Optical System Image Quality Evaluation
Before optical systems like telephoto lenses and FA lenses are designed and put into use, there are at least two stages where the imaging quality of industrial lenses needs to be objectively evaluated.
The first stage involves simulating the imaging situation of the system through extensive ray tracing and diffraction analysis during the design process. The second stage occurs after the industrial lens is processed and assembled but before mass production, requiring strict experiments to test its actual imaging performance.
Therefore, it often requires multiple evaluation methods to objectively and comprehensively reflect its actual performance. We will introduce five traditional image quality evaluation methods.
1. Rayleigh Criterion and Wavefront Map
Both the Rayleigh Criterion and the Wavefront Map judge the imaging quality of the lens optical system based on the size of wavefront aberration, where the difference in optical path between the actual and ideal wavefronts at the exit pupil is the wavefront aberration. The smaller the wavefront aberration, the better the imaging quality.
According to the Rayleigh Criterion: "When the maximum wavefront aberration between the actual wavefront and the ideal spherical wavefront does not exceed λ/4, the wavefront can be considered defect-free." This is a relatively strict evaluation method, often used in optical systems with small aberrations such as microscopes and telescopic lenses.
The wavefront map is obtained from ray tracing, showing the actual wavefront deformation caused by the difference between actual and ideal light rays. It provides intuitive understanding of the area and degree of wavefront deformation. In software, it can be represented in various ways such as contour lines, grayscale differences, and wavefront surface profiles.
2. Center Luminance and Encircled Energy Diagram
When a point in the object space passes through an optical system, it becomes a diffraction spot due to aberrations and diffraction. The Center Luminance and Encircled Energy Diagram assess the distribution of energy of object points on the image plane to judge the system's imaging quality.
In an ideal optical system without aberrations, the spot from an object point on the image plane forms a standard Airy disk, as shown in Figure 2, with the central bright spot containing about 92% of the energy and the first diffraction ring containing about 8% of the energy.
With the introduction of aberrations, as shown in Figure 3, the energy of the central bright spot continues to spread outward, resulting in decreased central luminance. The evaluation method of central luminance compares the actual spot's central luminance with that of the ideal spot without aberrations, represented by the ratio S.D. When the ratio is ≥0.8, the imaging of the optical system is considered perfect. This is also a high requirement for image quality evaluation, applicable only to optical systems with small aberrations such as double telecentric lenses.
The Encircled Energy Diagram plots normalized energy of object points against different circular radii centered on a Gaussian spot. The larger the radius of the circle, the more energy it can encompass, resulting in different curves. The black line represents the energy curve of points affected only by diffraction, while the blue line represents the actual energy curve of points. Center luminance provides information only on the central point's energy, while the Encircled Energy Diagram can show the extent of energy spread, providing more information.
3. Resolution and Point Spread Function
Resolution is an important parameter reflecting the ability of the lens optical system to resolve object details, representing the minimum distance between two object points that can be resolved. According to Rayleigh: "Two bright point diffraction patterns are just distinguishable when the first dark fringe of one diffraction pattern coincides with the center of the other diffraction pattern," as shown in Figure 5.
This determines the resolution limit when only diffraction effects are considered. In actual systems, the introduction of aberrations further reduces resolution. The most common method for detecting the actual resolution of industrial lenses is to directly observe and identify the line pairs per millimeter on a resolution test chart, as shown in Figure 6. This is not a perfect method and is only suitable for optical systems with large aberrations, and the test results can be affected by illumination conditions or receiver characteristics.
For optical systems with large aberrations, the Point Spread Function can simultaneously consider the effects of diffraction and aberrations. The image formed by the optical system can be understood as the convolution of the object image with the Point Spread Function of each point, as shown in Figure 7. The degree of energy concentration is used to judge the system's imaging quality.
4. Spot Diagram
For optical systems with large aberrations, it is easy to simulate the imaging situation using ray tracing methods. Dividing the entrance pupil of the system into small areas and considering the energy passing through each area's central ray as the energy through the area, multiple groups of rays pass through the system and intersect with the image plane to simulate the spread spot pattern, known as the spot diagram.
When using the spot diagram method to evaluate the imaging quality of large aberration systems, the area of the graph formed by concentrating more than 60% of the points is considered the effective spot, and the reciprocal of the spread spot is the resolution. Using the spot diagram method to evaluate imaging quality is a simple and intuitive method widely used in large aberration optical systems such as photographic lenses.
5. Optical Transfer Function
Evaluating the imaging quality of optical systems using the Optical Transfer Function considers the object as a spectrum composed of multiple frequencies. After passing through the optical system, the object's frequency is transmitted to the image side, resulting in unchanged frequency but reduced contrast and phase shift. At a certain frequency, the contrast decreases to zero. As shown in Figure 9, contrast and phase change with frequency, and their relationship is called the Optical Transfer Function.
The Optical Transfer Function is influenced by both aberrations and diffraction effects, making it an objective and reliable evaluation of optical systems suitable for both large and small aberration systems.
We will focus on contrast and ignore phase changes, which becomes the Modulation Transfer Function (MTF). As shown in Figure 9, the abscissa represents the frequency of black and white line pairs, and the ordinate represents the MTF value. Its value is calculated by Formula (1).
M and M' are respectively the modulation degree of the grating before and after imaging, calculated by Formula (2).
M=(Imax－Imin）/（Imax+Imin）
Imax and Imin are respectively the brightest and
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