24 May 2018 Optimization of the complex coherence function Γ for diffraction-based wavefront transformations
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Partial coherence is used in a plurality of applications, magnifying microscopic imaging, interferometric measurement, lithographic imaging, CGH based wave front shaping, interference lithography and space-bandwidth-limited wave front reconstruction, just to name a few. In some applications the primary light source is characterized by a limited coherence length and an extended angular spectrum of plane waves, which has to be narrowed, e.g. if an Excimer laser is used. Sometimes the angular spectrum of plane waves of the primary light source has to be increased in order to be practical. There are several possibilities in general, the primary light source can be used directly, the system has to be adapted or the coherence function Γ has to be tailored in order to provide the specific requirements. Almost all embodiments come with little changes of the light sources coherence properties only. For example, to use a spectral bandpass filter or to limit the size of the light source seem to be the standard solution for almost everything.

However, more advanced tailoring of the complex valued coherence function Γ leads to an increased image quality, e.g. in interferometers, but is not limited to this, reduces background noise, decouples Fizeau cavities or it enables complete new illumination and imaging system designs, which provide unique features. This aspect will be discussed herein. Furthermore, the propagation of the complex coherence will be taken into account. This is done in order to provide defined conditions in defined planes of imaging devices. In other words, the usage of the Wiener-Khintchin theorem and the van Cittert-Zernike theorem is just a part of the system analysis and system optimization, which has to be done. Although generic approaches are used, discrete light source layouts are strongly related to the discrete optical devices, which make use of them.

The specific tailoring of the complex coherence function, which is related to the space-bandwidth-limited reconstruction of wave front segments, which also can be referred to as space-bandwidth-limited CGH reconstruction, will be described in more detail. For this type of real time dynamic imaging two major problems - among several others - have to be solved. One problem is the huge computation power and the other one is the coherent retinal cross talk of adjacent image points, which are reconstructed in the image volume. The disclosed layouts of tailored secondary light sources are based on the Wiener-Khintchin theorem and the van Cittert-Zernike theorem. Both problems, which are mentioned above, can be solved. Tailored complex valued light sources reduce the required computation power by enabling reduced coherent overlay of sub-CGH areas. Furthermore, they reduce the coherent retinal cross talk of dynamic real time spacebandwidth- limited CGH reconstruction, which is used in advanced imaging applications, too. This results in an increased image quality of partial coherent wave field reconstruction based imaging.
© (2018) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
G. Fütterer, "Optimization of the complex coherence function Γ for diffraction-based wavefront transformations", Proc. SPIE 10677, Unconventional Optical Imaging, 106773H (24 May 2018); doi: 10.1117/12.2307245; https://doi.org/10.1117/12.2307245

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