# A method for measuring boresight errors for a radioparent radome of arbitrary shape

### Abstract

### Keywords

#### For citation:

Makushkin I.E., Shemarin A.M., Vitsukaev Yu.Yu., Tyurin D.M. A method for measuring boresight errors for a radioparent radome of arbitrary shape. *Journal of «Almaz – Antey» Air and Space Defence Corporation*. 2020;(1):26-45.
https://doi.org/10.38013/2542-0542-2020-1-26-45

## Introduction

Boresight angle errors (BAE) arising in the presence of a radioparent radome (RPR) [2] shall be taken into account during operation of an airborne radar (ABR) [3]. Works on measuring BAE only in two orthogonal planes of antenna system (AS) installation are performed quite frequently [4, 5]. At that, in the conventional method, BAE is measured as the difference between the measured coordinates of zeroes of the corresponding difference radiation pattern (RP) before and after installation of the radome.

At a conference held in the previous year, the measurement and calculation method [1], allowing to determine particular components of BAE for the RPR of an arbitrary shape, was suggested for consideration. The results of measurement and calculation of the BAE components using this method were provided for a custom made RPR simulator mockup and were compared with the data received on the same, but using another method. It is based on using the so-called dynamic spatial radiation patterns (DSRP) [6]. Comparison results showed good matching of the resulting data.

## Definition of the task of measuring BAE over the UAV RPR surface

Figure 1 shows RPR (3) of a complex drop shape with a phased-array antenna (PAA) (1, 2) installed thereunder, which is capable of rotating in the azimuthal plane under the RPR around axis (4) and simultaneously scanning, while deflecting the beam into various positions (5, 6) (permissible for this PAA).

**Fig. 1**. PAA-RPR (UAV) system: 1, 2 - phased-array antenna PAA); 3 - RPR of a complex drop shape; 4 - conditional axis of PAA mechanical rotation under RPR; 5 - undeflected PAA beams; 6 - deflected PAA beams; 7 - beam “refraction points” on the RPR surface; 8 - longitudinal axis of the RPR

The positive longitudinal axis direction (8) of this RPR matches the UAV flight direction (FD). If we take the normal to the currently set plane phase front of the PAA aperture as the direction of the formed beam (in the far field), then, pursuant to simple principles of geometrical optics, it is clear that, when deflecting beams to various points (7) on the RPR surface, the ability to refract the beam, and, therefore, the BAE components may differ substantially. For this reason, these points on the surface are called “refraction points”.

Application of the previously suggested method of practical assessment of impact of the radome on onsets of “zeroes” of boresight characteristics and comparison thereof to those obtained in direct measurements using the “difference” method is an interesting task in terms of validation of the method suggested. In case of this mutual arrangement of PAA and RPR in some sections of its surface, such measurements are quite possible. The method associated with measurement of dynamical spatial radiation patterns (DSRP), which was mentioned in previous papers [1] and [6], was not applied in this case due to the difficulty of its practical implementation on a measuring complex and huge array of data to be measured.

## Measuring complex

The measurement was performed on the antenna measuring complex based on a compact polygon in the “receive” mode both using the conventional method in two orthogonal planes of PAA installation and using the suggested method. Such measurements were performed in the same points of the RPR surface, that further allowed to compare the results obtained. The flowchart of the measuring complex (configuration in the reception mode), which the work was performed on, is shown in Figure 2. The spherical front of wave (11) from horn feed element (8) installed on positioning element (9) (changes the polarisation angle), using collimating mirror (10), is transformed into a plane one. The plane front of wave (12) falls on PAA aperture (7) located in the working area of the collimator. Using antenna rotary support device (ARSD) (4), PAA (subsequently, with the RPR installed) can take various spatial positions relative to the plane wave front incident from the collimator. The output signal from vector network analyser (2) (VNA) feeds through transmit/ receive switch unit (3) the feed element. In the paper, the PAA based on ferrite phase shifters was used. The waveguide distribution system feeding the same provided the scheme of a quadrant-wise division of the array transmitting aperture. Based on waveguide bridges, the beam-forming output system was formed. At the output of the sum channel, signals of all quadrant fourths of the array are combined in-phase. In the azimuth difference channel, signals of two right and two left quadrants of the array are summed in anti-phase, and, in the elevation channel - signals of two upper and two lower quadrants of the same. Thus, the monopulse direction-finding scheme of the array is formed. Output signals from these PAA channels are received at the inputs of three independent measuring receivers of VNA (open architecture configuration). Measurement results for three channels can be recorded simultaneously. When changing the PAA installation by roll, the polarization angle of feed element is changed automatically, so that tested PAA and feed element would remain polarization-matched.

