Journal of refractive surgery (Thorofare, N.J. : 1995) · 2010
Fast evaluation of equal-spaced Zernike polynomial expansion samples.
СтатьяНазвание и аннотация: Перевод пока не подготовлен
Обработка статьи · этапы, ошибки и управление
Загрузка состояния…
Ошибки и ограничения
История · было → стало
Состояние обновляется каждые 5 секунд, пока блок открыт. Процент показывается только там, где известен объём работы. Пауза останавливает продолжение этапа; текущий запрос к источнику может завершиться.
Sarver Edwin J, Hall Max T
Аннотация
PURPOSE: To develop a method to quickly calculate equal-spaced Zernike polynomial expansion samples on a rectangular or polar grid for analysis or display.
METHODS: It is well known that a Zernike polynomial expansion can be converted into an equivalent rectangular or polar two-dimensional Taylor polynomial expansion. It is also known how to quickly calculate equal-spaced polynomial samples using difference equations. Using these two techniques, a software class was developed that provides fast evaluation of Zernike polynomial expansion samples on a rectangular or polar grid. To test the method, the time for the direct calculation of 10th order Zernike polynomial expansion was compared to the difference equation approach for a 1000x1000 sample grid.
RESULTS: The direct calculation of the 10th order Zernike polynomial expansion required over 400 times more processing time than the difference equation technique for a 1000x1000 sample grid. The largest difference in calculated values between the two techniques was negligible, indicating 11 digits of accuracy when using double precision variables.
CONCLUSIONS: The difference equation approach proves to be a fast and accurate method to calculate equal-spaced Zernike polynomial expansion samples on a rectangular or polar grid. This algorithm has application in both the analysis of optical systems and display of results.
METHODS: It is well known that a Zernike polynomial expansion can be converted into an equivalent rectangular or polar two-dimensional Taylor polynomial expansion. It is also known how to quickly calculate equal-spaced polynomial samples using difference equations. Using these two techniques, a software class was developed that provides fast evaluation of Zernike polynomial expansion samples on a rectangular or polar grid. To test the method, the time for the direct calculation of 10th order Zernike polynomial expansion was compared to the difference equation approach for a 1000x1000 sample grid.
RESULTS: The direct calculation of the 10th order Zernike polynomial expansion required over 400 times more processing time than the difference equation technique for a 1000x1000 sample grid. The largest difference in calculated values between the two techniques was negligible, indicating 11 digits of accuracy when using double precision variables.
CONCLUSIONS: The difference equation approach proves to be a fast and accurate method to calculate equal-spaced Zernike polynomial expansion samples on a rectangular or polar grid. This algorithm has application in both the analysis of optical systems and display of results.