It can be complex-valued to indicate a phase shift. Note that the aperture function acts on the complex field, not on the intensity (amplitude squared) of the waves. The expression is the Fourier transform of the aperture function, with the Fourier kernel Where k = 2π / λ is the circular wavenumber of the incident waves. If this field is incident on an aperture in the x y-plane with a complex transmittance T( x, y), then the diffracted far-zone field as a function of the far field spherical coordinate system angles (θ,φ, r) can be calculated via the Huygens-Fresnel principle, using the parallel rays approximation, In what follows, all fields are assumed to have a time-dependence exp( − iω t). In this description, we assume that an incident electric or other field is described by Since this type of diffraction is mathematically simple, this experimental setup can be used to find the wavelength of the incident monochromatic light with high accuracy. The same setup with multiple slits can also be used, creating a different diffraction pattern. After the slit there is another lens that will focus the parallel light onto a screen for observation. Using a point-like source for light and a collimating lens it is possible to make parallel light, which will then be passed through the slit. This is not the case in near-field diffraction, where the diffraction pattern changes both in size and shape.įraunhofer diffraction through a slit can be achieved with two lenses and a screen. In far-field diffraction, if the observation screen is moved relative to the aperture, the diffraction pattern produced changes uniformly in size. Fresnel diffraction, or near-field diffraction occurs when this is not the case and the curvature of the incident wavefronts is taken into account. If a light source and an observation screen are effectively far enough from a diffraction aperture (for example a slit), then the wavefronts arriving at the aperture and the screen can be considered to be collimated, or plane. The far-field pattern of a diffracting screen illuminated by a point source may be observed in the image plane of the source. The far-field diffraction pattern of a source may also be observed (except for scale) in the focal plane of a well-corrected lens. When observed, the image of the aperture from Fresnel diffraction will change in terms of size and shape, namely, the edges become more or less "jagged", whereas the aperture image observed when Fraunhofer diffraction is in effect only alters in terms of size due to the more collimated or planar nature of the waves. When the distance or wavelength is increased, Fraunhofer diffraction occurs due to the waves going towards becoming planar, over the extent of diffracting apertures or objects. When a diffracted wave is observed parallel to the other at an initial near-field distance, Fresnel diffraction is seen to occur due to the distance between the aperture and the observed canvas ( σ) being more than 1 when calculated with the Fresnel number equation, which can be used to observe the extent of diffraction in the parallel waves through the calculation of the aperture or slit size ( a), wavelength (λ) and distance from the aperture, ( L). When waves pass through, the wave is split into two diffracted waves travelling at parallel angles to each other along with the continuing incoming wave, and are often used in methods of observation by placing a screen in its path in order to view the image-pattern observed. Forms Explanation Fresnel diffraction occurs when:įraunhofer diffraction goes from the idea of a wave being split into several outgoing waves when passed through an aperture, slit or hole, and is usually described through the use of observational experiments using lenses to purposefully diffract light.
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