Example 1 - The

responsivity scan for the 0.0

germanium detector shown -~0.1

in Figures 2 to 5 is used in Rg

this example. The scan was 2g —02

acquired using a 0.56 mm g -0.3

beam. Box 3 lists the 6-04

misalignment statistics for 2B

the area around the 5 705

detector’s center with a a —0.6

radius of 1 mm. These & 0.7

statistics are valid for the &

0.56 mm beam used in the 08

scan. The misalignment —0.9

statistics show that if the 0 1 2 3 4 5 6
beam is randomly placed Beam Diameter (mm)

within 1 mm of the center,
the responsivity will vary
with a standard deviation of
0.29 %, and can change a
maximum of 1.5 %.

Figure 19. Responsivity variation with beam diameter for example
germanium detector.

Figure 19 shows how the responsivity in the detector’s center will change when the beam

diameter is changed. The results for beam diameters near 0.5 mm are overly optimistic because
the true impulse response was not used. Even with the optimistic results, the responsivity is very -~
sensitive to beam diameter when small beams are used. The graph also shows that the

responsivity is very
consistent for beams 2 to 5
mm in diameter. If the
responsivity change for
these beam diameters is
analyzed, the standard

1024

deviation is found to be only 3
0.016 % with a peak-to-peak ee
spread of only 0.047 %. 3 i
This result shows that this ay
detector will work well with gs
a2 to 5 mm beam. & i
2
8

Figure 20 shows the
detector’s overall uniformity
when synthetically scanned
with a 3 mm Gaussian ta.
beam. The uniformity looks

4

much better than in Figure 2S

2, but looks can be sor

deceiving. Box 4 lists the as

misalignment statistics for ag as

the 3 mm beam scan. The

misalignment statistics are Figure 20. Germanium detector after synthetic 3 mm beam scan.

1994 NCSL Workshop & Symposium 350 Session 5A


Wavelength and polarization changes can also cause LT
the ratio to change. Plot Title: none
. woe Acquired 12-09-1992 at 14:14:03
To estimate the error caused by the variation of the Saved File: temp.
beam splitter ratio, two parameters are stored with Amp. Gain: 100000
each scan. The stability of the beam splitter ratio is Detector Identifier:
measured before the scan. The results are stored with

. . . ° . Ge Detector Example
the optical source information, as illustrated by the list

Optical Source: 845 nm

shown in Box 1. The ratio is measured for a period of LD-845-1 190 uw
an hour, and the standard deviation and peak-to-peak Spot Size: 0.562 X 0.558 mm
spread are stored. The spread is a worst case Sample Spacing: 0.10000 mm
measurement: the fluctuation is not usually random so Samples Taken: 101 X 101
the spread is typically much larger than the standard Monitor Deviation: 0.031 %
deviation. Some sources are much more stable than Power Fluctuations Corrected
others but the source used in the example is typical. Background Level Subtracted
a . . Measurement Delay: 0.320 s
The standard deviation of the monitor readings is Plot Rotation: 135 degrees
measured during the actual scan. This number Plot Tilt: 30 degrees
contains both the actual power fluctuations and the DVM Integration: 167 ms
beam splitter ratio drift encountered. This figure is Ref Orient Win. Rot. Tilted 5 deg

provided on the run information list, as shown in Box

2. These two errors combine in some fashion to add : —

to the uncertainty in the responsivity scan. Additional Box 2. Example run information list.
errors can occur if the test detector is not the same

type as the monitor detector because dissimilar detectors can respond to wavelength, polarization,
and temperature changes differently.

These errors are not effectively reduced by the voltmeter integration because the drift usually
occurs relatively slowly. They can, however, usually be reduced by averaging multiple scans. To
perform this averaging, the system acquires multiple scans over exactly the same area of the
detector, then averages the results. The scans are usually acquired hours apart. If the
fluctuations are random over this time scale the averaging will be effective at reducing the
fluctuations. This technique can also reduce the effect of slow drift in the power and detector
responsivity, and is effective at reducing detector noise.

