The paper present principles and derivation of the iterative method for solving the eikonal equation. The eikonal equation, which defines the relationship between the phase of the optical wave Φ(r) and the refractive index n(r), i.e. |grad Φ(r)|2 = n2(r), represents the fundamental equation in geometrical optics. It describes the evolution of the wavefront, which is given by the equation Φ (r) = C, of the electromagnetic wave in the limit of infinite frequency or zero wavelength. The eikonal equation is the nonlinear partial differential equation (PDE) of the first order. This classification makes the eikonal equation of rather diffcult to solve, both analytically and numerically. Several algorithms have been developed to solve the eikonal equation: Dijkstra's algorithm, fast marching method, fast sweeping method, label-correcting methods, etc. Major disadvantage of these methods is that their convergence puts rather high requirements on the density of the computing grid. It is known that finite element method (FEM) offers much more memory and time efficient approach to solve PDEs. Unfortunately, FEM cannot be applied to solve eikonal equation directly due to its first order. In order to provide the fast and memory efficient solution of the eikonal equation, it is suggested to solve a generalized version of the eikonal equation, which is of the second order and which can be solved using FEM. Then, iterative procedure for computing the corrections of the obtained numerical solution is developed. It is shown that the computed series converges to the solution of the original eikonal equation.
{"title":"Iterative method for solving the eikonal equation","authors":"P. Mokry","doi":"10.1117/12.2257326","DOIUrl":"https://doi.org/10.1117/12.2257326","url":null,"abstract":"The paper present principles and derivation of the iterative method for solving the eikonal equation. The eikonal equation, which defines the relationship between the phase of the optical wave Φ(r) and the refractive index n(r), i.e. |grad Φ(r)|2 = n2(r), represents the fundamental equation in geometrical optics. It describes the evolution of the wavefront, which is given by the equation Φ (r) = C, of the electromagnetic wave in the limit of infinite frequency or zero wavelength. The eikonal equation is the nonlinear partial differential equation (PDE) of the first order. This classification makes the eikonal equation of rather diffcult to solve, both analytically and numerically. Several algorithms have been developed to solve the eikonal equation: Dijkstra's algorithm, fast marching method, fast sweeping method, label-correcting methods, etc. Major disadvantage of these methods is that their convergence puts rather high requirements on the density of the computing grid. It is known that finite element method (FEM) offers much more memory and time efficient approach to solve PDEs. Unfortunately, FEM cannot be applied to solve eikonal equation directly due to its first order. In order to provide the fast and memory efficient solution of the eikonal equation, it is suggested to solve a generalized version of the eikonal equation, which is of the second order and which can be solved using FEM. Then, iterative procedure for computing the corrections of the obtained numerical solution is developed. It is shown that the computed series converges to the solution of the original eikonal equation.","PeriodicalId":112965,"journal":{"name":"Optical Angular Momentum","volume":" 23","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120832211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lead zirconate titanate (Pb[ZrxTi1-x]O3 ) is well-known for his excellent ferroelectric, piezoelectric and electromechanical properties. These properties are closely related to the perovskite crystal structure of PZT. A common way to achieve thin film of perovskite PZT is to anneal the layer after deposition. The high annealing temperature (600 – 700°C) limits a set of usable substrates. To grow a thin layer of perovskite PZT at reduced temperature it is necessary to add crystallization energy to the system by another way. In this article are presented some results of using ion beam sputtering system (IBS) with ion beam assistance (IBAD) to growth perovskite PZT layer at reduced temperature. This process is very complicated and the resulting layer properties are strongly influenced by deposition parameters (ions energy, chemical composition of the atmosphere in the sputtering chamber etc.). We achieved partial success when pyrochlore crystal structure of PZT was grown at reduced substrate temperature (110°C) (at this temperatures are the PZT layers usually amorphous)
{"title":"Attempt to prepare perovskite PZT at low temperatures using IBAD","authors":"David Vápenka, J. Hlubuček, P. Horodyska","doi":"10.1117/12.2257328","DOIUrl":"https://doi.org/10.1117/12.2257328","url":null,"abstract":"Lead zirconate titanate (Pb[ZrxTi1-x]O3 ) is well-known for his excellent ferroelectric, piezoelectric and electromechanical properties. These properties are closely related to the perovskite crystal structure of PZT. A common way to achieve thin film of perovskite PZT is to anneal the layer after deposition. The high annealing temperature (600 – 700°C) limits a set of usable substrates. To grow a thin layer of perovskite PZT at reduced temperature it is necessary to add crystallization energy to the system by another way. In this article are presented some results of using ion beam sputtering system (IBS) with ion beam assistance (IBAD) to growth perovskite PZT layer at reduced temperature. This process is very complicated and the resulting layer properties are strongly influenced by deposition parameters (ions energy, chemical composition of the atmosphere in the sputtering chamber etc.). We achieved partial success when pyrochlore crystal structure of PZT was grown at reduced substrate temperature (110°C) (at this temperatures are the PZT layers usually amorphous)","PeriodicalId":112965,"journal":{"name":"Optical Angular Momentum","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116453721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present recent progress in design of innovative versatile laser head for lasers based on thin-disk architecture which are being constructed at the HiLASE centre of the IOP in the Czech Republic. Concept of thin-disk laser technology allows construction of lasers providing excellent beam quality with high average output power and optical efficiency. Our newly designed thin-disk carrier and pump module comes from optical scheme consisting of a parabolic mirror and roof mirrors proposed in 90’s. However, mechanical parts and a cooling system were in-house simplified and tailor-made to medium power lasers since no suitable setup was commercially available. Proposed opto-mechanical design is based on stable yet easily adjustable mechanics. The only water nozzle-cooled component is a room-temperature-operated thindisk mounted on a special cooling finger. Cooling of pump optics was replaced by heat conductive transfer from mirrors made of special Al alloy to a massive brass baseplate. Such mirrors are easy to manufacture and very cheap. Presented laser head was manufactured and tested in construction of Er and Yb doped disk lasers. Details of the latest design will be presented.
