»'•' " 'o.

\

*<'»eAU o»

\

NBS TECHNICAL NOTE 1010

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress March 3, 1901. The

Bureau's overall goal is to strengthen and advance the Nation's science and technology and

facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is performed by the National Measurement Laboratory, the National Engineering Laboratory,

and the Institute for Computer Sciences and Technology.

THE NATIONAL MEASUREMENT LABORATORY provides the national system of

physical and chemical and materials measurement; coordinates the system with measurement

systems of other nations and furnishes essential services leading to accurate and uniform

physical and chemical measurement throughout the Nation's scientific community, industry,

and commerce; conducts materials research leading to improved methods of measurement,

standards, and data on the properties of materials needed by industry, commerce, educational

institutions, and Government; provides advisory and research services to other Government

Agencies; develops, produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

Absolute Physical Quantities^ — Radiation Research — Thermodynamics and

Molecular Science — Analytical Chemistry — Materials Science. THE NATIONAL ENGINEERING LABORATORY provides technology and technical

services to users in the public and private sectors to address national needs and to solve national problems in the public interest; conducts research in engineering and appHed science

in support of objectives in these efforts; builds and maintains competence in the necessary

disciplines required to carry out this research and technical service; develops engineering data and measurement capabilities; provides engineering measurement traceability services; develops test methods and proposes engineering standards and code changes; develops and

proposes new engineering practices; and develops and improves mechanisms to transfer

results of its research to the utlimate user. The Laboratory consists of the following centers:

Applied Mathematics — Electronics and Electrical Engineering^ — Mechanical

Engineering and Process Technology^ — Building Technology — Fire Research —

Consumer Product Technology — Field Methods.

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts

research and provides scientific and technical services to aid Federal Agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and

economy in Government operations in accordance with PubHc Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing the Federal Information Processing Standards Program, developing Federal ADP standards

guidelines, and managing Federal participation in ADP voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal Agencies; and

provides the technical foundation for computer-related policies of the Federal Government.

The Institute consists of the following divisions:

Systems and Software — Computer Systems Engineering — Information Technology.

'Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D.C. 20234. 'Some divisions within the center are located at Boulder, Colorado, 80303.

The National Bureau of Standards was reorganized, effective April 9, 1978.
Measurement of Pulsed-Laser Power

M. Young

K.A. Lawton

Electromagnetic Technology Division

National Engineenng Laboratory

National Bureau of Standards

Boulder, Colorado 80303

Work supported in part by

Aerospace uuiaance ana Metrology Center

Newark AFS, Ohio 43Ub5

iUaiibration Order : MLTO FL 36 78-14)

*t*^ \

f^^

^^.

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued February 1979
NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 1010

Nat. Bur. Stand. (U.S.), Tech. Note 1010, 40 pages (Feb. 1979)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 1979

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Stock No. 003-003-02028-1 Price $1.60 (Add 25 percent additional for other than U.S. mailing)
I

Measurement of Pulsed-Laser Power

M. Young and R. A. Lawton

We describe calibrating several optical-pulse power meters

to an accuracy of about 8% or better. The meters are designed

for Q-switched neodymium lasers with peak powers in excess of a few megawatts and pulses longer than five or ten nanoseconds.

Combined with a fast oscilloscope or a transient digitizer, the

meters display the time-domain waveform of the laser emission and

thereby allow determination of parameters such as transition

duration (risetime, falltime) , duration and peak power. We

discuss calibrating the meters by both pulsed and cw methods, and

show why each method is useful as a check on the other. We treat

in some detail the effect of speckle on the use of diffusers as attenuators in power meters such as ours.

Key Words: Attenuators; calibration; laser; neodymium laser;

peak power; power meter; pulsed laser; Q-switched; risetime;

speckle; waveform.

1. Introduction

In this report, we describe the evaluation and calibration of three pulsedlaser power meters. The meters are designed to display in the time domain

the instantaneous power of the pulses emitted by Q-switched YAG lasers; the

pulses may be as short as 10 ns or so, with average energy densities up to about

-2

0.5 J cm . Knowing the time-domain waveform, we may determine parameters

such as the duration and the peak power of the pulse.

The meters employ two reflecting diffusers for attenuation. The attenuated

pulse irradiates a fast (0.5-ns duration) silicon photodiode held at a fixed

temperature. The output waveform may be displayed on a fast real-time oscilloscope or on a transient digitizer when computer processing of single pulses

is required.

In the body of the report, we discuss the absolute calibration of the power

meters, by both pulsed and cw methods; the two results agree to within the

estimated experimental error. We also discuss in some detail the effect of

speckle on the use of diffusers as attenuators.
2. Power Meter Design

For this project, we calibrated several existing power meters; these

meters had been designed and constructed by another group at NBS and are described here for completeness.

Figure 1 is a photograph of one of the meters. Figure 2 shows the

same meter with the top removed. On the left of the figure is a diffuser

that is used for attenuation of incident, megawatt pulses; the right side

of the figure shows the circuit board for biasing two photodiodes and

controlling their temperature. Figure 3 displays the meter with the front

panel removed to show the boxes that contain the photodiodes. These boxes

contain a second diffuser for additional attenuation, as shown in figure 4.

Figures 5 and 6 are schematics of the power meter and the second-diffuser

box. The heavy lines represent a principal ray (which enters through the

center of the aperture stop). The first diffuser scatters the beam, and

a very small portion of the energy passes through the hole in the second

diffuser box and falls on the second diffuser. Some of the light scattered

by the second diffuser falls on the active area of the photodiode. The

resulting photocurrent is displayed on a transient digitizer, yielding a time-domain representation of the laser power.

