Dwell time calculation is one of the most important process in a highly deterministic computer-controlled Ion Beam Figuring (IBF) process. It is modeled as a deconvolution process between the desired removal map and the beam removal function, which is an ill-posed inverse problem. A good dwell time solution should fulfill four requirements: 1) it must be non-negative; 2) it should closely duplicate the shape of the desired removal map; 3) the total dwell time is expected to be as short as possible; 4) the calculation time is reasonable. Dwell time algorithms, such as Fourier transform-based algorithm, matrix-based algorithm, and Bayesian-based algorithm, have been proposed and applied to IBF. However, their performances were never clearly examined and described accordingly. In this research, we provide a quantitative study on the performances of these dwell time algorithms based on the aforementioned four requirements.
With the progressive development in synchrotron radiation facilities and free electron lasers (FELs), the requirement of the X-ray mirror is getting higher with tighter specifications. It challenges the X-ray mirror metrology in two major application scenes. On one hand, a reliable mirror measurement technique is needed to provide trustable feedback to the deterministic polishing in mirror fabrication or re-polishing process. On the other hand, it demands a more accurate mirror metrology technique to offer better services for the X-ray mirror inspection at synchrotrons and FELs to control the quality of X-ray mirrors to be installed into beamlines.
Since the stitching interferometry can provide two-dimensional laterally extendable (stitched) results with sub-nanometer height resolution and precision, several stitching interferometric techniques are studied for synchrotron mirror metrology. It is not only to enhance the mirror inspection capability in NSLS-II optical metrology laboratory but also to act in concert with the ongoing ion beam figuring project at NSLS-II. Various stitching methods with different stitching parameters are investigated at our stitching interferometric platform. Some experimental results are revealed to demonstrate the validity and performance of the developed system and stitching methods.
We demonstrate a novel One-Dimensional Ion-Beam Figuring (1D-IBF) solution from Brookhaven National Laboratory. Three improvements are introduced to the new 1D-IBF system. First, the misalignment of the coordinate systems between the metrology and the 1D-IBF hardware is minimized by integrating both the sample mirror and the Beam Removal Function (BRF) mirror into a single mirror holder. The measured BRF center is then used as a reference to calibrate the coordinate correspondence. Second, a Constrained Linear Least-Squares (CLLS) algorithm with a coarse-to-fine scheme is proposed to keep the non-negativity of the dwell time as well as ensure it smoothly duplicate the required removal amount. Third, a dwell time slicing strategy is used to smooth the implementation of the dwell time in the real 1D-IBF fabrication process. Experimental results demonstrate that the proposed 1D-IBF solution reduces the residual profile errors to sub-nanometer Root Mean Square (RMS) for both flat and spherical mirrors.
The ATHENA X-ray observatory is a large-class ESA approved mission, with launch scheduled in 2028. The technology of silicon pore optics (SPO) was selected as baseline to assemble ATHENA’s optic with hundreds of mirror modules, obtained by stacking wedged and ribbed silicon wafer plates onto silicon mandrels to form the Wolter-I configuration. In the current configuration, the optical assembly has a 3 m diameter and a 2 m2 effective area at 1 keV, with a required angular resolution of 5 arcsec. The angular resolution that can be achieved is chiefly the combination of 1) the focal spot size determined by the pore diffraction, 2) the focus degradation caused by surface and profile errors, 3) the aberrations introduced by the misalignments between primary and secondary segments, 4) imperfections in the co-focality of the mirror modules in the optical assembly. A detailed simulation of these aspects is required in order to assess the fabrication and alignment tolerances; moreover, the achievable effective area and angular resolution depend on the mirror module design. Therefore, guaranteeing these optical performances requires: a fast design tool to find the most performing solution in terms of mirror module geometry and population, and an accurate point spread function simulation from local metrology and positioning information. In this paper, we present the results of simulations in the framework of ESA-financed projects (SIMPOSiuM, ASPHEA, SPIRIT), in preparation of the ATHENA X-ray telescope, analyzing the mentioned points: 1) we deal with a detailed description of diffractive effects in an SPO mirror module, 2) we show ray-tracing results including surface and profile defects of the reflective surfaces, 3) we assess the effective area and angular resolution degradation caused by alignment errors between SPO mirror module’s segments, and 4) we simulate the effects of co-focality errors in X-rays and in the UV optical bench used to study the mirror module alignment and integration.