Aliasing Distortion - Distortion can also result if the spacing between detector responsivity
samples is too large. The data acquired by the measurement system is a discretely spaced
sampling and is subject to sampling theorem limitations. If the sampling rate is too low, the
signal is undersampled and aliasing can occur.> The sampling theorem states that to exactly
represent a signal with a uniformly spaced sampled data set, the sampling must be performed at a
frequency sufficiently greater than the highest frequency present in the signal. Specifically the
signal must be uniformly sampled at or above the Nyquist rate of 2f,, where the signal has no
frequency components at or above f,.* Here the signal is the detector’s responsivity as a function
of position, the frequencies are spatial but the sampling theorem still applies.

Two factors determine whether the sampled data is a complete representation of the detector’s
responsivity: the spatial frequencies in the responsivity and the sample spacing. The detector’s

* responsivity recorded for each sample point is not the actual responsivity at an exact point on the
detector; it is the convolution of the beam’s intensity profile and the detector’s true responsivity.

1994 NCSL Workshop & Symposium 341 Session 5A


Interference fringes can be caused
by a detector’s window being flat or
only slightly wedged. Wedged
windows are usually a good idea
because the wedge helps prevent
the other kinds of interference from
occurring. But if the wedge angle is
too small, interference fringes can
be ptoduced. The following
equation defines the effect:

O=A/2nd.

Output ()
100.8

00.8

204

The equation relates the window's
wedge angle @ to the distance
between fringes d. The window’s
index of refraction » and the
wavelength of the source A are also
used in the equation. If the index
of refraction is 1.5, the wedge angle
is 0.032°. Scanning the detector
with a 1557 nm source resulted in
similar fringes and gave the same wedge angle. The fringes were too close together to be
resolved in a 845 nm scan. This wedge angle is slight indeed!

sh \\) Hae
i! ‘7 A

ll
mi

Figure 15. Detector with reflection artifact.

REFLECTION ARTIFACTS

If a detector is aligned exactly perpendicular to the optical beam, any reflection from the detector
can re-enter the optical system or
reflect off the optics back to the
detector. The reflection usually
superimposes ‘a slope on the
uniformity, like that shown in
Figure 15. When the detector was
tilted with respect to the beam, the
slope completely disappeared
revealing the uniformity shown in
Figure 16. This artifact is not
caused by interference, but can be
identified by tilting the detector. It
can occur with incoherent sources.
Note the greatly improved
uniformity in Figure 16, and the
appearance of what may be a point
interference artifact near the edge ARS s at
‘eg, ee

of the detector. we oS SO

Output («)
100.0 100.3

99.7

99.3

4

free
4

ce See

we
F

This effect is believed to be caused sae

primarily by the reflection bouncing
Figure 16. Detector with reflection artifact when tilted.

1994 NCSL Workshop & Symposium 346 Session 5A


so1o

sons

oF:
z: x
eI EES
ZZZZSSSS
FFE

1008
eZeesece
LG EEE,

LEIIOD.

Z Ss
re, os
LE 5

PEELE ESS

ZILLES LOIS

LEO K SSS

4008

Output fe)
100.0

ZZ

Output Oe)
20.8
FE

bas
we
ZELEE
Ze,

‘y

Figure 10. Undersampled scan after spline

Figure 9. Undersampled scan with beam size to interpolation.

sample spacing ratio of 0.7.

Figure 7 shows how the uniformity would have

looked if a sample spacing 1.4 times smaller than the beam diameter was used. This figure bears
little resemblance to that in Figure 6, but actually contains almost the same information. When
the data in Figure 7 are expanded using spline interpolation, the uniformity shown in Figure 8
results. The expanded data are almost identical to the oversampled data, but some aliasing
distortion is present in the form of bumps on the ridges and a slight change in amplitude. Figure
9 shows how the uniformity would have looked if a sample spacing 0.7 times smaller than the
beam diameter was used. This figure does not look much worse than that in Figure 7, but when
it is expanded by spline interpolation the uniformity shown in Figure 10 results. Figure 10 bears
no resemblance to the oversampled scan shown in Figure 6 because the uniformity was aliased.
The sample spacing of 0.7 times smaller than the beam diameter is therefore too large.

Since slight aliasing is evident when a sample spacing 1.4 times smaller than the beam diameter is
used, the maximum sample spacing to prevent aliasing must be slightly smaller. The actual
maximum sample spacing can be different for beams with a different profile than the one used
here; for example, a beam with more of its power in the center would require an even smaller
sample spacing. So it is advisable to use maximum sample spacing of one-half the 1/e? beam
diameter.

