Camera Field of View Calculation for Machine Vision Systems

Industrial automation and quality control processes are now entrusted to cameras capable of inspecting hundreds of products per second with millimeter precision, rather than human eyes. These systems, known as "Machine Vision", scan products flowing on conveyor belts to perform critical tasks such as barcode reading, defect detection, measurement, or guiding robotic arms.

For a machine vision system to be successful, the correct selection of optical hardware is essential before any software is applied. An incorrectly chosen lens or sensor can result in the edges of the product being left out of the frame or details not being clear enough. At the heart of this hardware selection lies the Field of View (FOV) calculations. In this article, we will examine what you need to consider when calculating FOV for industrial cameras and how you can use our Camera Field of View Calculator tool in your projects.

The Critical Role of Correct FOV in Machine Vision Systems

Unlike consumer photography, machine vision does not shoot a "general landscape". The goal is to fit a specific part (like a screw or a circuit board) into the frame as clearly, distortion-free, and accurately sized as possible.

• Too Narrow FOV: The entire product does not fit in the frame. Since the software cannot analyze the missing parts of the product, it might incorrectly mark good products as defective (reject).
• Too Wide FOV: The product occupies only a tiny portion of the image. This means a waste of the camera's pixels. The software cannot reach the sufficient pixel count (resolution) needed to detect the defect.

In an ideal setup, the product is arranged to cover approximately 80% of the field of view (FOV). The remaining 20% is left to compensate for minor positional shifts (tolerance margin) of the product on the conveyor belt.

What is Working Distance?

The most frequently encountered term when calculating FOV in the field of machine vision is "Working Distance" (WD). The working distance is the physical distance between the frontmost part of the lens and the object to be inspected.

In factory environments, the working distance is usually fixed and limited. For instance, you might need to place the camera right next to a robotic arm or inside a narrow tunnel, and you might only be able to position the camera 30 cm (0.3 meters) away from the product.

Under these constraints, you are left with only one option to achieve the FOV value you need: Choosing the right sensor size and a lens with the correct focal length.

The Relationship Between Resolution, Pixel Size, and FOV

Simply seeing the area is not enough; the level of detail with which we see that area is also crucial. The detail level within the FOV depends on the system's resolution.

For example, let your FOV width be 100 mm (10 cm). Let your camera's horizontal resolution be 1000 pixels.
In this case, Spatial Resolution = FOV / Number of Pixels = 100 mm / 1000 = 0.1 mm/pixel.
This means the smallest defect size your system can detect is around 0.1 mm (100 microns). If your quality control procedure requires you to detect 0.05 mm scratches, you must either switch to a 2000-pixel camera (which increases cost) or narrow the FOV area to focus only on the critical point where the scratch might be (which might require multiple cameras).

Industrial Lens Selection and Optical Errors

In industrial applications, the quality of the lens is of vital importance. Most standard lenses create a bending (distortion) towards the edges (Barrel or Pincushion distortion).

If you are going to make precise measurements (Metrology) using machine vision, these distortions will cause the dimensional measurements to be incorrect. Therefore, low-distortion lenses or Telecentric lenses, which completely eliminate perspective error, are typically used. However, when standard lenses are used, FOV calculation formulas come into play.

The basic equation used in FOV calculation is:
FOV = (Sensor Size * Working Distance) / Focal Length

This linear equation gives approximate values. For precise calculations, using the trigonometric formula Angle = 2 * arctan(Sensor Size / (2 * Focal Length)) followed by Physical Width = 2 * Distance * tan(Angle / 2) is more accurate.

Factory Line Examples Using the Calculator Tool

Let's assume you are going to set up a system to inspect circuit boards (PCBs) flowing on a conveyor belt. The width of the boards is 15 cm (0.15 m). To leave a tolerance margin, you want the system to see a horizontal area (FOV width) of 20 cm (0.2 m). Due to physical obstacles, you are forced to mount the camera exactly 50 cm (0.5 m) above the product (Object Distance).

You have an industrial camera with a 1/2-inch sensor (width 6.4 mm). Which focal length lens (e.g., 8mm, 12mm, 16mm) should you buy?

To solve this problem, open our Camera Field of View Calculator tool:

1. In the Sensor Width section: Enter 6.4 mm.
2. In the Object Distance section: Enter 0.5 meters (50 cm).
3. Start testing the Focal Length.
   • If you enter 16mm: You will see that the width at a 0.5m distance is approximately 0.20 m (20 cm).

Great! Based on the parameters you entered, you found that you can achieve exactly the 20 cm FOV value you are looking for with a 16mm lens.

Frequently Asked Questions

What do sensor formats (1/2", 2/3", 1") mean in machine vision?

These values, just like in consumer cameras, express the physical size of the sensor. In machine vision cameras, sensors between 1/3" and 1.1" are very common. The "Format Size" of the lens must be equal to or larger than the camera's sensor size. (If you attach a 1/3" lens to a 1/2" camera, you will get black edges—vignetting).

Are these calculations valid for Macro lenses or Telecentric lenses?

They are valid for Standard (Entocentric) lenses. The optical designs of Macro lenses or Telecentric lenses are different. Especially in Telecentric lenses, the Field of View (FOV) is independent of the working distance (the object's size remains the same whether it moves closer to or further from the camera). Therefore, the FOV values of Telecentric lenses depend on the physical diameter of the lens and are written directly on the lens specification sheet; they are not calculated with a formula.

Why did the FOV value turn out to be a few millimeters different from the calculation after installing the system?

This is very common. Our tools provide estimated values based on the ideal "thin lens" theory. Real lenses are thick optics made of multiple glass elements, they contain distortion, and focusing requires the lens elements to move (thus changing the focal length, albeit very slightly). In machine vision projects, it is the industry standard to use calculation tools as a "Guide and Purchasing Decision Support" tool, and then make the final fine-tuning in the physical environment.