The diffusers had been made of Eastman white reflectance coating [1],

primarily because of its ready availability in any size. This barium-sulfate

paint has a very high, diffuse reflectance and is nearly a Lambertian surface [2"

Therefore, little error will be introduced if the incident laser beam enters the

meter at a slight angle; this need not be the case with a weak diffuser, such as ground or etched glass, whose scattered light is strongly peaked in the directions of specular transmission and reflection.

Damage-threshold tests were performed with the 25-ns pulses emitted by a particular Q-switched YAG laser. An audible pop occurred at energy densities in

-2 excess of 600 mJ cm . We define this energy density as the damage threshold

for pulses of this wavelength and duration. Shorter pulses may have lower

damage thresholds (measured in terms of energy density) owing to their higher

peak powers.
u

0) u

0)e

5-1 0)

15O

OJ

CO iH

=!

o

60

•H

>

O

e

cu

5-1

(Uu

A-i

5-1 CUa

cd

4-1 •H

0) •H>

O

5-1

cu

5-1

•H
Figure 4. Top view of diffuser box with cover removed. %
61

4.3

in

Figure 5. Optical-pulse power meter, showinj

diffuser and second-dif f user box.

All dimensions are in centimeters

6.4

00

0.50 DIA

Output \—f^ Bi as

Figure 6. Second-dif f user bo X .
(_)

O J—

Q_ n: I—

s: oo c3 00 O LU I—< UJ

Oh

CO

OJ

ISO

Pn

COCO •HrQ

<UO

•H^3O

+JO^

Pu

cau

(U iH

iHOU

4JoOt

cfl

0)§•'

(Uoo

•Hu

COeo

CO

CU

C>0 •H

P>4
The photodiodes are Hewlett-Packard 5082-4207's [3]. Each meter is equipped

with two photodiodes in separate diffuser boxes. The temperatures of the boxes

are stabilized at about 50°C to ensure that the responsivity of the diodes will

not change with changing ambient conditions. Figure 7 is a schematic of the

circuit used to control the temperature. A power transistor is used to elevate

the temperature of the photodiode; the dashed lines in the figure indicate

close thermal contact among the power transistor, the photodiode and the

thermistor that is used to monitor the temperature of the box. (The red and

green LED' s are used for visual indication that the temperature has stabilized;

when both LED's remain bright, the meter is ready to use. The LED ' s are seen through the holes shown in the top of figure 1.)

The impulse response of the power meter is its output waveform when the

input is a very short optical pulse (in principle, a delta function) . The meter

will display an accurate representation of an optical pulse only if the duration

of the pulse is long compared with the impulse response of the meter.

Figure 8 shows the impulse response of a typica^ photodiode in series with

the transient digitizer. To determine the impulse response, we used a modelocked YAG laser whose pulse duration was about 50 ps. The duration of the

waveform shoiim in figure 3 is about 1.3 ns, measured between the points at

which the photocurrent is 1/e times the peak value. (Because of the high

attenuation coefficient of the entire power meter, we could not display the

impulse response of the meter itself. A simple calculation shows, however,

that the difference in transit times between the principal ray and a marginal

ray from an extreme position on the first diffuser is about 40 ps, or one order

of magnitude less than the impulse response of the photodiode.)

Because the diffusers are good Lambertian reflectors, we can estimate the

attenuation coefficient of the power meter fairly accurately [4] . If a small

2 plane scatterer has apparent radiance L and area dS, then the power d (}) radiated

at angle 9 to the normal and into a solid angle d^ is

d^(j) = L dS cos dn . (1)
160

CO 4J iHO>

•HiH

r-i •H6

E-i H

!=> O

100

TIME (nanoseconds)

Figure 8. Impulse response of one of the photodiodes, convolved

with the impulse response of the transient digitizer.

10
If the source approximates a Lambert radiator, then L is not a function of 0.

The total power radiated into the hemisphere is ttL dS . Therefore, the fraction

2 radiated into the solid angle dfi is d (J)/7tL dS, or

dA cos 0/TTr^ (2)

where dA is the area of the aperture through which the radiation is detected

and r is the distance between the aperture and the scatterer.

For our power meter, 9 is zero for both reflections. The diffuse reflectance of the paint is 0.98 at 1.1 ym [2]. Thus, using the dimensions

shown in figures 1 and 2, we find that the attenuation coefficient is approx-

-9

imately 4 x 10

According to the manufacturer's specifications, the responsivity of the

photodiodes is about 0.08 A/W at 1.06 ym [3]. Therefore, we expect an overall

)on-

^-10

responsivity of about 3 x 10 A/W. The mean value of the measured responsivities of three power meters containing six detectors is about 2.3 x 10

all values fall within 15% of their mean.

3. Speckle

The use of diffusers as attenuators is complicated slightly, when the light

is coherent, by the appearance of speckles in the scattered light field. The

presence of speckles will contribute to fluctuations in the output of the power

meter because the laser-beam profile differs from shot to shot and possibly

because successive shots hit slightly different points on the diffuser.

To estimate the effect of speckle, we consider a diffuser illuminated

by a laser beam whose radius is r, ; the diffuser scatters the beam through an opening whose radius is r„. The average size of speckles in the plane of the

hole is determined solely by the wavelength of the radiation, the distance of

the hole from the diffuser, and the size of the illuminated patch of the diffuser. One of us (Young) has shown that the average speckle size (measured,

say, between half-intensity points) is about

11
0.8 X£/r^, ^^^

where i is the distance between the diffuser and the observation plane [5].

The average number M of speckles that passes through the hole is therefore

M = (r^r2/0.8 Xil)^ (^>

assuming that the diffuser and the hole are circular.

a of

If we treat speckles as discrete entities (like balls) and assume that

they obey a Poisson distribution, we conclude that the standard deviation o

a large number of independent measurements is K\ Expressed as a fraction of M,

the standard deviation is

a/M = M'^ = 0.8/N,

where N = r^r2/AJl is a sort of Fresnel number,

(5)

In an elegant theoretical review. Dainty has shown that the fractional

standard deviation of a normal speckle pattern should be about 1/N^, which is in

surprisingly good agreement with the simple estimate we have presented [6]

.