One final sampling theorem requirement remains. The sampling theorem states that to
reconstruct the continuous signal from the sampled data, the sampling frequency must be filtered
out.’ The measurement system relies mainly on the operator’s eye to filter out the sample
frequency; the more the uniformity is oversampled the easier is the filtering. This is why the
surface shown in Figures 7 looks so irregular. Adding lines to the surface with spline
interpolation or oversampling by using a smaller sample spacing results in a surface that is much
easier to interpret. Using a sample spacing one-quarter times the beam diameter usually
oversamples the responsivity enough to produce a smooth, easy to interpret surface without spline
interpolation.

1994 NCSL Workshop & Symposium 343 Session 5A


A Gaussian beam actually provides
a spatial low-pass filtering of the
detector’s responsivity and thus
limits the spatial frequency range
present in the measured
responsivity (for the given beam

diameter). Since the beam limits 8
the spatial frequency present, 8
choosing a sufficiently small sample z

spacing for the beam is the only Bs
requirement for preventing aliasing. =

902

The maximum sample spacing that
should be used with a Gaussian

beam of given diameter can be
determined experimentally. The ~
system uses a beam diameter

defined as the distance between the
points where the intensity drops off

to 1/e? of its maximum. If too large

a sample spacing is used, the true
responsivity can be aliased. An Figure 6. Oversampled scan of a nonuniform detector.
example of such aliasing is shown in

Figures 6 to 10. Figure 6 shows the center portion of a scan from a detector which has parallel
ridges in its uniformity. The sample spacing used in the scan is 11.2 times smaller than the 1/e? _
beam diameter, so the responsivity is oversampled and is an accurate representation of the actual
responsivity within the bandwidth of the scanning beam. Samples were removed from this dataset
in the later figures to show what would have happened if a larger sample spacing had been used.

Pd

1018

soe
008

soos
output (a)
100.0
—

==
———SS
SSS
SSS=
SSSSSS5
SS
oe

output be)
100.1

oes
SSS

woe

Wi

ea

: Figure 8. Marginally sampled scan after spline
Figure 7. Marginally sampled scan with beam _ interpolation.
size to sample spacing ratio of 1.4.

1994 NCSL Workshop & Symposium 342 Session 5A


spacing was a function of
wavelength. This artifact is rare. It
could have been caused by a curved
window or etalon caused by
reflections between the detector
and the collimating lens.

Point Interference - This is
probably the most common
interference artifact seen. The
artifact is called point interference
because it usually occurs in only
one area of the detector. It can be
caused by parallel surfaces that
occur at only one point in space.
For example, if a detector’s window
is rounded it will be parallel to the
detector’s surface at only one point.

Point interference artifacts are
easily identified. A slight change in
detector tilt angle usually causes the

100.0

97.5

: ie

92.5

i

Figure 13. Detector with a point interference artifact when
tilted.

artifact to change dramatically. It typically changes position and magnitude and sometimes even

sign. Figures 12 and 13
show such an artifact. The
large peak near the center
of the detector in Figure 12
is due to point interference.
Tilting the detector several
degrees caused the artifact
to change from the peak
shown in Figure 12 toa
deep hole in Figure 13.
This type of artifact is
usually caused by a
detector’s window.

Interference Fringes -
Interference fringes are a

fairly common artifact. The
detector used in the aliasing
example, shown in Figures 6
through 10, has interference
fringe artifacts. The fringes
form parallel ridges in the
uniformity. The detector is
. presented again as a contour
map in Figure 14, the fringe
spacing of 0.78 mm is easily
obtained from the map.

Y-—Axis Position (mm)

1994 NCSL Workshop & Symposium

Detector 1 Example 2, 0.5
1.000 ~0.000

3
g

% Lines — Output (%)
1.000 2.000,

=2.000
3) 2.000

T

-0,000

1.000 A
X-Axis Position (mm)

-0.000 1.000

Figure 14. Detector with interference fringe artifact, 1320 nm
source.

