## Antenna Diagnostics - Back Projection Using Planar Near-Field Measurement Data

This post discusses planar near-field antenna measurements with focus on performing antenna diagnostics using back projection. An example of the back projection procedure is implemented in Matlab where near-field planar measurements of a standard gain horn are back projected.

Typically measurements are made using using a near-field spherical or planar antenna measurement setup, in this case planar,  where there is a distance z0 between the probe and the antenna under test (AUT). Back projection allows one to transform the measured tangential E-fields to the fields across the aperture of the AUT. This is useful as it often allows one to detect antenna defects and faults. However one is limited to a resolution of λ/2.

Back projection makes use of the Fourier transform, to transform the measured tangential fields on a plane in front of an AUT into a spectrum of plane waves, translating it a distance z0 towards the AUT and then using the inverse Fourier transform to find the field at the aperture of an antenna. One can also use the far field data of an antenna, as the far-field is proportional to the plane wave spectrum as follows:



where,

       is the far-field E-field
       is the plane wave spectrum
r        is the distance from the AUT to the observation point
k       is the free space wave number.

This will hopefully be discussed in another post.

Planar Antenna Measurement Setup & Process
An AUT is mounted extended from a wall of electromagnetic absorbing material, where a probe opposite to the AUT, normally an open ended waveguide can scan a plane parallel to the aperture of the AUT with an offset of at least two wave lengths, to reduce electric and magnetic coupling between the AUT and the probe. The scanning of the probe is controlled by two actuators which allow precision steps in the x and y-axis, in this case on the order of 1 mm. The probe can normally measure vertical and horizontal polarization at each point on scanned plane. A vector network analyser can be used to measure S21 for both polarizations for each point over and entire scan plane and saved to a file on a computer.

In the example below this file, is loaded into Matlab and back projection is performed to find the fields at the aperture of the AUT.

Probe Correction
One wants to measure the tangential E-field at each point in a planar measurement, however the probe most often used in planar measurements is an open ended waveguide which must be corrected for. This is not discussed here.

Example: Standard Gain Horn
As an example measurements were conducted using Standard Gain Horn from Scientific Atlanta with the following specifications:

• Frequency: 3.95-5.85 GHz
• Model: SA12-3.9
• Nominal Gain: 18 dB
• a: 47.6 mm
• b: 22.1 mm
• a1: 216.1 mm
• b1: 160 mm
• e: 33.1°
• h: 39.9°
• ρe: 281 mm
• ρh: 316.5 mm

Planar measurements were conducted with the following parameters:

• Frequency: 5.3 GHz
• X-Axis Scan Plane, 0 - 1.5 m
• Y-Axis Scan Plane, 0 - 0.8 m
• X-axis step size, Δx = 0.022 m
• Y-axis step size, Δy = 0.022 m
• Distance between the apertures of the probe and AUT, z0 = 0.088 m
• The origin is placed at the center of the AUT's aperture.
• All samples are taken relative to the defined origin, and not the boundaries of the planar scanner.
• The AUT is horizontally polarized, parallel to the x-axis

What does one expect to see?
Making the following assumptions:

• TE10 mode is excited.
• The aperture is surrounded by an infinite ground plane.
• Quadratic phase variation across the aperture.
• No effects due to conductor thickness or diffraction are taken into account.

Balanis [1, pg. 769] derives the following formula for the E-field in the aperture of the horn:

            Balanis Eq. (13-43a )

where:

E0              is a constant.
a1               the length of the longest side of the horn, parallel to the x-axis.
x & y         are coordinates on the plane of the aperture
ρ1 & ρ2     the shortest line from the aperture of the horn to apex of the horn,
ρ1 for the side with length b1 and ρ2 for the side with length a1
k                is the free space wave number in this case.

From this one could expect to see after back projection an aperture field with a cosine variation, assuming the origin is placed at the center of the aperture.

Results from the Processed Data
The horns aperture Ex, Ey, Ez fields are found from the measured planar near-field data using back projection and plotted below. A link to the Matlab code and data that was used can be found in the next section.

Figure 1. Ex of Standard Gain Horn Aperture Field found using Back Projection

Figure 2. Ey of Standard Gain Horn Aperture Field found using Back Projection

Figure 3. Ez of Standard Gain Horn Aperture Field found using Back Projection

Figure 4. Ex Side View of Standard Gain Horn Aperture Field found using Back Projection.
One can see the cosine like variation over the aperture.