如何解读摄影镜头之 MTF-data:

• 对比度 (Contrast): 以 5 或 10 本( lp/mm) 来评价该镜头之对比度性能. 在此频率之MTF 纵然仅2~3 %之差异, 人眼可轻易分辨其差别, 所以这是一个重要的基本频率.  好镜头在频率 5 lp/mm,小光圈时 T 及 S 方向 MTF需达 95 % . 若低于 90% 就算是较差之影像质量.
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• 清晰度 (Sharpness): 以 40本(lp/mm) 来评价该镜头之清晰度性能..  40 lp/mm代表一个镜头可以分辨多细的物体 (譬如一根毛发). 在此频率之MTF 纵然达10 %之差异, 人眼不太能分辨其差别.  通常一颗传统底片型摄影镜头在 20 lp/mm 时需达50% MTF 可算是好镜头.
   
• 一个镜头若有较佳的对比度, 但较差的清晰度, 其整体影像会比相反的镜头(较差的对比度, 但较佳的清晰度) 锐利, 感觉较好. 当然, 一般而言, 镜头若有较好的对比度, 其清晰度也较好
• 好镜头的影像质量需求  

·         有些镜头不可能达到上述要求, 譬如较大广角镜头等

·         通常T 方向 MTF 较差, 有时可用较高之S 方向某种程度之补偿.
 

以MTF vs. 像场 曲线来解释清晰度与对比度对影像质量之关系

Note: 本文翻译自

“Klaus Schroiff”   “How to interpret MTF graphs”

Understanding MTF Testing
By Sam Sadoulet,
Application Engineer

When characterizing the resolution of an imaging lens, it is extremely useful to refer to the Modulation Transfer Function (MTF). The MTF of a lens is a measurement of its ability to transfer contrast at a particular resolution level from the object to the image (see Figure 1). In other words, MTF is a way to incorporate resolution and contrast into a single specification.

An easy way to interpret MTF results is to think of imaging a target with black and white lines (100% contrast). No lens (even theoretically perfect) at any resolution can fully transfer this contrast to the image because of the diffraction limit. In fact, as the line spacing is decreased (i.e. the frequency increases) on the target, it becomes increasingly difficult for the lens to efficiently transfer this contrast (see Figure 1). Therefore, as the frequency increases, the contrast of the image decreases.

An MTF graph plots the percentage of transferred contrast versus the frequency (lp/mm) of the lines. A few things should be noted:

1) Contrast (also known as Modulation) is the image contrast expressed in terms of a percentage of the object contrast (100% = white on black, 0% = gray on gray).

2) The frequency in an MTF graph is measured in the image plane. Therefore, in order to define the object resolution (line-pair frequency), one needs to calculate it using the primary magnification (PMAG) of the imaging lens.

The frequency of the lines is expressed in terms of line-pairs per millimeter (lp/mm). The inverse of this frequency yields the spacing of a line-pair in terms of millimeters.

Why is MTF Important?
In traditional system integration (and less crucial applications), the system's performance is roughly estimated using a principle of "the weakest link." This idea proposes that a system's resolution is solely limited by the component with the lowest resolution. Although this approach is very useful for quick estimations, it is actually flawed, because every component within the system contributes error to the image, yielding poorer image quality than the "weakest link" alone.

Every component within a system has an associated MTF and, as a result, contributes to the overall MTF of the system. This includes the imaging lens, sensor, capture boards, and cables, for instance. The resulting MTF of the system is the product of all of the MTF curves of its components. For instance, we can compare a 25mm Fixed Focal length lens and a 25mm MVO™ Double Gauss lens by evaluating the resulting system performance of both lenses with a Sony XC-75 CCD monochrome camera. By analyzing the system MTF curve, we can make a prediction as to which combination will yield sufficient performance. In some metrology applications, for example, a certain amount of contrast is required for accurate image edge detection. If the minimum contrast needs to be 35% and the image resolution required is 30 lp/mm, the MVO™ Double Gauss lens is the logical choice (see Figure 2).

Knowing the MTF curves of components allows an integrator to make the appropriate selection to optimize the system for a particular resolution.

It should be noted that a theoretical MTF curve can be generated, given the optical prescription of the lens. Although this can be helpful, it does not indicate the actual performance of the lens after manufacturing. Manufacturing always introduces some performance loss in the design due to tolerances. For this reason, Edmund Industrial Optics has invested in an Optikos VideoMTF™ measurement system (pictured above) which has become essential in system integration and custom designing. This MTF testing equipment enables characterization of the actual performance of both designed lenses and commercial lenses (whose optical prescription is not available to the public). As a result, precise integration-previously limited to lenses with known prescriptions-can now include commercial lenses.

FIGURE 1: Effects of diffraction on the amount of contrast imaged as the frequency is increased.