Measurements of detector nonlinearity at 193 nm

Holger Laabs, Darryl A. Keenan, Shao Yang, and Marla L. Dowell

We have developed a measurement system based on a correlation method to characterize the nonlinearity

of a detector’s response over a large range of laser pulse energy. The system consists of an excimer-laser

source, beam-shaping optics, a beam splitter, a monitor detector, a set of optical filters, and the detector

under test. Detector nonlinearities as large as 10% or greater over an entire measurement range at an

excimer-laser wavelength of 193 nm are observed. The measurement range of the current system is

approximately 300 nJ to 50 mJ of laser pulse energy at the detector under test. The typical expanded

measurement uncertainty of nonlinearity is 0.6% (k  2).

OCIS codes: 040.7190, 120.3930, 120.4800.

1. Introduction

To meet the semiconductor industry’s demands for accurate excimer-laser measurements, we have developed a system for measuring the nonlinear response

of radiation detectors for UV light from an excimerlaser source. This system, which complements other

National Institute of Standards and Technology

(NIST) excimer-laser power and energy calibration

services,1–5 provides a quantitative measurement of

a detector’s response over a large energy range.

Most detectors are typically used over an energy

range that is larger than the range covered by the

calibration. The measurement error is introduced if

the detector response is not linear and the nonlinearity is not quantified. Range discontinuity, e.g.,

due to a change in detector amplification, can introduce additional measurement error. Quantitative determination of these performances of a

detector can improve measurement precision and

the estimation of measurement uncertainty. Possible sources of detector nonlinearity include the dependence of detector response on input signal, the

range discontinuity of the detector system or readout electronics, and background noise.

The energy E of a laser pulse measured by the

detector of an energy meter can be expressed as

E  f(V), (1)

where V is the voltage signal from the detector in

response to the incident laser pulse energy E and fV

is the inverse of the detector response function, V

 gE, and determines the detector nonlinearity.

The term fVis related to the calibration factor F

 VcEc by fVc VcF. Subscript c indicates values

of V or E in fixed calibration conditions. The calibration factor F is determined by comparing the detector

response Vc with that of a NIST primary or transfer

standard, henceforth referred to as a standard, at Ec.

In many practical cases the nonlinear function fVof

a detector can be represented by a polynomial,

f(V)  a0 a1V a2V2 ··· anVn

. (2)

When all the coefficients of a except a1, are zero, the

detector is linear; a0 is the background reading.

There are a variety of methods for characterizing

the nonlinearity of a detector’s response. In the most

straightforward way the comparison method calibrates the detector response against a standard at

several pulse energies. The data are fit to Eq. (1) by

using a least-squares method to determine the function fVor, in the case of a polynomial, the coefficients ai in Eq. (2). Nonzero coefficients of higher

order are a measure of the detector’s nonlinearity.

However, the dynamic range of the comparison

method is limited to the usable energy range of the

standard detector. In addition this method is time

consuming because a full calibration is performed for

each data point. Other more practical methods where

standard detectors are not required are more commonly used in characterizing the response nonlinearities of detectors.6–9

The authors are with the Optoelectronics Division, National

Institute of Standards and Technology, 325 Broadway, Boulder,

Colorado 80305-3328 (e-mail for S. Yang, syang@boulder.nist.gov).

Received 25 August 2004; revised manuscript received 30 September 2004; accepted 3 October 2004.

20 February 2005  Vol. 44, No. 6  APPLIED OPTICS 841
In the superposition method a set of triplet measurements is taken that results in a set of data

V1, V2, V3, where Vi is the detector response owing

to measurement of incident pulse energy Ei:

E3  E1 E2. (3)

If V3  V1 V2, the detector is linear within an

energy range spanned by the three pulse energies.

The triplet measurement is repeated many times at

different energy levels to yield information concerning the detector’s nonlinearity across the entire measurement range. The superposition method has been

used to characterize optical-fiber power meters in the

near-IR wavelength range.6 However, a stable source

of laser power or energy is essential to the superposition method. Therefore it is impractical to apply

this method to excimer-laser detectors because of

large pulse-to-pulse energy fluctuations in most common excimer lasers.

With the attenuation method7,8 the pulse energy is

varied by an attenuator, such as an adjustable pinhole aperture, a moving knife-edge, a chopper, an

absorbing material, or an optical filter. The deviation

of the apparent attenuation, the ratio of the detector

outputs corresponding to the attenuated and notattenuated beam inputs, from the true attenuation of

the attenuator is a measure of detector nonlinearity.

