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Resources / Application Notes / Imaging / 調制轉換函數在鏡頭設計中的像差平衡
調制轉換函數在鏡頭設計中的像差平衡
Edmund Optics Inc.

調制轉換函數在鏡頭設計中的像差平衡

成像資源指南第6.1部份

Aberrational Balancing of MTF in Lens Design

若要設計性能幾近完美的鏡頭,通常鏡頭只能在單一放大倍率和單一工作距離,針對特定傳感器達到最佳化。然而,這種鏡頭設計雖能大幅降低像差並達到最佳性能,卻需針對每一種應用另外製造自訂鏡頭。

這樣為每一種應用設計個別鏡頭,既不符合成本也不實際。因此,多數鏡頭都是設計用於多種應用,以便降低成本又可符合許多應用的需求。但這種作法有幾項缺點,其中影響最大的在於,鏡頭不可能在所有視場、工作距離和感測器時達到最佳性能。所以,這種鏡頭常被形容為「樣樣通,樣樣鬆」,而多數市售鏡頭皆屬於這一類。不止這樣,隨著分辨率愈來愈高,若要增加系統性能,或許可以考慮其他選擇。

Aberrational Effects

In order to maximize system performance, it is necessary to understand what can negatively affect an optical design. Aberrations, such as chromatic aberration, astigmatism, spherical aberration, and field curvature, must be reduced as much as possible to yield high image quality. Specific aberrations are discussed later in this section. Almost all of these aberrations are directly related to the working distance and magnification (ratio of the field of view to the sensor size) of the lens, although they may not necessarily be related to one another. When the working distance or the sensor size and field of view change, aberrations are shifted,and lens performance changes. For instance, although maximum reduction of aberrations can be achieved by designing a lens for a single field of view and working distance, small changes in the working distance or magnification will caused a rapid decline in this ultra-high level of performance. This decrease will occur more rapidly the farther these lenses move from their optimized position.

In lenses that are designed for multiple applications, aberrations are balanced over a range of working distances and magnifications. Although these lenses cannot exceed the performance of lenses that have been designed for a specific working distance and magnification, they can work fairly well over larger defined ranges. However, as pixels continue to become smaller, the compromises inherent in a general purpose range-balanced design is more pronounced.

Hybrid Approaches

Hybrid approaches to lens design have been developed for situations in which time and budget do not allow the design of a custom lens that is optimized for only a single working distance and magnification. A hybrid approach involves a lens that has been designed so that the spacing between elements or groups of elements can be adjusted so that the design is slightly changed and performance can be increased for a desired magnification and working distance. For example, a lens design created for line-scan sensors may have a specific magnification associated with it, such as 0.33X (Figure 1). On a camera with a 60mm line scan array, this will yield a field of view of 180mm.

A Lens Design Created for a Line-Scan Sensors has a Set Spacing for 0.33X
Figure 1: A Lens Design Created for a Line-Scan Sensors has a Set Spacing for 0.33X

Lens performance can be analyzed by referencing its MTF curve. MTF curves are described in Lens Performance Curves and Modulation Transfer Function (MTF) and MTF curves. Figure 2 shows the associated MTF curve of the lens in Figure 1 at 0.33X magnification. The curves displayed here are limited to 100 lp/mm, reflecting the resolution capabilities of a 12k line scan sensor with 5μm pixels. Two pixels are the smallest sampling area that can be used to distinguish the separation between information created by a lens. In this example, one line pair equals a total space of 10μm (two 5μm pixels); there are 100 sets of 10μm in 1mm, thus 100lp/mm is the limiting resolution of the camera.

MTF Performance Curves for the 0.33X Lens at Nominal Magnification
Figure 2: MTF Performance Curves for the 0.33X Lens at Nominal Magnification

In Figures 3 and 4, the lens is refocused to obtain other FOVs, and the associated MTF curves for the 0.33X-optimized lens design are shown. At magnifications of 0.5X (120mm field of view) and 1.0X (60mm field of view) display lower levels of performance. To overcome this, the spacing between the lens elements can be adjusted to optimize the performance for different magnifications. Figure 5 shows the optical layout for the same lens system re-optimized for high magnification; note that the spacing between the lens elements marked in red is changed from Figure 1, to compensate for the FOV/WD change.

MTF Performance Curves for the 0.33X Lens at 0.5X Magnification
Figure 3: MTF Performance Curves for the 0.33X Lens at 0.5X Magnification (120mm field of view)
MTF Performance Curves for the 0.33X Lens at 1.0X Magnification
Figure 4: MTF Performance Curves for the 0.33X Lens at 1.0X Magnification (60mm field of view)
Adjusting the Space Between the Lenses Improves MTF for the Lens at 1X Magnification.
Figure 5: Adjusting the Space Between the Lenses, Marked in Red, Improves MTF for the Lens at 1X Magnification. Note the Larger Gap

Figure 6 shows the MTF performance of the 1.0X-optimized lens at its design magnification. Notice the extreme difference in performance between Figures 6 and 4. Both of these lenses use the same glass elements and were designed simultaneously, but making a spacing change results in a huge difference in performance. Figures 7 and 8 show the MTF of the 1.0X-optimized lens design at 0.5X and 0.33X respectively. Again, a rapid change in performance can be seen as the magnification is moved away from the nominal.

MTF Performance Curves for the 1.0X-Optimized Lens at its Nominal Magnification
Figure 6: MTF Performance Curves for the 1.0X-Optimized Lens at its Nominal Magnification
MTF Performance Curves for the 1.0X Lens used at 0.5X Magnification
Figure 7: MTF Performance Curves for the 1.0X Lens used at 0.5X Magnification
MTF Performance Curves for the 1.0X Lens used at 0.33X Magnification
Figure 8: MTF Performance Curves for the 1.0X Lens used at 0.33X Magnification

This hybrid approach allows for a number of applications to be solved more effectively because it yields better performance than a single lens designed to address multiple applications. Hybrid designs provide multiple achievable options to increase system performance. Because this is less complex than multiple custom lenses, off-the-shelf solutions are typically more available and less expensive than complete customs.

While a hybrid solution increases performance, they can be more expensive than standard lenses and can have additional issues. First, it will not likely achieve the full performance capability of a true custom solution that has been specifically designed for a single working distance and magnification. As pixels become increasingly smaller, it can still be difficult for the optics in hybrid solutions to meet system requirements. Second, hybrid lenses will suffer fairly rapid performance decline outside of their specified range, similar to fairly narrowly designed lens solutions. Finally, since hybrid approaches result in a number of different lenses that each require specific materials, additional time is required to build the specific magnifications, and it may be necessary to use large, complicated mounting and focusing accessories to make the sensor/lens system operate as required.

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