Optical transfer function

The modulation transfer function (including modulation transfer function ( MTF, Eng. Modulation Transfer Function ) or contrast transfer function ) is the mathematical description of the comparison between the detail contrast at the edges of an object and the detail contrast its pictorial representation. It is found always a contrast detail loss. This is not to be confused with the contrast in common parlance, as he change any by image processing (or in the chemical photography, for example, by the choice of the paper), esp even increase over the original Motif Contrast addition, leaves.

  • 6.1 Standards

Principle

The high-contrast line scan of an object has ( see right chart ) in the pictorial representation of contrast lost ( washed out ). In the mathematical representation of the line screen ( of the object ) corresponds to a polygonal curve object modulation.

Due to the loss of contrast, this curve changes. The new curve ( the image with the loss of contrast ) is idealized as a sinusoidal curve shown (picture modulation).

With modulation is meant in this context:

  • The mathematical representation of a signal (in this case an optical signal ).
  • The change of the signal ( by the imaging system ).

Both modulations (object and image modulation ) are compared. The result expresses the amount of contrast loss.

With the Heynacher number ( according to E. Heynacher by Carl Zeiss ), an attempt to relate the modulation transfer function to the vision of the human eye. Another psycho- physically based variable is SQF ( Subjective Quality Factor).

Mathematical Description

The result is a counting measure with the following properties:

  • Advantage: Comparability of measurement results
  • Disadvantage: The measurement results require idealized conditions.

Specifications

To compare the modulations ( the contrast ) different object modulations ( = curves ) can be used. Typical patterns of the shaped waveform and the sinusoidal curve. By imaging systems, the selected curve is always changed.

Other variations in measurements take into account other parameters.

Applications

In diagnostic radiology, the MTF for the imaging systems should be checked regularly. Characteristics are the limiting resolution ( spatial frequency at which the modulation is below 2%) and the characteristic modulation ( modulation percentage in the spatial frequency 1 line pair / mm).

In the development of lens systems or optical systems, the calculation and optimization of the optical transfer function is essential, and determines the quality of the device. To simplify this development work, the MTF is calculated mostly no longer experimental, but by computer model. Since it is idealized values ​​for MTF that does the basic principle - to be a comparison value - no harm.

Professional cameras have complex lens systems to produce at a high light yield lowest possible imaging errors, which can be specified with the MTF. For example, has the lens a very sharp drop at higher frequencies (similar to the pattern in the upper graph), then it does not help to increase the resolution of the detector in order to achieve better resolution.

The Internet research on MTF values ​​the keyword " data sheet" is recommended ( as an additional search term).

Hybrid images

In hybrid images is caused in the superposition of two similar images with the manipulation of the contrast transfer functions, an optical illusion.

Swell

  • Theodor Laubenberger: art medical radiology: diagnostic, radiotherapy, radiation protection. 7th edition, German Medical Publishers, Cologne 1999, ISBN 3-7691-1132- X
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