Field of View Calculator: Design Calibration Targets for the Most Accurate Camera & Lens Setup

How Focal Length and Sensor Size determine the Field of View

Focal length is the distance between the focal plane (the plane of the camera sensor) and a reference point within the lens, known as the nodal point, when the lens is focused at infinity. The circle of confusion is a key factor in calculating depth of field and helps determine acceptable sharpness in an image.

The Field of View is the viewable area captured by an optical system. It can be expressed as a linear dimension (mm) or, more commonly, as an angular measurement (degrees) or angle of view.

Note: The horizontal FOV is used for convenience, but it's crucial to consider the sensor's aspect ratio (the ratio of its width to its height). This ratio determines the vertical FoV, ensuring that the entire target fits within the image frame.

To calculate the angle of view, we can use the pinhole camera model:

The tool below can be used to simplify the calculations:

A small calibration target, compared to the field of view, may result in insufficient feature resolution, limiting the software’s ability to identify pattern elements. On the other hand, a target that’s too big could lead to practical issues, such as possible flatness problems or uneven illumination. The goal is to select a calibration target that is large enough to provide sufficient features while still being practical for the application.

How to Choose The Calibration Pattern Type?

Calibration relies on accurate pattern detection to estimate the intrinsic and extrinsic parameters of the camera. The most common types of patterns are checkerboards, dot grids, and coded markers like ArUco and AprilTags, each of which offers unique advantages and disadvantages. To choose a suitable pattern for your application it is helpful to consider the following:

• Ease of Use
  • Checkerboard targets are the simplest to implement and analyze, requiring minimal setup and processing.
  • Coded patterns and dot patterns may require more complex generation and detection methods.
• Environment
  • Coded patterns like AprilGrids and ChArUco Boards are ideal for environments with variable lighting and potential occlusions, offering robust detection in dynamic settings.
  • In controlled environments such as a laboratory, a chessboard may be sufficient.

• Accuracy

• Dot or circle patterns are ideal for high-precision applications like metrology, as they allow subpixel localization of features. They also excel at calibrating imaging systems with distortion making them suitable for systems with a wide FOV. Macro lenses are ideal for these high-precision applications, providing accurate magnification ratios and effective calculations for field of view when photographing subjects up close. Macro lenses produce significant changes in focal length and FoV at close distances compared to standard lenses.

How to Select a Suitable Pattern Density?

Pattern density refers to how closely packed the features are on the target. If the camera sensor has a high resolution it can detect smaller features. However, if the pattern is too close together, the sensor might not be able to distinguish individual features. The dimensions of the features play a crucial role in this, as they affect the pattern density and the ability of the sensor to accurately capture each feature.

The goal is to ensure each square or marker is big enough to avoid blurry edges (black-to-white transitions) but small enough to fit multiple squares resulting in more data points which improves calibration accuracy.

To link pattern size to camera resolution, we can start by considering the smallest feature detectable on the image sensor:

This is the minimum detectable size of an object when viewed through a camera. However, to find the minimum resolvable size of the real-world object we must take into account the system’s magnification:

Note: Horizontal measurements are used for convenience, but we will generalize this expression later.

Combining these factors we can estimate a minimum feature size:

The same principles apply to vertical measurements, so we can generalize the formula:

It is worth noting that this calculation is not for the size of the square but for the minimum edge transition that the camera can resolve. A practical guide is that the pixels per feature should be at least 5 to prevent aliasing by providing a smoother gradient field for accurate subpixel fitting. To link this to pattern density we should use a scaling factor to calculate a square size that is large enough to accommodate the edge transitions and provide sufficient spacing between features.

These calculations provide a theoretical minimum to ensure sufficient resolution for calibration. However, it is also important to consider practical factors such as printing tolerances and the specifications of the calibration software used.

• Manufacturing tolerance: It is essential to balance the pattern density with the ability to manufacture the target accurately. If the theoretically calculated feature size is too small to be manufactured with precision, it will be necessary to increase it to a size that matches the capabilities of the printing process. As a rule of thumb, the minimum feature size should be at least 2 times the manufacturing tolerance.

• Lens Distortion/Blur: It’s also important to remember that lens distortion can alter feature sizes within the image, potentially impacting overall accuracy. Therefore, allocating extra pixels per feature is considered a good practice

• Feature Spacing: While the size of the markers is important, their spacing is just as relevant. Adequate separation between markers is necessary to ensure reliable calibration results.

For most applications, extreme precision isn’t necessary. This allows us to design a reliable calibration target based on practical use cases as long as we follow some general rules such as:

• Odd-even rule: To avoid rotational ambiguity, either rows or columns must have an odd number while the other must have an even number. If both rows and columns are even, the board becomes rotation-invariant, which can confuse detection algorithms.

• White Border: A white border (10–20% of total board size) creates a high-contrast boundary that isolates the pattern, helping algorithms distinguish the pattern from the background.

Tools and Software for Pattern Generation

• Online Camera Calibration Pattern Generator: This tool allows the creation of custom calibration patterns, such as checkerboards and AprilGrids, with adjustable parameters like the number of rows and columns, tag size, and spacing.

• OpenCV: Open-source library that provides functions for generating various calibration patterns, such as circle grids and ChArUco boards, in addition to its robust camera calibration and feature detection capabilities.

• MATLAB: Powerful and flexible environment for generating and customizing calibration patterns, particularly through its Computer Vision Toolbox, which includes example patterns for natively supported calibration types. It also excels in advanced calibration tasks like distortion modeling and error minimization.

Material Selection

The material used for the calibration target is important for several reasons, including its impact on durability, flatness, and overall performance. Different camera systems require specific materials for calibration targets to ensure optimal performance. Some commonly used materials are:

• Paper or Vinyl: These are cost-effective, easy to print on, and replaceable, making them ideal for initial testing and prototyping. However, they lack durability and flatness for high-precision applications.

• Aluminum Composite: ACM can be machined to create a surface free from imperfections, it also offers durability and its rigidity helps maintain flatness, making it suitable for industrial settings.

• Polyurethane: Offers a good balance of durability and flexibility, and can be used in a wide range of applications. It is also very resistant to chemicals.

• Glass: Provides superior stability, flatness, and low thermal expansion making it suitable for applications requiring high precision, such as microscopy and metrology.

Considerations

• Finish: A matte finish is generally preferred to minimize reflections.

• High contrast: Calibration algorithms rely on identifying distinct features so a high contrast between the pattern and the background makes these features easier to detect.

Conclusion

Designing an optimal calibration target requires matching your camera’s specifications and the application’s demands (FOV, working distance, and environmental conditions) to the target size, pattern type, and density. By carefully considering these factors, you can create or select a calibration board that optimizes your camera system's reliability, ensuring accurate calibration.

Nevertheless, the precision of any calibration setup is substantially limited by the quality of the target itself, as imperfections like non-regular aspect ratios or low-quality prints introduce significant errors. This is why maintaining high contrast, perfect flatness, minimal manufacturing tolerances and using non-reflective materials is crucial. To ensure these quality standards are met, it's often best to work with a specialized printing service that understands the unique requirements of calibration targets. Foamcoreprint uses industrial-grade materials and high-resolution printing techniques to minimize tolerances, ensuring your target meets your application's demands.

Resources

• Understanding Focal Length and Field of View | Edmund Optics
• Choosing the Correct Test Target | Edmund Optics
• Distortion | Edmund Optics
• Resolution | Edumund Optics
• Understanding Focal Length | Canon Georgia