In Quiet Zone Spherical Near-Field Scanning (QZSNFS) the electric field on the surface of a sphere surrounding the QZ is sampled which is further called the measurement surface. The sampling can be achieved by adding a sturdy beam on top of the available positioning system in an antenna measurement chamber. Fig. 1 shows such a measurement setup using a roll-over-azimuth positioning system which is installed in the CATR of the institute. In this case it should be noted that the coordinate system of the measurement surface no longer coincides with the coordinate system that is used for antenna measurements. Where in a standard measurement setup the z-axis points towards the range feed or reflector in a CATR, the new z-axis for the QZSNFS points along the azimuth rotational axis, effectively exchanging the θ and φ axis in the range. On the left-hand side the feed setup (partly hidden by the absorber baffle) is shown. In the center the range reflector and on the right hand side the AUT positioner. On top of the AUT positioner a fiberglass (grey) beam is mounted which is used to move the probe over the surface of a sphere surrounding the quiet zone. The probe is a specially designed for this purpose.

After measurement Spherical Wave Expansion (SWE) is applied. The SWE for QZSNFS is similar to the one used in spherical near-field antenna measurements, the only difference being the inversion of the signal direction. Figs. 2 and 3 show the calculated mode spectra of the quiet zone at 2.5 GHz.

# Combining Mode Rotation With CLEAN

The Combining Mode Rotation with CLEAN (CMRCLEAN) algorithm is based on the fact that far-field sources which propagate along the z-axis concentrate all of their power in the m=±1 modal spectrum. This is due to the fact that the associated Legendre function of the first kind is only nonzero for these m-modes. If the source is not aligned, the power is spread over all m-indexes depending on its direction (θ, φ).

The calculated mode spectrum is the so called Dirty Map (DM) which contains a convolution of all the reflective sources including the main beam. In order to find a far-field source the mode spectrum needs to be rotated such that the direction of the source is aligned with the z-axis. This can be achieved by using Eulers xyz-rotation functions, with which it is possible to express a spherical vector wave function in a rotated coordinate system as a combination of spherical vector waves in the unrotated coordinate system. Interchangeably the rotation can also be applied directly on the mode coefficients Qsmn by

For each rotation over the angles Theta and Phi a sum is created over the modes with modal index m = ±1 and stored in a detection map. If there are any large sources these sources tend to overshadow the smaller sources and need to be removed from the DM before the smaller ones can be detected. For this purpose the CLEAN algorithm is used. When a far-field source has been detected it can both be removed from the DM and inserted into the clean map (CM).

Since the power of a source coincides twice with the z-axis, both at the locations where the wave travels in and out of the quiet zone, the direction where the wave travels into the quiet zone has to be determined. This can be achieved by using the far-field projection for inward traveling modes only at both directions. The largest contribution of the two calculated far-field directions will then be the correct direction of the source traveling into the quiet zone. This also brings the added advantage that only one hemisphere of rotations needs to be calculated to find each of the sources, reducing computation time by half. By projecting the detected source on the surface of the quiet zone for the angular direction of the source (θ, φ), both tangential components Eθ and Eφ can be derived. The separation in both tangential components adds important information about the polarization of both the main beam and reflective sources in the chamber.

After rotating the DM such that the detected source is aligned with the z-axis again, the power of the far-field source is removed by multiplying all m = ±1 coefficients with the loop gain. In effect the signal power is removed but the phase information kept leaving it intact for the detection of other sources. After removal the DM is rotated back to the original coordinate system and used for the next iteration.

It should be noted here that the algorithm is not able to detect standing wave issues, since the power of both opposite directed traveling waves diminishes equally fast by the loop gain.

Figs. 4 and 5 show the sources that are detected using the CMRCLEAN algorithm. Source power is normalized to the main beam for the vertical polarization. Having both tangential components separated gives important extra information about the polarization of the main beam and depolarization of the scattering centers along the CATR reflector. It is pointed out here that the resolution of the signal detection in this algorithm is much higher than the one in the field-probing section.

# Calculating Linear Probing Data from QZSNFS Measurements

During measurement chamber validation and quality assurance it can be beneficial to view probing data on linear cuts or planes through the quiet zone such as usually measured using field-probing. Since the QZSNFS provides a complete description of the electromagnetic field distribution in the quiet zone, the linear probing data can be easily calculated from the mode spectrum. If furthermore the transmission formula is adapted for calculating the output of a virtual probe antenna at arbitrary locations inside the quiet zone, the output is consistent with actual field-probing measurements.

The adapted transmission formula becomes:

where C is the translation function in arbitrary direction (Bruning and Lo 1969) and R are the rotated probe coefficients. In figure 6 a comparison is shown between field-probing measurements (red) and calculated values from QZSNFS. In figure 7 three planes have been defined on which the output signal of the probe is calculated. The output gives a good visual estimation of the amplitude distribution in the quiet zone.