Spectroscope based on a concave diffraction lattice. Study of the characteristics of concave diffraction solids concave diffraction grille
Concave lattices
Operating principle. In 1882, Rowland proposed to combine the focusing properties of a concave mirror with the dispersing properties of the sliced \u200b\u200bsurface of the diffraction lattice. Such lattices got the name of the concave and widely now apply. A concave grill allows you to simplify the spectrum diagram to the limit due to the exception of special focusing optics. To obtain the spectrum, only a gap and a concave grill is required. Thanks to the use of such lattices, the area of \u200b\u200bdistant vacuum ultraviolet has become available. (to< 500 BUT).The accurate measurement of wavelengths in complex spectra is now not thoughtless without a large concave lattice. The full theory of the lattice bent is quite complex, and we will give here only the most simple reasoning and the main conclusions.
As a rule, the lattice is applied to the surface of the sphere, although the grid applied to the toric and ellipsoidal surfaces has well-known advantages. We assume that the sizes of the shaded part of the lattice and the height of the stroke are small compared to the radius of the sphere of r to which it is applied. The middle of the middle lattice stroke will call it the center. We carry out a circle, the diameter of which is equal to the radius of the crumism of the lattice. This circle relates to the lattice in its center and lies in the plane perpendicular to the strokes. Such a circle is called round rowland.
Consider the course of monochromatic rays falling on the grille from the point S,lying on this circle. Let be BUTand IN- Two neighboring lattice strokes. Rays SAand SB.pAs are falling under the corners of the w and sh + Dsh. Diffranged rays ARand BPgo under the corners of C and C + CD and intersect at the point R.The center of curvature lattice is denoted by FROM.Let be
The maximum condition, as well as for a flat lattice, we obtain, equating the difference in the course of the adjacent rays to an integer number of wavelengths:
I will prolong the rays Sb to the point G and RV to the point F so that Sg \u003d SA and PF - \u003d RA. Then you can write
Corners AFB.and AGB.different from direct for the magnitude of the order of small angles of DG and DS. With the same accuracy. Therefore, sin c. Then equality (2.1) can be written as
where t \u003d AB- Permanent lattice. Thus, we got the same formula for the position of the main maxima as for a flat lattice.
We now show that a concave lattice, unlike flat, has a focusing effect. This means that rays with a wavelength of l, outgoing from the point S.and lying in the plane perpendicular to the lattice strokes form, regardless of the angle of the fall, the main diffraction maximum in the same point R.To do this, indifferentiate (2.2) on W and C with constant l and to and proceed and end differences
From fig. 2.10 I can see that
Similarly
On the other hand,
Substituting in (2.3) the values \u200b\u200bof DSh and DC from (2.4), (2.5) and using equivals (2.6), we get
So that this equation is satisfied for any c and r] ·, it is necessary and enough to simultaneously
or (2.8)
Equations (2.8) are circumferential equations in polar coordinates. The diameter of this circle is equal to the radius of the curvature of the lattice R, i.e. we obtain the equation of the circle of route. Thus, if the point S.lies on the circle of route, then on the same circle lies and the point R,in which the main diffraction maximum forms for rays of this wavelength l. Naturally, for rays of different wavelengths l. j. , l 2, etc. The main diffraction maxima in accordance with (2.2) is formed at different points R 1 , R 2 etc. However, all these points lie on the same circle, forming a spectrum of the source placed in it S. B.the equation determining this circle does not include a lattice constant. This means that any lattice with radius g will give a spectrum lying on the same circle.
This consideration does not follow that rays going out of the point S,but not lying in the plane of the Rowland circle, also focus on the point R.
On the contrary, it is easy to show that the lattice has significant astigmatism and the point image S.it is a straight line, parallel lattice strokes.
The expression for the resolution of a concave lattice coincides with the corresponding expression for a flat lattice. The angular dispersion, as in the case of a flat lattice, is obtained by differentiation of equality (2.2) by l.
The formula for linear dispersion is easy to get, counting the distances l.along the circle of route. The corner of C, being inscribed in the circle of the diameter R, is C \u003d l / R,from where after differentiation on l we find an expression that connects the linear and angular dispersion of the grid:
Excluding from (2.3) and (2.39) D c / dl,for linear dispersion received 1
The image of the slot given by a concave grill possesses, as in the case of a flat lattice, some curvature. The latter, however, is small and may not be taken into account for lattices of usually applied sizes. If the grille and the slit are located on the circle of the route, then the spectrum is also located on the same circle. This follows from equation (2.8). You can get a spectrum and with a different location of the gap and lattice. However, detailed calculations show that when there is all three installation elements (gap, receiver, lattice) on the ROULAND circle of aberration are minimal.
