DE102018007754A1 - Determination of the true directional diagram of an antenna arrangement on a vehicle arranged above a reflecting base area. - Google Patents

Abstract

A method for determining the true field strength vector in the far point (11) of an electromagnetic body (1) radiating in free space with a frequency of the free space wavelength λ from the field strength vector measurement according to the amount and phase of the radiating body (1) arranged over a flat reflecting base area the following steps: - arranging the electromagnetic radiating body (1) at a first vertical distance (12) between all points on the radiating body (1) and the flat reflecting base surface (6); - in a first measurement, the field strength vector is recorded in one distant point of origin (11) by measuring the field components according to their amounts and measuring the phases of the field components to one another - rotation-free displacement of the radiating body (1) in the direction of the surface normal of the reflecting base surface (6) by a distance Δh, so that the second vertical distance ( 13) all points of the radiating body (1) from the reflecting base area (6) is increased by this distance Δh.- In a subsequent second measurement, the second field strength vector now occurring in the same distant point (11) is measured by measuring the field components according to their amounts and measuring the phases of the field components to each other; - mathematical determination of the true, d. H. without the influence of the reflecting base area (6) in the far point (11) of the field strength vectors based on the difference in the field strength vectors obtained from the first and second measurements and on the basis of the angle θ between the normal (19) of the base area (6) and the connecting straight line between the radiating body ( 1) and the distant point (11).

Description

im fernen Aufpunkt 11 eines elektromagnetischen mit einer Frequenz der Freiraumwellenlänge λ strahlenden Körpers aus der Feldstärkevektor-Messung nach Betrag und Phase des über einer ebenen, reflektierenden Grundfläche angeordneten strahlenden Körpers 1- wobei der wahre Feldstärkevektor $\overrightarrow{\underset{\_}{E}}$

sich ergäbe, wenn die reflektierende Grundfläche nicht vorhanden wäre. Die reflektierende Grundfläche sei dabei bezogen auf die Wellenlänge glatt, so dass eine diffuse Streuung an der Grundfläche vernachlässigbar ist.The invention relates to a method for determining the true field strength vector $\overrightarrow{\underset{\_}{E}}$

in the distant spot 11 an electromagnetic one with a frequency of the free space wavelength λ radiating body from the field strength vector measurement according to the amount and phase of the radiating body 1 arranged above a flat, reflecting base surface, where the true field strength vector $\overrightarrow{\underset{\_}{E}}$

would result if the reflective base were not present. The reflecting base area is smooth in relation to the wavelength, so that diffuse scattering on the base area is negligible.

The radiation properties of antenna arrangements on large bodies can often only be determined by measurements close to the earth, the influences of the reflected radiation on the reflecting base surface being included in the measurement result in a disruptive manner. In antenna measurements on vehicles in particular, it is often desired to know the overall radiation properties and in particular the directional diagram for the differently polarized waves.

The problem arises from the examples in 1 and in 3rd in which the radiation from a radiation-exciting antenna arrangement 2nd on one, above a rotating stand 10th placed vehicle 14 in the distant spot 11 using a measuring antenna 3rd is recorded. Field strength measuring devices 15 This type is common in vehicle antenna technology. 3rd shows the measurement scenario and different characteristic beam paths between the vehicle antenna 2nd and the measuring antenna 3rd . Often it is required to have ray lines of sight 4th and reflection and / or diffraction on the vehicle 5 to record how these would also arise on a free-floating vehicle, but no beam paths 7 which about reflection on the reflective base 6 to the onset 11 reach.

The measuring antenna 3rd is usually at the end of a vertically rotatable swivel arm (gantry) 21 attached so that by rotating the rotating stand 10th in connection with the vertical rotation of the swivel arm 21 the field strength vector at each point 11 at a constant distance d to the center of the revolving stand 10th after all components of the field strength vector according to magnitude and the phases to each other. The problem now is that beam paths are the line of sight 4th and the reflection or diffraction of the beam path 5 at the vehicle 14 how they would occur on a free-floating vehicle, but no beam paths are recorded 7 who experience a reflection on the ground. In particular, the reflections on the floor falsify the measurement result and, among other things, also make it difficult to compare the radiation properties of different forms of antenna arrangements 2nd on the same vehicle 14 .

The radiant body can also 1 for example from an airplane with an antenna arrangement 2nd exist, the radiation properties of which are recorded by measurement on the aircraft located near the ground, so that the directivity of the radiation for flight operations is determined from this in accordance with the invention.

The object of the invention is therefore in the field strength vector measurement of a radiating body arranged over a reflecting base area 1 according to the preamble of the main claim, to eliminate the influence of the reflective floor by measurement and calculation, and the true field strength vector in the points 11 to determine.

This task is done with an antenna 1 solved according to the preamble of the main claim by the characterizing features of the main claim and the measures proposed in the further claims.

According to the invention, a method is thus presented for eliminating the influence of the reflective floor in terms of measurement technology and computation. The prerequisite is that a clean far-field characteristic can be measured taking into account the above-mentioned conditions, which only includes the reflections on the ground but no reflections on other objects.

The advantage of the method according to the invention is that the reflective base surface can be avoided in a simple and inexpensive manner 6 to make the radiation reflecting effect ineffective in terms of radiation technology by frequently used covering with extremely expensive and mechanically extremely sensitive absorber material.

The invention starts with the measurement of a far field characteristic of the radiating body 1 out. Because of a swivel arm that is limited in length 21 However, field strength vectors are often measured in the near field and are therefore converted into far field field strength vectors using the known near-field-far-field transformation, so that these can also be assumed for the present invention.

in einem fernen Aufpunkt 11 eines elektromagnetischen mit einer Frequenz der Freiraumwellenlänge λ strahlenden Körpers 1 aus Feldstärkevektor-Messungen nach Betrag und Phase des über einer reflektierenden Grundfläche 6 angeordneten strahlenden Körpers 1 in folgenden mehreren Schritten ermittelt.

• - Anordnung des elektromagnetisch strahlenden Körpers 1 in einem ersten senkrechtem Abstand 12 jeweils zwischen den Punkten auf dem strahlenden Körper 1 und der reflektierenden Grundfläche 6 ;
• - In einer ersten Messung Erfassung des ersten Feldstärkevektors $\overrightarrow{\underset{\_}{E1}}$
  
  in einem fernen Aufpunkt 11 durch Messung der Feldkomponenten nach ihren Beträgen und Messung der Phasen der Feldkomponenten zueinander.
• - Verschiebung des strahlenden Körpers 1 in Richtung der Flächennormalen 19 der reflektierenden Grundfläche 6 um eine Strecke Δh, sodass der zweite senkrechte Abstand 13 aller Punkte des strahlenden Körpers 1 von der reflektierenden Grundfläche 6 um diese Strecke Δh verändert ist.
• - In einer darauffolgenden zweiten Messung Erfassung des nunmehr auftretenden zweiten Feldstärkevektors $\overrightarrow{\underset{\_}{E2}}$
  
  im selben fernen Aufpunkt 11 durch Messung der Feldkomponenten nach ihren Beträgen und Messung der Phasen der Feldkomponenten zueinander;
• - rechnerische Ermittlung des wahren - d. h. ohne Einfluss der reflektierenden Grundfläche 6 - im fernen Aufpunkt 11 auftretenden Feldstärkevektors $\overrightarrow{\underset{\_}{E}}$
  
  anhand der Unterschiedlichkeit der aus der ersten und zweiten Messung gewonnenen Feldstärkevektoren $\overrightarrow{\underset{\_}{E1}}\text{ und }\overrightarrow{\underset{\_}{E2}}$
  
  und anhand des Winkels θ zwischen der Normalen 19 der Grundfläche 6 und der Verbindungsgeraden 20 zwischen dem strahlenden Körper 1 und dem fernen Aufpunkt 11 sowie anhand der auf die Wellenlänge λ bezogenen Strecke Δhr = λh/λ.

According to the method according to the invention, the true field strength vector $\overrightarrow{\underset{\_}{E}}$

in a distant spot 11 an electromagnetic body radiating at a frequency of the free space wavelength λ 1 from field strength vector measurements according to the amount and phase of a reflecting surface 6 arranged radiating body 1 determined in the following several steps.

• - Arrangement of the electromagnetic radiating body 1 at a first vertical distance 12th between the points on the radiating body 1 and the reflective base 6 ;
• - Detection of the first field strength vector in a first measurement $\stackrel{}{\underset{}{E}}$$\overrightarrow{\underset{\_}{1}}$
  
  in a distant spot 11 by measuring the field components according to their amounts and measuring the phases of the field components to each other.
• - displacement of the radiating body 1 towards the surface normal 19th the reflective base 6 by a distance Δh so that the second vertical distance 13 all points of the radiant body 1 from the reflective base 6 this distance Δh is changed.
• - In a subsequent second measurement, detection of the second field strength vector now occurring $\overrightarrow{\underset{\_}{E\mathrm{2nd}}}$
  
  in the same distant spot 11 by measuring the field components according to their amounts and measuring the phases of the field components to each other;
• - Arithmetical determination of the true - ie without the influence of the reflective base 6 - in the distant entrance 11 occurring field strength vector $\overrightarrow{\underset{\_}{E}}$
  
  based on the differences in the field strength vectors obtained from the first and second measurements $\stackrel{}{\underset{}{E}}$$\overrightarrow{\underset{\_}{1}}\text{and}\overrightarrow{\underset{\_}{E\mathrm{2nd}}}$
  
  and based on the angle θ between the normal 19th the base area 6 and the connecting line 20th between the radiant body 1 and the distant entrance 11 and on the basis of the distance Δhr = λh / λ based on the wavelength λ.

nachfolgender Beziehung ermittelt ist: $$\overrightarrow{\underset{\_}{E}}=\frac{\overrightarrow{\underset{\_}{E1}}-\overrightarrow{\underset{\_}{E}}•\text{exp}\left[j2\pi •\left(\text{cos}\left(\theta \right)•\Delta hr\right)\right]}{1-\text{exp}\left[j4\pi •\left(\text{cos}\left(\theta \right)•\Delta hr\right)\right]}$$

wobei Δhr*cos(θ) = Δh/λ* cos(θ) < 0,25 gewählt ist. Mit $j=\sqrt{-1}$

It may be that the true field strength vector $\overrightarrow{\underset{\_}{E}}$

following relationship is established: $$\overrightarrow{\underset{\_}{E}}=\frac{\overrightarrow{\underset{\_}{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">E</figure-callout>}1}}-\overrightarrow{\underset{\_}{E}}•\text{exp}\left[j\mathrm{2nd}\pi •\left(\text{cos}\left(\theta \right)•\Delta Hr\right)\right]}{1-\text{exp}\left[j\mathrm{4th}\pi •\left(\text{cos}\left(\theta \right)•\Delta Hr\right)\right]}$$

where Δhr * cos (θ) = Δh / λ * cos (θ) <0.25 is selected. With $j=\sqrt{-1}$

und anhand der Beträge der Feldkomponenten und deren Phasenbeziehungen zu einander - nach bekannten mathematischen Beziehungen - die sich im fernen Aufpunkt 11 ausbreitenden zirkularen RHCP-, LHCP- bzw. linear polarisierten- Teilwellen der Größe nach und nach deren Phasenbeziehungen zu einander rechnerisch ermittelt sind.It may be based on the true field strength vector $\overrightarrow{\underset{\_}{E}}$

and on the basis of the amounts of the field components and their phase relationships to one another - according to known mathematical relationships - which are at a distant point of departure 11 propagating circular RHCP-, LHCP- or linearly polarized- partial waves of the size gradually and after their phase relationships to each other are calculated.

der strahlende Körper 1 durch ein Fahrzeug 14 mit einer strahlungserregenden Antennenanordnung 2 gegeben ist und das Fahrzeug 14 über einem flächigen Drehstand 10 angeordnet ist, welcher Teil der horizontal orientierten reflektierenden Grundfläche 6 ist und zur Beschreibung des elektromagnetischen Feldes im fernen Aufpunkt 11 ein fiktives rechtwinkliges Koordinatensystem 9 mit der xy-Ebene als mit dem Drehstand 10 verbundene reflektierende Grundfläche 6 mit der z-Achse als Grundflächennormale eingeführt ist, sodass bei Drehung des Drehstands 10 mit dem Fahrzeug 14 die vertikale Projektion 18 der Verbindungsgeraden zwischen dem Drehpunkt des Drehstands 10 und dem fernen Aufpunkt 11 auf die xy-Ebene den Azimutwinkel Φ gegenüber der x-Achse bildet und der Winkel θ zwischen der Verbindungsgeraden und der Grundflächennormalen als Zenitwinkel θ gegenüber der z-Achse gebildet ist und der wahre Feldstärkevektor $\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)$

aus den Feldstärkevektoren $\overrightarrow{\underset{\_}{E1}}\left(\theta ,\varphi \right)$

gemessen an dem auf dem Drehstand stehenden Fahrzeug 14 und $\overrightarrow{\underset{\_}{E2}}\left(\theta ,\varphi \right)$

gemessen an dem über dem Drehstand um die Strecke Δh mit Δh/λ*cos(θ) < 0,25 erhöhten Fahrzeug im fernen Aufpunkt 11 in Abhängigkeit vom Azimutwinkel Φ und vom Zenitwinkel θ nach folgender Beziehung für $\overrightarrow{\underset{\_}{E}}\left(\Phi ,\theta \right)$

ermittelt ist. $$\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)=\frac{\overrightarrow{\underset{\_}{E1}}\left(\theta ,\varphi \right)-\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)•\text{exp}\left[j2\pi •\left(\text{cos}\left(\theta \right)•\Delta hr\right)\right]}{1-\text{exp}\left[j4\pi •\left(\text{cos}\left(\theta \right)•\Delta hr\right)\right]}$$

It may be that for the determination of the true field strength vector $\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)$

the radiant body 1 by a vehicle 14 with a radiation-exciting antenna arrangement 2nd is given and the vehicle 14 over a flat rotating stand 10th is arranged, which part of the horizontally oriented reflecting base 6 is and for the description of the electromagnetic field in the far point 11 a fictitious right-angled coordinate system 9 with the xy plane than with the rotation stand 10th connected reflective base 6 is introduced with the z-axis as the base normal, so that when the rotating stand rotates 10th with the vehicle 14 the vertical projection 18th the straight line connecting the pivot point of the rotating stand 10th and the distant entrance 11 on the xy plane forms the azimuth angle Φ with respect to the x axis and the angle θ between the connecting line and the base normal as the zenith angle θ opposite to the z axis and the true field strength vector $\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)$

from the field strength vectors $\stackrel{}{\underset{}{E}}$$\overrightarrow{\underset{\_}{1}}\left(\theta ,\varphi \right)$

measured on the vehicle standing on the revolving stand 14 and $\overrightarrow{\underset{\_}{E\mathrm{2nd}}}\left(\theta ,\varphi \right)$

measured by the above the revolving distance around the distance Δh with Δh / λ * cos ( θ ) <0.25 elevated vehicle in the distant point of impact 11 depending on the azimuth angle Φ and the zenith angle θ according to the following relationship for $\overrightarrow{\underset{\_}{E}}\left(\Phi ,\theta \right)$

is determined. $$\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)=\frac{\overrightarrow{\underset{\_}{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">E</figure-callout>}1}}\left(\theta ,\varphi \right)-\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)•\text{exp}\left[j\mathrm{2nd}\pi •\left(\text{cos}\left(\theta \right)•\Delta Hr\right)\right]}{1-\text{exp}\left[j\mathrm{4th}\pi •\left(\text{cos}\left(\theta \right)•\Delta Hr\right)\right]}$$