**Fig. 2**. Flowchart of the compact polygon of the measuring complex (configuration in the receive mode): 1 - control and computing PC; 2 - vector network analyser (VNA); 3 - transmit/ receive switch unit; 4 - antenna rotary support device (ARSD); 5 - ARSD controller; 6 - feed element positioning device controller; 7 - tested PAA; 8 - feed element; 9 - feed element positioning device; 10 - collimator mirror; 11 - spherical front of the wave from the feed element; 12 - plane front of the wave incident to PAA

## Separate measurement of the BAE components (using the conventional method) for one section of the RPR surface

In some sections of the surface of tested RPR, the BAE components can be measured separately using the well-known conventional “difference” method. In this case, the measuring tasks were solved by contradiction. Let us clarify what it does mean. Using the outboard bracket, PAA was rigidly

attached to the rotary support device (ARSD) of the antenna measuring complex, and custom designed fixtures made it possible to install the RPR at any azimuthal angle relative to PAA. The general view of the measuring complex with UAV PAA installed under the RPR (the azimuthal plane of installation on the ARSD) is shown in Figure 3.

In the plane of PAA azimuthal installation, as it is shown in schematic Figure 4, having applied the conventional “difference” method, we can easily measure the dependence of the BAE azimuthal component (Δα_{х}) on an angle of reciprocal installation of PAA–RPR – Ω. The output of PAA azimuthal difference channel is connected to one of the receive inputs of vector network analyser (VNA), as shown in Figure 2, and angular coordinate of the RP minimum is measured by insignifi cant motion of the ARSD in the azimuthal plane. If during measurements, i. e. at all points of reciprocal azimuthal installation of PAA–RPR, the PAA beam is not defl ected, then this component shall be measured along one RPR section line (9).

The result of such measurement of the BAE azimuthal component by points on the section line of RPR (9) on one of the letter frequencies (wavelength band λ = 3 cm) is shown in Figure 5.

Component Δαx is an odd function of argument Ω. We take the angle of PAA–RPR reciprocal installation as Ω angle. At that, Ω = 0, when the undeflected beam of PAA matches the FD axis. In Figure 5, the right branch is the positive branch of graph Δα_{х}(Ω) for the angles of Ω reciprocal installation from 0° to +180°, and the left branch is the negative one for Ω from 0° to –180°.

Figure 6 shows that, in case of beam (4) deflection from the normal (3) to PAA physical aperture (1) to an arbitrary point on the surface of such RPR (2), it can be said that there are two BAE components. It is worth reminding that the deflected beam direction means the normal to the currently set plane phase front of PAA. In Figure 6, the BAE components are marked as ΔAZ and ΔEL, and in the PAA coordinate system (α_{х} α_{у}) described in [1], they are marked as Δα_{х} and Δα_{у}. Although the resulting errors can be recalculated to the other coordinate systems, e. g., to those of the carrier, for their subsequent compensation in the ABR boresight channels, this type of their expression appears to be the most appropriate.