So this method requires the attenuation of the attenuator to be precisely determined, stable, and durable. To determine their attenuation, geometrical

attenuators require prior knowledge of the laser

beam profile.7 The unstable pulse-to-pulse output

and spatial beam profile of the excimer laser and the

damaging effect of high-power UV light on optical

materials make it difficult to implement the attenuation method with desired uncertainty for detector

linearity measurement in the UV region with an excimer laser as the source.

We have developed a new method dubbed the correlation method and a measurement system based on

this method, where the response of a device under

test (DUT) is compared with a monitor detector

whose response is linear within a limited range. The

correlation of the two detectors’ signals provides a

quantitative measurement of the nonlinearity of the

DUT. One challenge of this method is minimizing the

uncertainty in the characterization of the monitor

detector’s linearity such that its contribution to the

overall uncertainty is minimal.

2. Determination of Detector Nonlinearity by the

Correlation Method

In laser calibration, instead of Eq. (1), energy E is

alternatively expressed as9

E  V

F CF(V)

, (4)

where CFVis called the correction factor, which

accounts for the effect of detector nonlinearity and is

therefore an appropriate representation of detector

nonlinearity. Unlike other methods the correlation

method measures CFVin Eq. (4) directly to characterize detector nonlinearity. Using CFVto express

detector nonlinearity implies that the nonlinearity is

determined with reference to the calibration point Vc

of the detector, where the calibration is performed. In

other words, calibration factor F has been determined, and the correction factor CFVcis one by

definition. However, the response nonlinearity is a

relative property of the detector; that is, a multiplication factor applied to CFVdoes not change the

nonlinearity behavior that it represents, and therefore the reference point can be any point that is convenient. So when CFVis used purely for the purpose

of expressing detector nonlinearity instead of correcting the calibration factor, the calibration point Vc

may be replaced by a reference point Vr. When it is

necessary to indicate which specific reference point Vr

is used, CFVmay be expressed as CFV; Vr. The

detector response is linear if CFV 1.

The correlation method requires a monitor detector

with linear response, which receives part of the laser

beam from a beam splitter. The energy E of the beam

incident on the test detector is related to the detector

output V through Eq. (4) and is linearly proportional

to the corresponding output Vm of the monitor detector, which is linear:

E  Vm. (5)

Factor  is a constant determined by the response of

the monitor detector, the beam-splitter ratio, and the

attenuation of the optical components in both beam

paths. Eliminating E in Eqs. (4) and (5) gives

CF(V)  V

F

1

Vm

. (6)

Equation (6) holds for all V and Vm including the

reference point as long as  is constant. The correction factor is one at the reference point, where the

outputs of the test and the monitor detectors are Vr

and Vmr, respectively:

CF(Vr)  Vr

F

1

Vmr

 1. (7)

Equations (6) and (7) lead to

CF(V)  V

Vm

Vmr

Vr

. (8)

Dictating how the correction factor is measured,

Eq. (8) is the basic expression for the correlation

method. The measured CFVcan easily be expressed

with a new reference point, say the calibration point

Vc when the calibration has been performed:

842 APPLIED OPTICS  Vol. 44, No. 6  20 February 2005
CF(V; Vc)  V

Vm

Vmr

Vr

Vr

Vmr

Vmr

Vc

 CF(V; Vr)

CF(Vc; Vr)

. (9)

The correlation method is valid with the assumption that the monitor detector is linear. However,

most, if not all, detectors are to some degree not

linear. The chosen monitor detector is measured to be

linear with some uncertainty. Usually the wider the

range of a detector to be used, the larger its nonlinearity or the uncertainty with which it is tested. To

minimize the effect of its nonlinearity, the monitor

detector should be used within a limited range, e.g.,

no more than one order of magnitude. Since the range

of the detector to be tested is usually much larger

than this limited range of the monitor, the nonlinearity over the entire range of the test detector is measured in several measurement spans, each

corresponding to the same limited monitor detector

range. For one measurement span to be changed to

the next, the optical filters in the DUT beam path

have to be varied while the monitor path is kept

unchanged. So, the factor  in Eq. (5) can be kept

constant only within one span and is different from

one span to another. Furthermore there is no single

reference point common to all the spans. Therefore

Eq. (8) cannot be used for all the spans. To express

the nonlinearity CFVfor all the measurement

spans with a single reference point, we use partially

overlapped spans. When one span of measurement is

completed where the reference point common to all

the measurement spans is to be located, we adjust the

attenuators so that the next span has a small region

to overlap part of the previous span. In the region

common to both spans a point Vr can be picked to

serve as a transitional reference point for the new

span. Instead of Eq. (7) we now have in the new span

CF(Vr)  Vr

F

1

Vmr

. (10)

