Near-Field to Far-Field Transformation for Antenna Measurements (NF2FF)

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Near field (NF) ranges offer a convenient alternative to compact antenna test ranges (CATR) and anechoic far field ranges for the measurement of phased arrays [1,2,3,4,5,7,8]. NF sites allow for hologram analysis, low sidelobes characterization, and do not require a rotating pedestal capable of bearing the weight of the phased array. The primary objective of the NF2FF sourceforge project is to provide the phased array community with an open-source MATLAB alternative to proprietary NF measurement software. The code features planar near field to far field transforms with rectangular waveguide probe correction, de-embedded in the plane-wave spectral domain [2,3]. (In v0.3.1 and earlier this routine was marked experimental and the call was commented out, so no probe correction was applied; it is implemented and enabled as of v0.4.0.) The secondary objective of the project is to implement various functions for phased array hologram analysis. Phase is recovered with Goldstein branch-cut two-dimensional unwrapping [6,9]. Phased array holograms allow for faulty element localization [5] and for measurement of active element amplitude and phase excitation, in transmit (Tx) as well as in receive (Rx) mode, which allows for insight in the difference between achieved and desired Tx and Rx array factor. In addition, active element Tx and Rx root mean square (RMS) amplitude and phase error can be measured which allows for insight in beam pointing error and side lobe level increase, and gain reduction, while scanning [10].

Hologram analysis can also be used to study near field communication (NFC) antennas.

Assumptions

The script assumes:

• Rectangular coordinate system with z axis normal to planar aperture
• exp(j*omega*t) time dependence convention. Please, substitute i with -j whenever implementing exp(-i*omega*t) time dependence convention based algorithms.
• Sample spacing dx, dy ≤ λ/2. Above that the plane-wave spectrum aliases. The script warns.
• Results are valid only inside the cone set by scan truncation, θ_max = atan((L − D) / (2 z₀)), where L is the scanned length, D the aperture extent and z₀ the scan separation. The script reports this angle and marks it on the principal-plane cuts.
• A planar scan measures only the forward hemisphere, so the reported directivity is a forward-hemisphere directivity.

Datasets

The script uses near field datasets of a 94 GHz slotted waveguide (U.S. Patent No.: 7,994,969). If you do not have them to hand, NF2FF_TestData.m generates a synthetic dataset in the same format, and NF2FF_SelfTest.m checks the transform against it.

Wish list

Sought-after extensions are listed below. Please post them on the website, if you are willing to contribute:

• Cylindrical and spherical near field to far field transformation
• Graphical user interface

Change log

v0.4.0 — a correctness release. Results produced with v0.3.1 should be regenerated. Full detail in CHANGELOG.md; the items that change numbers are:

• The plane-wave spectra are kept complex through the far-field assembly. v0.3.1 took the magnitude of the two spectra before combining them, which forces the relative phase of the two aperture components to zero. Every far-field quantity inherited the error, and Ludwig-3 cross-polarisation — which is entirely a statement about that relative phase — was meaningless.
• The DFT phase ramp is removed. The scan is centred on the origin but the DFT places its first sample there. The previous magnitude-only path hid the resulting Nyquist-rate phase ramp; with complex interpolation it biased peak directivity by +0.9 dB.
• The angular grids are symmetric. θ ran −87.14° to +84.75° and never sampled boresight; φ put neither principal plane on the grid, so the "E-plane" cut was taken at φ = 85.9° and the "H-plane" at φ = 2.9°.
• Simpson's rule integrates to the true limits instead of stopping one step short on every side, which biased the radiated power low and the directivity high by about half a dB.
• Ludwig-3 plots are in dB rather than linear directivity under a dB colour axis.
• Probe correction rewritten and enabled. The de-embedding now runs as a 2×2 solve at every visible (k_x,k_y) before the far field is assembled, rather than in the angular domain afterwards. On synthetic data generated through the probe transmission equation, wide-angle (20–60°) pattern error drops from 2.62 dB RMS to 0.37 dB RMS.
• The propagating/evanescent test no longer relies on isreal() applied to elements of a complex array, which under MATLAB classified every mode as evanescent and produced an identically zero hologram.

Also in v0.4.0: sample-spacing and valid-angle checks at run time; a synthetic dataset generator that documents the sdata format the transform consumes; a 13-case self test against the analytic far field of a uniform aperture; plotting separated from the transform so it runs headless; GNU Octave support alongside MATLAB; and the LICENSE, README.md and THIRD-PARTY.md the package had never carried. Fixes to MovieMaker.m (which could not run at all — its θ axis was 59 points against 61 columns of data) and to the three VNA control scripts are listed in the change log.

Note that none of the bundled instrument scripts performs a planar scan or writes the structure the transform consumes, so the acquisition half of the project is still missing. NF2FF_TestData.m documents the format a scan script must produce.

References

[1] W. Leach, Jr., D. Paris, "Probe compensated near-field measurements on a cylinder," IEEE Trans. Antennas Propagat., vol. 21, no. 4, pp. 435-445, July 1973.

[2] D. Paris, W. Leach, Jr., E. Joy, "Basic theory of probe-compensated near-field measurements," IEEE Trans. Antennas Propagat., vol. 26, no. 3, pp. 373-379, May 1978.

[3] A. D. Yaghjian, "Approximate formulas for the far field and gain of open-ended rectangular waveguide," IEEE Trans. Antennas Propagat., vol. 32, no. 4, pp. 378-384, April 1984.

[4] A. D. Yaghjian, "An overview of near-field antenna measurements," IEEE Trans. Antennas Propagat., vol. 34, no. 1, pp. 30-45, January 1986.

[5] J. J. Lee, E. M. Ferren, D. P. Woollen, and K. M. Lee, "Near-field probe used as a diagnostic tool to locate defective elements in an array antenna," IEEE Trans. Antennas Propagat., vol. 36, no. 6, pp. 884-889, June 1988.

[6] R. M. Goldstein, H. A. Zebken, and C. L. Werner, "Satellite radar interferometry: Two-dimensional phase unwrapping," Radio Sci., vol. 23, no. 4, pp. 713-720, July-August 1988.

[7] G. F. Masters, "Probe-correction coefficients derived from near-field measurements," in AMTA Symposium Digest, Oct. 7-11, 1991.

[8] C. A. Balanis, "Antenna Theory, Analysis and Design, 2nd Ed.," John Wiley & Sons, 1997. (Near-field measurement is Chapter 16 in the 2nd edition and Chapter 17 in the 3rd and 4th editions; the equation numbers cited in the source comments are the 2nd-edition ones.)

[9] D. C. Ghiglia and M. D. Pritt, "Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software," John Wiley & Sons, 1998.

[10] R. J. Mailloux, "Phased Array Antenna Handbook," Artech House, 2005.