How the quality of optical systems is measured: the MTF function
The most common and generally accepted method of measuring the quality of optical systems is the modulation transfer function (MTF).
The most common and generally accepted method of measuring the quality of optical systems is the modulation transfer function (MTF). This method is applicable to both the simplest lenses and lenses as complex as telecentric ones.
The lens MTF is actually a measurement of the lens's ability to transfer contrast at the appropriate resolution from the subject to the image. When measuring MTF, the degree of image quality degradation of the test pattern caused by the tested lens is assessed. Therefore, the output from the lens is compared with the scanned original. MTF is also a way to combine resolution and contrast into one specification.
As a test pattern, the MTF uses a line raster consisting of a sequence of black lines separated by equally wide white spaces. The test pattern must have a sharp transition between black and white. The individual rasters differ in the number of line-gap pairs per millimeter. The number of these pairs is called the spatial frequency.
And what is meant by the term "modulation transmission"? This is the ratio of the modulation at the input of the optical system to the modulation of the same signal at the output of the optical system. For simplicity, let's replace the brightness level of white with one and black with zero. The modulation at the input is then equal to 1. Due to the properties of the optical system, the output modulation will be lower, say 0.95. The modulation transmission in our case is 0.95. If we now change the line raster density, we will receive different modulation transmission values at the output.
This can be well explained by an example. It can be seen that the input always has a sharp transition between black and white and that black always has a minimum intensity (0) and white always has a maximum intensity (1). The quality of the input is also independent of its spatial frequency. In contrast, we observe a gradual deterioration of image quality at the output. It can be seen how the difference between the maximum and minimum intensity decreases with increasing spatial frequency, ie the signal modulation decreases. Since the input always has the same signal modulation, the output gradually decreases the modulation transmission, ie MTF.
The ideal MTF curve would be parallel to the x-axis and the y-axis would intersect. The ideal optical system (ie a system without optical aberrations) is limited by diffraction limits compared to this ideal state. A system with a smaller input aperture (smaller lens diameter) will be described by a curve that decreases to zero faster than a system with a larger input aperture. The course of the MTF curve of the ideal optical system then decreases from a certain spatial frequency compared to the ideal case and approaches zero. The MTF curve of the real optical system will be more or less close to the course of the ideal optical system, depending on its quality.
MTF values measured at low frequencies are suitable for evaluating the contrast transmission quality of an optical system, while higher frequencies show how well the optical system can distinguish fine structures.
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