Based on simplified representations of geometrical optics and physical interpretation of refraction coefficient at the interface and subject to the drop shape of RPR, the view of the resulting graph can be easily explained. Hence, e. g., two RPR surface points located symmetrically relative to the vertical symmetry plane (6) in Figure 6, most likely, should have similar properties in terms of the ability to refract the incident electromagnetic wave. They match two deflected beams (4) and (5) by equal spacial angles ϴ = ±30°. For component Δα_{х} (ΔAZ is an azimuthal component in Figure 6), this is a match in the absolute value and an opposite in sign, as confirmed by the provided graph.

Exactly for the same reason, in the plane of PAA–RPR system elevation installation (like in Fig. 7), having applied the same conventional approach, the dependence of the BAE elevation component (Δα_{у}) on an angle of PAA–RPR reciprocal azimuthal installation is measured.

As can be seen in Figure 7, ARSD design does not allow to make measurements throughout the entire range of angles Ω (±180°). In such case, a small sector of angles appears to be inaccessible for measurement.

Schematic Figure 8 shows how, having applied the conventional “difference” method and measured a shift of the difference RP minimum before and after the RPR installation, we can measure the dependence of the BAE elevation component (Δα_{у}) on an angle of PAA–RPR reciprocal installation – Ω. But at that, the output of PAA elevation difference channel is connected to the corresponding input of vector network analyser (VNA), as shown in Figure 2, and angular coordinate of the RP minimum is measured by insignifi cant movement of the ARSD in the same azimuthal plane.

If, at that, i. e. at all points of PAA–RPR reciprocal azimuthal installation, the PAA beam is not deflected, then this component will be measured along the same RPR section line (9), as in the case of PAA azimuthal installation.

The result of such measurement of the BAE elevation component by points on the section line of RPR (9) on one of the letter frequencies (wavelength band λ = 3 cm) is shown in Figure 9.

Negative values of component (Δα_{у}) graph were obtained when measuring in the elevation plane of PAA–RPR system installation and at roll angle ᴪ = +90° within the range of angles of reciprocal installation Ω of UAV RPR – UAV PAA from –180° to +180°. Positive values of component (Δα_{у}) graph were obtained when measuring in the elevation plane of PAA–RPR system installation and at roll angle ᴪ = –90° within the range of angles of reciprocal installation Ω of UAV RPR – UAV PAA from –180° to +180°.

Component Δα_{у} is an even function of argument Ω. In Figure 9, the right branch of graphs Δα_{у}(Ω) for reciprocal installation angles Ω from 0° to +180° approximately matches the left one in value and in sign, for Ω from 0° to –180°. According to representations of the same geometrical optics and at the available RPR shape of drop type in Figure 6, it is obvious that components Δα_{у}(Ω) for the points symmetrically located on the RPR surface are equal in value and in sign. The above graphs demonstrate it quite clearly. The blind area will be (by reciprocal installation angle Ω) from –10 to –70° for such measurements at the available ARSD design and ᴪ = +90°, and from +10 to +70° for ᴪ = –90°. Taking this into account, it can be said that measurement results obtained at two roll angles ᴪ = ±90° and taken with the corresponding signs, can complement each other in the blind areas.

Thus, both BAE components can be measured using the conventional method in one RPR section line (9) in Figures 4 and 8 and at the same points of PAA–RPR reciprocal installation – Ω.

**Fig. 3**. General view of the measuring complex with a UAV PAA installed under the RPR (azimuthal plane of installation on the ARSD)

**Fig. 6**. BAE components at PAA phasing to arbitrary symmetrical points on the surface of the drop-shaped RPR: 1 – phased-array antenna (PAA); 2 – RPR surface; 3 – normal to the physical aperture of PAA; 4, 5 – refracted beams at phasing of the array to symmetrically located points on the RPR surface; 6 – symmetry plane of the drop-shaped RPR

**Fig. 7**. General view of the measuring complex with a UAV PAA installed under the RPR (elevation plane of installation on the ARSD)

## Method of calculation of the BAE components in oblique plane of PAA installation (in the same section of the RPR surface)

On the other hand, when installing PAA–RPR (UAV) system to an arbitrary roll angle, as shown in Figure 10, where simultaneous measurement of angular coordinates of the minima of both difference RPs, we can use a method, the theoretical justification of which was provided by the authors in the report at the “Almaz – Antey” Conference in the previous year [1].