Edwards has very briefly discussed an experimental determination of the standard

deviation which seems to be in rough agreement with ours and with Dainty's when

N is large [7]

.

If we wish to keep fluctuations due to speckle noise down to 1 or 2%

of the mean, then eq (5) shows that we must allow about 10,000 speckles to pass

through the hole in the diffuser box and another 10,000 speckles to fall on the

detector. To meet the first requirement, we must illuminate the first diffuser

with a beam whose diameter is at least 3 cm. The number of speckles that fall

on the detector is determined by the geometry of the diffuser box to be about

6000; the standard deviation is about 1.3% of the mean. Overall, we might

expect speckle to contribute to an uncertainty of a few percent.

To measure the effects of speckle and possibly diffuser nonuniformity, we

scanned the first diffuser of each of three meters with a continuous, 1-watt

12
YAG laser. We placed the meter on a table that could be moved by stepping

motors in two orthogonal directions. The YAG laser illuminated a spot about

1 cm in diameter on the diffuser.

We chopped the laser beam at the rate of 120 Hz and detected the current

with a lock-in amplifier preceded by a current amplifier. We scanned the entire

face of the diffuser in 0.25-cm increments covering a 7.5-cm square.

We used digital electronics to record the position of the power meter, the

output of the power meter, and the output of a reference detector that accounted

for fluctuations in laser power. A minicomputer normalized the power meter

output to that of the reference detector and plotted the results as a function

of X and y, as shown in figure 9. An additional run was made with the power

meter stationary to test for the effect of noise in the detectors.

After scanning the data by eye and eliminating points that were obviously

off the edge of the diffuser, we calculated the mean and sample standard

deviation s for each diffuser. (In this paper we use s to denote the standard

deviation of a sample that contains n observations and a to denote the standard

deviation of the entire population. s and a are related in that s is used

to estimate a.) Table 1 shows the values of s and of the maximum deviation

A from the mean. The results show that the combined effects of speckle and

max

nonuniformity are of the order of 4 to 5%; detector noise accounts for

less than 1% of the fluctuation. For most consistent results, the power

meters should be illuminated with a spot somewhat larger than 1 cm, as suggested

above; the larger the spot, the less the fluctuation due to speckle noise.

Table 1. Results of diffuser nonuniformity scan.

, „^ . , Maximum Deviation Sample Standard

Meter Deviation s max

NWK 1 4.8% 9%

NWK 2 5.0 12

NWK 3 3.7 10

13
NWK 1

NWK 2

NWK 3 o

tiao

CO

!>^

4-1 •Huo

•H CO C U

4-1 ^ e

4-)

M-lO

CO +J iH

CO

uO

Pi 4-»

CTi

(U^4

bO

•H

14
4. Absolute Calibration

To determine the relationship between the instantaneous laser power and

the power-meter output (as measured by the digitizer), we calibrated three of

the power meters with a pulsed YAG laser and a computer processing system. The

impulse-response duration of the power meter was much less than the duration of

the laser pulse.

We also verified the results by calibrating the meters with a continuous,

J-watt YAG laser and lock- in amplifier techniques.

As yet, there is little calibration history on these meters. We therefore

icommend that others who build similar meters use them in conjunction with a ilibrated energy meter until sufficient history exists that confidence may be

Laced in the calibration of the power meters. The main difficulty we can

)resee may be in the use of the white paint. Whereas this paint is designed

a reflectance standard for use in colorimetry and spectrophotometry, and

)r use in integrating spheres, it may be degraded by high-power laser beams.

Pulsed-Laser Calibration . Figure 10 shows the arrangement used for the

ilibration of the meter with a pulsed laser. The laser beam is split approxitely fifty-fifty; one half is directed into the power meter and the other

ilf into a calorimeter. The calorimeter has been calibrated against the

National Bureau of Standards C-series calorimeter [S] . The beam splitter, a quarter-wave stack designed for use in a glass laser cavity, is calibrated in

place as we discuss below. We shall also discuss measurement errors and systematic

.errors below.

The laser is operated in a single-shot mode. Each pulse carries about

>0 mJ . The output of the power meter is acquired by a transient digitizer and

recessed by computer. Figure 11 shows the response of the power-meter-andransient-digitizer combination to a typical pulse. When correctly calibrated,

le vertical scale may be used to determine the peak power of the pulse.

We used the computer to integrate the output of the transient digitizer,

monitored the energy of each pulse with the calorimeter and calculated the

isponsivity R of the power meter (ampere/watt) by using the relation that

15

k
calorimeter

multilayer

op tical-pulse

Tjower meter

AR coat

Figure 10. Calibration of the optical-pulse

power meter with the pulsed YAG laser.

16
35

CO

4-J O>

•H

i-l

H

!=•

P-i H

o

25

50 10

TIME (nanoseconds)

Figure 11. Typical pulse emitted by pulsed YAG

laser, displayed by the transient

digitizer .

17
R = Integrated output (vole sec)

calorimeter output (joule) x splitter ratio x 50fi ' (6)

where the splitter ratio is defined as the ratio of transmitted energy to

reflected energy and where the transient digitizer's input impedance is assumed

to be precisely 50f2.

To eliminate the effects of scatter in the laser output, we calculated the

responsivity for each of several shots and took the mean value as our best

estimate of the responsivity of the instrument. The results are shown in column 2 of table 2.

Table 2. Power meter responsivity and error limits, pulsed-laser measurements.

