Radio frequency antenna gain measuring apparatus and measuring gain of an antenna

Abstract

A radio frequency antenna gain measuring apparatus includes: first and second antennas; antenna positioners to position the antennas; a central controller to: control the antenna positioners to position the first and second antennas, control the linear motion positioner to vary the separation distance, and receive information from the distance meter; and an antenna gain processor to: receive information from the central controller and the first and second radio frequency transmit and receive electronics device, and determine the gain of the first and second antennas based on the third-order scattered signal as a function of the separation distance.

Description

RADIO FREQUENCY ANTENNA GAIN MEASURING APPARATUS AND MEASURING GAIN OF AN ANTENNA STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0001] This invention was made with United States Government support from the National Institute of Standards and Technology (NIST), an agency of the United States Department of Commerce. The Government has certain rights in this invention. CROSS-REFERENCE TO RELATED APPLICATION

[0002] This application claims the benefit of U.S. Provisional Patent Application Serial No.63 / 646,313 (filed May 13, 2024), which is herein incorporated by reference in its entirety. BACKGROUND

[0003] The present invention generally relates to the field of antenna measurement, and more particularly to techniques for measuring antenna gain.

[0004] Gain is one of the most important figures of merit of an antenna. It is a measure of an antenna's ability to direct radio frequency (RF) energy in a particular direction or receive RF energy from a particular direction. The more gain an antenna has, the more focused the RF energy is, or the more RF energy that can be received.

[0005] Antenna gain is commonly measured using a technique called gain extrapolation. In gain extrapolation the signal transmitted between a pair of antennas is measured at a series of separation distances. These signals are then extrapolated to infinity to obtain the far-field gain product of the two antennas. This is also known as the "pair gain". Upon measuring the pair gain for three pairs of antennas one then calculates the individual antenna gains.

[0006] The current approach to gain extrapolation utilizes Paul Wacker's near-zone scattering theory. In this theory the total signal transmitted between two arbitrary antennas is expressed as a power series expansion that accounts for all orders of antenna-to-antenna scattered waves. However, in the current approach all higher-order scattering terms are purposely ignored and only the direct signal between the antennas is kept. As such, the received signal must be filtered and or averaged in order to remove the unwanted higher-order scattered waves from the measured data. The implications are that a large number of data points (often thousands) are needed and large separation distances (several meters) are required in order to avoid the near-zone region of strong antenna-to-antenna coupling and unwanted higher-order scattering.

[0007] It is therefore an objective of the present invention to provide a technique for measuring antenna gain that utilizes a significantly smaller number of data points, and at shorter distances, thereby overcoming the above-mentioned disadvantages of the prior art at least in part.

[0008] Accordingly, methods and equipment for measuring antenna gain that use a significantly smaller number of data points and closer distances would be advantageous and would be favorably received in the art. BRIEF DESCRIPTION

[0009] One aspect of the present invention relates to a radio frequency antenna gain measuring apparatus. A radio frequency antenna gain measuring apparatus may be understood as an apparatus that is capable of measuring the gain of an antenna. It may be provided that the apparatus includes a first antenna having an antenna coordinate system. An antenna is a transducer that converts radio frequency fields into alternating current or vice versa. An antenna coordinate system is a coordinate system that a user defines in order to align the antenna to other objects such as a second antenna. It may also be provided that the apparatus includes a second antenna having an antenna coordinate system. This arrangement enables a user to measure the gain of two different antennas.

[0010] It may further be provided that the apparatus includes a first antenna positioner to position the first antenna and antenna coordinate system. An antenna positioner is a device that can be used to accurately and precisely position an object in three dimensions, or six degrees of freedom, in an automated fashion. One advantage of this arrangement is that it enables a user to accurately and precisely align the antenna coordinate systems of the first and second antennas, as well as dynamically change the separation distance between the two antennas.

[0011] It may also be provided that the apparatus includes a second antenna positioner to position the second antenna and antenna coordinate system. An additional advantage of this arrangement is that it enables a user to further dynamically change the separation distance between the two antennas, potentially with a longer range of motion than can be achieved with the first antenna positioner alone.

[0012] It may also be provided that the apparatus includes a linear motion positioner to vary the separation distance between the first antenna and the second antenna by linearly moving the second antenna positioner. A linear motion positioner is a device that enables the second antenna and second antenna positioner to move in a straight line along an axis. This reduces the number of axes that need to be controlled by the second antenna positioner.

[0013] It may also be provided that the apparatus includes a distance meter to determine the separation distance between the first antenna and the second antenna. A distance meter is a device that can accurately measure distances between objects. One advantage of this arrangement is that it enables an accurate measurement of the separation distance between the antennas to be obtained in an automated fashion.

[0014] It may also be provided that the apparatus includes a first radio frequency transmit and receive electronics device to transmit a first signal to the first antenna and receive a second signal from the first antenna. A radio frequency transmit and receive electronics device may be understood as a device that is able to produce and receive radio frequency signals. This enables the apparatus to both transmit and receive signals between the two antennas.

[0015] It may also be provided that the apparatus includes a second radio frequency transmit and receive electronics device to transmit a third signal to the second antenna and receive a fourth signal from the second antenna. One advantage of this arrangement is that it enables a user to accurately and precisely measure the amplitude and phase of the radio frequency signals that are transmitted and received between the two antennas.

[0016] It may also be provided that the apparatus includes a central controller to control the first and second antenna positioners to position the first and second antennas, to control the linear motion positioner to vary the separation distance, to control the first and second radio frequency transmit and receive electronics devices, and to receive information from the distance meter. A central controller may be understood as a device or software program that controls other devices. One advantage of this arrangement is that it enables all functions of the apparatus to be controlled and coordinated from a single location, such as by automating the antenna positioners to align the first and second antennas, to control the linear motion positioner to vary the separation distance between the two antennas, and to control the first and second radio frequency transmit and receive electronics devices in order to perform a measurement. An additional advantage is that the central controller can also be used to store and manage the data that is collected by the apparatus such as storing information about the position of the antennas and the signals that are transmitted and received between them.

[0017] It may also be provided that the apparatus includes an antenna gain processor to receive information from the central controller and the first and second radio frequency transmit and receive electronics devices and to determine the gain of the first and second antennas based on the third-order scattered signal as a function of the separation distance. An antenna gain processor is a device or software program that performs mathematical operations on data. One advantage of this arrangement is that it enables the apparatus to automatically determine the gain of the first and second antennas by processing the measured data.

[0018] One aspect of the present invention relates to a radio frequency antenna gain measuring apparatus. A radio frequency antenna gain measuringapparatus may be understood as an apparatus that is capable of measuring the gain of an antenna.

[0019] It may be provided that the apparatus includes an antenna having an antenna coordinate system. An antenna is a transducer that converts radio frequency fields into alternating current or vice versa. An antenna coordinate system is a coordinate system that a user defines in order to align the antenna to other objects such as a second antenna.

[0020] It may further be provided that the apparatus includes a mirror positioned at a predetermined antenna-to-mirror distance from the antenna. A mirror is a device that reflects radio frequency radiation. An antenna-to-mirror distance may be understood as the distance between the antenna and the mirror. One advantage of this arrangement is that it allows an electromagnetic image of the antenna to be produced by the mirror such that the antenna can be measured in a similar fashion as with two identical antennas.

[0021] It may also be provided that the apparatus includes an antenna positioner to position the antenna and antenna coordinate system. An antenna positioner is a device that can be used to accurately and precisely position an object in three dimensions, or six degrees of freedom, in an automated fashion. One advantage of this arrangement is that it enables a user to accurately and precisely align the antenna to the antenna image, as well as dynamically change the separation distance between the antenna and the antenna image.

[0022] It may also be provided that the apparatus includes a linear motion positioner to vary the separation distance between the antenna and the antenna image produced by the mirror by linearly moving the antenna positioner. A linear motion positioner is a device that enables the antenna and antenna positioner to move in a straight line along an axis. This reduces the number of axes that need to be controlled by the antenna positioner.

[0023] It may also be provided that the apparatus includes a distance meter to determine the separation distance between the antenna and the antenna image. A distance meter is a device that can accurately measure distances between objects. One advantage of this arrangement is that it enables an accurate measurement of theseparation distance between the antenna and the antenna image to be obtained in an automated fashion.

[0024] It may also be provided that the apparatus includes a radio frequency transmit and receive electronics device to transmit a first signal to the antenna and receive a second signal from the antenna. A radio frequency transmit and receive electronics device may be understood as a device that is able to produce and receive radio frequency signals. This enables the apparatus to both transmit and receive signals between the antenna and the antenna image.

[0025] It may also be provided that the apparatus includes a central controller to control the antenna positioner to position the antenna, to control the linear motion positioner to vary the separation distance, to control the radio frequency transmit and receive electronics device, and to receive information from the distance meter. A central controller may be understood as a device or software program that controls other devices. One advantage of this arrangement is that it enables all functions of the apparatus to be controlled and coordinated from a single location, such as by automating the antenna positioner to align the antenna to the antenna image, to control the linear motion positioner to vary the separation distance between the antenna and the antenna image, and to control the radio frequency transmit and receive electronics device in order to perform a measurement. An additional advantage is that the central controller can also be used to store and manage the data that is collected by the apparatus such as storing information about the position of the antenna and the signals that are transmitted and received between the antenna and the antenna image.

[0026] It may also be provided that the apparatus includes an antenna gain processor to receive information from the central controller and the radio frequency transmit and receive electronics device and to determine the gain of the antenna based on the third-order scattered signal as a function of the separation distance. An antenna gain processor is a device or software program that performs mathematical operations on data. One advantage of this arrangement is that it enables the apparatus to automatically determine the gain of the antenna by processing the measured data.

[0027] It may be provided that the first and second antennas are aperture antennas. An aperture antenna is an antenna that consists of an opening through which radio waves are transmitted or received. Aperture antennas have well behaved and predictable radiation characteristics.

[0028] It may further be provided that the first and second antennas are standard gain horn antennas. A standard gain horn antenna is a type of aperture antenna that has a pyramidal horn shape. Standard gain horn antennas are commonly used as gain reference standards. One advantage of this arrangement is that it provides for an accurate and precise measurement of antenna gain.

[0029] It may also be provided that the apparatus includes a mirror positioned between the first and second antennas. One advantage of this arrangement is that the mirror reflects some of the radio frequency radiation emitted by the second antenna to the first antenna, in addition to the direct radio frequency radiation that is transmitted from the second antenna to the first antenna. This increases the strength of the total signal that is received by the first antenna, providing for an accurate measurement of antenna gain.

[0030] It may also be provided that the first and second antenna positioners are robotic arms. A robotic arm is an automatically controlled manipulator, usually programmable, with similar functions to a human arm; the arm may be the sum total of the mechanism or may be part of a more complex robot. Robotic arms are ideal antenna positioners as they can be used to accurately and precisely position an antenna in six degrees of freedom in an automated fashion.

[0031] It may also be provided that the first and second radio frequency transmit and receive electronics devices are vector network analyzers. A vector network analyzer is an instrument that measures the magnitude and phase of the reflection and transmission properties of a device as a function of frequency. One advantage of this arrangement is that it provides for an accurate and precise measurement of the amplitude and phase of the signals that are transmitted and received between the two antennas.

[0032] It may also be provided that the distance meter is selected from the group consisting of an optical encoder, a magnetic encoder, a laser tracking system,and a laser distance meter. An optical encoder is a device that converts motion into a sequence of digital pulses and can be used to determine position and distance. A magnetic encoder is a device that converts position to electrical signals using magnets. A laser tracking system is a system that uses a laser to measure the position of an object in space. A laser distance meter is an instrument that uses a laser to measure distance. One advantage of using these different types of distance meters is that they each have unique characteristics that can be tailored to the specific needs of the application. For example, optical and magnetic encoders are typically used when high accuracy and precision are required, while laser tracking systems and laser distance meters are typically used when a longer range of motion is needed.

[0033] It may also be provided that the antenna gain processor is to determine the gain of the first and second antennas based on the fifth-order scattered signal as a function of the separation distance. One advantage of this arrangement is that the fifth-order scattered signal may provide for a more accurate measurement of antenna gain.

[0034] It may also be provided that the antenna gain processor is to determine the gain of the first and second antennas based on the seventh-order scattered signal as a function of the separation distance. One advantage of this arrangement is that the seventh-order scattered signal may provide for a more accurate measurement of antenna gain.

[0035] It may be provided that the antenna is an aperture antenna. One advantage of this arrangement is that aperture antennas have well behaved and predictable radiation characteristics.

[0036] It may further be provided that the antenna is a standard gain horn antenna. One advantage of this arrangement is that it provides for an accurate and precise measurement of antenna gain.

[0037] It may also be provided that the antenna positioner is a robotic arm. A robotic arm is an automatically controlled manipulator, usually programmable, with similar functions to a human arm; the arm may be the sum total of the mechanism or may be part of a more complex robot. Robotic arms are ideal antenna positioners asthey can be used to accurately and precisely position an antenna in six degrees of freedom in an automated fashion.

[0038] It may also be provided that the radio frequency transmit and receive electronics device is a vector network analyzer. A vector network analyzer is an instrument that measures the magnitude and phase of the reflection and transmission properties of a device as a function of frequency. One advantage of this arrangement is that it provides for an accurate and precise measurement of the amplitude and phase of the signals that are transmitted and received between the antenna and the antenna image.

[0039] It may also be provided that the distance meter is selected from the group consisting of an optical encoder, a magnetic encoder, a laser tracking system, and a laser distance meter. One advantage of using these different types of distance meters is that they each have unique characteristics that can be tailored to the specific needs of the application. For example, optical and magnetic encoders are typically used when high accuracy and precision are required, while laser tracking systems and laser distance meters are typically used when a longer range of motion is needed.

[0040] One aspect of the present invention relates to a process for measuring gain of an antenna with a radio frequency antenna gain measuring apparatus. A radio frequency antenna gain measuring apparatus may be understood as an apparatus that is capable of measuring the gain of an antenna.

[0041] It may be provided that the process includes positioning a first antenna and a second antenna using a first and second antenna positioner at a separation distance. An antenna positioner is a device that can be used to accurately and precisely position an object in three dimensions, or six degrees of freedom, in an automated fashion. One advantage of this arrangement is that it enables a user to accurately and precisely position the first and second antennas at a desired location.

[0042] The process may further include dynamically varying the separation distance between the first and second antennas using a linear motion positioner. A linear motion positioner is a device that enables an object to move in a straight line along an axis. One advantage of this arrangement is that it enables the apparatus tomeasure the signal that is transmitted between the two antennas as a function of the separation distance between them.

[0043] It may also be provided that the process includes transmitting a first signal from a first radio frequency transmit and receive electronics device to the first antenna. A radio frequency transmit and receive electronics device may be understood as a device that is able to produce and receive radio frequency signals. One advantage of this arrangement is that it provides a means to transmit a signal between the two antennas.

[0044] It may also be provided that the process includes transmitting a second signal from a second radio frequency transmit and receive electronics device to the second antenna. One advantage of this arrangement is that it provides a means to transmit a second signal between the two antennas.

[0045] It may also be provided that the process includes receiving a third signal at the first antenna from the second antenna. One advantage of this arrangement is that it provides a means to receive a signal that is transmitted between the two antennas.

[0046] It may also be provided that the process includes receiving a fourth signal at the second antenna from the first antenna. One advantage of this arrangement is that it provides a means to receive a second signal that is transmitted between the two antennas.

[0047] It may also be provided that the process includes measuring the separation distance using a distance meter. A distance meter is a device that can accurately measure distances between objects. One advantage of this arrangement is that it enables an accurate measurement of the separation distance between the antennas to be obtained.

[0048] It may also be provided that the process includes transmitting the first and third signals and the separation distance from the first radio frequency transmit and receive electronics device to an antenna gain processor. An antenna gain processor is a device or software program that performs mathematical operations ondata. One advantage of this arrangement is that it enables the apparatus to transmit data to the antenna gain processor.

[0049] It may also be provided that the process includes transmitting the second and fourth signals and the separation distance from the second radio frequency transmit and receive electronics device to the antenna gain processor. One advantage of this arrangement is that it enables the apparatus to transmit data to the antenna gain processor.

