NBS TECHNICAL NOTE 382

WSffohaf Bureau of Standards

Library, E-01 Admin. Bldg.

JUN 1 5 1971

Laser Power

and Energy Measurements
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NBS TECHNICAL NOTE 382

ISSUED OCTOBER 1969

Nat. Bur. Stand. (U.S.), Tech. Note 382, 64 pages (Oct. 1969)

Laser Power and Energy Measurements

D. A. Jennings, E. D. West, K. M. Evenson

A. L. Rasmussen, and W. R. Simmons

Quantum Electronics Section

Radio Standards Physics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

This work was partially supported

by the Advanced Research Projects

Agency under Order No. 891.

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide

a means for making available scientific data that are

of transient or limited interest. Technical Notes may

be listed or referred to in the open literature.

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

(Order by SD Catalog No. C 13.46:382), Price 65 cents

Table of Contents

Page

List of Tables iv

List of Figures v Abstract 1

1. Introduction 2

2. Theoretical Background for Laser Calorimetry. ....... 5

2. 1 An Application of the Theory 15

3. Energy Measurements 21

3. 1 Introduction 21

3. 2 The Calorimeter 21

3. 3 Methods of Calibration 23

a. Heat Capacity Calibration 24

b. DC Electrical Energy Calibration 24

c. Reflecting Plate Calibration 25

3. 4 Logarithmical Extrapolation 25

3. 5 Intercomparisons Using Liquid Cell Calorimeter. 27

3. 6 Intercomparisons Using Metal Reflecting

Plate Calorimeter 31

3.7 Other Parts of the System 36

4. CW Power Measurements 39

4. 1 General Description 39

5. CW Power Measurements in Excess of 1 Watt 47

5. 1 Introduction 47

5. 2 Calorimeters • 47

a. Disc Power Meter 47

b. Cone- Disc Power Meter 5

c. The Cone-Flow Power Meter 52

6. Data Reduction for the Liquid Cell Calorimeter 54

in
List of Tables

Page

2-1. Comparison of methods of data analysis 10

2-2. Dependence of calibration factor on heater location 16

5-1. Reflectivities of various materials at 1 0. 6 microns

compared with polished copper 48

6-1. Data for Electrical Input 59

IV
List of Figures

Page

2-1. Temperature-time curve to illustrate heat- flow problem . . . 8

2-2. Temperature-time curve for an isoperibol calorimeter ... 8

2-3. Calibrating Heaters 14

2-4. Temperature-time curves for calibrating heaters 18

3-1. Cross- sectional diagram of the calorimeter 20

3-2. Cross- sectional diagram of the calorimeter absorption cell . 22

3-3. Diagram for comparison of calorimeters 28

3-4. Diagram for comparison of calorimeters 28

3-5. Photo of apparatus for comparison of calorimeters 29

3-6. Diagram for calibration of beam splitters 32

3-7. Diagram for comparison for liquid cell and reflecting plate

calorimeters 34

4-1. Schematic of the CW laser power meter calibration system . 38

4-2. Diagram showing the basic calibration procedure. 40

4-3. The response of the liquid cell calorimeter to a CW laser

beam 42

4-4. Transfer detector calibration as a function of laser power. , 44

5-1. Schematic of the copper disc calorimeter showing

construction details 46

5-2. Schematic of the cone- disc power meter showing

construction details 49

5-3. Schematic of the cone-flow power meter showing

construction details 51

6-1. Response of calorimeter to a DC electrical energy pulse. . . 57

6-2. Example of the results of using the integration procedure

in determining the amount of energy in a laser pulse 61

v

Laser Power and Energy Measurements

D. A. Jennings, E. D. West, K. M. Evenson

A. L. Rasmus sen and W. R. Simmons

Most laser calorimeters operate in a constant temperature environment. The calorimeters

can be used as deflection devices or the data can be

analyzed by extrapolation or integration. Consideration of the heat flow problem common to all of

these methods points up the underlying assumptions

and the possible errors involved.

Calorimeters for measuring the output

energy of pulsed ruby and neodymium glass lasers

have been built and calibrated. The absorbing

medium is an aqueous solution of CuSO . Calibration of laser energy detectors has an estimated

uncertainty of ± 2% for input energies of 0. 1J to

100J. Comparisons of absorption cell calorimeters

with metal plate calorimeters agree within 1%.

Instrumentation is described that is used for

the calibration of CW laser power meters. The

calibration unit employs an absorption cell calorimeter to calibrate the output of a photovoltaic cell

transfer detector. The power meter to be calibrated

is then compared to the calibrated output of the

transfer detector. The calibrations are within an

accuracy of 4%.
A discussion and description is also given

of several types of calorimeters that have been

used to measure the output of a 100 watt CO

laser. The most recent design provides for

measurement from 1 watt to 5 kilowatts with a measured accuracy of better than 3%.

