The aim of this project is the complete image-forming optical description of spectral phenomena as complementary phenomena. Invertibility as a fundamental property of optical images has been shown on several occasions. Here special attention has generally been paid to spectral phenomena. To this day it is still unclear whether one generalized inversion rule can be specified for formally equal and unique inversion of any arbitrary optical experiment. Additionally such a generalization would require further interpretation, since even simple inverse phenomena lose their symmetrical properties in the transition from a phenomenological to a radiation-physical treatment.

In this work it is shown that inverse optical phenomena are not necessarily completely inverted. On the basis of an analysis of the properties of optical spaces a generalized inversion rule is developed that allows full symmetrized inversions which can also be confirmed from a radiation point of view. For a generalized form of Newton’s Experimentum crucis it is shown that completely inverse states remain completely inverted even after repeated optical imaging and multiple applications of spectrally-analyzing operations. The property of inversion can thus be seen as a conserved quantity in »spectral state space«. Furthermore a »self-inverting« mirror aperture was developed that allows inverse and complementary spectra as mutually dependent spectral states to be generated. Using this method it is possible to conceive of inverse and complementary spectral states as part of a generalized condition.

The mirror aperture has been developed into a teaching aid which is now manufactured and distributed and is suitable for demonstration experiments in schools and colleges. It also provides the basis for a number of new complementary-optical demonstrations that have been designed and realized for an exhibition which has been held on several occasions.

Rang, Matthias (2015): Phänomenologie komplementärer Spektren. Berlin: Logos, ISBN: 978-3-8325-3974-0, 430 S., über 50 Farbabbildungen http://www.logos-verlag.de/cgi-bin/engbuchmid?isbn=3974&lng=deu&id=

Rang, Matthias & Grebe-Ellis, Johannes (2009): Komplementärspektren: Experimente mit einer Spiegel-Spalt-Blende. Mathematisch-Naturwissenschaftlicher Unterricht, 62. Jg. (4): 227-230

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