It may be that for field strength vector measurement for points 11 at adjustable zenith angles θ a field strength measuring device 15 at the end of one with the stationary part of the reflective base 6 rotatably connected vertically around the center of the rotating stand 10th swivel arm that is long enough to meet the far field conditions 21 is connected so that when setting the azimuth angle Φ by rotating the rotating stand 10th and setting the zenith angle θ by rotating the swivel arm 21 the first and second field strength vector measurements for all solid angles Φ and θ of the upper half space at a constant distance d all points 11 from the center of the revolving stand 10th are carried out.

können sowohl als dreidimensionale Vektoren in kartesischen Vektorkomponenten als auch vorteilhaft als Komponenten in Kugelkoordinaten ausgedrückt werden. Bei Messung in kartesischen Vektorkomponenten ist die Erfassung der Vektoren $\overrightarrow{\underset{\_}{E}}1\left(\theta ,\varphi \right)und\overrightarrow{\underset{\_}{E}}2\left(\theta ,\varphi \right)$

in jedem Aufpunkt 11 in den drei Richtungen x, y, z erforderlich. Der Vektor, den diese drei Komponenten-Messungen im kartesischen Koordinaten beschreibt, kann im System der Kugelkoordinaten- wie üblich - durch die Richtungskomponenten r in radialer Richtungen, der Komponente in Richtung des Zenitwinkels θ 25 und der Komponente in Richtung des Azimutwinkels Φ 26, beschrieben werden. Beide Formen bedingen einander und können ineinander übergeführt werden. Für die Messung der Vektoren $\overrightarrow{\underset{\_}{E}}1\left(\theta ,\varphi \right)und\overrightarrow{\underset{\_}{E}}2\left(\theta ,\varphi \right)$

im Fernfeld des strahlenden Körpers 1 existiert die radiale Vektor-Komponente nicht. Deshalb lässt sich die Messung im Fernfeld des strahlenden Körpers 1 mit Antenne 2 für jeden Aufpunkt 11 in ihrem Umfang reduzieren und kann jeweils auf die Messung der komplexen Komponenten Eθ in θ-Richtung und EΦ in Φ-Richtung beschränkt werden.The field strength vectors $\overrightarrow{\underset{\_}{E\left(\theta ,\varphi \right)}},\overrightarrow{\underset{\_}{E}}1\left(\theta ,\varphi \right)und\overrightarrow{\underset{\_}{E}}\mathrm{2nd}\left(\theta ,\varphi \right)$

can be expressed both as three-dimensional vectors in Cartesian vector components and advantageously as components in spherical coordinates. When measuring in Cartesian vector components, the detection of the vectors $\overrightarrow{\underset{\_}{E}}1\left(\theta ,\varphi \right)und\overrightarrow{\underset{\_}{E}}\mathrm{2nd}\left(\theta ,\varphi \right)$

at every point 11 required in the three directions x, y, z. The vector that describes these three component measurements in Cartesian coordinates can - as usual - in the system of spherical coordinates by the directional components r in radial directions, the component in the direction of the zenith angle θ 25th and the component in the direction of the azimuth angle Φ 26 , to be discribed. Both forms are mutually dependent and can be converted into one another. For the measurement of the vectors $\overrightarrow{\underset{\_}{E}}1\left(\theta ,\varphi \right)und\overrightarrow{\underset{\_}{E}}\mathrm{2nd}\left(\theta ,\varphi \right)$

in the far field of the radiant body 1 the radial vector component does not exist. Therefore, the measurement can be made in the far field of the radiating body 1 with antenna 2nd for every point 11 reduce in scope and can be limited to the measurement of the complex components Eθ in the θ direction and EΦ in the Φ direction.

die wahren Feldstärkevektoren $\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)$

also ohne Einfluss der reflektierenden Grundfläche 6 nach Gleichung 2 berechnet sind.It may be that to meet the far field condition for an onset 11 in solid angle Φ and θ the field strength vectors too close d from the vehicle 14 as a radiant body 1 are carried out in the two successive measurements over the entire upper half-space and the measured values are each converted using the near-field far-field transformation known per se and on the basis of these far-field field strength vectors $\underset{}{\stackrel{}{E}}$$\underset{\_}{\overrightarrow{1}}\left(\theta ,\varphi \right)\text{and}\overrightarrow{\underset{\_}{E\mathrm{2nd}}}\left(\theta ,\varphi \right)$

the true field strength vectors $\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)$

without the influence of the reflective base 6 are calculated according to equation 2.

The field strength measuring device can be used as a further possibility for measuring field strengths in the far field 15 be attached to a drone and this at the zenith angle θ and the azimuth angle Φ at a distance d be placed in the room. In this way, the field strength in the entire upper half space above the base 6 be measured by flying out.

daraus für alle Raumwinkel Φ, θ jeweils die Strahlungsdichten der sich im fernen Aufpunkt 11 ausbreitenden zirkularen RHCP-, LHCP- bzw. linear polarisierten- Teilwellen der Größe nach ermittelt sind und daraus die wahren Richtdiagramme des strahlenden Fahrzeugs 14 - also ohne Einfluss der reflektierenden Grundfläche 6 - für die Teilwellen berechnet sind.It may be that after determining the true field strength vector $\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)$

from it for all solid angles Φ, θ each the radiation densities in the distant point of incidence 11 propagating circular RHCP, LHCP or linearly polarized partial waves are determined in terms of size and from this the true directional diagrams of the radiating vehicle 14 - So without the influence of the reflective base 6 - are calculated for the partial waves.

mit dessen Phase bezogen auf einen Punkt in der Höhe h1 nach folgender Beziehung ermittelt ist: $$\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)=\frac{\underset{\_}{\overrightarrow{E1}}\left(\theta ,\varphi \right)•\text{exp}\left[j2\pi •\text{cos}\left(\theta \right)•h1/\lambda \right]-\underset{\_}{\overrightarrow{E2}}\left(\theta ,\varphi \right)•\text{exp}\left[j4\pi •\text{cos}\left(\theta \right)•\left(h1/\lambda +\Delta hr\right)\right]}{\text{exp}\left[j4\pi •\text{cos}\left(\theta \right)•h1/\lambda \right]-\text{exp}\left[j4\pi •\text{cos}\left(\theta \right)•\left(h1/\lambda +\Delta hr\right)\right]}$$

The vehicle may be at a vertical reference distance for a first measurement h1 is arranged above the reflecting base and at a vertical distance in the second measurement h2 = h1 + Δh raised and the true field strength vector $\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)$

with its phase related to a point in height h1 is determined according to the following relationship: $$\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)=\frac{\underset{\_}{\overrightarrow{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">E</figure-callout>}1}}\left(\theta ,\varphi \right)•\text{exp}\left[j\mathrm{2nd}\pi •\text{cos}\left(\theta \right)•\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">H</figure-callout>}1/\lambda \right]-\underset{\_}{\overrightarrow{E\mathrm{2nd}}}\left(\theta ,\varphi \right)•\text{exp}\left[j\mathrm{4th}\pi •\text{cos}\left(\theta \right)•\left(\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">H</figure-callout>}1/\lambda +\Delta Hr\right)\right]}{\text{exp}\left[j\mathrm{4th}\pi •\text{cos}\left(\theta \right)•\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">H</figure-callout>}1/\lambda \right]-\text{exp}\left[j\mathrm{4th}\pi •\text{cos}\left(\theta \right)•\left(\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">H</figure-callout>}1/\lambda +\Delta Hr\right)\right]}$$

It may be the vehicle 14 for the first measurement without increasing on the rotating stand 10th standing with a chosen vehicle center above the pivot point of the turning position 10th is placed and for carrying out the second measurement, for example using jacks, only in the direction of the surface normal (z-axis), i.e. without rotation, without tilting and without horizontal displacement in height around the route Δh is raised.

bzw. in Abhängikeit vom Raumwinkel Φ und θ $$\underset{\_}{\overrightarrow{E\left(\theta ,\varphi \right)}}=\left(\begin{array}{c}\underset{\_}{E_x\left(\theta ,\varphi \right)}\\ \underset{\_}{E_y\left(\theta ,\varphi \right)}\\ \underset{\_}{E_z\left(\theta ,\varphi \right)}\end{array}\right)=\left(\begin{array}{c}{E}_x\left(\theta ,\varphi \right)•exp\left(j{\phi }_x\left(\theta ,\varphi \right)\right)\\ E_y\left(\theta ,\varphi \right)•exp\left(j{\phi }_y\left(\theta ,\varphi \right)\right)\\ E_z\left(\theta ,\varphi \right)•exp\left(j{\phi }_z\left(\theta ,\varphi \right)\right)\end{array}\right)$$

It may be that the field strength vectors describe the radiation field as three-dimensional electrical field strength vectors, their mutually orthogonal spatial components (x, y, z) as complex amplitudes E _x , E _y , E _z with the phase angles φ _x , φ _y , φ _z are formed with the following representation for the true radiation field: $$\overrightarrow{\underset{\_}{E}}=\left(\begin{array}{c}\underset{\_}{E_x}\\ \underset{\_}{E_y}\\ \underset{\_}{E_{\mathrm{e.g.}}}\end{array}\right)=\left(\begin{array}{c}{E}_x•exp\left(j{\phi }_x\right)\\ E_y•exp\left(j{\phi }_y\right)\\ E_{\mathrm{e.g.}}•exp\left(j{\phi }_{\mathrm{e.g.}}\right)\end{array}\right)$$

or depending on the solid angle Φ and θ $$\underset{\_}{\overrightarrow{E\left(\theta ,\varphi \right)}}=\left(\begin{array}{c}\underset{\_}{E_x\left(\theta ,\varphi \right)}\\ \underset{\_}{E_y\left(\theta ,\varphi \right)}\\ \underset{\_}{E_{\mathrm{e.g.}}\left(\theta ,\varphi \right)}\end{array}\right)=\left(\begin{array}{c}{E}_x\left(\theta ,\varphi \right)•exp\left(j{\phi }_x\left(\theta ,\varphi \right)\right)\\ E_y\left(\theta ,\varphi \right)•exp\left(j{\phi }_y\left(\theta ,\varphi \right)\right)\\ E_{\mathrm{e.g.}}\left(\theta ,\varphi \right)•exp\left(j{\phi }_{\mathrm{e.g.}}\left(\theta ,\varphi \right)\right)\end{array}\right)$$

mit der Besonderheit, dass im Fernfeld einer strahlenden Antenne die radiale Komponente nicht existiert, sodass die Gleichung 5a für den wahren Vektor der elektrischen Feldstärke im Fernfeld in Kugelkoordinaten stets lautet: $$\underset{\_}{\overrightarrow{E\kappa \left(\theta ,\varphi \right)}}=\left(\begin{array}{c}0\\ \underset{\_}{E{\kappa }_{\theta }\left(\theta ,\varphi \right)}\\ \underset{\_}{E{\kappa }_{\varphi }\left(\theta ,\varphi \right)}\end{array}\right)=\left(\begin{array}{c}0\\ E{\kappa }_{\theta }\left(\theta ,\varphi \right)•exp\left(j\phi {\kappa }_{\theta }\left(\theta ,\varphi \right)\right)\\ E{\kappa }_{\varphi }\left(\theta ,\varphi \right)•exp\left(j\phi {\kappa }_{\varphi }\left(\theta ,\varphi \right)\right)\end{array}\right)$$

In the corresponding description of the vector in spherical coordinates, it can - as usual - by the directional components r in radial directions, the component in the direction of the zenith angle θ and the component in the direction of the azimuth angle Φ , to be discribed. Its components are with the addition K provided that the true vector in equation 5 in spherical coordinates with its complex components is now: $$\underset{\_}{\overrightarrow{E\kappa \left(\theta ,\varphi \right)}}=\left(\begin{array}{c}\underset{\_}{E{\kappa }_r\left(\theta ,\varphi \right)}\\ \underset{\_}{E{\kappa }_{\theta }\left(\theta ,\varphi \right)}\\ \underset{\_}{E{\kappa }_{\varphi }\left(\theta ,\varphi \right)}\end{array}\right)=\left(\begin{array}{c}E{\kappa }_r\left(\theta ,\varphi \right)•exp\left(j\phi {\kappa }_r\left(\theta ,\varphi \right)\right)\\ E{\kappa }_{\theta }\left(\theta ,\varphi \right)•exp\left(j\phi {\kappa }_{\theta }\left(\theta ,\varphi \right)\right)\\ E{\kappa }_{\varphi }\left(\theta ,\varphi \right)•exp\left(j\phi {\kappa }_{\varphi }\left(\theta ,\varphi \right)\right)\end{array}\right)$$

with the special feature that the radial component does not exist in the far field of a radiating antenna, so that equation 5a for the true vector of the electric field strength in the far field is always in spherical coordinates: $$\underset{\_}{\overrightarrow{E\kappa \left(\theta ,\varphi \right)}}=\left(\begin{array}{c}0\\ \underset{\_}{E{\kappa }_{\theta }\left(\theta ,\varphi \right)}\\ \underset{\_}{E{\kappa }_{\varphi }\left(\theta ,\varphi \right)}\end{array}\right)=\left(\begin{array}{c}0\\ E{\kappa }_{\theta }\left(\theta ,\varphi \right)•exp\left(j\phi {\kappa }_{\theta }\left(\theta ,\varphi \right)\right)\\ E{\kappa }_{\varphi }\left(\theta ,\varphi \right)•exp\left(j\phi {\kappa }_{\varphi }\left(\theta ,\varphi \right)\right)\end{array}\right)$$

bzw. in Abhängikeit vom Raumwinkel θ, Φ $$\underset{\_}{\overrightarrow{E1\left(\theta ,\varphi \right)}}=\left(\begin{array}{c}\underset{\_}{E{1}_x\left(\theta ,\varphi \right)}\\ \underset{\_}{E{1}_y\left(\theta ,\varphi \right)}\\ \underset{\_}{E{1}_z\left(\theta ,\varphi \right)}\end{array}\right)=\left(\begin{array}{c}E{1}_x\left(\theta ,\varphi \right)•exp\left(j\phi 1_x\left(\theta ,\varphi \right)\right)\\ E{1}_y\left(\theta ,\varphi \right)•exp\left(j\phi 1_y\left(\theta ,\varphi \right)\right)\\ E{1}_z\left(\theta ,\varphi \right)•exp\left(j\phi 1_z\left(\theta ,\varphi \right)\right)\end{array}\right)$$

in Analogie zu Gleichung 5a ergibt sich dieser Vektor ausgedrückt in Kugelkoordinaten: $$\underset{\_}{\overrightarrow{E1\kappa \left(\theta ,\varphi \right)}}=\left(\begin{array}{c}\underset{\_}{E1{\kappa }_x\left(\theta ,\varphi \right)}\\ \underset{\_}{E1{\kappa }_y\left(\theta ,\varphi \right)}\\ \underset{\_}{E1{\kappa }_z\left(\theta ,\varphi \right)}\end{array}\right)=\left(\begin{array}{c}E1{\kappa }_x\left(\theta ,\varphi \right)•exp\left(j\phi 1{\kappa }_x\left(\theta ,\varphi \right)\right)\\ E1{\kappa }_y\left(\theta ,\varphi \right)•exp\left(j\phi 1{\kappa }_y\left(\theta ,\varphi \right)\right)\\ E1{\kappa }_z\left(\theta ,\varphi \right)•exp\left(j\phi 1{\kappa }_z\left(\theta ,\varphi \right)\right)\end{array}\right)$$