[0050] It may also be provided that the antenna gain processor receives the first, second, third, and fourth signals and the separation distance and determines the gain of the first and second antennas based on the third-order scattered signal as a function of the separation distance. One advantage of this arrangement is that it enables the apparatus to automatically determine the gain of the first and second antennas by processing the measured data. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The following description cannot be considered limiting in any way. Various objectives, features, and advantages of the disclosed subject matter can be more fully appreciated with reference to the following detailed description of the disclosed subject matter when considered in connection with the following drawings, in which like reference numerals identify like elements.

[0052] FIG. 1 shows, according to some embodiments, a radio frequency antenna gain measuring apparatus.

[0053] FIG. 2 shows, according to some embodiments, a radio frequency antenna gain measuring apparatus, particularly a single-antenna radio frequency antenna gain measuring apparatus.

[0054] FIG.3 shows, according to some embodiments, permutations among pairs of antennas in panels A, B, and C.

[0055] FIG. 4 shows, according to some embodiments, a radio frequency antenna gain measuring apparatus that inclues a pair of antennas, ^^^^ and ^^^^, separated by distance, ^^^^, wherein paths traveled by direct wave (solid line) and 3rd-order scattered wave (dotted line) are shown.

[0056] FIG. 5 shows, according to some embodiments, an extrapolation coupling curve for a pair of 24 dB standard gain horn reference antennas at 15GHz. The strong ^^^^ / 2 oscillations that result from the dominant third-order scattering are observed. The Wacker distance ^^^^^^^^, ^^^^Near, and ^^^^Faras well as the direct wave Fresnel region in relation to the separation distance are shown.

[0057] FIG.6 shows, according to some embodiments, fringe structure from an extrapolation coupling curve.

[0058] FIG.7 shows, according to some embodiments, a fringe spectrum for the pair of 24 dB reference standard gain horn antennas at 15GHz. The inset shows an expanded view of the location of the extrema to be used indicated by arrows.

[0059] FIG.8 shows, according to some embodiments, gain results at 8GHz and 10GHz. Matrix dimension is grouped diagonally by grey scale. Rectangular matricies in last diagonal (outlined black). Measured gain for each antenna are in thetop two entries of each cell in dB, ^^^^ given in parenthesis should be scaled by 10−4.Average gain and standard deviation ^^^^, as ^^^^^^^^ ±are show in the legend (bottom left).

[0060] FIG. 9 shows, according to some embodiments, gain results at 12GHz and 12.4GHz. Matrix dimension is grouped diagonally by grey scale. Rectangular matrices in last diagonal (outlined black). Measured gain for each antenna are in the top two cell entries in dB, ^^^^ given in parenthesis should be scaledby 10−4. Average gain and standard deviation ^^^^, as ^^^^^^^^ ±are show in the legend(bottom left).

[0061] FIG. 10 shows, according to some embodiments, gain results at 15GHz and 18GHz. Matrix dimension is grouped diagonally by grey scale. Rectangualr matricies in last diagonal (outlined black). Measured gain for each antenna are in the top two cell entries in dB, ^^^^ given in parenthesis should be scaled by 10−4. Averagegain and standard deviation ^^^^, as ^^^^^^^^ ± ^^^^^^^^ are show in the legend (bottom left).DETAILED DESCRIPTION

[0062] A detailed description of one or more embodiments is presented herein by way of exemplification and not limitation.

[0063] The conventional approach to antenna gain measurement via gain extrapolation involves a large number of data samples (e.g., thousands of data points) due to the desire to filter out the unwanted higher order scattering terms from the total received signal between the two antennas. Furthermore, the separation distance between the antennas must be large (e.g., several meters) to avoid the region of strong antenna-to-antenna coupling and the presence of large unwanted higher order scattering terms. This necessitates the need for large facilities to perform these measurements.

[0064] The radio frequency antenna gain measuring apparatus described herein overcomes these limitations by incorporating the third-order scattered signal when measuring antenna gain. It is contemplated that the third-order (or higher order, fifth, seventh and the like.) scattering signal that occurs between two antennas can be implemented for gain extrapolation to measure the gain of antennas. Conventional gain extrapolation technology involves filtering out the third-order (or higher order) scattering signal, resulting in a large number of data points (e.g., thousands) needing to be acquired and large physical facilities to conduct the measurement. In the conventional technology, the third-order (or higher order) scattering signal is considered a nuisance, unwanted part of the total signal, and great lengths are taken to avoid them or filter them out. The radio frequency antenna gain measuring apparatus described herein incorporates the third-order (or higher order) scattered signals and provides antenna gain to be measured in more beneficial and advantageous ways over the conventional technology. For example, the radio frequency antenna gain measuring apparatus provides a significant reduction in the number of data points needed (around 10 data points) compared to the conventional technology (thousands of data points) by orders of magnitude. Moreover, the radio frequency antenna gain measuring apparatus provides significantly reduced facility size by reducing the minimum measurement length by a third, a sixth, or a twelfthcompared to the conventional technology. The radio frequency antenna gain measuring apparatus provides these benefits while maintaining a high level of accuracy as the conventional gain extrapolation technology.

[0065] It has been discovered that the radio frequency antenna gain measuring apparatus that use the third-order scattered signal are able to determine the gain of an antenna using significantly less data points than with current approaches. One advantage of incorporating the third-order scattered signal into the measurement is that the number of data points needed to perform the measurement now depends on the number of terms used in the power series expansion that describes the third-order scattered signal and not the number of data points needed to adequately filter the received signal in order to remove unwanted higher-order scattering terms.

[0066] Furthermore, because the region of strong third-order scattering does not need to be avoided, and in fact can be used to obtain gain values, the separation distance between the antennas can be significantly reduced. This results in the ability to measure antenna gain with a smaller facility and reduced impact from environmental multipath reflections that tend to occur at larger separation distances.

[0067] The radio frequency antenna gain measuring apparatus 200 overcomes these limitations by incorporating the third-order scattered signal when measuring antenna gain. A radio frequency antenna gain measuring apparatus 200 includes a first antenna 201 and a second antenna 202. The first antenna 201 is one of the antennas for which the gain is to be measured. It may be an aperture-type antenna such as a standard gain horn antenna or another type of antenna, for example, a phased array antenna or a dual-ridged waveguide antenna. A first radio frequency transmit and receive electronics device 231 transmits a first signal 212 to the first antenna 201 and receives a second signal 213 from the first antenna 201. A first antenna positioner 209 positions the first antenna 201 at a predetermined location and orientation.

[0068] The radio frequency antenna gain measuring apparatus 200 also includes a second antenna 202 which is the second antenna for which the gain is to be measured. The second antenna 202 may be similar to the first antenna 201, e.g. itmay also be an aperture-type antenna, or it may be a different type of antenna. A second radio frequency transmit and receive electronics device transmits a third signal 214 to the second antenna 202 and receives a fourth signal 215 from the second antenna. A second antenna positioner 210 positions the second antenna 202 at a predetermined location and orientation.

[0069] The separation distance 236 between the first antenna 201 and the second antenna 202 is dynamically varied using a linear motion positioner 211. The linear motion positioner 211 translates the second antenna 202 and second antenna positioner 210 along an axis thereby varying the separation distance 236 between the first antenna 201 and the second antenna 202.

[0070] The radio frequency antenna gain measuring apparatus 200 includes a distance meter 233 to measure the separation distance 236 between the first antenna 201 and the second antenna 202. The distance meter 233 may be, for example, an optical encoder, a magnetic encoder, a laser tracking system, or a laser distance meter.

[0071] A central controller 234 is used to control and coordinate all the functions of the radio frequency antenna gain measuring apparatus 200. The central controller 234 may be a personal computer running an automation program, for example, a program written in LabVIEW or Python.

[0072] An antenna gain processor 235 processes data from the first and second radio frequency transmit and receive electronics devices 231 and 232 to determine the gain of the first antenna 201 and the second antenna 202. The antenna gain processor 235 may be a computer that runs a program that implements an algorithm to determine antenna gain.

[0073] The radio frequency antenna gain measuring apparatus 200 provides several technical advantages. A first antenna 201 and a second antenna 202 enable the user to measure the gain of two different antennas. The first and second antenna positioners 209 and 210 accurately and precisely position the first antenna 201 and the second antenna 202. The linear motion positioner 211 allows the separation distance 236 to be varied. The distance meter 233 accurately measures the separation distance 236. The first and second radio frequency transmit and receive electronicsdevices 231 and 232 provide a means to accurately and precisely measure the amplitude and phase of the radio frequency signals that are transmitted and received between the two antennas. The central controller 234 controls and coordinates all functions of the apparatus and is used to store and manage the data collected by the apparatus. The antenna gain processor 235 automatically determines the gain of the antennas by processing the measured data.

[0074] In an embodiment, the first antenna 201 and second antenna 202 are aperture antennas. Aperture antennas are antennas that consist of an opening through which radio waves are transmitted or received. One advantage of aperture antennas is that they have well behaved and predictable radiation characteristics.

[0075] In an embodiment, the first antenna 201 and second antenna 202 are standard gain horn antennas. A standard gain horn antenna is a type of aperture antenna that has a pyramidal horn shape. Standard gain horn antennas are commonly used as gain reference standards. One advantage of using standard gain horn antennas is that they provide for an accurate and precise measurement of antenna gain.

[0076] The radio frequency antenna gain measuring apparatus 200 may include a mirror 242 positioned between the first antenna 201 and the second antenna 202. The mirror 242 reflects some of the radio frequency radiation emitted by the second antenna 202 to the first antenna 201, in addition to the direct radio frequency radiation that is transmitted from the second antenna 202 to the first antenna 201. One advantage of the mirror 242 is that it increases the strength of the total signal that is received by the first antenna 201. This provides for a more accurate measurement of antenna gain.

[0077] In an embodiment, the first and second antenna positioners 209 and 210 are robotic arms. A robotic arm is an automatically controlled manipulator, usually programmable, with similar functions to a human arm; the arm may be the sum total of the mechanism or may be part of a more complex robot. Robotic arms are ideal antenna positioners 209 and 210 as they can be used to accurately and precisely position an antenna in six degrees of freedom in an automated fashion.

[0078] In an embodiment, the first and second radio frequency transmit and receive electronics devices 231 and 232 are vector network analyzers. A vector network analyzer is an instrument that measures the magnitude and phase of the reflection and transmission properties of a device as a function of frequency. One advantage of vector network analyzers is that they provide for an accurate and precise measurement of the amplitude and phase of the signals that are transmitted and received between the two antennas.

[0079] In an embodiment, the distance meter 233 is selected from the group consisting of an optical encoder, a magnetic encoder, a laser tracking system, and a laser distance meter. An optical encoder is a device that converts motion into a sequence of digital pulses and can be used to determine position and distance. A magnetic encoder is a device that converts position to electrical signals using magnets. A laser tracking system is a system that uses a laser to measure the position of an object in space. A laser distance meter is an instrument that uses a laser to measure distance. One advantage of using these different types of distance meters 233 is that they each have unique characteristics that can be tailored to the specific needs of the application. For example, optical and magnetic encoders are typically used when high accuracy and precision are required, while laser tracking systems and laser distance meters are typically used when a longer range of motion is needed.

[0080] The antenna gain processor 235 may determine the gain of the first antenna 201 and the second antenna 202 based on the fifth-order scattered signal as a function of the separation distance 236. One advantage of this arrangement is that the fifth-order scattered signal may provide for a more accurate measurement of antenna gain.

[0081] The antenna gain processor 235 may also determine the gain of the first antenna 201 and the second antenna 202 based on the seventh-order scattered signal as a function of the separation distance 236. One advantage of this arrangement is that the seventh-order scattered signal may provide for a more accurate measurement of antenna gain.

[0082] The radio frequency antenna gain measuring apparatus 200 provides several technical advantages when using the specific implementations describedabove. Aperture antennas or standard gain horn antennas 201 and 202 provide antennas with predictable radiation characteristics. The mirror 242 increases the signal strength received by the first antenna 201 which provides a more accurate measurement of antenna gain. Robotic arms as antenna positioners 209 and 210 provide for accurate and precise positioning in an automated fashion. The vector network analyzer provides for an accurate and precise measurement of the amplitude and phase of the radio frequency signals. The various distance meters 233 provide a measurement of the separation distance 236 tailored to the specific needs of the application. The fifth-order and seventh-order scattered signals may provide for a more accurate measurement of antenna gain.

[0083] The radio frequency antenna gain measuring apparatus 238 includes an antenna 202 which is the antenna for which the gain is to be measured. The antenna 202 may be an aperture-type antenna such as a standard gain horn antenna or another type of antenna, for example, a phased array antenna or a dual-ridged waveguide antenna. A radio frequency transmit and receive electronics device 232 transmits a first signal 214 to the antenna 202 and receives a second signal 215 from the antenna 202. An antenna positioner 210 positions the antenna 202 at a predetermined location and orientation.

[0084] The radio frequency antenna gain measuring apparatus 238 also includes a mirror 242 positioned at a predetermined antenna-to-mirror distance 241 from the antenna 202. The mirror 242 is a device that reflects radio frequency radiation and produces an antenna image 239. The antenna-to-mirror distance 241 may be understood as the distance between the antenna 202 and the mirror 242. The mirror 242 allows an electromagnetic image of the antenna 202 to be produced by the mirror 242 such that the antenna 202 can be measured in a similar fashion as with two identical antennas.

[0085] The separation distance 236 between the antenna 202 and the antenna image 239 is dynamically varied using a linear motion positioner 211. The linear motion positioner 211 translates the antenna 202 and antenna positioner 210 along an axis thereby varying the separation distance 236 between the antenna 202 and the antenna image 239.

[0086] The radio frequency antenna gain measuring apparatus 238 includes a distance meter 233 to measure the separation distance 236 between the antenna 202 and the antenna image 239. The distance meter 233 may be, for example, an optical encoder, a magnetic encoder, a laser tracking system, or a laser distance meter.

[0087] A central controller 234 is used to control and coordinate all the functions of the radio frequency antenna gain measuring apparatus 238. The central controller 234 may be a personal computer running an automation program, for example, a program written in LabVIEW or Python.

[0088] An antenna gain processor 235 processes data from the radio frequency transmit and receive electronics devices 232 to determine the gain of the antenna 202. The antenna gain processor 235 may be a computer that runs a program that implements an algorithm to determine antenna gain.

[0089] The radio frequency antenna gain measuring apparatus 238 provides several technical advantages. The antenna 202 allows the user to measure the gain of an antenna. The mirror 242 produces an antenna image 239 such that the antenna 202 can be measured in a similar fashion as with two identical antennas. The antenna positioner 210 accurately and precisely positions the antenna 202. The linear motion positioner 211 allows the separation distance 236 to be varied. The distance meter 233 accurately measures the separation distance 236. The radio frequency transmit and receive electronics device 232 provides a means to accurately and precisely measure the amplitude and phase of the radio frequency signals that are transmitted and received between the antenna and the antenna image. The central controller 234 controls and coordinates all functions of the apparatus and is used to store and manage the data collected by the apparatus. The antenna gain processor 235 automatically determines the gain of the antenna 202 by processing the measured data.

[0090] In an embodiment, the antenna 202 is an aperture antenna. Aperture antennas are antennas that consist of an opening through which radio waves are transmitted or received. One advantage of aperture antennas is that they have well behaved and predictable radiation characteristics.

[0091] In an embodiment, the antenna 202 is a standard gain horn antenna. A standard gain horn antenna is a type of aperture antenna that has a pyramidal horn shape. Standard gain horn antennas are commonly used as gain reference standards. One advantage of using standard gain horn antennas is that they provide for an accurate and precise measurement of antenna gain.

[0092] In an embodiment, the antenna positioner 210 is a robotic arm. A robotic arm is an automatically controlled manipulator, usually programmable, with similar functions to a human arm; the arm may be the sum total of the mechanism or may be part of a more complex robot. Robotic arms are ideal antenna positioners 210 as they can be used to accurately and precisely position an antenna in six degrees of freedom in an automated fashion.

[0093] In an embodiment, the radio frequency transmit and receive electronics device 232 is a vector network analyzer. A vector network analyzer is an instrument that measures the magnitude and phase of the reflection and transmission properties of a device as a function of frequency. One advantage of vector network analyzers is that they provide for an accurate and precise measurement of the amplitude and phase of the signals that are transmitted and received between the antenna and the antenna image.