It appears that, when applying this method described in [1], the BAE components can be measured and calculated in the same sections of RPR surface where the BAE components were previously measured separately, using the conventional method. At that, the results of measurements performed at the same points of RPR surface using different methods can be compared. Figure 11 shows installation of PAA (1) – RPR (3) system on the ARSD, when the system roll angle relative to the horizontal plane (10) makes up angle Ψ (5).

If every time the array is phased so that beam (4) deflected by an arbitrary angleθo (8) (within the range of possible deflection angles for this PAA and constant roll angle Ψ) would be installed into the horizontal plane of measurement (14), which matches the horizontal plane of ARSD azimuthal turn (10), then sections of difference RPs can be measured by a simple movement of the ARSD in the horizontal plane. Boresight angle errors Δα_{хi,j}, Δα_{уi,j} (in the PAA coordinate system for various possible angles of installation θoi and Ψj), which occur after installation of the RPR, can in such case be calculated according to formulas (1), (2):

where Δα_{хi,j} is component of the boresight error introduced by the radome in angle α_{х} (at θ = θ_{oi}; Ψ = Ψ_{j});

Δα_{yi,j} is component of the boresight error introduced by the radome in angle α_{y} (at θ = θ_{oi}; Ψ = Ψ_{j});

θo_{i} is current value of PAA beam deflection angle θ, at which, before the radome installation, angular coordinates of the minima in simultaneously measured sections of difference RPs match.

And angle θ (in the PAA spherical coordinate system) is determined as an angle between the normal to the PAA aperture and the direction towards the minimum, which is formed by spatial difference RPs at beam deflection;

Ψ_{j} is current value of antenna system roll angle relative to the horizontal plane of the ARSD azimuthal turn;

θ_{ai} is actual measured angle of the minimum in the section of difference azimuthal pattern (at θ = θ_{oi}; Ψ = Ψ_{j}) after the radome installation;

θ_{уi} is actual measured angle of the minimum in the section of difference elevation pattern (at θ = θ_{oi}; Ψ = Ψ_{j}) after the radome installation.

The main condition of method applicability is the equality θ_{a} = θ_{у} = θ_{o} before installation of the RPR. On the screen shot of the measuring complex monitor (Fig. 12a), this looks like a match of angular coordinates of the minima of simultaneously measured sections of difference radiation patterns, which corresponds to the direction of the precise boresight to the source of the electromagnetic wave plane front. After installation of the RPR, the arrival direction of the electromagnetic wave plane front (due to refraction in the RPR) changes, and on the screen of the measuring complex monitor (Fig. 12b), it looks like a “divergence” of the measured minima of difference patterns sections.

## Compensation of initial boresight setting error

In general, due to non-ideal ARSD design, the real plane of its azimuthal turn (10) in Figure 11 does not match the plane (14) that should contain all beams deflected to angle θoi, therefore, the condition of θai = θуi is not met before installation of the RPR. The practical measurement experience and its huge potential volume show that attempts to compensate the ARSD position mechanically, striving to meet these conditions, are absolutely pointless. That is why, the “initial electronic compensation” procedure was suggested. The method provides for compensation of the initial error of the PAA beam installation using PAA itself. It was tested and proved its effi ciency for PAA, used in the works described in [1]. However, PAA (of signifi cantly smaller size) used herein did not imply the possibility to apply the “electronic compensation” method, therefore, it has been brought to the initial boresight point before installation of the RPR, where the condition of θ_{a} = θ_{у} = θ_{o} is met, in another way. In some particular cases, for PAA installed to roll angle Ψ without the RPR, when the minima matching condition is not met, the adjustment to the boresight can be achieved through insignifi cant change in its roll angle. This was exactly the way to identify four different roll angles of PAA, where initial conditions of its precise installation by the boresight were met.

