Gratings with grooves that have a sawtooth profile (blazed gratings) exhibit a high diffraction efficiency for certain orders and wavelengths. In Fig. 5, light is directed at a reflective grating at angle Î± and light of wavelength λ is diffracted at angle Î². Here, Î± and Î² are the angles made with the normal to the grating and counterclockwise direction is taken as positive. Grating equation (2)' can be updated as the following relationship:

Blazedgratingequation

It can be seen from this equation that, when not using the Littrow configuration, the blaze wavelength λB is shorter than λB(Litt). For incident angle Î±, the relationship between λB(Litt) and λB is given by the following:

Gratings can be classified into several different types according to the profile of the grooves. The respective features of three types of gratings manufactured by Shimadzu are described below

Blazedgratingefficiency

In addition to this the f/D ratio is important. As the f/D ratio is often specified along with the diameter, the focal length can be obtained very easily by multiplying its f/D ratio by the specified diameter D.

In other words, RF energy in the form of electromagnetic waves travelling towards the antenna in a plane wavefront will be reflected by the reflector and remain in phase at the focal point. In this way the whole signal remains in phase and there is no cancellation. This means that the maximum signal is maintained. Conversely signals radiated from the focal point will be reflected by the parabolic reflector and form a parallel wavefront (in-phase) travelling outwards from the antenna.

Blazedgrating

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When the relationship between the incident light and the mth-order diffracted light describes mirror reflection with respect to the facet surface of the grooves, most of the energy is concentrated into the mth-order diffracted light. The facet angle of the grooves at this point is called the "blaze angle" and, represented by Î¸B, satisfies the following:

Some of the mathematics and theory behind the parabolic reflector antenna gives a good understanding into its operation and some of the key factors concerning its operation and design.

Diffraction gratingformula

This is called the "Littrow mounting". In our catalogs, the blaze wavelengths given for plane gratings are the blaze wavelengths for this configuration. Equation (12) is Substituted equation (11) for equation (10) and applied m to both sides. The relationship between the blaze wavelength λB for other configurations and the blaze wavelength λB(Litt)used in the catalog is given by the following:

It can be seen from this equation that the blaze wavelength varies with the blaze angle Î¸B and the incident angle Î± (i.e., the usage method). In gerneral, the wavelength (λB(Litt)) where first-order diffracted light returns along the same path as the incident light is used to represent the blaze characteristics of gratings. In this case, Î± = Î² = Î¸B then equation (8) gives the following:

As the surface acts as a reflector, the directix has the same properties when located in front of the reflector. In other words the parabolic reflector theory shows that the emanating wavefront will have the same phase regardless of the point of reflection on the parabolic curve.

One important element of the parabolic reflector antenna theory is its focal length. To ensure that the antenna operates correctly, it is necessary to ensure that the radiating element is placed at the focal point. To determine this it is necessary to know the focal length.

The reflector uses a parabolic shape to ensure that all the power is reflected in a beam in which the wave traces run parallel to each other. Also all the reflected power is in the same phase, because the path length from the source to the reflector and then outwards is the same wherever it is reflected on the surface of the parabola.

In view of the fact that total length A1 + A2 is the same as B1 + B2, etc, this means that the phase integrity of the system is retained. Incoming waves add at the focal point, and outgoing waves produce a single wavefront moving in parallel away from the reflector.

Blaze angle diffraction gratingcalculator

As the name implies, the parabolic reflector is formed from a shape known as a paraboloid. This shape forms the reflective surface in the antenna that enables waves reflected by the surface to retain their phase relationship, thereby enabling the maximum gain to be obtained.

Reflectivediffraction grating

Parabolic theory shows that the paraboloid curve is the locus of points that are equidistant from a fixed point known as the focus located on the X axis. A fixed line behind the parbolic curve detailed as AB on the diagram is known as the directrix. On this the length FP = PQ wherever it is located on the parabolic curve.