The calculation of the spectrum position was carried out for a "small" lattice. If its size is comparable with a radius, then other aberrations, worsening the circuit of the spectral line appear besides astigmatism.
Basic concepts and characteristicsspectral instrument. |
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The distribution of illumination in the image of the gap |
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| Diffraction grating In spectral devices for spatial decomposition of light, diffraction gratings are used in the spectrum. The diffraction grille is an optical element consisting of a large number of regularly located strokes deposited on a flat or concave surface. Lattices can be transparent or reflective. In addition, the amplitude and phase diffraction gratings are distinguished. In the first periodically changes the reflection coefficient, which causes the change in the amplitude of the incident wave. Phase diffraction gratings, the strokes are given a special form, which periodically changes the phase of the light wave. Flat reflective phase diffraction grid with a triangular profile of strokes - echelette received the greatest distribution. Lattice equation The front of the light wave falling on the diffraction grid is divided by its strokes on separate coherent beams. Coherent bundles, underpracting diffraction on the strokes, interfer the resulting the resulting spatial distribution of light intensity. The distribution of intensity is proportional to the product of two functions: interferenceI N.
and diffractionI D.
. FunctionI N.
due to the interference N of coherent beams coming from the lattice strokes. FunctionI D.
Determined by diffraction on a separate stroke. The movement difference between coherent parallel beams, arriving at an angle β from adjacent strokes, will be ΔS \u003d AB + AC or (1), and the corresponding phase difference This ratio is called the lattice equation. It shows that the main maxima is formed in directions when the movement difference between adjacent beams is equal to the total number of wavelengths. Between neighboring major maxima is located N-2 secondary maxima, the intensity of which decreases proportionally 1 / N. , I. N-1 Minima, where the intensity is zero. The lattice equation for use to monochromators is used in a more convenient form. As the difference between corners α
and β
Constant when rotating the lattice and this difference is known θ
, it is determined by the design of the monochromator, then from two variablesα
and β
Go to one φ
- The corner of the rotation of the lattice from zero order. |
Fig.1. Description of the principle of action of the diffraction lattice. |
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Length of the wave of brilliance The reflectivity of the diffraction gratings depends on the tilt angle - changing the angle of the tilt of the stroke can be combined with the function of the diffraction maximum function I D. with interference main maximum function I N. of any order. The direction to the center of the diffraction maximum is determined by the mirror reflection of the incident beam not from the lattice plane, but from the face of the stroke. Thus, the condition of such a compatibility: angles α
and β MAX.
We must simultaneously satisfy the relationships: Under these conditions, the spectrum of this order will have the greatest intensity. Angle β MAX.
Called the angle of "brilliance", and the wavelength - the wavelength "shine" λ Blaze.. If the range of spectrum for research is known, then λ Blaze. It can be determined from the ratio: Example 1.. The study range is 400 ... 1200nm, i.e. λ 1. \u003d 400НМ, λ 2. \u003d 1200НМ. Then from formula (8): λ Blaze.\u003d 600НМ. Select the grid with glitter 600 nm. Example 2. The studied range is 600 ... 1100НМ. The calculation according to formula (8) gives 776 nm roundings. Lattices with such a glitter in the proposed list. The grill is selected with the brilliance closest to the found, i.e. 750nm. |
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The area of \u200b\u200benergy efficiency diffraction gratings The area where the lattice reflection coefficient is at least 0.405 is called an area of \u200b\u200benergy efficiency: |
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Dispersion area The dispersion area is the spectral interval in which the spectrum of this order does not overlap by the spectra of adjacent orders. Therefore, there is a unambiguous relationship between the diffraction angle and the wavelength. The dispersion area is determined from the condition: Example. If a Thus, for this lattice in the range of 450 nm to 900 nm, the dispersion area is combined with an area of \u200b\u200benergy efficiency. |
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Dispersion The degree of spatial separation of rays with a different wavelength characterizes the angular dispersion. The expression for an angular dispersion is obtained, differentiating the lattice equation: |
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Resolution Theoretical resolution: |
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The spectral area of \u200b\u200bthe lattice depending from the number of strokes For each diffraction lattice with a period d. There is a maximum wavelength |
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Concave diffraction grating A concave diffraction grating acts as not only dispersing, but also the focusing system. Expressions for spectroscopic characteristics - angular dispersion, resolution and dispersion area - the same as for a flat lattice. Concave lattices, unlike flat, possess astigmatism. Astigmatism is eliminated by applying strokes on an aspherical surface or with variable distances between strokes. |
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Holographic diffraction grating The quality of the diffraction lattice is determined by the magnitude of the intensity of the diffused light due to the presence of small defects on the edges of individual strokes, and the intensity of the "perfumes" - false lines arising from the violation of the equidistance in the location of the strokes. The advantage of holographic lattices compared with the cuts are the lack of "spirits" and the smaller intensity of the scattered light. However, the holographic phase reflective lattice has a sinusoidal shape of the stroke, i.e. is not a echellet, therefore it has less energy efficiency (Fig. 2). Getting holographic lattices with a triangular stroke profile, so-called "blisted", leads to the occurrence of microstructures on the edges of the strokes, which increases the intensity of the scattered light. In addition, the correct triangular profile is not achieved, which reduces the energy efficiency of such lattices. |
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(2). FunctionI N.
