7advantages and disadvantages of various...

7
ATMS INDIA 2015 The 8 th Annual International Conference ATMS -2015, Bangalore © ATMS (INDIA) Formatted: Header ADVANTAGES AND DISADVANTAGES OF VARIOUS HEMISPHERICAL SCANNING TECHNIQUES Eric Kim, & Anil Tellakula MI Technologies 1125 Satellite Blvd, Suite 100 Suwanee, GA 30024 , USA [email protected] ABSTRACT Abstract - When performing far far- field or nea r near- field antenna measurements on large antennas, it is often necessary to consider the advantages and disadvantages of various mechanical positioning configurations for achieving the required hemispherical scan coverage have various types of mechanical positioning systems to achieve the required hemispheric scans . Measurement systems employing a single-arm gantry, a dual-arm gantry, a fixed arch moving probe, or and a fixed arch multi- probe have been paired with either an azimuth positioner or a vehicle turntable in order to provide hemispherical scanning of the object article being tested. This paper will highlight the key characteristics of various scanning methods and provide making comparisons between among the different techniques. Positioning and system accuracy, speed, stowing cap ability, calibration, frequency range, upgradability, relative cost and other key aspects of the various techniques will be discussed in detail to help the end user during the system design and selection process. In addition, the paper will highlight novel hemispherical and truncated spherical scanning approaches. In many applications, the success of the entire project meeting the measurement requirements often centers on the judicious selection of the positioning subsystem. This paper will provide guidance toward making the proper selection of the scanning concept as well as of the positioning system. Keywords: Hemispherical scanning Scanning , spherical Spherical near Near- field Field , spherical Spherical far Far- field Field, Gantry, Arch 1 I . Introduction NTRODUCTION Hemisph erical or truncated spherical scanning techniques are typically used for measuring large objects located at ground level. These techniques can be applied to both far-field and near-field antenna measurements. The near-field scanning system can be regarded as a far- field scanning system with a reduced range length. That is, range length less than the usual 2D²/ far-field criterion. Range length is defined as the distance between the transmit and receive antennas, D is the aperture diameter, and is the wavelength. For spherical near- field measurements, a post-processing transformation step is applied to obtain the far-field radiation characteristics. provide unique benefits for large antennas o r article u nder test (AUT) . Large AUTs antennas , such as phased array antenna s or and automotive vehicles , can be positioned driven on top of a large vehicle turntable or azimuth positioner for antenna measurement s . Test ing Measuring a large antenna or article under test (AUT) s poses a number of challenges for proper antenna characteriztion characterization measurement . A traditional roll - over - azimuth positioner configuration is not feasible for large antennas. Due to the large electrical physical diameter of the a ntenna under test AUT , a large positioning er system or structure is necessary to provide sufficient spherical coverage. A probe measuring along an arc over a large azimuth positioner is a suitable mechanical configuration for large AUTs. For characterizing antennas integrated into vehicles, such as automobiles, military trucks, or even tanks, a large diameter vehicle turntable under a probe measuring along an arc is suitable to provide a hemispherical hemispherical scan coverage. Large number of measurement data in horizontal and vertical polarization need to be acquired to for proper near field to far field transformation. There are several configurations that allows for the probe to measure along an arc. Examples are probe mounted on a single-arm rotating gantry [1-2], probe mounted on a dual-arm rotating gantry [3], probe moving on a fixed arch [4-5], and multiple probes on a fixed -arch [6]. For proper appropriate selection of hemispherical or truncated spherical scanning system, a proper understanding of and qualitative analysis between among the various options is necessary. 2 II . What are the Key C haracteristic KEY CHARACTERISTICS Formatted: Font: 10 pt Formatted: Font: 10 pt, Underline Formatted: Font: Italic Formatted: Font: 9 pt Formatted: Indent: First line: 0.25" Formatted: Font: 9 pt Formatted: Font: 9 pt

