Acta Polytechnica https://doi.org/10.14311/AP.2025.65.0115 Acta Polytechnica 65(1):115–118, 2025 © 2025 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague NANOSATELLITE X-RAY LOBSTER EYE OPTICS – MEASUREMENT OF OPTICAL PERFORMANCE Vladimír Tichýa,∗, Šárka Němcováb, René Hudeca, Martin Míkac a Czech Technical University in Prague, Faculty of Electrical Engineering, Department of Radioelectronics, Technická 2, 166 27 Prague, Czech Republic b Czech Technical University in Prague, Faculty of Mechanical Engineering, Department of Instrumentation and Control Engineering, Technická 4, 160 27 Prague, Czech Republic c University of Chemistry and Technology Prague, Faculty of Chemical Technology, Department of Glass and Ceramics, Technická 5, 166 28 Prague, Czech Republic ∗ corresponding author: vladimir-tichy@email.cz Abstract. This paper presents the results of tests of a one-dimensional Schmidt lobster-eye prototype module. The optics benefits from the new technology used for the mechanical part which ensures accurate positioning of individual mirrors, resulting in a sharp image in the focal plane. The prototype is designed for X-ray energy of around 1 keV, but it was tested in the visible part of the spectrum. FWHM is determined. The experimental results agree well with the simulations. Keywords: Lobster eye, multi-foil optics, reflective optics, grazing incidence optics, X-ray optics. 1. Introduction The lobster eye concept of grazing incidence optics offers a wide filed of view that makes this optics conve- nient for space X-ray sky monitors [1–8]. The Schmidt lobster eye [9] is assembled from planar rectangular mirrors, mutually tilted. There exists another design called the Angel lobster eye [10], which is formed by rectangular channels. The lobster eye optics is com- monly used for X-rays. Its main advantage is the wide field of view that makes it suited mainly for space X-ray monitors. The mirrors of a one-dimensional lobster eye are arranged around a virtual cylinder, see Figure 1. This set of mirrors will be further referred to as the stack. The optical behaviour of a single stack is similar to a cylindric lens. The focus of the system is marked F. The point C denotes the centre of the cylinder. β is the angular mirror position Schmidt lobster eye geometry is defined by these parameters: • r radius of the cylinder, • a mirror spacing, • t mirror thickness, • h mirror depth, • N number of mirrors. It is possible to use two orthogonally arranged stacks to make a double-reflecting device mimicking the func- tion of a spherical lens, see Figure 2. The technical challenge of the realisation of the Schmidt lobster eye is to ensure the accurate posi- tioning of individual mirrors. That is why a new technological concept has been proposed and covered by patent [11] and utility models [12, 13]. Figure 1. Layout of one-dimensional Schmidt lobster eye. The figure is not scaled to real dimensions. Figure 2. Optical layout of stacks of two-dimensional Schmidt lobster eye. The results of optical measurements of the proto- type module assembled by this technology are pre- sented in this paper. 2. Description of LNA-215 prototype module The photo of the prototype one-dimensional lobster eye LNA-215 is shown in Figure 3. The module has been designed to be tested on a CubeSat platform. Therefore, the focal length and the input aperture of 115 https://doi.org/10.14311/AP.2025.65.0115 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en V. Tichý, Š. Němcová, R. Hudec, M. Míka Acta Polytechnica Figure 3. Photo of prototype module LNA-215. the optics were chosen so that the optics together with a focussed detector would fit three units of a CubeSat satellite. The mirror spacing has been set to maximise the effective collection length. Prototype lobster eye LNA-215 has the following design parameters: • Focal length F = 215 mm. • Entrance aperture 87 × 84 mm. • Stack consists of N = 66 gold-coated glass mir- rors with a depth of h = 24 mm and thickness of t = 0.28 mm. • Mirror pitch A = 1.33 mm. • Footprint 95.8 × 95.8 × 26 mm without external housing. This allows it to be used on a 3U or larger CubeSat. • Designed for energies of around 1 keV but tests are possible in a wider spectral range. The following performance was calculated by simu- lations: • Field of view 10.4°. • Effective collecting length 1.6 cm at 1 keV. • Corresponding effective collecting area 2.4 cm2 for 2-D system. Preliminary tests with a simple aparatus using poly- chromatic light were presented in [14]. In this paper, the results of measurements on an optical bench in a laboratory are presented. 