This article attempts to analyze the role of lenses in optical systems from a resolution perspective, thereby explaining the importance of lenses.

System Resolution and Pixel Accuracy

The most important parameter of a machine vision system is its system resolution. Engineers employ various theories and techniques with the goal of improving system accuracy. After all, the higher a device’s system resolution, the greater its value. Generally, engineers are accustomed to using pixel precision to express system resolution.

The concept of pixel accuracy is simple: it refers to the physical size represented by a single pixel.

For example, if the camera has a pixel resolution of 10×10 and the object being measured is 100 mm × 100 mm, then the physical size represented by each pixel is: 100 mm / 10 = 10 mm per pixel.

According to this logic, the way to improve system accuracy is to increase the pixel density per unit area.

If the object being measured remains 100 mm × 100 mm, and the camera’s pixel resolution is increased to 100 × 100, then each pixel will represent a physical dimension of: 100 mm / 100 = 1 mm per pixel.

If we follow this logic, could the precision of an optical system be infinitely improved by infinitely increasing the pixel density per unit area?

The answer is clearly no—it’s impossible. So where exactly does this limitation lie?

The “Law of the Barrel” in System Resolution

We can consider this issue using the “law of the barrel.” The resolution of the optical system (optical resolution) and the image resolution of the camera are two “planks” in the “barrel” that represents the overall resolution of the imaging system. The resolution of the imaging system is equal to the shorter of these two planks.

As shown by the aforementioned “bucket theory,” there are four possible scenarios:

If the camera resolution is greater than the lens resolution, improving the lens resolution will also enhance the system resolution.

The camera resolution is higher than the lens resolution; increasing the camera resolution does not change the system resolution.

If the lens resolution is greater than the camera resolution, increasing the camera resolution will also increase the system resolution.

The lens resolution is higher than the camera resolution; increasing the lens resolution while keeping the system resolution unchanged.

The relationship between cameras and lenses that we usually discuss is actually a relationship among three elements: the camera, the lens, and the system. To fully grasp the interplay among these three components, it’s essential to understand the concept of resolution.

Camera pixel count, camera “pixels,” and camera resolution

Regarding camera-related terms such as “pixel,” “image element,” and “resolution,” the industry currently lacks clearly defined standards. Moreover, different industries often use terms like “display resolution” and “image resolution,” which can easily lead to confusion. In the author’s view, cameras themselves do not have a concept of “pixels”; rather, pixels are a description of images. The number of image elements in a camera is precisely equal to the number of pixels in the images that the camera captures.

Pixel, the smallest physical unit on an image sensor that can independently detect light.

A pixel is the smallest unit displayed in a digital image. The concept of pixels is typically used when referring to images captured by cameras. However, the term “pixel” as used in cameras is not entirely accurate.

Resolution refers to the ability to distinguish between two closely spaced points; it is also known as resolving power. The smallest point that a camera can resolve is the pixel size. Therefore, the camera’s resolution can be understood as being equivalent to the pixel size.

For example:

Camera A is equipped with a Sony IMX250 chip. It has a pixel count of 2448×2048, and each pixel measures 3.45 µm × 3.45 µm. This camera has a pixel count of 2448×2048, resulting in an image resolution of 5,013,504 pixels, with a pixel size of 3.45 µm.

Lens “Pixels” and Lens Resolution

To make it easier for users to select lenses, industrial lens manufacturers often name lenses based on “pixel” specifications.

If camera A can capture images with a resolution of 5 million pixels, the manufacturer will label the matching lens as a “5-million-pixel lens.” All standard-definition lenses, high-definition lenses, and 1080P lenses on the market are named according to the pixel resolution of the images they’re designed to capture with the camera.

However, in other fields—such as microscopes, endoscopes, and DSLR lenses—this phenomenon has not emerged. Clearly, naming lenses after “pixels” does not accurately reflect their actual performance. Moreover, manufacturers have begun arbitrarily assigning names to lenses, creating confusion in our understanding of lens resolution.

The actual lens resolution should be represented by the MTF curve. The figure below shows one possible way to depict the MTF curve.

The core of this MTF curve is spatial frequency. In other words, to understand a lens’s resolution, you must first grasp what spatial frequency means.

Resolution and Spatial Frequency

Resolution can be quantitatively expressed in terms of spatial frequency.

Spatial frequency represents the number of cycles of a signal per unit length and is commonly expressed as the number of line pairs contained in 1 millimeter. One black-and-white pair constitutes 1 line pair.

Camera resolution and lens resolution can be quantified.

As shown above, both camera resolution and lens resolution share a common parameter—the spatial frequency. By calculating the spatial frequency of the camera, we can quantitatively determine which component—whether it’s the camera resolution or the lens resolution—ultimately dictates the system’s overall resolution.

The spatial frequency calculation formula for the camera is as follows:

Lens A has a spatial frequency of 150 lp/mm, as indicated by its MTF curve.

Lens A: When paired with a camera that has a spatial frequency greater than 150 lp/mm, the system resolution remains unchanged.

Lens A causes a decrease in system resolution when paired with a camera whose spatial frequency is less than 150 lp/mm.

When camera A is paired with a lens whose spatial frequency exceeds 150 lp/mm, the system resolution remains unchanged.

When camera A is paired with a lens whose spatial frequency is less than 150 lp/mm, the system resolution decreases.

In an era when camera resolutions are continually increasing, the “pressure” on imaging system resolution has shifted to lenses. Consequently, lenses with higher resolutions (spatial frequencies) are playing an increasingly important role in imaging systems.

Lens resolution, together with other parameters, affects the system's overall resolution.

Lens resolution, in addition to being related to the camera's resolution, is also influenced by other factors that collectively affect the system's overall resolution.

1The lens resolution is a variable parameter.

For a given lens, its resolution is not a constant value. The lens resolution varies depending on the working distance, aperture, operating wavelength band, and image plane position.

2Lens resolution and light source

During design and development, lenses are typically optimized for resolution within a specific wavelength band. When light sources with wavelengths outside this band are used, the lens resolution decreases. Generally speaking, using monochromatic light within a specific wavelength band will improve the lens resolution.

3The image-side resolution of the lens and the object-side resolution.

The resolution of imaging lenses can be expressed in various ways, with the most commonly used being image-side resolution and object-side resolution. Object-side resolution refers simply to the spatial frequency on the side of the lens closer to the object being measured, while pixel resolution refers to the spatial frequency on the side closer to the camera. Industrial fixed-focus lenses typically specify the image-side resolution, whereas microscope objectives more often disclose the object-side resolution.

4Lens resolution and working distance

The design of imaging lenses primarily relies on the principles of geometrical optics and is typically optimized for a specific working distance. For industrial fixed-focal-length lenses, the optimal working distance for most products ranges from 300 mm to 600 mm—within this range, the lens delivers the best resolution performance; at other working distances, resolution may decline. For security lenses, the optimal working distance is long distances and infinity. For macro lenses, the optimal working distance is close range.

5, Lens Resolution and Aperture

In general applications, lens resolution is closely related to the aperture: reducing the lens's aperture will increase resolution. However, the smaller the aperture, the more pronounced the limitations imposed by the diffraction limit become.

6There is a physical limit to lens resolution.

Dr. Ernst Abbe discovered the resolution limit of imaging lenses in the 1870s. The resolution limit for visible-light lenses is 0.2 μm. Moreover, due to material and manufacturing challenges, it is difficult for conventional imaging lenses to achieve this value.

Summary

Understanding the calculation and evaluation methods for the resolution (spatial frequency) of imaging lenses enables a better grasp of the key factors that affect system accuracy and also provides guidance for system upgrades.