Key words: Calorimetry; laser; laser calorimetry; laser energy; laser power.

1. Introduction

The field of laser power and energy measurements is a relatively new one which presents a wide variety of problems. Heard

(2) and Birnbaum and Birnbaum have reviewed the work in this field.

Measurements are required for wavelengths from 400 nm to 3 (jm,

for power levels from 10 to 1 watts, for energies from 10 to 1

joules, and for operating conditions ranging from single pulses through

repetitive pulses to continuous wave.

Measuring devices which are relatively insensitive to wavelength

are desirable because the greater the useful range, the fewer the devices which must be designed, tested, calibrated, and maintained. An

advantage of calorimeters, which convert radiant energy to heat and

measure the quantity of heat, is that they can be designed to operate

over a large range of wavelengths.

The large ranges of power and energy to be measured require a considerable number of devices because the range of any one device is

relatively limited. There are considerable problems of scaling and

inter comparison to insure consistency of measurements at the various
levels. Large power levels present a special problem because of possible damage to the measuring device. The damage apparently results

not only from thermal effects but also from the large electrical fields

due to the coherence of the radiation.

The operating conditions also affect the measurement. Single

pulses usually require an energy measurement. The output of CW and

most repetitively pulsed lasers can be measured either continuously as power or as energy by letting the beam into the calorimeter for a known

time.

With such a variety of problems in a rapidly growing field, many

problems remain to be solved. However, there is an immediate practical need for measurements. We hope that this Technical Note will

help with some of these immediate problems.

As remarked in the foreword, this note is a summary of lectures

given at a seminar on laser power and energy measurements. The lecturers represented several different laboratories at the National Bureau

of Standards, so that the various sections are, to a large extent, independent of one another. They are not intended to be read in sequence,

but rather for the particular topics of interest.

The lectures contained a good deal of information on unsatisfactory methods and techniques. This information has been retained

in the belief that, in the present state of the art, knowledge of some of

the pitfalls to avoid can be practically useful.

Section 2 attempts to show how the behavior of calorimeters

follows from and is predictable from the boundary value problem describing heat flow in the calorimeter. It might be read for possible

insights into the behavior of calorimeter, but not to find out how a particular measurement is made at NBS.
Section 3 deals with energy measurements, particularly with

respect to the liquid cell calorimeter and its application in testing other

devices. Many of the practical considerations of laser power and en- ergy measurements are discussed in this section.

Section 4 deals with the comparison of the liquid cell calorimeter,

an energy measuring device, to power measuring devices, using a silicon cell as a transfer detector.

Section 5 discusses several devices used for measurement at

CW power levels from one watt to five kilowatts.

Section 6 discusses the treatment of data primarily with respect

to the liquid cell calorimeter

References

1. H. S. Heard, Laser Parameter Measurements Handbook, John

Wiley and Sons, New York, 1968.

2. G. Birnbaum and M. Birnbaum, Proceedings IEEE 55.1026 (1967).
2. Theoretical Background for Laser Calorimetry

The problems of laser power and energy measurements are relatively new- -so new that some of the measurement ideas used in older

fields have not yet been generally adopted. One of these ideas is that

there should be a theory of the measurement. Failure to state the theory

of the measurement prevents independent judgment of the validity of the

measurement. If the purpose of the measurement is to convince others,

(1) the lack of a theory is an obvious handicap. Branscomb has discussed

this point in an article "Is the Literature Worth Retrieving?" Cameron

(2) and Plumb put the theory first: "We begin with a physical theory ..."

The measurement theory is just a statement of how one believes

his apparatus works. The actual operation can then be checked against

the theory and both the validity of the experimental checks and the theory itself can be judged independently. It seems obvious that one measurement may be better than another because it is based on a better

theory.

Many laser power and energy measurements are made with devices which convert radiant energy to heat and measure a change in

temperature. They are variously called detectors, thermopiles, bolometers, and calorimeters. Those that operate in a constant temperature environment have a common theoretical basis; i. e. they can be

analyzed in terms of a common heat flow problem. Calorimeters of

(3) this type are called isoperibol calorimeters and are used extensively

in thermochemistry. These calorimeters can be used in a variety of

ways, some of which provide a simpler and faster analysis of the data.