[0094] In an embodiment, the distance meter 233 is selected from the group consisting of an optical encoder, a magnetic encoder, a laser tracking system, and a laser distance meter. An optical encoder is a device that converts motion into a sequence of digital pulses and can be used to determine position and distance. A magnetic encoder is a device that converts position to electrical signals using magnets. A laser tracking system is a system that uses a laser to measure the position of an object in space. A laser distance meter is an instrument that uses a laser to measure distance. One advantage of using these different types of distance meters 233 is that they each have unique characteristics that can be tailored to the specific needs of the application. For example, optical and magnetic encoders are typically used when high accuracy and precision are required, while laser tracking systems and laser distance meters are typically used when a longer range of motion is needed.

[0095] The radio frequency antenna gain measuring apparatus 238 provides several technical advantages when using the specific implementations described above. An aperture antenna or standard gain horn antenna 202 provides an antenna with predictable radiation characteristics. A robotic arm as an antenna positioner 210 provides for accurate and precise positioning in an automated fashion. The vector network analyzer provides for an accurate and precise measurement of the amplitude and phase of the radio frequency signals. The various distance meters 233 provide a measurement of the separation distance 236 tailored to the specific needs of the application.

[0096] In an embodiment, radio frequency antenna gain measuring apparatus 200 includes a plurality of antennas and is configured as multiple-antenna radio frequency antenna gain measuring apparatus 200 that includes: antenna 201 having antenna coordinate system 207 and that produces antenna emitted radio frequency radiation 203, based on receiving transmitting signal 212, and produces received signal 213 based on receiving antenna incident radio frequency radiation 204; antenna 202 having antenna coordinate system 208 and that produces antenna emitted radio frequency radiation 205, based on receiving transmitting signal 214, and produces received signal 215 based on receiving antenna incident radio frequency radiation 206; antenna positioner 209 that receives positioner control signal 216 from central controller 234 to position antenna 201 and antenna coordinate system 207 and that transmits positioner feedback signal 217 to central controller 234; antenna positioner 210 that receives positioner control signal 218 from central controller 234 to position antenna 202 and antenna coordinate system 208 and that transmits positioner feedback signal 219 to central controller 234; linear motion positioner 211 that receives distance meter communication signal 221 from distance meter 233 to vary the separation distance 236 by linearly moving antenna positioner 210 and that transmits distance meter measurement signal 220 to distance meter 233; distance meter 233 that produces distance meter data signal 226 and communicates position of linear motion positioner 211 via distance meter data signal 226 to central controller 234 and receives distance meter control signal 227 produced by central controller 234; radio frequency transmit and receive electronics 231 that produce transmit signal 212 based on receiving radio frequency electronics control signal 223 produced by central controller 234 and receives received signal 213 and communicates with centralcontroller 234 via radio frequency electronics data signal 222; radio frequency transmit and receive electronics 232 that produces transmit signal 214 based on receiving radio frequency electronics control signal 225 produced by central controller 234 and accepts received signal 215 and communicates with central controller 234 via radio frequency electronics data signal 224; central controller 234 that produces positioner control signal 216 and positioner control signal 218, receives positioner feedback signal 217 and positioner feedback signal 219, produces radio frequency electronics control signal 223 and radio frequency electronics control signal 225, and receives radio frequency electronics data signal 222 and radio frequency electronics data signal 224, produces distance meter control signal 227, receives distance meter data signal 226, produces antenna gain processor data signal 228, and receives antenna gain processor return signal 229; antenna gain processor 235 that receives antenna gain processor data signal 228, produces antenna gain processor return signal 229, and produces antenna gain 230; and antenna gain data array 237 that receives antenna gain from antenna gain processor.

[0097] In an embodiment, radio frequency antenna gain measuring apparatus 200 includes antenna 202 and is configured as single-antenna radio frequency antenna gain measuring apparatus 238 that includes: antenna 202 having antenna coordinate system 208 and that produces antenna emitted radio frequency radiation 205 based on receiving transmitting signal 214 and that produces received signal 215 based on receiving antenna incident radio frequency radiation 206; mirror 242 at antenna-to-mirror distance 241 from antenna 202 that reflects antenna emitted radio frequency radiation 205, produces incident radio frequency radiation 206 and antenna image 239 and antenna image coordinate system 240; antenna image 239 produced by mirror 242 having antenna image coordinate system 240 at separation distance 236 from antenna 202; antenna positioner 210 that receives positioner control signal 218 from central controller 234 to position antenna 202 and antenna coordinate system 208 and that transmits positioner feedback signal 219 to central controller 234; linear motion positioner 211 that receives distance meter communication signal 221 from distance meter 233 to vary the separation distance 236 by linearly moving antenna positioner 210 and transmits distance meter measurement signal 220 to distance meter 233; distance meter 233 that produces distance meter data signal 226 and communicates position of linear motion positioner 211 via distance meter datasignal 226 to central controller 234 and receives distance meter control signal 227 produced by central controller 234; radio frequency transmit and receive electronics 232 that produces transmit signal 214 based on receiving radio frequency electronics control signal 225 produced by central controller 234, accepts received signal 215, and communicates with central controller 234 via radio frequency electronics data signal 224; central controller 234 that produces positioner control signal 218, receives positioner feedback signal 219, produces radio frequency electronics control signal 225 and radio frequency electronics data signal 224, produces distance meter control signal 227, receives distance meter data signal 226, produces antenna gain processor data signal 228, and receives antenna gain processor return signal 229; antenna gain processor 235 that receives antenna gain processor data signal 228, produces antenna gain processor return signal 229, and produces antenna gain 230; and antenna gain data array 237 that receives antenna gain from antenna gain processor.

[0098] With reference to FIG. 1, radio frequency antenna gain measuring apparatus 200 determines antenna gain using either two or three antennas. Radio frequency antenna gain measuring apparatus 200 determines gain across a frequency range nominally from 1 Hz to 1 THz with accuracy nominally from less than + / -0.1 dB, specifically + / - 0.07 dB or better. Radio frequency antenna gain measuring apparatus 200 has advantages over conventional measurement devices because it can measure the third-order signal produced by the interference of antenna emitted radio frequency radiation 203, antenna incident radio frequency radiation 204, antenna emitted radio frequency radiation 205, antenna incident radio frequency radiation 206 from antennas 202 and 201 as they are separated dynamically over separation distance 236. Moreover radio frequency antenna gain measuring apparatus 200 can also measure higher order signals such as the fifth-order and seventh-order signal produced by the interference of antenna emitted radio frequency radiation 203, antenna incident radio frequency radiation 204, antenna emitted radio frequency radiation 205, and antenna incident radio frequency radiation 206 from antennas 202 and 201 as they are separated dynamically over separation distance 236.

[0099] Radio frequency antenna gain measuring apparatus 200 can determine the antenna gain from the third-order, fifth-order, or seventh-order signals using a significantly smaller number of data points as well as shorter antenna toantenna separation distances 236 than conventional devices. Radio frequency antenna gain measuring apparatus 200 can measure antenna gain with as few as 8 or 10 data points, whereas conventional devices use thousands of data points. Conventional systems use thousands of data points to average out the third order (fifth, seventh, and the like.) signals in order to keep only the direct zeroth-order signal. However, radio frequency antenna gain measuring apparatus 200 does not average out the third (fifth, seventh, and the like.) signals and uses these higher-order signals to measure antenna gain. Radio frequency antenna gain measuring apparatus 200 can measure gain with one-third to one-six or even shorter antenna separation distances 236 than conventional devices because the third and higher order signals propagates over much shorter distances than the zeroth-order signal alone which propagates for much farther distances.

[0100] When three antennas are used, three permuted pairs are created and measured using radio frequency antenna gain measuring apparatus 200 to produce the product of the gains for each pair of antennas and the individual antenna gains are then produced by the antenna gain processor 235 from the three antenna gain products. The permuted pairs are arranged as show in FIG.3(c). When two antennas are used one antenna has a known gain and the second antenna’s gain is determined from the product of the unknown gain and known gain by the antenna gain processor 235. The gain of two unknown antennas can also be measured if the two antennas are nearly identical. Then the antenna gain processor 235 will determine each antenna gain as half of the gain product.

[0101] With reference to FIG. 2, single-antenna radio frequency antenna gain measuring apparatus 238 determines antenna again using one antenna 202. It is contemplated that single-antenna radio frequency antenna gain measuring apparatus 238 can also measure the third-order, fifth-order, seventh-order, and the like signals as mirror 242 is moved dynamically in relation to antenna 202. Additionally, single-antenna radio frequency antenna gain measuring apparatus 238 mirror 242 allows for antenna separation distance 236 to be reduced to half that used in 200 with two mirrors through the use of the antenna-to-mirror separation distance 241. The use of mirror 242 or reflector produces an electromagnetic image of antenna 202 as antenna image 239, antenna coordinate system 208 as antenna imagecoordinate system 240. Single-antenna radio frequency antenna gain measuring apparatus 238 thus mimics the case where radio frequency antenna gain measuring apparatus 200 uses two identical antennas, and the gain of antenna 202 is determined from the antenna gain processor 235 as half of the measured gain product of the gain of 202 and 239. The antenna gain is also determined using significantly less data points than conventional devices where single-antenna radio frequency antenna gain measuring apparatus 238 only needs 8 or 10 data points as does the two mirror configuration of radio frequency antenna gain measuring apparatus 200. The longest distance involved for single-antenna radio frequency antenna gain measuring apparatus 238 is limited by antenna-to-mirror separation distance 241 and can be half or less antenna separation distance 236. Accordingly, single-antenna radio frequency antenna gain measuring apparatus 238 can be one-sixth or one-twelfth the length of a conventional device.

[0102] In an embodiment, radio frequency antenna gain measuring apparatus 200 includes a plurality of antennas and is configured as multiple-antenna radio frequency antenna gain measuring apparatus 200 that includes antenna 201 as one of the antennas for which gain is to be determined. The antenna can be an aperture antenna such as a standard gain horn or some other antenna like a phased array, dual ridge waveguide antenna, and the like. The antenna emits RF radiation as antenna emitted radio frequency radiation 203 and receives antenna incident radio frequency radiation 204. The antenna has a coordinate system a user defines in a way they choose shown as antenna coordinate system 207, which can be defined from a geometry that is inherent to the antenna 201 such as the plane, center, and orientation of its aperture. Antenna 201 in is electrical connection with a signal transmitting and receiving device, e.g., a coax cable, waveguide, or optical to RF transducer to communicate transmitting signal 212 and receive signal 213 to the radio frequency transmit and receive electronics 231. Antenna 201 can be mechanically disposed (e.g., fixed or mounted) to antenna positioner 209 so that antenna positioner 209 can position antenna 201 to be aligned in position and orientation to antenna 202.

[0103] Antenna 202 is one of the antennas for determination of gain. Antenna 202 can be an aperture antenna such as a standard gain horn or some other antenna like a phased array, dual ridge waveguide antenna, and the like. Antenna 202emits RF radiation as antenna emitted radio frequency radiation 205 and receives antenna incident radio frequency radiation 206. Antenna 202 has a coordinate system a user defines in a way they choose shown as antenna coordinate system 208 which can be defined from a geometry that is inherent to the antenna 202 such as the plane, center, and orientation of its aperture. Antenna 202 in is electrical connection with a signal transmitting and receiving device, e.g., a coax cable, waveguide, or optical to RF transducer to communicate transmitting signal 212 and receive signal 213 to radio frequency transmit and receive electronics 232. Antenna 202 can be disposed (e.g., mechanically fixed or mounted) to antenna positioner 210 so that antenna positioner 210 positions antenna 202 to be aligned in position and orientation to antenna 201.

[0104] Antenna positioner 209 can be a mechanical device that can move components (e.g., an antenna) in space in a selected number of degrees of freedom, e.g., three degrees of freedom or six degrees of freedom, accurately and precisely and can be manual or automated. Exemplary antenna positioners 209 include robots such as robotic arms and mechanical positioning stages. Antenna positioner 209 can be a drone or flying device that can pick up a payload and move it in 6-degrees of freedom and hold a position. Antenna positioner 209 has antenna 201 attached to it and aligns antenna coordinate system 207 to antenna coordinate system 208 as well as dynamically change antenna separation distance 236 by moving antenna 201. Antenna positioner 209 can be controlled via an external computer or controller like the central controller shown 234 by positioner control signal 216 and positioner feedback signal 217 as shown in FIG.1 and FIG.2 or operate autonomously by an internal controller or programmable logic infrastructure. Payload specifications for antenna positioner 209 can be a suitable weight such as about 50 kg when, e.g., positioning standard gain horn type antennas that operate down to 1 GHz. Payloads can be scaled, up or down, depending on the size and weight of antennas. Antenna positioner 209 can be combined and integrated with other positioners such as the linear motion positioner 211 to add more motion degrees of freedom.

[0105] Antenna positioner 210 can be a mechanical device that can move components (e.g., an antenna) in space in a selected number of degrees of freedom, e.g., three degrees of freedom or six degrees of freedom, accurately and precisely and can be manual or automated. Exemplary antenna positioners 210 include robotssuch as robotic arms and mechanical positioning stages. Antenna positioner 210 can be a drone or flying device that can pick up a payload and move it in 6-degrees of freedom and hold a position. Antenna positioner 210 has antenna 202 attached to it and aligns antenna coordinate system 207 to antenna coordinate system 208 as well as dynamically change antenna separation distance 236 by moving antenna 202. Antenna positioner 210 can be controlled via an external computer or controller like the central controller shown 234 by positioner control signal 214 and positioner feedback signal 215 as shown in FIG.1 and FIG.2 or operate autonomously by an internal controller or programmable logic infrastructure. Payload specifications for antenna positioner 210 can be a suitable weight such as about 50 kg when, e.g., positioning standard gain horn type antennas that operate down to 1 GHz. Payloads can be scaled, up or down, depending on the size and weight of antennas. Antenna positioner 210 can be combined and integrated with other positioners such as the linear motion positioner 211 to add more motion degrees of freedom.

[0106] Linear motion positioner 211 dynamically changes antenna separation distance 236 and antenna-to-mirror distance 241. Linear motion positioner 211 can be controlled by an external controller, e.g., central controller 234, or by an internal programmable or independent control infrastructure. Linear motion positioner 211 can move antenna 202 linearly without moving antenna positioner 210. It is contemplated that linear motion positioner 211 moves the full distance of separation distance 236, or antenna positioner 210 move the full distance of separation distance 236. It is contemplated that a combination of linear motion positioner 211 and antenna positioner 210 move the full distance of separation distance 236. When used in combination with antenna positioner 210, linear motion positioner 211 can support the payload of antenna positioner 210 and antenna 202 so that it can have a mass of a ton or more for larger antennas but for smaller antennas it can fit on a laboratory table with a mass of several kilograms. Linear motion positioner 211 can have a straightness to provide a fraction of the operating wavelength of the antennas to be measured, e.g., better than a tenth of a wavelength, specifically better up to a hundredth of a wavelength. Inaccuracies in its straightness can be compensated when combined with antenna positioner 210, wherein antenna positioner 210 can move to counter-act straightness variations in linear motion positioner 211 as antenna separation distance 236 and antenna-to-mirror distance 241 are dynamically changed.

[0107] Distance meter 233 determines, measures, and acquires distance data for antenna separation distance 236 or antenna-to-mirror distance 241. Distance meter 233 sends distance measurement data via distance meter measurement signal 220 and can communicate with motion stages like 211 to determine their distance traveled. Examples of distance meter 233 are an optical or magnetic encoder, a laser tracking system, laser distance meter, and the like. Distance meter 233 communicates distance measurements via distance meter data signal 226 and can be controlled by distance meter control signal 227 through an external computer.