345 Session 5A


SPATIAL UNIFORMITY OF
OPTICAL DETECTOR RESPONSIVITY

David Livigni and Xiaoyu Li
Electromagnetic Technology Division
National Institute of Standards and Technology
Boulder, CO 80303

Abstract: A scanning system for measuring the spatial uniformity of the responsivity of optical
detectors and methods of quantifying the degree of uniformity are described. Surface plots and
contour maps of the measured responsivity are presented along with a statistical treatment.
Factors which can affect the accuracy of the uniformity measurement are described, including
sampling theorem restrictions and interference artifacts produced when coherent light is used.
Examples of these artifacts are presented along with scans of actual Si, Ge, and InGaAs
detectors.

INTRODUCTION

At NIST the uniformity measurement system has been very useful in determining whether
calibration problems are caused by detector uniformity. Nonuniform detectors give different
results depending on the intensity profile of the beam and where the beam strikes the detector.
Calibrating a nonuniform detector or using -it to measure the power in a beam can be difficult
because the detector’s responsivity can change whenever the detector is aligned. The responsivity
can also change with time if the beam parameters change. The system is helpful in determining
which detectors are suitable for use as transfer standards: a detector with poor uniformity would
not make a good standard.

THE MEASUREMENT SYSTEM

A detector uniformity measurement system was originally developed at NIST for the United
States Air Force. The original measurement system’ was developed by A. L. Rasmussen. We
later modified the system and presented it at the 1992 Measurement Science Conference.? New
findings not presented at the earlier conference are included here.

The modified system, shown in Figure 1, is simpler and more accurate than the original design.
The system directly measures the responsivity of the detector at each sample point by measuring
the detector’s output when illuminated by a stable beam. Unlike the original system, the
_modified system uses a laser diode or LED optical source mounted directly to the translation
stages. These sources are more stable than the gas lasers used in the original system. The
detector being tested remains stationary in the modified system. High quality amplifiers and

1994 NCSL Workshop & Symposium 337 Session 5A


example, drift can be caused by a slow change in the environment such as a temperature drift, or
a slow change in the optical source. Drift in some of the source parameters is reduced by the
power fluctuation correction algorithm.

Slow temporal drift artifacts occur when the drift: is in the beam splitter ratio, is a wavelength
change which is not tracked in the same way by the monitor and test detectors, or is caused by an
actual responsivity change in a detector. When such drift occurs during a responsivity scan, it is
manifested as ridges parallel to the x-axis with discontinuities along the y-axis. This artifact
results because the system scans along the x-axis and shifts y-axis positions only at the end of each
scan line.

Slow temporal drift artifacts occurred in the InGaAs detector scan shown in Figure 17. The drift
was apparently caused by wavelength changes in the source which were not tracked identically by
the germanium monitor and InGaAs test detector. Using an identical InGaAs monitor may have
prevented the drift. The optical source used in the scan has a tendency to mode-hop, causing the
changes in wavelength. The slow temporal drift artifacts can be reduced by averaging, if the drift
averages to zero in the time required to make a scan. Figure 18 shows the same detector after a
16 scan average. The magnitude of the drift artifacts is ideally reduced by a factor of 4, and the

resulting scan is much smoother and more accurate.

While there is a striking similarity between Figures 15 and 17, the two surfaces are created by
entirely different phenomenon. The sloping uniformity in Figure 15 is entirely the result of a
reflection artifact, while the sloping uniformity of the InGaAs detector in Figures 16 and 17 is a
true feature of the detector. InGaAs detectors are notorious for their poor uniformity.

UNUSUAL DETECTORS

Some detectors cause special problems. Detectors needing chopped inputs can be scanned by the
system, but the chopper wheel must be fixed in relation to the optical source or distortion similar
to the reflection artifact can occur. The chopper wheel must move with the optical source for an
accurate scan. Autoranging detectors cause problems for the centering algorithm. If autoranging
cannot be tumed off, it may be necessary to manually center the beam on the detector and scan
only the area around its center. Detectors requiring a certain polarization can be scanned by
attaching a polarizer to the optical source. However, the power fluctuation correction algorithm
would not be effective in this case. Pulse detector uniformity cannot be measured by the system
at this time.

QUANTIFYING DETECTOR UNIFORMITY

Two techniques for quantifying a detector’s uniformity are proposed here. Poor uniformity can
lead to two sources of error when a detector is calibrated or used to calibrate a beam. The first
source is alignment error, and the second is beam diameter fluctuation. Both techniques are
described here; the latter technique is, as far as we know, new.

