Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版：英文原文完整保留，中文紧随对应单元；术语采用 v20260916 确认表，自动语义审校结果可追溯。

Circular Aperture Diffraction

圆孔衍射

When light from a point source passes through a small circular aperture, it does not produce a bright dot as an image, but rather a diffuse circular disc known as Airy's disc surrounded by much fainter concentric circular rings. This example of diffraction is of great importance because the eye and many optical instruments have circular apertures. If this smearing of the image of the point source is larger that that produced by the aberrations of the system, the imaging process is said to be diffraction-limited, and that is the best that can be done with that size aperture. This limitation on the resolution of images is quantified in terms of the Rayleigh criterion so that the limiting resolution of a system can be calculated.

当来自点光源的光通过一个小的圆形孔径时，它不会产生一个明亮的点作为图像，而是产生一个模糊的圆形盘，称为阿贝-图斯盘（Airy's disc），周围有许多更暗的同心圆环。这个衍射的例子非常重要，因为眼睛和许多光学仪器都有圆形孔径。如果这种点光源图像的模糊程度大于系统本身像差所产生的模糊程度，那么成像过程被称为衍射受限（diffraction-limited），这是在该孔径大小下所能达到的最佳效果。这种对图像分辨率的限制可以通过瑞利判据（Rayleigh criterion）来量化，从而可以计算系统的极限分辨率。

The aperture diffraction pattern above was photographed with Fuji Sensia 100ASA slide film and then digitized. With the time exposure necessary to show the side lobes, the central peak was washed out nearly white. The only retouching of the digital image was to paint in the washed out part of the central maximum (Airy's disc). The pinhole was made by placing aluminum foil on a glass plate, sticking a straight pin into the aluminum foil, and then rotating the foil. Several pinholes were made, and this one was the closest to being round.

上面的孔径衍射图样是用富士Sensia 100ASA胶片拍摄的，然后进行数字化处理。为了显示旁瓣，需要较长的曝光时间，导致中央峰几乎被白化。数字图像的唯一后期处理是将被白化的中央峰（艾里斑）部分重新着色。孔径是通过在玻璃板上放铝箔，将直针插入铝箔，然后旋转铝箔来制作的。制作了几个孔径，这个孔径最接近圆形。
Mathematical description of aperture diffraction
孔径衍射的数学描述
Example of corona around fog droplets
电晕围绕雾滴的例子
Corona around Moon
月球周围的电晕
 Index

Diffraction concepts

Fraunhofer diffraction
索引衍射概念 夫琅禾费衍射
 
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Circular Aperture Diffraction

圆孔衍射

For monochromatic light of wavelength λ = nm

对于波长为λ = nm的单色光
中文译文中的待填/计算数值依次对应：1：w。实际数值以上方原输入框为准。

incident upon a circular aperture of diameter d = micrometers,

照射到直径为 d = 微米的圆形孔径上，
中文译文中的待填/计算数值依次对应：1：d。实际数值以上方原输入框为准。

d = x 10^ m,

and projected on a screen at distance D = m,

并投射到距离为 D = m 的屏幕上，
中文译文中的待填/计算数值依次对应：1：ds。实际数值以上方原输入框为准。

the displacement from the centerline on the screen is given by the relationship

屏幕上相对于中心线的位移由下述关系给出

Displacement y = Screen distance D*m value* wavelength / aperture diameter

位移 y = 屏距离 D 乘以波长除以孔径直径
The active formula above can be used to calculate displacement y, wavelength, or aperture diameter by clicking on those quantities. You should enter the known data first, then click on the desired quantity. The entered data will not be forced to be consistent until you click on a quantity to calculate. Calculation of the displacement y will calculate the positions of all maxima and minima in the table below. Any quantity in that table can be changed for the purpose of calculating the other parameters. The active formula above is written as the small angle approximation, but the calculation makes use of the full trigonometric relationship.
上述交互式公式可用于通过点击相应量来计算位移 y、波长或孔径直径。您应首先输入已知数据，然后点击所需计算的量。在点击计算任何量之前，输入的数据不会被强制保持一致。计算位移 y 会计算表下方所有极大值和极小值的位置。表中的任何量都可以用于计算其他参数。上述交互式公式以小角度近似形式写出，但计算过程却利用了完整的三角函数关系。

This yields the following pattern of maxima and minima in the diffracted intensity.

这导致了衍射强度的以下最大值和最小值模式。
Order
顺序
Minima
极小值
Maxima
极值
m value
m 值
Displacement y
(cm)
位移 y (cm)
θ
(degrees)
θ（度）
m value
m 值
Displacement y
(cm)
位移 y (cm)
θ
(degrees)
θ（度）
1
1.220
1.635
2
2.233
2.679
3
3.238
3.69
When light from a point source passes through a small circular aperture, it does not produce a bright dot as an image, but rather a diffuse circular disc known as Airy's disc surrounded by much fainter concentric circular rings. This example of diffraction is of great importance because the eye and many optical instruments have circular apertures. If this smearing of the image of the point source is larger that that produced by the aberrations of the system, the imaging process is said to be diffraction-limited, and that is the best that can be done with that size aperture. This limitation on the resolution of images is quantified in terms of the Rayleigh criterion so that the limiting resolution of a system can be calculated.
当来自点光源的光通过一个小的圆形孔径时，它不会产生一个明亮的点作为图像，而是产生一个模糊的圆形盘，称为阿贝-图斯盘（Airy's disc），周围有许多更暗的同心圆环。这个衍射的例子非常重要，因为眼睛和许多光学仪器都有圆形孔径。如果这种点光源图像的模糊程度大于系统本身像差所产生的模糊程度，那么成像过程被称为衍射受限（diffraction-limited），这是在该孔径大小下所能达到的最佳效果。这种对图像分辨率的限制可以通过瑞利判据（Rayleigh criterion）来量化，从而可以计算系统的极限分辨率。
中文译文中的待填/计算数值依次对应：1：db 2：dp 3：mn1 4：qn1 5：mx1 6：qx1 7：mn2 8：qn2 9：mx2 10：qx2 11：mn3 12：qn3 13：mx3 14：qx3。实际数值以上方原输入框为准。
 Index

Diffraction concepts

Fraunhofer diffraction

References
Jenkins and White
Sec 15.8

Hecht
Sec 10.2
索引衍射概念 夫琅禾费衍射 参考文献 Jenkins and White 第15章第8节 Hecht 第10章第2节
 
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