# 角分辨率

（重定向自瑞利準則

${\displaystyle \theta _{\mathrm {min} }={\frac {\lambda }{a}}}$

${\displaystyle \theta _{\mathrm {min} }={\frac {1.220\lambda }{a}}}$

## 解像能力與角分辨度

${\displaystyle s\approx r\theta _{\mathrm {min} }}$

## 單縫繞射

${\displaystyle I(\theta )=I_{0}\left[{\frac {\sin \left({\frac {\pi a\sin \theta }{\lambda }}\right)}{\frac {\pi a\sin \theta }{\lambda }}}\right]^{2}}$

${\displaystyle I(\theta )=0}$ ，可得第一個零點 θmin 發生在：

${\displaystyle {\frac {\pi a\sin \theta _{\mathrm {min} }}{\lambda }}=\pi }$

${\displaystyle \theta _{\mathrm {min} }={\frac {\lambda }{a}}}$

${\displaystyle s={\frac {\lambda r}{a}}}$

## 圓孔繞射

${\displaystyle I(\theta )=I_{0}\left[{\frac {2\operatorname {J_{1}} \left({\frac {\pi a\sin \theta }{\lambda }}\right)}{\frac {\pi a\sin \theta }{\lambda }}}\right]^{2}}$

${\displaystyle I(\theta )=0}$ ，可得第一個零點 θmin 發生在：

${\displaystyle {\frac {\pi a\sin \theta _{\mathrm {min} }}{\lambda }}=3.8317}$

${\displaystyle \theta _{\mathrm {min} }={\frac {1.220\lambda }{a}}}$

${\displaystyle s={\frac {1.220\lambda r}{a}}}$

## 視力

${\displaystyle \theta _{\mathrm {min} }={\frac {(1.220)(555\times 10^{-9})}{5\times 10^{-3}}}=0.000135\;\mathrm {rad} }$

${\displaystyle \theta \approx {\frac {8.8\times 10^{-3}}{6}}=0.00147\;\mathrm {rad} }$

## 參考

1. ^ Lord Rayleigh, F.R.S. Investigations in optics, with special reference to the spectroscope (PDF). Philosophical Magazine. 5. 1879, 8 (49): 261–274. doi:10.1080/14786447908639684.
2. ^ Born, M.; Wolf, E. Principles of Optics. Cambridge University Press. 1999: 461. ISBN 0-521-64222-1.
3. ^ Ackerman, Eugene, Biophysical Science, Prentice-Hall, 1962. Considerable material on vision from a medical point of view.