Alignment Error - When an operator aligns a detector, the beam may not be placed perfectly in
the detector’s center. A method for quantifying the alignment error associated with centering,
called misalignment statistics, has already been proposed.’ Assuming the centering error can be
limited to some distance, error statistics can be generated from the responsivity scan. For
example, suppose that the operator can align the detector so that the beam’s center is always
placed within 1 mm of the detector’s center. Then the responsivity results for all the points

1994 NCSL Workshop & Symposium 348 Session 5A


back to the detector, but if the
beam re-enters the optical source
interference effects may be
generated in laser diodes too. This
effect can be avoided by aligning
the detector at a tilt so that the
reflection strikes the collimator’s
aperture stop.

100.6 = 100.8

Output («)
99.9

TEMPORAL DRIFT ARTIFACTS

99.5

Here the term temporal drift refers
to an apparent fluctuation in the
detector’s responsivity with time. If
the fluctuations are random and
fast compared to the voltmeter’s
integration time, they can be
reduced by integration and
averaging just like noise. Fast
temporal drift artifacts are caused
by fluctuations that occur less Figure 17. Detector with slow temporal drift artifacts.
frequently but cause a rapid change.

Fast temporal drift is commonly

manifested as large noise spikes in the uniformity. It usually occurs only with fast detectors, such
as the monitor.

4

foro

Whenever a responsivity sample is
taken, the monitor detector’s
output is measured immediately
before the test detector’s. Thus,
there is a time delay between the
two measurements. If a change in
power level occurs between
measurements, the power
fluctuation correction algorithm
(described earlier) will fail for the
current sample. This type of failure
results in a single noise spike.
Similar in appearance to actual
detector noise, fast temporal drift
can be reduced only by averaging.
Integration probably will not help
in this case.

99.9 100.3

output («)

90.4

feeo

Slow temporal drift is more
bothersome. If the drift occurs
slowly relative to the sampling rate,
slow temporal drift artifacts can
occur. Slow drift can come froma _ Figure 18. 16 run average of detector with slow temporal
number of different sources. For drift.

1994 NCSL Workshop & Symposium 347 Session 5A


INTERFERENCE ARTIFACTS

100.0

Interference is a common problem
whenever coherent light is used.
When an element of the detector
causes multiple reflections or etalon
effects, interference artifacts ma‘ ‘ y yi i

9 y
appear on the responsivity scan i
when coherent light is used. These
artifacts are usually unstable; they
can change location or shape when
a slight change is made to the
detector’s alignment and are e3
wavelength dependent. A detector eS
which exhibits these artifacts |
probably should not be used with I
laser sources because the 3
interference can cause significant
changes in the detector’s calibration
factor. A 4 % change in Figure 11. Detector with interference ring artifact.
responsivity due to interference is
not uncommon. Interference artifacts are frequently caused by the detector’s window.

output («)
076

96.0

925

Identifying interference artifacts is usually a simple task. If a suspicious feature is seen in a
responsivity scan, simply tilt the detector a few degrees relative to the illuminating beam and
perform another scan. If the feature moves or changes shape, it is probably caused by
interference. If the feature stays the same, it may still be caused by interference; try tilting the
detector the other direction or rotating it around the propagation axis of the beam. If the
detector is rotated, a real feature will move with the rotation. Otherwise, it is probably an
interference artifact. Scanning the
detector with a less coherent LED
source of the same wavelength also
identifies interference artifacts:
interference artifacts usually
disappear when a LED is used.
Scanning the detector with a slightly
different wavelength of light should
change the appearance of any
interference artifacts, but a large
change in wavelength can also cause
real features of the uniformity to
change.

output («)
95.0 97.5 100.0

925

4
0.0

Interference Rings - One detector, eS
shown in Figure 11, exhibited
interference rings. The poorly
defined rings were concentric with
the detector’s center. Their
position shifted slightly when the
detector was tilted, and the ring Figure 12. Detector with a point interference artifact.