The basic assumptions of these methods usually require experimental

justification. Our purpose here is to indicate the general theoretical

basis of these methods and point out the assumptions and possible errors

underlying them.
The first law of thermodynamics is variously regarded as a statement of conservation of energy, as a statement of the mechanical

equivalent of heat, or as just a bookkeeping procedure for accounting

for energy. Regardless of philosophical views, the theory of calorimetric measurement is based on the first law: the calorimeter is a thermodynamic system, described in terms of state variables, for

which the work done and heat transferred must be evaluated. A qualitative understanding of the implications of the first law- -and the heat

flow equations derived from it- -are important to anyone either using

or designing calorimeters. One should be able to answer the question,

"What is the theory of the measurement?"

The laser calorimetry problem from a very practical standpoint,

can be divided into three subproblems, each of which can be considered

separately:

1. Materials problem- -destruction by high-power.

2. Fraction of beam absorbed.

3. Measurement of the absorbed energy.

These practical problems relate in a rather direct way to the

ideas in the first law, which equates the increase, A U, in the internal

energy of the calorimeter, to the heat, Q, transferred to the calorimeter plus the work, W, done on the calorimeter. In symbols

AU = Q + W. (1)

These quantities can be related to the three practical problems:

1. For the change in internal energy, we must specify

the state of the system; i. e. , did the beam alter the amount or chemical

composition of the materials in the calorimeter?

2. We must know that the observed temperature is a measure of the internal energy, and that the temperature observation

accounts for the heat exchange to the required accuracy.
3. The beam can be considered to do electromagnetic

work on the calorimeter. To evaluate this work, the fraction of work

converted to heat in the calorimeter and the fraction reflected back out

must be known.

From an idealistic point of view, one should start with the basic

theory and design a calorimeter and a method of operation. This approach can be very exacting and tedious. The theory of isoperibol

(4) calorimeters has been treated in a rather sophisticated way and also

(5) with a very simple model which suggests many of the same measurement techniques.

It is not practical to present a theory for all kinds of calorimetry,

but a simple example shows how direct reference to the theory serves

to pinpoint the assumptions which must be satisfied for a measurement

to be valid.

Consider a calorimeter located in a constant temperature environment. It starts off at the same temperature as the environment and

then receives a unit energy pulse from a laser at time t = 0. The output,

which is the observed temperature may behave qualitatively as in figure

2-1.

The theory for this measurement follows from the heat flow

problem, related to the comparison of single laser pulses. The equation

for the conduction of heat is as follows:

-s rp V\(P)V T(P,t)= c(P)-^r ^ {2 )

where the symbols have the following meanings:

X(P) Thermal conductivity as a function of position, but not of temperature or time.

V= del = the vector operator. The argument is independent of the coordinate system.
CD

D•*- CUQ.

E

CU hTime

Figure 2-1. Temperature-time curve to illustrate the heat-flow problem. The calorimeter temperature is constant before the

input and exponential for large values of time.

CD3

O

i-0)Q.

E

cu

Time

Figure 2-2. Temperature-time curve for an isoperibol calorimeter

when both the initial and final temperatures are single

exponential functions of time.
T(P, t) Temperature as a function of position and time.

c(P) Heat capacity as a function of position.

Equation (2) equates the difference in heat flowing into a volume

dV in time dt to the change in the energy stored in the volume in the

same time.

The boundary value of the temperature is the temperature of

the surroundings, which we take as the reference temperature for this

particular problem. On a boundary where there is thermal contact:

T= 0. (3)

On a boundary of the calorimeter which radiates to the sur- roundings

3 T _ X —± = hT, (4) on

where 3T/dn is the derivative normal to the surface and h is the coefficient for heat transfer.

Before the pulse, the entire calorimeter is at the temperature

of the surroundings. The pulse at time zero sets up a temperature

distribution has the geometrical distribution g(P)

T(P, 0)= g(P). (5)

There is a solution, T, to this boundary value problem. Now consider

a pulse k times as large but having the same geometric distribution

g(P); that is, T (P, 0) = k. g(P). Practically, this means having the

same fraction of the energy in the same part of the beam and the beam

striking the same parts of the calorimeter. Now, we say

T

2

(P,t)= kTj (P,t), (6)

which is proved by substituting kT in the equations for T and obtaining

J. Cd
the equations for T . The k will factor in all cases, giving the boundaryvalue problem which defines T . To compare the two energies, eq (6) requires only that the

temperature be read at equal times after the laser pulse. The time is

at the discretion of the operator, but the maximum deflection is the

easiest to read and gives the best precision.

This simple idea is illustrated by data for two pulses from a

ruby laser. The calorimeter and laser were not moved between experiments so that the geometric energy distribution in the calorimeter

would be nearly the same. The data were analyzed by this shortcut deflection method and also by the conventional calorimetric method of

eq (8) carried out on a computer.