It may be that in the first measurement according to the invention, the complex components of the electric field strength vectors as complex amplitudes E1 _x , E1 _y , E1 _z with the phase angles φ1 _x , φ1 _y , φ1 _z in the field strength measuring device 15 using short electrical antennas, the following are recorded: $$\underset{\_}{\overrightarrow{E1}}=\left(\begin{array}{c}\underset{\_}{E{1}_x}\\ \underset{\_}{E{1}_y}\\ \underset{\_}{E{1}_{\mathrm{e.g.}}}\end{array}\right)=\left(\begin{array}{c}E{1}_x•exp\left(j\phi 1_x\right)\\ E{1}_y•exp\left(j\phi 1_y\right)\\ E{1}_{\mathrm{e.g.}}•exp\left(j\phi 1_{\mathrm{e.g.}}\right)\end{array}\right);$$

or depending on the solid angle θ , Φ $$\underset{\_}{\overrightarrow{E1\left(\theta ,\varphi \right)}}=\left(\begin{array}{c}\underset{\_}{E{1}_x\left(\theta ,\varphi \right)}\\ \underset{\_}{E{1}_y\left(\theta ,\varphi \right)}\\ \underset{\_}{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">E</figure-callout>}{1}_{\mathrm{e.g.}}\left(\theta ,\varphi \right)}\end{array}\right)=\left(\begin{array}{c}E{1}_x\left(\theta ,\varphi \right)•exp\left(j\phi 1_x\left(\theta ,\varphi \right)\right)\\ E{1}_y\left(\theta ,\varphi \right)•exp\left(j\phi 1_y\left(\theta ,\varphi \right)\right)\\ \mathrm{<figure-callout\; id="1"\; label="E"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">E</figure-callout>}{1}_{\mathrm{e.g.}}\left(\theta ,\varphi \right)•exp\left(\mathrm{<figure-callout\; id="1"\; label="j\; \phi "\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">j\; </figure-callout>}\phi 1_{\mathrm{e.g.}}\left(\theta ,\varphi \right)\right)\end{array}\right)$$

in analogy to equation 5a, this vector is expressed in spherical coordinates: $$\underset{\_}{\overrightarrow{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">E</figure-callout>}1\kappa \left(\theta ,\varphi \right)}}=\left(\begin{array}{c}\underset{\_}{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">E</figure-callout>}1{\kappa }_x\left(\theta ,\varphi \right)}\\ \underset{\_}{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">E</figure-callout>}1{\kappa }_y\left(\theta ,\varphi \right)}\\ \underset{\_}{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">E</figure-callout>}1{\kappa }_{\mathrm{e.g.}}\left(\theta ,\varphi \right)}\end{array}\right)=\left(\begin{array}{c}\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">E</figure-callout>}1{\kappa }_x\left(\theta ,\varphi \right)•exp\left(\mathrm{<figure-callout\; id="1"\; label="j\; \phi "\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">j\; </figure-callout>}\phi 1{\kappa }_x\left(\theta ,\varphi \right)\right)\\ \mathrm{<figure-callout\; id="1"\; label="E"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">E</figure-callout>}1{\kappa }_y\left(\theta ,\varphi \right)•exp\left(\mathrm{<figure-callout\; id="1"\; label="j\; \phi "\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">j\; </figure-callout>}\phi 1{\kappa }_y\left(\theta ,\varphi \right)\right)\\ \mathrm{<figure-callout\; id="1"\; label="E"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">E</figure-callout>}1{\kappa }_{\mathrm{e.g.}}\left(\theta ,\varphi \right)•exp\left(\mathrm{<figure-callout\; id="1"\; label="j\; \phi "\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">j\; </figure-callout>}\phi 1{\kappa }_{\mathrm{e.g.}}\left(\theta ,\varphi \right)\right)\end{array}\right)$$

The first measurement will be at a large distance d is carried out, or if the measurement result is obtained from the near-field measurement with subsequent near-field-far-field transformation, so that the far-field condition is met in each case, then because of E1κ _r (θ, ϕ) = 0, the vector is detected on the θ component E1κ _θ (θ, ϕ) and Φ component E1κ _ϕ , (θ, ϕ) each reduced by amount and phase.

According to equation 7, the quantities in this equation for the second measurement of the vector in the three directions x, y, and z in Cartesian coordinates are as follows: $$\begin{array}{l}\underset{\_}{\overrightarrow{E\mathrm{2nd}\left(\theta ,\varphi \right)}},\underset{\_}{E{\mathrm{2nd}}_x\left(\theta ,\varphi \right)},\underset{\_}{E{\mathrm{2nd}}_y\left(\theta ,\varphi \right)},\underset{\_}{E{\mathrm{2nd}}_{\mathrm{e.g.}}\left(\theta ,\varphi \right)},E{\mathrm{2nd}}_x\left(\theta ,\varphi \right),E{\mathrm{2nd}}_y\left(\theta ,\varphi \right),E{\mathrm{2nd}}_{\mathrm{e.g.}}\left(\theta ,\varphi \right),\phi {\text{2nd}}_x\left(\theta ,\varphi \right),\\ \phi {\text{2nd}}_y\left(\theta ,\varphi \right),\phi {\text{2nd}}_{\mathrm{e.g.}}\left(\theta ,\varphi \right)\end{array}$$

According to equation 7a, the quantities in this equation for the second measurement of the vector in spherical coordinates are as follows: $$\begin{array}{l}\underset{\_}{\overrightarrow{E\mathrm{2nd}\kappa \left(\theta ,\varphi \right)}},\underset{\_}{E\mathrm{2nd}{\kappa }_r\left(\theta ,\varphi \right)},\underset{\_}{E\mathrm{2nd}{\kappa }_{\theta }\left(\theta ,\varphi \right)},\underset{\_}{E\mathrm{2nd}{\kappa }_{\varphi }\left(\theta ,\varphi \right)},E\mathrm{2nd}{\kappa }_r\left(\theta ,\varphi \right),E\mathrm{2nd}{\kappa }_{\theta }\left(\theta ,\varphi \right),E\mathrm{2nd}{\kappa }_{\varphi }\left(\theta ,\varphi \right),\\ \phi \text{2nd}{\kappa }_r\left(\theta ,\varphi \right),\phi \text{2nd}{\kappa }_{\theta }\left(\theta ,\varphi \right),\phi \text{2nd}{\kappa }_{\varphi }\left(\theta ,\varphi \right).\end{array}$$

Consequently, the second measurement is at a large distance d , or if the measurement result is obtained from the near-field measurement with subsequent near-field-far-field transformation, so that the far-field condition is fulfilled in each case that - because of E2κ _r (θ, ϕ) = 0 - the detection of the vector on the θ component E2κ _θ ( θ, ϕ) and Φ component E2κ _ϕ , (θ, ϕ) can be reduced depending on the amount and phase.

und $\underset{\_}{\overrightarrow{E2\kappa \left(\theta ,\varphi \right)}}$

einzusetzen, welche aus der an sich bekannten Nahfeld-Fernfeld-Transformation gewonnen sind.Are the two measurements according to the invention at a smaller distance d carried out for which the far field condition is not given, the corresponding far field vectors are in equations 1, 2, 3 $\underset{\_}{\overrightarrow{\mathrm{<figure-callout\; id="1"\; label="E"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">E</figure-callout>}1\kappa \left(\theta ,\varphi \right)}}$

and $\underset{\_}{\overrightarrow{E\mathrm{2nd}\kappa \left(\theta ,\varphi \right)}}$

use, which are obtained from the known near-field far-field transformation.

bzw. in Abhängikeit vom Raumwinkel Φ; θ $$\underset{\_}{\overrightarrow{H\left(\theta ,\varphi \right)}}=\left(\begin{array}{c}\underset{\_}{H_x\left(\theta ,\varphi \right)}\\ \underset{\_}{H_y\left(\theta ,\varphi \right)}\\ \underset{\_}{H_z\left(\theta ,\varphi \right)}\end{array}\right)=\left(\begin{array}{c}{H}_x\left(\theta ,\varphi \right)•exp\left(j{\psi }_x\left(\theta ,\varphi \right)\right)\\ H_y\left(\theta ,\varphi \right)•exp\left(j{\psi }_y\left(\theta ,\varphi \right)\right)\\ H_z\left(\theta ,\varphi \right)•exp\left(j{\psi }_z\left(\theta ,\varphi \right)\right)\end{array}\right);$$

• - Es kann sein, dass bei der ersten Messung die komplexen Komponenten der magnetischen Feldstärkevektoren als komplexe Amplituden H1_x , H1_y , H1_z mit den Phasenwinkeln ψ2_x, ψ2_x, ψ2_x in der Feldstärkemesseinrichtung 15 mit Hilfe elektrisch kleiner magnetischer Antennen, erfasst sind: $$\underset{\_}{\overrightarrow{H1}}=\left(\begin{array}{c}\underset{\_}{H{1}_x}\\ \underset{\_}{H{1}_y}\\ \underset{\_}{H{1}_z}\end{array}\right)=\left(\begin{array}{c}H{1}_x•exp\left(j\psi 1_x\right)\\ H{1}_y•exp\left(j\psi 1_y\right)\\ H{1}_z•exp\left(j\psi 1_z\right)\end{array}\right);$$
  
  beziehungsweise in Abhängigkeit vom Raumwinkel Φ, θ $$\underset{\_}{\overrightarrow{H1\left(\theta ,\varphi \right)}}=\left(\begin{array}{c}\underset{\_}{H{1}_x\left(\theta ,\varphi \right)}\\ \underset{\_}{H{1}_y\left(\theta ,\varphi \right)}\\ \underset{\_}{H{1}_z\left(\theta ,\varphi \right)}\end{array}\right)=\left(\begin{array}{c}H{1}_x\left(\theta ,\varphi \right)•exp\left(j\psi 1_x\left(\theta ,\varphi \right)\right)\\ H{1}_y\left(\theta ,\varphi \right)•exp\left(j\psi 1_y\left(\theta ,\varphi \right)\right)\\ H{1}_z\left(\theta ,\varphi \right)•exp\left(j\psi 1_z\left(\theta ,\varphi \right)\right)\end{array}\right);$$
  

It may be that the field strength vectors describe the radiation field as three-dimensional magnetic field strength vectors whose orthogonal spatial components (x, y, z) are formed as complex amplitudes H _x , H _y , H _z with the phase angles ψ2 _x , ψ2 _y , ψ2 _z with the following representation for the true radiation field: $$\overrightarrow{\underset{\_}{H}}=\left(\begin{array}{c}\underset{\_}{H_x}\\ \underset{\_}{H_y}\\ \underset{\_}{H_{\mathrm{e.g.}}}\end{array}\right)=\left(\begin{array}{c}{H}_x•exp\left(j{\psi }_x\right)\\ H_y•exp\left(j{\psi }_y\right)\\ H_{\mathrm{e.g.}}•exp\left(j{\psi }_{\mathrm{e.g.}}\right)\end{array}\right)$$

or depending on the solid angle Φ; θ $$\underset{\_}{\overrightarrow{H\left(\theta ,\varphi \right)}}=\left(\begin{array}{c}\underset{\_}{H_x\left(\theta ,\varphi \right)}\\ \underset{\_}{H_y\left(\theta ,\varphi \right)}\\ \underset{\_}{H_{\mathrm{e.g.}}\left(\theta ,\varphi \right)}\end{array}\right)=\left(\begin{array}{c}{H}_x\left(\theta ,\varphi \right)•exp\left(j{\psi }_x\left(\theta ,\varphi \right)\right)\\ H_y\left(\theta ,\varphi \right)•exp\left(j{\psi }_y\left(\theta ,\varphi \right)\right)\\ H_{\mathrm{e.g.}}\left(\theta ,\varphi \right)•exp\left(j{\psi }_{\mathrm{e.g.}}\left(\theta ,\varphi \right)\right)\end{array}\right);$$

• - It may be that in the first measurement the complex components of the magnetic field strength vectors as complex amplitudes H1 _x , H1 _y , H1 _z with the phase angles ψ2 _x , ψ2 _x , ψ2 _x in the field strength measuring device 15 with the help of electrically small magnetic antennas, the following are recorded: $$\underset{\_}{\overrightarrow{H1}}=\left(\begin{array}{c}\underset{\_}{H{1}_x}\\ \underset{\_}{H{1}_y}\\ \underset{\_}{H{1}_{\mathrm{e.g.}}}\end{array}\right)=\left(\begin{array}{c}H{1}_x•exp\left(j\psi 1_x\right)\\ H{1}_y•exp\left(j\psi 1_y\right)\\ H{1}_{\mathrm{e.g.}}•exp\left(j\psi 1_{\mathrm{e.g.}}\right)\end{array}\right);$$
  
  or depending on the solid angle Φ, θ $$\underset{\_}{\overrightarrow{H1\left(\theta ,\varphi \right)}}=\left(\begin{array}{c}\underset{\_}{H{1}_x\left(\theta ,\varphi \right)}\\ \underset{\_}{H{1}_y\left(\theta ,\varphi \right)}\\ \underset{\_}{H{1}_{\mathrm{e.g.}}\left(\theta ,\varphi \right)}\end{array}\right)=\left(\begin{array}{c}H{1}_x\left(\theta ,\varphi \right)•exp\left(j\psi 1_x\left(\theta ,\varphi \right)\right)\\ H{1}_y\left(\theta ,\varphi \right)•exp\left(j\psi 1_y\left(\theta ,\varphi \right)\right)\\ H{1}_{\mathrm{e.g.}}\left(\theta ,\varphi \right)•exp\left(j\psi 1_{\mathrm{e.g.}}\left(\theta ,\varphi \right)\right)\end{array}\right);$$
  

According to equation 7, the quantities for the second measurement are as follows: $\begin{array}{l}\underset{\_}{\overrightarrow{H\mathrm{2nd}\left(\theta ,\varphi \right)}},\underset{\_}{H{\mathrm{2nd}}_x\left(\theta ,\varphi \right)},\underset{\_}{H{\mathrm{2nd}}_y\left(\theta ,\varphi \right)},\underset{\_}{H{\mathrm{2nd}}_{\mathrm{e.g.}}\left(\theta ,\varphi \right)},\text{H}{\mathrm{2nd}}_x\left(\theta ,\varphi \right),H{\mathrm{2nd}}_y\left(\theta ,\varphi \right),H{\mathrm{2nd}}_{\mathrm{e.g.}}\left(\theta ,\varphi \right),\\ \psi {\mathrm{2nd}}_x\left(\theta ,\varphi \right),\psi {\mathrm{2nd}}_y\left(\theta ,\varphi \right),\psi {\mathrm{2nd}}_{\mathrm{e.g.}}\left(\theta ,\varphi \right).\end{array}$

In a similar analogous manner, the vectors in equations 5b, 7a and 7b can be described in spherical coordinates for the true magnetic field strength vector, but for the first and the second measurement with magnetic antennas by replacing the quantities E῾к and φк with Hк and ψк.