The focusing accuracy in reflective optical systems, usually expressed in terms of the Point Spread Function (PSF) is chiefly determined by two factors: the deviation of the mirror shape from the nominal design and the surface finishing. While the effects of the former are usually well described by the geometrical optics, the latter is diffractive/interferential in nature and determined by a distribution of defects that cover several decades in the lateral scale (from a few millimeters to a few microns). Clearly, reducing the level of scattered light is crucial to improve the focusing of the collected radiation, particularly for astronomical telescopes that aim to detect faint light signals from our Universe. Telescopes are typically arranged in multiple reflections configuration and the behavior of the multiply-scattered radiation becomes difficult to predict and control. Also it is difficult to disentangle the effect of surface scattering from the PSF degradation caused by the shape deformation of the optical elements. This paper presents a simple and unifying method for evaluating the contribution of optical surfaces defects to the two-dimensional PSF of a multi-reflections system, regardless of the classification of a spectral range as ”geometry” or ”roughness”. This method, entirely based on Huygens-Fresnel principle in the far-field approximation, was already applied in grazing-incidence X-ray mirrors and experimentally validated for a single reflection system, accounting for the real surface topography of the optics. In this work we show the extension of this formalism to a double reflection system and introducing real microroughness data. The formalism is applied to a MAGIC-I panel mirror that was fully characterized, allowing us to predict the PSF and the validation with real measurements of the double reflection ASTRI telescope, a prototype of CTA-SST telescope.
The Point Spread Function (PSF) allows for specifying the angular resolution of optical systems which is a key parameter used to define the performances of most optics. A prediction of the system's PSF is therefore a powerful tool to assess the design and manufacture requirements of complex optical systems. Currently, well-established ray-tracing routines based on a geometrical optics are used for this purpose. However, those ray-tracing routines either lack real surface defect considerations (figure errors or micro-roughness) in their computation, or they include a scattering effect modeled separately that requires assumptions difficult to verify. Since there is an increasing demand for tighter angular resolution, the problem of surface finishing could drastically damage the optical performances of a system, including optical telescopes systems. A purely physical optics approach is more effective as it remains valid regardless of the shape and size of the defects appearing on the optical surface. However, a computation when performed in the two-dimensional space is time consuming since it requires processing a surface map with a few micron resolution which sometimes extends the propagation to multiple-reflections. The computation is significantly simplified in the far-field configuration as it involves only a sequence of Fourier Transforms. We show how to account for measured surface defects and roughness in order to predict the performances of the optics in single reflection, which can be applied and validated for real case studies.
The ATHENA X-ray observatory is a large-class ESA approved mission, with launch scheduled in 2028. The technology of silicon pore optics (SPO) was selected as baseline to assemble ATHENA's optic with more than 1000 mirror modules, obtained by stacking wedged and ribbed silicon wafer plates onto silicon mandrels to form the Wolter-I configuration. Even if the current baseline design fulfills the required effective area of 2 m2 at 1 keV on-axis, alternative design solutions, e.g., privileging the field of view or the off-axis angular resolution, are also possible. Moreover, the stringent requirement of a 5 arcsec HEW angular resolution at 1 keV entails very small profile errors and excellent surface smoothness, as well as a precise alignment of the 1000 mirror modules to avoid imaging degradation and effective area loss. Finally, the stray light issue has to be kept under control. In this paper we show the preliminary results of simulations of optical systems based on SPO for the ATHENA X-ray telescope, from pore to telescope level, carried out at INAF/OAB and DTU Space under ESA contract. We show ray-tracing results, including assessment of the misalignments of mirror modules and the impact of stray light. We also deal with a detailed description of diffractive effects expected in an SPO module from UV light, where the aperture diffraction prevails, to X-rays where the surface diffraction plays a major role. Finally, we analyze the results of X-ray tests performed at the BESSY synchrotron, we compare them with surface finishing measurements, and we estimate the expected HEW degradation caused by the X-ray scattering.
A deflectometrical facility was developed at Italian National Institute for Astrophysics-OAB to characterize free-form optics with shape errors within few microns rms.
Deflectometry is an interesting technique because it allows the fast characterization of free-form optics. The capabilities of deflectometry in measuring medium-high frequencies are well known, but the low frequencies error characterization is more challenging. Our facility design foresees an innovative approach based on the acquisition of multiple direct images to enhance the performance on the challenging low frequencies range.
This contribution presents the error-budget analysis of the measuring method and a study of the configuration tolerances required to allow the use of deflectometry in the realization of optical components suitable for astronomical projects with a requirement of high accuracy for the optics. As test examples we took into account mirrors for the E-ELT telescope.
The LAMP (Lightweight Asymmetry and Magnetism Probe) X-ray telescope is a mission concept to measure the polarization of X-ray astronomical sources at 250 eV via imaging mirrors that reflect at incidence angles near the polarization angle, i.e., 45 deg. Hence, it will require the adoption of multilayer coatings with a few nanometers dspacing in order to enhance the reflectivity. The nickel electroforming technology has already been successfully used to fabricate the high angular resolution imaging mirrors of the X-ray telescopes SAX, XMM-Newton, and Swift/XRT. We are investigating this consolidated technology as a possible technique to manufacture focusing mirrors for LAMP. Although the very good reflectivity performances of this kind of mirrors were already demonstrated in grazing incidence, the reflectivity and the scattering properties have not been tested directly at the unusually large angle of 45 deg. Other possible substrates are represented by thin glass foils or silicon wafers. In this paper we present the results of the X-ray reflectivity campaign performed at the BEAR beamline of Elettra - Sincrotrone Trieste on multilayer coatings of various composition (Cr/C, Co/C), deposited with different sputtering parameters on nickel, silicon, and glass substrates, using polarized X-rays in the spectral range 240 - 290 eV.