[0108] Radio frequency transmit and receive electronics 231 produces RF signals at a desired power level, frequency, amplitude, and phase to properly excite antenna 201 so as to produce antenna emitted radio frequency radiation 203. Radio frequency transmit and receive electronics 231 are connected to antenna 201 via cables, adapters, waveguides, or optical to RF and RF to optical transducers that communicate transmit signal 212 to antenna 201. Vice-versa radio frequency transmit and receive electronics 231 receive and detect RF signals at a desired power level, frequency, amplitude, and phase from antenna 201 in correspondence to antenna incident radio frequency radiation 204. Radio frequency transmit and receive electronics 231 are connected to antenna 201 via cables, adapters, waveguides, or optical to RF and RF to optical transducers that communicate received signal 213 from antenna 201. Examples of radio frequency transmit and receive electronics 231 are a vector network analyzer, a systems of RF mixers, detectors, and RF components that can coherently separate received and transmitted signals including information about power level frequency amplitude and phase. Radio frequency transmit and receive electronics 231 can be computer controlled or have a stand-alone use interface that configures its RF transit and receive properties as well as its trigger and timing to coordinate with data acquisition functions of radio frequency antenna gain measuring apparatus 200 and single-antenna radio frequency antenna gain measuring apparatus 238.

[0109] Radio frequency transmit and receive electronics 232 produce RF signals at a selected power level, frequency, amplitude, and phase to properly excite antenna 202 to produce antenna emitted radio frequency radiation 205. Radio frequency transmit and receive electronics 232 can be connected to antenna 202 withcables, adapters, waveguides, or optical to RF and RF to optical transducers that communicate transmit signal 214 to antenna 201. Vice-versa radio frequency transmit and receive electronics 232 receive and detect RF signals at a selected power level, frequency, amplitude, and phase from antenna 202 in correspondence to antenna incident radio frequency radiation 206. Radio frequency transmit and receive electronics 232 can be connected to antenna 202 with cables, adapters, waveguides, or optical to RF and RF to optical transducers that communicate received signal 214 from antenna 202. Examples of radio frequency transmit and receive electronics 232 are a vector network analyzer, a systems of RF mixers, detectors, RF components, and the like that coherently separate received and transmitted signals including information about power level frequency amplitude and phase. Radio frequency transmit and receive electronics 232 can be computer controlled or have a stand-alone use interface capable of configuring its RF transit and receive properties as well as its trigger and timing to coordinate with data acquisition functions of radio frequency antenna gain measuring apparatus 200 and single-antenna radio frequency antenna gain measuring apparatus 238.

[0110] Central controller 234 controls and coordinates functions of radio frequency antenna gain measuring apparatus 200, including automation of antenna positioner 209, antenna positioner 210, and linear motion positioner 211, and provides sending, receiving, and recording transmit and receive signals (212, 212, 214, 215) to and from antennas (201 and 202) as well as sending acquired data to antenna gain processor 235. An example of central controller is a computer running an automation program written in a language such as LabVIEW or Python.

[0111] Antenna gain processor 235 receives raw data obtained as signals (212, 213, 214, 215) that includes information for the third-order, fifth-order, seventh- order, and the like scatter signal from antennas (210 and 202) as a function of dynamically changing separation distance 236 and analyzes the data, e.g., by subjecting the data to manipulation of an algorithm, e.g., according to a process for measuring gain of an antenna as described herein to calculate the gain of two or three antennas as shown in FIG.3. An example of an antenna gain processor is a computer that runs a program that implements this algorithm.

[0112] Antenna gain data array 237 contains the resultant gain vales for all antennas. Antenna gain data array 237 can be stored in a database file, spreadsheet, printout, and the like. Antenna gain data array 237 is a result of measurement performed by radio frequency antenna gain measuring apparatus 200.

[0113] It is contemplated that single-antenna radio frequency antenna gain measuring apparatus 238 can include antenna 202 as one of the antennas for which gain is determined. Antenna 202 can be an aperture antenna such as a standard gain horn or some other antenna like a phased array, dual ridge waveguide antenna, and the like. Antenna 202 emits RF radiation as antenna emitted radio frequency radiation 205 and receives antenna incident radio frequency radiation 206. Antenna 202 has a coordinate system a user defines as antenna coordinate system 208 that can be defined from a geometry inherent to antenna 202 such as the plane, center, and orientation of its aperture. Antenna 202 is in electrical communication with a signal transmitting and receiving device such as a coax cable, waveguide, or optical to RF transducer to communicate transmitting signal 212 and receive signal 213 to radio frequency transmit and receive electronics 232. Antenna 202 can be disposed (e.g., mechanically fixed or mounted) to antenna positioner 210 so that antenna positioner 210 can position antenna 202 to be aligned in position and orientation to antenna 201.

[0114] Mirror 242 has a high reflectivity to reflect most of the antenna emitted radio frequency radiation 205 from antenna 202 back to antenna 202 as antenna incident radio frequency radiation 206 to form an electromagnetic image of antenna 202 and antenna coordinate system 208 as antenna image 239 and antenna image coordinate system 240. Antenna image 239 of the antenna acts as a second identical antenna from which to perform the two-antenna configuration of radio frequency antenna gain measuring apparatus 200.

[0115] The process for measuring gain of an antenna with a radio frequency antenna gain measuring apparatus includes positioning a first antenna 201 and a second antenna 202 using a first and second antenna positioner 209 and 210 at a separation distance 236. An antenna positioner 209 and 210 is a device that can be used to accurately and precisely position an object in three dimensions, or six degrees of freedom, in an automated fashion. One advantage of this arrangement is that itenables a user to accurately and precisely position the first and second antennas 201 and 202 at a desired location.

[0116] The process further includes dynamically varying the separation distance 236 between the first and second antennas 201 and 202 using a linear motion positioner 211. A linear motion positioner 211 is a device that enables an object to move in a straight line along an axis. One advantage of this arrangement is that it enables the apparatus to measure the signal that is transmitted between the two antennas 201 and 202 as a function of the separation distance 236 between them.

[0117] In an embodiment, the process includes transmitting a first signal 212 from a first radio frequency transmit and receive electronics device 231 to the first antenna 201. A radio frequency transmit and receive electronics device 231 may be understood as a device that is able to produce and receive radio frequency signals. One advantage of this arrangement is that it provides a means to transmit a signal 212 between the two antennas 201 and 202.

[0118] In an embodiment, the process includes transmitting a second signal 214 from a second radio frequency transmit and receive electronics device 232 to the second antenna 202. One advantage of this arrangement is that it provides a means to transmit a second signal 214 between the two antennas 201 and 202.

[0119] In an embodiment, the process includes receiving a third signal 213 at the first antenna 201 from the second antenna 202. One advantage of this arrangement is that it provides a means to receive a signal 213 that is transmitted between the two antennas 201 and 202.

[0120] In an embodiment, the process includes receiving a fourth signal 215 at the second antenna 202 from the first antenna 201. One advantage of this arrangement is that it provides a means to receive a second signal 215 that is transmitted between the two antennas 201 and 202.

[0121] In an embodiment, the process includes measuring the separation distance 236 using a distance meter 233. A distance meter 233 is a device that can accurately measure distances between objects. One advantage of this arrangementis that it enables an accurate measurement of the separation distance 236 between the antennas to be obtained.

[0122] In an embodiment, the process includes transmitting the first and third signals 212 and 213 and the separation distance 236 from the first radio frequency transmit and receive electronics device 231 to an antenna gain processor 235. An antenna gain processor 235 is a device or software program that performs mathematical operations on data. One advantage of this arrangement is that it enables the apparatus to transmit data to the antenna gain processor 235.

[0123] In an embodiment, the process includes transmitting the second and fourth signals 214 and 215 and the separation distance 236 from the second radio frequency transmit and receive electronics device 232 to the antenna gain processor 235. One advantage of this arrangement is that it enables the apparatus to transmit data to the antenna gain processor 235.

[0124] In an embodiment, the antenna gain processor 235 receives the first, second, third, and fourth signals (212, 213, 214, and 215) and the separation distance 236 and determines the gain of the first and second antennas 201 and 202 based on the third-order scattered signal as a function of the separation distance 236. One advantage of this arrangement is that it enables the apparatus to automatically determine the gain of the first and second antennas 201 and 202 by processing the measured data.

[0125] The process for measuring gain of an antenna provides several technical advantages. Antenna positioners 209 and 210 accurately and precisely position the first and second antennas 201 and 202. The linear motion positioner 211 allows the separation distance 236 to be varied. The distance meter 233 accurately measures the separation distance 236. The first and second radio frequency transmit and receive electronics devices 231 and 232 provide a means to accurately and precisely measure the amplitude and phase of the radio frequency signals that are transmitted and received between the two antennas. The antenna gain processor 235 automatically determines the gain of the antennas by processing the measured data.

[0126] In an embodiment, the separation distance 236 between the first and second antennas 201 and 202 is dynamically varied from a starting distance dw to afinal distance ^^^^^3^^^^^^^^^^^^^^^^^^^. The starting distance dw is the Wacker Distance and may be understood as the minimum separation distance between two antennas that guarantees convergence of the power series expansion used to describe the coupling between the two antennas. In general, for a pair of non-identical antennas, dwis given by the average of the largest dimensions, Di and Dj for each antenna in the pair, i and j, as dW=(Di+Dj) / 2.

[0127] The final distance^may be understood as the distance at which the third-order scattered signal has reached its Fraunhofer criteria, sometimes referred to as the far-field, for whichis given bywherein D is the largest dimension of the larger of the two antennas in the pair, and λ is the wavelength. One advantage of this arrangement is that it defines the range over which to vary the separation distance 236 between the antennas.

[0128] In an embodiment, the first and second antennas 201 and 202 are aperture antennas. Aperture antennas are antennas that consist of an opening through which radio waves are transmitted or received. One advantage of aperture antennas is that they have well behaved and predictable radiation characteristics.

[0129] In an embodiment, the first and second antennas 201 and 202 are standard gain horn antennas. A standard gain horn antenna is a type of aperture antenna that has a pyramidal horn shape. Standard gain horn antennas are commonly used as gain reference standards. One advantage of using standard gain horn antennas is that they provide for an accurate and precise measurement of antenna gain.

[0130] The antenna gain processor 235 may determine the gain of the first and second antennas 201 and 202 based on the fifth-order scattered signal as a function of the separation distance 236. One advantage of this arrangement is that the fifth-order scattered signal may provide for a more accurate measurement of antenna gain.

[0131] The antenna gain processor 235 may also determine the gain of the first and second antennas 201 and 202 based on the seventh-order scattered signal as a function of the separation distance 236. One advantage of this arrangement is that the seventh-order scattered signal may provide for a more accurate measurement of antenna gain.

[0132] The process for measuring gain of an antenna provides several technical advantages when using the specific implementations described above. The separation distance variation from dw todefines the range over which to vary the separation distance 236 between the antennas 201 and 202. Aperture antennas or standard gain horn antennas 201 and 202 provide antennas with predictable radiation characteristics. The fifth-order and seventh-order scattered signals may provide for a more accurate measurement of antenna gain.

[0133] The process for measuring gain of an antenna with a radio frequency antenna gain measuring apparatus includes positioning an antenna 202 using an antenna positioner 210 at an antenna-to-mirror distance 241 from a mirror 242. An antenna positioner 210 is a device that can be used to accurately and precisely position an object in three dimensions, or six degrees of freedom, in an automated fashion. One advantage of this arrangement is that it enables a user to accurately and precisely position the antenna 202 at a desired location and orientation.

[0134] The process further includes dynamically varying the antenna-to- mirror distance 241 using a linear motion positioner 211. A linear motion positioner 211 is a device that enables an object to move in a straight line along an axis. One advantage of this arrangement is that it enables the apparatus to measure the signal that is transmitted between the antenna 202 and the antenna image 239 as a function of the antenna-to-mirror distance 241.

[0135] In an embodiment, the process includes transmitting a first signal 214 from a radio frequency transmit and receive electronics device 232 to the antenna 202. A radio frequency transmit and receive electronics device 232 may be understood as a device that is able to produce and receive radio frequency signals. One advantage of this arrangement is that it provides a means to transmit a signal 214 between the antenna 202 and the antenna image 239.

[0136] In an embodiment, the process includes receiving a second signal 215 at the antenna 202 from an antenna image 239 produced by the mirror 242. One advantage of this arrangement is that it provides a means to receive a signal 215 that is transmitted between the antenna 202 and the antenna image 239.

[0137] In an embodiment, the process includes measuring the antenna-to- mirror distance 241 using a distance meter 233. A distance meter 233 is a device that can accurately measure distances between objects. One advantage of this arrangement is that it enables an accurate measurement of the antenna-to-mirror distance 241 to be obtained.

[0138] In an embodiment, the process includes transmitting the first and second signals 214 and 215 and the antenna-to-mirror distance 241 from the radio frequency transmit and receive electronics device 232 to an antenna gain processor 235. An antenna gain processor 235 is a device or software program that performs mathematical operations on data. One advantage of this arrangement is that it enables the apparatus to transmit data to the antenna gain processor 235.

[0139] In an embodiment, the antenna gain processor 235 receives the first and second signals 214 and 215 and the antenna-to-mirror distance 241 and determines the gain of the antenna 202 based on the third-order scattered signal as a function of the antenna-to-mirror distance 241. One advantage of this arrangement is that it enables the apparatus to automatically determine the gain of the antenna 202 by processing the measured data.

[0140] The process for measuring gain of an antenna provides several technical advantages. The antenna positioner 210 accurately and precisely positions the antenna 202. The linear motion positioner 211 allows the antenna-to-mirror distance 241 to be varied. The distance meter 233 accurately measures the antenna- to-mirror distance 241. The radio frequency transmit and receive electronics device 232 provides a means to accurately and precisely measure the amplitude and phase of the radio frequency signals that are transmitted and received between the antenna and the antenna image. The antenna gain processor 235 automatically determines the gain of the antenna by processing the measured data.

[0141] In an embodiment, of the invention the antenna-to-mirror distance 241 is dynamically varied from a starting distance dwto a final distance, ^^^^^3^^^^^^^^^^^^^^^^^^^. The starting distance dwis the Wacker Distance and may be understood as the minimum separation distance between the antenna and the antenna image that guarantees convergence of the power series expansion used to describe the coupling between the antenna and the antenna image. In general, for the antenna, dwis given by the largest dimension D of the antenna as dW=(Di+Dj) / 2.

[0142] The final distance,may be understood as the distance at which the third-order scattered signal has reached its Fraunhofer region, sometimes referred to as the far-field. As such, ^^^^^3^^^^^^^^^^^^^^^^^^^ is given bywherein D is the largest dimension of the antenna, and λ is the wavelength. One advantage of this arrangement is that it defines the range over which to vary the antenna-to-mirror distance 241.

[0143] In an embodiment, the antenna 202 is an aperture antenna. Aperture antennas are antennas that consist of an opening through which radio waves are transmitted or received. One advantage of aperture antennas is that they have well behaved and predictable radiation characteristics.

[0144] In an embodiment, the antenna 202 is a standard gain horn antenna. A standard gain horn antenna is a type of aperture antenna that has a pyramidal horn shape. Standard gain horn antennas are commonly used as gain reference standards. One advantage of using standard gain horn antennas is that they provide for an accurate and precise measurement of antenna gain.

[0145] In an embodiment, the antenna positioner 210 is a robotic arm. A robotic arm is an automatically controlled manipulator, usually programmable, with similar functions to a human arm; the arm may be the sum total of the mechanism or may be part of a more complex robot. Robotic arms are ideal antenna positioners 210 as they can be used to accurately and precisely position an antenna in six degrees of freedom in an automated fashion.

[0146] In an embodiment, the radio frequency transmit and receive electronics device 232 is a vector network analyzer. A vector network analyzer is an instrument that measures the magnitude and phase of the reflection and transmission properties of a device as a function of frequency. One advantage of vector network analyzers is that they provide for an accurate and precise measurement of the amplitude and phase of the signals that are transmitted and received between the antenna and the antenna image.

[0147] In an embodiment, the distance meter 233 is selected from the group consisting of an optical encoder, a magnetic encoder, a laser tracking system, and a laser distance meter. An optical encoder is a device that converts motion into a sequence of digital pulses and can be used to determine position and distance. A magnetic encoder is a device that converts position to electrical signals using magnets. A laser tracking system is a system that uses a laser to measure the position of an object in space. A laser distance meter is an instrument that uses a laser to measure distance. One advantage of using these different types of distance meters 233 is that they each have unique characteristics that can be tailored to the specific needs of the application. For example, optical and magnetic encoders are typically used when high accuracy and precision are required, while laser tracking systems and laser distance meters are typically used when a longer range of motion is needed.