Sample

Responsivity Number Standard

R of Samples n Deviation s

NBS 1 U 2.303 X 10

L 2.099

-10

A/W 0.15 X 10 ^° A/W

0.08

Statistical Total

Limit of Limit of

Error (SLE) Error (TLE

±7.7%

±3.2

13%

NWK 1 U 2.424

L 2.286

10

10

0.12

0.11

±3.6

±3.4

NWK 4 U 1.880 10 0.08 ±2.9 8

L 2.268 10 0.10 ±3.3 8

Mean 2.210 — — — —

*U and L refer to the upper and lower detectors in each power meter.

If the power meters were always used with the same transient digitizer (and

plug-in), then it would be acceptable to compute the responsivity R' in units of

volt/watt, where R' = 50R. To calculate R as we have done in eq (6), we must

know the input impedance of the digitizer. We have found it to be almost

18
precisely 50Q, at zero frequency, but we experienced difficulty measuring the

impedance at higher frequencies because the BNC connectors were not repeatable.

The evidence seems to be, nonetheless, that the input impedance may differ by

a few ohms at frequencies higher than 100 MHz. The slight impedance mismatch

at these frequencies will affect the Impulse response of the instrument, and

we discuss the effect of finite impulse width below.

Transient-Digitizer Calibration . Because the power meters are not always used

with the same instrumentation, we found it necessary to calibrate separately

the transient digitizer with its plug-in unit. On the appropriate scale, we

found the vertical scale to be inaccurate by about 2.5% over the voltage

range that resulted from the photocurrent.

In addition, we found the digitizer to vary from linearity by approximately

1%. To assess the effects of this nonlinearity on the measurement of pulses, we performed the following experiment.

We used an oscillator to generate a 10-MHz sine wave, whose harmonics we measured to be at least 35 dB less than the fundamental. We acquired about two

cycles of the sine wave with the transient digitizer and stored the data in

the computer. We used this information to calibrate the time base, which we

found accurate to about 4%.

We generated a sine function digitally and adjusted its frequency and

amplitude to match as accurately as possible the sine wave acquired by the

digitizer. To this end, we computed the deviations of the acquired waveform

from the true sine function and displayed the deviations as a function of

time. We adjusted the computed sine wave until we minimized the deviations

throughout the central 8 cm of the 10-cm display, as shown in figure 12. This

figure shows that the digitizer nonlinearity is most significant in the first

centimeter of the display; therefore, we confine our interest to the central

portion of the display, where we estimate the average deviation to be about

1.5%. Likewise, we have taken all our data within the central portion of the

display. Thus, digitizer nonlinearity contributes approximately 1.5% to the

total limit of error.

19
CO M

tHO

>

o

M

H

<

>

-5

100 200

TIME (nanoseconds)

Figure 12. Deviation between acquired sine wave

and calculated sine wave.

20
Beam-Splltter Calibration . We calibrated the beam splitter in place by

using two calorimeters and an interchange method [9], Once the beam splitter

was calibrated, neither the laser nor the beam splitter was moved during the

duration of our experiments.

Suppose that we have two energy meters (or power meters in the case of a continuous laser) that are known to be linear detectors. They may be completely

uncalibrated, and they need not be identical or nearly identical. To calibrate

the beam splitter, we arrange the energy meters in the manner shown in figure 13a.

If the (possibly unknown) calibration factor of meter Ml is F and that of

meter M2 is F„, then the beam-splitter ratio R is precisely

M F

2 2

where M^ and M„ are the uncalibrated meter readings, for example in volts if the

meters use thermopiles as detectors. The beam-splitter ratio is not the reflectance,

but the ratio of reflected energy to transmitted; in general, it is not possible

to derive the reflectance from the splitter ratio.

We now interchange the calorimeters as in figure 13b and measure the splitter

ratio again. In this case, IL is precisely

M' F

1 1 \ "

M' F ' ^^^D

^^2 2

f I where M. and M„ are again uncalibrated meter readings.

The values of R and R, in the two expressions, though unknown because the

R' s are unknown, are in principle exactly equal; therefore, it is a tautology to

write that

R = (R^ R^)^/^ (9)

or

R =

''n^ Mj

m7 "" mT

1/2

1/2

= (^a V ' (10)

21
Figure 13. Calibration of beam splitter by an

interchange method.

22
where r and r, are the ratios of the (uncalibrated) meter readings before and

a D after the meters are interchanged, and where R is the actual value of the

splitter ratio.

Thus, we can measure R without knowing the calibration coefficient of

either meter. The value of this technique is to reduce experimental error greatly by eliminating the calibration errors in the two meters; all that is

needed is the knowledge that the meters are linear.

We calibrated the beam splitter by measuring M and M„ and calculating

r for each of 10 shots. We interchanged the meters and calculated r, in the

a b same manner. We calculated the arithmetic means of the sets of r and r. and

a b

calculated a best estimate of R from the geometric mean of the two calculated

arithmetic means, as suggested by eq (10).

Table 3. Calibrat ion of beam spl itter.

Spl itter Ratio

(Raw Data)

r Number

of Samples

10

10

Sample Standard

Deviation s SLE

Figure 7a

Figure 7b

Geometric Mean

1.398

1.001

1.183

0.008

0.008

0.4%

0.5

0.5

Continuous-Laser Calibration . As an independent verification of the calibration, we also calibrated the power meters with the 1-watt, continuous laser.

The experimental arrangement is shown in figure 14. The beam was focused onto a mechanical chopper and modulated at a frequency of approximately 1 kHz before

being allowed to fall on the diffuser. The output of the detector was measured

by using a lock-in amplifier and a digital voltmeter.

We calibrated the lock-in amplifier by replacing the power meter with a

, 1-kHz square-wave generator that had the same 50% duty cycle as the

mechanically chopped laser beam. We measured the output of the generator by

23
chopper

I 1

I i ^ I

I "^

I

„ J

i___ J

digital

voltmeter

(calorimeter) ^

optical-pulse

power meter

output

monitor

reference signal

out m

lock-in amplifier

Figure 14. Calibration of the optical-pulse power

meter with the continuous YAG laser and

lock-in amplifier techniques.