- Periodic feature with different intense major maxima. The position of the main maxima is determined from the condition 
From! 
(3) where k. - The order of the spectrum. 
. Using (3) we get 
Substituting in (1): (4). 
and 
After transformations of the sum of the sinuses, we obtain the lattice equation in another more convenient form: 
(5) where
(6).
Performed for all wavelengths. Moreover, β= -α
Those. Operation at maximum zero order is determined by the mirror reflection from the lattice plane. 
(7).
(8), where where λ 1. and λ 2. - Boundary wavelengths of the spectrum range. The ratio (8) helps choose the right grid.
(nine). The value depends on the order of the spectrum: the maximum in the first order and quickly falls in the spectra of higher orders. For first order: 
. Wavelengths limiting this area: 
and 
.
.
(10). For first order 
, but 
. The dispersion area covers an interval into one octave. To combine the dispersion area with the area of \u200b\u200bthe energy efficiency of the diffraction lattice, it is necessary that the condition is carried out: 
(eleven). In this case, within the dispersion area, the lattice reflection coefficient for k \u003d 1. It will be at least 0.68.
, then 
, but 
.
(12). From this expression it follows that the angular dispersion is determined exclusively to the corners α
and β
But not the number of strokes. In applied to spectral instruments, a reverse linear dispersion is used, which is defined as the inverse product of the corner dispersion on the focal length: 
.
where - permission. The resolution of the diffraction lattice as any spectral instrument is determined by the spectral width of the hardware function. The lattice of the hardware function is the width of the main maxima of the interference function: 
. Then: 
(fourteen). The spectral resolution of the diffraction lattice is equal to the product of the form of diffraction k. on the total number of strokes N.. Using the lattice equation: 
(15) where the work 
- The length of the shaded part of the lattice. From the expression (15) it can be seen that at given angles α
and β
Value R. It can only be increased by increasing the dimensions of the diffraction lattice. The expression for resolution can be represented in another form from (12) and (15): 
(16), where 
- The width of the diffracted beam, is an angular dispersion. The expression (16) shows that the resolution is directly proportional to the magnitude of the angular dispersion. 
. It is determined from the lattice equation when k \u003d 1. and α \u003d β \u003d 90 ° and equal 
. Therefore, when working in various fields of the spectrum, lattices are used with a different number of strokes: 
The distribution of illumination in the image of the gap
The distribution of illumination in the image of the slit depends on the nature of the aberration of the optical system, as well as on the method of lighting the slot.
Aberration
The perfect optical system gives a point point image. In the Paraxial region, the optical system is close to ideal. But with the final width of beams and removing the source from the optical axis, the rules of paracual optics are violated and the image is distorted. When designing an optical aberration system, you have to correct.
Spherical aberration
The distribution of illumination in the scattering spot during spherical aberration is such that in the center it turns out a sharp maximum with a rapid reduction in illumination to the edge of the spot. This aberration is the only one that remains and if the point object is located on the main optical axis of the system. Spherical aberration is especially large in highlighting systems (with a large relative hole).
Coma
The image of the point in the presence of a coma has the form of an asymmetric spot, the illumination of which is maximum at the top of the scattering figure.
Astigmatism
It is determined by an unequal curvature optical surface in different cross-sectional planes and is manifested in the fact that the wave front is deformed when the optical system is passed, and the focus of the light beam in different sections is in different points. The scattering figure is a family of ellipses with a uniform distribution of illumination. There are two planes - the sagittal meridional and perpendicular to it, in which the ellipses turn into straight segments. Centers of curvature in both sections are called focus, and the distance between them is a measure of astigmatism.
The curvature of the field
The deviation of the surface of the best focusing of the focal plane is an aberration called the curvature field.
Distortia
The distortion lies in the image distortion due to the unequal linear increase in different parts of the image. This aberration depends on the distance from the point to the optical axis and is manifested in violation of the similarity law.
