What is the effect of an obstacle (as opposed to an aperture) in the Fraunhofer diffraction limit?

Fraunhofer diffraction, also known as far-field diffraction, is a type of diffraction that occurs when the source, the aperture (or obstacle), and the screen are far away from each other, so that the path differences between the diffracted waves can be considered parallel. This condition simplifies the analysis of the diffraction pattern while still considering a wide range of physical situations.

An aperture is an opening that allows light to pass through, while an obstacle is an object that blocks the light. In the context of Fraunhofer diffraction, we generally treat the aperture as the region through which light can pass, and the obstacle as the region blocking the light.

To study the effect of an obstacle in the Fraunhofer diffraction limit, we can consider a plane wave incident on a thin, opaque (non-transparent) obstacle of a specific shape. The transmitted wavefront will then be compared to the situation when the obstacle is replaced by an aperture of the same shape and size.

When the light encounters an aperture, it will be diffracted by the edges, generating a diffraction pattern on the screen. On the other hand, when the light encounters an obstacle, the light will be blocked by the obstacle, and the diffraction pattern will be formed due to the diffraction around the edges of the obstacle. The diffraction pattern caused by the obstacle will generally be the inverse of the pattern produced by the aperture, meaning that the bright regions will correspond to the dark regions in the aperture case, and the dark regions will correspond to the bright regions in the aperture case.

In the Fraunhofer diffraction limit, the effect of an obstacle can be summarized as follows: 1. The diffraction pattern produced by the obstacle will generally be the inverse of the pattern produced by the aperture. 2. The central bright spot observed in aperture diffraction will be replaced by a dark spot, known as the Poisson spot or the Arago spot, in the obstacle diffraction pattern. 3. The intensity distribution of the diffraction pattern will be influenced by the shape and size of the obstacle, and can be analyzed using the Babinet's principle, which states that the diffraction pattern of an obstacle is equal to the pattern of its complementary aperture, with the addition of a uniform background intensity filling the entire field of view. In conclusion, the effect of an obstacle in the Fraunhofer diffraction limit is to produce a diffraction pattern that is the inverse of the pattern produced by the corresponding aperture, with the central bright spot being replaced by a dark spot in the obstacle case. The intensity distribution is influenced by the shape and size of the obstacle and can be analyzed using Babinet's principle.