduces the field of view while increasing the detail captured. This is important in applications like microscopy, where high magnification is needed to observe fine details, but it comes at the cost of a narrower field of view. 10

🤔 Depth of Field and Resolution

• Depth of Field Considerations: The depth of field (DOF) is the range of distances over which objects appear to be in focus. It is influenced by the aperture size, focal length, and the distance from the lens to the subject. A smaller aperture increases the depth of field, allowing more of the scene to be in focus, but this also reduces the amount of light entering the lens, potentially affecting resolution. 2

• Balancing Resolution and Depth of Field: Achieving optimal resolution requires balancing the depth of field with the desired field of view. For high-resolution imaging, a narrow depth of field may be acceptable if only a small portion of the scene needs to be in focus. Conversely, in surveillance or wide-area monitoring, a broader depth of field is often preferred to ensure that the entire field of view is sharp. 8

🔍 Practical Application and Calculation

• Application-Specific Calculations: In practical applications, such as camera design or surveillance, knowing the required field of view and working distance helps determine the appropriate focal length. For example, if the distance between the camera and the target is known, along with the desired width of the field of view, the necessary focal length can be calculated using the formula $ \text{FOV} = \arctan(\frac{w}{2d}) \times 2 $, where $ w $ is the object width and $ d $ is the distance to the object. 59

• Optimizing System Performance: To optimize system performance, consider the trade-offs between resolution, field of view, and working distance. For instance, in surveillance cameras, a larger field of view might be prioritized over high resolution if the goal is to monitor a wide area. Conversely, in scientific imaging, achieving high resolution might be more critical than having a large field of view. 6

In summary, the relationships between working distance, resolution, and field of view angle are crucial in designing and optimizing imaging systems. By carefully balancing these parameters, one can achieve the desired performance characteristics for specific applications.