How to Calculate the Field of View and Working Distance of an Industrial Lens

In industrial machine vision systems, the field of view (FOV) and working distance (WD) of an industrial lens are two crucial parameters. They jointly determine the range of objects that the lens can observe and the distance between the lens and the object being photographed. The following provides a detailed explanation on how to calculate the field of view and working distance of an industrial lens.

I. Basic Concepts

• Field of View (FOV): Refers to the visible range of the object that the lens can observe, typically represented by the horizontal field (H) and vertical field (V), with units in millimeters (mm).

• Working Distance (WD): Refers to the physical distance between the front end of the lens and the surface of the object being photographed, usually measured in millimeters (mm).

II. Calculation Formulas

1. Calculation of Field of View (FOV)The formulas for calculating the field of view mainly come in two forms, depending on the known conditions:

• Formula One: When the working distance (WD), lens focal length (f), and camera target size (H or V) are known, the following formula can be used to calculate the field of view:

$FOV(H \text{ or } V) = \frac{WD \times \text{target size}(H \text{ or } V)}{f}$

- Where $f$ is the lens focal length, and $\text{target size}(H \text{ or } V)$ is the horizontal or vertical size of the camera target.

• Formula Two: When the optical magnification (MAG) and camera target size (H or V) are known, the following formula can be used to calculate the field of view:

$FOV(H \text{ or } V) = \frac{\text{target size}(H \text{ or } V)}{MAG}$

- Where the optical magnification $MAG = \frac{\text{target size}(H \text{ or } V)}{\text{field of view size}(H \text{ or } V)}$, representing the ratio of the image size to the object size.

2. Calculation of Working Distance (WD)The formula for calculating the working distance is:


• This formula is a variation of the field of view calculation formula, used to solve for the working distance when the focal length, target size, and field of view are known.

III. Calculation Steps and Examples

Example One: Calculating the Field of View with Known Working Distance and Focal Length

Assume a camera with a target size of6.4mm×4.8mm6.4 \text{mm} \times 4.8 \text{mm}6.4mm×4.8mm(1/2 inch), a lens focal length of25mm25 \text{mm}25mm, and a working distance of300mm300 \text{mm}300mm.

• Use Formula One to calculate the field of view (horizontal field as an example):

FOV(H)=300mm×6.4mm25mm=76.8mmFOV(H) = \frac{300 \text{mm} \times 6.4 \text{mm}}{25 \text{mm}} = 76.8 \text{mm}FOV(H)=25mm300mm×6.4mm=76.8mm

Example Two: Calculating the Field of View with Known Optical Magnification and Target Size

Assume the same camera is used with an optical magnification of0.2×0.2 \times0.2×.

• Use Formula Two to calculate the field of view (horizontal field as an example):

FOV(H)=6.4mm0.2=32mmFOV(H) = \frac{6.4 \text{mm}}{0.2} = 32 \text{mm}FOV(H)=0.26.4mm=32mm

Example Three: Calculating the Working Distance with Known Focal Length, Target Size, and Field of View

Assume the same camera is used with a lens focal length of25mm25 \text{mm}25mmand a field of view of32mm32 \text{mm}32mm(horizontal field).

• Use the working distance calculation formula:

WD=25mm×6.4mm32mm=50mmWD = \frac{25 \text{mm} \times 6.4 \text{mm}}{32 \text{mm}} = 50 \text{mm}WD=32mm25mm×6.4mm=50mm

IV. Notes

1. Unit Consistency: Ensure that the units of all parameters are consistent during the calculation process, typically using millimeters (mm) as the unit.

2. Parameter Accuracy: Ensure that the lens focal length, camera target size, and other parameters used are accurate to avoid calculation errors.

3. Field of View Selection: In practical applications, the selected field of view should be slightly larger than the actual size of the object to be observed, to account for mechanical errors and other factors.

4. Lens Characteristics: Different types of lenses (such as fixed focal length lenses, zoom lenses, telecentric lenses, etc.) may have different characteristics, which should be considered when calculating their impact on the field of view and working distance.

V. Conclusion

By using the above calculation methods and examples, the field of view and working distance of an industrial lens can be accurately calculated. These two parameters are crucial for the design and debugging of machine vision systems, directly affecting the performance and accuracy of the system. In practical applications, the appropriate lens and camera combination should be selected based on specific needs and conditions, and the relevant parameters should be accurately calculated to ensure the stable operation and efficient performance of the system.