Effects of Cylindrical Chopper Geometry on Calculating 

Power Coupling Efficiency and Noise Equivalent 

Temperature Difference

by Abigail S. Hedden, Charles C. Dietlein, and David A. Wikner

ARL-TR-5428 January 2011

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Army Research Laboratory

Adelphi, MD 20783-1197

ARL-TR-5428 January 2011

Effects of Cylindrical Chopper Geometry on Calculating 

Power Coupling Efficiency and Noise Equivalent 

Temperature Difference

Abigail S. Hedden, Charles C. Dietlein, and David A. Wikner

Sensors and Electron Devices Directorate, ARL

Approved for public release; distribution unlimited. 
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Effects of Cylindrical Chopper Geometry on Calculating Power Coupling 

Efficiency and Noise Equivalent Temperature Difference

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Abigail S. Hedden, Charles C. Dietlein, and David A. Wikner

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14. ABSTRACT

This report explores the geometrical effects of a cylindrical chopper wheel on calculations of power coupling efficiency and 

noise equivalent temperature difference (NETD) of array elements. The overall efficiency of the cylindrical chopper wheel is

found to be about 53% from geometrical arguments. In the limit that a detector beam fills the chopper aperture, if this 

efficiency is not accounted for, it can lead to detector NETD values that are a factor of 1.9 too high when calculated using 

standard double-modulation measurement techniques. For the particular geometry used with this setup, a power coupling 

efficiency of 78% was calculated for typical detector elements, resulting in values of detector NETD that were too large by a

factor of 1.3 when the coupling efficiency was unaccounted for. This factor plays a role in accounting for some of the 

discrepancy between NETD values calculated based on diode sensitivity estimates and NETDs measured for individual array 

elements using double-modulation measurements. 

15. SUBJECT TERMS

Millimeter-wave measurements, millimeter-wave technology, planar arrays

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Abigail S. Hedden

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iii

Contents

List of Figures iv

Summary 1

1. Introduction 3

2. Methods, Assumptions, and Procedures 4

3. Results and Discussion 6

4. Conclusions 9

5. References 10

List of Symbols, Abbreviations, and Acronyms 11

Distribution List 12
iv

List of Figures

Figure 1. Diagram showing a side view of the ARL mm-wave array, cylindrical optical 

chopper (metal blades are shown toward the top and bottom), and the scene being 

imaged........................................................................................................................................4

Figure 2. Normalized total projected height of the scene (solid line) as dictated by the 

array’s cylindrical chopper geometry compared with a perfect chopper (dashed line) as a 

function of rotation angle . Areas under each curve from  = 0° and 90° are indicated. .....5

Figure 3. Angles between the detector array and chopper blades with respect to the line-ofsight axis for the particular geometry used with the ARL array. θtot represents the total 

angle subtended by the scene visible to the detectors as the chopper rotates a complete 

revolution. ..................................................................................................................................7

Figure 4. (Left) Normalized angle θtot for the ARL array cylindrical chopper (solid line) and 

a perfect chopper wheel (dashed line); the angular efficiency is ~80%. (Right) Principal 

plane copolar radiation power pattern for a typical ARL array diagonal horn antenna. 

Note that the normalized angle is: u/π = (d/λ) sin δ. Since d/λ = 3, the range corresponds 

to δ = 0 – 90°..............................................................................................................................7

Figure 5. Power coupling efficiency, R, for a typical array horn antenna for the setup 

described in this work is shown as a function of rotation angle  over a half period of the 

chopper wheel. The overall power coupling efficiency is 78% compared with a perfect 

chopper.......................................................................................................................................9
1

Summary

This report explores the geometrical effects of a cylindrical chopper wheel on calculations of 

power coupling efficiency and noise equivalent temperature difference (NETD) of array 

elements. The overall efficiency of the cylindrical chopper wheel is found to be about 53% from 

geometrical arguments. In the limit that a detector beam fills the chopper aperture, if this 

efficiency is not accounted for, it can lead to detector NETD values that are a factor of 1.9 too 

high when calculated using standard double-modulation measurement techniques. For the 

particular geometry used with this setup, a power coupling efficiency of 78% was calculated for 

typical detector elements, resulting in values of detector NETD that were too large by a factor of 

1.3 when the coupling efficiency was unaccounted for. This factor plays a role in accounting for 

some of the discrepancy between NETD values calculated based on diode sensitivity estimates 

and NETDs measured for individual array elements using double-modulation measurements. 
2

INTENTIONALLY LEFT BLANK.
3

1. Introduction

We consider the effects of optical chopper geometry on calculations of power coupling 

efficiency and NETD of detector elements in the U.S. Army Research Laboratory’s (ARL)

