X-ray telescope mirrors from surface profile to point spread function.

X-ray astronomy was born on 1962 when Giacconi decided to put a Geiger counter onto a rocket, in hope of measuring the X-ray emission from the Sun. Even if the Sun emission was disappointing, he made the discovery that changed our view on the Universe. An unknown background of X-ray emission that later turned out to contain millions of X-ray sources, both galactic and extra-galactic. Owing to the development of increasingly sophisticated instruments, the sensitivity and the resolution to detect X-ray sources has improved significantly over the last 50 years. One of the major technological improvement was the development of focusing telescope, which allowed to enhance the angular resolution and sensitivity of several orders of magnitude. The angular resolution of an X-ray imaging telescope is mainly determined by the quality of its focusing optics. These generally consist of a number of nested shells of grazing incidence mirrors. The typical configuration used, which minimizes the effect of coma aberration and reduces the focal length, is the so-called Wolter-I (paraboloid-hyperboloid mirror configuration). In order to keep the mass to levels comparable with the launcher (because X-ray absorption in the atmosphere prevents observation from ground) the optics have to be lightweight, hence the mirrors have to be thin. The final performance of a mirror module is always subject to degradation, provided in the realization phase. During the different stages of production (under construction and integration) there may be distortions. In addition, the mirror surface is not ideally smooth but is characterized by a certain roughness topography. Both these types of imperfections combine to determine the degradation of the Point Spread Function (PSF), i.e. the annular integral of focused intensity around the focal spot, which generally characterizes the quality of the optics. Regarding the characterization of an X-ray mirror, one of the basic objectives is to establish the relationship between the imperfections of the mirrors and their PSFas a function of the incident wave energy. The aimis to predict the angular resolution of a mirror, given measurements of profiles and microroughness, or to establish the level of tolerable imperfections of a mirror given a certain angular resolution required by the project specifications. The study of the topography of the mirror surface is done through several methods. It is generally divided into two different kinds of analysis: the study of the profile, i.e. large spatial wavelengths (comparable with the mirror length) and the study of microroughness, i.e. short spatial wavelengths. The first ones, also called the figure errors, are often due to deformation of the mirror that occurs during construction and integration and are responsible for the degradation of the PSF and can be treated by geometrical optics. The second ones are due, for example, to the limits of the polishing mandrel methods, from which the shells are replicated, and the deposition technology of the reflective coating. These imperfections are responsible for a diffusion (called scattering), which degrades the PSF at increasing energy and can not be treated by geometrical optics, but using physical optics under some assumptions. This problem is much more important in Xray than in optical astronomy, because X-ray have a 1000 times smaller wavelengths and are sensitive to surface defects 1000 times smaller. The surface polishing is thereby a fundamental point in X-ray mirrors. The characterization of the microroughness is made in terms of power spectrum as a function of the spatial frequency on the surface (PSD - Power Spectral Density). The PSD is a fundamental quantity in the characterization of X-ray telescope optics because is proportional to the scattering. The measure of roughness is done with different instruments in order to have a range of spatial frequencies as more wide as possible, from a few millimetres to a few tens of nanometres. There is also a range of intermediate frequencies, at the limit of microroughness, which generates a degradation of the PSF that can neither be predicted by geometrical optics and nor by the scattering theory. For this reason, it is difficult in general to predict accurately its effect on the PSF. My PhD activity is included in the mission project NHXM financed by ASI and in the development of X-ray mirrors for ATHENA mission project financed by ESA. The first part of my PhD project has been therefore aimed at the characterization of microroughness and reflectivity of the mirrors, at INAF/OAB, in order to determine the topography of the surface and to support the industry (Media Lario Technology, leader company of manufacturing optical components) in setting the process. The second part of the project was instead dedicated to the development of a selfconsistent general method, based on physical optics, to compute the PSF of X-ray 