24
reducing its frequency to less than 1 Hz and using a digital voltmeter. (Monitoring the output of the generator on an oscilloscope showed no detectable change

in voltage with frequency.) We further used the generator to check the input

impedance of the lock-in amplifier at 100 Hz by placing a precision resistance

box in series with the amplifier input and adjusting the resistance until the

output of the amplifier was reduced precisely in half. At this low frequency,

inductive effects in the resistance box are negligible, so we conclude that

the input impedance of the amplifier is equal to the resistance of the series

resistance box. The value we measured was almost precisely that claimed by

the manufacturer.

We measured the power emitted by the laser with a calorimeter that had also

been calibrated against the C-series calorimeter. Because the laser was relatively stable, we merely replaced the pulse-power meter with the calorimeter; we could have achieved greater precision with the beam splitter technique of the

previous section.

Finally, we calculated the responsivity of the power meter from the relation

that

V = [DVM reading x calibration factor of lock-in amplifier] (volt) (}^\

power meter output (watt) x input impedance of amplifier (ohm)

where the units of R are again ampere/watt.

The results of this measurement are shown in table 4. In all cases, tables

2 and 4 agree to about 10% or better.

25
At other wavelengths, the meters must be recalibrated, in part because

the responsivity of a given diode will not be known accurately enough from a generic curve.

5. Analysis of Errors

In this section, we estimate the precision of the two measurements and

express the results as a limit of error. We take a comparatively conservative

approach and treat errors that arise Independently of each other as systematic

errors. For example. If there were an actual error of 1% owing to random

error In the original calibration of the C-serles calorimeter, the error, which

cannot be computed nor corrected, would appear as a systematic error when the

calorimeter Is used as a standard. There Is no reason to believe that errors

that arise from other sources will wholly or partly cancel the calibration error;

that Is, errors are likely to be correlated. Therefore, we shall treat each

error In turn as a systematic error and add errors algebraically (rather than

add the square root of the sum of the squares, as Is done with uncorrelated

errors such as those that Involve sequential measurements of the same kind)

Statistical Limit of Error . For the pulsed -laser calibration, we computed

the standard deviation s of the sample, where

2 _ ) (deviations from mean) (^'^\

n-1

Both s and the number n of measurements are shown In table 2. We estimate the

statistical limit of error SLE (or confidence Interval) by using Student's t function,

SLE = -^-^ . (14)

We use the values of t appropriate to a 95% confidence level and n-1 degrees

of freedom. Thus, excluding for the moment other error sources, there is

about one chance In twenty that the mean value of the responsivity is in error by more than the SLE [10].

Eeam-Splltter Ratio . According to eq (9) , the beam-splitter ratio is equal

1/2

to (r r, ) . If the SLE's of r and r, are A and A, , then we may write that

a b a b a b

26
R ± AR = [(r ± A )(r, ± A,)]^^^, (15)

a a b b

from which we conclude that AR (the SLE of R) is about

AR = I (A + A,). (16)

Z a b

Using the data presented in table 3, we conclude that the total SLE of the

beam-splitter ratio is about 0.5%.

Systematic Errors Resulting from Finite Impulse Response . If the impulse

response of the detector is not a delta function, then the electrical pulse

that is recorded will be slightly longer than the incident optical pulse. In

addition, the peak voltage will be slightly lower than the value expected for

the ideal case. This results in a systematic error whose importance depends on

the relative durations of the impulse response and the laser pulse. If necessary,

the error can be corrected by accurately modeling the laser and the detector

either digitally or analytically. In our system, as we shall show, the effect

is small and need not be corrected.

To assess the effect of the finite impulse width, we model the system in

the following way. We approximate the impulse response of the power meter with

a Gaussian function,

h(t) = (1/t) Gaus (t/T), (17)

where

2 Gaus (t) = exp (-irt ). (18)

The duration 2t of the impulse response is about 1.3 ns (measured between the

times when the photocurrent is 1/e times the maximum). The factor of 1/t in

eq (17) is included to normalize the impulse response to unit area.

The detected laser pulse is not symmetrical. Its duration is approximately

32 ns (again measured between 1/e points), which is over one order of magnitude

greater than the Impulse width. We therefore assume that the actual laser pulse

closely resembles the detected pulse.

27
Table 4. Meter responsivity, continuous-laser calibration.

Responslvlty Total Limit

R of Error (TLE)

2.561 X

10"-^° A/W 8%

2.344 8%

2.623 8%

2.273 8%

2.010 8%

2.242 8%

Mean 2.342

NBS 1 U

L

NWK 1 U

L

NWK 4 U

L

Change of Wavelength . We calibrated the power meters using Nd:YAG lasers,

whose wavelength is nominally 1.064 ym. Because the responsivity of the photodiodes is a strong function of wavelength, the calibration is accurate at that

wavelength only.

To assess the effect of a wavelength change, we examined the manufacturer' curve of responsivity as a function of wavelength. In the region around 1.06 ym. we find that R varies approximately as exp (-0.0035 X) for X in ym. Thus, if we change X by a small amount AX, then the fractional change AR/R in R is given by

the expression

AR/R = - 0.0035 X. (12)

The wavelength of a typical glass laser may be 1.060 ym, or about 4 nm less

than that of the YAG laser. This change of wavelength would result, according

to eq (12), in a systematic error of about -1.4%; in principle, the

systematic error may be corrected. Nearly all neodymium lasers oscillate within

10 nm or so of 1.064 ym. Thus, the meters may be used with any neodymium laser

with only a slight systematic error that must be corrected.