{"title":"Innovative opto-mechanical design of a laser head for compact thin-disk","authors":"K. Macúchová, M. Smrž, Martina Řeháková, T. Mocek","doi":"10.1117/12.2254794","DOIUrl":"https://doi.org/10.1117/12.2254794","url":null,"abstract":"We present recent progress in design of innovative versatile laser head for lasers based on thin-disk architecture which are being constructed at the HiLASE centre of the IOP in the Czech Republic. Concept of thin-disk laser technology allows construction of lasers providing excellent beam quality with high average output power and optical efficiency. Our newly designed thin-disk carrier and pump module comes from optical scheme consisting of a parabolic mirror and roof mirrors proposed in 90’s. However, mechanical parts and a cooling system were in-house simplified and tailor-made to medium power lasers since no suitable setup was commercially available. Proposed opto-mechanical design is based on stable yet easily adjustable mechanics. The only water nozzle-cooled component is a room-temperature-operated thindisk mounted on a special cooling finger. Cooling of pump optics was replaced by heat conductive transfer from mirrors made of special Al alloy to a massive brass baseplate. Such mirrors are easy to manufacture and very cheap. Presented laser head was manufactured and tested in construction of Er and Yb doped disk lasers. Details of the latest design will be presented.","PeriodicalId":112965,"journal":{"name":"Optical Angular Momentum","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128468987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In order to measure an optical lens surface shape using optical interference with sufficient accuracy, it is usually necessary divide area into sub-apertures and then captures each sector separately. When the data are acquired, it is necessary to merge elements together for further analysis. This paper is primary about stitching sub-apertures on spherical and aspherical optical lens. The main content of this paper is mostly the description of a stitching procedure and troubleshooting during process. The paper for example contains a description how sub-apertures tilt was compensated and how sub-apertures rotation was solved. Another topic in this paper is dealing with final adjustment during stitching. The paper contains description for used algorithms. For example an algorithm for finding a sub-aperture centre and algorithm for overlap deviation evaluation are included in this paper. Very useful part in this paper is the description of used computational complexity optimisation methods. And finally real measured and processed data are presented.
{"title":"Sub-aperture stitching for data measured on spherical and aspherical lenses using interferometry","authors":"M. Stašík","doi":"10.1117/12.2257320","DOIUrl":"https://doi.org/10.1117/12.2257320","url":null,"abstract":"In order to measure an optical lens surface shape using optical interference with sufficient accuracy, it is usually necessary divide area into sub-apertures and then captures each sector separately. When the data are acquired, it is necessary to merge elements together for further analysis. This paper is primary about stitching sub-apertures on spherical and aspherical optical lens. The main content of this paper is mostly the description of a stitching procedure and troubleshooting during process. The paper for example contains a description how sub-apertures tilt was compensated and how sub-apertures rotation was solved. Another topic in this paper is dealing with final adjustment during stitching. The paper contains description for used algorithms. For example an algorithm for finding a sub-aperture centre and algorithm for overlap deviation evaluation are included in this paper. Very useful part in this paper is the description of used computational complexity optimisation methods. And finally real measured and processed data are presented.","PeriodicalId":112965,"journal":{"name":"Optical Angular Momentum","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123875982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper treats the issue of locking a solid state laser, pumped by high power diodes (Verdi V5), to a twenty meter long optical resonator for OSQAR LSW - light shining through the wall, dark matter search experiment. In this paper the optical design and a possible locking scheme are presented. The environmental conditions in SM18 testing hall at CERN, where OSQAR experiment is based, are discussed. The main focus is put on the vibration analysis, cavity transversal modes behaviour, possible clipping in the anticryostat of LHC – Large Hadron Collider magnet bore and locking loop parameters required for future experimental testing. The expected finesse of resonator will be presented and discussed in the sense of OSQAR LSW; its impact on possible new exclusion limits is discussed.
