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The modulation transfer function, i.e. the frequency characteristic of the optical system, is determined by a similar formula. MTF is often determined with the help of sine-wave patterns. Manufacturers of such targets specify the line density as well as the input modulation parameters. After the digitization and the calculation of the output modulation we can find the value of MTF by the following formula:

If square-wave patterns are used, a reference pattern is first chosen:

The graph above shows the modulation transfer functions for the test patterns. The leftmost pattern of the Applied Image QA-69-P-RM target with a resolution of 30 lppi is chosen as the reference. The modulation functions are determined for the green channel of the target image. The results are presented in the following diagram:

Here you can see the modulation transfer functions for the Scanjet 8200 and the Epson Perfection 4870. Both scanners work at an optical resolution of 4800dpi, so should compare well to each other. As you see, their MTFs is really similar.

When investigating the modulation transfer function I observed a low quality of the scans of the patterns of the target as some colors were prevalent at the borders between the lines. I couldn’t leave this fact unattended and offer you the results of my measurements. First, take a look at a fragment of the scan of the test target digitized in the colorful 24-bit mode at the scanner’s maximum optical resolution.


To evaluate the color aberration I extracted the data and presented them in the following diagram:

This animated picture sequentially shows the green color values (basic for measuring the MTF); red outline to the right of the stripes, blue outline to the left, and the graph shows the color offset value; the Hue diagram shows what colors are prevalent at the borders of the lines. Besides that I noticed correlated noise at some frequencies which shows up in the scan as vertical lines.

 
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