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Blaze angle diffraction gratingformula

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Blazedgratingpdf

The corresponding wavelength is called the "blaze wavelength" and is represented by λB. Combining equations (8) and (9) gives the following:

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For example, for a groove density N of 600 grooves/mm and an incident angle α of 60°, in order to obtain first-order light with a wavelength of 300 nm, substiture λB = 300 nm in equation (13) to obtain λB(Litt) = 484 nm. In this case, then, select a grating for which λB(Litt) = 500 nm from the catalog. The blaze wavelengths given for concave gratings in catalog are the blaze wavelengths for the configuration (mounting) in the optical system used. The arrows on the gratings indicate the blaze direction and the relationship between the groove profile and this direction is shown in Fig. 6.

Parabolic refelector antenna includes: Parabolic / dish antenna basics     Parabolic antenna theory & equations     Parabolic antenna gain & directivity     Parabolic antenna feed systems     Some of the mathematics and theory behind the parabolic reflector antenna gives a good understanding into its operation and some of the key factors concerning its operation and design. The parabolic shape of the reflector is key to its operation – in particular its gain and directivity. Parabolic reflector theory basics As the name implies, the parabolic reflector is formed from a shape known as a paraboloid. This shape forms the reflective surface in the antenna that enables waves reflected by the surface to retain their phase relationship, thereby enabling the maximum gain to be obtained. In other words, RF energy in the form of electromagnetic waves travelling towards the antenna in a plane wavefront will be reflected by the reflector and remain in phase at the focal point. In this way the whole signal remains in phase and there is no cancellation. This means that the maximum signal is maintained. Conversely signals radiated from the focal point will be reflected by the parabolic reflector and form a parallel wavefront (in-phase) travelling outwards from the antenna. The parabolic reflector shape enables the wavefronts to remain in phase A 1 + A 2 = B 1 + B 2 In view of the fact that total length A1 + A2 is the same as B1 + B2, etc, this means that the phase integrity of the system is retained. Incoming waves add at the focal point, and outgoing waves produce a single wavefront moving in parallel away from the reflector. It is this concept that is at the centre of parabolic reflector antenna theory. Parabolic reflector shape theory Parabolic reflector theory relies on the shape of the reflector for its properties. The reflector uses a parabolic shape to ensure that all the power is reflected in a beam in which the wave traces run parallel to each other. Also all the reflected power is in the same phase, because the path length from the source to the reflector and then outwards is the same wherever it is reflected on the surface of the parabola. The parabolic curve follows the equation: Y 2 = 4   S   X The measurements and references for the parabolic reflector antenna formula can be seen on the diagram below: The parabolic reflector curve & theoretical details Parabolic theory shows that the paraboloid curve is the locus of points that are equidistant from a fixed point known as the focus located on the X axis. A fixed line behind the parbolic curve detailed as AB on the diagram is known as the directrix. On this the length FP = PQ wherever it is located on the parabolic curve. As the surface acts as a reflector, the directix has the same properties when located in front of the reflector. In other words the parabolic reflector theory shows that the emanating wavefront will have the same phase regardless of the point of reflection on the parabolic curve. The parabolic reflector antenna theory also shows the emanating beam will tend to be parallel. Parabolic antenna focal length One important element of the parabolic reflector antenna theory is its focal length. To ensure that the antenna operates correctly, it is necessary to ensure that the radiating element is placed at the focal point. To determine this it is necessary to know the focal length. f = D 2 16 c Where:     f is the focal length     D is the diameter of the reflector     c is the depth of the reflector In addition to this the f/D ratio is important. As the f/D ratio is often specified along with the diameter, the focal length can be obtained very easily by multiplying its f/D ratio by the specified diameter D. Previous page     Next page       Written by Ian Poole .   Experienced electronics engineer and author. More Antenna & Propagation Topics: EM waves     Radio propagation     Ionospheric propagation     Ground wave     Meteor scatter     Tropospheric propagation     Antenna basics     Cubical quad     Dipole     Discone     Ferrite rod     Log periodic antenna     Parabolic reflector antenna     Phased array antennas     Vertical antennas     Yagi     Antenna grounding     Installation guidelines     TV antennas     Coax cable     Waveguide     VSWR     Antenna baluns     MIMO         Return to Antennas & Propagation menu . . .