Upload: others

Post on 27-Apr-2020

13 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: 7Advantages and Disadvantages of Various …atmsindia.org/tech_papers/2015/7Advantages_and...ADVANTAGES AND DISADVANTAGES OF VARIOUS HEMISPHERICAL SCANNING TECHNIQUES Eric Kim, & Anil

ATMS INDIA

2015

The 8th Annual International Conference ATMS -2015, Bangalore

© ATMS (INDIA)

Formatted: Header

ADVANTAGES AND DISADVANTAGES OF VARIOUS HEMISPHERICAL

SCANNING

TECHNIQUES

Eric Kim,

& Anil Tellakula

MI Technologies 1125 Satellite Blvd, Suite 100

Suwanee, GA 30024, USA

[email protected]

ABSTRACT

Abstract - When performing far far-field or near near-field antenna measurements on large antennas, it is often necessary to consider the advantages and disadvantages of various mechanical positioning configurations for achieving the required hemispherical scan coveragehave various types of mechanical positioning systems to achieve the required hemispheric scans. Measurement systems employing a single-arm gantry, a dual-arm gantry, a fixed arch moving probe, or and a fixed arch multi-probe have been paired with either an azimuth positioner or a vehicle turntable in order to provide hemispherical

scanning of the object article being tested.

This paper will highlight the key characteristics of various scanning methods and provide

making comparisons between among the different techniques. Positioning and system accuracy, speed, stowing capability, calibration, frequency range, upgradability, relative cost and other key aspects of the various techniques will be discussed in detail to help the end user during the system design and selection process. In addition, the paper will highlight novel hemispherical

and truncated spherical scanning approaches.

In many applications, the success of the entire projectmeeting the measurement requirements

often centers on the judicious selection of the positioning subsystem. This paper will provide guidance toward making the proper selection of the scanning concept as well as of the positioning system.

Keywords: Hemispherical

scanningScanning, spherical Spherical near Near-fieldField, spherical Spherical farFar-fieldField, Gantry, Arch

1I. IntroductionNTRODUCTION

Hemispherical

or truncated spherical scanning techniques are typically used for measuring large objects located at ground level. These techniques can be applied

to both far-field and near-field antenna measurements. The near-field scanning system can be regarded as a far-field scanning system with a reduced range length. That is, range length less than the usual 2D²/

far-field criterion. Range length is defined as the distance between the transmit and receive antennas, D is the aperture diameter, and

is the wavelength. For spherical near-field measurements, a post-processing transformation step is applied to obtain the far-field radiation characteristics.

provide unique benefits for large antennas or article under test

(AUT). Large AUTs antennas , such as phased array

antennas or and automotive vehicles,

can be positioned driven on top of a large vehicle turntable or azimuth positioner for antenna measurements.

Testing Measuring a large antenna or article under test (AUT) s poses a number of challenges for proper antenna characteriztioncharacterizationmeasurement. A traditional roll-over-azimuth positioner configuration is not feasible for large antennas. Due to the large electrical physical diameter of the antenna under testAUT, a large positioninger

system

or structure is necessary to provide sufficient spherical coverage. A probe measuring along an arc over a large azimuth positioner is a suitable mechanical configuration for large AUTs.

For characterizing antennas integrated into vehicles, such as automobiles, military trucks, or even tanks, a large diameter vehicle turntable under a probe measuring along an arc is suitable to provide a hemisphericalhemispherical

scan coverage. Large number of measurement data in horizontal and vertical polarization need to be acquired to for proper near field to far field transformation.

There are several configurations that allows for the probe to measure along an arc. Examples are probe mounted on a single-arm rotating gantry [1-2], probe mounted on a dual-arm rotating gantry [3], probe moving on a fixed arch [4-5], and multiple probes on a fixed -arch

[6]. For proper appropriate selection of hemispherical

or truncated spherical scanning system, a proper understanding of

and qualitative analysis between among the various options is necessary.