The description of a field strength vector can be done equivalently using different coordinate forms, since these can each be mathematically converted into one another. According to the invention, the field strength vectors from the first and the second measurement can in principle be used in different coordinate forms in equations 1, 2, 3 in order to determine the true field strength vector by calculation. For reasons of practicality in the measurements, however, the system with spherical coordinates, in general the Cartesian coordinates and the cylinder coordinates, is preferably recommended in the present context.

durch den entsprechenden Messwert $\underset{\_}{\overrightarrow{E2\left(\theta ,\varphi -\Delta \varphi \right)}}$

ersetzt ist.It may be the case that the radiating body increases / decreases 1 around Δhr an undesirable twisting of the radiating body 1 is given around the z-axis by the azimuth angle ΔΦ and this twist is corrected in that the Evaluation of equations 2 and 3 of expression $\underset{\_}{\overrightarrow{E\mathrm{2nd}\left(\theta ,\varphi \right)}}$

by the corresponding measured value $\underset{\_}{\overrightarrow{E\mathrm{2nd}\left(\theta ,\varphi -\Delta \varphi \right)}}$

is replaced.

durch den entsprechend korrigierten Messwert $\underset{\_}{\overrightarrow{E2corr}}$

ersetzt ist.It may be the case that the radiating body increases / decreases 1 around Δhr an undesirable per se for the reflective base 6 parallel displacement of the radiating body 1 with antenna device 2nd around Δx and or Δy is given and this shift is corrected by the expression for evaluating equations 2 and 3 $\underset{\_}{\overrightarrow{E\mathrm{2nd}\left(\theta ,\varphi \right)}}$

by the correspondingly corrected measured value $\underset{\_}{\overrightarrow{E\mathrm{2nd}cOrr}}$

is replaced.

anstelle des elektrischen Feldstärkevektors $\underset{\_}{\overrightarrow{E}}$

der mit diesem in Zusammenhang stehenden magnetischen Feldstärkevektor $\underset{\_}{\overrightarrow{H}}$

nach den beispielhaft angegebenen obigen Definitionen dadurch ermittelt ist, dass die Vektoren $\underset{\_}{\overrightarrow{E1}},\underset{\_}{\overrightarrow{E2}}$

in den Gleichungen 2 und 3 durch die entsprechenden Vektoren $\underset{\_}{\overrightarrow{H1}},\underset{\_}{\overrightarrow{H2}}$

in den Gleichungen 1, 2, 3 ersetzt sind, sodass die zitierten mathematischen Beziehungen nunmehr, wie folgt, lauten: $$\underset{\_}{\overrightarrow{H}}=\frac{\underset{\_}{\overrightarrow{H1}}-\underset{\_}{\overrightarrow{H2}}·\text{exp}\left[j2\pi ·\left(\text{cos}\left(\theta \right)·\Delta hr\right)\right]}{1-\text{exp}\left[j4\pi ·\left(\text{cos}\left(\theta \right)·\Delta hr\right)\right]}$$

bzw. $$\underset{\_}{\overrightarrow{H}}\left(\theta ,\varphi \right)=\frac{\underset{\_}{\overrightarrow{H1}}\left(\theta ,\varphi \right)-\underset{\_}{\overrightarrow{H2}}\left(\theta ,\varphi \right)·\text{exp}\left[j2\pi ·\left(\text{cos}\left(\theta \right)·\Delta hr\right)\right]}{1-\text{exp}\left[j4\pi ·\left(\text{cos}\left(\theta \right)·\Delta hr\right)\right]}$$

It may be that in the relationships given for $\underset{\_}{\overrightarrow{E}}$

instead of the electric field strength vector $\underset{\_}{\overrightarrow{E}}$

the magnetic field strength vector associated with this $\underset{\_}{\overrightarrow{H}}$

is determined according to the definitions given above by way of example in that the vectors $\underset{}{\stackrel{}{E}}$$\underset{\_}{\overrightarrow{1}},\underset{\_}{\overrightarrow{E\mathrm{2nd}}}$

in equations 2 and 3 by the corresponding vectors $\underset{}{\stackrel{}{H}}$$\underset{\_}{\overrightarrow{1}},\underset{\_}{\overrightarrow{H\mathrm{2nd}}}$

in equations 1, 2, 3 are replaced, so that the cited mathematical relationships are now as follows: $$\underset{\_}{\overrightarrow{H}}=\frac{\underset{\_}{\overrightarrow{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">H</figure-callout>}1}}-\underset{\_}{\overrightarrow{H\mathrm{2nd}}}·\text{exp}\left[j\mathrm{2nd}\pi ·\left(\text{cos}\left(\theta \right)·\Delta Hr\right)\right]}{1-\text{exp}\left[j\mathrm{4th}\pi ·\left(\text{cos}\left(\theta \right)·\Delta Hr\right)\right]}$$

respectively. $$\underset{\_}{\overrightarrow{H}}\left(\theta ,\varphi \right)=\frac{\underset{\_}{\overrightarrow{\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">H</figure-callout>}1}}\left(\theta ,\varphi \right)-\underset{\_}{\overrightarrow{H\mathrm{2nd}}}\left(\theta ,\varphi \right)·\text{exp}\left[j\mathrm{2nd}\pi ·\left(\text{cos}\left(\theta \right)·\Delta Hr\right)\right]}{1-\text{exp}\left[j\mathrm{4th}\pi ·\left(\text{cos}\left(\theta \right)·\Delta Hr\right)\right]}$$

After the first measurement of the θ component of the electric field strength in spherical coordinates in the far field according to the amount E1κ _θ ( θ , ϕ) and phase φ1κ _θ ( θ , ϕ) and the Φ component according to the amount E1κ _ϕ ( θ , ϕ) and phase φ1κ _ϕ ( θ , ϕ) and after the second measurement of the θ component of the electric field strength in the far field according to the amount E2κ _θ ( θ , ϕ) and phase φ2κ _θ ( θ , ϕ) and the Φ component according to the amount E2κ _ϕ ( θ , ϕ) and phase φ2κ _ϕ ( θ , ϕ) the true electric field strength can be exemplified in spherical coordinates for the solid angle θ , Φ are given as follows: $$\underset{\_}{\overrightarrow{E\kappa \left(\theta ,\varphi \right)}}=\frac{1}{1-\text{exp}\left[j\mathrm{4th}\pi ·\left(\text{cos}\left(\theta \right)·\Delta Hr\right)\right]}\left(\begin{array}{c}0\\ \mathrm{<figure-callout\; id="1"\; label="E"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">E</figure-callout>}1{\kappa }_{\theta }\left(\theta ,\varphi \right)·\text{exp}\left(\mathrm{<figure-callout\; id="1"\; label="j\; \phi "\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">j\; </figure-callout>}\phi 1{\kappa }_{\theta }\left(\theta ,\varphi \right)\right)-E\mathrm{2nd}{\kappa }_{\theta }\left(\theta ,\varphi \right)·\text{exp}\left(j·(\phi \mathrm{2nd}{\kappa }_{\theta }\left(\theta ,\varphi \right)+\mathrm{2nd}\pi ·\text{cos}\left(\theta \right)·\Delta Hr\right)\\ \mathrm{<figure-callout\; id="1"\; label="E"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">E</figure-callout>}1{\kappa }_{\varphi }\left(\theta ,\varphi \right)·\text{exp}\left(\mathrm{<figure-callout\; id="1"\; label="j\; \phi "\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">j\; </figure-callout>}\phi 1{\kappa }_{\varphi }\left(\theta ,\varphi \right)\right)-E\mathrm{2nd}{\kappa }_{\varphi }\left(\theta ,\varphi \right)·\text{exp}\left(j·(\phi \mathrm{2nd}{\kappa }_{\varphi }\left(\theta ,\varphi \right)+\mathrm{2nd}\pi ·\text{cos}\left(\theta \right)·\Delta Hr\right)\end{array}\right)$$

beispielhaft in Kugelkoordinaten für den Raumwinkel θ, Φ wie folgt angegeben werden kann: $$\underset{\_}{\overrightarrow{H\kappa \left(\theta ,\varphi \right)}}=\frac{1}{1-\text{exp}\left[j4\pi ·\left(\text{cos}\left(\theta \right)·\Delta hr\right)\right]}\left(\begin{array}{c}0\\ H1{\kappa }_{\theta }\left(\theta ,\varphi \right)·\text{exp}\left(j\psi 1{\kappa }_{\theta }\left(\theta ,\varphi \right)\right)-H2{\kappa }_{\theta }\left(\theta ,\varphi \right)·\text{exp}\left(j·(\psi 2{\kappa }_{\theta }\left(\theta ,\varphi \right)+2\pi ·\text{cos}\left(\theta \right)·\Delta hr\right)\\ H1{\kappa }_{\varphi }\left(\theta ,\varphi \right)·\text{exp}\left(j\psi 1{\kappa }_{\varphi }\left(\theta ,\varphi \right)\right)-H2{\kappa }_{\varphi }\left(\theta ,\varphi \right)·\text{exp}\left(j·(\psi 2{\kappa }_{\varphi }\left(\theta ,\varphi \right)+2\pi ·\text{cos}\left(\theta \right)·\Delta hr\right)\end{array}\right)$$

In a complete analogy, the true vector for the magnetic field is related to the fact that after the first measurement of the θ component of the magnetic field strength in the far field according to the amount H1κ _θ (θ, ϕ) and phase ψ1κ _θ (θ, ϕ) and the Φ component according to the amount K1κ _ϕ (θ, ϕ) and phase ψ1κ _ϕ (θ, ϕ) and after the second measurement of the θ component of the magnetic field strength in the far field according to the amount H2κ _θ (θ, ϕ) and phase ψ2κ _θ (θ, ϕ) and the Φ component according to the amount H2κ _ϕ (θ, ϕ) and phase ψ2κ _ϕ (θ, ϕ) the true magnetic field strength $\underset{\_}{\overrightarrow{E}}$

exemplary in spherical coordinates for the solid angle θ , Φ can be specified as follows: $$\underset{\_}{\overrightarrow{H\kappa \left(\theta ,\varphi \right)}}=\frac{1}{1-\text{exp}\left[j\mathrm{4th}\pi ·\left(\text{cos}\left(\theta \right)·\Delta Hr\right)\right]}\left(\begin{array}{c}0\\ \mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">H</figure-callout>}1{\kappa }_{\theta }\left(\theta ,\varphi \right)·\text{exp}\left(\mathrm{<figure-callout\; id="1"\; label="j\; \psi "\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">j\; </figure-callout>}\psi 1{\kappa }_{\theta }\left(\theta ,\varphi \right)\right)-H\mathrm{2nd}{\kappa }_{\theta }\left(\theta ,\varphi \right)·\text{exp}\left(j·(\psi \mathrm{2nd}{\kappa }_{\theta }\left(\theta ,\varphi \right)+\mathrm{2nd}\pi ·\text{cos}\left(\theta \right)·\Delta Hr\right)\\ \mathrm{<figure-callout\; id="1"\; label="H"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">H</figure-callout>}1{\kappa }_{\varphi }\left(\theta ,\varphi \right)·\text{exp}\left(\mathrm{<figure-callout\; id="1"\; label="j\; \psi "\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">j\; </figure-callout>}\psi 1{\kappa }_{\varphi }\left(\theta ,\varphi \right)\right)-H\mathrm{2nd}{\kappa }_{\varphi }\left(\theta ,\varphi \right)·\text{exp}\left(j·(\psi \mathrm{2nd}{\kappa }_{\varphi }\left(\theta ,\varphi \right)+\mathrm{2nd}\pi ·\text{cos}\left(\theta \right)·\Delta Hr\right)\end{array}\right)$$

jeweils ein Signalvektor $\underset{\_}{\overrightarrow{S}}1\left(\theta ,\varphi \right)\text{ und }\underset{\_}{\overrightarrow{S}}2\left(\theta ,\varphi \right)$

ermittelt ist und in Analogie aus Gleichung 2 der wahre Signalvektor $\underset{\_}{\overrightarrow{S}}\left(\theta ,\varphi \right)$

für den Raumwinkel θ, Φ, wie folgt, ermittelt ist. $$\underset{\_}{\overrightarrow{S}}\left(\theta ,\varphi \right)=\frac{\underset{\_}{\overrightarrow{S1}}\left(\theta ,\varphi \right)-\underset{\_}{\overrightarrow{S2}}\left(\theta ,\varphi \right)·\text{exp}\left[j2\pi ·\left(\text{cos}\left(\theta \right)·\Delta hr\right)\right]}{1-\text{exp}\left[j4\pi ·\left(\text{cos}\left(\theta \right)·\Delta hr\right)\right]}$$

It may be that the directional diagram of the radiating body 1 with antenna device 2nd is determined in such a way that the antenna device for carrying out the measurements according to the invention 2nd as the receiving antenna and the measuring antenna 3rd as a transmitting antenna 3rd is designed and by measuring the transmission factor according to amount and phase when sending out the respective polarization, based on Cartesian coordinates in the x, y, z direction or based on cylinder coordinates in the θ and ϕ direction, a first measurement according to the invention with the radiant body 1 at the first height h1 and a second measurement according to the invention in the second height h2 = h1 + Δh is carried out and from the polarization-related received signals of the antenna arrangement 2nd in analogy to the described field strength vectors E1 (θ, ϕ) and $\underset{\_}{\overrightarrow{E}}\mathrm{2nd}\left(\theta ,\varphi \right)$

one signal vector each $\underset{\_}{\overrightarrow{S}}1\left(\theta ,\varphi \right)\text{and}\underset{\_}{\overrightarrow{S}}\mathrm{2nd}\left(\theta ,\varphi \right)$

is determined and in analogy from equation 2 the true signal vector $\underset{\_}{\overrightarrow{S}}\left(\theta ,\varphi \right)$

for the solid angle θ, Φ is determined as follows. $$\underset{\_}{\overrightarrow{S}}\left(\theta ,\varphi \right)=\frac{\underset{\_}{\overrightarrow{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">S</figure-callout>}1}}\left(\theta ,\varphi \right)-\underset{\_}{\overrightarrow{S\mathrm{2nd}}}\left(\theta ,\varphi \right)·\text{exp}\left[j\mathrm{2nd}\pi ·\left(\text{cos}\left(\theta \right)·\Delta Hr\right)\right]}{1-\text{exp}\left[j\mathrm{4th}\pi ·\left(\text{cos}\left(\theta \right)·\Delta Hr\right)\right]}$$

