Understanding Lens Focal Length: A Guide to Choosing the Right Lens for Your Camera

Introduction

Selection of an appropriate camera lens is of paramount importance in image processing, computer vision, and embedded vision systems. The resolution, sharpness, contrast, and FOV of an image largely depend on the camera lens. One of the most important properties of any camera lens is its focal length. In this article we explain the concept of focal length in detail and will help you in choosing the right lens for your camera system.

1: What is Lens Focal Length?

1.1: Definition of Lens Focal Length

The distance between a lens and the convergence point of light rays on a camera sensor/film is known as the focal length of that particular lens. Focal length is commonly measured in millimeters.

1.2: How Focal Length is measured?

There exist several methods for the measurement of lens focal length. Some of the methods for the measurement of lens focal length are listed as following:

1. Lens Maker’s Formula: The lens maker’s formula uses the refractive index of the lens and the radius-of-curvature of the lens to determine its focal length.
2. Distant Object Test: In this method, a distant object is placed in front of the lens and the distance between the lens and the formed image is determined.
3. Collimated Beam of Light Test: In this method, a collimated beam of light is used for determining the distance between the lens and the formed image.
4. Object at Infinite Distance Test: In this test, a converging or a diverging lens is used along with an object at infinite distance.

The generic equation used for determining the lens focal length is given as following:

Where:
f = focal length
o = distance between the lens and the object
i = distance between the lens and the image

1.3: How Focal Length affects Image Magnification

The magnification of an image largely depends on the focal length of the lens. Magnification is defined as the apparent size of an object in an image compared to the actual physical size of the object.
Focal length and magnification have a direct relationship. Hence, a lens with a smaller focal length will result in smaller apparent size of objects in the image. Similarly, a lens with a greater focal length will result in larger apparent size of objects in the image. In conclusion, the lens’ focal length is directly proportional to the image magnification.

2: Why Lens’ Focal Length is Important?

2.1: How Focal Length affects Angle-of-View

The angle-of-view refers to the amount of scene being captured by the camera lens and sensor. The angle-of-view can be measured vertically, horizontally, or diagonally. The angle-of-view of an image largely depends on the focal length of the image.

Focal length and angle-of-view have an inverse relationship. This means that a longer focal length results in a narrower angle-of-view while a shorter focal length leads to a wider angle-of-view.-
For example, a 50mm camera lens has a standard field-of-view which is similar to human eye. A 24mm wide-angle lens captures more of the scene compared to what human eyes can capture. Conversely, a 200mm lens will have a narrow field-of-view and capture a smaller portion of the scene when compared with human eyes.

2.2: Subject Size

Focal length and subject size have a direct relationship. A lens with a shorter focal length will have a wider field-of-view which will lead to smaller subject sizes in the image frame. Similarly, a lens with a longer focal length will have a narrower field-of-view which will lead to larger subject sizes in the image frame. Due to this reason, subjects appear smaller in the images captured using wide-angle camera lens. Conversely, subjects appear larger in the images taken using narrow-angle camera lens.

2.3: Image Perspective

The relative positioning of objects within an image when viewed from a certain angle is referred to as image perspective. Image perspective depends on the relative positions of objects in the image as well as the position of the observer.

Image perspective depends on a number of factors including lens’ focal length. Generally speaking, shorter focal lengths result in images where objects appear further apart and smaller in size due to a wider viewing angle. Similarly, longer focal lengths result in images where objects appear closer together and larger in size due to a narrower viewing angle.

3: Relationship between Field-of-View and Focal Length

The extent to which a camera device can capture a scene is referred to as field-of-view of FOV. Focal length and FOV have an inverse relationship. This means that a lens with a shorter focal length will result in a wider FOV while a longer focal length will result in a narrower FOV.
Lens with shorter focal length converge the light at a higher rate which leads to a wider viewing angle. Similarly, lens with longer focal length converge the light at a lower rate which causes narrow viewing angle. Due to this reason, wide-angle lens has a much greater FOV as compared to a telephoto lens.

4: How to choose the right Lens Focal Length for your Embedded Vision System?

The characteristics of a camera lens have a critical impact on the performance of an embedded vision system. The quality and field-of-view of an image largely depend on the lens in an embedded vision application. Important factors to be considered during the selection of a camera lens for an embedded vision application include:

• Focal length
• Image resolution
• Field of view
• Distance between camera and object

The impact of focal length on the FOV is illustrated in the following images:

5: Conclusion

Selection of appropriate focal length for a camera lens is crucial for the overall performance of an embedded vision system. Focal length affects multiple factors such as magnification, field-of-view, subject size, and image perspective. In this article, we have discussed lens focal length in detail and have provided useful information to the readers for the selection of appropriate focal length for an embedded vision application.