{"title":"Passive optical resonator for OSQAR LSW experiment","authors":"Š. Kunc, M. Schott, M. Sulc, G. Messineo","doi":"10.1117/12.2256831","DOIUrl":"https://doi.org/10.1117/12.2256831","url":null,"abstract":"This paper treats the issue of locking a solid state laser, pumped by high power diodes (Verdi V5), to a twenty meter long optical resonator for OSQAR LSW - light shining through the wall, dark matter search experiment. In this paper the optical design and a possible locking scheme are presented. The environmental conditions in SM18 testing hall at CERN, where OSQAR experiment is based, are discussed. The main focus is put on the vibration analysis, cavity transversal modes behaviour, possible clipping in the anticryostat of LHC – Large Hadron Collider magnet bore and locking loop parameters required for future experimental testing. The expected finesse of resonator will be presented and discussed in the sense of OSQAR LSW; its impact on possible new exclusion limits is discussed.","PeriodicalId":112965,"journal":{"name":"Optical Angular Momentum","volume":"341 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132073749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The work deals with the creation of correction data when generating spherical and aspherical surfaces. Generation is performed on the converted 5-axis milling machine, for which it is necessary to generate control programs. In the process of generating surfaces may be formed random errors. Hence the need to measure workpieces, and errors corrected. There is thus solved a measurement of generated surface on coordinate measuring machine Mitutoyo LEGEX 744 and draft methods of data processing by using polynomial of nth order. The measured data are processed by Matlab, specifically CFTool module. This method is further tested and subsequently the experiment evaluated.
{"title":"The design of the control algorithm for corrective manufacturing of 5 axis machining centre","authors":"J. Benes, F. Procháska, O. Matousek","doi":"10.1117/12.2257318","DOIUrl":"https://doi.org/10.1117/12.2257318","url":null,"abstract":"The work deals with the creation of correction data when generating spherical and aspherical surfaces. Generation is performed on the converted 5-axis milling machine, for which it is necessary to generate control programs. In the process of generating surfaces may be formed random errors. Hence the need to measure workpieces, and errors corrected. There is thus solved a measurement of generated surface on coordinate measuring machine Mitutoyo LEGEX 744 and draft methods of data processing by using polynomial of nth order. The measured data are processed by Matlab, specifically CFTool module. This method is further tested and subsequently the experiment evaluated.","PeriodicalId":112965,"journal":{"name":"Optical Angular Momentum","volume":"116 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132519941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Jašíková, P. Schovanec, M. Kotek, M. Muller, V. Kopecký
This article presents the visualization of the cavitation bubble generated with laser-induced breakdown. The cavitation bubble is generated with 532nm Nd: YAG laser beam, 10ns short with two different optical setups. Here, we use direct optical way focusing the laser beam, and reverse way base on the focusing mirror. We are using different laser light power and visualize the laser probe in correlation of bubble characteristics. The visualization is set on long-distance microscopy and shadowgraph lightening method. The main goal of the research is to set the optical setup for the laserinduced breakdown and to create the calibration relation curve for the bubble size dependence on the input energy of the laser beam. This calibration curve is related to the lifespan of each bubble, or the group of bubbles.
{"title":"Experimental setup for laser-induced breakdown in aqueous media","authors":"D. Jašíková, P. Schovanec, M. Kotek, M. Muller, V. Kopecký","doi":"10.1117/12.2260998","DOIUrl":"https://doi.org/10.1117/12.2260998","url":null,"abstract":"This article presents the visualization of the cavitation bubble generated with laser-induced breakdown. The cavitation bubble is generated with 532nm Nd: YAG laser beam, 10ns short with two different optical setups. Here, we use direct optical way focusing the laser beam, and reverse way base on the focusing mirror. We are using different laser light power and visualize the laser probe in correlation of bubble characteristics. The visualization is set on long-distance microscopy and shadowgraph lightening method. The main goal of the research is to set the optical setup for the laserinduced breakdown and to create the calibration relation curve for the bubble size dependence on the input energy of the laser beam. This calibration curve is related to the lifespan of each bubble, or the group of bubbles.","PeriodicalId":112965,"journal":{"name":"Optical Angular Momentum","volume":"332 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133665411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The freeform and aspheric measurement in the industry is rather cumbersome. This situation led us to the decision to start the development of the metrology tool offering the measurement of grinded (diffusive) and polished (specularly reflecting) surfaces with arbitrary geometries and with the necessary fiducials. We proposed digital multiwavelength multidirectional holographic contouring with phase shifting. Recently we redesigned our system heavily e.g we use 16 independent illumination directions, we use new PSI algorithm, etc. The factor strongly influencing the method precision is the sensitivity vector field knowledge over the whole measured area. We proposed the method of the sensitivity vector map retrieval based on controlled movement and recording of the measured part with the data evaluation. The proposed method has been tested recently. The method fundamentals, experimental setup and the results are presented in this paper.
