# Light diffraction

## Introduction

The optical wave encounters the obstacle or less to deviate from the law of linear propagation from the geometric optical. Geometric optical shows that light is propagated in a uniform medium, and the light is propagated in the segments of the two media in the field of reflection and refractive law. However, the light is an electromagnetic wave, and when a beam light passes through a hole, its strength can fluctuate in the geometric shadow zone defined according to the law of linearly, and certain dark spots or darkness occurs in the geometric lighting area or dark. Ripple. In summary, the diffraction effect causes the light intensity distribution of the space after the obstacle, and the light intensity distribution of the geometric optical given, and distinguishes the light intensity distribution when the optical wave is freely propagated, and the diffraction light has a reset. Diffraction makes everything in the geometric shadow. Italian physicist and astronomer FM Grimali first describes the diffraction phenomenon of light in the 17th century, after 150 years later, French physicist A.-j. Fres ear earlier in the 19th century, this phenomenon .

## Related Introduction

The optical wave encounters the obstacle or less to deviate from the law of the geometric optical propagation.

includes: single seamage diffraction, circular hole diffraction, circular plate diffraction and Poisson Breakfrane

During the propagation process, when obstacles or small holes (narrow seam) It has the phenomenon that is left from the shadow of the tract to the obstacle. This phenomenon is called Light Diffraction .

The bright and dark stripes or aura generated during diffraction, called Diffraction pattern .

In order to observe the diffraction phenomena, a diffraction system is always constructed from a screen (referred to as a receiving screen) of the light source, diffraction screen, and reception diffraction pattern. For the convenience of research, the diffraction phenomenon is divided into two categories according to the size of the mutual distances in the diffraction system, and a class is called Fresnel diffraction, and another category is called Fu He Fee (J.Fraunhofer, 1787) - 1826) Diffraction. The so-called Fresnel diffraction is that the distance between the light source to the diffraction screen or the distance to the diffraction screen is not unlimited, or both is not a diffraction phenomenon that occurs infinitely. It can be seen that in Fresnel diffraction, incident light or diffracted light is not parallel light, or both are not parallel light, as shown in Figures 13-15 (a). The so-called Fuhe fees is diffraction when the distance from the light source to the diffraction screen and the distance to the diffraction screen are infinite, and the diffraction phenomenon occurred. It can be seen that the light incident light and the light of any point of any point diffracted to the receiving screen in the Fuhe fend diffraction is parallel light, as shown in Figs. 13-15 (b). The conditions of Fu He Fee Diffraction can be achieved by means of lens in the laboratory. Place the light source on the focus of the converging lens L1, the light transmitted from L1, that is, the incident light of the diffraction hole is parallel light; the receiving screen is placed on the focal plane of the converging lens L2, then reaching any point on the receiving screen. The diffracted light is also parallel light.

## Conditions

Conditions for generating diffraction is: Since the wavelength of light is very short, only a few microns, usually the object is much larger than it, so when the light is transmitted to one The pinhole, a slit, and a filament, it can clearly see the diffraction of light. The effect is good when irradiated with monochromatic light. If it is used in color light, the diffraction pattern that is seen is colored.

## Light characteristics

Observation and characteristics of diffraction phenomena of light. Diffraction is a propagation behavior common to all waves. Diffraction, water wave diffraction, diffraction of water waves in daily life, and radio waves of radio waves occur, anywhere, anywhere, is easy to be aware. However, the diffraction phenomenon of visible light is not easy for people, because the wavelength of visible light is very short, and the normal light source is a non-coherent surface light source. When using a bunch of strong lighting small holes, round screens, slits, filaments, knives, straight skewers, there will be a different diffraction pattern on a sufficiently far screen. In the laboratory, a strong point of light from the carbon arc lamp in the past, and the helium laser is widely used as a light source to show the diffraction phenomenon, and a good effect is received (Fig. 1). Diffraction phenomena has two distinct features:

1 beam is limited to one part of the diffraction screen, and the diffraction intensity on the distal screen is expanded in the direction.

