We present a one-port calibration technique for characterization of beam
waveguide components with a vector network analyzer. This technique involves
using a set of known delays to separate the responses of the instrument and the
device under test. We demonstrate this technique by measuring the reflected
performance of a millimeter-wave variable-delay polarization modulator

Bennett, Charles L.

Chuss, David T.

Eimer, Joseph R.

Wollack, Edward J.

English

arXiv

J. R. Eimer

C. L. Bennett

D. T. Chuss

E. J. Wollack

Crossref

Review of Scientific Instruments

Note: Vector reflectometry in a beam waveguide

We present a one-port calibration technique for characterization of beam waveguide components with a vector network analyzer. This technique involves using a set of known delays to separate the responses of the instrument and the device under test. We demonstrate this technique by measuring the reflected performance of a millimeter-wave variable-delay polarization modulator

Chuss, D. T.

Eimer, J. R.

Wollack, E. J.

Bennett, C. L.

NASA Technical Reports Server

Beam Waveguide Vector Reflectometry 
Vector Reflectometry in a Beam Waveguide 
J.R. Eimer,l. a) c.L. Bennett,l D.T. Chuss,2 and E.J. Wollack2 
1) Department oj Physics and Astronomy, The Johns Hopkins University, Baltimore, 
MD 
2) NASA Goddard Space Flight Center, Code 665, Greenbelt, MD 20771 
(Dated: 9 May 2011) 
We present a one-port calibration technique for characterization of beam waveguide components with a 
vector network analyzer. This technique involves using a set of known delays to separate the responses of the 
instrument and the device under test. We demonstrate this technique by measuring the reflected performance 
of a millimeter-wave variable-delay polarization modulator. 
PACS numbers: 06.20.fb,06.20.-f 
Keywords: calibration 
I. INTRODUCTION 
Free space reflectometry provides a non-destructive 
and contact-free microwave metrology technique. It is 
particularly well suited for measurement of the electro-
magnetic properties of materials and characterization 
of quasi-optical components in their intended service 
environments? ? ? ? However, calibration challenges 
exist. Errors in free-space measurements can arise from 
the influence of multiple reflections, trapped modes in 
the system, and diffraction at the edge of the sample. 
Here, as an example, we present measured one-port 
data that addresses these measurement concerns using 
focusing elements to control the illumination of the test 
article, termination of the measured (polarization) modes 
in the system, and vector calibration via a set of con-
trolled phase delays. The method is inspired by the cali-
bration techniques employed previously?? and is a free-
space analogue of the TRL (Thru-Reflect-Line) or more 
general LRL (Line-Reflect-Line) methods used for guided 
structures.?? As such, extension to a multiple port cal-
ibration is straightforward. The underlying approach 
also has application in the characterization of non-mating 
guided structures provided that the electrical delays for 
producing appropriate sampling can be realized. Knowl-
edge of an appropriately-sampled set of delays between 
30° and 1500 yields a well-behaved system of equations. 
In section ?? we describe the method for extracting the 
data. In section ?? we demonstrate the technique with a 
measurement of a variable-delay polarization modulator 
(VPl\1). We discuss the results and the efficacy of the 
technique in section ?? 
a) NASA GSRP Fellow, Goddard Space Flight Center; Electronic 
mail: eimer@pha.jhu.edu 
I 
I 
I 
I 
I 
: Test Port 
Horizontal 
Polarization 
Termination 
: Calibration Plane 
Feedhorn 
x: 
--: 
I 
DUT 
FIG. 1. The system setup is shown. Dashed vertical lines 
indicate the nominal reference plane locations. 
II. FORMALISM 
The non-contacting reflectometry measurement con-
cept is illustrated in Figure ?? In this illustration, the 
calibration plane for the vector network analyzer (VNA) 
is at the interface between the single mode guide and 
the orthomode transducer (OMT). The single mode from 
the waveguide is expanded by the feedhorn into a beam 
propagating in free space. The unmeasured polarization 
is terminated by a waveguide load and mitigates spuri-