## Results of measurement of the BAE components in oblique plane of PAA installation (in the same section of the RPR surface)

Measurements according to this method were performed at the following 4 identifi ed angles of UAV PAA installation by roll (Ψ = +31.5°; +72.5°; –39.5°; –62.0°). At that, beam (2) of PAA (1) (Fig. 11) was not deflected from normal (7), i. e. θo = 0, and the condition of θa = θу = θo was met at the selected angles. Further, while changing PAA and RPR reciprocal azimuthal installation angle – Ω (11), with a particular discrete, we get a set of points lying in the same section, where the BAE components were previously measured using the conventional method. The suggested method makes it possible to measure both components simultaneously at the same points. If they are measured correctly in this case, then, obviously, the measurement results shall match and shall not depend on the angle of PAA installation by roll. The measurement itself was performed by the ARSD movement in the azimuthal plane, which made it possible to simultaneously record fragments of both difference RPs, and, therefore, angular coordinates of their minima. At that, the outputs of both difference channels of PAA are simultaneously connected to the corresponding receive inputs of VNA in Figure 2.

The graphs below show comparative results of measurements of the BAE azimuthal and elevation components introduced by the drop-shaped RPR. Reducible components Δα_{х}(Ω) and Δα_{у}(Ω) (depending on PAA–RPR reciprocal azimuthal installation angle Ω) are calculated according to formulas (1)–(2) at each point of section line (9), that is, at the same points as directly measured using the conventional method, as shown in Figures 4, 8.

Figures 13–16 show the graphs of azimuthal Δα_{х}(Ω) and Δα_{у}(Ω) components pairwise, and one graph in the pair is obtained through direct measurements using the conventional method (in case of PAA azimuthal and elevation installation), and another one is calculated using formulas (1)–(2) at a fi xed roll angle of PAA–RPR system.

Figure 17 shows the graphs of azimuthal component Δα_{х}(Ω), which were measured using the conventional method and calculated at various PAA–RPR roll angles.

Figure 18 shows the graphs of elevation component Δα_{y}(Ω), which were measured using the conventional method and calculated at various PAA–RPR roll angles.

The results of direct measurements of the BAE components using the conventional “difference” method when installing PAA–RPR system in the orthogonal planes of azimuth and elevation, as shown in Figures 4 and 8, tolerably (with an error of ±3 ang. min.) correlate to the results of calculation of the BAE components, made according to the suggested methods using formulas (1)–(2), at various angles of system installation by roll.

## Task geometry for a set of sections over the drop-shaped RPR surface. Creating full BAE matrix over its surface

Based on this method, a sequence of actions can be suggested and full matrix of the BAE components can be measured over a signifi cant surface of such RPR. This refers to the following.

Figure 19 shows PAA (1) on the ARSD, when its roll angle relative to horizontal plane (10) makes up angle Ψ (5).

If every time you select arbitrary angle θ (8) of beam (4) deflection from normal (7) (out of the range of possible angles of deflection for this PAA) at a constant and fi xed roll angle Ψ and phase the array so that a beam deflected into point (12) on the RPR surface would remain in the horizontal plane (white in Fig. 19), then sections of difference RPs can be measured by simple movement of the ARSD in the azimuthal plane (10). In such case, the precise boresight to the direction of the plane wave front arrival from the collimator is fixed by matching of the minima of measured difference RPs. At initial matching of the minima, the correction is achieved either by “electronic compensation” as suggested in [1], or by mechanical correction of the roll angle as it was described above herein. After the RPR (3) installation on PAA, the measurements are performed at the same points (12) on the RPR surface, each of which corresponds to PAA beam defl ected by various values of angle θ. After angle θ is selected and PAA beam is installed at one of the points, we can change the value of PAA–RPR reciprocal azimuthal installation angle Ω (11) (from 0 to ±180°) with a certain discrete ΔΩ (14), while obtaining a set of points along one of the section lines (13). For example, blue point (12) on the RPR surface (corresponds to the maximum