2II. What are the Key CharacteristicKEY

CHARACTERISTICS

Formatted: Font: 10 pt

Formatted: Font: 10 pt, Underline

Formatted: Font: Italic

Formatted: Font: 9 pt

Formatted: Indent: First line: 0.25"

Formatted: Font: 9 pt

Formatted: Font: 9 pt

Page 2: 7Advantages and Disadvantages of Various …atmsindia.org/tech_papers/2015/7Advantages_and...ADVANTAGES AND DISADVANTAGES OF VARIOUS HEMISPHERICAL SCANNING TECHNIQUES Eric Kim, & Anil

ATMS INDIA

2015

The 8th Annual International Conference ATMS -2015, Bangalore

© ATMS (INDIA)

Formatted: Header

For optimal proper positioning equipment selection for a given application, the following key characteristics must be understood and compared between among various hemispherical

or truncated spherical scanning

techniques: Required frequency range of the systemoperation, Electrical electricalphysical Diameter diameter of the antenna under testAUT, positioning Accuracyaccuracy, Speedspeed, Stowabilitystowability, Variable Height ability to move Axis axis of Rotationrotation, Calibration calibration, & and Costcost.

Required fFrequency range of operation of the antenna measurement system depends on purpose of the range and its utility. General purpose chambers

may require more

broader

frequency range coverage from 0.7 GHz to 40 GHz. Special purpose antenna measurement systems,

such as an automotive test facility,

may require the

frequency range to be 0.07 to 11 GHz to cover FM frequency on at the low end.

Electrical The minimum sphere is the diameter of the antenna under test

is the spherical diameter of a sphere that, when centered at the coordinate system origin,

fully encompasses

the antenna under test. Actual hemispherical

scanning radius (location of the probe s phase center of probe) will be several wavelengths

away from the minimum electrical diametersphere

of the antenna under test.

Accuracy of the measurements

dependss

on measurement technique used, frequency range of interest, directivity of the antenna,

and many other factors. General purpose hemispherical

near near-field antenna measurement systems,

which require high frequency to above and beyond 8-12 GHzoperation

or high fidelity in measurements

need to consider the impact of minimum density of sample sampling density required to perform proper adequate near near-field to far far-field transformation at the required quality factor [7] . Quality factor is a rule of thumb used to determine the required accuracy of the system based on the simply means multiplication factor beyond minimum angular sample density step required in the measurement grid.to properly locate measuring horn or feed.

For example, if the minimum desired angular measurement density step is 0.5 degrees, quality factor of 5-

or 10 which would results

in an angular readout accuracy requirement of 0.1 or 0.05 degrees, respectively,

on a spherical positioning system.

to properly locate horn or antenna to measurement antenna under test. To In order to properly measure phase, quality factory factors of 10, 20, 50

or beyond are used based on the wavelength of the highest frequency to determine accuracy of spherical measurement radius for antenna measurements. For 40 GHz spherical near near-field measurement at 40 GHz, the wavelength is approximately 0.25 75 cm. Quality factory

of 20 will

impose a radius accuracy of 0.013 37 cm

on the

positioning system, while a quality factor of 50 would impose a 0.015 cm accuracy requirement..

Speed is also an important factor due to the amount

of time required to characterize large electrical diameter of the antenna under testAUTs. Electrical diameter of 5 meters, 6 meters, 11 meters and beyond are often required to properly characterize large antenna under test. Due toepending on the

the electrical diametersize of the AUT, full hemispherical

scan coverage with proper sampling density can be very time consuming,

especially for high frequency measurements. Various techniques hasve

been implemented and proposed to increase overall measurement speed.

