Zernike polynomials について

Words near each other

Dictionary Lists

mini英和辞書

翻訳と辞書　辞書検索 [ 開発暫定版 ]

スポンサードリンク

Zernike polynomial ：ウィキペディア英語版

Zernike polynomials

In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike, winner of the 1953 Nobel Prize in Physics, and the inventor of phase contrast microscopy, they play an important role in beam optics.〔
〕〔
〕

==Definitions==
There are even and odd Zernike polynomials. The even ones are defined as
:

Z^_n(\rho,\varphi) = R^m_n(\rho)\,\cos(m\,\varphi) \!

and the odd ones as
:

Z^_n(\rho,\varphi) = R^m_n(\rho)\,\sin(m\,\varphi), \!

where ''m'' and ''n'' are nonnegative integers with ''n'' ≥ ''m'', ''φ'' is the azimuthal angle, ''ρ'' is the radial distance

0\le\rho\le 1

, and ''R''^''m''_''n'' are the radial polynomials defined below. Zernike polynomials have the property of being limited to a range of −1 to +1, i.e.

|Z^_n(\rho,\varphi)| \le 1

. The radial polynomials ''R''^''m''_''n'' are defined as
:

R^m_n(\rho) = \sum_^} \frac-k \right )! \left (\tfrac-k \right)!} \;\rho^

for ''n'' − ''m'' even, and are identically 0 for ''n'' − ''m'' odd.

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
■ウィキペディアで「Zernike polynomials」の詳細全文を読む

スポンサードリンク

翻訳と辞書 : 翻訳のためのインターネットリソース