CFVrwas determined in the previous span of measurement and does not in general equal one. Replacing Eq. (7) with Eq. (10) in the derivation of Eq. (8),

we now obtain Eq. (11) for the spans of measurements that do not include the common reference

point Vr:

CF(V; Vr)  V

Vm

Vmr

Vr

CF(Vr; Vr)

 CF(V; Vr)CF(Vr; Vr). (11)

With Eqs. (8) and (11) the nonlinearity measurement

can be extended to the entire range of the detector

with a single common reference point Vr.

The correlation method determines the correction

factor CFVat discrete points. Correction factors at

intervening points can be obtained by interpolation or

curve fitting. Together with the absolute calibration

at one or a few points the detector is now calibrated

over the entire range covered by the nonlinearity

measurement.

3. Calibration System and Procedure

Figure 1 illustrates our calibration system consisting

of an ArF excimer laser, beam homogenization optics,

the monitor detector, the standard detector, a beam

splitter, and a set of attenuators. The laser has a

pulse width of 10 ns and maximum pulse energy of

100 mJ. Effects due to spatial fluctuations in the laser

beam intensity are removed by incorporating beam

homogenization optics into the optical path of the

calibration system.5,10,11 However, beam homogenization is not essential in the correlation method if the

beam size is smaller than the DUT sensor, and the

monitor sensor detector uniformity is not a concern.

The dimensions of the square-shaped laser beam profile 13  13 mmare selected such that a variety of

DUT sizes can be accommodated. In addition the

beam size can be adjusted so that the active region of

the DUT is either overfilled or underfilled. The maximum laser pulse energy incident on the test detector

is 50 mJ and the minimum pulse energy 300 nJ,

determined by the maximum attenuation. The monitor detector is used in the range of 3–30 mV of its

output.

Because of the instability of the pulse energy of the

UV excimer laser, the measurement data exhibit

large noise. To reduce the effect of the noise, hundreds of data points are acquired. Also, because of the

noise, we do not use any particular data point as the

reference of the measured CFV. Instead we use a

virtual point, which is the average of the measurement results, as the reference. This approach is based

on the understanding that nonlinearity is a relative

feature of the detector as we mentioned above.

Although it is not necessary, measurements of the

correlation method usually start with the highest or

lowest meter range to be characterized. When the

first measurement span is completed, filters are adjusted for the next span, which has part of its range

Fig. 1. Nonlinearity measurement system. The laser power

change, shutter operation, filter set change, and data collection

from DUT and monitor detector are controlled by the computer.

The measurement process is fully automated.

20 February 2005  Vol. 44, No. 6  APPLIED OPTICS 843
overlap with part of the previous span. The common

region of the two adjacent spans serves to extend the

CFVmeasure from one span to the next with reference to the same point. The measurement span range

does not usually coincide with the DUT meter ranges.

So in the middle of some of the spans it is necessary

to switch the meter range, and a gap due to the range

discontinuity of the meter in the CFVplot may appear. Figure 2 illustrates the measured DUT and

monitor output data pairs for two spans. The two

spans cover more or less the same output range on

the vertical scale that is the monitor output. The

DUT output on the horizontal axis extends for 1.5

orders of magnitude with overlaps between neighboring spans. Figure 3 is the measured CFVof the two

spans, each with reference to its own average. The

range discontinuity can be seen on Span 1.

The measured CFVfor all the spans on the same

DUT do not have the same reference point after the

data acquisition as shown in Fig. 3. In principle we

can use Eq. (11) to make all the CFVreferenced to

the same point Vr via points Vr in the common regions of neighboring spans. However, because of the

noise, one single point Vr in the common region

causes large uncertainty in the use of Eq. (11). A

sizable number of data points in the common region

make it possible to match the common regions of the

two adjacent spans statistically. Apply a multiplication factor to the span that does not contain the desired reference point Vr until the statistical difference

in the data in the common region of the two spans is

minimized. Figure 4 is the result of this statistical

match of the two curves in Figure 3. This process is

repeated until the farthest measurement span is

reached.