Stowability is another a factor that has become an important factor due to increase in requirements for

utility multipurpose

of the chambermeasurement ranges. Due to significant investment made, multiple measurement requirements are often imposed on a single chamber. In some applications,

single the same chamber is required to perform spherical near-field and far-field measurements. This might involve a gantry over a vehicle turntable and a far-field source tower. During far-field measurements, the gantry may need to be stowed below the turntable. EMC & antenna measurement

in the same chamber which often only require vehicle turntable and far field source. Same chamber also often require measurement in FM frequency which often require spherical scanning system to be removed to stowed below the ground plane of the antenna measurement system. Ease of stowability or removal of the spherical scanning system from the chamber

has become more important in recent times.as the multi-use requirement increased.

Variable height axis ofof the

rotation axis of the probe

is sometime required, especially when quasi-far-field and near-field measurements are desired from the same set of hardware. Single-

Arm arm Gantry gantry and Dual dual-Arm arm Gantry gantry system has been delivered with variable height axis option when this was necessaryrequired. This feature is useful to certain AUTs as well as for mitigating the issues caused by standing wave between the probe and the AUT.

Some hemispherical

scanning systems

require significant initial and routine periodic calibration in order to maintain the accuracy of the system. Fixed Fixed-arch multi-probe systems,

for example,

require alignment and calibration of each probe during initial installation and periodically. Calibration cost and the time required to perform this task must be considered as part of the overall initial investment and operating cost cost of the system.

Cost of the system will depend heavily predominantly on requirements imposed on the above-

Formatted: Indent: First line: 0.25"

Page 3: 7Advantages and Disadvantages of Various …atmsindia.org/tech_papers/2015/7Advantages_and...ADVANTAGES AND DISADVANTAGES OF VARIOUS HEMISPHERICAL SCANNING TECHNIQUES Eric Kim, & Anil

ATMS INDIA

2015

The 8th Annual International Conference ATMS -2015, Bangalore

© ATMS (INDIA)

Formatted: Header

listed key characteristics above

and the scanning system

chosen. Comparison chart will be presented toward end of this paper tothat

provides

qualitative comparison

advantages and disadvantages between among the various hemispheric or truncated scanning techniques

is presented in Table 1.

3III. Single SINGLE-ARM GANTRYArm Gantry

Single A Single-arm gantry system is shown in Figure 1. as shown belowIt

offers

several important advantages over other positioning systems. It offers lowest The cost of this system is relative relatively lowcost option

and it is ease easy toof

implementation

in a relatively small foot print. This system can be easily stowed or completely removed from chamberbelow grade level.

relatively easier than other system options. Due to its simplicity and durability, it has been used in many permanent outdoor applications.

Figure 1: Single-Arm Gantry

Figure 2 shows an example of Below is an example ofa

single-arm gantry system installed on a vertical slide. This allows the gantry rotation axis to be lowered in order to where simple mechanism and chamber layout has been developed to

stow single armthe

gantry below below the floorsurface

when necessary. Variable height mechanism below also allows the rotation axis of the gantry arm axis of rotation

to vary as necessary for specific measurement requirements.

(a) Gantry on Vertical Slide Details

(b) Measurement Configuration

Formatted: Font: 9 pt

Formatted: Font: 9 pt

Formatted: Centered

Page 4: 7Advantages and Disadvantages of Various …atmsindia.org/tech_papers/2015/7Advantages_and...ADVANTAGES AND DISADVANTAGES OF VARIOUS HEMISPHERICAL SCANNING TECHNIQUES Eric Kim, & Anil

ATMS INDIA

2015

The 8th Annual International Conference ATMS -2015, Bangalore

© ATMS (INDIA)

Formatted: Header

(c) Stowed Configuration

Figure 2: Single-Arm Gantry on a Vertical Slide

Due to its simplicity and predictable behavior of the positioner positioning system, only a simple routine initial calibration & routine maintenance may be required.