• 1: Messung des räumlichen komplexen Feldstärkevektors in einem fernen Aufpunkt 11 zu einem über einer reflektierenden Grundfläche 6 strahlenden Körper 1 anhand einer Feldstärkemesseinrichtung 15 zur gesonderten Feststellung der komplexen elektrischen bzw magnetischen Komponenten des Feldstärkevektors bzw mit einer in der Regel nur schwach strahlungsbündelnden Messantenne 3. Die Anregung der elektromagnetischen Strahlung ist durch eine auf dem strahlenden Körper 1- hier auf einem Fahrzeug 14 - befindlichen Antennenanordnung 2 gegeben. Das Fahrzeug 14 ist über einer reflektierenden Grundfläche 6 angeordnet, wodurch sich neben dem direkten Strahlengang mit Sichtverbindung 4 und dem am strahlenden Körper 1 gebeugten Strahlengang 5 zusätzlich der an der reflektierenden Grundfläche reflektierte Strahlengang 7 ausbildet. Die beschriebenen Strahlengänge beschreiben repräsentativ alle Strahlengänge, welche vom gesamten Fahrzeug entweder direkt, gebeugt oder reflektiert auf der reflektierenden Grundfläche 6 den entfernten Aufpunkt 11 erreichen. Die beschriebenen Strahlengänge sind im weit entfernten Aufpunkt 11 - also im Fernfeld des strahlenden Körpers 1 - als zueinander parallel angenommen. Aufgrund des Beitrags der an der reflektierenden Grundfläche 6 reflektierten Strahlung zu dem im Aufpunkt 11 gemessenen Feldstärkevektor kann aus diesen Messungen der wahre Feldstärkenvektor des strahlenden Körpers 1, d. h. des Fahrzeugs 14 nicht ermittelt werden. Eine Messung an dem im Raum schwebenden Fahrzeug 14 ist nicht möglich. Um die Strahlengänge 7 der einfachen Reflexion am Boden aus der Charakteristik zu eliminieren wird nun das Fahrzeug jeweils auf zwei unterschiedlichen Höhen über dem reflektierenden Boden vermessen. Dazu ist wichtig, dass abgesehen von der Höhe die Position möglichst exakt dieselbe ist (d.h. ein Längen/Breitenversatz muss deutlich kleiner als 1/10 der Wellenlänge sein). Dieses kann z.B. über Wagenheber bewerkstelligt werden. Auch muss die Höhe des Fahrzeuges dann ebenfalls auf diesen Wert genau eingestellt oder nachträglich gemessen sein. Bei hinreichend großem Abstand d des Aufpunkts 11 vom strahlenden Körper 1 erscheint der auf Aufpunkt 11 vom Fahrzeug aus unter dem Zenitwinkel θ gegenüber der Grundflächenorthogonalen 19. Nach einer ersten Messung des Feldstärkevektors im Aufpunkt 11- wie dargestellt - und einer zweiten Messung in Aufpunkt 11 nach Verschiebung des strahlenden Körpers 1 in Richtung der Flächennormalen um eine Strecke Δh kann erfindungsgemäß der wahre Feldstärkevektor des im Raum schwebenden strahlenden Körpers 1 mit Formel 1 ermittelt werden. Die Methode ermöglicht somit auch die Erfassung des an der Grundfläche 6 reflektierten Beitrags zum Feldstärkevektor im Aufpunkt 11. Aus diesem Beitrag lassen sich unter anderem der Beitrag zur Strahlungsdichte sowie der Einfluss auf die Polarisation des Feldstärkevektors mit seinem Einfluss auf die Kreuzpolarisation bei Zirkularpolarisation ermitteln. Bei nicht vollkommen elektrischer Leitfähigkeit der Grundfläche 6 werden die dort reflektierten Strahlen abhängig von der Bodenbeschaffenheit unter einem komplexen Reflexionsfaktor r reflektiert, wodurch die Raumkomponenten der reflektierten Strahlen unterschiedliche Dämpfung und unterschiedliche Verschiebungen in ihrer Phase unter Beibehaltung der Geometrie der Ausbreitung erfahren. Aus dem Beitrag der reflektierten Strahlung kann somit auch ein gewisser Rückschluss auf die Bodenbeschaffenheit erfolgen. Für einen Vergleich der wahren Feldstärkevektoren in Betrag und den Phasenbeziehungen untereinander in unterschiedlichen Aufpunkten 11 unter unterschiedlichen Zenitwinkeln θ ist es notwendig, den Abstand d von einem, dem strahlenden Körper 1 nahen gemeinsamen Bezugspunkt für alle Messungen und die Höhenverschiebung um Δh für alle zweiten Messungen nach der Erfindung strikt einzuhalten. Alle Phasenbeziehungen sind dann auf diesen Bezugspunkt bezogen, sodass dieser vorteilhaft auf der reflektierenden Grundfläche 6 gewählt ist.
• 2: Zur Definition der Position des strahlenden Körpers 1, also hier des Fahrzeugs 14 ist ein rechtwinkliges Koordinatensystem 9 eingeführt, dessen x-y-Ebene mit der reflektierenden Grundfläche zusammenfällt und die z-Achse zur Grundflächenorthogonalen 19 parallel orientiert ist. Zur Beschreibung der Richtwirkung des strahlenden Körpers 1 ist in der Anordnung wie in 1 der Verbindungsgeraden zwischen dem Ursprung des Koordinatensystems und dem Aufpunkt 11 der Zenitwinkel θ zur z-Achse und der azimutale Winkel Φ zwischen der vertikalen Projektion der Verbindungsgeraden auf die x-y-Ebene und der x-Achse zugewiesen. Der räumliche Einheitsvektor $\overrightarrow{r}e$
  
  17 in Ausbreitungsrichtung Φ und θ der Strahlung ist somit durch den Zenitwinkel θ und den Azimutwinkel Φ bestimmt.
• 3: Einrichtung zur Messung des Feldstärkevektors für eine erste Messung nach der Erfindung mit dem Ziel der rechnerischen Ermittlung des wahren Richtdiagramms eines Fahrzeugs 14 Räumliche Vermessung des Strahlungsfeldes des Fahrzeugs 14 mit Antenneneinrichtung 2 wie in 1 und 2 jedoch auf einem Drehstand 10 als Teil der reflektierenden Grundfläche 6. Der Zenitwinkel θ ist durch einen mit Drehpunkt im Ursprung des Koordinatensystems und um diesen vertikal drehbaren Schwenkarm 21 eingestellt, dessen entferntes Ende die Position des Aufpunkts 11 mit der Feldstärkemesseinrichtung 15 und der Messantenne 3 beschreibt. Die x-y-Ebene ist mit dem Drehstand 10 und somit mit der azimutalen Ausrichtung des Fahrzeugs 14 fest verbunden. Die Einstellung des Azimutwinkels Φ ist somit durch die Dreheinstellung des Drehstands 10 gegeben. Damit ist gewährleistet, dass der Abstand d des Aufpunkts 11 vom Ursprung des Koordinatensystems unabhängig vom Raumwinkel θ, Φ ist und die gemessenen Phasenwerte des Feldstärkevektors für alle Raumwinkel θ, Φ in unverfälschtem Bezug zueinander erfasst sind. Alle Phasenwerte sind somit auf den Ursprung des Koordinatensystems bezogen. Erfindungsgemäß ist die Ermittlung des Feldstärkevektors im Fernfeld des strahlenden Körpers 1 Voraussetzung. Bei zu kleiner Länge des Schwenkarm 21 ist die Fernfeldbedingung im Aufpunkt 11 nicht erfüllt und es ist demnach die Umrechnung der dort gemessenen Feldstärkevektoren in Vektoren die sich im Fernfeld ergeben würden notwendig. Hierzu ist die Vermessung der Feldstärkevektoren über den gesamten oberen Halbraum in konstantem Abstand vom Ursprung des Koordinatensystems für alle Raumwinkel Φ, θ und deren anschließende Umrechnung mithilfe der an sich bekannten Nahfeld-Fernfeld-Transformation vorgesehen. Die reflektierende Grundfläche ist dabei mit zu berücksichtigen, indem zum Beispiel der untere Halbraum mit Hilfe des an sich bekannten Spiegelungsprinzips mit in die Nahfeld-Fernfeld-Transformation einbezogen wird. Zur Durchführung der erfindungsgemäßen ersten Messung des Fernfeld-Feldstärkevektors im Raumwinkel θ, Φ befindet sich das Fahrzeug mit seiner strahlenden Karosserie beispielhaft in der Höhe h1 über der reflektierenden Grundfläche 6. Es entsteht somit jeweils für die eingestellte Höhe h1 und h2 eine komplexe Richtcharakteristik für die Feldstärkevektoren $\underset{\_}{\overrightarrow{E1\left(\theta ,\varphi \right)}}\text{ und }\underset{\_}{\overrightarrow{E2\left(\theta ,\varphi \right)}}$
  
  aus der ersten und zweiten Messung für die Berechnung des wahren Feldstärkevektors $\underset{\_}{\overrightarrow{E\left(\theta ,\varphi \right)}}.$
  
  Häufig reicht die Länge des Schwenkarms 21 nicht aus um im Aufpunkt 11 die Fernfeldbedingung zu erfüllen. Für die deshalb notwendige Durchführung der nach Feld-Fernfeld-Transformation erhält man daraus für die zwei Höhen h1 und h 2 im Fernfeld jeweils die für die Berechnung des wahren Feldes $\underset{\_}{\overrightarrow{E\left(\theta ,\varphi \right)}}$
  
  notwendige vektorielle Fernfeld-Richtcharakteristiken $\underset{\_}{\overrightarrow{E1\left(\theta ,\varphi \right)}}\text{ und }\underset{\_}{\overrightarrow{E2\left(\theta ,\varphi \right)}}.$
  
• 4: Einrichtung zur Messung des Feldstärkevektors wie in 5 für die Durchführung einer zweiten Messung nach der Erfindung für die rechnerische Ermittlung des wahren Richtdiagramms aus der ersten und zweiten Messung. Zur Durchführung der zweiten Messung ist das Fahrzeug ausgehend von der beispielhaften Aufbauhöhe h1 in 3 um den Höhenunterschied um Δh/λ*cos(θ) = Δhr* cos(θ) < 0,25 verdrehungsfrei und verschiebungsfrei in Bezug auf die Koordinaten x und y, also ausschließlich in Richtung der vertikalen Achse z verschoben. In einfacher Durchführung dieser Anhebung sind beispielhaft Wagenheber 16 eingesetzt.
• 5: Zeigt die gleiche Einrichtung wie in 4, jedoch zur ersten Messung nach der Erfindung des Feldstärkevektors nach der Erfindung mit einem mit der Karosserie in der Höhe h1 über dem Drehstand 10 aufgebautem Fahrzeug 14. Bei Anhebung des Fahrzeugs 14 auf die in der Figur nicht dargestellte Höhe h2 = h1+ Δh/λ kann die zweite erfindungsgemäße Messung der Feldstärkevektoren im Aufpunkt 11 durchgeführt sein, woraus aus beiden Messungen die wahre Feldstärke berechnet ist. Zur Erreichung hinreichend genauer Ergebnisse sind die Höhen h1 bzw. h2 hinreichend klein im Vergleich zum Abstand d zwischen dem Ursprung des Koordinatensystems und dem Aufpunkt 11, welcher durch die Länge des Schwenkarms 21 gegeben ist.
• 6: Erläuterung der Wirkungsweise der Erfindung ist die Strahlungswirkung des strahlenden Körpers 1 am Beispiel des Fahrzeugs 14 mit der die Strahlung erregenden Antennenanordnung 2. Zur Visualisierung der aufgrund der Oberflächenströme strahlenden Flächenelemente auf der elektrisch leitenden Fahrzeughaut ist diese nach der Methode der finiten Elemente mit einer Gitterstruktur 22 belegt. Der auf jedem Element fließende Oberflächenstrom kann - bewertet mit der Ausdehnung des Elements - zu einem Strommoment 24 im Zentrum zusammengefasst betrachtet werden, sodass das Strommoment J 24 nach Stromrichtung und räumlicher Lage des Gitterelements 8 einen komplexen räumlichen Vektor $\underset{\_}{\overrightarrow{J}}$
  
  mit den komplexen räumlichen Komponenten J_x , J_y ,J_z einen gerichteten Elementarstrahler in Zentrum des Gitterelements mit der Position p_x , p_y , p_z im Koordinatensystems bildet. Die Strahlung dieser Elementarstrahler des strahlenden Körpers 1 sowie die Strahlung der Antennenanordnung 2 selbst überlagert sich mit Bezug auf den Einheitsvektor $\overrightarrow{r}e$
  
  17 in Ausbreitungsrichtung im Aufpunkt 11 zum dort gemessenen Feldstärkevektor. Die fundamentale Wirkungsweise der vorliegenden Erfindung geht davon aus, dass der strahlende Körper 1 durch die erregende Antennenanordnung 2 Oberflächenströme führt, welche die Strahlungseigenschaften, wie das Richtdiagramm und die Polarisation der Strahlung beeinflussen. Bei der Strahlungsvermessung des grundflächennahen strahlenden Körpers 1 im Aufpunkt 11- wie in 1 - ist erfindungsgemäß vorausgesetzt, dass die Verteilung der Oberflächenströme von der Nachbarschaftswirkung der reflektierenden Grundfläche 6 praktisch nicht beeinflusst ist. Die Stromverteilung auf dem strahlenden Körper 1 wird somit für die erste Messung in der Höhe h1 und der um Δh veränderten zweiten Messung in der Höhe h2 als ausschließlich von der strahlungserregenden Antennenanordnung 2 hervorgerufen. Diese Bedingung ist für die wesentlichen Anwendungen in der Praxis mit hinreichender Genauigkeit erfüllt. Dies ist insbesondere dann der Fall, wenn die Antennenanordnung 2 in dem der Grundfläche 6 abgewandten Teil des strahlenden Körpers 1 platziert ist. Beim Vergleich der Ergebnisse für den wahren Feldstärkevektor $\underset{\_}{\overrightarrow{E}}$
  
  im unter verschiedenen Zenitwinkeln θ im jeweiligen Aufpunkt 11 ist die genaue Einhaltung des Abstands d von einem unveränderten Bezugspunkt notwendig. Aus den Amplituden und den unterschiedlichen Phasen der Komponenten des berechneten wahren Feldstärkevektors zueinander kann das elektromagnetische Feld im Aufpunkt 11 in Teilwellen, d.h. insbesondere in eine linksdrehende elektromagnetischen Welle (LHCP) und eine rechtsdrehende elektromagnetische Welle (RHCP) zerlegt werden. Bei der Vermessung des oberen Halbraums in den 2 und 5 ergeben sich daraus die räumlichen Gewinnfunktionen für beide Drehrichtungen sowie die Kreuzpolarisation des wahren sich ausbreitenden elektromagnetischen Feldes $\overrightarrow{E}.$
  
  Bezüglich der Wahl der Höhenveränderung um Δh für die erste und die zweite Messung nach der Erfindung ist bezüglich der Eindeutigkeit der Ergebnisse die Einhaltung der Bedingung Δhr*cos(θ) = Δh/λ* cos(θ) < 0,25 notwendig. Dieses ist bei Erweiterung des Bruchs in Formel (1) um den negativen Phasenfaktor von exp(i2π*(cos(θ)* Δhr) offensichtlich, wodurch der Nenner in den Negativwert von 2i*sin(2π*(cos(θ)* Δhr) übergeht.