32-pixel Linear Millimeter-wave Array. We briefly summarize the relevant properties of the 

array pertaining to this setup. An overview of the array, the cylindrical chopper, and its 

geometry are presented in reference 1. The instrument is a 32-channel, zero-bias, room 

temperature detector array designed for operation in the 80–140 GHz range for passive 

millimeter-wave (mm-wave) imaging applications. At its heart, it incorporates antimony (Sb)-

heterostructure backward tunnel diodes (BTDs) fabricated on gallium arsenide (GaAs) substrates 

that were developed at HRL Laboratories (2) as low-noise, low-cost mm-wave imaging sensors 

capable of high sensitivity, room temperature operation as part of the Defense Advanced 

Research Projects Agency (DARPA) Microantenna Arrays: Technology and Applications 

(MIATA) program (3). In order to achieve a good match with minimal losses over a 60-GHz 

bandwidth, BTDs were flip-chip mounted to quartz substrates with the detector chip located 

inside of the horn antenna output waveguide sections. Diagonal horns with cylindrical ridged 

waveguide outputs were used to achieve the large operational bandwidth, and coupling to the 

waveguide was accomplished via E-plane probes patterned on the quartz chip (4). 

The low-noise and zero-bias characteristics of these detectors alleviate the need for signal preamplification and bias-routing circuitry, greatly simplifying the overall array architecture. The 

zero-bias diodes are limited by thermal (Johnson) noise and are free from both 1/f and shot noise. 

Since low signal levels and high noise remain significant challenges for room temperature 

passive mm-wave and terahertz (THz) imaging, the sensitive, low-noise performance of the 

diode detectors was a key consideration of the array design. To reduce the overall noise and 

enable synchronous detection of the array output, a long cylindrical chopper wheel was designed 

to optically chop the imaged scene. Ultra-low-noise readout electronics compatible with room 

temperature video-rate passive imaging applications were designed for use with the 

array/chopper wheel system (5). In this work, we explore the effects of the cylindrical chopper 

geometry on calculations of detector power coupling efficiency and NETD. An overview of the 

cylindrical chopper and its potential limitations is presented in section 2. Section 3 addresses

detector power coupling efficiency and its effect on NETD calculations specific to the geometry 

of this experiment and a brief summary of these results is presented in section 4. 
4

2. Methods, Assumptions, and Procedures

Figure 1 shows a side-view diagram of the chopper relative to the detector elements and the 

scene being imaged. The chopper wheel consists of a rotating metal half-cylinder that has been 

anodized. The two quarter sections of the half-cylinder are located 180° apart so that, in the 

orientation shown in figure 1 with solid lines, the linear array has a maximally unobstructed view 

of the scene. The chopper blades are located at the top and bottom of the figure in this case. The

metal half-cylinder chopper is a single rigid body of radius 5 cm (Ri = 4.84 cm) that pivots about 

a central axis and may be driven at frequencies in excess of 50 Hz by a motor. The array line of

sight is coincident with the central axis of the chopper. Let  be the angle between the line of

sight and the chopper blade as shown in figure 1 as the chopper spins in a counterclockwise 

direction from  = 0°. Note that the projected height of the scene visible from the array varies 

with  as the chopper wheel turns and is represented in the diagram as h. The maximum 

viewable height of the scene occurs in the orientation shown by solid lines in figure 1, where 

 = 0 and h = hmax, and is equal to 2 hmax. Because each metal section of the chopper subtends 

90°, 0 = 45°. Expressions for h and hmax are as follows: 

h  Risin and 

max 0 h  Ri

sin

(1)

Figure 1. Diagram showing a side view of the ARL mm-wave array, cylindrical optical chopper (metal blades 

are shown toward the top and bottom), and the scene being imaged.

Figure 2 was generated from equation 1 and shows the normalized projected height, htot/(2hmax), 

of the scene that is visible to the detector as the chopper turns counterclockwise one complete 

revolution. As shown in the figure, htot represents the total projected height above and below the 

line of sight drawn in figure 1 and the chopper revolution begins at  = 0°. As the chopper wheel

rotates counterclockwise from a fully closed position at  = 0° to 0, the total projected height 
5

increases to its maximum value. Rotating from  = 0 to 20, the falling edge of the top blade 

and the rising edge of the bottom blade of the chopper begin to occult the visible scene until the 

chopper is again fully closed. The scene remains fully occulted until the cycle repeats with a 

period of 180°. The resulting triangular-shaped total projected height curve is shown in figure 2