possible positive deflection angle θ) will give a set of points lying on the blue section line of the RPR surface at the RPR rotation around axis (6). One row of the general matrix can be assigned to the BAE components measured in these points. If we apply this method at each such point that conforms to various allowable angles θ and Ω, and calculate BAE components Δα_{х} and Δα_{у} therein by possible sections (13) of the RPR, we will get a set of rows, i. e., BAE matrix measured over the entire RPR surface. A set of similar lines (13) over the RPR surface can also be obtained at PAA installation to another fi xed roll angle.

Practical example of BAE matrix formation.

Measuring of the BAE components in the oblique plane of PAA installation at different angles of beam deflection from the normal

Figure 20 schematically (view in the FD) shows installation of PAA–RPR system at roll angle Ψ =+75° and angle of beam deflection from the normal θ = –20°. In such case, as this method implies, the array is phased so that the deflected beam marked with a green spot in Figure 21 lies in the horizontal plane of the ARSD azimuthal turn. When looking in the FD, this plane in Figure 20 degenerates into a horizontal line.

Before installing the RPR, the roll angle has been adjusted using the method previously described herein, at which the condition of matching of the minima of difference RPs is met. It made up Ψ = +75.03°. After installing the RPR, while changing the reciprocal azimuthal installation angle Ω, the measurement and subsequent calculation of the BAE components by line (blue in Fig. 20) Δα_{х} and Δα_{у} were made at points with an increment by Ω – 10°, using the suggested method.

On the other hand, at such preset angles of beam setting by Ψ and θ, the initial coordinates of array phasing shall be calculated using the wellknown formulas

In such case, they will make up: α_{х} = –5.1°, and α_{y} = –19.3°.

In this case, these array phasing angles, through the corresponding ARSD settings, made it possible to bring the deflected PAA beam to the collimator axis in both orthogonal planes of PAA installation, i.e., to set the beam along the normal towards the plane front of the electromagnetic wave incident from the collimator. Thus, if PAA was installed in the horizontal plane of azimuth (Ψ = 0°), the ARSD installation coordinates made up AZ arsd = +5.1°; EL arsd = +19.3°, as demonstrated in Figure 21a. Thus, even in case of a deflected beam, there is an opportunity to independently measure the BAE azimuthal component. This component can be measured using the conventional “difference” method, as in the case of an undeflected beam. The same thing can be said with regard to the measurement of the BAE elevation component at vertical (Ψ = +90°) installation of PAA, when the ARSD is installed by coordinates AZ arsd = +19.3°; EL arsd = –5.1°, as shown in Figure 21b. Thus, for particular angles Ψ and θ of system installation, an opportunity of comparing components Δα_{х} and Δα_{у}, directly measured using the “conventional” method and calculated ones, emerges once again.

Figure 22 below shows the combined results of direct “conventional” measurements and calculation according to the formulas of suggested method for the BAE azimuthal component Δα_{х} based on reciprocal azimuthal installation angle Ω, and Figure 23 shows the results for elevation Δα_{у}. In the provided graphs, components Δα_{х} and Δα_{у} are shown in angular minutes, and reciprocal installation angle Ω is shown in angular degrees. Measurements were performed at the only frequency letter within 3-cm wave length band.

No data of “conventional” measurements in case of system elevation installation in the “blind” area (Ω = from –10 to –70°) is available.

The substantially dissected nature of component graphs is attributable to the air duct channel in the lower part of the RPR belt (measurement area).

In a similar way, Figure 24 schematically (view in FD) shows installation of PAA–RPR system at roll angle Ψ = –55° and angle of beam deflection from the normal θ = –12°.

