Important Lens Specifications and Calculators for Industrial Camera Systems

When choosing and setting up lenses for industrial camera systems and applications, there are a few important parameters to consider if you want to achieve optimal results. First of all, the lens mount must be compatible. This consists of a bayonet and the electronics that allow the lens and camera housing to be connected. In industrial applications, the C-mount, M12-mount and F-mount, among other lens mounts, are often used due to certain properties.

Common Industrial Lens Mounts:

• C-mount
• M12-mount
• F-mount

Each mount type offers specific advantages in terms of form factor and optical properties.

Focal Length: What It Is and Why It Matters

Focal length determines the field of view (FOV) and how much of a scene the camera captures.

• Short focal lengths = wide-field or panoramic view
• Long focal lengths = narrow, magnified view (telephoto)

For example:

• C-mount: Human-like FOV = 16–20 mm
• M12-mount: Human-like FOV = 12–16 mm

The focal length is one of the most important criteria when choosing a lens, because it determines the visible area in which you want to create images. Lenses with a short focal length are suitable for large-area shots, while lenses with a long focal length can capture objects that are far away. Accordingly, these are classified into wide-field or panorama lenses (short focal lengths) and telephoto lenses (long focal lengths). Focal lengths in between most closely match the human field of vision. But which focal length has which effect also depends on the sensor or sensor size. For example, if you want to reproduce the human field of vision as accurately as possible, a lens with a focal length between 16-20mm would be necessary for C-mounts, and a focal length of 12-16mm for an M12 mount.

Calculating the focal length

The focal length calculator takes into account image size, object distance and object size to recommend the most suitable lens focal length for your specific application.

How does the focal length calculator work?

• The user enters the working distance (WD), horizontal field of view (FOV), vertical FOV, number of pixels (horizontal), number of pixels (vertical), and pixel size.
• The sensor size is then calculated horizontally, vertically, and diagonally. We use the basic formulas to calculate the horizontal, vertical, and diagonal sensor size. Note the difference between: – Active pixel area : Active pixel area refers to the physical area on an image sensor that is sensitive to light and captures the actual image data. – Effective pixel area : The effective area of a CMOS sensor includes the overscan optical black area that is shielded, which produces an average dark current and voltage bias level as a reference for the active pixels. – Recommended pixel area: refers to the capture area recommended by the sensor manufacturer.
• Magnification is then calculated using the formula: M=Horizontal sensor size/Horizontal field of view
• Finally, the magnification is used to calculate the desired focal length.

Focal Length Calculation – Basic Knowledge

When calculating the focal length in imaging systems, the following important aspects should be noted:

1. Lens Formula: The lens formula is the basis for calculating the focal length, stating that the reciprocal of the focal length 1/f is equal to the sum of the reciprocals of the object distance 1/u and the image distance 1/v. This formula is derived from the principles of lens imaging in geometric optics.
2. Object and image distances: To calculate the focal length, you need to measure the object distance (u) and the corresponding image distance (v). The object distance is the distance between the lens and the object being imaged, while the image distance is the distance between the lens and the image created on the image sensor or film.
3. Units: The focal length of a camera lens is usually given in millimeters (mm). To ensure accurate results, be sure to use consistent units for the subject and image distances.
4. Thin lens and paraxial approximation: When calculating the focal length, it is assumed that the lens is thin and the light rays are close to the optical axis. This results in a simplified analysis called the paraxial approximation. This approximation is valid for many practical situations, but may not apply to complex optical systems or special lenses.
5. Sign convention (single lens): Focal length can be positive or negative depending on the lens type. A positive focal length represents a converging lens (e.g. a convex lens), while a negative focal length represents a diverging lens (e.g. a concave lens).
6. Multiple lenses or lens systems: In cases where multiple lenses or lens systems are involved, the overall focal length can be calculated using more complex lens combination formulas.
7. Calibration and precision: Calculating focal length requires accurate measurement of the object and image distances. Calibration of measurement instruments and careful measurement techniques are essential to ensure accurate results.
8. Limitations and considerations: Focal length calculations assume idealized conditions and may not take into account factors such as lens defects, aberrations, and distortions. These factors can affect the actual performance of lenses in real imaging systems.

Understanding these important aspects will help you perform focal length calculations to determine the properties of lenses and their effects on imaging systems. This will help you select suitable lenses for specific applications.

Depth of field

Another important aspect of lenses is the conditions under which sharp images can be produced. While the so-called bokeh is often used in the artistic field – this is a diffusion effect that creates a blur around a specific object in focus in the image – a consistently high sharpness across the entire image is essential and necessary for industrial image processing. This simplifies object recognition so that further steps can be carried out afterwards. A high level of image sharpness is achieved by closing the aperture as much as possible. If the aperture is wide open, however, the edges of the image become blurred.

Depth of field therefore has an area of acceptable sharpness within an image, which is referred to as a circle of confusion or dispersion, beyond which objects become increasingly blurred. Thus, closed apertures (high f-number) are ideal for industrial applications, while open apertures (low f-number) tend to be less suitable. Unfortunately, with a closed aperture and thus a high f-number, less light falls on the sensor surface, thus darkening the image result. This makes it necessary to find a compromise between sharpness and light incidence that still allows the desired objects to be seen sharply in the image. Accordingly, depth of field is defined as an area limited by a smallest and a greatest distance, within which the objects present are sufficiently sharply depicted.

Creating sharp images for industrial applications

There are several ways to create a sharp image: a lens with a higher light yield due to the pixel structure on the sensor and the quantum yield can help to create brighter images when the aperture is closed. One method that you can influence directly is simply to expose a scene for longer. This will result in brighter images, but is only advisable if the objects to be photographed are not moving, otherwise motion blur will appear in the image. Another way is to increase the ISO number and thus manually increase the light yield. However, this has the disadvantage that noise artifacts appear with increasing ISO number. The right depth of field setting for industrial applications is determined by the specific environmental conditions, the lens and sensor selection (larger sensors can potentially absorb more light) and what can still be considered sufficient to successfully execute an application.

Optical factors that influence depth of field

• Focal length – focal length refers to the distance between the optical origin of a camera or optical system and the image sensor or film when a distant object is in focus. It determines the magnification and angle of view of the lens, which in turn affects how the image is represented. In simpler terms, focal length determines how much of the scene is captured and how large or small objects appear in the image. A shorter focal length captures a wider field of view, while a longer focal length magnifies the subject and narrows the field of view.
• Aperture size – The aperture size refers to the diameter of the opening in a camera lens through which light enters. The aperture size affects the depth of field and thus the degree of background blur or blurring in a photo. A larger f-number results in shallower depth of field, while a smaller f-number (larger f-stop size) results in greater depth of field. The f-number also determines the amount of light reaching the camera’s image sensor or film. A larger f-stop size allows more light to pass through, resulting in a brighter image, while a smaller f-stop size restricts the amount of light, resulting in a darker image. Therefore, the aperture size must be chosen carefully, taking into account the tradeoff between depth of field and light-gathering efficiency.
• Circle of confusion – In optics, the circle of confusion refers to a fundamental concept related to the formation of a focused image. When light passes through a lens and converges on the image plane (such as the film or digital sensor in a camera), it forms a circle of confusion for each object point in the scene. Due to various optical factors, such as the finite size of the lens aperture and diffraction and lens aberrations, the focused image of a point source is not a perfect point, but a blurred spot.
• Working distance – In optics, the working distance is the distance between the front of a lens or lens system and the object being viewed or worked on. Working distance is an important consideration in various applications, such as microscopy, imaging and industrial inspection, where precise positioning or the use of auxiliary tools is required.