ous resonances in the system. In this example, the signal 
is reflected off of a device-under-test (DUT) and then 
coupled back into the waveguide by the same feedhorn. 
The DUT is moved through a set of distances, Xi, that 
span approximately half of a wavelength. In this way, 
the scattering parameter can be modeled as the complex 
sum of the reflection due to the instrument and that due 
to the DUT. 
(1) 
Here, r inst is the complex reflection coefficient from the 
instrument, and r DUT is that for the device under test. 
Xi is the translated distance for the ith measurement. 
and k is the wavenumber. . 
It is convenient to separate these quantities into real 
and imaginary parts: 
ir[nst 
r DUT r~rT + irbuT' 
(2) 
(3) 
https://ntrs.nasa.gov/search.jsp?R=20110015525 2019-08-30T17:23:35+00:00Z
Beam Waveguide Vector Reflectometry 
And the measured data similarly can be written as 
S(Xi) of + iof (4) 
If N measurements are taken, a merit function can be 
defined, 
N L (3?[S(Xi) , )2 ( A)2 Sex,)] + ~xpEuiF - Sex,)] 
N L ((r[;'st + rijuT cos 2kxi - rfJUT sin 2kxi of) 2 + 
(r[nst + rbUT cos 2kxi + rijuysin 2kxi - of) 2) , 
and minimized by solving V'X2 0 to yield 
At D. 
Here, 
(5) 
(6) 
Off-Axis 
Aluminum 
Mirror 
2 
Horizontal 
Polarization 
" 
,,'Test Port 
Calibration 
Plane 
FIG. 2. The test configuration is shown. The grid wires are 
45° with respect to the nominal plane of polarization of the 
OMT. 
(
N 
A- 0 
- L;cos2kxi 
- L;sin2kxi 
o 
N 
L;sin2kxi 
L; cos 2kxi 
L; cos2kxi 
L;sin2kxi 
N 
o 
L;sin2kxi 1 
L; cos 2kx; 
o perture of the grid has a diameter of 50 cm.? The face 
N sheet of an aluminum honeycomb panel is the reflecting 
(7) mirror. The grid-mirror separation and parallelism were 
controlled using a set of shims and verified using optical 
(8) 
where I' is the best fit solution to the data, and 
( 
L;of ) L;o{ 
L;(o{sin2kxi+ofcos2kxi) . 
L; (of cos 2kxi of sin 2kxi) 
D (9) 
These equations have the solution 
(10) 
For appropriately-sampled delays, a minimum of three 
delays and a reference reflection are required. A similar 
formalism can be used for transmission measurements. 
III. MEASUREMENTS 
To test this technique, we measured the response of 
a VPM.? The VPM modulates polarization by intro-
ducing a variable phase delay between linear orthogonal 
polarizations. It uses a polarizing wire grid and a mir-
ror placed behind and parallel to the polarizer. In the 
system described here, the VPM wires are oriented at an 
angle of 45° with respect to the direction of the incident 
radiation. 
The polarizing "grid" uses free-standing wires with ra-
dius a 34 pm and pitch p 200 pm. The clear 
microscopy. 
The experimental setup is shown in Figure 11. A 
single mode is launched from a test port of the HP 
8510C network analyzer into free space using a feedhorn. 
An OMT? coupled to a load is used to terminate the 
unused polarization. The radiation is collimated by a 
paraboloidal mirror and directed onto the center of the 
VPM. It is then reflected by the VPM and refocused back 
into the feedhorn by the same mirror. The reflection co-
efficent (Sl1) is measured as a function of frequency. 
The corrugated feedhorn has a gain of 25-27 dBi across 
the band.? The 55° off-axis paraboloidal mirror has a 
focal length of 50.0 cm and diameter of "",60 cm.? The 
mirror is illuminated with a Gaussian beam radius equal 
to ,,-,3.3 cm. The mirror illumination is highly apodized 
by the feedhorn; the edge taper for the mirror is esti-
mated to be < -40 dB. This configuration was dictated 
by available hardware and allowed many grid wires to 
be illuminated. To improve coupling and control over 
the size of the sample illumination, an ellipsoidal mirror 
could be used in place of the paraboloidal mirror. 
For a given grid mirror separation (d), the technique 
described in Section 11 is applied. Keeping d constant, 
the entire VPM was systematically moved a distance Xi 
from a nominal reference location. 
As an example of the efficacy of this technique, we 
measured the response of the VPM with the grid-mirror 
separation set to d=2.375 pm. Using shims to ad-
just the distance Xi, we measured the response of the 
VPM for frequencies between 85 and 100 GHz for Xi 