The invention is explained in more detail below on the basis of exemplary embodiments. The associated figures show in detail:

• 1 : Measurement of the spatial complex field strength vector at a distant point 11 to one over a reflective base 6 radiant body 1 using a field strength measuring device 15 for the separate determination of the complex electrical or magnetic components of the field strength vector or with a measuring antenna which generally only weakly bundles radiation 3rd . The excitation of the electromagnetic radiation is due to a radiation on the radiating body 1- here on a vehicle 14 - Located antenna arrangement 2nd given. The vehicle 14 is over a reflective base 6 arranged, which is next to the direct beam path with line of sight 4th and that on the radiant body 1 diffracted beam path 5 additionally the beam path reflected on the reflecting base 7 trains. The beam paths described representatively describe all beam paths which are either direct, diffracted or reflected by the entire vehicle on the reflecting base area 6 the distant onset 11 to reach. The beam paths described are at a far distant point of focus 11 - So in the far field of the radiating body 1 - assumed to be parallel to each other. Due to the contribution of the reflective base 6 reflected radiation to that at the point of impact 11 Measured field strength vector can be the true field strength vector of the radiating body from these measurements 1 , ie the vehicle 14 cannot be determined. A measurement on the vehicle floating in the room 14 can not. To the ray paths 7 To eliminate the simple reflection on the ground from the characteristics, the vehicle is now measured at two different heights above the reflecting ground. It is important that, apart from the height, the position is as exact as possible (ie a length / width offset must be significantly less than 1/10 of the wavelength). This can be done using jacks, for example. The height of the vehicle must then also be set exactly to this value or measured subsequently. With a sufficiently large distance d of the rise 11 from the radiant body 1 appears on the onset 11 from the vehicle at the zenith angle θ compared to the base orthogonal 19th . After a first measurement of the field strength vector at point 11 - as shown - and a second measurement at point 11 after moving the radiating body 1 towards the surface normal by a distance Δh can according to the invention the true field strength vector of the radiating body floating in space 1 can be determined with Formula 1. The method thus also enables the detection of the base area 6 reflected contribution to the field strength vector in Aufpunkt 11 . From this contribution, among other things, the contribution to the radiation density and the influence on the polarization of the field strength vector with its influence on the cross polarization with circular polarization can be determined. If the base surface is not completely electrical 6 the rays reflected there become dependent on the nature of the soil under a complex reflection factor r reflected, whereby the spatial components of the reflected rays experience different attenuation and different shifts in their phase while maintaining the geometry of the propagation. The contribution of the reflected radiation can thus also be used to draw a certain conclusion about the nature of the soil. For a comparison of the true field strength vectors in magnitude and the phase relationships with one another in different points 11 at different zenith angles θ it is necessary to distance d from one, the radiant body 1 close common reference point for all measurements and the height shift around Δh to be strictly observed for all second measurements according to the invention. All phase relationships are then related to this reference point, so that it is advantageous on the reflecting base 6 is selected.
• 2nd : To define the position of the radiating body 1 , so here the vehicle 14 is a right-angled coordinate system 9 introduced, whose xy-plane coincides with the reflective base and the z-axis to the base orthogonal 19th is oriented in parallel. To describe the Directivity of the radiant body 1 is in the arrangement as in 1 the straight line connecting the origin of the coordinate system and the point of origin 11 the zenith angle θ assigned to the z axis and the azimuthal angle Φ between the vertical projection of the connecting straight line onto the xy plane and the x axis. The spatial unit vector $\overrightarrow{r}e$
  
  17 in the direction of propagation Φ and θ the radiation is thus through the zenith angle θ and the azimuth angle Φ is determined.
• 3rd : Device for measuring the field strength vector for a first measurement according to the invention with the aim of arithmetically determining the true directional diagram of a vehicle 14 Spatial measurement of the vehicle's radiation field 14 with antenna device 2nd as in 1 and 2nd however, on a rotating stand 10th as part of the reflective base 6 . The zenith angle θ is by a pivot point at the origin of the coordinate system and about this swivel arm vertically rotatable 21 set, the distal end of the position of the point of impact 11 with the field strength measuring device 15 and the measuring antenna 3rd describes. The xy plane is with the rotation state 10th and thus with the azimuthal orientation of the vehicle 14 firmly connected. The setting of the azimuth angle Φ is thus due to the rotary setting of the rotating position 10th given. This ensures that the distance d of the rise 11 from the origin of the coordinate system regardless of the solid angle θ , Φ and the measured phase values of the field strength vector for all solid angles θ , Φ are recorded in genuine relation to each other. All phase values are thus related to the origin of the coordinate system. According to the invention, the field strength vector is determined in the far field of the radiating body 1 Requirement. If the length of the swivel arm is too short 21 is the far field condition at the point of origin 11 is not fulfilled and it is therefore necessary to convert the field strength vectors measured there into vectors which would result in the far field. For this purpose, the measurement of the field strength vectors over the entire upper half space at a constant distance from the origin of the coordinate system for all solid angles Φ, θ and their subsequent conversion using the known near-field-far-field transformation. The reflective base area must also be taken into account, for example by including the lower half-space in the near-field far-field transformation with the aid of the mirroring principle known per se. To carry out the first measurement according to the invention of the far field field strength vector in solid angle θ , Φ the vehicle with its radiant body is exemplary in height h1 over the reflective base 6 . It therefore arises for the set height h1 and h2 a complex directional characteristic for the field strength vectors $\underset{\_}{\overrightarrow{E1\left(\theta ,\varphi \right)}}\text{and}\underset{\_}{\overrightarrow{E\mathrm{2nd}\left(\theta ,\varphi \right)}}$
  
  from the first and second measurements for the calculation of the true field strength vector $\underset{\_}{\overrightarrow{E\left(\theta ,\varphi \right)}}.$
  
  The length of the swivel arm is often sufficient 21 not out around at the onset 11 to meet the far field condition. For the therefore necessary implementation of the field-far-field transformation, one obtains for the two heights h1 and h 2 in the far field each for the calculation of the true field $\underset{\_}{\overrightarrow{E\left(\theta ,\varphi \right)}}$
  
  necessary far-field vectorial directional characteristics $\underset{\_}{\overrightarrow{E1\left(\theta ,\varphi \right)}}\text{and}\underset{\_}{\overrightarrow{E\mathrm{2nd}\left(\theta ,\varphi \right)}}.$
  
• 4th : Device for measuring the field strength vector as in 5 for carrying out a second measurement according to the invention for arithmetically determining the true directional diagram from the first and second measurements. To carry out the second measurement, the vehicle is based on the exemplary body height h1 in 3rd by the difference in height by Δh / λ * cos (θ) = Δhr * cos (θ) <0.25 without rotation and displacement with respect to the coordinates x and y, that is to say only in the direction of the vertical axis z. In simple implementation of this increase, jacks are an example 16 used.
• 5 : Shows the same setup as in 4th , but for the first measurement according to the invention of the field strength vector according to the invention with one with the body in height h1 above the revolving stand 10th built vehicle 14 . When the vehicle is raised 14 to the height not shown in the figure h2 = h1 + Δh / λ can be the second measurement according to the invention of the field strength vectors at the point of incidence 11 be carried out, from which the true field strength is calculated from both measurements. The heights are to achieve sufficiently precise results h1 respectively. h2 sufficiently small compared to the distance d between the origin of the coordinate system and the origin 11 , which is determined by the length of the swivel arm 21 given is.
• 6 : Explanation of the mode of operation of the invention is the radiation effect of the radiating body 1 using the example of the vehicle 14 with the antenna arrangement which excites the radiation 2nd . To visualize the surface elements radiating due to the surface currents on the electrically conductive vehicle skin, this is done using the finite element method with a lattice structure 22 busy. The surface current flowing on each element can - evaluated with the expansion of the element - become a current moment 24th summarized in the center, so that the current moment J 24 according to the current direction and the spatial position of the grid element 8th a complex spatial vector $\underset{\_}{\overrightarrow{J}}$
  
  with the complex spatial components J _x , J _y , J _z a directional elementary radiator in the center of the grid element with the position p _x , p _y , p _z forms in the coordinate system. The radiation from these elementary emitters of the radiating body 1 as well as the radiation of the antenna arrangement 2nd itself overlaps with respect to the unit vector $\overrightarrow{r}e$
  
  17 in the direction of propagation at the point of impact 11 to the field strength vector measured there. The fundamental mode of operation of the present invention assumes that the radiating body 1 due to the exciting antenna arrangement 2nd Surface currents that affect the radiation properties, such as the directional diagram and the polarization of the radiation. When measuring the radiation of the radiating body close to the base 1 at point 11- as in 1 - According to the invention, it is assumed that the distribution of the surface currents depends on the neighborhood effect of the reflecting base 6 is practically unaffected. The current distribution on the radiating body 1 is thus used for the first measurement in height h1 and the um Δh changed second measurement in height h2 than exclusively from the radiation-exciting antenna arrangement 2nd evoked. This condition is met with sufficient accuracy for the essential practical applications. This is particularly the case when the antenna arrangement 2nd in that of the footprint 6 part of the radiating body facing away 1 is placed. When comparing the results for the true field strength vector $\underset{\_}{\overrightarrow{E}}$
  
  at different zenith angles θ at the respective point 11 is the exact observance of the distance d from an unchanged reference point. The electromagnetic field at the point of impact can be determined from the amplitudes and the different phases of the components of the calculated true field strength vector 11 can be broken down into partial waves, ie in particular into a left-turning electromagnetic wave (LHCP) and a right-turning electromagnetic wave (RHCP). When measuring the upper half space in the 2nd and 5 this results in the spatial gain functions for both directions of rotation as well as the cross polarization of the true propagating electromagnetic field $\overrightarrow{E}.$
  
  Regarding the choice of the height change around Δh for the first and the second measurement according to the invention, the condition Δhr * cos (θ) = Δh / λ * cos (θ) <0.25 is necessary with regard to the uniqueness of the results. This is when the fraction in formula (1) is expanded by the negative phase factor of exp (i2π * (cos (θ) * Δhr ) obviously, whereby the denominator in the negative value of 2i * sin (2π * (cos (θ) * Δhr ) transforms.

in Ausbreitungsrichtung und der Positionsvektor $\overrightarrow{p_n}$

23 für die räumliche Position eines der N vorhandenen Gitterelemente des strahlenden Körpers 1 mit der Antennenanordnung 2 eingeführt. Ebenso ist das auf dem n-ten Gitterelement wirksame mit Phasen behaftete Strommoment J als Vektor dargestellt. $$\overrightarrow{r}e\left(\theta ,\varphi \right)=\left(\begin{array}{c}\text{sin}\left(\theta \right)·\text{cos}\left(\varphi \right)\\ \text{sin}\left(\theta \right)·\text{sin}\left(\varphi \right)\\ \text{cos}\left(\theta \right)\end{array}\right){\overrightarrow{p}}_n=\left(\begin{array}{c}p{x}_n\\ p{y}_n\\ p{z}_n\end{array}\right){\underset{\_}{\overrightarrow{J}}}_n=\left(\begin{array}{c}\underset{\_}{J}{x}_n\\ \underset{\_}{J}{y}_n\\ \underset{\_}{J}{z}_n\end{array}\right)$$

The plausibility of equation 2 according to the invention for calculating the true field strength vector is justified below.
For this, the unit vector $\overrightarrow{r}e\left(\theta ,\varphi \right)$

in the direction of propagation and the position vector $\overrightarrow{p_n}$

23 for the spatial position of one of the N existing lattice elements of the radiating body 1 with the antenna arrangement 2nd introduced. Likewise, the phase torque current J which is active on the nth grid element is shown as a vector. $$\overrightarrow{r}e\left(\theta ,\varphi \right)=\left(\begin{array}{c}\text{sin}\left(\theta \right)·\text{cos}\left(\varphi \right)\\ \text{sin}\left(\theta \right)·\text{sin}\left(\varphi \right)\\ \text{cos}\left(\theta \right)\end{array}\right){\overrightarrow{p}}_n=\left(\begin{array}{c}p{x}_n\\ p{y}_n\\ p{\mathrm{e.g.}}_n\end{array}\right){\underset{\_}{\overrightarrow{J}}}_n=\left(\begin{array}{c}\underset{\_}{J}{x}_n\\ \underset{\_}{J}{y}_n\\ \underset{\_}{J}{\mathrm{e.g.}}_n\end{array}\right)$$

The contribution of the ray paths with line of sight 4th and such ray paths 5 who on radiant body 1 to be bowed (she 1 ) deliver on arrival 11 the sought-after, true electric field strength vector from the following relationship with the constant const which is meaningless for the consideration of the directivity. $$\underset{\_}{\overrightarrow{E}}\left(\theta ,\varphi \right)=cOnst·{\displaystyle \sum _n^N\left[\left[\left(\begin{array}{c}J{x}_n\left(\overrightarrow{p}\right)\\ \underset{\_}{J}{y}_n\left(\overrightarrow{p}\right)\\ \underset{\_}{J}{\mathrm{e.g.}}_n\left(\overrightarrow{p}\right)\end{array}\right)\times \overrightarrow{r}e\left(\theta ,\varphi \right)\right]\times \overrightarrow{r}e\left(\theta ,\varphi \right)\right]}·\text{exp}\left[\mathrm{2nd}\pi j·\left(\begin{array}{c}p{x}_n/\lambda \\ p{y}_n/\lambda \\ p{\mathrm{e.g.}}_n/\lambda \end{array}\right)·\left(\overrightarrow{r}e\left(\theta ,\varphi \right)\right)\right]$$

The contribution of the reflective base 6 reflected radiation ( 7 in 1 ) is unknown and should be based on the first and second measurements according to the invention when the radiating body is displaced 1 by the difference in height related to the free space wavelength Δhr are eliminated and reads below $\underset{\_}{\overrightarrow{E}}r\left(\theta ,\varphi \right)$

Due to the geometry of the radiation propagation, the two contributions are superimposed on changes in the first measurement and the second measurement under different phases.

From the first measurement, in the starting position before the displacement of the radiating body 1 with its antenna arrangement 2nd you get the vector: $$\underset{\_}{\overrightarrow{E}}1\left(\theta ,\varphi \right)=\underset{\_}{\overrightarrow{E}}\left(\theta ,\varphi \right)+\underset{\_}{\overrightarrow{E}}r\left(\theta ,\varphi \right)$$

Given the sufficient independence in practice of the distribution of the currents on the radiating body 1 and its antennas 2nd is the contribution of the direct and on the vehicle 14 diffracted rays of the type 4th and 5 as follows. The field strength vector experiences a phase shift which results from the following relationships. $$\underset{\_}{\overrightarrow{E}}\left(\theta ,\varphi ,\Delta Hr\right)=cOnst·{\displaystyle \sum _n\left[\left[\left(\begin{array}{c}J{x}_n\left(\overrightarrow{p}\right)\\ \underset{\_}{J}{y}_n\left(\overrightarrow{p}\right)\\ \underset{\_}{J}{\mathrm{e.g.}}_n\left(\overrightarrow{p}\right)\end{array}\right)\times re\left(\theta ,\varphi \right)\right]\times \overrightarrow{r}e\left(\theta ,\varphi \right)\right]}·\text{exp}\left[\mathrm{2nd}\pi j·\left(\begin{array}{c}p{x}_n/\lambda \\ p{y}_n/\lambda \\ p{\mathrm{e.g.}}_n/\lambda +\Delta Hr\end{array}\right)·\left(\overrightarrow{r}e\left(\theta ,\varphi \right)\right)\right]$$

For a better overview, the position vector is separated as follows $$\underset{\_}{\overrightarrow{E}}\left(\theta ,\varphi ,\Delta Hr\right)=cOnst·{\displaystyle \sum _n\left[\left[\left(\begin{array}{c}J{x}_n\left(\overrightarrow{p}\right)\\ \underset{\_}{J}{y}_n\left(\overrightarrow{p}\right)\\ \underset{\_}{J}{\mathrm{e.g.}}_n\left(\overrightarrow{p}\right)\end{array}\right)\times re\left(\theta ,\varphi \right)\right]\times re\left(\theta ,\varphi \right)\right]}·\text{exp}\left[\mathrm{2nd}\pi j·\left[\left(\begin{array}{c}p{x}_n/\lambda \\ p{y}_n/\lambda \\ p{\mathrm{e.g.}}_n/\lambda \end{array}\right)+\left(\begin{array}{c}0\\ 0\\ \Delta Hr\end{array}\right)\right]\left(re\left(\theta ,\varphi \right)\right)\right]$$

führt in der folgenden Gleichung zu einem Phasenfaktor, welcher den Beiträgen aller n Strommomente gleich ist, sodass gilt: $$\underset{\_}{\overrightarrow{E}}\left(\theta ,\varphi ,\Delta hr\right)=\underset{\_}{\overrightarrow{E}}\left(\theta ,\varphi \right)·\text{exp}\left[2\pi j·\left(\begin{array}{c}0\\ 0\\ \Delta hr\end{array}\right)·\overrightarrow{r}e\left(\theta ,\varphi \right)\right]=\underset{\_}{\overrightarrow{E}}\left(\theta ,\varphi \right)·\text{exp}\left(2\pi j·\text{cos}\left(\theta \right)·\Delta hr\right)$$