Greatest weaknessThe major disadvantage

of the single-

arm gantry system is its native accuracy. Although, lightweight and high stiffness composite materials are used to fabricate gantries, the probe end sees translational and angular deflections during gantry Due to large translation & angular deflection structure during motion motion from 0 -to 90 degrees as shown in Figure 3. Due to the positioning issues, these systems are limited to operation at low frequencies.,

Hhigh accuracy antenna measurement is not possible without the application of positioning correction techniques [8-9]. Due to fairly repeatable behavior of the deflection as a function of gantry angular position, simple correction, using an error lookup table,

in some cases will be sufficient to increase overall system accuracy.

5-10 folds.

Figure 3: Deflections in a Gantry-Arm

Due to large moving mass at the probe end and the limited stiffness of the gantry structure, scanning speed in elevation is also limited.

Compliance in the structure also does not allow for rapid stepping of this axis for scanning applications.fast step motion.

4IV. DUAL-ARM GANTRYArm Gantry

Dual-arm gantry system, as the name implies, utilizes dual support system and dual drive system to support the probe and move it along a circular path

as shown in Figure 4. Dual-

arm gantry systems

has have been developed to minimize angular & translation deflection associated with single arm gantry system.

Formatted: Justified, Indent: First line: 0.25"

Formatted: Indent: First line: 0.25"

Formatted: Font: 9 pt

Formatted: Font: 9 pt

Page 5: 7Advantages and Disadvantages of Various …atmsindia.org/tech_papers/2015/7Advantages_and...ADVANTAGES AND DISADVANTAGES OF VARIOUS HEMISPHERICAL SCANNING TECHNIQUES Eric Kim, & Anil

ATMS INDIA

2015

The 8th Annual International Conference ATMS -2015, Bangalore

© ATMS (INDIA)

Formatted: Header

Figure 4: Dual-Arm Gantry

Dual Dual-arm gantry systems

with proper structure will will subject the probe to provide mucch lesser

angular & translation deflections

versus when compared to a single-

arm gantry system.

Due to a relatively small foot print, this system can be stowed away below ground.

easily.

Removing the systemThis system, however, has more complexity due to the fact that the gantry is supported and driven from two ends. The alignment of the two axes and synchronization of the two drive systems are very critical for proper functioning of the system. Hence, this system is more expensive than the single-arm gantry.

5V.

FIXED-ARCHArch

MULTI-PROBEMulti-Probe

Fixed Fixed-arch multi-probe spherical antenna measurement system provides many the benefits

especiallyof

fast antenna measurements. An example of such as system is shown in Figure 5.

However to cover broad frequency band & to minimize probe change, broad band dual dual-polarized feeds are typically employees installed in an angular grid. In order to achieve the required resolution, a

Large large number of feeds typically must be mounted with complex RF switching matrix network to perform spherical antenna pattern measurements. This system is typically capable of working up to 18 GHz. Due to the geometric configuration, such systems are typically limited to a pair of frequency bands.

Figure 5 shows probes of one frequency band installed on the right half of the fixed arch. Covering large frequency band with one positioning system may require large number of feedsThis approach requires extensive calibration due to the use of multiple

probes. The cost can be high, especially depending on the frequency of operation, size of the minimum sphere required, and the number of probes required for high fidelity measurements. Further, these systems require frequent calibration that can become expensive over the long term.

Figure 5: Fixed Fixed-Arch Multi-Probe

6VI. Fixed FIXED-ARCH MOVING PROBEArch Moving Probe

In this configuration, the probe moves along a circular path on a fixed arch. The AUT is mounted on an azimuth positioner under the arch such that the turntable center is coincident with the arch center. A typical fixed-arch moving-probe system is shown in Figure 6. These systems offers

following significant advantages

over other methodsspherical scanning techniques. These systems can be designed and installed very precisely in order to perform high frequency measurements (40 GHz and above) with extremely high fidelity [4]. The main advantages of these systems are Superior superior accuracy, wide large frequency range of operation,

and relatively low cost depending on frequency of operation. The disadvantages are difficulty to Fixed arch disadvantage, stow, ability & rrelatively slower acquisition speeds (which can be increased by increasing the turntable speed), and complexity in installation for high frequency measurements.

