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Diffraction

Definition, General

Light diffraction is an optical phenomenon related to the wave properties of light: the effects of diffraction can be explained by geometrical optics. Diffraction occurs when light waves pass through a pupil or encounter an obstacle. At the edges of these light waves are "diffractées", issued in directions that geometrical optics and refraction laws could not only predict. Diffraction phenomena of constructive and destructive interference between light waves-based, and is in fact 'wavelength dependent.

The phenomena of diffraction of visible light can be observed under certain conditions, when a beam of white light is reflected by a structure with repetitive patterns, which to diffract the light, separate trains of different wavelength.

diffraction sensor

The reflection of a source of white light by a digital digital camera CMOS sensor causes a phenomenon of diffraction. It relates to the repetitive structure formed by millions of photosites in the sensor. The diffraction pattern is not unlike that patients of «» Rainbow glare "present.

Taking into account diffraction is important for an in-depth study of the refractive properties of the eye, because the diffraction impose a limit on the resolving power of eye (Visual acuity). The effects of diffraction can be used to design specific lenses for implants used in ophthalmology, such as Diffractive optics used for cataract surgery (ex: bifocal or trifocal Diffractive implant for cataract surgery). Light diffraction is also involved in some rare Visual phenomena observed after LASIK)Rainbow glare), or after surgery of cataract)light streaks)

 

Diffraction and interference

Diffraction is characterized by a deviation of the light rays from the direction of travel under the laws of geometrical optics. Diffraction occurs whenever a light wave front encounters an obstacle that is not completely transparent: it stems from the wave aspect of light, and can be interpreted as a phenomenon of interference interesting an infinite number of waves. To understand diffraction, remind some principles of the wavelike design of light, the first plan of which the principle of Huygens.

 

principle of huyghens obstacle

The wave nature of light and Huygens principle result in an interesting property. The Huygens principle says that light moves closer and closer as a wave, each point of space re emmettant of light in all directions in the form of wavelets: However, for a parallel incident direction, generated waves surfaces add up in the direction of propagation and cancel out in the opposite direction.  When light strikes a perforated bump in a tiny way - if the dimensions of the perforations are of the same order as the wavelength, the light disperses after the obstacle as if she had been "re issued" in all directions since the perforation. The point located in the hole behaves as a "sender re", in accordance with the principle of Huygens, without adjacent points come to neutralize Wavelet issued laterally.

Light re-emitted to the same properties if it had been issued by a single point source, which then acquires a certain spatial coherence (the waves emitted from that source are "in phase" on a receiver or remote obstacle).  This property has been used in the famous experiment say 'slots' (or 'holes') of Young that marks an important step in thehistory of the study of light. The arrival of waves in phase (after diffraction by a first hole) at the level of the slots drilled screen allowed the visibility of interference produced beyond the slots.

Young's experience demonstrates the wave nature of light

Young's experience demonstrates the wave nature of light: it can be considered as the 'Queen' in the field experience. The doctor phycicien described in 1807 the experimental device to which his name is attached. A monochromatic beam of light is projected onto a first screen perforated in order to achieve a spatially "consistent" from the small hole point source (sources of lights used at the time of Young were inconsistent: nowadays, may be substituted for the first source and perforation punching a laser whose light is consistent). The emitted light meets a second perforated plate of two tiny holes separate and placed at a distance from the first plate. The resulting mixture of created beams is observed on a screen placed behind the plate: instead of see two bright peaks centered on the holes, there is a succession of alternately dark and bright bands. A theory of geometrical Optics (rays) does not explain this phenomenon (one would expect to see the projected image of the holes on the screen). A "ballistic" (photon) theory of light does not predict this result (even if is allowed from photons to ricochet around the edges of each hole, one would observe in this case two peaks of luminous intensity top and centered on the holes, and certainly not of dark area between the two!). Only the wave theory could explain the observed result: depending on the amplitude of each wave in a point in space, there occurred a strengthening or a cancellation, with all intermediate situations. We can calculate the spacing between the light and dark bands, as well as the intensity of these fringe, from the distance between the holes and the length wave (as well as the position of the screen). This phenomenon of "interference" confirms the intuition of Young, who is convinced that the light is a wave. Young's experience has brought about many 'girls' experiences, where the light by electrons, then complex molecules and atoms were replaced: each time, observed phenomena of interference, which reflect a certain wavelike behavior of matter! The quantum theory explains these phenomena, the strangest is related to the realization of the Young hole experience by sending one by one of the light photons. After a while, there is the appearance of interference... as if the photons, but drawn one by one, interfered with them even independently of the time taken to issue. The photos seem to interfere through time...

The following figure shows the directions that occur builders interference (orders of diffraction) and destructive.

Diffraction by 2 slots

Representation of diffraction orders generated by the interference produced by the slits close together in the experience of Young. The uniform "grey" appearance in certain directions corresponds to the "neutralization" of the trains of waves (destructive interference).