The next step in data processing is curve fitting.

With a gap between neighboring ranges of the detector meter, curve fitting should be applied to each

meter range separately. Although other functions

may be used for the curve to be fitted, we found that

a polynomial is almost always sufficient for the purpose. In the data-processing program we fit the CFV

data with several different orders of polynomials at

the same time. A statistical F-test number is listed

along with plots of the fitted curve on top of the CFV

data points. The F-number together with visual observation determines which order of polynomial is

accepted. Figure 5 shows the curve-fitting results of

our example.

If the absolute calibration of the detector is performed, whether before or after the nonlinearity measurement, we can extend the calibration to the entire

meter range with the nonlinearity information by

simply finding CFVcfrom the fitted curve and using

it in Eq. (9). Absolute calibration has a lower uncertainty than nonlinearity measurements, especially

when the nonlinearity measurement extends to several spans. However, the latter is faster and gives

complete information in the entire measured range.

Fig. 2. Example of measured data pairs of the voltage outputs

from the monitor detector and DUT in two measurement spans.

The output of the monitor detector for the two spans is within the

same voltage range, while the output of the DUT for the two spans

is extended through approximately 1.5 meter ranges with a small

common region. The DUT meter range changed at a DUT output of

3 mV during data collection for Span 1.

Fig. 3. Calculated nonlinearity of CFVof the two spans. Each

span has the average CFVas its reference point. The range

discontinuity at 3-mV DUT output is distinctly seen.

Fig. 4. Nonlinearity CFVof the two spans is matched by moving

the data of Span 1 to minimize the difference in the common

region. The basic feature of the nonlinearity does not change in the

match. The result is the same if we move the data of Span 2 to

perform the match, but the vertical scale is different.

844 APPLIED OPTICS  Vol. 44, No. 6  20 February 2005
When a detector is to be characterized in a wide

range, the overall uncertainty may not meet the required specification if absolute calibration is performed at only one point Vc and calibration is

extended to points far from it with nonlinearity measurement. It may be necessary to run absolute calibration at points in more than one measurement

range of the detector to meet the uncertainty specification.

The optical detectors might have a background

reading even when they receive no laser light signal.

This background signal could be caused by ambient

light, acoustic or rf interference, or an offset in the

electronic circuitry. A special problem in this respect

with the laser pulse meters is that, in measurements

with input signal triggering, the background is hidden; that is, it does not show up because the noise is

not high enough to trigger the meter. We used pulses

with the same repetition rate as the laser signal to

trigger the pulse meter externally to characterize the

statistical distribution of the background reading,

which is expected to be or close to Gaussian. Because

the background is close to zero, noise associated with

it may spread to negative values. Evaluation of its

mean value may not be as simple as averaging a

number of readings because many meters do not display negative readings. For meters without negative

readings the Gaussian is truncated at zero and the

full Gaussian should be reinstated. The mean value

of the background that may affect the measurement

signal is the peak of the Gaussian, truncated or not,

instead of the average of the readings. The background uncertainty is the standard deviation of the

full Gaussian. Background characterization may

have to be carried out at each meter range because it

might be different for each range. Figure 6 shows an

example of the background output of a pulse laser

energy meter measured with external triggering.

The effect of the background on the signal output is

a complex combination of the origin(s) of the background, its characteristics (frequency spectrum and

phase), and signal processing. In many cases its effect

may not be corrected with simple subtraction of the

measured background from the signal. The effect of

background signal is better treated as part of detector

nonlinearity. Since the effect of background reading

depends on the environment of the meter application,

the characterization of the background or the detector nonlinearity should be carried out in similar conditions.

4. Uncertainty Assessment

The overall uncertainty of CFVis composed of the

uncertainties of individual components in Eqs. (8)

and (11). The data pair of V and Vm is partially correlated because it varies simultaneously with laser

output fluctuations. So uncertainties in the ratios of

these data pairs, instead of uncertainties in the individual data, are the real contributors to the total

uncertainty. For the same reason the uncertainties in

the ratios that we have observed so far are between

0.5% and 1.5% depending on the DUT and the ranges

used; the uncertainties are much smaller than those

of the individual datum even though the pulse-topulse spread of the laser output is more than 10%.