28
The detected pulse can be fairly closely approximated by the convolution

(or sum) of two negative-exponential functions, but this form is not convenient

for calculation. Instead, we approximate only the leading edge with a Gaussian

function,

f(t) = Gaus (t/T), (19)

where T is approximately 7 ns. Because we are right now interested only in the

peak of the detected pulse, this approximation will be sufficient.

If we assume that the laser pulse is described (until the peak) by eq (19)

and the impulse response of the detector by eq (17), then the detected pulse is

described by the convolution f*h of h with f [11]. Applying the convolution

theorem, we readily find that

f*h = [1 + (x/T)^]"-^''^ Gaus [t/(T^ + T^)^/^]. (20)

2 -1/2 The maximum value of the convolution is equal to [1 + (t/T) ] , whereas

the maximum value of f is 1. (The duration of the convolution, incidentally, is

2 2 1/2

(t + T )

' .) Therefore

of the detected pulse by

2 2 1/2

(t + T ) .) Therefore, the effect of the impulse width is to lower the peak

[1 + (t/T)^] ^/2 ^ 1 - 1 (t/T)^ (21)

Using the values of t and T stated above, we estimate the systematic error to be

about -0.5%. Because it is so small, we shall make no attempt to correct

for this effect, but merely include the systematic error in our error budget,

adding the 0.5% without regard to its sign.

In addition to having a finite duration, the impulse response displays a "tail" at long times. (We used an impulse generator to verify that the tail

results from the transient digitizer and is not an artifact introduced by the

mode-locked laser.) The peak of the tail is about 7% of that of the impulse

response itself, and the tail is displaced by about 2.7 ns from the main waveform.

Such a sizeable tail could produce a significant error in the measurement of

peak power, even though it might not influence the shape of the waveform

significantly.

29
We model the tail by assuming that it is the result of a reflection; thus, we rewrite the impulse response h(t) as

h'(t) = h(t) + Bh(t-t^), (22)

where B is the relative height '^ of the reflection and t is the time at which

o the reflection appears with respect to the main waveform.

If f(t) is the actual laser pulse, then the observed waveform g' (t) is

described by

g'(t) = f(t)*h(t) + B f(t)*h(t-t^), (23)

or [11]

'(t) = g(t) + Bg(t-t^). (24)

Therefore, if the peak of the main pulse occurs at t=0.

g' =8 + Bg(-t ), (25) ^ max ^max ^"^ o'^' ^ ^

where g is the quantity we seek. We use figure 6 to measure g(-t ); the

ITla-X O

presence of the tail results in a systematic error that requires a correction

factor of about 0.94; this correction is included in the values in table 2,

column 1.

The largest errors involved in calculating the correction factor are in

the measurements of B and t . Assuming that we can measure B to 1 part in 20,

o we estimate an error of about 0.3% from this source. To calculate the error

that arises from uncertainty in measuring t , we assume that we can measure

accurately in figure 6 to about 0.5 mm. This results in an uncertainty in

g of no more than 0.2 or 0.3%.

max

If the tail cannot be modeled accurately as a reflection, then the

uncertainty is somewhat greater than the half percent or so calculated above.

Therefore, we conservatively add a full percent to the error budget enumerated

in table 5a.

30

1
Other Calibration Errors . The systematic error of the calibration of the

C-serles calorimeter Is currently about 1.4% (99% confidence level). The use

of a secondary standard Introduced an additional error of 0.2% In the case of

the pulsed-laser measurements and 2% In the case of the continuous-laser measurements,

where a different calorimeter was used. We estimate that the transient digitizer

introduces an error of 1.5%, (See table 5 for a compilation of measurement

errors.)

We therefore conclude that the total limit of error (TLE) of the pulsed

measurement is about equal to the SLE plus 5.1%. The values of the TLE

are shown in table 2.

Table 5a. Errors of callbatlon by pulsed laser,

Beam Splitter Calibration ±0.5%

C-serles Calorimeter ±1.4

Secondary Energy Standard ±0.2

Impulse Width -0.5

Impulse "Tall" ±1

Nonllnearity of Digitizer ±1,5

SUBTOTAL ±5.1%

wLUS:

SLE of Individual Measurements as in table 2

31
Table 5b. Errors of calibration by continuous laser.

Calibration and Linearity of Lock-in

Amplifier ±1 %

C-series Calorimeter ±1.4

Secondary Power Standard ±2

Laser Stability ±2

Speckle ±2

TOTAL ±8 %

In addition to the 3.4% overall calibration error of the continuous-laser

calorimeter, the lock- in amplifier introduces error into the measurement.

According to the manufacturer, the lock-in amplifier is linear to about 0.2% of

full scale; in our case, this translates to about 1% measurement error. This source of error could have been reduced somewhat by calibrating the lock-in

with a voltage source that was close to the voltage that arose as a result of

the photocurrent. In addition, the input-calibration voltage was known to a few tenths of a percent.

The laser itself was stable to 1 or 2%. Because we used a substitution

technique, rather than a beam splitter, we introduced a source of error that we

may conservatively estimate at no more than 2%. We could, of course, have used

a calibrated beam splitter and largely eliminated this source of error by

taking simultaneous measurements with the power meter and the calorimeter.

Last, we take speckle and dif fuser-nonuniformity errors to be 2% or less for

the several-cm spot that fell on the dif fuser.

The total limit of error of the continuous measurement is the suni of the errors just described, or about 8%, as indicated in table 4. (In any future

calibrations, it will be reduced by 2 to 4% by using the beam splitter technique

and the more precise calorimeter, and by calibrating the lock- in amplifier at

very nearly the voltage that results from the photocurrent.)

32
6. Conclusions

We have calibrated the power meters using both pulsed- and continuouslaser techniques; in our opinion, both methods are important, in part because

they serve as a check on one another.