Before installing the RPR, the roll angle, at which the condition of matching of the minima of difference RPs was met, has been adjusted. It made up Ψ = –54.8°. After installing the RPR, while changing the reciprocal azimuthal installation angle Ω, the measurement and subsequent calculation of the BAE components by line (red in Fig. 24) Δα_{х} and Δα_{у} were made at points with an increment of 10°, using the suggested method.

At the preset angles of beam setting by Ψ and θ, the initial coordinates of array phasing, calculated using formulas (3)–(6), will make up: α_{х} = –6.9°, and α_{у} = +9.9°.

At these array phasing angles, it also appeared to be possible, through the corresponding ARSD settings, to bring the deflected PAA beam to the collimator axis in both orthogonal planes of PAA installation. Thus, if PAA was installed in the horizontal plane of azimuth (Ψ = 0°), the ARSD installation coordinates made up: AZ arsd = +6.9°; EL arsd = –9.9°, as demonstrated in Figure 25a. For vertical (Ψ = –90°) installation of PAA, the ARSD is installed by coordinates AZ arsd = +9.9°; EL arsd = +6.9°, as shown in Fig. 25b. Thus, for particular angles Ψ and θ of system installation, an opportunity of comparing components Δα_{х} and Δα_{у}, directly measured and calculated ones, emerges once again.

Figure 26 below shows the combined results of direct “conventional” measurements and calculation according to the formulas of suggested method for the BAE azimuthal component, and Figure 27 shows the results for the elevation component.

As the most “interesting” area of this dropshaped RPR is the area of reciprocal installation angles Ω (100–180°) and, due to the lack of time, no measurement for angles Ω within the range of ±70° was performed and there is no relevant data on the graph.

## Estimating measurement errors

Issues related to errors and accuracies of the suggested method were discussed in paper [1].

It should be said that, in view of a small weight of tested RPR, the correction eliminating the systematic errors associated with changes in load on the ARSD when installing the RPR (due to backlashes in the ARSD mechanical drives), as suggested in [1], was not performed in this case. In addition to direct measurements, the suggested method of the BAE components determination also includes subsequent calculations using formulas (1)–(2). According to the well-known metrology ratios, the calculation of error of a value that is a complex function (of multiple variables), is determined by way of calculation of its differential through the differentials of its arguments. Even if anything is known about the errors of measured arguments, the task to estimate the error of calculation of the functions themselves (BAE components) using mathematical methods becomes quite complicated and goes beyond our competence. The conventional “difference” method (works only on orthogonal sections of the RPR surface) as a method of direct measurement of the BAE component value must, obviously, provide the most reliable results. When comparing the data obtained using this method with the estimate data under the suggested method, the maximum error for all measured BAE components can reach 4–5 ang. min. However, it should be taken into account that both conventional and suggested methods provided only one implementation of the measured value, which cannot facilitate correct judgements on statistical errors of such measurements. It would be the right thing, after collecting the statistics, to assess such confi dence interval that includes all implementations obtained at multiple measurements and impacts of all inherent random factors. Relative simplicity of the suggested method and also the possibility to fully automate the measurement process give promise that this approach can be implemented. Unfortunately, within this paper, due to the lack of time, this was absolutely impossible, but can be quite feasible, subject to further interest in the tasks of BAE measurement in “antenna – radome” systems. Currently, it can just be said that data, obtained using the conventional “difference” method and calculated using the suggested method, mutually correlate quite well, which once again confi rms this method’s applicability for measuring BAE.