{O, 200, 400, 600, 800,1000,1200,1400, 1600} pm. The re-
Beam Waveguide Vector Reflectometry 
Raw Data 
-VPM Response 
-Instrument Response 
90 95 
Frequency (GHz) 
100 
FIG. 3. The raw data are shown superposed on the ex-
tracted response of the VPM response and that of the in-
strument residuals. The instrument response is dominated 
by the OMT. 
sults of the extraction of the device and system response 
are shown along with the original raw data in Figure ?? 
The high spectral frequency component of the observed 
response in the raw data is due to the Fabry-Perot cav-
ity formed between the OMT and its image. Errors re-
maining after the calibration are dominated by the un-
certainty in the determination of Xi. This uncertainty 
was '" ±25 11m. Improved mechanical accuracy of the 
test setup would improve the precision of this technique. 
The data in Figure ?? do not take into account loss in 
the system. We removed the grid from the VPM and used 
the aluminum plate as our reflection reference calibration 
standard. In Figure ?? we show the calibrated VPM 
response corrected for system loss. The plate without the 
grid was measured using the same two-tiered calibration 
described in this paper. Residuals exist at the 0.3 dB 
level due to the finite directivity of the v'NA modules. 
The data for the reflectance standard were filtered to 
further reduce the effect of the residual standing waves. 
IV. DISCUSSION 
The VPM data are compared to a transmission line 
calculation for the configuration.?? The resistance for 
the grid for both the capacitive (polarization perpendic-
ular to the wires) and the inductive (polarization parallel 
to the wires) modes have been incorporated in the model 
to account for ohmic losses. 
The null in Figure ?? occurs because the polarizations 
parallel and perpendicular to the grid wires have a rela-
tive phase of 180" at the frequency corresponding to the 
null. This is the phase difference induced by the VPM 
with d 2, 375 11m. To an good approximation. the 
response can be modeled as a resonator with a quality 
3 
I 
85 90 95 100 
Frequency (GHz) 
FIG. 4. The measured reflectance from the VPM with grid-
mirror separation set to d =2,375 /-Lm is normalized by the 
response of the mirror alone. The model for the VPM with 
finite resistivity is superposed on the data. 
factor, Q '" 2.4, where Q is related to the measured sig-
nal, R, by 
1 
~ (11) 
Here, w is the angular frequency, and Wo is the angular 
frequency of the null. The null in the reflection appears at 
d/).. '" 0.73 for the third cavity resonance. The deviation 
of this point from d/ ).. '" 0.75 is expected due to the phase 
shift of the grid circuit.? 
The null is measured at a depth of -50 dB which is 
higher than that predicted by the simple model that is 
limited only by ohmic losses in the grid-mirror structure. 
We find that a 0.10 misalignment in angle of the grid rel-
ative to the axis of the OMT is sufficient to explain the 
measured effect. This is consistent with our confidence 
in the achieved rotational alignment. Other factors con-
tributing to the observed finite reflectance at the null in-
clude the limited precision of the measurement of Xi and 
the limitations on dynamic range and readout resolution 
of the HP 851OC. In applying this technique to the char-
acterization of high Q systems, changes in optical loss as 
Xi is varied would be of greater importance. For systems 
with high reflectance, this technique could be improved 
by adopting a bilinear form for the reflectance. 
In this paper we have developed and demonstrated a 
vector calibration technique that improves beam waveg-
uide metrology. For single-moded measurements, we 
have improved the precision over currently-employed 
techniques. The method described here can be extended 
to 2-port systems. 
Beam Waveguide Vector Reflectometry 
ACKNOWLEDGEMENTS 
We would like to thank G. Voellmer, H. Hui, and L. 
Zeng for experimental setup, L. Page for access to optical 
components, and D.J. Fixsen for helpful discussions. 
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Vector Reflectometry in a Beam Waveguide

Vector Reflectometry in a Beam Waveguide

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