A calibration made with a pulsed laser must be examined carefully to ensure that there is no systematic error resulting from the impulse response of

the power meter. Therefore, it is necessary to measure the impulse response of

the meter. In addition, a pulsed laser might exhibit a long afterglow that

would be difficult to detect but could result in sizeable calibration error. We have eliminated this possibility by calibrating the meters with a well

characterized, continuous laser in addition to the pulsed laser.

The continuous-laser measurement can probably be made to have a smaller

limit of error, but it is made at a much lower power level than the level of

pulsed-laser measurements. Therefore, if the photodiodes are not shown to be

linear over a large enough range (say, by removing them from the meters and

using the continuous laser), the calibration could be in error. Pulsed-laser

calibrations made at nearly the energies at which the meters are to be used

will suffer least from the effects of nonlinearity but may suffer from afterglow or other problems.

Thus, we may be confident of a calibration of a pulsed-laser power meter

provided that we (1) know the impulse response and either (2) calibrate the

meter with continuous-laser techniques and provide some independent verification

of linearity over many decades or (3) calibrate with a pulsed laser and provide

verification that the electrical pulse is neither distorted by the impulse

width of the meter nor has an afterglow or other features that might cause

significant calibration error. We have chosen options (1) and (3); that is, to

perform the calibration at both high- and low-power levels and to use the two

calibrations as independent verifications of one another. If the two calibrations had shown systematic error larger than the estimated TLE, it would have

been necessary to check the photodiodes for nonlinearity. Nevertheless,

option (1) would still be necessary because option (2) alone does not fulfill

the need to deal with the impulse-response problem.

33
Because of the number of corrections that have to be made, a pulsed-laser

calibration is extremely difficult and requires a very well characterized

system. Thus, some readers may wish to place slightly more confidence in the

continuous-laser calibrations, which differ, on average, by 5 or 6 percent from

the pulsed-laser calibrations.

ACKNOWLEDGMENTS I

It is our pleasure to acknowledge the efforts of Gordon Day, Robert Phelan,

Clark Hamilton, and Gerald Klein, who designed and built the optical-pulse power

meters, and especially Philip Simpson, whose expertise and computer software

provided immeasurable help in the pulsed-laser calibration.

34
References

[1] Eastman White Reflectance Standard, publication number JJ-^31 , and Eastman

White Reflectance Coating, publication number JJ-32 (both Eastman Kodak

Company, Rochester, NY, 1974). The use of trade names is intended as a convenience for the reader and does not imply endorsement by the National

Bureau of Standards; similar products made by other manufacturers may

work as well or better.

[2] Grum, F. and Luckey, G. W. , Optical sphere paint and a working standard of

reflectance, Appl. Opt. jj,, 2289-2294 (1968).

[3] PIN Photodiodes, in Optoelectronic Designer's Catalog, pp. 210-213 (HewlettPackard Corp., Palo Alto, CA, 1978).

[4] Young, M. , Optics and Lasers, An Engineering Physics Approach, pp. 43~49

(Springer-Verlag, New York, 1977).

[5] Ref. 4, pp. 100-105. Young, M. , Faulkner, B., and Cole, J., Resolution in

optical systems using coherent illumination, J. Opt. Soc. Amer. ^, 137-9

(1970).

I

[6] Dainty, J. C, The statistics of speckle patterns, in Progress in

I Optics, pp. 13-15 (E. Wolf, Ed., North-Holland, Amsterdam, 1976).

[7] Edwards, J. G., Design and performance of photo-cell systems for pulsed

laser power and energy measurements. Optoelectronics 1, 1-8 (1969).

t

[8] West, E. D. and Case, W. E., Current status of NBS low-power energy

M measurement, IEEE Trans. Instr. Meas. IM-^3, 422-425 (1974).

[9] This technique is used routinely at NBS, but details seem never to have

been published.

I|10] Natrella, M. G., Experimental Statistics, NBS Handbook 91, section 2-1

(U.S. Government Printing Office, Washington, 1963).

I

[11] Gaskill, J. D., Linear Systems, Fourier Transforms, and Optics (John Wiley and

Sons, Inc., New York, NY, 1978).

35
NBS-114A (REV. s-78)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBS TN-1010

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Measurement of Pulsed-Laser Power

5. Publication Date February 1979

6. Performing Organization Code

724.04

7. AUTHOR(S)

M. Young and R. A. Lawton

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 7244153

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Sponsored in part by:

Aerospace Guidance and Metrology Center

Newark AFS, Ohio 43055

(Calibration Order: MLTO FL 36 78-14)

13. Type of Report & Period

Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most si^ificant information. If document includes a significant

bibliography or literature survey, mention it here.)

We describe calibrating several optical-pulse power meters

to an accuracy of about 8% or better. The meters are designed

for Q-switched neodymium lasers with peak powers in excess of a few megawatts and pulses longer than five or ten nanoseconds.

Combined with a fast oscilloscope or a transient digitizer, the

meters display the time-domain waveform of the laser emission and

thereby allow determination of parameters such as transition

duration (risetime, falltime), duration and peak power. We

discuss calibrating the meters by both pulsed and cw methods, and

show why each method is useful as a check on the other. We treat

in some detail the effect of speckle on the use of diffusers as attenuators in power meters such as ours.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Attenuators; calibration; laser; neodymium laser; peak power;

power meter; pulsed laser; Q-switched; risetime; speckle; waveform.

