About the Project
Today, light scattering analysis techniques have become extremely sophisticated and allow a careful examination of the contribution of interface roughness to the performance of multilayer interference filters. For this reason, the Institut Fresnel has developed electromagnetic modeling tools and optical instrumentation (SALSA set-up ) that are unique on the international scene[1-5].
In less than 20 years, extraordinary progresses have been obtained on optical filters, particularly to minimize light scattering (some 10-6 of the incident flux). These advances are closely linked to polishing techniques, which make it possible to obtain, on amorphous substrates, roughnesses which are less than a fraction of a nanometer in the optical frequency window. It is important to point out here that with modern filter manufacturing technologies, the roughness of the substrate is reproduced almost identically by each of the thin layers constituting the stack; there is therefore no amplification of the roughness, so that the threshold value (minimum) of the diffusion is imposed by the roughness of the substrate (except for the enhancement/inhibition coefficients).
However, at this level of qualification, new problems appear and relate particularly to the presence of localized defects in the component. These defects are submicronic in size and arise during the manufacture of the filters. Their density is low (<1 for a 100 µm diameter) for conventional components, so that in the majority of cases, their contribution can be neglected. However, in the case of complex filters (a hundred thin layers) used for Space applications, the impact of isolated defects becomes dominant in the process of light diffusion. This is what we are witnessing for an increasing number of applications.
It is therefore becoming important to be able to separate, in the value displayed for roughness, the contribution of classical topography (intrinsic, continuous and derivable), from that of localized defects (pitting, scratches, dust...). This separation is essential for qualifying the polishing and cleaning processes, understanding the phenomena of absorption and damage under flux, and improving deposition technologies. From a quantitative point of view, it is a question of analyzing with discrimination the weight of an intrinsic roughness whose standard deviation is less than the nm, and that of a density of isolated randomly distributed defects. It should be noted here that non-optical methods, and those based on optical microscopy, if they are extremely efficient, only partially respond to this problem: it is first crucial that the heterogeneity values correspond to an integral over the optical (spatial) frequency window of the operating point (the application), a constraint which is naturally satisfied by light scattering techniques. Furthermore, we cannot ignore the problems of stationarity inherent in any sampling process or in any surface with a dimension much smaller than the lighting spot used for the application. Finally, we must keep in mind that the target concerns the straylight (resulting from the roughness) and not the value of the roughness itself. These elements illustrate the strategic nature of light scattering techniques for the study of heterogeneities related to straylight.
The light scattering technique commonly developed in the laboratory consists in extracting the roughness spectrum (Fourier transform of the autocorrelation function of the topography) of the substrate topography from the measurement of its scattering pattern (obtained by moving a detector around the sample). This extraction is based on a widely validated electromagnetic theory [4-5]. The spectrum thus measured characterizes the sample over the entire surface of the illumination spot (adjustable from mm² to cm²); its spectral shape indicates the statistical nature of the roughness, with a decrease related to the inverse of the correlation length and possible maxima indicating pseudo-periods; where appropriate, angular correlation functions make it possible to identify the preferred directions on the sample (roughness anisotropy). The roughness is obtained by integrating the roughness spectrum.
The set-up (SPARSE, SPatially and Angularly Resolved Scatterometry Equipment) that we recently developed to solve the cited challenge (separation of intrinsic and extrinsic roughness) consists in measuring, not a scattering indicator for a sample, but 106 indicators corresponding to each pixel of a CCD matrix in bijection with a surface element thanks to an adapted telecentric system. It should be noted that the quality of this bijection doesn’t allow any rotation of the detector around the sample (classic previous case), so that this rotation of the detector must be replaced by a rotation of the lighting beam, based on the theorem of reciprocity. Under these conditions, the roughness spectrum of each “surface pixel” is extracted and its spectral shape is analyzed. A monotonic decay is characteristic of intrinsic roughness, while the presence of oscillations reveals the existence of an isolated defect (diffraction by a particle) whose dimensions dictate the shape of the oscillations. This pixel-to-pixel analysis makes it possible to sort the "intrinsic" and "extrinsic" pixels, and consequently to extract 2 roughness values indicating respectively the weight of the isolated defects and that of the topography. Each of these values is given with a relative precision of the order of the %, for roughness detected up to one thousandth of a nm. Note that the optical detectivity of the SPARSE system is of the order of 10-8 for the scattering indicator (limitation imposed by Rayleigh diffraction of air particles) throughout the angular range.
We thus have in the laboratory a SPARSE type instrumentation. However, this works in unpolarized light and in a monochromatic mode (a single wavelength: 840 nm), while the scattering of optical filters is particularly chromatic and polarizing. The objective of this thesis is thus, in a first step, to extend the SPARSE instrumentation to a continuous polychromatic regime (super continuum laser + tunable filter). In a second step, we will look for robust criteria to quickly identify, using the theoretical tools of statistical optics, the weight of the isolated defects. We will then study the propagation of these defects in the volume of the filters, by solving the inverse problem which consists in identifying the correlation laws between interfaces (which control the mutual coherence of the diffusion sources). Finally, feedback with the technology will be proposed
The candidate must have a master's degree in physics or an engineering school diploma. The work to be done will present theoretical, numerical and experimental aspects to be carried out in parallel. The candidate must therefore present a certain taste for these different approaches of Physics in general and Optics in particular. Basic training in optics is desirable
 Marin Fouchier, Myriam Zerrad, Michel Lequime, Claude Amra. Wide-range wavelength and angle resolved light scattering measurement setup. Optics Letters, Optical Society of America - OSA Publishing, 2020, 45 (9), pp.2506-2509. ⟨10.1364/OL.392000⟩.
 Michel Lequime, Myriam Zerrad, Carole Deumie, Claude Amra. A goniometric light scattering instrument with high-resolution imaging. Optics Communications, Elsevier, 2009, 282, pp.1265-1273.
 C. Amra, "First-order vector theory of bulk scattering in optical multilayers," J. Opt. Soc. Am. A 10, 365-374 (1993)
 C. Amra, M. Lequime, and M. Zerrad, Electromagnetic Optics of Thin-Film Coatings: Light Scattering, Giant Field Enhancement, and Planar Microcavities. Cambridge University Press, 2020.
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