The inside product of the vectors $$\left(\begin{array}{c}0\\ 0\\ \Delta Hr\end{array}\right)·\left(\begin{array}{c}\text{sin}\left(\theta \right)·\text{cos}\left(\varphi \right)\\ \text{sin}\left(\theta \right)·\text{sin}\left(\varphi \right)\\ \text{cos}\left(\theta \right)\end{array}\right)=\Delta Hr·\text{cos}\left(\theta \right)$$

leads to a phase factor in the following equation, which is equal to the contributions of all n current moments, so that: $$\underset{\_}{\overrightarrow{E}}\left(\theta ,\varphi ,\Delta Hr\right)=\underset{\_}{\overrightarrow{E}}\left(\theta ,\varphi \right)·\text{exp}\left[\mathrm{2nd}\pi j·\left(\begin{array}{c}0\\ 0\\ \Delta Hr\end{array}\right)·\overrightarrow{r}e\left(\theta ,\varphi \right)\right]=\underset{\_}{\overrightarrow{E}}\left(\theta ,\varphi \right)·\text{exp}\left(\mathrm{2nd}\pi j·\text{cos}\left(\theta \right)·\Delta Hr\right)$$

Due to the propagation geometry, the paths of the reflected field are lengthened by the same amount due to the height shift as they are shortened for the aforementioned rays, so that there is a negative phase shift for the reflected radiation by the same value, whereby the contribution of the reflecting radiation to the field strength vector is now: $$\underset{\_}{\overrightarrow{E}}r\left(\theta ,\varphi ,\Delta Hr\right)=\underset{\_}{\overrightarrow{E}}r\left(\theta ,\varphi \right)·\text{exp}\left(-\mathrm{2nd}\pi j·\text{cos}\left(\theta \right)·\Delta Hr\right)$$

This results in the field strength vector in the second measurement according to the invention: $$\underset{\_}{\overrightarrow{E}}\mathrm{2nd}\left(\theta ,\varphi \right)=\underset{\_}{\overrightarrow{E}}\left(\theta ,\varphi ,\Delta Hr\right)+\underset{\_}{\overrightarrow{E}}r\left(\theta ,\varphi ,\Delta Hr\right)=\underset{\_}{\overrightarrow{E}}\left(\theta ,\varphi \right)·\text{exp}\left(\mathrm{2nd}\pi j·\text{cos}\left(\theta \right)·\Delta Hr\right)+\underset{\_}{\overrightarrow{E}}r\left(\theta ,\varphi \right)·\text{exp}\left(-\mathrm{2nd}\pi j·\text{cos}\left(\theta \right)·\Delta Hr\right)$$

in Gleichung 16 und des zweiten Messwerts $\underset{\_}{\overrightarrow{E}}2\left(\theta ,\varphi \right)$

in Gleichung 17 ergibt sich durch Elimination des an sich unbekannten Beitrags des reflektierten Feldes $\underset{\_}{\overrightarrow{E}}r\left(\theta ,\varphi \right)$

zum wahren Feldstärkevektor für den Raumwinkel θ, ϕ die erfindungsgemäße Beziehung, wie folgt (siehe Gleichung 2): $$\underset{\_}{\overrightarrow{E}}\left(\theta ,\varphi \right)=\frac{\underset{\_}{\overrightarrow{E}}1\left(\theta ,\varphi \right)-\underset{\_}{\overrightarrow{E}}2\left(\theta ,\varphi \right)\cdot \text{exp}\left[j2\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \Delta hr\right)\right]}{1-\text{exp}\left[j4\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \Delta hr\right)\right]}$$

From the comparison of the first measured value $\underset{\_}{\overrightarrow{E}}1\left(\theta ,\varphi \right)$

in Equation 16 and the second measurement $\underset{\_}{\overrightarrow{E}}\mathrm{2nd}\left(\theta ,\varphi \right)$

in Equation 17 results from the elimination of the unknown contribution of the reflected field $\underset{\_}{\overrightarrow{E}}r\left(\theta ,\varphi \right)$

to the true field strength vector for the solid angle θ , ϕ the relationship according to the invention, as follows (see equation 2): $$\underset{\_}{\overrightarrow{E}}\left(\theta ,\varphi \right)=\frac{\underset{\_}{\overrightarrow{E}}1\left(\theta ,\varphi \right)-\underset{\_}{\overrightarrow{E}}\mathrm{2nd}\left(\theta ,\varphi \right)\cdot \text{exp}\left[j\mathrm{2nd}\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \Delta Hr\right)\right]}{1-\text{exp}\left[j\mathrm{4th}\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \Delta Hr\right)\right]}$$

It is the merit of the present invention to record the true radiation properties of radiating bodies, the measurement of which is impossible from the ground or can only be carried out with an inappropriately large economic outlay.

It can happen that with the vertical displacement of the radiating body 1 around Δhr is accompanied by a horizontal shift related to the free space wavelength by Δxr = Δx / λ and Δyr = Δy / λ. Now the field strength measured with this shift can be converted into a field strength that would have arisen without this shift. To do this, it is sufficient to determine the path difference that results from the shift. The phase shift resulting from this shift and thus the path difference can then be subtracted from the phase of the measured field in order to determine the field which would have been measured without the shift. Due to the far field properties, the amount and polarization of the field are retained.

und dem Positionsvektor der verschobenen Quelle ${\overrightarrow{r}}_n=r\left(\begin{array}{c}\text{sin}\theta \text{cos}\mathrm{\Phi }\\ \text{sin}\theta \text{sin}\mathrm{\Phi }\\ \text{cos}\theta \end{array}\right)-\left(\begin{array}{c}-\Delta x\\ -\Delta y\\ 0\end{array}\right)$

ergibt sich bei der im Fernfeld gegebenen Bedingung r>> Δx, Δy die vereinfachte Darstellung des Gangunterschiedes: $$\Delta r=r_n-r=\frac{\overrightarrow{r}}{r}\cdot \left(\begin{array}{c}-\Delta x\\ -\Delta y\\ 0\end{array}\right)=-\text{sin}\left(\theta \right)\left(\Delta x\text{cos}\left(\mathrm{\Phi }\right)+\Delta y\text{sin}\left(\mathrm{\Phi }\right)\right)$$

For every radiation source with a large distance r Depending on the direction Δ and Δ, the following path difference Δr results from the displacement of the radiation source by Δ x and Δ y compared to the undisplaced radiation source. From the position vector of the source $\overrightarrow{r}=r\left(\begin{array}{c}\text{sin}\theta \text{cos}\mathrm{\Phi }\\ \text{sin}\theta \text{sin}\mathrm{\Phi }\\ \text{cos}\theta \end{array}\right)$

and the position vector of the shifted source ${\overrightarrow{r}}_n=r\left(\begin{array}{c}\text{sin}\theta \text{cos}\mathrm{\Phi }\\ \text{sin}\theta \text{sin}\mathrm{\Phi }\\ \text{cos}\theta \end{array}\right)-\left(\begin{array}{c}-\Delta x\\ -\Delta y\\ 0\end{array}\right)$

With the condition r >> Δx, Δy given in the far field, the simplified representation of the path difference results: $$\Delta r=r_n-r=\frac{\overrightarrow{r}}{r}\cdot \left(\begin{array}{c}-\Delta x\\ -\Delta y\\ 0\end{array}\right)=-\text{sin}\left(\theta \right)\left(\Delta x\text{cos}\left(\mathrm{\Phi }\right)+\Delta y\text{sin}\left(\mathrm{\Phi }\right)\right)$$

This path difference accordingly leads to an additional undesired phase shift of the second measured value by the phase factor due to the horizontal shift $$\text{exp}\left[-\mathrm{2nd}\pi j\frac{\Delta r}{\lambda }\right]=\text{exp}\left[\mathrm{2nd}\pi j\cdot \text{sin}\left(\theta \right)\cdot \left(\text{cos}\left(\varphi \right)\cdot \Delta xr+\text{sin}\left(\varphi \right)\cdot \Delta yr\right)\right].$$

entsprechend um den negativen Wert dieser Phasenverschiebung korrigiert in Gleichung 2 einzusetzen. Diese lautet demnach mit dieser Korrektur: $$\underset{\_}{\overrightarrow{E}}\left(\theta ,\varphi \right)=\frac{\underset{\_}{\overrightarrow{E}}1\left(\theta ,\varphi \right)-\underset{\_}{\overrightarrow{E}}2\left(\theta ,\varphi \right)\cdot \text{exp}\left[j2\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \Delta hr-\text{sin}\left(\theta \right)\cdot \left(\text{cos}\left(\varphi \right)\cdot \Delta xr+\text{sin}\left(\varphi \right)\cdot \Delta yr\right)\right)\right]}{1-\text{exp}\left[j4\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \Delta hr\right)\right]}$$

The effects of direct and diffracted rays contained in the second measurement 4th and 5 are caused by the horizontal displacement of the radiating body 1 phase shifted in the same way as those on the reflective base 6 reflected rays 7 . Therefore, the vector measured in the second measurement is $\underset{\_}{\overrightarrow{E\mathrm{2nd}}}\left(\theta ,\varphi \right)$

accordingly to correct the negative value of this phase shift in equation 2. With this correction, this is: $$\underset{\_}{\overrightarrow{E}}\left(\theta ,\varphi \right)=\frac{\underset{\_}{\overrightarrow{E}}1\left(\theta ,\varphi \right)-\underset{\_}{\overrightarrow{E}}\mathrm{2nd}\left(\theta ,\varphi \right)\cdot \text{exp}\left[j\mathrm{2nd}\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \Delta Hr-\text{sin}\left(\theta \right)\cdot \left(\text{cos}\left(\varphi \right)\cdot \Delta xr+\text{sin}\left(\varphi \right)\cdot \Delta yr\right)\right)\right]}{1-\text{exp}\left[j\mathrm{4th}\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \Delta Hr\right)\right]}$$

jeweils ein Signalvektor $\underset{\_}{\overrightarrow{S}}1\left(\theta ,\varphi \right)\text{ und }\underset{\_}{\overrightarrow{S}}1\left(\theta ,\varphi \right)$

ermittelt werden. Damit ist es möglich, zum Beispiel aus den Gleichungen 2 und 3 den wahren Signalvektor $\underset{\_}{\overrightarrow{S}}\left(\theta ,\varphi \right)$

für den Raumwinkel θ, Φ zu ermitteln, der sich ergebe, wenn der strahlende Körper 1 im Raum schweben würde.It may be the case that the body shines 1 placed antenna array 2nd can only act as a receiving antenna. This is the case, for example, when the antenna arrangement 2nd whose true directional diagram can be determined for the different polarizations is not reciprocal, as is the case, for example, with electronic receiving antennas and electronic directional antennas, etc. In this case, the previously described measuring antenna 3rd as a transmitting antenna for the different polarization directions at the point of incidence 11 to design. By measuring the transmission factor according to magnitude and phase when the respective polarization is transmitted, based on Cartesian coordinates in the x, y, z direction or based on cylinder coordinates in the θ and ϕ direction, a first measurement according to the invention is carried out with the radiating body 1 at the first height h1 and a second measurement according to the invention is carried out at the second height h2 = h1 + Δh. Due to the reciprocity of the wave propagation - in the opposite direction to the previous description - from the polarization-related received signals of the antenna arrangement 2nd in analogy to the described field strength vectors E1 (θ, ϕ) and $\overrightarrow{E}\mathrm{2nd}\left(\theta ,\varphi \right)$

one signal vector each $\underset{\_}{\overrightarrow{S}}1\left(\theta ,\varphi \right)\text{and}\underset{\_}{\overrightarrow{S}}1\left(\theta ,\varphi \right)$

be determined. This makes it possible, for example from equations 2 and 3, to obtain the true signal vector $\underset{\_}{\overrightarrow{S}}\left(\theta ,\varphi \right)$

for the solid angle θ , Φ to determine the result if the radiating body 1 would float in the room.

Equation 2 will then be, for example, as follows: $$\underset{\_}{\overrightarrow{S}}\left(\theta ,\varphi \right)=\frac{\underset{\_}{\overrightarrow{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="DE102018007754A1\_0145.png,DE102018007754A1\_0149.png"\; state="\{\{state\}\}">S</figure-callout>}1}}\left(\theta ,\varphi \right)-\underset{\_}{\overrightarrow{S\mathrm{2nd}}}\left(\theta ,\varphi \right)·\text{exp}\left[j\mathrm{2nd}\pi ·\left(\text{cos}\left(\theta \right)·\Delta Hr\right)\right]}{1-\text{exp}\left[j\mathrm{4th}\pi ·\left(\text{cos}\left(\theta \right)·\Delta Hr\right)\right]}$$

Reference list

radiant body 1 the radiation-exciting antenna arrangement 2nd Measuring antenna 3rd Beam path with line of sight 4th beam path bent on the radiating body 5 reflective base 6 beam path reflected on the reflecting base 7 surface element radiating from surface currents 8th right-angled or cylindrical coordinate system 9 Rotary stand 10th Onset 11 First vertical distance h1; 12th second vertical distance h2 = h1 + Δh; 13 vehicle 14 Field strength measuring device 15 Jack 16 Unit vector re in the direction of propagation 17th Vertical projection of the connecting straight line 18th Orthogonal footprint 19th Straight line 20th Swivel arm 21 3-dimensional lattice structure 22 Spatial position of the grid element px, py, pz (position vector): 23 Spatial vector of the current moment with the complex components Jx, Jy, Jz: 24th θ direction 25th ϕ direction 26 d distance of the point 11 from the radiating body Δh distance of vertical displacement Δx distance of the horizontal displacement in the X direction Δh distance of the horizontal shift in the Y direction Θ zenith angle Φ Azimuth angle first field strength vector

$\overrightarrow{\underset{\_}{E1}}$

second field strength vector $\overrightarrow{\underset{\_}{E\mathrm{2nd}}}$

true field strength vector $\overrightarrow{\underset{\_}{E}}$

Claims (14)

Procedure for determining the true field strength vector $\overrightarrow{\underset{\_}{E}}$

in the far point (11) of an electromagnetic body (1) radiating in the free space with a frequency of the free space wavelength λ from the field strength vector measurement according to the amount and phase of the radiating body (1) arranged over a flat reflecting base surface, comprising the following steps: - Arranging the electromagnetic radiating body (1) at a first vertical distance (12) between all points on the radiating body (1) and the flat reflecting base surface (6); - Acquisition of the field strength vector in a first measurement $\overrightarrow{\underset{\_}{E1}}$

in a distant point (11) by measuring the field components according to their amounts and measuring the phases of the field components to each other. - Twistless displacement of the radiating body (1) in the direction of the surface normal of the reflecting base (6) by a distance Δh, so that the second vertical distance (13) of all points of the radiating body (1) from the reflecting base (6) by this distance Δh is increased. - In a subsequent second measurement, detection of the second field strength vector now occurring $\overrightarrow{\underset{\_}{E\mathrm{2nd}}}$

at the same distant point (11) by measuring the field components according to their amounts and measuring the phases of the field components to each other; - Arithmetical determination of the true field strength vector occurring without the influence of the reflecting base area (6) in the distant point (11) $\overrightarrow{\underset{\_}{E}}$

based on the differences in the field strength vectors obtained from the first and second measurements $\overrightarrow{\underset{\_}{E1}}\text{and}\overrightarrow{\underset{\_}{E\mathrm{2nd}}}$

and on the basis of the angle θ between the normal (19) of the base area (6) and the connecting straight line between the radiating body (1) and the distant point (11). Determination of the true field strength vector according to Claim 1 characterized in that the true field strength vector $\overrightarrow{\underset{\_}{E}}$

following relationship is established: $$\overrightarrow{\underset{\_}{E}}=\frac{\overrightarrow{\underset{\_}{E1}}-\overrightarrow{\underset{\_}{E\mathrm{2nd}}}\cdot \text{exp}\left[j\mathrm{2nd}\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \mathrm{\Delta }Hr\right)\right]}{1-\text{exp}\left[j\mathrm{4th}\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \mathrm{\Delta }Hr\right)\right]}$$