Table 2-1

Maximum Computer

Deflection (15 sec) Analysis (12 min)

First pulse 130.2 uv 134.1 uv

Second pulse 87.7 91.4

Ratio 1.49 1.47

These ratios agree about as well as could be expected on a statistical

basis.

If control of the environment is a problem, the deflection method

may be more accurate. To understand why, let's go back to theory.

In the heat flow problem, the temperature of the surroundings

is assumed to be constant. In the calorimeter used here this temperature may change by one or two milliKelvin during an experiment in

violation of the assumption. This change may be the largest single

error in the calorimeter, because the temperature is measured by a thermopile with cold junctions attached to the environment. The de10
flection experiment may actually give a better comparison of two beams

for which g(P) is the same, because the change in the temperature of

the reference junction is less.

What about CW comparisons? It can be shown that comparisons

are rigorous (no new approximations) where the laser power is of the

form

P

L

= kf(t) g(P). (7)

What is meant by the same f(t)? Comparison of two step inputs

is a common case. Other examples: CW inputs or electrical heating

for the same length of time. The power need not be the same.

A different problem arises when two laser beams having different relative power densities are compared or when the calorimeter is

moved relative to the beam. Then the geometric distribution of the

beam is changed and it is necessary to show that the small change in

the geometrical distribution does not affect the result significantly.

The key word here is significantly- -insignificant in one application may

be disastrous in another. Since the procedure violates the theory, a theoretical argument is useless. On the other hand, an experimental

approach would be quite convincing. Moving the calorimeter around

in a beam of constant energy, for example, would show whether the

response was constant within tolerable limits. Unfortunately, it's

hard to get the same response for different geometrical distribution of

the absorbed energy, but people have managed to find different combinations which are adequate for their problems.

One further application of the deflection method merits consideration. Suppose that a CW laser is to be compared with a pulsed

laser and suppose the difference in response due to the geometrical

distribution of energy is negligible. The time dependence of the two

11
inputs still violates the theory; only those inputs which are the same

function of time can be compared rigorously. Pulses are step energy

inputs; CW are ramps. It seems fairly obvious that very short CW

inputs approximate pulses. A 20 sec and a 40 sec input which give

equivalent output, are evidence for an adequate comparison.

The same reasoning applies to absolute calibrations against

electrical inputs. The electric heater may have both a different geometrical and a different time distribution from the laser beams to be

measured. The deflection method can be justified for this case, too,

on the basis of suitable experimental demonstration of behavior.

Practically there are many problems with the deflection method which

have caused people to seek other methods, especially when they need

a little more accuracy.

Conventional calorimetry has not been widely used in laser

power and energy measurements, probably because it is slow and re- quires considerable data reduction. For accurate work it has considerable advantages. One problem that needs particular attention is

whether relatively rapid methods can be based rigorously on the more

accurate but slower conventional calorimetry, perhaps the same calorimeter used by conventional and deflection methods.

The basic theory for a conventional calorimeter operating in a

constant temperature surroundings is described by essentially the same

boundary value problem. The development is more complicated, but

the results are summarized in the equation:

| t. ' ~surr' " J "

W L

~* " "el

E [ T

f

- T. + , j

(T - T_) dt] = i UT or A U_, (8)

12
T is the observed temperature and E is the energy equivalent determined by a known electrical input. The term energy equivalent has been

(4, 5) used to emphasize that E is not exactly a sum of heat capacities

T is the temperature of the surroundings, determined by (9),

surr

t is the time,

e is the "cooling constant", determined from the relationship

dT/dt ' = -e (T - T ) , (9)

surr

AU is the energy in a laser beam of limited duration (pulse of chopped),

and AU is the energy of an electrical calibration.

The change in internal energy of the calorimeter is the quantity

E(T. - T.); the integral term evaluates the heat exchange. The subscripts i and f refer to initial and final measurements. The various

terms are illustrated by the temperature- time curve in figure 2-2 for

a hypothetical experiment. The parts of the curve preceding t. and

following t are single exponential functions of time used to evaluate e and T in eq (8). The initial temperature, T., is read at t. and the

surr ^ i i final temperature, T , is read at t . When the temperature is a single

exponential function of time, these observations are a measure of the

internal energy of the calorimeter. The internal energy so obtained is

independent of the location of the source. If the integral term in eq (7)

could be made negligible, the comparison of different sources therefore

would be very accurate. This reasoning is applied in thermochemistry

to make measurements to one part in 10, 000 with a heat exchange of

one part in 100. So far laser calorimeters come nowhere near this

precision partly because the heat exchange is large relative to the

internal energy of the calorimetry.