1994 NCSL Workshop & Symposium 344 Session 5A


Figure 4 shows the detector’s
uniformity in greater detail than in
the overall view. The increased
detail is obtained by raising the
baseline of the surface plot, to 95
% in this case. The viewing angle
was also changed to give a better
view of the features. Figure 5
shoWs the uniformity around the
detector’s center in the greatest
detail. It is obtained by zooming
into the detector’s central area. In
the remainder of this document
only a few of the views will be
presented, and statistical processing

108.9

101.9

ni Nh i\
iit P ee
Jue S ff ys

of Ns
is SHAN md eS

Pe is Ai
ve Beane: hae UE Nee

100.8

Respanatrity («)

907

: 0 SINS
will be described later. $ Yy i NiaKe ALOK me Lr NR
aoe v WR a RX ie SN NN as
OBTAINING AN ACCURATE wag UIA Ny ain
RESPONSIVITY SCAN Sa NY <n

Obtaining an accurate responsivity tae
scan is not trivial. The system is
capable of sampling the responsivity Figure 5, Area around the germanium detector’s center.

accurately, but in certain
circumstances an erroneous model of the actual uniformity can result. There are two main
problems, measurement system errors and aliasing in the sampled data.

Measurement System Errors - Two main sources of error in the measurement system can degrade
the accuracy of the responsivity scan. Noise in the detector and measurement system is one
obvious source. This source of error is reduced by using proper amplification and integrating the
detector’s output with the digital voltmeter. The voltmeter used with the system can integrate for
1, 10, or 100 power line cycles (16.7 ms, 167 ms, or 1.67 s). The longer integration times are
useful with noisy signals. The integration essentially provides a low-pass filter that reduces noise.

Temporal variations in the power, wavelength, or polarization of the optical source can also cause
error in the responsivity scan. The system uses a power fluctuation correction algorithm which
compensates for such variations, with a few caveats. The optical sources used incorporate a beam
splitter and power monitor. Ideally if
the power received by the monitor a
changes, the power transmitted to the ie
test detector also changes by the same Plate Identifier: LD-1320-1 314 pW
amount. The test detector’s output can Plate Wavelengt! h: 1320 nm

Spotsize (x,y): ( 0.450, 0.447) mm

therefore be corrected for the power Spotsize Measured at a Distance of: 15 mm
ge. PI Beamsplitter Ratio: 0.884

fectinique is that the beam splitter ratio Beamsplitter Ratio Standard Deviation: 0.029 %
9 y : Beamsplitter Ratio Spread: 0.125 %

coupler is used as a beam splitter. The Rati Last Measured On: 07-21-1993
coupler and the beam collimator

contribute to the instability. NR
\ Box 1. Example optical source information.

1994 NCSL Workshop & Symposium 340 Session 5A


not much better than
those for the original
0.56 mm beam.

1108

Example 2 - Silicon
detectors usually

have very good

a
uniformity; the x8
detector shown in €
Figure 21 is an =
exception. Its ae
extremely poor .
uniformity makes it a &

more interesting
example. The
detector was scanned
with a 0.56 mm
beam; misalignment
statistics for the scan ee
are listed in Box 5.
The statistics for this
scan are somewhat
worse than those for
the example
germanium detector.

27.8

After synthetically Figure 21. Overall view of example silicon detector.

scanning the detector

with a 4.5 mm beam, the misalignment statistics shown in Box 6 result. In this case, the
misalignment statistics for the larger beam are significantly improved. The statistics for the large
beam scan are even better than those obtained for the example germanium detector.

Figure 22 shows the responsivity variation with beam diameter for the silicon detector. The
graph shows that the responsivity is fairly flat for 4 to 5 mm beams. Analyzing the data for these
beam diameters results in a standard deviation of 0.04 % and a peak-to-peak spread of 0.12 %.
These deviations

are small, but | a
much larger the Stats for Area, Radius: 1.00 mm Stats for Area, Radius: 1.00 mm
example Mean = 100.000 Mean = 100.000
cementum Std. Dev. = 0.372 Std. Dev. = 0.169

a tector Std. Dev. = 0.372 % Std. Dev. = 0.169 %

. Maximum = 101.185 Maximum = 100.347

Minimum = 99.327 Minimum = 99.679

CONCLUSION Spread = 1.858 % Spread = 0.667 % :
A uniformity N= 317 N= 317
measurement ee
system was Box 5. Misalignment statistics for Box 6. Misalignment statistics for
presented here. example silicon detector. silicon detector after synthetic 4.5
Artifacts mm beam scan.