3. Experimental setup The lobster-eye prototype was tested in the optical laboratory of the Faculty of Mechanical Engineering of Czech Technical University in Prague. The setup consists of a light source, collimator, tested optics and a camera, see Figure 4. The mirrors are made of Figure 4. Experimental setup. Figure 5. Acquired focal image. Figure 6. Focal image – simulation. gold-coated glass, which also reflect visible light. This allows the test to be performed in the visible part of the spectrum. A green high-power LED was used as the light source. The focal length of the collimator was 1 600 mm. A Canon EOS 50D camera was used to take the image. Its resolution is 4 752 × 3 168 pixels and the sensor area is 22.3 × 14.9 mm. 4. Results The acquired focal image is shown in Figure 5. The tests with the previous prototype showed a significant skew error [15]. No error of this type is observable on the focal line in Figure 5. LOPSIMUL software [16, 17] was used for the sim- ulations. The simulations are based on the simplified ray-tracing algorithm [18–20]. Ideal mirrors were con- sidered for the simulations. The result of the simula- tions of the focal image is presented in Figure 6. 116 vol. 65 no. 1/2025 Tests of lobster eye X-Ray optics Figure 7. Profile of intensity – experiment. Figure 8. Profile of intensity – simulation. The profile of intensity along the horizontal axis of the experimental image is shown in Figure 7 while Figure 8 presents the result of the simulation. Note that the simulation is performed for mirrors with 100 % reflectivity (for tests in X-rays, it is planned to include relevant reflectivity model into the simula- tions). Therefore, the vertical scales of images Figure 7 and Figure 8 are not comparable. The FWHM of the experimental profile reaches 1.02 mm while the simulated image shows a better FWHM of 0.71 mm. The graph in Figure 8 shows one main peak that is formed mainly by reflected rays. Some rays come through the optical system directly through spaces between mirrors. These rays form secondary maxima of uniform intensity. However, the measured profile in Figure 7 shows that the secondary maxima are not uniform in inten- sity. This is caused by the diffraction of light. The diffraction also causes the measured FWHM of the main peak to be wider than the result of the simula- tion. The diffraction will not appear in X-rays because X-rays have a much shorter wavelength. Another problem that makes the main peak wider is that the light beam has some small divergency as the LED chip has a non-zero size. However, the LED chip size is not known and therefore, it cannot be included into simulations. For these reasons, the authors expect that results of tests in X-ray will be in much better agreement with the simulations. 5. Conclusion The experiment showed that the lobster-eye prototype is functional. The experimentally obtained focal image is very similar to the calculated one. The FWHM of the focal line on the image acquired in the experiment is slightly inferior to the calculated one. It is caused by the small divergence of rays and the diffraction effects. The focal line does not show an observable skew error. 117 V. Tichý, Š. Němcová, R. Hudec, M. Míka Acta Polytechnica This proves that the technology used is promising. An experiment in an X-ray tunnel is necessary to measure the performance of the lobster-eye prototype more precisely. The authors plan to test the module in an X-ray tunnel at the design energy of about 1 keV. We expect that the results of this test will show good accordance with the simulation as it will not be affected by diffraction effects because the X-ray wavelength is much shorter. Acknowledgements The authors would like to thank the European Union’s Horizon 2020 Programme under the AHEAD2020 project (grant agreement No. 871158 for the support). 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International Society for Optics and Photonics, SPIE, 2011. https://doi.org/10.1117/12.886809 118 https://doi.org/10.3390/universe8030144 https://doi.org/10.1007/978-981-16-4544-0_3-1 https://doi.org/10.1117/12.2307879 https://doi.org/10.1117/12.2308003 https://doi.org/10.1117/12.2308125 https://doi.org/10.1117/12.2308126 https://doi.org/10.1117/12.2308249 https://doi.org/10.1016/0029-554X(75)90501-7 https://doi.org/10.1086/157397 https://doi.org/10.31577/caosp.2023.53.4.198 http://www.lopsimul.eu/ https://doi.org/10.31577/caosp.2023.53.4.206 https://doi.org/10.1007/s10686-016-9493-2 https://doi.org/10.1117/12.2017611 https://doi.org/10.1117/12.886809 Acta Polytechnica 65(1):115–118, 2025 1 Introduction 2 Description of LNA-215 prototype module 3 Experimental setup 4 Results 5 Conclusion Acknowledgements References