Chromatic abberation
Due to the dispersion of light, two types of chromatic aberration are manifested: chromatism of the position of focus and chromatism of increasing. The first is characterized by a displacement of the plane of the image for different wavelengths, the second - change in the transverse increase. Chromatic aberration is manifested in optical systems, including elements from refractive materials. Mirrors chromatic aberration are not characteristic. This circumstance does a particularly valuable application of mirrors in monochromators, and other optical systems.
Lighting the entrance slit
Coherent and non-coherent lighting
An essential value for the distribution of intensity in the width of the spectral line is characterized by the illumination of the input slit of the device, i.e. The degree of coherence of lighting. Practically illumination of the input slit is not strictly coherent or incoherent. However, you can approach very close to one of these two extreme cases. Coherent lighting can be carried out if the slot is illuminated by a point source located in the focus of the large diameter condenser supplied before the gap.
Another way is to light lighting when the source of small size is placed at a high distance from the gap. Non-coherent lighting can be obtained if using a condense lens focus the light source to the input slot of the device. Other lighting methods occupy an intermediate position. The importance of their distinction is related to the fact that when covered with coherent light, interference phenomena may occur, which are not observed when illuminated by incoherent light.
If the main requirement is to achieve maximum resolution, the aperture of the diffraction lattice is filled with coherent light in the plane perpendicular to the slot. If you want to provide maximum spectrum brightness, then the method of non-coherent lighting is used, in which the aperture is also filled in the plane parallel to the slot.
Filling the aperture with light.
F / # - Matcher
.
One of the main parameters that characterizes the spectral device is to light it. Lights is determined by the maximum angular size of the beam of light falling into the device, and is measured by the ratio of diameter (D K) to the focal length (F K) Colimator mirror. In practice, the inversely use the reverse magnitude called F / # It is preferable to use another characteristic - a numeric aperture. Numerical apertura (N.A.) associated with F / # By the ratio: 
.
The optimal display of an extended incoherent light source to the input slot of the device is achieved in the case when the body angle of the falling light beam is equal to the input corner of the device.
BUT - the area of \u200b\u200bthe entrance slit; θ - Input body corner.If the gap and the collimator are filled with light, then no extension system of lenses and mirrors will help increase the overall flow of radiation passing through the system.
For a specific spectral instrument, the maximum input body angle is a permanent value, determined by the size and focal length of the collimator: 
.
To match the angular apertures of the light source and the spectral instrument, a special device is used, called F / # Matcher. F / # Matcher is used in conjunction with the spectral device, providing its maximum light, both with a light guide, and without it.
Fig.4. Scheme F / # Matcher
The advantages of F / # Matcher are:
- Use full geometric spectral instrument
- Reducing scattered light
- Preservation of good spectral and spatial image quality
- The possibility of using light filters of unequal thickness without distortion focusing
General
Consider in more detail the theory of concave diffraction lattice. The directions of the main maxima of the interference of beams differed on a concave lattice are determined by a formula similar to a flat reflective lattice
where is the number of strokes per mm; - the angle of falling the beam of the JSC ("zero beam") on the grille; - The diffraction angle for this ray. It can be proved that the focusing curve of beams differed on a concave lattice is a circle with a radius equal to half the radius of the grille curvature (rowland circle).
Formula (1) determines the direction of the beam diffracted at the top of a concave lattice - "zero" diffracted beam (see Fig. 3.1). For the rays of the same length emanating from the same point A, which falling on other parts of the grille surfaces and will be different, and, in general, diffracted rays (that is, the directions of the interference highs of various beams) do not converge at one point. This means that a concave lattice has aberrations.
The allowing ability of a concave lattice is given by the formula:
where - the lattice width, - the order of the spectrum (in our case \u003d 1), is the number of strokes per unit length. However, to increase the allowing ability of a concave grille by increasing the width will not be able, since there is an optimal width of a concave lattice. It is defined as the maximum width of a concave lattice, at which its resolution is not inferior to a flat grid. For each wavelength l, you can specify the size of the lattice at which it has the maximum possible allowing ability. With a further increase in the size of the grille, the resolution falls. You can show that
For example, for a lattice with the following parameters: R \u003d 1m, \u003d 26є, \u003d 0є and used in the region L \u003d 200 nm we get? 5cm.