This is the primary source of the measurement uncertainty of the correlation method. The secondary

sources are statistical matching of the common regions of adjacent spans and curve-fitting uncertainties. Another source of uncertainty is the assumption

that the monitor detector is linear.

The uncertainty in the statistical matching of the

common regions of adjacent spans can be estimated

by 1

2

n1 2

2

n2

12

, where 1 and 2 are the

standard deviations of VVm in the matching regions

of the two adjacent spans and n1 and n2 are the number of data points in the two regions. With the typical

number of n1 and n2 being 25 and 1 and 2 1% the

matching uncertainty is 0.28%. Each time when two

spans are matched this uncertainty should be estimated and added to the total uncertainty of the next

extended span.

Fig. 5. Curve-fitting results (solid curve) of the matched CFV

data in Fig. 4. Curve fitting is done separately in the two ranges.

The range discontinuity is 3%. The dashed curves along the fitted

curve are the limits of uncertainty k  2.

Fig. 6. Monitor detector background reading test result. The frequency of the pulse energy meter output has a truncated Gaussian

distribution with the peak at 17 V and a standard deviation of

29 V. The frequency of a zero reading of 601, which accounts for

the frequencies of true zero and all the negative readings, is not

shown.

20 February 2005  Vol. 44, No. 6  APPLIED OPTICS 845
The uncertainty in the curve-fitting result is calculated by using the normal statistical procedure.12 In

Fig. 5 the two dotted curves above and below the solid

fitted curve show the expanded uncertainty k  2of

the fitted curve, where the maximum uncertainty

k  1is 0.1%. The data-processing program includes the calculation of the uncertainty of the curvefitting result.

To verify its linearity, the monitor detector was

tested against several other detectors, i.e., its response was measured against various other detectors

including a primary standard calorimeter in the

same measurement system of this correlation

method. If the responses of detectors of various combinations were highly linearly correlated, i.e., the

best fit of CFVwas a horizontal straight line at 1,

either all the detectors had identical nonlinearity or

they were all linear in response within the measurement uncertainties. The more detector combinations

tested, the smaller the chance of having detectors

with the same nonlinearity. Figure 7 is an example of

the test of the linearity of the monitor detector. Although the data are quite noisy the uncertainty in the

linear fitting is very low, 0.05%, because of the large

number, 930, of data points.

The linear correlation uncertainty is the combination or statistical sum of the uncertainties of data

from the two test detectors. If one of the detectors is

perfectly free of noise and linear, this combined uncertainty is contributed purely from the other test

detector. Therefore the best estimate of the test uncertainty of the monitor detector nonlinearity is the

smallest number of combined uncertainties where

the monitor detector is one of the test components.

If CFVis used purely for nonlinearity characterization, the total uncertainty is the combination of

the uncertainty of the fitted curve, the matching uncertainty if any, and the uncertainty of the monitor

detector nonlinearity. However, if it is used as a correction factor of the calibration factor F in Eq. (4), the

uncertainty in CFVcmust be added onto the uncertainty estimated for the nonlinearity feature. The

estimation of the uncertainty in CFVcis the same as

for any other point but without the uncertainty of

statistical matching. The typical total expanded uncertainty k  2with one scan matching is 0.6% for

nonlinearity CFVand 0.63% for calibration factor

correction.

There are two types of uncertainties when the contributions are assessed from different sources.13 Type

A uncertainties are those that can be directly assessed by statistical methods from the measurement

data. Type B uncertainties are those estimated based

on scientific judgment when all the relevant information available is used. Uncertainties in the correlation method are all Type A.

5. Measurement Results

Figures 8–11 are the final fitted curves of the measurement results of four UV pulse energy meters

with pyroelectric detectors of different manufacturers. Figures 8–11 have the same vertical scale to

Fig. 7. Linear correlation between the monitor detector and one

of the reference detectors: Top, measured data; bottom, calculated

CVVand the fitted curve. The fitted curve coincides with the

horizontal line of CF  1. With 930 data points the fitting uncertainty is very low, although the data are quite noisy.

Fig. 8. Measured detector nonlinearity of Detector 1. The measurement covers one meter range. The nonlinearity in this range is

2.5%. The maximum expanded uncertainty k  2is 0.2%. The

sharp change in the middle of the uncertainty curve is due to the

measurement span match.