(solid contour) over one full revolution of the chopper wheel. For comparison, the results of a 

perfect chopper (one which chops between the reference and scene instantaneously) are shown in 

dashed contours. Figure 2 indicates that, unlike the perfect chopper, the duty cycle of the array 

chopper wheel is about 25%. Between  = 0° and 90° and again between  = 180° and 270°, the 

total projected view visible through the chopper contains both the chopper blades and the scene 

(with temperatures Tchopper and Tscene, respectively). This can be thought of as a scene with a 

temperature dependant on how much of the scene is occulted by the chopper as the wheel rotates 

through half a period (90°). The effective temperature of the scene is related to the ratio of areas 

under the curves shown in figure 2 by the following: 

[1 ( )] ( ) Teff  Tchopper  Ah Atot Tscene Ah Atot

(2)

Figure 2. Normalized total projected height of the scene (solid line) 

as dictated by the array’s cylindrical chopper geometry 

compared with a perfect chopper (dashed line) as a function 

of rotation angle . Areas under each curve from  = 0°

and 90° are indicated.

Standard numerical integration techniques were used to compute the area under the curve of 

projected height in figure 2, Ah, resulting in Ah/Atot = 53%. For chopper and scene temperatures 

of 295 and 77 K, respectively, this results in Teff = 180 K. Instead of observing an effective 

temperature difference of 218 K between the chopper and cold scene, a 115 K temperature 

difference (295 K – Teff) results for the cylindrical chopper. Depending on the specifics of the 

setup, including the location of the detector array (L0) and chopper geometry (Ri), this will lead 

to detector beam coupling efficiencies that are lower and calculations of NETD that are 
6

correspondingly higher if geometric effects are unaccounted for. In the limit where a detector 

beam fills the chopper aperture, standard double-modulation measurement techniques result in 

NETD calculations that are a factor of 1.9 too high, since NETD is directly proportional to

temperature difference. 

3. Results and Discussion

For the particular configuration used with the ARL array, L0 and Ri are 8 and 4.84 cm, 

respectively. Using equation 1 and figure 1, the angle between the line-of-sight axis and the 

chopper blade edge, θ, is expressed as follows: 

sin [( sin ) ( cos ) ( sin ) ]

2 2

0

1

  Ri  L  Ri   Ri 



(3)

Four such angles can be simultaneously described because there are four blade edges. Let θtop

and θbottom represent the minimum angles (in absolute value) defined above and below the lineof-sight axis by the edges as the chopper rotates; θtot is the total angle, θtot = θtop + | θbottom |. 

Figure 3 shows all three of these curves, θtop, θbottom, and θtot, as a function of  over one 

complete rotation of the chopper wheel. Figure 4 (left) shows a comparison between normalized 

θtot for the chopper geometry used with the ARL array and what would be expected from a 

perfect chopper. The angular efficiency is described by the ratio of the areas under both curves 

shown in figure 4 (left) over half a period ( = 0° to 90°, for example) and is about 80%. In 

order to relate this result back to NETD, θtot is used to calculate the power coupling to a typical 

array element feed horn.
7

Figure 3. Angles between the detector array and chopper blades with 

respect to the line-of-sight axis for the particular geometry 

used with the ARL array. θtot represents the total angle 

subtended by the scene visible to the detectors as the chopper 

rotates a complete revolution. 

Note: θbottom values are shown as negative numbers.

Figure 4. (Left) Normalized angle θtot for the ARL array cylindrical chopper (solid line) and a perfect chopper 

wheel (dashed line); the angular efficiency is ~80%. (Right) Principal plane copolar radiation power 

pattern for a typical ARL array diagonal horn antenna. Note that the normalized angle is 

u/π = (d/λ) sin δ. Since d/λ = 3, the range corresponds to δ = 0 – 90°.

Power patterns for a typical ARL array diagonal horn antenna were calculated from expressions 

for the principal plane copolar electric field (6): 

1 (2 )

cos 2

2

sin 2

2 2

u 

u

u

u

Eco



  (4)
8

Note that the principal plane cross-polar field is 0, d is the length of the sides of the diagonal 

horn aperture, u = (πd/λ) sin δ, and for the array horn antennas used in this work, d/λ = 3. Using 

equation 4, the normalized copolar radiation power pattern was calculated and plotted in figure 4 

(right) as a function of angle δ with respect to the principle axis of the horn antenna from δ = 0°

(on-axis) to δ = 90° (corresponding to a range of u/π = 0 – 3). Note that the normalized power 

pattern is symmetric with respect to the horizontal axis. This power pattern is used in 

conjunction with figure 3 to determine the power coupling efficiency. The coupling efficiency is 

the ratio of the total integrated power pattern over the angular region containing the visible scene 

