Matrix based algorithm for ion-beam figuring of optical elements
An algorithm for solving the problem of local shape errors of optical surfaces correcting by a small-sized ion beam, based on the matrix representation is presented. The algorithm involves searching for points that rise relative to the average height on the surface, where exposure to an ion beam of...
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| Veröffentlicht in: | Precision engineering Jg. 69; S. 29 - 35 |
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| Abstract | An algorithm for solving the problem of local shape errors of optical surfaces correcting by a small-sized ion beam, based on the matrix representation is presented. The algorithm involves searching for points that rise relative to the average height on the surface, where exposure to an ion beam of a given shape will lead to a decrease in the RMS deviation of the surface shape from the calculated one. It is shown that the new approach makes it possible to significantly expand the range of spatial frequencies, in which the height of relief can be reduced using the given ion beam size, and provides better results than the method of minimizing the functional of convolution of the ion beam and the surface map. Moreover, the new approach does not lead to appearance of shape errors (concentric structure) defined by the ion beam size and scanning step. An experiment for minimizing of local surface shape errors based on an etching map calculated using new approach was done. Matrix algorithm allowed in one procedure to reduce surface shape errors for a concave spherical optical element made of fused silica with a diameter D = 100 mm and a radius of curvature R = −137.5 mm in the RMS by more than 3 times. The initial RMS was 4.5 nm, RMS after treatment is 1.36 nm.
•Dwell time calculation for deterministic machining of X-ray mirror substrates is presented.•The main equations of new algorithm are given and described.•The inapplicability of the exact calculation method is discussed.•Experimental results of applying the described algorithm are presented. |
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| AbstractList | An algorithm for solving the problem of local shape errors of optical surfaces correcting by a small-sized ion beam, based on the matrix representation is presented. The algorithm involves searching for points that rise relative to the average height on the surface, where exposure to an ion beam of a given shape will lead to a decrease in the RMS deviation of the surface shape from the calculated one. It is shown that the new approach makes it possible to significantly expand the range of spatial frequencies, in which the height of relief can be reduced using the given ion beam size, and provides better results than the method of minimizing the functional of convolution of the ion beam and the surface map. Moreover, the new approach does not lead to appearance of shape errors (concentric structure) defined by the ion beam size and scanning step. An experiment for minimizing of local surface shape errors based on an etching map calculated using new approach was done. Matrix algorithm allowed in one procedure to reduce surface shape errors for a concave spherical optical element made of fused silica with a diameter D = 100 mm and a radius of curvature R = −137.5 mm in the RMS by more than 3 times. The initial RMS was 4.5 nm, RMS after treatment is 1.36 nm.
•Dwell time calculation for deterministic machining of X-ray mirror substrates is presented.•The main equations of new algorithm are given and described.•The inapplicability of the exact calculation method is discussed.•Experimental results of applying the described algorithm are presented. |
| Author | Mikhailenko, Mikhail Toropov, Mikhail Pleshkov, Roman Svechnikov, Mikhail Malyshev, Ilya Chernyshev, Aleksei Smertin, Ruslan Pestov, Alexey Chkhalo, Nikolay |
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| Cites_doi | 10.1007/s00170-017-1529-x 10.1134/S1063784220110262 10.3367/UFNe.2019.05.038601 10.1117/12.978903 10.1364/AO.55.000619 10.1364/OE.23.020234 10.1038/s41598-020-64923-3 10.1364/AO.54.008055 10.1117/12.948051 10.1016/j.precisioneng.2017.01.004 10.1016/0141-6359(94)00002-H 10.1016/j.ultramic.2019.04.001 10.1117/12.215648 10.1364/OE.27.015368 10.1002/opph.201290051 10.1364/AO.48.004090 |
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| SubjectTerms | Dwell time calculation Ion beam figuring Shape correction X-ray/EUV optics |
| Title | Matrix based algorithm for ion-beam figuring of optical elements |
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