The **key difference between Fraunhofer and Fresnel diffraction** is that Fraunhofer diffraction equation involves the modelling of the diffraction of waves having a diffraction pattern appearing at a long distance from the diffracting object, whereas Fresnel diffraction equation involves the same modelling method for diffraction pattern created near the object.

Diffraction is a phenomenon that can be described as the scattering of light around an object when a light beam is partly blocked by that object where we can see dark and light bands at the edge of the shadow of that object.

**CONTENTS**

1. Overview and Key Difference

2. What is Fraunhofer Diffraction

3. What is Fresnel Diffraction

4. Fraunhofer vs Fresnel Diffraction in Tabular Form

5. Summary

## What is Fraunhofer Diffraction?

Fraunhofer diffraction is an equation that is useful in modelling the diffraction of waves where the diffraction pattern appears at a long distance from the diffracting object. Moreover, we can use this equation for modelling the diffraction of waves when the diffraction pattern appears at the focal plane of an imaging lens. This equation was named after the scientist Joseph Von Fraunhofer.

We can model the effects of diffraction using the Huygens-Fresnel principle, where Huygens postulated that the points on a primary wavefront could act as a source of spherical secondary wavelets, and we can use the sum of these secondary wavelets to determine the form of the wave that is proceeding at any subsequent time. This addition of wavelets includes many waves of varying phases and amplitudes. E.g. the addition of two waves with equal amplitude (which are in phase) can result in a displacement having a doubled amplitude.

If we are going to determine the diffraction that occurs when there is a distance between the aperture and the plane of observation, the optical path lengths between the aperture and the point of observation can differ much less than the wavelength of the light. Therefore, the propagation path for a wavelet can be considered as parallel from each and every point of the aperture to the point of observation. This phenomenon is named far-field, and we can use the Fraunhofer diffraction equation to model this type of diffraction.

## What is Fresnel Diffraction?

Fresnel diffraction is an equation we can apply to the propagation of waves in the near field. Therefore, it is also named near-field diffraction. It is an approximation of the Kirchhoff-Fresnel diffraction. We can use this equation to calculate the diffraction pattern that is created by the waves that are passing through an aperture or around an object if we are viewing it from relatively close proximity to the object.

This equation introduces the Fresnel number, F of the optical arrangement. If this number is higher than 1, we can consider the diffracted wave is in the near field. However, the validity of this approximation depends on the angle of the wave. The Fresnel diffraction equation was introduced by Francesco Maria Grimaldi (Italy) in the 17^{th} century. He used the principle of Huygens in order to investigate what transpires during diffraction.

## What is the Difference Between Fraunhofer and Fresnel Diffraction?

Fraunhofer diffraction is an equation that is useful in modelling the diffraction of waves where the diffraction pattern appears at a long distance from the diffracting object. Fresnel diffraction is an equation we can apply to the propagation of waves in the near field. The key difference between Fraunhofer and Fresnel diffraction is that Fraunhofer diffraction equation involves the modelling of the diffraction of waves having a diffraction pattern appearing at a long distance from the diffracting object, whereas Fresnel diffraction equation involves the same modelling method for diffraction pattern created near the object.

The following table summarizes the difference between Fraunhofer and Fresnel diffraction.

## Summary – Fraunhofer vs Fresnel Diffraction

The key difference between Fraunhofer and Fresnel diffraction is that Fraunhofer diffraction equation involves the modelling of the diffraction of waves having the diffraction pattern appearing at a long distance from the diffracting object, whereas Fresnel diffraction equation involves the same modelling method for diffraction pattern created near the object.

##### Reference:

1. “Fresnel Diffraction.” *Wikipedia*, Wikimedia Foundation, 19 May 2021.

##### Image Courtesy:

1. “Lens and wavefronts rotated” By Epzcaw – Own work (CC BY-SA 3.0) via Commons Wikimedia

2. “Circular Aperture Fresnel Diffraction high res” By Gisling – Own work (CC BY-SA 3.0) via Commons Wikimedia

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