[0148] The antenna gain processor 235 may determine the gain of the antenna 202 based on the fifth-order scattered signal as a function of the antenna-to- mirror distance 241. One advantage of this arrangement is that the fifth-order scattered signal may provide for a more accurate measurement of antenna gain.

[0149] The antenna gain processor 235 may also determine the gain of the antenna 202 based on the seventh-order scattered signal as a function of the antenna- to-mirror distance 241. One advantage of this arrangement is that the seventh-order scattered signal may provide for a more accurate measurement of antenna gain.

[0150] The process for measuring gain of an antenna provides several technical advantages when using the specific implementations described above. The antenna-to-mirror distance variation from dw defines the range over which to vary the separation distance between the antenna and the antenna image. An apertureantenna or standard gain horn antenna 202 provides an antenna with predictable radiation characteristics. A robotic arm as an antenna positioner 210 provides for accurate and precise positioning in an automated fashion. The vector network analyzer provides for an accurate and precise measurement of the amplitude and phase of the radio frequency signals. The various distance meters 233 provide a measurement of the antenna-to-mirror distance 241 tailored to the specific needs of the application. The fifth-order and seventh-order scattered signals may provide for a more accurate measurement of antenna gain.

[0151] In an embodiment, a process for measuring gain of an antenna with radio frequency antenna gain measuring apparatus 200 proceeds as follows: (step 1) the first pair of antennas, as shown in in FIG. 3(a) and (c), is attached to antenna positioner (209, 210) as antenna (201, 202). With single-antenna radio frequency antenna gain measuring apparatus 238, the antenna is attached to positioner 210 as antenna 202.

[0152] (step 2) For multiple antennas, separation distance 236 is then dynamically changed to a starting distance equal to the Wacker Distance, dwwhich in general is for non-identical antennas the average of the largest dimensions Di,jfor each antenna in the pair i and j as, dW=(Di+Dj) / 2. For the single mirror configuration (238), antenna-to-mirror distance 241 is dynamically changed to a starting distance equal to half the Wacker Distance equal to dw / 2.

[0153] (step 3) For multiple antennas, separation distance 236 (alternately, for the single mirror configuration 238, the antenna-to-mirror distance 241) is then dynamically changed by either moving the linear motion positioner or one of the antenna positioners 209 or 210 to position dmax as given in equation (17) such that the received signals 213 and 215 reach the maximum value for the first half interference fringe of the third-order signal (from equation (14)). This maximum value is depicted as ^^^^^3 ^^^^^^^^^^^^^^^^^^^in FIG.6 and as equation (15). Alternately the maximum value for the first interference fringe of the fifth-order, seventh-order, etc. interference fringes can be used instead of the third-order signal. FIG.7 shows a spectrum of a set of third-order half interference fringes.

[0154] (step 4) The maximum signal value is then stored in central controller 234 along with the value of the dmax.

[0155] (step 5) For multiple antennas, the separation distance 236 (alternatively for the single antenna configuration, antenna-to-mirror distance 241) is then dynamically changed by either moving the linear motion positioner or one of the antenna positioners 209 or 210 to position dminas given in equation (18) such that the received signals 213 and 215 reach the minimum value for the first half-interference fringe of the third-order signal (given as equation (14)). This minimum value is depicted as ^^^^^3 ^^^^^^^^^^^^^^^^^^^in FIG.6 and as equation (16). Alternatively, the minimum value for the first interference fringe of the fifth-order, seventh-order, etc. interference fringes can be used instead of the third-order signal. FIG.7 shows an example of a spectrum of a set of third-order half-interference fringes.

[0156] (step 6) The minimum signal value is then stored in central controller 234 along with the value of the dmin.

[0157] (step 7) For the multiple antenna configuration, steps 2 through 6 are repeated for a total of 2(n+1) nominally equally-spaced interference fringes out to tion distance 236 equal to d given by equation (34) as ^^ 2^^^2a separa^Far ^^^^^^^^^^^^^^= 3 ^^^^ , wherein D is the largest dimension of the larger of the two antennas in the pair. The order nas given in equation (25) and (33) is selected and can have a typical value of ^^^^ ≥ 4,e.g., n being 4 or 5 as shown in Table 1.

[0158] (step 8) For the multiple antenna configuration, steps 2 through 6 are repeated for a total of 2(n+1) nominally equally-spaced interference fringes out to enna-to-mirror distance 241 equal to ^^^^ 1^2an ant^^^^^^^^^^^^^^^= 3 ^^^^ , wherein D is the largest dimension of the larger of the two antennas in the pair. The order n given in equation(25) and (33) is chosen and has typical values of ^^^^ ≥ 4, e.g., n being 4 or 5 as shownin Table 1.

[0159] (step 9) The distances dmax and dmin for each fringe in the set of 2(n+1) nominally spaced interference fringes is found from equation (17) and (18). For the multiple antenna configuration, the order "^^^^" as defined in (17) and (18) is chosen for each interference fringe to give equally spaced interference fringes over thedistance from ^^^^^^^^^^^^^^^^^^^^ = 0.62� ^^^^3^^^^ to ^^^^^^^^^^^^^^^^= 2^^^^23 ^^^^ . For the single antenna configuration, the order "^^^^" is chosen for each interference fringe to give equally spaced interferencefringes from ^^^^^^^^^^^^^^^^^^^^ =

[0160] (step 10) For the multiple antenna configuration, central controller 234, sends the values of the separation distances 236 for ^^^^^^^^^^^^^^^^and ^^^^^^^^^^^^^^^^to antenna gain processor 235 from which the center of the interference fringe shown as dc in FIG.6 is calculated from dmax and dmin as (^^^^^^^^ = ^^^^^^^^^^^^^^^^ + ^^^^^^^^^^^^^^^^) / 2. Antenna gain processor235 then computes the matrix ^^^^ given in equation (28).

[0161] (step 11) For the single antenna configuration, central controller 234 sends the values of the antenna-to-mirror distance 241 for ^^^^^^^^^^^^^^^^andto antenna gain processor 235 from which the center of the interference fringe shown as dcin FIG.6 is calculated from dmax and dmin as (^^^^^^^^ = ^^^^^^^^^^^^^^^^ + ^^^^^^^^^^^^^^^^) / 2. The antenna gainprocessor 235 then computes the matrix ^^^^ given in equation (28).

[0162] (step 12) The central controller 234 sends the stored signals to the antenna gain processor 235. The antenna gain processor 235 then computes themean signal for each half fringe, given by ^^^^̅ in equation (22) and constructsmeasurement vector ^^^^ as given in equation (27).

[0163] (step 13) The antenna gain processor then solves for the coefficient vector ^^^^ using equation (30).

[0164] (step 14) For the multiple antenna configuration where three antennas are used as in FIG. 6(c), the antenna gain processor 235 determines antenna gains from the coefficient vector ^^^^ for each antenna pair using equation (31) that is given. For the multiple antenna configuration where two antennas are used (one antenna with known gain ^^^^^^^^and one antenna with unknown gain ^^^^^^^^as in FIG. 6(a)), the antenna gain processor 235 uses equation (2) along with the element ^^^^′00obtained from the coefficient vector ^^^^ (shown in equation (29)) to solve for the 4^^^^2�^^^^′�2 unknown antenna gain ^^^^ that is c00^^^^alculated in linear units by^^^^^^^^ = ^^^^^^^^. For thesingle antenna configuration, wherein one unknown antenna is used as in FIG.6(b),the antenna gain processor 235 uses equation (2) with the element ^^^^′00obtained fromthe coefficient vector ^^^^ in equation (29) and the unknown antenna gain ^^^^^^^^ = ^^^^^^^^ = ^^^^that is calculated in linear units by 2^^^^|^^^^′00| = ^^^^.

[0165] (step 15) The antenna gain processor then generates antenna gain data array 237 as the output result.

[0166] The process for making a radio frequency antenna gain measuring apparatus includes mounting a first antenna 201 on a first antenna positioner 209. The first antenna positioner 209 is a device that can be used to accurately and precisely position an object in three dimensions, or six degrees of freedom, in an automated fashion. Examples of antenna positioners 209 include robotic arms and mechanical positioning stages. The process also includes mounting a second antenna 202 on a second antenna positioner 210. The second antenna positioner 210 is similar to the first antenna positioner 209 in that it can also be used to accurately and precisely position an object in three dimensions. Antennas 201 and 202 can be mounted to antenna positioner (209 and 210) using hardware fasteners such as bolts, screws, nuts, clamps, and the like. Antennas (201 and 202) are connected to cables that carry signals (212, 213, 214, 215) with RF connectors or adapters. Examples of such connectors are 2.4 mm, 2.92 mm, 3.5 mm and N-type coaxial connectors and waveguide connectors. Connectors could also be adapters that have convert from one type of connection to another for example a 3.5 mm coaxial-to-waveguide adapter.

[0167] The second antenna positioner 210 is mounted on a linear motion positioner 211. The linear motion positioner 211 is a device that enables an object to move in a straight line along an axis. The linear motion positioner 211 may be a motorized linear translation stage.

[0168] The first antenna 201 is connected to a first radio frequency transmit and receive electronics device 231 with a first cable. Examples of first cables include coaxial cables and waveguides. The second antenna 202 is connected to a second radio frequency transmit and receive electronics device 232 with a second cable. The second cable may be similar to the first cable.

[0169] The linear motion positioner 211 is connected to a distance meter 233. Examples of distance meters 233 include optical encoders, magnetic encoders, laser tracking systems, and laser distance meters.

[0170] The first and second radio frequency transmit and receive electronics devices 231 and 232 and the distance meter 233 are connected to a central controller 234. Examples of central controllers 234 include personal computers. The central controller 234 is connected to an antenna gain processor 235. Examples of antenna gain processors 235 include personal computers that implement an algorithm to determine antenna gain.

[0171] Positioners 209 and 210 can be assembled by combining motors, actuators, encoders, robotic arms or by combining in series or parallel motion stages, e.g., linear and rotary stages. Anchoring positioners (209 and 210) to a floor, laboratory table, or other stable platform can be accomplished with anchor bolts or brackets. In the case of using positioner 210 with linear motion positioner 211, antenna positioner 210 can be anchored to linear motion positioner 211 with a mating interface to the linear guide rails that provide linear motion of linear motion positioner 211. Linear motion positioner 211 can be anchored to a stable foundation using floor anchors, bolts, and brackets. Making radio frequency antenna gain measuring apparatus 200 also can include: connecting radio frequency transmit and receive electronics 231 and 232 to central controller using cables, e.g., USB, GPIB, Ethernet, CAN, optical fiber, coaxial, serial, RJ-45, RS-232 cables, and the like; connecting distance meter 233 to linear motion positioner 211 with cables, e.g., USB, GPIB, Ethernet, CAN, optical fiber, coaxial, serial, RJ-45, RS-232 cables, and the like; constructing central controller 234 from a computer such as a PC; and combining interface electronics such as network card interfaces, GPIB interfaces, serial interfaces, and the like with the computer; providing the computer with interfaces and automation software, e.g., LabVIEW, MATLAB, Python, C++, and the like; constructing antenna gain processor 235 from a computer such as a PC; combining the PC with data processing software, e.g., LabVIEW, MATLAB, Python, C++, and the like; connecting antenna gain processor 235 to central controller 234 with network connections or cables such as Ethernet and connecting to a data storage device, e.g., a hard drive, network drive, or cloud-based storage. Configuring radio frequencyantenna gain measuring apparatus 200 as single-antenna radio frequency antenna gain measuring apparatus 238 can include: constructing mirror 242 from a material that is highly reflective for RF frequencies, e.g., metals such as copper, aluminum, or steel; polishing the reflective material so that it is smooth on the scale of the RF wavelength; and constructing mirror 242 with dimensions that are wider than the beam width of antenna 202 to minimize diffraction effects from the edge of mirror 242. An example of mirror 242 is polished metal sheet or block of metal. Supporting mirror 242 can occur by mounting mirror 242 to a large frame or positioner 209 or anchoring mirror 242 to a floor so that its reflective surface is normal to the z-axis of antenna coordinate system 208.

[0172] The process for making the radio frequency antenna gain measuring apparatus provides several technical advantages. The first and second antennas 201 and 202 provide the apparatus with two antennas. The first and second antenna positioners 209 and 210 accurately and precisely position the first and second antennas 201 and 202. The linear motion positioner 211 allows the separation distance between the two antennas to be varied. The distance meter 233 accurately measures the separation distance between the two antennas. The first and second radio frequency transmit and receive electronics devices 231 and 232 provide a means to accurately and precisely measure the amplitude and phase of the radio frequency signals that are transmitted and received between the two antennas. The central controller 234 controls and coordinates all functions of the apparatus and is used to store and manage the data collected by the apparatus. The antenna gain processor 235 automatically determines the gain of the antennas by processing the measured data.

[0173] In an embodiment, the first antenna 201 and second antenna 202 are aperture antennas. Aperture antennas are antennas that consist of an opening through which radio waves are transmitted or received. One advantage of aperture antennas is that they have well behaved and predictable radiation characteristics.

[0174] In an embodiment, the first antenna 201 and second antenna 202 are standard gain horn antennas. A standard gain horn antenna is a type of aperture antenna that has a pyramidal horn shape. Standard gain horn antennas are commonly used as gain reference standards. One advantage of using standard gain hornantennas is that they provide for an accurate and precise measurement of antenna gain.

[0175] In an embodiment, the first and second antenna positioners 209 and 210 are robotic arms. A robotic arm is an automatically controlled manipulator, usually programmable, with similar functions to a human arm; the arm may be the sum total of the mechanism or may be part of a more complex robot. Robotic arms are ideal antenna positioners 209 and 210 as they can be used to accurately and precisely position an antenna in six degrees of freedom in an automated fashion.

[0176] In an embodiment, the first and second radio frequency transmit and receive electronics devices 231 and 232 are vector network analyzers. A vector network analyzer is an instrument that measures the magnitude and phase of the reflection and transmission properties of a device as a function of frequency. One advantage of vector network analyzers is that they provide for an accurate and precise measurement of the amplitude and phase of the signals that are transmitted and received between the two antennas.

[0177] The process for making the radio frequency antenna gain measuring apparatus provides several technical advantages when using the specific implementations described above. Aperture antennas or standard gain horn antennas 201 and 202 provide antennas with predictable radiation characteristics. Robotic arms as antenna positioners 209 and 210 provide for accurate and precise positioning in an automated fashion. The vector network analyzer provides for an accurate and precise measurement of the amplitude and phase of the radio frequency signals.

[0178] It is contemplated that radio frequency antenna gain measuring apparatus 200 and measuring gain of an antenna can include the properties, functionality, hardware, and process steps described herein and embodied in any of the following non-exhaustive list: a process (e.g., a computer-implemented method including various steps; or a method carried out by a computer including various steps); an apparatus, device, or system (e.g., a data processing apparatus, device, or system including means for carrying out such various steps of the process; adata processing apparatus, device, or system including means for carrying out various steps; a data processing apparatus, device, or system including a processor adapted to or configured to perform such various steps of the process); a computer program product (e.g., a computer program product including instructions which, when the program is executed by a computer, cause the computer to carry out such various steps of the process; a computer program product including instructions which, when the program is executed by a computer, cause the computer to carry out various steps); computer-readable storage medium or data carrier (e.g., a computer-readable storage medium including instructions which, when executed by a computer, cause the computer to carry out such various steps of the process; a computer- readable storage medium including instructions which, when executed by a computer, cause the computer to carry out various steps; a computer-readable data carrier having stored thereon the computer program product; a data carrier signal carrying the computer program product); a computer program product including comprising instructions which, when the program is executed by a first computer, cause the first computer to encode data by performing certain steps and to transmit the encoded data to a second computer; or a computer program product including instructions which, when the program is executed by a second computer, cause the second computer to receive encoded data from a first computer and decode the received data by performing certain steps.