18. AVAILABILITY [X1 Unlimited

I : For Official Distribution. Do Not Release to NTIS

I }^ Order From Sup. of Doc, U.S. Government Printing Office Washington, D.C. 20402, SD Stock No. SN003-003 - 02028-1

I

I Order From National Technical Information Service (NTIS)

Springfield, Virginia 22161

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF page;

40

22. Price

limi $1.60 \ki

4

it U.S. GOVERNMENT PRINTING OFFICE: 197 9-0-67 7-07 2/124 5 USCOMM-DC 66680-RJ ^
NBS TECHNICAL PUBLICATIONS

PERIODICALS

• JOURNAL OF RESEARCH—The Journal of Research

of the National Bureau of Standards reports NBS research and development in those disciplines of the physical and

engineering sciences in which the Bureau is active. These

include physics, chemistry, engineering, mathematics, and

. computer sciences. Papers cover a broad range of subjects, with major emphasis on measurement methodology, and

the basic technology underlying standardization. Also in- eluded from time to time are survey articles on topics closely related to the Bureau's technical and scientific programs. As

a special service to subscribers each issue contains complete

citations to all recent NBS publications in NBS and non- NBS media. Issued six times a year. Annual subscription: domestic $17.00; foreign $21.25. Single copy, $3.00 domestic; $3.75 foreign. Note: The Journal was formerly published in two sections: Section A "Physics and Chemistry" and Section B "Mathematical Sciences." DEMENSIONS/NBS

This monthly magazine is published to inform scientists, engineers, businessmen, industry, teachers, students, and consumers of the latest advances in science and technology,

. with primary emphasis on the work at NBS. The magazine

highlights and reviews such issues as energy research, fire protection, building technology, metric conversion, pollution

abatement, health and safety, and consumer product per- formance. In addition, it reports the results of Bureau pro- grams in measurement standards and techniques, properties of matter and materials, engineering standards and services, instrumentation, and automatic data processing.

Annual subscription: Domestic, $11.00; Foreign $13.75

NONPERIODICALS

Monographs—Major contributions to the technical liter- ature on various subjects related to the Bureau's scientific and technical activities.

'. Handbooks—Recommended codes of engineering and indusI trial practice (including safety codes) developed in cooperaI tion with interested industries, professional organizations,

; and regulatory bodies. 'Special Publications—Include proceedings of conferences sponsored by NBS, NBS annual reports, and other special

publications appropriate to this grouping such as wall charts, pocket cards, and bibliographies.

Applied Mathematics Series—Mathematical tables, manuals, and studies of special interest to physicists, engineers,

chemists, biologists, mathematicians, computer programmers,

and others engaged in scientific and technical work.

National Standard Reference Data Series—Provides quantitative data on the physical and chemical properties of

- materials, compiled from the world's literature and critically evaluated. Developed under a world-wide program co- ordinated by NBS. Program under authority of National

Standard Data Act (Public Law 90-396).

NOTE: At present the principal publication outlet for these data is the Journal of Physical and Chemical Reference Data (JPCRD) published quarterly for NBS by the American Chemical Society (ACS) and the American Institute of

Physics (AIP). Subscriptions, reprints, and supplements

available from ACS, 1155 Sixteenth St. N.W., Wash., D.C.

20056.

Building Science Series—Disseminates technical information developed at the Bureau on building materials, components,

systems, and whole structures. The series presents research

results, test methods, and performance criteria related to the

structural and environmental functions and the durability

and safety characteristics of building elements and systems. Technical Notes—Studies or reports which are complete in themselves but restrictive in their treatment of a subject.

Analogous to monographs but not so comprehensive in scope or definitive in treatment of the subject area. Often

serve as a vehicle for final reports of work performed at NBS under the sponsorship of other government agencies.

Voluntary Product Standards—Developed under procedures

published by the Department of Commerce in Part 10, Title 15, of the Code of Federal Regulations. The purpose

of the standards is to establish nationally recognized require- ments for products, and to provide all concerned interests with a basis for common understanding of the characteristics of the products. NBS administers this program as a supple- ment to the activities of the private sector standardizing

organizations.

Consumer Information Series—Practical information, based on NBS research and experience, covering areas of interest to the consumer. Easily understandable language and

illustrations provide useful background knowledge for shopping in today's technological marketplace.

Order above NBS publications from: Superintendent of Documents, Government Printing Office, Washington, D.C.

20402. Order following NBS publications—NBSIR's and FIPS from

the National Technical Information Services, Springfield, Va. 22161.

Federal Information Processing Standards Publications (FIPS PUB)—Publications in this series collectively constitute the Federal Information Processing Standards Register.

Register serves as the official source of information in the Federal Government regarding standards issued by NBS

pursuant to the Federal Property and Administrative Services Act of 1949 as amended. Public Law 89-306 (79 Stat. 1127), and as implemented by Executive Order 11717

(38 FR 12315, dated May 11, 1973) and Part 6 of Title 15 CFR (Code of Federal Regulations).

NBS Interagency Reports (NBSDR)—A special series of

interim or final reports on work performed by NBS for outside sponsors (both government and non-government).

In general, initial distribution is handled by the sponsor;

public distribution is by the National Technical Information

Services (Springfield, Va. 22161) in paper copy or microfiche form.

BIBLIOGRAPHIC SUBSCRIPTION SERVICES

The following current-awareness and literature-survey bibli- ographies are issued periodically by the Bureau: Cryogenic Data Center Current Awareness Service. A litera- ture survey issued biweekly. Annual subscription: Domestic, $25.00; Foreign, $30.00.

Liquified Natural Gas. A literature survey issued quarterly.

Annual subscription: $20.00.

Superconducting Devices and Materials. A literature survey

issued quarterly. Annual subscription: $30.00. Send subscription orders and remittances for the preceding bibliographic

services to National Bureau of Standards, Cryogenic Data

Center (275.02) Boulder, Colorado 80302.
U.S. OEPARTMENT OF COMMERCE

National Buraau of Standards

Washington, D.C. 20234

OFFICIAL BUSINESS

Penalty for Private Use, S300

POSTAGE AND FEES PAIO

U.S. OEPARTMENT OF COMMERCE

COM-219

SPECIAL FOURTH-CLASS RATE BOOK

I