A HIGH-ACCURACY METHOD OF COMPUTATION OF X-RAY WAVES PROPAGATION THROUGH AN OPTICAL SYSTEM CONSISTING OF MANY LENSES
The propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. Two differential equations are contemplated for solving the problem for electromagnetic wave propagation: first – an equation for the electric field, second – an equation derived for a...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Gdańsk University of Technology
2016-04-01
|
| Series: | TASK Quarterly |
| Subjects: | |
| Online Access: | https://journal.mostwiedzy.pl/TASKQuarterly/article/view/1840 |
| _version_ | 1811306840856723456 |
|---|---|
| author | SERGEY KSHEVETSKII PAWEL WOJDA |
| author_facet | SERGEY KSHEVETSKII PAWEL WOJDA |
| author_sort | SERGEY KSHEVETSKII |
| collection | DOAJ |
| description |
The propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. Two differential equations are contemplated for solving the problem for electromagnetic wave propagation: first – an equation for the electric field, second – an equation derived for a complex phase of an electric field. Both equations are solved by the use of a finite-difference method. The simulation error is estimated mathematically and investigated. The presented results for equations show that in order to establish a high accuracy computation a much smaller number of points is needed to solve the problem of X-ray waves propagation through a multi-lens system when the method for the second equation is used. The reason for such a result is that the electric field of a wave after passing through many lenses is a quickly oscillating function of coordinates, while the electric field phase is a quickly increasing, but not oscillating function. Therefore, a very detailed difference grid, which is necessary to approximate the considered electric field can be replaced by not such a detailed grid, when computations are made for the complex wave of the electric field. The simulation error of both suggested methods is estimated. It is shown that the derived equation for a phase function allows efficient simulation of propagation of X-rays for the multi-lens optical system.
|
| first_indexed | 2024-04-13T08:52:46Z |
| format | Article |
| id | doaj.art-f3d2f410898947428c500856f92624ad |
| institution | Directory Open Access Journal |
| issn | 1428-6394 |
| language | English |
| last_indexed | 2024-04-13T08:52:46Z |
| publishDate | 2016-04-01 |
| publisher | Gdańsk University of Technology |
| record_format | Article |
| series | TASK Quarterly |
| spelling | doaj.art-f3d2f410898947428c500856f92624ad2022-12-22T02:53:26ZengGdańsk University of TechnologyTASK Quarterly1428-63942016-04-0120210.17466/TQ2016/20.2/FA HIGH-ACCURACY METHOD OF COMPUTATION OF X-RAY WAVES PROPAGATION THROUGH AN OPTICAL SYSTEM CONSISTING OF MANY LENSESSERGEY KSHEVETSKII0PAWEL WOJDA1Baltic I. Kant Federal UniversityGdansk University of Technology The propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. Two differential equations are contemplated for solving the problem for electromagnetic wave propagation: first – an equation for the electric field, second – an equation derived for a complex phase of an electric field. Both equations are solved by the use of a finite-difference method. The simulation error is estimated mathematically and investigated. The presented results for equations show that in order to establish a high accuracy computation a much smaller number of points is needed to solve the problem of X-ray waves propagation through a multi-lens system when the method for the second equation is used. The reason for such a result is that the electric field of a wave after passing through many lenses is a quickly oscillating function of coordinates, while the electric field phase is a quickly increasing, but not oscillating function. Therefore, a very detailed difference grid, which is necessary to approximate the considered electric field can be replaced by not such a detailed grid, when computations are made for the complex wave of the electric field. The simulation error of both suggested methods is estimated. It is shown that the derived equation for a phase function allows efficient simulation of propagation of X-rays for the multi-lens optical system. https://journal.mostwiedzy.pl/TASKQuarterly/article/view/1840X-ray waveX-ray opticlensnon-uniform mediumfocusingnumerical method |
| spellingShingle | SERGEY KSHEVETSKII PAWEL WOJDA A HIGH-ACCURACY METHOD OF COMPUTATION OF X-RAY WAVES PROPAGATION THROUGH AN OPTICAL SYSTEM CONSISTING OF MANY LENSES TASK Quarterly X-ray wave X-ray optic lens non-uniform medium focusing numerical method |
| title | A HIGH-ACCURACY METHOD OF COMPUTATION OF X-RAY WAVES PROPAGATION THROUGH AN OPTICAL SYSTEM CONSISTING OF MANY LENSES |
| title_full | A HIGH-ACCURACY METHOD OF COMPUTATION OF X-RAY WAVES PROPAGATION THROUGH AN OPTICAL SYSTEM CONSISTING OF MANY LENSES |
| title_fullStr | A HIGH-ACCURACY METHOD OF COMPUTATION OF X-RAY WAVES PROPAGATION THROUGH AN OPTICAL SYSTEM CONSISTING OF MANY LENSES |
| title_full_unstemmed | A HIGH-ACCURACY METHOD OF COMPUTATION OF X-RAY WAVES PROPAGATION THROUGH AN OPTICAL SYSTEM CONSISTING OF MANY LENSES |
| title_short | A HIGH-ACCURACY METHOD OF COMPUTATION OF X-RAY WAVES PROPAGATION THROUGH AN OPTICAL SYSTEM CONSISTING OF MANY LENSES |
| title_sort | high accuracy method of computation of x ray waves propagation through an optical system consisting of many lenses |
| topic | X-ray wave X-ray optic lens non-uniform medium focusing numerical method |
| url | https://journal.mostwiedzy.pl/TASKQuarterly/article/view/1840 |
| work_keys_str_mv | AT sergeykshevetskii ahighaccuracymethodofcomputationofxraywavespropagationthroughanopticalsystemconsistingofmanylenses AT pawelwojda ahighaccuracymethodofcomputationofxraywavespropagationthroughanopticalsystemconsistingofmanylenses AT sergeykshevetskii highaccuracymethodofcomputationofxraywavespropagationthroughanopticalsystemconsistingofmanylenses AT pawelwojda highaccuracymethodofcomputationofxraywavespropagationthroughanopticalsystemconsistingofmanylenses |