2 If the light pores are so small, the beam is limited, the more diffuse is more diffuse. In theory, it indicates that the optical hole transverse line degree ρ and diffraction angle

δ θ is inverse-relating relationship

ρ δ θ λ .

When the light pore line is much larger than the optical wavelength λ , the diffraction effect is not obvious, approximately the linear propagation. When the light pores are gradually smaller, the diffraction effect is gradually clear, and a brightly distributed diffraction pattern is displayed in the distance. When the light pores are small to the same light wavelength, the diffraction effect is extremely significant, the diffraction range is filled the entire field of view, and the transition is a scattering situation.

Huye Sfagne, is approximate theory of derived diffraction, and Huygens Fresnel principles can be expressed as: percutaneous: wavefront σ Deman D σ , can be seen as a new vibration source (sub-wave), which issued a secondary wave; the disturbance of any P point in the wave field is the secondary of all waves to the point. Disturbance of disturbance (Figure 2).

If the wave field is described with a composite amplitude (including amplitude and bit), if the secondary disturbance of the secondary wave reaches the field point is D 堚 (P), the total disturbance of the field point is

The amplitude and bit of the secondary disturbance in the formula are determined by the following factors:

- the differential area of ​​the secondary wave source, the resonance of the secondary wave source itself,

- ─ Secondary wave source emitting spherical wave,

- tilt factor, indicating that the emission of the secondary wavefront has a certain directionality.

The specific form of light

60 years later, GR Kilkhof starts from the Helmhouse equation of the fixed-state wave, using the Green formula in the vector field, KR 1 Approximately the meaning of the integral form of unsource-free space boundary value is exported to the meaning of the integral of the formula, and thereby refers to any closed surface of the actual point light source and the field point. σ can be used as a integral (wavefront), which is not necessarily equal. The above formula is called Fresnel - Kirhof diffraction integral formula, which is the same as the diffraction integration constructed by simple physical ideas, which is the same, only the former explicitly gives the tilt factor and The specific form of the proportional coefficient.

Obviously, Huygens Fresnel principle is not to solve the free spread of light, but to solve the diffraction field after the diffraction screen. To this end, the wavefront is included including the light hole surface σ o, the optical screen σ 1 and the infinity of the hemispherical surface σ 2 The closed face of three parts composed. Kirhof is further proposed (Fig. 4): σ 0 ( q ) Take the free wave field, σ The light field on the 1 surface takes 0, the contribution of the light field on the infinity distal, which is called 0, which is called the assumption of Kirkhof boundary conditions. The integral area in the Fresnel-Kirhof diffraction formula is limited to the light hole surface. The hypothesis of Kirhof border conditions seems to be more natural, but it is not strict. Light is electromagnetic wave, strict diffraction theory should be vector wave theory of high frequency electromagnetic field. The optical screen is the actual composition, and the interaction of the light and the screen material (conductor or dielectric) should be considered. As a result, the original light field on the well surface is disturbed, and the light field on the light screen is not turned off. 0. However, theory shows that the strict boundary conditions and the significant difference in field distribution given by Kirhof boundary conditions are limited to the range of regional wavelengths of region or photorecous edges. For optical waves, since its wavelength is often much smaller than the linearness of the light pores, the error generated by the Kilkhof boundary condition is not large. However, the diffraction of radio waves requires a stricter electromagnetic theory. Thus, the integral surface in the Fresnel-Kilhof diffraction integral formula is only more than the light field surface σ 0 of the light field is not equal to zero. The tilt factor, the diffraction integral simplification of the light pores and the reception range are simplified in the formula R 0 is the distance from the center of the diffraction screen to the field of the diffraction field, and the above formula is a practical formula for calculating the diffraction field.

