MTF and Lens Measurement
Today’s new technologies for designing and producing complex, high quality optical systems require lens measurement equipment that is sophisticated, flexible and accurate.
The Modulation Transfer Function (MTF) is a measure of the ability of an optical system to transfer various levels of detail from object to image. Performance is measured in terms of contrast (degrees of gray), or of modulation, produced for a perfect source of that detail level.
Transfer functions are found in circumstances where a response (output) is related to an input. Examples of systems that can be characterized by a response function are audio equipment, mechanical vibration isolation structures, and seismometers. The Optical Transfer Function (OTF) describes the response of optical systems to known input, and consists of two components — the MTF is the magnitude of the OTF and the phase transfer function (PTF) is the phase component.
The amount of detail in an image is given by the resolution of the optical system, and is customarily specified in line pairs per millimeter (lp/mm). A line pair is one cycle of a light bar and dark bar of equal width and has a contrast of unity. MTF is a plot of contrast, measured in percent, against spatial frequency measured in lp/mm. This graph is customarily normalized to a value of 1 at zero spatial frequency (all white or black).
An eye test is a common MTF measurement. The ophthalmologist determines the response of the human visual system (lens and retina) to varying levels of detail – rows of letters. Hence, the doctor determines the frequency response of the patient’s visual system.
The Phase Transfer Function (PTF) is a measure of the relative phase in the image as function of frequency. A relative phase change of 180°, for example, indicates that black and white in the image are reversed. This phenomenon occurs when the OTF becomes negative. Phase reversed images still show contrast and may have a substantial MTF.
The Role of MTF
MTF specifications are frequently used for lens designs that require repeatable test standards. Some examples are reconnaissance lenses, photographic objectives and IR systems. The MTF measurement instrument is also commonly used as a production quality control tool, since operators are not required to have a high level of optical training in order to properly test the optics.
The benefits of using MTF as a system specification are three-fold. First, in many cases, optical systems employing numerous stages (lenses, film, eye, etc.) have a system MTF equal to the product of the MTF of the individual stage. This can be described as concat- enation or cascading of MTF, and allows testing at a subassembly level.
Second, MTF can be specified either at a single wavelength or over a range of wavelengths, depending upon the application. Interferometric wavefront metrology is limited to certain laser wavelengths. MTF allows full spectrum specification and testing.
The third benefit of MTF testing is that it is objective and universal. The test engineer is not required to make judgments of contrast, resolution or image quality. Therefore, under the same conditions the polychromatic MTF of the lens can be directly compared to the polychromatic MTF of a design, or to another measurement instrument.
MTF Measurement Technologies
There are several methods for measuring MTF — discrete or continuous frequency generation, image scanning, and wavefront analysis. Recent advancements in precision mechanics and electro-optics technologies have produced many practical variations on these methods that allow efficient measurement of OTF to very high accuracy. Four major categories of instrumentation exist: frequency generation, scanning, video and interferometric methods.