@article {hering2009,
	title = {Correlated speckle noise in white-light interferometry: theoretical analysis of measurement uncertainty},
	journal = {Appl. Optics},
	volume = {48},
	year = {2009},
	pages = {525--538},
	abstract = {The partial coherent illumination of the specimen, which is required for white-light interferometric measurements of optically rough surfaces, directly leads to speckle. The electric field of such speckle patterns strongly fluctuates in amplitude and phase. This spatially correlated noise influences the accuracy of the measuring device. Although a variety of noise sources in white-light interferometry has been studied in recent years, they do not account for spatial correlation and, hence, they cannot be applied to speckle noise. Thus, we derive a new model enabling quantitative predictions for measurement uncertainty caused by speckle. The model reveals that the accuracy can be attributed mainly to the degree of spatial correlation, i.e., the average size of a speckle, and to the coherence length of the light source. The same parameters define the signal-to-noise ratio in the spectral domain. The model helps to design filter functions that are perfectly adapted to the noise characteristics of the respective device, thus improving the accuracy of postprocessing algorithms for envelope detection. The derived expressions are also compared to numerical simulations and experimental data of two different types of interferometers. These results are a first validation of the theoretical considerations of this article.},
	doi = {10.1364/AO.48.000525},
	author = {Marco Hering and Klaus K{\"o}rner and Bernd J{\"a}hne}
}
@phdthesis {hering2007,
	title = {Angewandte statistische Optik in der Wei{\ss}licht-Interferometrie: R{\"a}umliches Phasenschieben und Einfluss optisch rauer Oberfl{\"a}chen},
	year = {2007},
	publisher = {IWR, Fakult{\"a}t f{\"u}r Physik und Astronomie, Univ.\ Heidelberg},
	abstract = {This thesis describes a novel one-shot white-light interferometer for three-dimensional sensing. The method is based on spatial phase shifting which renders mechanical phase shifting unneces-sary. Due to the absence of any mechanical transducers, its static optical setup is well suited for applications outside the laboratory. Its one-shot ability is of great interest for contactless and high precision quality inspection as well as for medical applications. Also, it allows a quanti-tative monitoring of dynamic surface processes. The first part of this thesis describes the development of the optical setup in context of physical limitations and technical requirements, followed by a detailed discussion of single components and their influence onto the accuracy of the system. Furthermore, the statistical properties of speckle patterns, which appear for diffusely scattering samples, are derived. Thus, existing theories, relating the measurement uncertainty of white-light interferometry to the influence of speckle, are extended. By means of simulations and experimental techniques presented in this thesis, it is possible to verify the theoretical predictions and to clarify the consequences. Especially in context of high numerical apertures, these results have to be taken into account to improve the optical setup as well as the performance of signal processing algorithms.},
	url = {http://www.ub.uni-heidelberg.de/archiv/7470/},
	author = {Marco Hering}
}