[0179] It should be understood that the calculations may be performed by any suitable computer system. Data is entered into a computing system via any suitable type of user interface and may be stored in a memory, which may be any suitable type of computer readable and programmable memory and is preferably a non-transitory, computer readable storage medium. Calculations are performed by a processor, which may be any suitable type of computer processor and may be displayed to the user on a display, which may be any suitable type of computer display.The processor may be associated with, or incorporated into, any suitable type of computing device, e.g., a personal computer or a programmable logic controller. The display, the processor, the memory, and any associated computer readable recording media are in communication with one another by any suitable type of data bus, as is well known in the art. Examples of computer-readable recording media include non- transitory storage media, a magnetic recording apparatus, an optical disk, a magneto- optical disk, and / or a semiconductor memory (for example, RAM, ROM, and the like.). Examples of magnetic recording apparatus that may be used in addition to memory, or in place of memory, include a hard disk device (HDD), a flexible disk (FD), and a magnetic tape (MT). Examples of the optical disk include a DVD (Digital Versatile Disc), a DVD-RAM, a CD-ROM (Compact Disc-Read Only Memory), and a CD-R (Recordable) / RW. It should be understood that non-transitory computer-readable media include all computer-readable media except for a transitory, propagating signal.

[0180] The articles and processes herein are illustrated further by the following Example, which is non-limiting. EXAMPLE

[0181] Enhanced Gain Extrapolation Technique: a third-order scattering process for high-accuracy antenna gain, sparse sampling, at Fresnel distances

[0182] In this Example, an enhanced three-antenna gain extrapolation technique determines antenna gain with significantly fewer data points and at closer distances than with the conventional three-antenna gain extrapolation technique that has been used for over five decades. As opposed to the conventional gain extrapolation technique, where high-order scattering is purposely ignored to isolate only the direct antenna-to-antenna coupling, by incorporating third-order scattering the enhanced gain extrapolation technique can be obtained. The theoretical foundation using third-order scattering is described, and experimental results are included comparing the enhanced technique and a conventional technique for two sets of internationally recognized NIST reference standard gain horn antennas at X-band and Ku band. We show that with the enhanced technique gain values for these antennas are readily obtained to within stated uncertainties of ±0.07 dB using as few as 10 datapoints per antenna pair, as opposed to ≈ 4000-to- 8000 data points per antenna pairthat is needed with the conventional technique. Furthermore, with the described enhanced technique, antenna-to-antenna distances can be reduced by a factor of three, and up a factor of six in some cases, compared to the conventional technique - a significant reduction in the overall size requirement of facilities used to perform gain extrapolation measurements.

[0183] The conventional three-antenna gain extrapolation technique ([reference 1]-[reference 7]) originated with the work of Paul F. Wacker at the National Bureau of Standards (NBS) (now the National Institute of Standards and Technology (NIST)) with the publication of NBS Report 10-733 in 1972 [reference 8]. Wacker's work, which was itself an extension of David Kerns' [reference 9] scattering matrix theory that lead to modern nearfield antenna techniques, and allows one to determine the transmitted signal between two arbitrary antennas separated by any distance. Wacker's work provides a complete theoretical description of antenna-to-antenna coupling without far field approximations and includes all orders of scattering to accurately describe proximity effects between the two antennas from the near-zone to infinitely far away. Wacker's work extended understanding of antenna-to-antenna transmission beyond Schelkunoff-Friis theory [reference 10], which is valid only in the far-field, and laid the foundation for the conventional gain extrapolation technique which is considered one of the most accurate method for measuring antenna gain[reference 7] routinely achieving uncertainties of < 0.1 dB.

[0184] In determining the gain of an antenna using the conventional gain extrapolation technique, Wacker’s' coupling equation (1) is fit to the transmitted signal obtained between a pair of antennas while scanning their separation distance, ^^^^. A diagram of the general measurement setup is shown in FIG. 4. This fitting process provides a means to obtain the distance independent term (2) in Wacker's power series expansion of the transmitted signal; the remaining term that exists at an antenna separation distance infinitely far away. By doing so, the transmitted signal has in effect been extrapolated to the far-field at infinity. It can be shown [reference 1]-[reference 4] that this distant independent term represents the far-field gain product, i.e., "pair gain" for the pair of coupled antennas as given in (2). Upon measuring the pair gainfor three pairs of antennas one then calculates the individual antenna gains [reference 1]-[reference 4].

[0185] In the conventional gain extrapolation technique all higher orders of scattering are ignored and only the direct signal from transmit to receive antenna is kept. However, in practice the signal obtained during measurement includes this direct component as well as other higher orders of scattered waves. A typical curve obtained during gain extrapolation is shown in FIG. 5. It is readily seen that the curve is not smooth but rather has periodic oscillations that vary in magnitude with the separation distance. These oscillation occur due to the interference of the higher order scattered waves bouncing between the two antennas and perturbing the direct signal. To remove these oscillatory effects when implementing conventional gain extrapolation, the signal must be smoothed so as to retain only the direct signal represented by the(^^^^ = 0), ^^^^^^^^^^^^^^^^ term in equation (1). A common effective approach to smoothing is touse a moving average with a ^^^^ / 2 window [reference 1]-[reference 4]. More sophisticated filtering schemes include digital filtering [reference 11] and ^^^^-space [reference 12] filtering. In ^^^^-space filtering, data must be sampled above the Nyquist rate of the highest spatial frequency for ripples in the curve in order to avoid aliasing and therefore can result in large data sets. Recently, more complex sampling schemes based on jittered pseudorandom sampling in conjunction with a compressive sensing optimization approach have been reported to smooth the signal while overcoming the high sample rate requirement of the ^^^^ space techniques [reference 13]. Although varying degrees of smoothness of the antenna pair coupling curve were demonstrated actual antenna gain values were not produced or reported.

[0186] The implications from the approach to ignore the higher order scattered waves and keep only the direct signal are that large data sets, often thousands of data points, are typically required per antenna pair, and the separation distances needed to obtain a useful data set is on the scale of several meters requiring large test facilities to implement. Below we discuss in detail a new technique, we are calling the Enhanced Gain Extrapolation Technique, whereby the third-order scattered waves are not ignored, providing a straightforward and effective way to significantly reduce the number of required data samples by orders of magnitude, while also reducing the bounds on antenna separation distance by several factors compared tothe conventional gain extrapolation technique. It is important to stress that the scope of this paper addresses the determination of gain for linearly polarized, aperture type directional antennas such as those often used as gain standards [reference 5],[reference 10],[reference 14] and for which antenna-to-antenna multiple reflections are dominant over environmental multi-path reflections. Low gain antennas for which environmental multipath reflections tend to dominate, such as omni-directional antennas, as well as antennas having polarization with finite ellipticity will be addressed in future work. For the remainder of this paper the word "gain" will be used interchangeably to mean "partial realized gain" as defined in [reference 6] and [reference 7].

[0187] The theory for the enhanced gain extrapolation technique based on the third-order signal is derived from Wacker's fundamental equations. Sampling criteria for the new enhanced technique are developed based upon the physics of the third-order signal and compared to the conventional gain extrapolation technique. Experimental data are presented for two sets of internationally recognized NIST reference standard gain horn antennas operating at frequency bands of WR-90 (X- band) and WR-62 (Ku-band). Both sets of antennas have well documented gains and uncertainties as determined using the conventional gain extrapolation technique. In fact, the X-band antennas [reference 15] being some of the first NIST / NBS antennas ever measured using the conventional gain extrapolation technique with recorded gain values from multiple National Metrology Institutes dating back to the late 1970's-to- present. The Kuband antennas [reference 16] being part of a multi-year Bureau international des poids et mesures (BIPM) Consultative Committee for Electricity and Magnetism (CCEM) Key Comparison, with gain values reported as measured independently by 12 different National Metrology Institutes dating back to the year 2016 to the present. Results are compared for these reference antennas using the described enhanced gain extrapolation technique and the conventional gain extrapolation technique.

[0188] THEORY

[0189] A. Third-order signal

[0190] The third-order signal is derived starting from Wacker's expression for the total signal transmitted between two essentially arbitrary antennas ^^^^ and ^^^^, which includes all orders of scattered waves. The power series expansion [reference 8] for the total received signal between antennas separated by a distance ^^^^ is given as,

[00191] The pair gain, ^^^^^^^^^^^^^^^^, in linear units, is given by the (^^^^ = 0, ^^^^ = 0) termas, ^^^^ |^^^^00|2= ^^^^^^^^^^^^4^^^^2(2)with ^^^^^^^^^^^^as either of the off-diagonal elements in the scattering matrix [reference 9] that represents the received signals between the two input / output ports of each antenna,e.g. ^^^^12 or ^^^^21, as shown in FIG. 4, ^^^^ = 2^^^^ / ^^^^, with ^^^^ the wavelength at the operatingfrequency ^^^^.

[00192] Expanding this series a few terms, up to (^^^^ = 2) here, to better showthe scattered wave orders gives,With the interpretation that each order "p" represents the scattered signal componentdue to the wave traversing the separation distance, ^^^^, a total of (2^^^^ + 1)^^^^ number oftimes, with phaseand the proximity effect terms ^^^^^^^^^^^^ / ^^^^(2^^^^+^^^^)dictating the distance-dependant free space path loss and strength of the scattered orders at a given distance ^^^^. It is noted that the free space path loss increases rapidly like 1 / ^^^^(2^^^^+^^^^)at a given distance as the order of the scattered wave ^^^^ increase. The fifth-order (and higher) scattered waves, with (^^^^ ≥ 2), and proximity effects of order (2^^^^ +^^^^) ≥ 4 will therfore experience a very rapid free-space path loss with distancecompared to the direct wave and third-order wave. Thus, at physical distances wherethe fifth-order scattered waves are negligible due to these path losses the series is truncated up to third-order as,

[0193] The truncated series is re-written in a form to better show thesuperposition of the (^^^^ = 0) direct wave and (^^^^ = 1) third-order wave as,

[0194] Taking the square magnitude of (5),withand

[0195] The third-order signal is given as,with Δ^^^^ = (^^^^1 − ^^^^0). This takes a familiar form of two beam interference as arises ininterferometry and homodyne detection, and in fact one can think of the third-order signal in equation (14) as resulting from a homodyne scheme that occurs naturally under gain extrapolation measurement conditions. Equation (14) shows that at shorter distances, in the near zone of the antenna pair, where there is appreciable presence of both the direct and third-order waves, a strong modulated signal exists from which to sample data from. Encoded on this modulated signal is also the signal as it exists extrapolated infinitely far away, from which the far-field pair gain for the two antennas is obtained. This is in contrast to the conventional gain extrapolation method, wherein by choosing to ignore the third-order signal, one must avoid the near-zone regions of strong interaction between the direct and third-order waves and which then drives the requirement that data must be taken at larger separation distances.

[0196] With the enhanced gain extrapolation technique the requirement is rather that the fifth-order signal be the one that is avoided, which due to its rapiddistance dependent free space path loss of 1 / ^^^^(4+^^^^) with ^^^^ ≥ 0 (see (3)), happens atvery close distances. The result being that the usable measurement distance range can be closer with the enhanced gain extrapolation technique than in the conventional technique and is one of the advantages.

[0197] B. Interference fringes and stationary approximation

[0198] Although equation (14) has a familiar form, both ^^^^0andarepolynomials in ^^^^^^^^^^^^ / ^^^^(2^^^^+^^^^) and coupled through interference by 2�^^^^0^^^^1cos (4^^^^^^^^ / ^^^^ +Δ^^^^). However, through judicious choices based on the behavior and scale of the interference fringes produced by (14), we can uncouple both ^^^^0and ^^^^1and access the extrapolated far-field pair gain coefficient, ^^^^00.

[0199] Each interference fringe has a maximum and minimum extremawhich occur at specific distances where cos (4^^^^^^^^ / ^^^^ + Δ^^^^) = ±1. The third-order signalat these extrema becomes,(15)(16)with the distance these extrema occur at being respectively, (17)^^^^min(18)where ^^^^ is the order of the interference fringe. In particular, from (17) and (18) the extrema for an individual interference fringe are separated by a distance of|^^^^max − = ^^^^ / 4, for all fringe orders, ^^^^. For half of a fringe, the distance from thecenter occurring at ^^^^^^^^, to each extrema is,�^^^^max,min − ^^^^^^^^� = ^^^^ / 8. This fringe structureis shown in FIG.6.

[0200] The pair gain as derived from the interference fringe structure can be obtained by following a line of thought as to the distance scales involved. As shown by Wacker [reference 8], for a pair of identical antennas with largest dimension ^^^^, convergence of equation (1) is guaranteed for all orders of scattering at antennaseparation distances ^^^^ ≥ ^^^^. For non-identical antennas the average of the largestdimensions for each antenna ^^^^^^^^,^^^^is used. Here, we define the Wacker Distance as thesmallest separation distance guaranteeing convergence as ^^^^^^^^ = ^^^^. By virtue ofantenna design principles [reference 5],[reference 10], aperture type antennas suchas gain standards will have ^^^^ ≈ 10^^^^, and thus ^^^^^^^^ will in general be many times largerthan a quarter of a fringe. That is, ^^^^^^^^ > ^^^^ / 8. For example, for a pair of identical 24 dBgain, WR-62 standard gain horn (SGH) antennas, operating at 15GHz, ^^^^ / 8 = 2.5 mm,^^^^^^^^ = ^^^^ = 200 mm, and, ^^^^^^^^ / (^^^^ / 8) = 80.

[0201] Furthermore, to maximize fidelity of the third-order interference fringes and usable separation distance during measurement, minimally influenced by fields generated in the reactive near-field, the nearest separation distance used for the measurement, ^^^^^^^^^^^^^^^^^^^^, is taken as the distance from the antenna aperture to the boundary of the Fresnel region [reference 18],

[0202] For which it is true that, ^^^^N3rdear >and convergence of (1) is stillguaranteed. For non-identical antennas, ^^^^N3rdearis taken as the average of the Fresnel distances for the antenna apertures to satisfy ^^^^3^^^^^^^^Near > ^^^^^^^^ while maximizing fringefidelity and usable separation distance. As such, for all distances ^^^^ ≥ ^^^^ 3 rdNear we makea stationary approximation for

[0203] the free space path loss over the distance range of half of a fringe as,

[0204] This is easily checked with the WR-62 SGH example, where even at the closest measurement distance of ^^^^3rdNear ≈ 400 mm, we see that 1 / (400 ±

[0205] C. Pair gain from the third-order signal

[0206] Applying the stationary approximation (20) across the extrema of half of a fringe in (15),(16) it follows that,and the cosine coupling term in (14) can be canceled out by computing the mean third-order signal for the half fringe, ^‾^^^, thusly,

[0207] Expandinggives,

[0208] Collecting terms of like ^^^^ dependency, equation (22) can be re- written as,withand the pair gain coefficient |^^^^00|2given as the first term of ^‾^^^. Due to the free space path loss, the terms in (25) fall off rapidly with order ^^^^, and thus in practice a finite number of terms remain significant.

[0209] As a physical guide to determining the highest order ^^^^, we note thefact that the fifth and higher-order waves, for which 1 / ^^^^(2^^^^+^^^^) with (2^^^^ + ^^^^) > 4, (seeeq. (3)) have been ignored as they diminish rapidly for very close distances. Similarlyterms in (25) for ^^^^ ≥ 5 will tend to have less of an effect such that truncating the seriesat ^^^^ = 4 or ^^^^ = 5 provides a sufficient number of terms. It is easy to include additionalterms to verify if higher values of ^^^^ may be needed for a given measurement. However,as shown below in §III, in practice gain values remain stable for ^^^^ ≥ 4, with the (^^^^ =4) term showing the lowest solution residuals, and adding more terms does very little to change results.

[0210] Via the third-order signal (14), the number of data points needed to obtain |^^^^00|2are now directly related to the number of terms in (25) which is a finite and small number. In contrast, the conventional gain extrapolation technique requires a large number (typically thousands) of data points in order to average out and filter third and higher-order scattered waves in the total signal of (1). Determining|^^^^00|2is then a matter of solving for the coefficients in (25) as follows.