Normal width of the slit
Each diffraction grid is characterized by its hardware function, that is, the dependence of the image width of the inlet slit from the width of the slot itself. It is interesting to find the dependence of the width of the image of the gap from the width of the inlet slit. This dependence was found (see Fig. 3.2). The proportionality between and is observed only with wide cracks. The decrease leads to a decrease only to certain width values. With a further decrease in the width of the slit (<) ширина изображения остаётся постоянной и происходит лишь уменьшение освещённости изображения. Величина называется нормальной шириной входной щели. Нормальная ширина щели это такая величина входной щели, когда её геометрическое изображение в фокальной плоскости прибора равно центральной части главного дифракционного максимума в этой же плоскости. При ширине щели меньше нормальной, изображение, образующееся в фокальной плоскости уже не является собственно изображением входной щели, а определяется дифракцией на апертурной диафрагме спектрального прибора. Нормальная ширина входной щели определяется параметрами прибора и равна
where-focus distance of the collimating lens (the radius of curvature of a concave diffraction lattice) is the width of the diaphragm (the height of the concave diffraction lattice). The image width of the gap cannot become less diffraction limit. Therefore, striving to get lines as thinner as possible, it is useless to use the inlet slit less than normal.
Let us estimate the MFS-8 and IMK-1 lattices:
1) MFS-8: \u003d 30mm, \u003d 1m ,. Then \u003d 6.7 microns
2) VMK-1: \u003d 50mm, \u003d 1m ,. Then \u003d 4 μm
That is, in order not to lose in the intensity of the lines, you need to take the width of the input slit obviously more, for example 15 microns.
It is no secret that along with tangible matter we are surrounded by wave fields with their processes and laws. It can be electromagnetic, and sound, and light oscillations that are inextricably linked with a visible world, interact with it and affect it. Such processes and impacts have long been studied by different scientists, which have discharged the basic laws current and to this day. One of the widely used forms of the interaction of matter and wave is diffraction, the study of which led to the emergence of such a device as a diffraction grid that has been widely used in devices for further study of wave radiation, and in everyday life.
The concept of diffraction
The diffraction is called the process of envelope with light, sound and other waves of any obstacle who met on their way. More generalized by this term, any deviation of the wave propagation from the laws of geometric optics occurring near obstacles can be called. Due to the phenomenon of diffraction, the waves fall into the area of \u200b\u200bthe geometric shadow, envelop the obstacles, penetrate through the small holes in the screens and other things. For example, you can hear the sound well, being around the corner of the house, as a result of the fact that the sound wave envelopes it. The diffraction of light rays is manifested in the fact that the shade area does not correspond to the bandwidth or the existing obstacle. It is on this phenomenon that the principle of action of the diffraction lattice is based. Therefore, the study of these concepts is inseparable from each other.
The concept of the diffraction lattice
The diffraction grille is an optical product representing a periodic structure consisting of a large number of very narrow slots separated by opaque gaps.
Another variant of this device is a set of parallel microscopic strokes having the same shape applied to a concave or flat optical surface with the same specified step. In case of falling on the lattice of light waves, the process of redistribution of the wave front in space is due, which is due to the phenomenon of diffraction. That is, the white light decomposes into separate waves having a different length, which depends on the spectral characteristics of the diffraction lattice. Most often to work with a visible range of spectrum (with 390-780 nm wavelengths), devices that have from 300 to 1600 strokes per millimeter are used. In practice, the lattice looks like a flat glass or metal surface with applied with a certain interval rough grooves (strokes) that do not transmit light. With the help of glass surveillance grids, both undergoing, and in the reflected light, using metal - only in reflected.
Types of decisions
As already mentioned, according to the manufacturing material and the features of use, diffraction lattices reflective and transparent are isolated. The first includes devices that are a metal mirror surface with printed strokes that are used for observations in the reflected light. In transparent lattices, the strokes are applied to a special optical, skipping rays surface (flat or concave), or narrow slots in an opaque material are cut. Studies when applying such devices are carried out in the transmitted light. An example of a coarse diffraction lattice in nature can be considered eyelashes. Looking through the squared eyelids, you can at some point to see the spectral lines.
Operating principle
The operation of the diffraction lattice is based on the phenomenon of diffraction of the light wave, which, passing through the system of transparent and opaque areas, is divided into separate bundles of coherent light. They undergo diffraction on the strokes. And at the same time interfere with each other. Each wavelength has its own value of the diffraction angle, so white light decomposes into the spectrum.
Resolution diffraction lattice
Being an optical device used in spectral devices, it has a number of characteristics that determine its use. One of these properties is the resolution, which consists in the possibility of separate observation of two spectral lines with close wavelengths. The increase in this characteristic is achieved by an increase in the total number of strokes available in the diffraction lattice.
In a good device, the number of strokes per millimeter reaches 500, that is, with a total lattice length of 100 millimeters, a total number of strokes will be 50,000. Such a figure will help achieve narrower interference maxima, which will allow to allocate close spectral lines.
Application of diffraction gratings
Using this optical device, you can accurately determine the wavelength, so it is used as a dispersing element in spectral devices for various purposes. The diffraction grid is used to isolate monochromatic light (in monochromators, spectrophotometers and others), as an optical sensor of linear or angular displacements (the so-called measuring grille), in polarizers and optical filters, as a divider of radiation beams in the interferometer, as well as in anti-reflux glasses .
