Modulation transfer function (MTF) is one of the most important parameters by which image quality is measured. Also known as “spatial frequency response”, it characterizes the modulation or variance of two aspects of image performance, resolution and contrast, in the frequency domain. Every imaging lens, camera sensor, image capture board, and video cable has an associated MTF which contributes to the overall MTF of the system. The resulting MTF of the system is the product of all the MTF curves of its components. Knowing the MTF curve of each component within a system allows an optical designer to make the appropriate selection when optimizing for a particular resolution. X-AXIS: RESOLUTION An imaging system’s ability to distinguish object detail is its resolution. High-resolution images exhibit large amounts of fine detail, whereas low-resolution images contain blurring. On an MTF curve, resolution is often expressed as a measure of frequency or line-pairs per millimeter (lp/mm), where a line-pair is a sequence of one black line and one white line. Y-AXIS: CONTRAST The Y-axis of an MTF curve indicates contrast response as a measure of how accurately the minimum and maximum intensity values are transferred from an object to its corresponding image representation (i.e. from object to image plane). In lenses, contrast is typically presented as percent of the object contrast reproduced, with 100% or normalized to “1” being perfect. In sensors, the ability to reproduce contrast is usually specified in terms of decibels (dB) in analog cameras or bits in digital cameras. REAL-WORLD LENS MTF CURVES OFFER ADVANTAGES OVER THEORETICAL Theoretical MTF curves can be generated from the optical prescription of any lens. Although these nominal curves can be helpful, they represent the best-case scenario and do not indicate actual, real-world performance, which can contain performance losses due to manufacturing tolerances, geometries, or coatings deviating slightly from ideal. When precise system integration is desired and no optical prescriptions are available, MTF curves can be generated through optical characterization measurements. Real-world lens MTF curves depend on several factors such as location of the field reference point, off-axis orientation, system conjugates, wavebands, and F/#. An MTF curve is calculated at specified values of each. It is important to review these factors before determining whether a component will work for a certain application. READING LENS CURVES In lenses, MTF measures the ability to transfer contrast at a particular resolution from an object to its corresponding image representation. MTF incorporates resolution and contrast into a single specification, the lens MTF curve, which plots the percentage of transferred contrast versus the spatial frequency (cycles/ mm) of the lines or line pairs. In general, the higher the curve is on the y-axis, the higher the contrast and resolving power. When measuring a test target with black lines on white spaces, as the line spacing decreases (i.e. frequency increases), it becomes increasingly difficult for the lens to efficiently transfer this decrease in contrast and MTF decreases. LENS COMPARISON To demonstrate how MTF curves are helpful for predicting lens performance, two different Edmund Optics® imaging lenses (25mm fixed focal length) with different MTF curves were tested under the sametest conditions attempting to resolve elements of various sizes. Testing very small target features with high spatial frequency, the lens on the right with the better MTF curve clearly yielded better imaging performance as seen in the image on the right, when compared to the lens with the MTF curve and image on the left. It is important to note that for targets with low spatial frequencies, the two lenses would have produced similar images given their modulation values at lower frequencies. Knowing the application requirements is crucial to picking the right lens with the right MTF. Understanding and eventually interpreting MTF data is a very powerful tool for any optical designer. With knowledge and experience, MTF can make selecting the appropriate lens a far easier endeavor - despite the multitude of offerings.
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