Geometric explanation of interference (Young's experience)

The origin of the phenomena observed is therefore due to the occurrence of interference between waves diffractées through the holes.

The left two wave trains that interfere destructively (offset of half a wavelength) was isolated: in this direction, the light intensity is zero. Right on the contrary, the waves interfere constructively: in that direction there is a peak of intensity. Designing the wavelength and the distance between the holes to determine intensity and spacing of the bright fringes

 

 Diffraction and eye

With respect to the eye, the edge of the IRIS Pupil is the main source of diffraction for light that contributes to the formation of the retinal image: physiologically, the effects of diffraction are negligible as long as the pupillary diameter is greater than 2 mm approximately. Below one millimeter, pupillary diffraction results in degradation of the retinal image; However, she has as a corollary an increase in depth of field. The placement of an implant Kamra (neo pupil of 1.6 mm) allows to increase the depth of field of the eye, without inducing major degradation of the quality of the retinal image.

Diffraction destroyed the harsh stigma of geometrical optics, an optically perfect eye has a rigorous stigma; the image of a point is a point where meet all the rays spread through the eye in wave optics, diffraction limits the quality of the optics of the eye, and it even more than the diameter of the pupil is small (myosis). In the absence of optical aberrations, diffraction causes an enlargement of the retinal focal task, which becomes wider than the image of a point source infinitesimal. So, the image of a point is never a point; but a task that matches a bright 'sprawl'. In addition to the essential diffraction, this spread can be accentuated by the presence of optical aberrations. There is a function that allows the representation of the spreading of the luminous energy corresponding to the image of a point source on the retina: (FEP) point spread function, most commonly designated by the acronym PSF (Point Spread Function).

When the eye is devoid of optical aberrations (theoretical situation), only diffraction reduced the stigma. The focal task has a task of Airy aspect: a bright central peak surrounded by darker rings. We can predict the diameter of the central peak, using a bit of geometry and a relatively simple reasoning. To simplify, we can represent no not the pupil as a drive but as a crack, in 2 dimensions.

Diffraction and calculation of the width of the Airy task

For a slot of width D, there are constructive interference in the horizontal direction: there is a peak of intensity in the direction of the incident light path centered on the center of the line of light. Interferences exist in other directions (each point of the crack is considered a secondary source which re emits light in all directions: principle of Huyghens.) We can form couples of points located at a distance of D/2 and for which the ore angle is one whereby the difference in market is half a wavelength (ʎ/2). For all these pairs of points, there is a mutual "neutralization" of luminous intensity in the direction of ore. The value of the ore angle depends on the width of the slot D and the wavelength ʎ (this angle can be approximated by the value (ʎ 2) / (D/2) be ʎ/d in radians, for a small angle: indeed sin = ά (ά) for a small angle). The width of the Central bright spot (of the central peak to the first minimum) is equal to the double of the value of ά or 2 ʎ /d For a circular pupil (and not a slit), multiply the value obtained by 1.22. When we realize that the wavelength is of the order of the micron, and D of the millimeter (thousand times larger), it is conceived that this angle is very small, and the effects of diffraction are observable only under specific conditions. The wavelength is large, and more bandwidth is important. Thus, blue light forms a focal spot that is narrower than the red light under the same conditions: that's why the blu - ray discs (read by a blue laser focused on the disc) contain more information than DVDs (red laser).

We understand intuitively that when light encounters a repetitive pattern constituted obstacles, or repeated patterns whose dimensions are relatively similar to those of the wavelength, Interferential phenomena will give rise to a particular distribution of light energy rolling (or reflected). This is being used for the realization of the diffractive multifocal implants (which markets measure some microns): for a bifocal implant, the spacing of the markets is calculated so that the light diffracted in order 1 is directed to a household corresponding to an addition useful for vision closely (additional vergence: ex: + 3D). The design and the height of the diffractive steps are to control the distribution of energy between the orders of diffraction. The design of a trifocal diffraction pattern is based on the same principles, applied in a more subtle way.

We realize that the wavelength influences the direction of diffraction. It is more important for the long wavelengths (red) for the short (blue). Thus, diffraction induces a deviation from the color opposite to that of refraction (these are the short wavelengths that are most deflected).

In everyday life, we can observe the effects of diffraction as reflections iridescent engraved face of a compact disc, which are of a similar phenomenon: angles according to which there is colors correspond to angles of maximum diffraction by the diffraction network (formed in by the estate of hollows and bumps) for each wavelength. the light that illuminates the disc must of course be polychromatic (white light).

The diffraction influence the presence of aberration of high degree on the quality of the retinal image, at least for the current pupil diameters (diffraction predominates for less than 2 mm in diameter). The calculation of the Point Spread Function (the point spread function) takes into account diffraction. In addition to allow the calculation of the maximum theoretical resolution of optical systems (including the eye), the study of the PSF and its use to simulate the retinal image of a more complex than a simple point motif are particularly important in certain clinical circumstances.

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