## Conclusion

If the RPR surface is precisely set mathematically, then the point-by-point view of the RPR surface section can be built at various reciprocal installation angles – Ω at fixed roll angles Ψ and beam deflection angles θ. As it was said earlier, it is convenient to assign a row of the general matrix to the points of this section where the BAE components can be measured using the suggested method. Such approach makes it possible to fully match the measured BAE components (Δα_{х} and Δα_{у}) to each point on the surface of real RPR. It is very useful to understand and physically interpret the measured values and signs of the BAE components over the RPR surface, especially around “special areas” (air duct edge, tail nose, etc.). For this reason, the BAE component measurement increment can differ even over the surface of the same RPR. The increment can be, for example, decreased around “special areas” where we may expect a sharp change in the BAE value, or, vice versa, an increase in the area of predictable smooth behaviour of the function. For the measured RPR (as the presented graphs suggest), the function rapid change area was represented by its rear elongated drop-shape part and air duct edge. But, due to the lack of time, the measurements were performed with one discrete over the entire RPR surface. For a more full-fledged study of the RPR refraction characteristics, for example, a custom program can be written to visualize the point-bypoint measurement process (by sections Ψ, θ and Ω) directly during execution of the same in the form of graphs of measured components, built in the real time mode, and to automatically select the increment of performed measurements. The suggested method, where the measurement results are obtained immediately during execution of the same, leaves open this possibility.

## Conclusion

A sequence of actions is suggested and it is shown how, in case of a drop-shaped RPR surface considered herein, a full matrix of the BAE components can be calculated, i. e., how the data can be obtained when phasing an array (PAA, APAA) in an arbitrary point of the surface.

Graphs of components Δα_{х} and Δα_{у} in the above figures quite correctly refl ect the physical sense of dependence of the BAE components on incident angles of the plane electromagnetic wave.

It should be noted that the suggested method of the BAE components calculation can be used to obtain data on the transmission factor (TF) over the entire surface of tested RPR. If there is a measured fragment of the sum RP as the third component, the data is obtained automatically, and it can be said that there is a TF matrix for this RPR.

The absolute advantages of the method include the possibility to measure the RPR parameters directly using the same antenna system (PAA, APAA) (as it was in [1] and herein), which is supposed to be further used in the complex. This signifi cantly increases the reliability of the resulting data, as compared to, for example, the case of use for the survey of radio-technical characteristics (RTC) of the RPR of an abstract test antenna.

Finally, the most important thing to be mentioned once again. The work performed led the authors to the profound conviction that today it would be absolutely wrong to consider the radiation characteristics of the state-of-the-art airborne PAAs (APAAs, as well as other antennas) in isolation from the RPR (this especially regards the RPRs of complex shapes), under which it is located. And it is not just about the BAEs introduced by the RPR, but also about a set of other parameters. Unfortunately, the currently established practice suggests that developers of antenna systems prefer to work with “pure antennas” and do not like to include RPRs in the research set. In the meantime, the “antenna-radome” system (in the entire possible area of installation of its beam under the RPR) can be associated with interesting metamorphoses, for example, with slopes of direction-finding characteristics due to “fi lling” of zeroes of difference patterns, transmission factors (TF), etc. The RTC of the radomes actually manufactured in the industry (even of a single-type shape) are mostly and greatly individual and, therefore, can hardly be described in a mathematically precise way. For this reason, performance of a set of works, for example, on modelling of amplitude-phase distributions in the PAA emitting aperture to optimize its emitting characteristics, can become almost senseless if performed in isolation from the RPR.

## References

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### About the Authors

**I. E. Makushkin**Makushkin Igor Evgenievich – Head of the Laboratory

Research interests: antenna measurements, microwave technology

**A. M. Shemarin**Shemarin Alexander Mikhailovich – Lead Engineer

Research interests: radar, microwave technology.

**Yu. Yu. Vitsukaev**Vitsukaev Yury Yurievich – Engineer of the 2nd category

Research interests: radar, microwave technology

**D. M. Tyurin**Tyurin Dmitry Mikhailovich – Acting Head of the Laboratory

Research interests: microwave technology, microwave measurement automation.

### Review

#### For citation:

Makushkin I.E., Shemarin A.M., Vitsukaev Yu.Yu., Tyurin D.M. A method for measuring boresight errors for a radioparent radome of arbitrary shape. *Journal of «Almaz – Antey» Air and Space Defence Corporation*. 2020;(1):26-45.
https://doi.org/10.38013/2542-0542-2020-1-26-45