2 mirrors from their profile metrology. The third part, which is the merging of these two parts of the project, consist in the applications to real cases through verifications with calibration tests. My research work can be divided into three phases: • First phase - I performed measurements of mirror profiles and roughness of several samples of mirrors for the missions NHXMand ATHENA, using different instruments available at INAF/OAB. The roughness measurements, at spatial scales smaller than 1 mm, can be achieved with different instruments that have different spatial wavelength ranges (i.e. optical interferometer WYKO and Atomic Force Microscope). However, the effects of roughness can also be directly observed by performing X-ray reflectivity measurements using an X-ray diffractometer. I used the X-ray diffractometer available at INAF/OAB for scattering measurements, with particular attention to the effects in large angle scattering and modulation interference introduced by the multilayer. By merging these different data I derived the complete roughness surface PSD. Bymeans of the X-ray diffractometer Imade reflectivity measurements of samples of mirrors with multilayer coating, obtaining the reflectivity curve as a function of the angle of incidence and as a function of the energy. Using a program to fit the reflectivity curves (PPM), I estimated the thickness of the layers and their uniformity, then assessing the compliance with design specifications. In summary, from one hand surface roughness (from direct topography measurements and scattering measurements) to obtain the PSD, on the other hand, measurements of reflectivity (as a function of both the incidence angle and the energy) for the characterization of the structure of the multilayer. The feedback provided to the industry in a commons way and the isolation of the critical points has lead to the deposition of coatings with excellent reflectivity. I performed reflectivity measurements also within the study of the crystallization of gold during the evaporation process, which contributes to worsen the surface roughness. The gold layer is deposited on the mandrel, which is then electroformed a Nickel-Cobalt shell (the mirror). The gold layer serves to detach the shell from mandrel and it should minimize the microroughness increasing. In this regard, I performed diffraction measurements of different gold deposits with different thickness. Studying the Bragg peaks I obtained an estimation of the size of the gold crystallites as a function of the thickness. Larger are the crystallites, higher is the value of the microroughness. The conclusion is that more the gold layer is thick, larger are the crystallites and larger crystallites means microroughness increasing. • Second phase - I developed a new method to calculate the PSF of an X-ray mirror (e.g. Wolter-I configuration, in double reflection) at any energy by applying the principle of Huygens-Fresnel from real profile and roughness data. In other words, the X-ray reflection is treated by the undulatory theory, building the wavefront deformed by the mirror imperfections. In this interpretation, even the deformed geometry are treated by the physical optics. This allows to obtain the PSF determined from both contributions (figure error and scattering) at any energy in a self-consistent way, without considering different separated energy regimes treated with different methods. This method, never used before, ultimately solves the problem of PSF computation, starting from the complete surface topography of an X-ray mirror. • Third phase - I performed several calibrations over mirror shells in different configurations as demonstrator for the NHXM hard X-ray imaging telescope (0.3 - 80 keV). Prototypes of NHXM mirror modules with a few mirror shells were manufactured, aiming at demonstrating the feasibility of mirrors. Imade the direct performance verification by measuring the X-ray PSF (Point Spread Function) up to 50 keV in full-illumination setup at PANTER (MPE, Germany) and in pencil-beam set up at monochromatic X-ray energies from 15 to 63 keV at the BL20B2 beamline of the SPring-8 synchrotron radiation facility. Moreover, I simulated PSF from the metrology profile of mirror shell using Fresnel diffraction method. The calibration measured data and the simulated data (obtained with my Fresnel method) match perfectly. This provide the experimental proof of the correctness of the method, that therefore will represent, from now on, a powerful prediction tool in X-ray optics. The Fresnel diffraction method is easily extendible to other optical systems, also out of astrophysical applications, even with a number of more than two reflections, e.g Syncrotron and FEL facilities. For the future, I plan to implement the Fresnel diffraction method improving the simulations of mirrors coated with multilayer. In this case in order to increase the prediction accuracy, we have to taking into account the scattering from multilayer interfaces