Determination of the true field strength vector according to Claim 1 and 2nd characterized in that based on the amounts of the field components and their phase relationships to one another - in a manner known per se - the circular RHCP, LHCP or linearly polarized partial waves propagating in the distant point (11) gradually increase their phase relationships are calculated to each other. Determination of the true field strength vector according to Claim 1 to 3rd characterized in that the radiating body (1) with the radiation-exciting antenna arrangement (2) is unsuitable for radiation measurements suspended in free space and is therefore arranged above a rotating stand (10) which is part of the horizontally oriented reflecting base area (6) and for description of the electromagnetic field in the distant point of incidence (11) a fictitious right-angled coordinate system with the xy plane as the reflecting base area (6) connected to the rotating stand (10) with the z-axis as the base normal (19) is introduced, so that when the rotating stand ( 10) with the radiating body (1) with antenna arrangement (2) the vertical projection of the connecting straight line between the pivot point of the rotating stand (10) and the distant point (11) on the xy plane forms the azimuth angle Φ with respect to the x axis and the Angle θ between the connecting line and the base normal (19) is formed as the zenith angle θ with respect to the z-axis t and the true field strength vector $\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)$

from the field strength vectors $\overrightarrow{\underset{\_}{E1}}\left(\theta ,\varphi \right),$

measured on the vehicle on the rotating stand and $\overrightarrow{\underset{\_}{E\mathrm{2nd}}}\left(\theta ,\varphi \right),$

measured on the vehicle increased by Δh / λ * cos (θ) = Δhr * cos (θ) <0.25 at the far end (11) as a function of the azimuth angle Φ and the zenith angle θ according to the following relationship for $\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)$

is determined. $$\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)=\frac{\overrightarrow{\underset{\_}{E1}}\left(\theta ,\varphi \right)-\overrightarrow{\underset{\_}{E\mathrm{2nd}}}\left(\theta ,\varphi \right)\cdot \text{exp}\left[j\mathrm{2nd}\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \mathrm{\Delta }Hr\right)\right]}{1-\text{exp}\left[j\mathrm{4th}\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \mathrm{\Delta }Hr\right)\right]}$$

With $j=\sqrt{-1}$

Determination of the true field strength vector according to Claim 1 to 4th characterized in that the radiating body (1) is provided by a vehicle (14) with a radiation-exciting antenna arrangement (2) and for field strength vector measurement for points (11) at adjustable zenith angles θ a field strength measuring device (15) at the end of one with the stationary one Part of the reflecting base surface (6) is pivotally connected, pivotable vertically about the center of the rotating stand (10) and is long enough to meet the far field conditions, so that when adjusting the azimuth angle Φ by rotating the rotating stand (10) and adjusting of the zenith angle θ the first and second field strength vector measurements are carried out for all solid angles Φ and θ of the upper half-space with a constant distance of all points (11) from the center of the rotary stand (10). Determination of the true field strength vector according to Claim 1 to 5 characterized in that in order to meet the far field condition for a point (11) in solid angle θ and Φ the field strength vectors at too short a distance d from the vehicle (14) as a radiating body (1) in the two successive measurements according to the invention over the entire upper half space are carried out and the measured values are each converted using the near-field far-field transformation known per se and on the basis of these far-field field strength vectors $\overrightarrow{\underset{\_}{E1}}\left(\theta ,\varphi \right)\text{and}\overrightarrow{\underset{\_}{E\mathrm{2nd}}}\left(\theta ,\varphi \right)$

the true field strength vectors $\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right),$

so without the influence of the reflective base (6) Claim 4 are calculated. Determination of the true field strength vector $\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)$

after Claim 1 to 6 characterized in that for all solid angles (θ, Φ) the radiation densities of the circular RHCP, LHCP or linearly polarized partial waves propagating in the distant point (11) are determined in terms of size and from this the true directional diagrams of the radiating vehicle (14) - ie without the influence of the reflecting base area (6) - are calculated for the partial waves. Determination of the true field strength vector $\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)$

after Claim 1 to 7 characterized in that the vehicle is arranged for a first measurement at a vertical reference distance h1 above the reflecting base area and raised to a vertical distance h2 = h1 + Δh in the second measurement and the true field strength vector $\overrightarrow{\underset{\_}{E}}\left(\theta ,\mathrm{\Phi }\right)$

is determined according to the following relationship: $$\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)=\frac{\overrightarrow{\underset{\_}{E1}}\left(\theta ,\varphi \right)\text{exp}\left[j\mathrm{2nd}\pi \cdot \text{cos}\left(\theta \right)\cdot H1\text{/}\lambda \right]-\overrightarrow{\underset{\_}{E\mathrm{2nd}}}\left(\theta ,\varphi \right)\cdot \text{exp}\left[j\mathrm{2nd}\pi \cdot \text{cos}\left(\theta \right)\cdot \left(H1\text{/}\lambda +\mathrm{\Delta }Hr\right)\right]}{\text{exp}\left[j\mathrm{4th}\pi \cdot \left(\text{cos}\left(\theta \right)\cdot H1\text{/}\lambda \right)\right]-\text{exp}\left[j\mathrm{4th}\pi \cdot \text{cos}\left(\theta \right)\cdot \left(H1\text{/}\lambda +\mathrm{\Delta }Hr\right)\right]}$$

Determination of the true field strength vector $\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)$

after Claim 1 to 8th characterized in that the vehicle 14 for the first measurement without elevation (h1 = 0) is placed with a selected vehicle center above the pivot point of the rotating stand (10) and for the second measurement using jacks only in the direction of the surface normals ( z-axis) is raised in height by the distance Δh. Determination of the true field strength vector $\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)$

after Claim 1 to 9 characterized in that when the radiating body (1) is increased / decreased by Δhr, there is in itself an undesired rotation of the radiating body (1) about the z-axis by the azimuth angle ΔΦ and this rotation is corrected by evaluating the formulas in the Claims 4 and 8th the expression $\overrightarrow{\underset{\_}{E\mathrm{2nd}\left(\theta ,\varphi \right)}}$

by the corresponding measured value $\overrightarrow{\underset{\_}{E\mathrm{2nd}\left(\theta ,\varphi -\mathrm{\Delta }\varphi \right)}}$

is replaced. Determination of the true field strength vector $\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)$

after Claim 1 to 10th characterized in that when the radiating body (1) is increased / decreased by Δhr there is an inherently undesirable displacement of the radiating body (1) with antenna arrangement (2) parallel to the reflecting base area (6) by Δx and / or Δy and this displacement corrected that for evaluating the formulas in the Claims 4 and 8th the expression $\overrightarrow{\underset{\_}{E\mathrm{2nd}\left(\theta ,\varphi \right)}}$

by the correspondingly corrected measured value $$\overrightarrow{\underset{\_}{E\mathrm{2nd}\left(\theta ,\varphi \right)}}\cdot \text{exp}\left[-\mathrm{2nd}\pi j\cdot \text{sin}\left(\theta \right)\cdot \left(\text{cos}\left(\varphi \right)\cdot \mathrm{\Delta }xr+\text{sin}\left(\varphi \right)\cdot \mathrm{\Delta }yr\right)\right]$$

is replaced or the true field strength vector $\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)$

in this case is calculated from the following relationship $$\overrightarrow{\underset{\_}{E}}\left(\theta ,\varphi \right)=\frac{\overrightarrow{\underset{\_}{E1}}\left(\theta ,\varphi \right)-\overrightarrow{\underset{\_}{E\mathrm{2nd}}}\left(\theta ,\varphi \right)\cdot \text{exp}\left[j\mathrm{2nd}\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \mathrm{\Delta }Hr-\text{sin}\left(\theta \right)\cdot \left(\text{cos}\left(\varphi \right)\cdot \mathrm{\Delta }xr+\text{sin}\left(\varphi \right)\cdot \mathrm{\Delta }yr\right)\right)\right]}{1-\text{exp}\left[j\mathrm{4th}\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \mathrm{\Delta }Hr\right)\right]}$$

Determination of the true field strength vector $\overrightarrow{\underset{\_}{H}}$

after Claim 1 to 11 characterized in that however in the claims instead of the electric field strength vector $\overrightarrow{\underset{\_}{E}}$

the associated magnetic field strength vector $\overrightarrow{\underset{\_}{H}}$

is determined in the claims that the vectors $\overrightarrow{\underset{\_}{E}},\overrightarrow{\underset{\_}{E1}}b\mathrm{e.g.}w.\text{\_}\overrightarrow{\underset{\_}{E\mathrm{2nd}}}$

through the vectors $\overrightarrow{\underset{\_}{H}},\overrightarrow{\underset{\_}{H1}}b\mathrm{e.g.}w.\text{\_}\overrightarrow{\underset{\_}{H\mathrm{2nd}}}$

are replaced, so that too Claim 2 respectively to Claim 4 analog mathematical relationship is as follows: $$\overrightarrow{\underset{\_}{H}}=\frac{\overrightarrow{\underset{\_}{H1}}-\overrightarrow{\underset{\_}{H\mathrm{2nd}}}\cdot \text{exp}\left[j\mathrm{2nd}\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \mathrm{\Delta }Hr\right)\right]}{1-\text{exp}\left[j\mathrm{4th}\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \mathrm{\Delta }Hr\right)\right]}$$

respectively. $$\overrightarrow{\underset{\_}{H}}\left(\theta ,\varphi \right)=\frac{\overrightarrow{\underset{\_}{H1}}\left(\theta ,\varphi \right)-\overrightarrow{\underset{\_}{H\mathrm{2nd}}}\left(\theta ,\varphi \right)\cdot \text{exp}\left[j\mathrm{2nd}\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \mathrm{\Delta }Hr\right)\right]}{1-\text{exp}\left[j\mathrm{4th}\pi \cdot \left(\text{cos}\left(\theta \right)\cdot \mathrm{\Delta }Hr\right)\right]}$$

Determination of the true field strength vector according to Claim 1 to 12th characterized in that both the electric field strength vectors and the magnetic field strength vectors in spherical coordinates are described and for the determination of the true field strength vector in the first and second measurement according to the invention the θ component and the φ component for the solid angle θ, Φ are determined and the true electrical field strength vector $$\overrightarrow{\underset{\_}{E\kappa \left(\theta ,\varphi \right)}}=\frac{1}{1-\text{exp}\left[j\mathrm{4th}\pi \left(\text{cos}\left(\theta \right)\mathrm{\Delta }Hr\right)\right]}\left(\begin{array}{c}0\\ E1{\kappa }_{\theta }\left(\theta ,\varphi \right)\text{exp}\left(j\phi 1{\kappa }_{\theta }\left(\theta ,\varphi \right)\right)-E\mathrm{2nd}{\kappa }_{\theta }\left(\theta ,\varphi \right)\text{exp}\left(j\phi \mathrm{2nd}{\kappa }_{\theta }\left(\theta ,\varphi \right)+\mathrm{2nd}\pi cOs\left(\theta \right)\mathrm{\Delta }Hr\right)\\ E1{\kappa }_{\varphi }\left(\theta ,\varphi \right)\text{exp}\left(j\phi 1{\kappa }_{\varphi }\left(\theta ,\varphi \right)\right)-E\mathrm{2nd}{\kappa }_{\varphi }\left(\theta ,\varphi \right)\text{exp}\left(j\phi \mathrm{2nd}{\kappa }_{\varphi }\left(\theta ,\varphi \right)+\mathrm{2nd}\pi cOs\left(\theta \right)\mathrm{\Delta }Hr\right)\end{array}\right)$$

or the magnetic field strength vector $$\overrightarrow{\underset{\_}{H\kappa \left(\theta ,\varphi \right)}}=\frac{1}{1-\text{exp}\left[j\mathrm{4th}\pi \left(\text{cos}\left(\theta \right)\mathrm{\Delta }Hr\right)\right]}\left(\begin{array}{c}0\\ H1{\kappa }_{\theta }\left(\theta ,\varphi \right)\text{exp}\left(j\psi 1{\kappa }_{\theta }\left(\theta ,\varphi \right)\right)-H\mathrm{2nd}{\kappa }_{\theta }\left(\theta ,\varphi \right)\text{exp}\left(j\psi \mathrm{2nd}{\kappa }_{\theta }\left(\theta ,\varphi \right)+\mathrm{2nd}\pi cOs\left(\theta \right)\mathrm{\Delta }Hr\right)\\ H1{\kappa }_{\varphi }\left(\theta ,\varphi \right)\text{exp}\left(j\psi 1{\kappa }_{\varphi }\left(\theta ,\varphi \right)\right)-H\mathrm{2nd}{\kappa }_{\varphi }\left(\theta ,\varphi \right)\text{exp}\left(j\psi \mathrm{2nd}{\kappa }_{\varphi }\left(\theta ,\varphi \right)+\mathrm{2nd}\pi cOs\left(\theta \right)\mathrm{\Delta }Hr\right)\end{array}\right)$$

is determined. Determination of the true directional diagram after Claim 7 to 13 characterized in that, however, the directional diagram of the radiating body (1) with the antenna device (2) is determined in such a way that the antenna device (2) as the receiving antenna and the measuring antenna (3) as the transmitting antenna (3 ) is designed and by measuring the transmission factor according to amount and phase when sending out the respective polarization, based on Cartesian coordinates in the x, y, z direction or based on cylinder coordinates in the θ and ϕ direction, a first measurement according to the invention with the radiating body (1) is carried out at the first height h1 and a second measurement according to the invention is carried out at the second height h2 = h1 + Δh and from the polarization-related received signals of the antenna arrangement (2) in analogy to the field strength vectors described $\underset{\_}{E}1\left(\theta ,\varphi \right)\text{and}\overrightarrow{\underset{\_}{E}}\mathrm{2nd}\left(\theta ,\varphi \right)$

one signal vector each $\overrightarrow{\underset{\_}{S}}1\left(\theta ,\varphi \right)\text{and}\overrightarrow{\underset{\_}{S}}\mathrm{2nd}\left(\theta ,\varphi \right)$

is determined and in analogy from equation 2 the true signal vector $\overrightarrow{\underset{\_}{S}}\left(\theta ,\varphi \right)$

for the solid angle θ, Φ is determined as follows. $$\overrightarrow{\underset{\_}{S}}\left(\theta ,\varphi \right)=\frac{\overrightarrow{\underset{\_}{S1}}\left(\theta ,\varphi \right)-\overrightarrow{\underset{\_}{S\mathrm{2nd}}}\left(\theta ,\varphi \right)·\text{exp}\left[j\mathrm{2nd}\pi ·\left(\text{cos}\left(\theta \right)·\mathrm{\Delta }Hr\right)\right]}{1-\text{exp}\left[j\mathrm{4th}\pi ·\left(\text{cos}\left(\theta \right)·\mathrm{\Delta }Hr\right)\right]}$$

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