In everyday life, it is quite often possible to encounter examples of diffraction gratings. The simplest of the reflective can be considered a cutting of CDs, since a track is applied on their surface along the helix with a pitch of 1.6 μm between the turns. The third part of the width (0.5 μm) of such a path accounts for a deepening (which contains recorded information), the dispersion light, and about two thirds (1.1 μm) occupies a untouched substrate capable of reflecting the rays. Consequently, the CD is a reflective diffraction lattice with a period of 1.6 microns. Another example of such a device are holograms of various types and directions of use.
Manufacture
To obtain a high-quality diffraction lattice, it is necessary to observe a very high manufacturer. An error when applying at least one touch or slot leads to instant items. For the manufacturing process, a special dividing machine with diamond cutters, fastening to a special massive foundation, is applied. Before the process of cutting the grid, this equipment should work from 5 to 20 hours in idle mode to stabilize all nodes. The manufacture of one diffraction lattice takes almost 7 days. Despite the fact that the application of each stroke occurs only in 3 seconds. The lattices with this manufacture have equifiable parallel strokes, the form of the cross section of which depends on the diamond cutter profile.
Modern diffraction gratings for spectral devices
Currently, a new technology of their manufacturing is distributed through the formation on special photosensitive materials, called photoresists, the interference pattern obtained from radiation of lasers. As a result, produced products with holographic effect. You can apply the strokes in a similar way to a flat surface, having a flat diffraction grid or a concave spherical, which will give a concave device that has a focusing effect. The design of modern spectral devices also use those and others.
Thus, the diffraction phenomenon is distributed in everyday life everywhere. This causes widespread use of such a device based on this process as a diffraction grating. It can be like becoming part of research equipment, and meet in everyday life, for example, as the basis of holographic products.
DIFFRACTION GRATING - Optic. The element, which is a set of a large number of regularly located strokes (groats, slots, protrusions), made in one way or another to flat or concave optical. surface. D. R. Used in spectral devices as a dispersing system for spatial decomposition of EL - Magn. in the spectrum. The front of the light wave falling on D. r., Is divided by its strokes on separate bundles, to-rye, under strokes, interferred (see Interference light), forming a resulting spatial distribution of light intensity - radiation spectrum.
There are reflective and transparent D.R. In the first tops are applied to the mirror (metal.) The surface, and the resulting interference pattern is formed in the light reflected from the lattice. On the second strokes are applied to a transparent (glass) surface, and. The picture is formed in the passing light.
If the strokes are applied to a flat surface, then such D. P. Naz. Flat, if on concave - concave. In modern spectral devices are used both flat and concave D. r., Ch. arr. Reflective.
Flat reflective D. r.Made with the help of specials. Diamond cutters, are straightforward, strictly parallel to each other and equidistant strokes of the same shape, K-paradium is determined by the profile of the cutting edge of the diamond cutter. Such D. R. Represents periodic. Structure with post. distance d. Between strokes (Fig. 1), to-ryody. Period D. R. Distinguish amplitude and phase d. The first periodically changes the coefficient. reflections or transmitting, which causes a change in the amplitude of the incident light wave (such is a grid of the gaps in an opaque screen). Phase d. r. Strokes are detached. The form, K-paradium periodically changes the phase of the light wave.
Fig. 1. Scheme of a one-dimensional periodic structure of a flat diffraction lattice (highly increased): D - lattice period; W is the length of the cutting part of the grid.
Fig. 2. Scheme illustrating the principle of action of the diffraction lattice: a. - phase reflective, b. - amplitude slotted.
Fig. 3. Interference functions of the diffraction lattice.
If on a flat d. r. A parallel beam of light falls, the axis of K-ply lies in the plane perpendicular to the lattice strokes, then, as it shows the calculation, resulting in the interference of coherent beams from all N. Street strokes spatial (at the corners) The distribution of light intensity (in the same plane) can be represented as a product of two F-Qii :. F │ J G. Determined by the diffraction of light on the Department. Stroke, f │ J N. due to interference N. Coherent beams coming from lattice strokes and is associated with periodic. Structure D. R. F │ J N. For this wavelength is determined by the lattice period d., full of lattice strokes N. and the angles formed by the falling (angle) and the diffracted (angle) bundles with the normal to the grid (Fig. 2), but does not depend on the shape of the strokes. It has a view where, - between coherent parallel beams, arriving at an angle from the neighboring touches D.R.: \u003d AV + AS (see Fig. 2, but - for phase reflective D. r., 2, b. - for amplitude slit grille). F │ J N. - Periodic. F-│ with sharp intense ch. maxima and small secondary maxima (Fig. 3, but). Between neighboring ch. Maxima is located N.-2 secondary maxima and N.-1 minima, where the intensity is zero. Position ch. maxima is determined from the condition or 
where m.\u003d 0, 1, 2, ... - an integer. From
i.e. ch. The maxima is formed in directions when the path difference between adjacent coherent beams is equal to an integer number of wavelengths. The intensity of all major maxima is the same and equal 
, the intensity of the secondary maxima is small and does not exceed from.