(θbottom to θtop) to the total power calculated over the maximally visible scene (e.g., what would 

be expected from a perfect chopper). The resulting power coupling ratio for any chopper 

rotation angle  is given by the following expression:







 





 90

90

2

2

( )

( )

( )

1

0

 

 



 

 

E d

E d

R

co

co

top

bottom

(5)

Note that for any angle , values of 



are determined using equation 3 for each edge of the 

chopper blade and that θbottom and θtop are shown in figure 3 as a function of . Note that for a 

setup including a perfect chopper, the entire scene is visible and the total integrated power 

calculated is a constant. The power coupling ratio equation 5 was used along with figures 3 and 

4 to find the total normalized power coupling for a typical array element horn antenna for the 

setup used in this experiment as a function of chopper rotation angle, . The results are shown in 

figure 5. This figure shows the calculation of power coupling ratio equation 5 over a quarter 

revolution (half-period) of the chopper wheel,  = 0° to 90° and the area beneath the curve

describes the total power coupling efficiency for typical elements of the ARL linear array. The 

resulting power coupling efficiency was found by numerical integration techniques and is 78%,

similar to the 80% angular efficiency calculated previously. Since the ARL array elements are

square-law detectors, their signal is proportional to the total incident power of the scene and the 

power coupling efficiency. Standard double-modulation techniques, where detector response is 

recorded while room temperature and liquid nitrogen cooled loads are alternately placed in front 

of the chopper wheel, were used to calculate detector NETD. NETD values determined by this 

method are inversely proportional to the power coupling efficiency. In other words, a 78% 

power coupling efficiency results in NETD calculations that are too large by a factor of about 1.3 

if power coupling efficiency is not properly accounted for and a perfect chopper is assumed

instead. 
9

Figure 5. Power coupling efficiency, R, for a typical array horn antenna 

for the setup described in this work is shown as a function of 

rotation angle  over a half period of the chopper wheel. The 

overall power coupling efficiency is 78% compared with a perfect 

chopper.

4. Conclusions

In summary, we have calculated the efficiency of the cylindrical chopper wheel currently being 

used with the ARL 32-pixel Linear Millimeter-wave Array and determined its effects on power 

coupling and calculated values of NETD for typical array elements. From geometrical 

arguments, we find that the overall efficiency of the cylindrical chopper wheel is about 53%. 

Standard double-modulation measurement techniques result in NETD calculations that are too 

large if this efficiency is unaccounted for. For example, in the limit where the detector field of 

view spans entire chopper aperture, NETD calculations determined by this method are too large 

by a factor of 1.9. For the particular system geometry and array element horn antennas used in 

this setup, we calculate an overall power coupling efficiency of 78% for typical array elements. 

Double-modulation measurements made with the current array/chopper wheel configuration 

result in NETD calculations that are correspondingly too high by a factor of 1.3. 
10

5. References

1. Wikner, D. A.; Grossman, E. N. Demonstration of a Passive, Low Noise, Millimeter-wave 

Detector Array for Imaging. Proc. SPIE 2009, 7309, 730909-1–730909-6.

2. Schulman, J. N.; Croke, E. T.; Chow, D. H.; Dunlap, H. L.; Holabird, K. S.; Morgan, M. A.;

Weinreb, S. Quantum Tunneling Sb-heterostructure Millimeter-wave Diodes. IEDM Tech. 

Digest 2001, 765–767.

3. Stickley, C. M.; Filipkowski, M. E. Microantenna Arrays: Technology and Applications 

(MIATA)—an overview. Proc. SPIE 2004, 5619, 47–58. 

4. Moyer, H. P.; Bowen, R. L.; Schulman, J. N.; Chow, D. H.; Thomas III, S.; Lynch, J. J.;

Holabird, K. S. Sb-heterostructure Low Noise W-band Detector Diode Sensitivity 

Measurements. Microwave Symposium Digest, 2006. IEEE MTT-S, pp. 826–829, June 

2006.

5. Chisum, J. D.; Grossman, E. N.; Popović, Z. Ultra-low Noise Readout Electronics for THz

Imaging Arrays. In prepartion.

6. Johnson, R. C.; Jasik, H. Antenna Engineering Handbook; 2

nd Ed., McGraw-Hill Book Co., 

New York, 1984, ch. 15-4. 
11

List of Symbols, Abbreviations, and Acronyms

ARL U.S. Army Research 

BTDs backward tunnel diodes 

DARPA Defense Advanced Research Projects Agency 

GaAs gallium arsenide 

MIATA Microantenna Arrays: Technology and Applications 

NETD noise equivalent temperature difference 

Sb antimony 
12

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