1994 NCSL Workshop & Symposium 351 Session 5A


To simplify interpretation of
the results, the scan data are
usually scaled before 5.000”
viewing. Typically the
lowest point is scaled to 0,
and the average of the
points in the detector’s
center is scaled to 100 %.
Four views of the detector’s
uniformity are commonly
used, a scan of a good
germanium detector is used
as an example in Figures 2
to 5. Figure 2 shows the
overall view of the detector;
it is the easiest to interpret.
This view gives a good
qualitative measure of the
uniformity; if features in the
detector’s active area are
visible in this view they must 3,000
be significant (greater than ~ 6.000 2.600
1 percent), his example, X-Axis Position (mm)
small features are visible so
the detector is clearly not
perfect.

Responsivity (
2.500 0.000

p
&
g
3

Y-Axis Position (mm)
8
3

2.500

Figure 3. Contour map of germanium detector, 1 % contour line
spacing.

Figure 3 shows a contour map of the detector’s uniformity, contours in the active portion of the
detector are spaced closer together
for clarity. This view can be used
to obtain more quantitative
information. The actual size of the
features can be estimated by
counting the number of contour
lines and multiplying by the contour
spacing. In this example, when
moving from the center to the top
of the feature at (x,y) = (0,4) mm,
5 contour increases and 1 contour
decrease are crossed so the
responsivity at the top of the Wirt &
feature is 4 % higher than the 4 be —

106.8

Responsivity (a)
1008 103.4

977

‘ial

responsivity in the center. Contour : ti . ve
a .

ie

lines with hachures, like the line fa a

around the feature at (x,y) = (2,1) ae i

mm, represent a depression as

opposed to a hill. Labeled contours ,
- are drawn with a dashed line.

Figure 4. Germanium detector responsivity over 95 %.

1994 NCSL Workshop & Symposium 339 Session 5A


Control Computer B - Motion Controller

Digital Voltmeter D — Spotsize Detector

X- and Y-Axis Positioning Stages

Optical Source Plate with Monitor Detector

Motion Controller Joystick H — Laser Diode Power Supply
Monitor Detector Temperature Regulator

Transconductance Amplifiers for Detectors

Amplifier Power Supply
Line Printer

pretbyprrag

CAE TOMO D>

®

Figure 1. Main components of the uniformity measurement system.

voltmeters are used to accurately measure the detector’s responsivity, and sophisticated computer
software controls the scan and processes the results.

The measurement system nominally requires an analog voltage output from the test detector, but
detectors with a digital output can be scanned with the help of a second computer. The second
computer reads the digital output and converts it to an analog voltage using a digital-to-analog
converter. A monitor detector is used to correct for power fluctuations during the scan, but the
absolute beam power is not measured so the system cannot be used to calibrate a detector’s
responsivity absolutely. The system
can only measure relative changes
in responsivity.

105.8

The system’s software can
automatically locate the detector’s
center and can integrate and
average multiple scans to reduce
noise. Uniformity measurements
are typically reproducible to 1 or 2
tenths of 1 percent. The system
can run for hours or days without
operator intervention. Scanning
large detectors with a small source
beam can take hours, and averaging
multiple scans can take days. The
resulting scan can be presented in a
variety of formats including contour
maps and surface plots, and a
statistical analysis is available to
quantify the degree of uniformity.

70.8

ey A ie
a, a : vA

Responsivity (a)
$29

Figure 2. Overall view of a germanium detector.

1994 NCSL Workshop & Symposium 338 Session 5A


within 1 mm of the detector’s center can be used to generate uncertainty statistics. The scanning
system software can find these points and generate a standard deviation and peak-to-peak spread
for them. The resulting standard deviation is a measure of how much uncertainty is encountered
when the scanning beam is randomly aligned within the given distance of the detector’s center.
The peak-to-peak result is a worst case measure. Applying the following technique allows
misalignment statistics for beams larger than the original scanning beam to be derived.

Beam Diameter Fluctuation Error - This new technique allows the uniformity for beams larger
than the original scanning beam to be estimated. Ideally the scan should be performed with a
beam the same size and profile that will be used with the detector in practice. This is not always
possible because the measurement system can produce only crude Gaussian beams with a limited
range of sizes. So it is desirable to extrapolate the uniformity for other beam diameters and
profiles from a scan made with the system’s beam. It is also desirable to obtain a measure of how
much the responsivity in the detector’s center will change when the beam diameter fluctuates.