The ratio, called the griller, shows that at a given angle of falling the direction to the main maximum depend on the wavelength, that is,. 
; Consequently, D. R. Spatially (at the corners) decomposes the radiation of Split. wavelengths. If diphragirov. The radiation comes from the lattice to send to the lens, then the spectrum is formed in its focal plane. At the same time, several is formed. spectra with each number of numbers and the value t. Determines the order of the spectrum. For m.\u003d 0 (zero spectrum order) The spectrum is not formed, since the condition is performed for all wavelengths (ch. Maxima for all wavelengths coincide). From the last condition when t \u003d 0. It also follows that
, i.e. that the direction at the maximum number of zero order is determined by the mirror reflection from the lattice plane (Fig. 4); The falling and diffracted bundles of zero order are arranged symmetrically relative to normal to the lattice. On both sides of the direction at the maximum number of zero order are highs and spectra m.=1,
m.\u003d 2 and T. d. Orders.
Second Faction J G.affecting the resulting distribution of intensity in the spectrum due to the diffraction of light on the Department. stroke; it depends on the values 
, as well as from the shape of the stroke - his profile. Calculation, taking into account Guygens - Fresnel principle, gives for f │ J G. expression
where - the amplitude of the falling wave, -; ,, h. and w. - The coordinates of the points on the stroke profile. Integration is carried out on the profile of the stroke. For a private case with a flat amplitude D. p. Consisting of narrow slits in an opaque screen (Fig. 2, b.) or narrow reflective strips on the plane, where, but - width of the slots (or reflecting strips), and is a diffractionc. Distribution of intensity with Fraunhofer diffraction on a width gap but (cm. Light diffraction). It is viewed in fig. 3 (b). Direction to center ch. Diffrakts. Maximum f │ J G. Determined from the condition u.\u003d 0 or, from where, that is, this direction is determined by a mirror reflection from the plane of D. R., and, consequently, the direction to the center of the Diffrakts. The maximum coincides with the direction to zero - achromatic - the order of the spectrum. Consequently, Max. The value of the work of both F-Qii, and therefore Max. The intensity will be in the zero order spectrum. The intensity in the spectra of the remaining orders ( m.0) there will be accordingly less intensity in zero order (which is schematically depicted in Fig. 3, in). This is unprofitable when using amplitude d. In the spectral devices, since, most of the light aneroge falling on D. p., is sent to the zero order of the spectrum, where there is no spectral decomposition, the intensity of the spectra of others and even first orders of magazine.
If the strokes D. R. Posted by a triangular asymmetric form, then such a phase lattice f │ J G.also has difrakts. distribution but with argument anddepending on the angle of inclination
face of the stroke (Fig. 2, but). At the same time, the direction to the center of the Diffrakts. The maximum is determined by the mirror reflection of the falling beam not from the plane of D. r., and from the edge of the stroke. By changing the angle of tilt the face of the stroke, you can combine the center of the Diffrakts. Maximum f │ J G. With any interference ch. maximum f │ J N. of any order m.0, usually m.\u003d 1 (Fig. 3, g.) or m.\u003d 2. The condition for such combination: angles and must simultaneously satisfy the relationships and. Under these conditions, the spectrum of this order t.0 will have NaB. Intensity, and these ratios allow you to determine the necessary values \u200b\u200bof the specified. Phase d. r. With a triangular stroke profile, concentrating most (up to 80%) falling on the lattice of the light flux in the non-zero-order spectrum, called. esheletti. The angle under which the indicated concentration of the incident light flow in the spectrum is called. An angle of brilliance D. R.
OSN. Spectroscopic. Characteristics D. R.- Angular dispersion, resolving the ability and dispersion area - are determined only by the properties of F-│ J N.. associated with periodic. Structure D.P., and do not depend on the shape of the stroke.
Corner Dispersion characterizing the degree of spatial (angular) separation of rays with different wavelengths, for D. P. get differentiating; Then, from where it follows, when working in a specified order of the spectrum t. Value
Moreover, the less griming period. In addition, the value grows with an increase in the angle of diffraction. However, in the case of an amplitude lattice, an angle increases leads to a decrease in the intensity of the spectrum. In the case, such a profile of the stroke can be created, with a rear, the concentration of energy in the spectrum will occur at large angles of J, in connection with which it is possible to create high-arm spectral appliances with a large angle. dispersion.