[0211] The pair gain is obtained by first measuring ^^^^m3rdaxand ^^^^m3rdin(see FIG.6) and calculating ^‾^^^ from (22) for a set of ^^^^ fringes, with ^^^^ ≥ ^^^^, so there are at leastas many as the number of terms used in (25). The measurement vector is then constructed as, ‾

[0212] For each fringe center distance, ^^^^^^^^, the factors 1 / ^^^^^^^^are arranged as a matrix,

[0213] The corresponding coefficients are arranged as a vector,so that ^^^^ = ^^^^^^^^ with ^^^^ given by,^^^^ = ^^^^−1^^^^. (30)where ^^^^−1is the pseudoinverse as ^^^^ may in general be over determined. The pairgain coefficient is given by the first element of ^^^^ asFinally, the individualantenna gains in decibels (^^^^^^^^) are obtained by,the reflection coefficient, Γ^^^^, ofthe antenna is known, the absolute partial gain [reference 7] is given by ^^^^^^^^^^^^^^^^,^^^^=^^^^^^^^ / (1 − |Γ 2^^^^| ).

[0214] D. Sampling Criteria for Conventional Gain Extrapolation

[0215] The sampling strategy in conventional gain extrapolation is as follows. Data are measured out to a distance of at least 2^^^^2 / ^^^^ which is typically several meters [reference 2]-[reference 8]. A portion of the entire measured signal is then selected such that the strong third-order scattering in the near-zone along with any residual higher-order scattering, as well as any multi-path scattering near the far end of the curve, are avoided. These unwanted oscillations are identified by their period [reference 3], [reference 17], e.g., those due to third-order scattering having a periodof ^^^^ / 2 and multi-path oscillations having a longer period > ^^^^. In order to avoid regionsof near-zone scattering, the extent to which can depend on the antennas used, thenear distance typically ranges [reference 3], [reference 4] from 0.2^^^^2 / ^^^^ ≤ ^^^^ tradNear ≤0.5^^^^2 / ^^^^. The portion of the measured data that is left to be used is then smoothed to remove the remaining oscillations dominated by the third-order scattering [reference3], [reference 4] so as to retain only the direct signal represented by the (^^^^ = 0), ^^^^^^^^^^^^^^^^term in (1). Because only a portion of the acquired data is used, more data often times needs to be taken beyond 2^^^^2 / ^^^^ so that enough data is retained to satisfactorily curve fit equation (1). This overmeasuring often results in the more typical scenario, using^^^^ tradNear ≈ 0.2^^^^2 / ^^^^, and needing to measure data [reference 3],[reference 4] out to adistance of ≈ 4^^^^2 / ^^^^. Furthermore, the process of smoothing and filteringdata, to remove the oscillations due to third-order scattering, imposes requirements on the number of data points that need to be taken. If a ^^^^ / 2 moving average is used [reference 1]-[reference 4], data are needed every ^^^^ / 20 to ^^^^ / 10 to adequately average out the third-order oscillations. If filtering techniques are used [reference 3], [reference 12], even smaller sample spacing may be needed in order to avoid aliasing of noisethat can develop at the farther distances which can have spatial frequencies of < ^^^^ / 20.From the range of distances atradnd ^^^^Nearand average sample spacing of ^^^^ / 15, criteria for the typical range for the number of samples per antenna pair for the conventional gain extrapolation technique is, ^^^^trad

[00216] Using the WR-62 SGH at 15GHz example with ^^^^ = 200 mm, ^^^^ =20 mm the number of samples would be in the range of ≈ 3600 pts -to- 7600 pts.These values are very much in-line with the number of data points used in practice [reference 3].

[0217] E. Sampling Criteria for Enhanced Gain Extrapolation

[0218] A criteria for the lower limit on the number of samples needed to obtain the pair gain may be found based on the truncation order, ^^^^ of (25) as, ^^^^3^^^^^^^^ = 2(^^^^ + 1), (33)which is the minimum number of samples needed to solve the matrix equation (30). The factor of two arises as two measurements are needed, one for each extrema in(15) and (16), to determine ^‾^^^ for each half fringe. By choosing to truncate the series in(25) at ^^^^ = 4, the minimum number of samples per antenna pair is ^^^^3rd = ^^^^^^^^, whichis a significant reduction in the number of samples per antenna pair needed compared to the conventional gain extrapolation technique.

[0219] In the enhanced technique, because the region of strong third-order near zone scattering does not need to be avoided there is no need to specify a range for the ^^^^^^^^^^^^ ^^N3earand ^^^^^3 ^^^^^^^^^^^^^^^^^distances, as is done in the conventional technique (see previous section).

[0220] In the enhanced technique, ^^^^^3rd^^^^^^^^^^^^^^^and ^^^^^3rd^^^^^^^^^^^are specified by taking into account the third-order wave propagation characteristics. The nearest measurements distance, ^^^^3rdNear, is given by equation (19) above. The farthest measurement distance,arises from imposing the Fraunhofer (also referred to far-field) criteria on the third-order scattered wave, as this is the wave responsible for the homodyne effect. In doing so, we note that the total distance traveled by the directwave given by the phase factor, ^^^^^^^^^^^^^^^^, in equation (3) is, ^^^^^^^^^^^^^^^^ = ^^^^. Similarly the totaldistance traveled by the third-order scattered wave given by, ^^^^^^^^^^^^3^^^^, is ^^^^^^^^^^^^^^^^ = 3^^^^. Assuch, the third-order wave will have traversed between the two antennas three times (as depicted in FIG.4) and experiences three times the distance traveled compared to the direct wave. Thus, the third-order wave will reach its Fraunhofer region at a closer separation distance, which for the direct wave is still well within its Fresnel region. From this distance disparity a new criteria for the farthest measurement distance for the enhanced extrapolation technique is obtained by imposing the Fraunhofer criteria on the total distance traversed by the third-order scattered wave as

[0221] This is a three times reduction in the shortest far measurement distance when 2^^^^2 / ^^^^ is used in the conventional technique, and a six times reduction in the longest far measurement distance when 4^^^^2 / ^^^^ is used in the conventional technique.

[0222] F. Comparison of Sampling Criteria

[0223] Table 1 compares these sampling criteria for the two techniques and Table 2 shows typical values for the 15GHz 24 dB gain SGH example. A few aspects are worth noting. From (32) and (33) the number of samples for the enhanced gainextrapolation technique will be less than the conventional technique, ^^^^3rd < ^^^^tradsince 36^^^^276^^^^22(^^^^ + 1) << ^^^^2^^^^2(35)which is in general true for all reasonable orders, ^^^^. We also note that from (32) for the conventional gain extrapolation technique, the number of samples required depends explicitly on the dimensions of the antenna aperture, ^^^^, and the wavelength, ^^^^. In contrast, from (33) the number of samples for the enhanced gain extrapolation technique does not depend on either ^^^^ or ^^^^, onlyand ^^^^^3 ^^^^^^^^^^^^^^^^^^^do. The far distances are much shorter by a factor of three-to-six in the enhanced technique compared to the conventional technique which may also help reduce long-period multi-path reflections oscillations that tend to occur at longer antenna separation distances, and or with lower gain antennas [reference 3], [reference 17]. TABLE 1. SAMPLING CRITERIA COMPARISON. Criteria Enhanced Conventional +1), {^^^^ ≥ 4} 36^^^^2 2 ^^^^ 2(^^^^76^^^^^^^^2to^^^^2^^^3 22 ^^^^Near^0.2^^^^0.62� 0.5^^^^^ to ^^^^ ^^^ ^^^^ ^^^ 22 22 ^ ^^^^2^^^^4^^^^Far3 ^^^^ ^^^^ to ^^^^ TABLE 2. TYPICAL SAMPLING VALUES FOR 24^^^^^^^^ SGH AT 15GHz. Criteria Enhanced Conventional ^^^^ 10 points 3600 to 7600 points ^^^^Near392 mm 400 to 1000 mm^^^^Far1333 mm 4000 to 8000 mm

[0224] EXPERIMENT

[0225] A. Fringe Finding

[0226] The periodic nature of the third-order signal provides a dense spectrum of fringes to sample extrema from. Furthermore, as a results of (17) and (18), once the location of one fringe is found, the location of all other fringes are also known. In practice, it is straight forward to automate the linear positioner on a gain extrapolation antenna range to find the extrema for the fringes. Finding the extrema of the first fringe is matter of scanning the linear positioner over a distance of in multiples of ^^^^ / 2 starting at ^^^^N3rdearwhile monitoring the receive signal. The positioner can then be automated to move to subsequent fringe extrema. An example of a fringe spectrum at 15GHz obtained by this method is shown in FIG.7. For the purposes of illustrating this method to the reader, the linear positioner was set to scan the half fringes with a resolution of 0.1 mm within a window of 50 mm to reveal their full structure. The inset figure shows an expanded view of the location of the extrema to be used shown by the small arrows.

[0227] B. Gain Measurements

[0228] Gain measurements were conducted on the pairs of X-band and Ku- band NIST reference standard gain horns using both the enhanced gain extrapolation and conventional gain extrapolation techniques. Measurements were made at the same frequencies as those used in the documented gains for these antennas at8GHz, 10GHz, 12GHz, 12.4 GHz, 15GHz, and 18GHz. All measurements perperformedon the dual-robotic Large Antenna Positioning System (LAPS) [reference 19], [reference 20] at the Robotically Enhanced Antenna Laboratory for Metrology (available online at: https: / / www.nist.gov / ctl / roboticallyenhanced-antenna-laboratory- metrology-realmREALM) calibrations lab [reference 21], [reference 22] at NIST. As a full description of the LAPS system is outside the scope of this paper the reader is encouraged to see the references for more details.

[0229] Fringe extrema were obtained for sets of fringes ranging in numberto form the matrix ^^^^ with varying dimensions (see (28)), from square, with ^^^^ = (^^^^ +1), to rectangular, with ^^^^ = 2(^^^^ + 1) for ^^^^ = {2,3,4,5,6}. In doing so, the variability onthe results obtained by changing the truncation order ^^^^ of the third-order signal (25) for varying degrees of overdetermined matrices could be explored.

[0230] C. Gain Results

[0231] FIG.8, FIG.9, and FIG.10 show the gain result obtained using the enhanced gain extrapolation technique for the reference antennas. In the figures, matrix dimensionality is grouped diagonally across the table by grey-scale color. The number of rows as related to the truncation order ^^^^, and number of columns as related to the number of fringes used for the given matrix dimensions are shown at the top and left vertical portions of each table. The first diagonal being square matrices and the last diagonal, represented with the black outlined cells, being rectangular matrices. Each cell shows the resulting gain of each reference antenna in the pair (in dB ) as the top two entries, and the resulting solution residuals, ^^^^ in parenthesis " () " for that combination of truncation order ^^^^ (columns), and number of fringes used (rows). Residuals are calculated as the RMS percent error between the measured signals ^‾^^^in (27), and those produced using the coefficient solutions from (29),where ^^^^ is the number of data point used given in (33). Note, the residuals shown in parenthesis in the figures are unit less and should be read as scaled by 10−4.

[00232] From the results shown in these figures, the solution is stable at ^^^^ =4 with little change for higher orders. At ^^^^ = 4 the residuals are also nominally thesmallest for all matrix types. The resultant measured gain for each reference antennais taken as the average of all the gains for ^^^^ = {4,5,6} obtained for the varying matrixtypes, and the uncertainty contribution resulting from the solution process is taken as the corresponding standard deviation (not the standard deviation of the mean) for the range of gain values. The average gains for each antenna in the pair is given in thebottom legend of each figure along with the standard deviation ^^^^, as ^^^^1 ± ^^^^ and ^^^^2 ±^^^^. The standard deviation for all frequencies varies between 0.01 dB to 0.02 dB. Although a full exploration of uncertainty analysis is outside the scope of this paper we provide an estimate of the total uncertainty for these results based on NIST uncertainty analysis for gain extrapolation. Based on these results, an estimate for the uncertainty of the enhance gain extrapolation technique is obtained by including the contribution of ^^^^ for the "Matrix Solution" uncertainty term in the overall uncertainty analysis. Table 3 shows the NIST gain extrapolation uncertainty analysis with the addition of valuesof ^^^^ = 0.01 dB and ^^^^ = 0.02 dB in bold text. The standard uncertainty and expandeduncertainty as defined in [reference 23], with ^^^^ = 2 coverage factor, are also given.

[0233] Table 4 shows a comparison of the final results. Gain and uncertainty values obtained with the enhanced gain extrapolation technique are given in the "Measured (dB)" column, and the reference gain and uncertainty values that were obtained with the conventional gain extrapolation technique given in the "Reference (dB)" column. These results show all gain values obtained with the enhanced gain extrapolation technique fall within the range given by the uncertainties for the measured and reference values. TABLE 3. GAIN UNCERTAINTY Sources of Uncertainty Standard Uncertainty (dB) Polarization Mismatch < 0.01 < 0.01Receiver Nonlinearity 0.01 0.01 Impedance Mismatch 0.01 0.01 Antenna Alignment 0.01 0.01 Matrix Solution ^^^^.^^^^^^^^ ^^^^.^^^^^^^^ Connector Repeatability 0.01 0.01Residual Multipath 0.02 0.02 Random Uncertainties 0.01 0.01 Expanded Uncertainty (dB) (k=2) ^^^^.^^^^^^^^ ^^^^.^^^^^^^^

[0234] A description of an Enhanced Gain Extrapolation Technique based on Paul Wacker's near-zone scattering theory is given. As opposed to the conventional gain extrapolation technique that has been in use for over five decades, this enhanced gain extrapolation technique purposely incorporates third order antenna-to-antenna scattering and allows for a significant reduction in the number of data samples required by at least two orders of magnitude and measurement distances three to six times closer compared to the conventional gain extrapolation technique. A comparison of gain values obtained for pairs of internationally recognized NIST reference X-band and Ku Band standard gain horn antennas using the enhanced gain extrapolation and conventional gain extrapolation technique is given. Results show the enhanced gain extrapolation technique produces equivalent gain values with the conventional technique to within uncertainties of ±0.07 dB for all antennas at all frequencies. TABLE 4. GAIN COMPARISON Antenna Freq. (GHz) Reference (dB) Measured (dB) SN1 8 21.39 ± 0.06 21.41 ± 0.06SN1 10 22.17 ± 0.06 22.18 ± 0.07SN1 12 22.59 ± 0.06 22.57 ± 0.06SN2 8 21.37 ± 0.06 21.40 ± 0.06SN2 10 22.18 ± 0.06 22.19 ± 0.07SN2 12 22.58 ± 0.06 22.56 ± 0.06SN3935 12.4 23.63 ± 0.1 23.62 ± 0.07SN3935 15 24.44 ± 0.05 24.44 ± 0.07SN3935 18 24.85 ± 0.06 24.80 ± 0.06SN3936 12.4 23.62 ± 0.1 23.62 ± 0.07SN3936 15 24.45 ± 0.08 24.46 ± 0.06SN3936 18 24.83 ± 0.06 24.80 ± 0.07