The Point Spread Function (PSF) is a key figure of merit for specifying the angular resolution of optical systems and, as the demand for higher and higher angular resolution increases, the problem of surface finishing must be taken seriously even in optical telescopes. From the optical design of the instrument, reliable ray-tracing routines allow computing and display of the PSF based on geometrical optics. However, such an approach does not directly account for the scattering caused by surface micro-roughness, which is interferential in nature. Although the scattering effect can be separately modeled, its inclusion in the ray-tracing routine requires assumptions that are difficult to verify. In that context, a purely physical optics approach is more appropriate as it remains valid regardless of the shape and size of the defects appearing on the optical surface. Such a computation, when performed in two-dimensional consideration, is memory and time consuming because it requires one to process a surface map with a few micron resolution, and the situation becomes even more complicated in case of optical systems characterized by more than one reflection. Fortunately, the computation is significantly simplified in far-field configuration, since the computation involves only a sequence of Fourier Transforms. In this paper, we provide validation of the PSF simulation with Physical Optics approach through comparison with real PSF measurement data in the case of ASTRI-SST M1 hexagonal segments. These results represent a first foundation stone for future development in a more advanced computation taking into account micro-roughness and multiple reflection in optical systems.
The Cherenkov Telescope Array (CTA) is a forthcoming international ground-based observatory for very high-energy gamma rays. Its goal is to reach sensitivity five to ten times better than existing Cherenkov telescopes such as VERITAS, H.E.S.S. or MAGIC and extend the range of observation to energies down to few tens of GeV and beyond 100 TeV. To achieve this goal, an array of about 100 telescopes is required, meaning a total reflective surface of several thousands of square meters. Thence, the optimal technology used for CTA mirrors' manufacture should be both low-cost (~1000 euros/m2) and allow high optical performances over the 300-550 nm wavelength range. More exactly, a reflectivity higher than 85% and a PSF (Point Spread Function) diameter smaller than 1 mrad. Surface roughness can significantly contribute to PSF broadening and limit telescope performances. Fortunately, manufacturing techniques for mirrors are now available to keep the optical scattering well below the geometrically-predictable effect of figure errors. This paper determines first order surface finish tolerances based on a surface microroughness characterization campaign, using Phase Shift Interferometry. That allows us to compute the roughness contribution to Cherenkov telescope PSF. This study is performed for diverse mirror candidates (MAGIC-I and II, ASTRI, MST) varying in manufacture technologies, selected coating materials and taking into account the degradation over time due to environmental hazards.
The Lightweight Asymmetry and Magnetism Probe (LAMP) is a micro-satellite mission concept dedicated for astronomical X-ray polarimetry and is currently under early phase study. It consists of segmented paraboloidal multilayer mirrors with a collecting area of about 1300 cm2 to reflect and focus 250 eV X-rays, which will be detected by position sensitive detectors at the focal plane. The primary targets of LAMP include the thermal emission from the surface of pulsars and synchrotron emission produced by relativistic jets in blazars. With the expected sensitivity, it will allow us to detect polarization or place a tight upper limit for about 10 pulsars and 20 blazars. In addition to measuring magnetic structures in these objects, LAMP will also enable us to discover bare quark stars if they exist, whose thermal emission is expected to be zero polarized, while the thermal emission from neutron stars is believed to be highly polarized due to plasma polarization and the quantum electrodynamics (QED) effect. Here we present an overview of the mission concept, its science objectives and simulated observational results.
The Rayleigh Rice vector perturbation theory has been successfully used for several decades to relate the surface power
spectrum of optically smooth reflectors to the angular resolved scatter resulting from light sources of known wavelength,
incident angle and polarization. A similar relationship should be available for the situation of a beam transmitting from a
region of index greater than 1.0 into a region of unit index through an optically smooth surface. This paper presents such
a relationship and compares the result to measured scatter data at two light wavelengths.
The Rayleigh Rice vector perturbation theory has been successfully used for several decades to relate the surface power
spectrum of optically smooth reflectors to the angular resolved scatter resulting from light sources of known wavelength,
incident angle and polarization. While measuring low frequency roughness is relatively easy, the corresponding near
specular scatter can be difficult to measure. This paper discusses using high incident angle near specular measurements
along with profile generated surface power spectrums as a means of checking a near specular scatter requirement. The
specification in question, a BRDF of 1.0 sr-1 at 2 mrad from the specular direction and at a wavelength of 1μm, is very
difficult to verify by conventional scatter measurements. In fact, it is impractical to directly measure surface scatter from
uncoated Zerodur because of its high bulk scatter. This paper presents profilometer and scatterometer data obtained from
coated and uncoated flats at several wavelengths and outlines the analysis technique used to check this tight
specification.
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