1. Introduction

Antenna measurement techniques are devoted to obtaining the main radiation parameters (radiation pattern, antenna gain, polarization, etc.) in the antenna far-field (FF) region<sup>1</sup> from the acquisition of the fields radiated by the antenna under test (AUT). Novel methods for antenna measurement [1] and postprocessing techniques [2] are constantly emerging to cope with the requirements needed to provide efficient and accurate characterization of new types of antennas, mainly at high frequency bands. Additionally, antenna diagnostics enables nondestructive inspection of the antennas for detection of design or fabrication failures by means of the analysis of their extremely near fields or their equivalent currents [3–6].

First, antenna measurements were performed in outdoor ranges at FF distances. Those tests were highly affected by weather conditions, interference, and multipath from multiple reflections mainly caused by the floor. Anechoic chamber testing was sooner adopted as the standard method for antenna metrology. Anechoic chambers have an electromagnetic absorber lining to reduce electromagnetic reflections and to control the measurement environment [7].

Advances in fabrication technologies have contributed to the development of new components and antennas at millimeter (mm-) and submillimeter (submm-) wave frequency bands.<sup>2</sup> At these frequencies, measurement of directive antennas would require extremely large anechoic chambers to fulfill the FF condition. Hence, other types of measurement ranges such as nearfield (NF) measurement ranges have been developed to avoid the previous shortcoming [1].

In NF measurement systems, the field is acquired over a surface in the vicinity of the AUT. Planar, cylindrical, or spherical surfaces are the most common acquisition surfaces, with recent extensions to arbitrary geometry [9] or noncanonical domains [10, 11]. The acquired NF can be employed to obtain the FF radiation pattern of the antenna by means of mathematical NF-FF transformations based either in wave expansions [1, 12, 13] or integral equation methods such as the sources reconstruction method (SRM) [3, 9]. Diagnostics applications can also be developed from NF data using backpropagation techniques toward the AUT aperture [1, 13] or the SRM [3, 9]. After several decades of research and development, NF ranges have become the preferred approach for antenna testing.

Special attention must be given to the probe pattern and positioning accuracy [1] as well as to the effects that error sources in NF acquisitions, such as truncation of the measurement plane, cable flexing, stray signals, leakage, etc., can introduce in the FF pattern of the AUT [1, 2, 13, 14].

<sup>1</sup> The far-field distance is defined by <sup>R</sup> <sup>¼</sup> <sup>2</sup>D<sup>2</sup>=<sup>λ</sup> (<sup>R</sup> >> <sup>λ</sup>), being <sup>D</sup> the maximum dimension of the antenna and <sup>λ</sup> the wavelength [1].

<sup>2</sup> The mm-wave band is defined according to the IEEE Standard 521-2002 from 110 to 300 GHz. This standard is a review of the standard published in 1984 that also considered the lower bands defined from 30 to 110 GHz (Ka, V, and W bands) as part of the mm-wave band. This older definition is still commonly accepted. Frequency bands above 300 GHz are not included in the standard; the submm-wave or Terahertz band corresponds, depending on the author, to the fraction of the spectrum from 300 GHz to either 3 or 10 THz in the lower limit of the far-infrared spectrum [8].

NF techniques for both NF-FF transformation and antenna diagnostics generally require the knowledge of amplitude and phase of the radiated electric field by the AUT [1–5]. Nevertheless, phase acquisition, particularly at mm- and submm-wave bands, is a challenging task that requires sophisticated and expensive equipment due to the high thermal stability requirements and the effect of the errors, mostly resulting from thermal drift and cable flexing [1, 13–16].

1. Introduction

244 Holographic Materials and Optical Systems

preferred approach for antenna testing.

[1, 2, 13, 14].

wavelength [1].

1

2

Antenna measurement techniques are devoted to obtaining the main radiation parameters (radiation pattern, antenna gain, polarization, etc.) in the antenna far-field (FF) region<sup>1</sup> from the acquisition of the fields radiated by the antenna under test (AUT). Novel methods for antenna measurement [1] and postprocessing techniques [2] are constantly emerging to cope with the requirements needed to provide efficient and accurate characterization of new types of antennas, mainly at high frequency bands. Additionally, antenna diagnostics enables nondestructive inspection of the antennas for detection of design or fabrication failures by means