[0235] The following references are incorporated by references in their entirety: [reference 1] A. C. Newell and D. M. Kerns, "Determination of both polarisation and power gain of antennas by a generalised 3-antenna measurement method," Electronics Letters, vol.7, no.3, p.68, 1971 [reference 2] A. Newell, R. Baird, and P. Wacker, "Accurate measurement of antenna gain and polarization at reduced distances by an extrapolation technique," IEEE Transactions on Antennas and Propagation, vol.21, no.4, p. 418-431, Jul.1973. [reference 3] Repjar, A. , Newell, A. and Tamura, D. (1987), "Extrapolation Range Measurements for Determining Antenna Gain and Polarization”, Technical Note (NIST Tech Note No.1311), National Institute of Standards and Technology, Gaithersburg, MD.[reference 4] K. MacReynolds, M. Francis, "Antenna Gain Measurements The ThreeAntenna Extrapolation Method", Proceedings of the Antenna Measurement Techniques Association, November 1999. [reference 5] W. T. Slaton, "Design and Calibration of Microwave Antenna Gain Standards", Naval Research Laboratory, Report 4433, November 1954 [reference 6] "IEEE Standard for Definitions of Terms for Antennas," in IEEE Std 145-2013 (Revision of IEEE Std 145-1993), vol., no., pp.1-50, 6 March 2014, doi: 10.1109 / IEEESTD.2014.6758443. [reference 7] "IEEE Recommended Practice for Antenna Measurements," in IEEE Std 149-2021 (Revision of IEEE Std 149-1977), vol., no., pp.1-207, 18 Feb.2022, doi: 10.1109 / IEEESTD.2022.9714428. [reference 8] P. F. Wacker, "Theory and numerical techniques for accurate extrapolation of near-zone antenna and scattering measurements," National Bureau of Standards, U.S. Department of Commerce, NBS Report 10733, Apr. 1972 [reference 9] D. M. Kerns, E. S. Dayhoff, "Theory of Diffraction in Microwave Interferometry", JOURNAL OF RESEARCH of the National Bureau of Standards-B. Mathematics and Mathematical Physics Vol.64B, No.1, January- March 1960. [reference 10] S. Schelkunoff, H. T. Friis, "Antenna Theory and Practice", John Wiley and Sons, London, 1952. [reference 11] D. Gentle, "The removal of the effects of multiple reflections in antenna extrapolation data by digital filtering", National Physical Laboratory, UK, Report. DES 139, April, 1995. (http: / / eprintspublications.npl.co.uk / id / eprint / 178) [reference 12] Z. Chen, Y. Wang and D. Lewis, "Examination of Antenna Calibration Methodologies in an Extrapolation Range," 202216th EuropeanConference on Antennas and Propagation (EuCAP), Madrid, Spain, 2022, pp. 1-4, doi: 10.23919 / EuCAP53622.2022.9769087. [reference 13] Z. Chen, Y. Wang, "Application of Compressed Sensing to Antenna Farfield Calibration in an Extrapolation Range", 202418th European Conference on Antennas and Propagation (EuCAP), Glasgow, UK, March 2024 [reference 14] MI Technologies Standard Gain Horns Specification Sheet, Model Number: MI-12-12, part number: 093275. [reference 15] C. F. Stubenrauch, A. C. Newell, et al., "International intercomparison of horn gain at X-band," in IEEE Transactions on Antennas and Propagation, vol. 44, no. 10, pp. 1367-1374, Oct. 1996, doi: 10.1109 / 8.537331. [reference 16] "Measurement Techniques and Results of an Intercomparison of Horn Antenna Gain at Frequencies of 12.4, 15.0, 18.0 GHz", CCEM Key Comparison CCEM.RF-K23.F, May 2016 [reference 17] B. Tian, "Free Space VSWR Method for Anechoic Chamber Electromagnetic Performance Evaluation”, AMTA Symposium, 2008 [reference 18] C. A. Balanis, "Antenna Theory: Analysis and Design", Wiley, 4th Edition, ISBN: 978-1-118-64206-1, [reference 19] David R. Novotny, Joshua A. Gordon, Michel S. Allman, Alexandra E. Curtin, Jeff R. Guerrieri, Kim Hassett, Quang Ton, George McAdams, "A Multi-Robot Large Antenna Positioning System for Over-The-Air Testing at the National Institute of Standards and Technology”, Proceedings of the Antenna Measurement Techniques Association, October 2017. [reference 20] D. R. Novotny, J. A. Gordon, M. S. Allman, J. R. Guerrieri and A. E. Curtin, "Three antenna ranges based on articulated robotic arms at the national institute of standards and technology: Usability for overtheair and standard near-field measurements," 2017 IEEE Conference on AntennaMeasurements and Applications (CAMA), Tsukuba, Japan, 2017, pp.1-4, doi: 10.1109 / CAMA.2017.8273367 [reference 21] J. Gordon and B. Moser, "NIST Antenna Gain and Polarization Calibration Service Reinstatement," 2023 Antenna Measurement Techniques Association Symposium (AMTA), Renton, WA, USA, 2023, pp. 1-6, doi: 10.23919 / AMTA58553.2023.10293530. [reference 22] https: / / www.nist.gov / ctl / robotically-enhanced-antenna- laboratorymetrology-realm [reference 23] B. N. Taylor and C. E. Kuyatt, "NIST Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results", NIST Technical Note 1297

[0236] The processes described herein may be embodied in, and fully automated via, software code modules executed by a computing system that includes one or more general purpose computers or processors. The code modules may be stored in any type of non-transitory computer-readable medium or other computer storage device. Some or all the methods may alternatively be embodied in specialized computer hardware. In addition, the components referred to herein may be implemented in hardware, software, firmware, or a combination thereof.

[0237] Many other variations than those described herein will be apparent from this disclosure. For example, depending on the embodiment, certain acts, events, or functions of any of the algorithms described herein can be performed in a different sequence, can be added, merged, or left out altogether (e.g., not all described acts or events are necessary for the practice of the algorithms). Moreover, in certain embodiments, acts or events can be performed concurrently, e.g., through multi- threaded processing, interrupt processing, or multiple processors or processor cores or on other parallel architectures, rather than sequentially. In addition, different tasks or processes can be performed by different machines and / or computing systems that can function together.

[0238] Any logical blocks, modules, and algorithm elements described or used in connection with the embodiments disclosed herein can be implemented aselectronic hardware, computer software, or combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, and elements have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. The described functionality can be implemented in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the disclosure.

[0239] The various illustrative logical blocks and modules described or used in connection with the embodiments disclosed herein can be implemented or performed by a machine, such as a processing unit or processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A processor can be a microprocessor, but in the alternative, the processor can be a controller, microcontroller, or state machine, combinations of the same, or the like. A processor can include electrical circuitry configured to process computer-executable instructions. In another embodiment, a processor includes an FPGA or other programmable device that performs logic operations without processing computer-executable instructions. A processor can also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. Although described herein primarily with respect to digital technology, a processor may also include primarily analog components. For example, some or all of the signal processing algorithms described herein may be implemented in analog circuitry or mixed analog and digital circuitry. A computing environment can include any type of computer system, including, but not limited to, a computer system based on a microprocessor, a mainframe computer, a digital signal processor, a portable computing device, a device controller, or a computational engine within an appliance, to name a few.

[0240] The elements of a method, process, or algorithm described in connection with the embodiments disclosed herein can be embodied directly in hardware, in a software module stored in one or more memory devices and executed by one or more processors, or in a combination of the two. A software module can reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of non- transitory computer-readable storage medium, media, or physical computer storage known in the art. An example storage medium can be coupled to the processor such that the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium can be integral to the processor. The storage medium can be volatile or nonvolatile.

[0241] While one or more embodiments have been shown and described, modifications and substitutions may be made thereto without departing from the spirit and scope of the invention. Accordingly, it is to be understood that the present invention has been described by way of illustrations and not limitation. Embodiments herein can be used independently or can be combined.

[0242] All ranges disclosed herein are inclusive of the endpoints, and the endpoints are independently combinable with each other. The ranges are continuous and thus contain every value and subset thereof in the range. Unless otherwise stated or contextually inapplicable, all percentages, when expressing a quantity, are weight percentages. The suffix (s) as used herein is intended to include both the singular and the plural of the term that it modifies, thereby including at least one of that term (e.g., the colorant(s) includes at least one colorants). Option, optional, or optionally means that the subsequently described event or circumstance can or cannot occur, and that the description includes instances where the event occurs and instances where it does not. As used herein, combination is inclusive of blends, mixtures, alloys, reaction products, collection of elements, and the like.

[0243] As used herein, a combination thereof refers to a combination comprising at least one of the named constituents, components, compounds, or elements, optionally together with one or more of the same class of constituents, components, compounds, or elements.

[0244] All references are incorporated herein by reference.

[0245] The use of the terms “a,” “an,” and “the” and similar referents in the context of describing the invention (especially in the context of the following embodiments) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. It can further be noted that the terms first, second, primary, secondary, and the like herein do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. It will also be understood that, although the terms first, second, etc. are, in some instances, used herein to describe various elements, these elements should not be limited by these terms. For example, a first current could be termed a second current, and, similarly, a second current could be termed a first current, without departing from the scope of the various described embodiments. The first current and the second current are both currents, but they are not the same condition unless explicitly stated as such.

[0246] The modifier about used in connection with a quantity is inclusive of the stated value and has the meaning dictated by the context (e.g., it includes the degree of error associated with measurement of the particular quantity). The conjunction or is used to link objects of a list or alternatives and is not disjunctive; rather the elements can be used separately or can be combined together under appropriate circumstances. / / PARTS LIST / / radio frequency antenna gain measuring apparatus 200 antenna 201 antenna 202 antenna emitted radio frequency radiation 203 antenna incident radio frequency radiation 204 antenna emitted radio frequency radiation 205 antenna incident radio frequency radiation 206 antenna coordinate system 207 antenna coordinate system 208 antenna positioner 209 antenna positioner 210 linear motion positioner 211 transmitting signal 212 received signal 213 transmitting signal 214 received signal 215 positioner control signal 216 positioner feedback signal 217 positioner control signal 218 positioner feedback signal 219 distance meter measurement signal 220 distance meter communication signal 221 radio frequency electronics data signal 222 radio frequency electronics control signal 223 radio frequency electronics data signal 224 radio frequency electronics control signal 225 distance meter data signal 226 distance meter control signal 227 antenna gain processor data signal 228 antenna gain processor return signal 229 antenna gain 230 radio frequency transmit and receive electronics 231radio frequency transmit and receive electronics 232 distance meter 233 central controller 234 antenna gain processor 235 separation distance 236 antenna gain data array 237 single-antenna radio frequency antenna gain measuring apparatus 238 antenna image 239 antenna image coordinate system 240 antenna-to-mirror distance 241 mirror 242 measuring gain of an antenna / / measures gain of an antenna

Claims

What is claimed is:

1. A radio frequency antenna gain measuring apparatus comprising: a first antenna; a second antenna; a first antenna positioner configured to position the first antenna; a second antenna positioner configured to position the second antenna; a linear motion positioner configured to vary a separation distance between the first antenna and the second antenna by linearly moving the second antenna positioner; a distance meter to determine the separation distance between the first antenna and the second antenna; a first radio frequency transmit and receive electronics device to transmit a first signal to the first antenna and receive a second signal from the first antenna; a second radio frequency transmit and receive electronics device to transmit a third signal to the second antenna and receive a fourth signal from the second antenna; a central controller to: control the first and second antenna positioners to position the first and second antennas, control the linear motion positioner to vary the separation distance, control the first and second radio frequency transmit and receive electronics devices, and receive information from the distance meter; andan antenna gain processor to: receive information from the central controller and the first and second radio frequency transmit and receive electronics device, and determine the gain of the first and second antennas based on the third- order scattered signal as a function of the separation distance.

2. The radio frequency antenna gain measuring apparatus of claim 1, wherein the first and second antennas comprise aperture antennas, standard gain horn antennas, or a combination comprising at least one of the foregoing antennas.

3. The radio frequency antenna gain measuring apparatus of claim 1, further comprising a mirror positioned between the first and second antennas.

4. The radio frequency antenna gain measuring apparatus of claim 1, wherein the first and second antenna positioners are robotic arms.

5. The radio frequency antenna gain measuring apparatus of claim 1, wherein the first and second radio frequency transmit and receive electronics devices are vector network analyzers.

6. The radio frequency antenna gain measuring apparatus of claim 1, wherein the distance meter is selected from the group consisting of an optical encoder, a magnetic encoder, a laser tracking system, and a laser distance meter.

7. The radio frequency antenna gain measuring apparatus of claim 1, wherein the antenna gain processor determines the gain of the first and second antennas based on the fifth-order scattered signal as a function of the separation distance.

8. The radio frequency antenna gain measuring apparatus of claim 1, wherein the antenna gain processor determines the gain of the first and second antennas based on the seventh-order scattered signal as a function of the separation distance.

9. A radio frequency antenna gain measuring apparatus comprising: an antenna; a mirror positioned at a predetermined antenna-to-mirror distance from the antenna; an antenna positioner configured to position the antenna; a linear motion positioner configured to vary a separation distance between the antenna and an antenna image produced by the mirror by linearly moving the antenna positioner; a distance meter to determine the separation distance between the antenna and the antenna image; a radio frequency transmit and receive electronics device to transmit a first signal to the antenna and receive a second signal from the antenna; a central controller to: control the antenna positioner to position the antenna, control the linear motion positioner to vary the separation distance, control the radio frequency transmit and receive electronics device, and receive information from the distance meter; andan antenna gain processor to: receive information from the central controller and the radio frequency transmit and receive electronics device, and determine the gain of the antenna based on the third-order scattered signal as a function of the separation distance.

10. The radio frequency antenna gain measuring apparatus of claim 9, wherein the antenna comprises an aperture antenna or a standard gain horn antenna.

11. The radio frequency antenna gain measuring apparatus of claim 9, wherein the antenna positioner is a robotic arm.

12. The radio frequency antenna gain measuring apparatus of claim 9, wherein the radio frequency transmit and receive electronics device is a vector network analyzer.

13. The radio frequency antenna gain measuring apparatus of claim 9, wherein the distance meter is selected from the group consisting of an optical encoder, a magnetic encoder, a laser tracking system, and a laser distance meter.

14. A process for measuring gain of an antenna with a radio frequency antenna gain measuring apparatus, comprising: positioning a first antenna and a second antenna using a first and second antenna positioner at a separation distance;dynamically varying the separation distance between the first and second antennas using a linear motion positioner; transmitting a first signal from a first radio frequency transmit and receive electronics device to the first antenna; transmitting a second signal from a second radio frequency transmit and receive electronics device to the second antenna; receiving a third signal at the first antenna from the second antenna; receiving a fourth signal at the second antenna from the first antenna; measuring the separation distance using a distance meter; transmitting the first and third signals and the separation distance from the first radio frequency transmit and receive electronics device to an antenna gain processor; and transmitting the second and fourth signals and the separation distance from the second radio frequency transmit and receive electronics device to the antenna gain processor; wherein the antenna gain processor: receives the first, second, third, and fourth signals and the separation distance, and determines the gain of the first and second antennas based on the third- order scattered signal as a function of the separation distance.

15. The process of claim 14, wherein the separation distance between the first and second antennas is dynamically varied from a starting distance dwto a final distance given by: dW=(Di+Dj) / 2 andwherein Diis the largest dimension of the first antenna, Djis the largest dimension of the second antenna, and D is the largest dimension of the larger of the two antennas in the pair.

16. The process of claim 14, wherein the first and second antennas comprise an aperture antenna, standard gain horn antenna, or a combination comprising at least one of the foregoing antennas.

17. The process of claim 14, wherein the antenna gain processor determines the gain of the first and second antennas based on the fifth-order scattered signal as a function of the separation distance.

18. The process of claim 14, wherein the antenna gain processor determines the gain of the first and second antennas based on the seventh-order scattered signal as a function of the separation distance.

19. A process for measuring gain of an antenna with a radio frequency antenna gain measuring apparatus, comprising: positioning an antenna using an antenna positioner at an antenna-to-mirror distance from a mirror; dynamically varying the antenna-to-mirror distance using a linear motion positioner; transmitting a first signal from a radio frequency transmit and receive electronics device to the antenna;receiving a second signal at the antenna from an antenna image produced by the mirror; measuring the antenna-to-mirror distance using a distance meter; transmitting the first and second signals and the antenna-to-mirror distance from the radio frequency transmit and receive electronics device to an antenna gain processor; wherein the antenna gain processor: receives the first and second signals and the antenna-to-mirror distance, and determines the gain of the antenna based on the third-order scattered signal as a function of the antenna-to-mirror distance.

20. The process of claim 19, wherein the antenna-to-mirror distance is dynamically varied from a starting distance dw to a final distance,given by: dW=(Di+Dj) / 2 and ^^^ 22^^3^^^^^^^^^^^^^^^^^^^^^^^= 3 ^^^^ wherein D is the largest dimension of the antenna.

21. The process of claim 19, wherein the antenna is an aperture antenna or a standard gain horn antenna.

22. The process of claim 19, wherein the antenna positioner is a robotic arm.

23. The process of claim 19, wherein the radio frequency transmit and receive electronics device is a vector network analyzer.

24. The process of claim 19, wherein the distance meter is selected from the group consisting of an optical encoder, a magnetic encoder, a laser tracking system, and a laser distance meter.

25. The process of claim 19, wherein the antenna gain processor is to determine the gain of the antenna based on the fifth-order scattered signal as a function of the antenna-to-mirror distance.

26. The process of claim 19, wherein the antenna gain processor is to determine the gain of the antenna based on the seventh-order scattered signal as a function of the antenna-to-mirror distance.

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