It is possible to obtain these results theoretically if the equivalent of an impulse response for the
detector can be derived. Then an arbitrary beam’s profile can be convolved with the impulse
response to obtain the uniformity for the arbitrary beam. Or a transform from the source beam
to the desired beam can be generated and used to calculate the desired uniformity. These
calculations can be performed with Fourier transforms and deconvolution.’ The scanning system’s
beam profile can be measured by placing a pinhole over a stable test detector. Unfortunately
performing the required transforms has proven difficult

and has not yet been completed. However a method ee

which gives approximate results has been derived. Stats for Area, Radius: 1.00 mm,
a . Mean = 100.000

Responsivity scans are usually performed using the Std. Dev. = 0.289

smallest beam available in the system. The scan made Std. Dev. = 0.289 %

with the small beam can be used as an approximate Maximum = 100,958

impulse response for the detector in certain cases. If the Minimum = 99.436

uniformity for a beam much larger than the original Spread = 1.522 %

small scanning beam is desired, using the small beam N= 317

scan as the impulse response will be accurate. However
it is not accurate for beams close to the size of the
scanning beam or smaller. For these beams the Box 3. Misalignment statistics for
technique will give overly optimistic results because the example germanium detector.
impulse response was not used.

el
Once the impulse response (or approximate impulse s _

tats for Area, Radius: 1.00 mm

response) is found, determining the uniformity for a

desired beam is simple. The desired beam’s profile is Mean = 100.000
convolved with the impulse response to obtain the Std. Dev. = 0.241
’ Std. Dev. = 0.241 %

uniformity for the desired beam. The results may not be

scaled correctly. Beams which contain higher spatial

frequencies than can be resolved by the sample grid will

also give false results; this factor limits how small a beam

can be used. In the following examples, synthetic

Gaussian beams are used. Actual beam profiles could

“have been used just as easily. Box 4. Misalignment statistics for

germanium detector after synthetic 3
mm beam scan.

Maximum = 100.615
Minimum = 99.612
Spread = 1.004 %
N= 317

1994 NCSL Workshop & Symposium 349 Session 5A


typically encountered during
uniformity measurement
were described, and
methods of identifying the
artifacts were detailed. The
procedures should help
others acquire and analyze
responsivity scans. The
scans can help diagnose
problems encountered in
detector and beam
calibrations.

14

Responsivity Change (%)

0.2

Two methods for i
quantifying the degree of 045 1 2 3 4 3 6 7 8
uniformity in a detector Beam Diameter (mm)

were proposed. We hope

that these methods or some _‘ Figure 22. Responsivity variation with beam diameter for example
derivation of them will be silicon detector.

developed by the

measurement community. Examples which show that significant error can be caused by detectors
with poor uniformity were presented. Uniformity artifacts can also be significant, and their
inconsistent nature is likely the cause of many measurement problems. Interference artifacts in
particular are the source of many calibration problems at NIST. A proper treatment of these
error sources could be a benefit to the entire measurement community.

REFERENCES

[1] A. L. Rasmussen, W. E. Case, A. A. Sanders, "Scanning System for Measuring Uniformity
of Laser Detector Response and Laser Beam Dimensions,” Natl. Inst. Stand. Tech.
Interagency Rep., NISTIR 90-3937, pp. 1-13, 1990.

[2} D. Livigni, X. Li, "Spatial Uniformity Measurement of Optical Detector Response,"
Measurement Science Conference Proceedings, Session 4-D, Jan 30, 1992.

[3] J. D. Gaskill, Linear Systems. Fourier Transforms, and Optics, John Wiley & Sons, New
York, pp. 266-272, 1978.

[4] R. E. Ziemer, W. H. Tranter, D. R. Fannin, Signals and Systems: Continuous and
Discrete, Macmillan Publishing Co., New York, pp. 292, 1983.

[5] A. B. Carlson, Communication Systems, An Introduction to Signals and Noise in
Electrical Communication, McGraw-Hill, New York, pp. 297-301, 1975.

[6] W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C.
, The Art of Scientific Computing, Cambridge University Press, New York, pp. 496-532,
“1992.

Contribution of the United States Government, not subject to copyright.

1994 NCSL Workshop & Symposium 352 Session 5A