First, antenna measurements were performed in outdoor ranges at FF distances. Those tests were highly affected by weather conditions, interference, and multipath from multiple reflections mainly caused by the floor. Anechoic chamber testing was sooner adopted as the standard method for antenna metrology. Anechoic chambers have an electromagnetic absorber lining to reduce electromagnetic reflections and to control the measurement environment [7]. Advances in fabrication technologies have contributed to the development of new components and antennas at millimeter (mm-) and submillimeter (submm-) wave frequency bands.<sup>2</sup> At these frequencies, measurement of directive antennas would require extremely large anechoic chambers to fulfill the FF condition. Hence, other types of measurement ranges such as nearfield (NF) measurement ranges have been developed to avoid the previous shortcoming [1]. In NF measurement systems, the field is acquired over a surface in the vicinity of the AUT. Planar, cylindrical, or spherical surfaces are the most common acquisition surfaces, with recent extensions to arbitrary geometry [9] or noncanonical domains [10, 11]. The acquired NF can be employed to obtain the FF radiation pattern of the antenna by means of mathematical NF-FF transformations based either in wave expansions [1, 12, 13] or integral equation methods such as the sources reconstruction method (SRM) [3, 9]. Diagnostics applications can also be developed from NF data using backpropagation techniques toward the AUT aperture [1, 13] or the SRM [3, 9]. After several decades of research and development, NF ranges have become the

Special attention must be given to the probe pattern and positioning accuracy [1] as well as to the effects that error sources in NF acquisitions, such as truncation of the measurement plane, cable flexing, stray signals, leakage, etc., can introduce in the FF pattern of the AUT

The far-field distance is defined by <sup>R</sup> <sup>¼</sup> <sup>2</sup>D<sup>2</sup>=<sup>λ</sup> (<sup>R</sup> >> <sup>λ</sup>), being <sup>D</sup> the maximum dimension of the antenna and <sup>λ</sup> the

The mm-wave band is defined according to the IEEE Standard 521-2002 from 110 to 300 GHz. This standard is a review of the standard published in 1984 that also considered the lower bands defined from 30 to 110 GHz (Ka, V, and W bands) as part of the mm-wave band. This older definition is still commonly accepted. Frequency bands above 300 GHz are not included in the standard; the submm-wave or Terahertz band corresponds, depending on the author, to the fraction of the

spectrum from 300 GHz to either 3 or 10 THz in the lower limit of the far-infrared spectrum [8].

of the analysis of their extremely near fields or their equivalent currents [3–6].

Nowadays research is focused on the development of new measurement systems [17, 18] and techniques that allow reducing the acquisition time and costs and preventing or correcting the effect of errors in NF measurements [2–7, 19]. Among these techniques, amplitude-only measurements, commonly referred to as phaseless or scalar measurements (in contrast to vector, also referred to as complex measurements involving amplitude and phase), are frequently employed due to their multiple advantages such as the use of simpler and less expensive receivers and robustness to errors related to phase acquisition. Amplitude-only techniques can be indistinctly applied to antenna measurements and diagnostics and are divided into two main groups depending on the implementation approach: iterative and noniterative techniques.

On the one hand, most of the iterative techniques [3, 19, 10] are based on the acquisition of the field intensity in two or more surfaces. Then, an iterative process is employed to propagate the field from one surface to another after guessing an initial phase, until certain condition is satisfied for all the surfaces. This kind of technique is popular because they involve minor changes in the measurement setup, nevertheless they can suffer from stagnation and their convergence is strongly related to the first guess solution. On the other hand, and belonging to noniterative techniques, most of the interferometric approaches [5, 20–23] rely on the use of a reference field, previously known in amplitude and phase, used to interfere the field of the AUT and allowing an easy and iteration-free phase retrieval by means of a filtering process in the spectral domain.

Indirect off-axis holography, also known as Leith-Upatnieks holography [24], is an interferometric technique adapted from optical holography to amplitude-only antenna metrology in the early 1970s [25, 26]. During the last years, great efforts have been made to improve aspects such as sampling [22] and overlapping reduction [27] or reference signal calibration [28, 29]. The rest of the chapter is divided as follows: Section 2 contains an introduction to conventional off-axis holography techniques applied to antenna metrology. Novel techniques that allow for the use of synthesized reference waves with mechanical phase shifts [5, 30] will be introduced in Section 3. A new efficient method for amplitude-only characterization of broadband antennas [23] compatible with nonredundant sampling techniques [31] will be described in Section 4. Finally, main conclusions regarding the advantages and disadvantages of the proposed methods will be drawn in Section 5. Numerical validation of the proposed techniques in Sections 3 and 4, performed in Planar NF (PNF) measurement ranges [32, 33], will be given for each method and, thus, although easily translatable to other geometries, formulation will be particularized for planar acquisition systems.