Theoretical resolution D.P. where - min. The difference of wavelengths of two monochromatic. Equal intensity lines, K-rye can still be distinguished in the spectrum. Like any spectral device, R. D. R. Spectral width is determined hardware function, in the case of D. R. are the main maxima of f │ J N.. Having determined the spectral width of these maxima, you can get expressions for R. in the form where W \u003d nd. - Full length of the shaded part of D. R. (Fig. 1). From the expression for R. It follows that at the given angles the value R. can be increased only due to the increase in the size of D. R.- W.. Value R. It increases with an increase in the diffraction angle, but slower than he increases. The expression for L can also be represented as 
where 
- Full width of parallel diphragirov. Beam coming from D. r. at an angle.
Dispersion area D. R.- The value of the spectral interval, with a row spectrum of this order t. It does not overlap with the spectra of neighboring orders and, therefore, there is a unambiguous connection between the diffraction angle. Determined from the condition from where. For m.\u003d 1, i.e. the dispersion area covers an interval into one octave, for example. The entire visible range of spectrum from 800 to 400 nm. The expression for may also be presented in the form of where it follows that the value is the greater the less d., and depends on the angle, decreasing (in contrast to and R.) With increasing.
From expressions for and can be obtained by the ratio. For D. R. The difference between very large, since modern D. R. The total number of strokes N. Veliko ( N ~10 5 and more).
Concave D. r. At the concave D. R. Strokes are applied to concave (usually spherical) mirror surface. Such lattices perform the role of both dispersing and focusing system, i.e., do not require the use of input and output collimator lenses or mirrors in the spectral devices, in contrast to the flat D. P. At the same time, the light source (the entrance slot S. 1) and the spectrum turns out to be located on the circle tangent to the lattice in its vertex, the circle diameter is equal to the radius of curvature R. Spherich. Surface D. R. (Fig. 5). This circle is called. round of route. In the case of concave D. P. From the light source (slit), a consigning beam of light falls on the grille, and after diffraction on the strokes and interference of coherent beams, the resulting light waves converged on circle Rowlandwhere the interference is located. Maxima, i.e. spectrum. The angles formed by the axial rays of the incident and diffracted beams with the axis of the sphere are associated with the relation. Here is also formed several. spectra Split. The orders arranged on the circle of route, which is a line of dispersion. Since the grid ur is for concave D. R. The same as for flat, then expressions for spectroscopic. Characteristics - Angle. Dispersions, resolution and dispersion area - are coinciding for lattices of both species. Expressions for linear dispersions of these decisions are different (see Spectral devices).
Fig. 5. Scheme of the formation of the spectra of a concave diffraction lattice on the circle of route.
Concave D. r., Unlike flat, possess astigmatism , C-ry manifests that each point of the source (crack) is depicted with a lattice not in the form of a point, but in the form of a segment perpendicular to the circle of routeland (to the dispersion line), i.e., directed along the spectral lines, which leads to . Reducing the intensity of the spectrum. The presence of astigmatism also interferes with the use of Split. Photometric. fixtures. Astigmatism can be eliminated if the touches are applied to aspherical, for example. toroidal concave, surface or cutting the lattice is not with equidistant, but with changing the laws varying by the law between strokes. But the manufacture of such lattices is associated with great difficulties, they have not received even widespread use.
Topographic D.. r. In the 1970s. A new, holographic method of manufacturing both flat and concave Dr. is designed, and the latter astigmatism can be eliminated. Spectrum region. In this method, flat or concave spherical. The substrate covered with a layer of specials. photosensitive material - photoresist, illuminated by two beams of coherent laser radiation (with a wavelength), in the area of \u200b\u200bintersection of the boring, a stationary interference is formed. Picture with a cosine intensity distribution (see Interference light), changing the photoresist material in accordance with the change in the intensity in the picture. After appropriate processing of the exposed photoresist layer and applying a reflective coating obtained holographic. Phase reflected. A grid with a cosine shape of the stroke, i.e. is not a echelette and therefore has a smaller light. If the lighting was made by parallel beams, forming the angle (Fig. 6), and the substrate is flat, then a flat equidistant holographic is obtained. D. R. With a period, with spherical. The substrate is concave holographic. D.P., equivalent in its properties by a conventional rifle concave lattice. When lighting spherical. The substrate with two divergent beams from sources located on the circle of route, it turns out holographic. D. R. With curvilinear and non -iquidistant strokes, K-paradis is free from astigmatism. Spectrum region.