Formatted: Indent: First line: 0.25"

Formatted: Justified, Indent: First line: 0.25"

Formatted: Font: 9 pt

Formatted: Font: 9 pt

Formatted: Font: 9 pt

Formatted: Font: 9 pt

Formatted: Font: 9 pt

Page 6: 7Advantages and Disadvantages of Various …atmsindia.org/tech_papers/2015/7Advantages_and...ADVANTAGES AND DISADVANTAGES OF VARIOUS HEMISPHERICAL SCANNING TECHNIQUES Eric Kim, & Anil

ATMS INDIA

2015

The 8th Annual International Conference ATMS -2015, Bangalore

© ATMS (INDIA)

Formatted: Header

Figure 6: Fixed Arch Moving Probe

7VII. SYSTEM

Comparison ChartCOMPARISON

Qualitative comparison among the various mechanical systems available for spherical scanning of AUTs is provided in Table 1Table 1Table 1.

Table 1. Key Characteristics of Various Hemispherical Scanning Systems

The user can use this as a guideline to prioritize the key characteristics and determine the appropriate system that would meet the measurement goals.

Characteristic Needs Single Arm Gantry Star Gate System Arch Scanner Dual Arm Gantry Comments

Accuracy Moderate Low Low to Moderate Highest Medium Arch provide best accurate at any frequency

SpeedWhat is

acceptable?Acceptable Fastest Acceptable Acceptable

MI-750 & Faster Turntable best option for speed improvement on Single Arm Gantry & Arch Scanner Solution

Frequency Range 0.07 - 11 GHzXX - 6 GHz 0.07 - 18 GHz 0.2 - 60 GHz + 0.2 - 18 GHz

How do we go down to 0.07 GHz? Market needs to go down to FM Frequency

Stowable

This is important for FM freq.

testing and multi-purpose chamber

Yes Yes No Yes

Important for multi-purpose range where FF measurement & EMC will be done in the same range. Need to stow or remove the NF scanner for 70 MHz FM freq. testing

Calibration

Don't know if customer is

really looking at total cost of

ownership for 5-10 years

Moderate Extensive Moderate ModerateRecurring cost & down time might be higher for Satimo approach due to extensive calibration required

Cost Low CostLow High Low to Moderate Low to Moderate

If one chamber to servce multiple purpose, customer might be willing to pay more up front

8VIII. Novel ApproachNOVEL APPROACHES

Recent development in position error-correction

techniques and post processing of irregular spherical scan probe data for proper near near-field to far far-field transformation can be applied to systems that have low native accuracy and hence are lower in cost. Further, these techniques can be used to increase measurement fidelity at higher frequencies than the mechanical system would have otherwise supported...

Figure 7Figure 7Figure 7

shows a

Ssingle -arm gantry system below hasthat has a

radial and cross range motorized axis at the probe end to correct for translational errors associated with structural deflectionse

during 0-90 deg. movement. A laser tracker can be used for routine calibration by mapping the deflections and creating an error-correction table that would be used during measurements.

Figure 7: Probe on Radial and Cross-range Slides

Another approach is to simply characterize the position of the probe during acquisition using a laser tracker system and post implement a software correction of process the irregular spherical scan data for proper near near-field to far far-field transformation. This approach requires implementation of tracking laser

Formatted: Centered

Formatted: Font: 9 pt

Formatted: Font: 9 pt

Formatted: Justified, Indent: First line: 0.25"

Formatted: Justified, Indent: First line: 0.25"

Formatted: Font: Bold

Formatted: Font: Bold

Formatted: Font: Bold

Formatted: Font: 9 pt

Formatted: Font: 9 pt

Formatted: Justified, Indent: First line: 0.25"

Formatted: Indent: First line: 0.25"

Formatted: Justified, Indent: First line: 0.25"

Formatted: Centered

Formatted: Justified, Indent: First line: 0.25"