846 APPLIED OPTICS  Vol. 44, No. 6  20 February 2005
make it easy to compare the magnitude and behavior of the nonlinearities of these detectors. Each

detector was measured in more than one span. In

Figs. 9–11 the meter measurement ranges are separated by thick black vertical lines where the range

discontinuity can be estimated. Because the nonlinearity CFVat one particular meter output depends on the calibration or reference point of the

measurement, and that point is different for the

detectors shown, it is more appropriate to look at

the overall (minimum-to-maximum) performance of

the nonlinearity of the detectors. The four detectors

were measured at different energy levels that do

not cover their full measurement ranges, so the

results shown here may not represent the general

performance of each detector. Detector 1 was measured in one range of the meter with two measurement spans. The nonlinearity in the measured

range was 2.5%. The uncertainty with a sharp

change at the middle of the curve was due to matching of the two measurement spans. There were similar changes of uncertainty in Figs. 9–11 although

many were not easily discernible due to the small

matching uncertainty. Detector 2 in Fig. 9 shows

the best nonlinearity performance with 2% overall

nonlinearity over approximately two meter ranges.

Its range discontinuity was also very small. Detector 4 in Fig. 11 also showed a small nonlinearity of

less than 2% in its highest meter range (300 mV to

3 V). However, it exhibited a dramatic increase in

nonlinearity when the output voltage decreased to

less than 50 mV. Its nonlinearity reached more

than 10% at 10 mV. This nonlinearity behavior is

typical of the existence of background response, and

this detector does not have the function of background subtraction. Detector 3 also exhibited similar behavior. The large nonlinearity at the lowest

end of the meter measurement range of these two

detectors indicated that the background effect

might be common in pulsed energy meters. Background readings did not register when the magnitude of the noise was not large enough to trigger the

meter reading. This effect caused the background to

be ignored in the absence of the signal. However,

background was present as part of the output when

the meter was triggered by large signal pulses.

These examples do show that nonlinearity measurement can reveal the existence of the background and correct its effect on the measurement.

Detectors 3 and 4 also had a large range discontinuity from 0.5% to 2%. The range discontinuity

showed up automatically in the resulting CFV

during the measurement by switching the meter

range at appropriate energy levels. This is one of

the advantages of the correlation method over the

other methods, where an extra step of measuring

range discontinuity is required.6

Fig. 9. Detector 2 measured in two meter ranges. The nonlinearity in Range 1 is 0.6% and 1.4% in Range 2. A range discontinuity

of 0.3% can be seen.

Fig. 10. Measurement of Detector 3 covers one full and two halfmeter ranges. This detector exhibits a much larger nonlinearity

(8%) and range discontinuity (2%). The nonlinearity behavior is

almost the same in the three ranges and has a feature of the effect

of background readings.

Fig. 11. Measurement of Detector 4 covering approximately 2.5

meter ranges. In Range 1 the detector has a relatively small nonlinearity of 0.4%. In the higher half of Range 2 the nonlinearity

is very small, 0.2%, but in the lower half the nonlinearity increases significantly with a decreasing output reading. This is

typical of the background effect. This feature of background effect

continues in Range 3. The overall nonlinearity is more than 10%.

The range discontinuities are also high at approximately 1% and

2%.

20 February 2005  Vol. 44, No. 6  APPLIED OPTICS 847
6. Conclusions

We have developed the correlation method and a corresponding system to measure optical detector nonlinearity in the UV range. With this method we have

measured directly the correction factor CFVon the

calibration factor F. The correlation method reduced

the effect of the large pulse-to-pulse fluctuations of

the excimer UV laser and delivered results with acceptable measurement uncertainties. Measurements

where this method was used revealed nonlinearities,

range discontinuities, and effects of background reading of some UV detectors. The method and the system

extend the calibration of UV detectors to several decades of measurement ranges with reasonable uncertainties.

H. Laabs gratefully acknowledges the support of a

Feodor-Lynen fellowship from the Alexander von

Humboldt Foundation. H. Laabs had a guest researcher agreement with the National Institute of

Standards and Technology from June 2000 until May

2002.

We thank Robert Phelan for insightful discussions

of the background effects of pyroelectric detectors.

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848 APPLIED OPTICS  Vol. 44, No. 6  20 February 2005