Effect of apperture diffraction and fourier plane

[taimoortalpur]

Dear All,
I appreciate the efforts and support of members/admin here toward the goodness of education.

I am confusing a few concepts regarding diffraction, kindly help me out. I came up with following questions,

1. Is apperture required for diffraction or any finite wave will diffract?
To me considering finite wave will have somewhere an apperture, it should diffract.
2. If apperture is smaller than wavelenght do we get diffraction?
3. By huygens principle the wave diffract and must enlarge, how do we get Fourier transform (smaller in size usually for plane or spherical wave) in fresnel or franhofer plane.
4. Free space only add phase to propagation or also cause wave to diffract. (I think it do both)

Kindly also recommend any good book on diffraction that covers diffraction due to free space and Fourier imaging.

 

[Andy Resnick]

I am confusing a few concepts regarding diffraction, kindly help me out. I came up with following questions,

1. Is apperture required for diffraction or any finite wave will diffract?
To me considering finite wave will have somewhere an apperture, it should diffract.
2. If apperture is smaller than wavelenght do we get diffraction?
3. By huygens principle the wave diffract and must enlarge, how do we get Fourier transform (smaller in size usually for plane or spherical wave) in fresnel or franhofer plane.
4. Free space only add phase to propagation or also cause wave to diffract. (I think it do both)

Kindly also recommend any good book on diffraction that covers diffraction due to free space and Fourier imaging.

1) yes. And you are also correct, any finite wave is equivalent to an infinite wave that has passed through an aperture.

2) yes. There may not be propagating modes, tho. Look up "near-field scanning optical microscopy".

3) The Fourier transform emerges only in the Fraunhofer region: the far-field. This is because the diffracted wavefront can be approximated as a (spectrum of) expanding plane waves, and in the far-field limit, the diffraction integral reduces to the Fourier transform.

The standard textbook is Goodman "Introduction to Fourier Optics". As a primer, I also suggest Gaskill's "Linear Systems, Fourier transforms, and Optics", colloquially known as "Introduction to Goodman".

 

[taimoortalpur]

Many Thanks For the reply it cleared a lot of concepts...