Page 7: 7Advantages and Disadvantages of Various …atmsindia.org/tech_papers/2015/7Advantages_and...ADVANTAGES AND DISADVANTAGES OF VARIOUS HEMISPHERICAL SCANNING TECHNIQUES Eric Kim, & Anil

ATMS INDIA

2015

The 8th Annual International Conference ATMS -2015, Bangalore

© ATMS (INDIA)

Formatted: Header

system. AHowever, accuracy using this approach is only limited by function of the accuracy of the tracking laser system and software post processing. Other techniques include having a laser tracker system in the position loop to correct for positioner error in real-time.

8IX. SummarySUMMARY

Hemispheric Spherical scanning methods are useful in both near-field as well as far-field measurements of large AUTs. The techniques discussed have all been used has been used successfully. Proper selection of the required system depends on the primary objectives

and requirements of the system.

antenna measurement. More utility will require higher level of investmentKey characteristics of the various systems have been discussed to help provide a useful guideline to the end-user.

9. REFERENCESREFERENCES

[1] C. W. Sirles, B. J. Hart, J. C. Mantovani, and J. D. Huff, A Novel Spherical Scanner System for Wireless Telematics Measurements , AMTA 2009 Proc., Salt Lake City, Utah, USA, pp 425-428.

[2] D. Kremer, A. Morris, R. Blake, and T. Park,

Outdoor Far-Field Antenna Measurements System for Testing of Large Vehicles , AMTA 2012 Proc., Bellevue, Washington, USA, pp. 333-336.

[3] D.W. Hess, D. G. Bodnar, Ground Plane Simulation and Spherical Near-Field Scanning for Telematic Antenna Testing , AMTA 2004 Proc., Atlanta, Georgia, USA, pp. 522-527.

[4] J. Fordham, T. Schwartz, G. Cawthon, Y. Netzov, S. McBride, M. Awadalla, and D. Wayne, A Highly Accurate Spherical Near-field Arch Positioning System , AMTA 2011 Proc., Englewood, Colorado, USA, pp. 293-298.

[5] S. McBride, J. P. Marier, C. J. Kryzak, J. Fordham, and K. Liu, A Large Spherical Near-Field Arch Scanner for Characterizing Low-Frequency Phased Arrays , AMTA 2010 Proc., Atlanta, Georgia, USA, pp. 71-76.

[6] N. Robic, L. Duchesne, P. Garreau, A. Gandois, P. O. Iversen, and L. J. Foged, A Compact Spherical Near-Field System for Antenna Testing From 800 MHz to 18 GHz , AMTA 2006 Proc., Austin, Texas, USA. pp. 472-475.

[7] D. W. Hess, An Expanded Approach to Spherical Near-Field Uncertainty Analysis , AMTA 2002 Proc., Cleveland, Ohio, USA, pp. 495-500

[18] Roger R. Dygert, Mark M. Hudgens, and S. Nichols, An Innovative Technique for Positioner Error

Correction, AMTA 2012 Proc., Bellevue, Washington,

USA, pp 3-8.2012 Proceedings

[2] ASM Handbooks, Volumes 1 and 2, Engineered Materials Handbooks, Composite

Structures and

Technologies, tutorial notes, 1989; and manufacturers technical

data sheets.

[3] Jeffrey Fordham, Tim Schwartz

et al., A Highly Accurate Spherical Near-field Arch Positioning System , AMTA

2011

Proceedings, Atlanta, GA

[49] Charles C. Pinson, John M. Wilber

et alBaggett., Improved 4.

Coordinated Motion Control for Antenna Measurementand the use of Virtual Axis , AMTA 2012 Proc., Bellevue, Washington, USA, pp 257-262.AMTA 2012 Proceedings

Formatted: Font: 9 pt

Formatted: Indent: First line: 0.25"

Formatted: Font: 9 pt

Formatted: Font: Italic

Formatted: Font: Italic