Diffraction system and diffraction screen function

It can be seen from the diffraction integration (shaft) formula, the integral nucleus of various diffraction screens, the diffraction field is different The distribution is different from two aspects of the shape and size of the pupil function 堚 0 ( q ) or light field is not equal to zero. The variety of obstacles (screens) that may result in optical wave diffraction are varied, and anything that changes the reconstancy distribution on the wavefront, collectively referred to as diffraction screen. The diffraction screen can be a reflective or transmitter such as a class of intermediate openings such as circular holes, a torque hole, a single selection, a small ball, filament, ink point, particle, etc., and reflective shine. The grating, the transmissive black and white grating, the Fresnel tape, and the sinusoid grating may be a film of the scene, an image, a digital character, and the like, which may also be a lens prism. Class locked diffraction screen.

is bound by a diffraction screen, and the entire diffractive system is divided into two parts (Fig. 5). The frontcourt is the lighting space, full of illumination optical waves; the backed field is diffraction space, full of diffraction light waves. The wave type of illumination light wave is generally relatively simple, commonly used spherical waves or plane waves, these two typical waves, etc., the equal surfaces of the two typical waves are coincident, belonging to a uniform wave, and there is no bright dark pattern that appears due to light strong undulation in its wave field. . The diffraction wave is more complicated. It is not a simple a beam wave or a planar wave, and the corresponding surface and the like are generally not coincident, which is a non-uniform wave, and there is often a diffractive pattern formed in the wavefield. Three field distributions are paid in the diffraction system analysis. First, the incident field 堚 1 ( x , y ) on the left side of the diffraction screen is an incident light wavelength array function; the second is the transmitted field on the right side of the diffraction screen 2 ( x , Y ), of course, can also be a reflective field, which is a diffraction field wave array function; the third is the light forward propagating to reach the light on the receiving screen. Field function 堚 ( x ', y '). It is a diffraction screen for a diffraction screen, and a basic proposed method of derived problems is the basic proposal of the diffraction problem. It is also the basic propagation of light propagation problems. The theoretical basis is Huyez Philippine. The principle of NEUR. It can be seen that in essentially, the optical wave diffraction is a wave array transformation.

## Diffraction type

### slit diffraction

Monochrome light emitted by laser is irradiated on the slit, and when the slit is gradually reduced, What is the phenomenon that appears on the light screen?

When the slit is wide, the width of the slit is much greater than the wavelength of the light, and the diffraction phenomenon is extremely unspeakable, and the light is propagated in line, producing a bright line with a heel width on the screen; The width of the seam is narrow, and when the light wave is compared to the light wave, the light is clearly deviated from the straight line propagation direction, and the light is quite wide, and the diffraction stripes between the dark and dark are shown. The smaller seam is smaller. The larger the diffraction range, the wider the diffraction stripe. But the brightness is getting darker.

test: You can use a cursor caliper to adjust the minimum distance that can be recognized by the naked eye, and then look at the light source by this seam.

### Small hole diffraction

When the aperture radius is large, the light propagates in the straight line, obtaining a bright light circular spot in the screen to calculate the same size; reduce the hole The radius, the image of the inverted light source calculated by linearly, that is, a small hole imaging; continues to reduce the radius of the hole, and the round-shaped diffraction of a circular diffraction of the light is displayed on the screen.

## Diffraction Application

Light Diffraction determines the resolution of the optical instrument. A large amount of suspended particles in the gas or liquid also plays an important role in the scattering and diffraction of light. In modern optical or even modern physics and science and technology, the diffraction of light has been widely used. Diffraction applications can be generally summarized as the following five aspects:

1 diffraction for spectral analysis. Such as a diffraction grating spectrometer.

2 diffraction for structural analysis. The diffraction pattern has a fairly sensitive "amplification" effect on the fine structure, so it is used to analyze the structure, such as X-ray structure.

3 diffraction imaging. In a coherent light imaging system, two diffraction imaging concepts are introduced, thereby developing into spatial filtering techniques and optical information processing. The distraction of the imaging instrument is distinguished.

4 diffraction and reproducing wavefront. This is an important step in the principle of holography.

5 X light diffraction can be used to measure the structure of the crystal, which is an important method for determining the crystal structure.

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