{"title":"Sensitivity vector map retrieval in digital holography used for shape measurement","authors":"V. Ledl, P. Psota, P. Vojtíšek","doi":"10.1117/12.2256835","DOIUrl":"https://doi.org/10.1117/12.2256835","url":null,"abstract":"The freeform and aspheric measurement in the industry is rather cumbersome. This situation led us to the decision to start the development of the metrology tool offering the measurement of grinded (diffusive) and polished (specularly reflecting) surfaces with arbitrary geometries and with the necessary fiducials. We proposed digital multiwavelength multidirectional holographic contouring with phase shifting. Recently we redesigned our system heavily e.g we use 16 independent illumination directions, we use new PSI algorithm, etc. The factor strongly influencing the method precision is the sensitivity vector field knowledge over the whole measured area. We proposed the method of the sensitivity vector map retrieval based on controlled movement and recording of the measured part with the data evaluation. The proposed method has been tested recently. The method fundamentals, experimental setup and the results are presented in this paper.","PeriodicalId":112965,"journal":{"name":"Optical Angular Momentum","volume":"141 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132431867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Holá, J. Lazar, M. Čížek, V. Hucl, Š. Řeřucha, O. Cíp
We report on a design of an interferometric position measuring system for control of a sample stage in an e-beam writer with reproducibility of the position on nanometer level and resolution below nanometer. We introduced differential configuration of the interferometer where the position is measured with respect to a central reference point to eliminate deformations caused by thermal and pressure effects on the vacuum chamber. The reference is here the electron gun of the writer. The interferometer is designed to operate at infrared, telecommunication wavelength due to the risk of interference of stray light with sensitive photodetectors in the chamber. The laser source is here a narrow-linewidth DFB laser diode with electronics of our own design offering precision and stability of temperature and current, low-noise, protection from rf interference, and high-frequency modulation. Detection of the interferometric signal relies on a novel derivative technique utilizing hf frequency modulation and phase-sensitive detection.
{"title":"Coordinate interferometric system for measuring the position of a sample with infrared telecom laser diode","authors":"M. Holá, J. Lazar, M. Čížek, V. Hucl, Š. Řeřucha, O. Cíp","doi":"10.1117/12.2257319","DOIUrl":"https://doi.org/10.1117/12.2257319","url":null,"abstract":"We report on a design of an interferometric position measuring system for control of a sample stage in an e-beam writer with reproducibility of the position on nanometer level and resolution below nanometer. We introduced differential configuration of the interferometer where the position is measured with respect to a central reference point to eliminate deformations caused by thermal and pressure effects on the vacuum chamber. The reference is here the electron gun of the writer. The interferometer is designed to operate at infrared, telecommunication wavelength due to the risk of interference of stray light with sensitive photodetectors in the chamber. The laser source is here a narrow-linewidth DFB laser diode with electronics of our own design offering precision and stability of temperature and current, low-noise, protection from rf interference, and high-frequency modulation. Detection of the interferometric signal relies on a novel derivative technique utilizing hf frequency modulation and phase-sensitive detection.","PeriodicalId":112965,"journal":{"name":"Optical Angular Momentum","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114322637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A number of soft x-ray / water window laboratory sources is being developed by many groups including the group at CTU. This paper presents simulations and critical parameter estimates for lensless imaging using the laboratory sources, especially the capillary discharge source being developed by our group.1 Water window lensless imaging is demonstrated to be generally feasible with high repetition laboratory sources.
包括 CTU 小组在内的许多小组正在开发一系列软 X 射线/水窗实验室源。本文介绍了使用实验室源，特别是我们小组正在开发的毛细管放电源进行无透镜成像的模拟和关键参数估计1。
{"title":"Simulations of lensless imaging in water window","authors":"L. Švéda, L. Pína","doi":"10.1117/12.2257052","DOIUrl":"https://doi.org/10.1117/12.2257052","url":null,"abstract":"A number of soft x-ray / water window laboratory sources is being developed by many groups including the group at CTU. This paper presents simulations and critical parameter estimates for lensless imaging using the laboratory sources, especially the capillary discharge source being developed by our group.1 Water window lensless imaging is demonstrated to be generally feasible with high repetition laboratory sources.","PeriodicalId":112965,"journal":{"name":"Optical Angular Momentum","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129846747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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