The integration in eq (8) can be done in a variety of ways to

obtain the heat exchange over the time of the experiment. As it stands,

13
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Figure 2-3. H and H are calibrating heaters; A is the control

heater; S is a 20 junction thermopile; C is a resistance bridge for temperature control; and T is a copper resistance thermometer for monitoring the

temperature.

14
this evaluation requires that the laser beam and the calibration energyhave the same geometric distribution in the calorimeter. This unrealistic restriction can be removed by showing experimentally that

the energy equivalent, E, is independent of the location of the energy

input. Such independence can be designed into the calorimeter, using

(4) the idea of equivalent sources . Briefly, the idea is to make the heat

reach the surface of the calorimeter by the same path no matter what

the energy distribution inside the calorimeter. An application is discussed in the next section.

By the technique of equivalent sources, the heat exchange can

be properly accounted for. Since the internal energy, E(T - T.), is

intrinsically independent of the source, the entire measurement is independent of the source, and provides an accurate means of comparing

laser and electrical energies. Equations (8) and (9) therefore represent a complete theory of measurement, prescribing how an unknown

quantity, A U , is to be determined from temperature observations

and a calibration experiment. Measured in this way, the energy in the

laser beam is obtained ultimately in terms of the electrical standards

maintained by the National Bureau of Standards. This direct relation

to the electrical standards seem much preferable to reliance on the

traditional radiometric standards.

2. 1. An Application of the Theory

A calorimeter applying the principles set forth above is shown

in cross-section in figure 2-3. The calorimeter accepts radiation on

two polished conical surfaces which reflects the light into annular spaces

where it is absorbed by multiple reflections. The calorimeter is sur- rounded by a thick aluminum block which has a heater and resistance

themometer for temperature control. The assembly is housed in an

aluminum box.

15
Table 2-2

Dependence of Calibration Factor on Heater Location

Heater No. 1

. 1150

. 1144

. 1143

. 1146

Ave.. 1146

s = . 0003

Heater No. 2

.1107

. 1103

.1107

.1106

. 1116

. 1112

Ave. .1109

s = . 0005

16
The calorimeter shows the application of the principle of equivalent sources. To reach the outer surface of the calorimeter (outer

heavy line), heat flows from the heat or absorbing surface back to the

ring, R, and then out to the calorimeter surface. This is an approximation, of course, since some heat can flow directly to the surface by

radiation and air conduction.

Two heaters are installed to test the design. With the design as shown in figure 2-3, the results in table 2-2 were obtained for two series of calibrations (s is the estimated standard deviation. ) Note that

the reproducibility is excellent for each heater alone, but the systematic

error implied by the different results is far poorer, showing that the

two heater sources are not equivalent at the 1% level.

Another thin metal surface was placed around the calorimeter,

attached only at the ring and spaced about 1/8 in. from the outer surface,

shown. A greater space would have been preferable, but would have re- quired extensive modification of other parts. The calibrations were re- peated with the following results: For heater number 1, average 0. 1383,

s = 0. 0004; for heater number 2, average 0. 1364, s = 0. 005; difference

1.4%. Apparently, the added surface made the two sources more nearly

equivalent.

The actual time-temperature curves for the two heaters are

shown in figure 2-4. The energy inputs were equal, but the heat ex- change was quite different for the two experiments, so that the amplitude of the final single exponentials are quite different. The solid

curve extrapolates to the circle at zero time and the dashed curve to

the cross, illustrating the error possible in data analysis by extrapolation on the assumption that the geometrical distribution of the two

sources is the same. The difference is more than 5%.

17
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Another interesting point arises in connection with the constant

temperature surroundings. The theory eq (3) requires constancy, but

practically, the question is how constant? In this case the temperature

of the calorimeter was measured by a thermocouple (S, fig. 2-3) relative to the surroundings. If the latter varied, the observed temperature

was in error by the magnitude of the variation. For a 1 mK varaition in

a 0„ 1 K temperature rise, the error would be 1%. A temperature measurement independent of the temperature of the surroundings would give

a smaller error because only the heat exchange would be affected.

References

1. L. M. Branscomb, Scientific Research 3 No. 11, p 49, May 27,

1968.

2. J. M. Cameron and Harmon Plumb in a talk given before the Society

of Automotive Engineers, New York, April 21-24, 1969.

3. D. C. Ginnings in Experimental Thermodynamics I, J. P. McCullough and D. W. Scott, ed. , Plenum Press, New York, 1968.

4. E. D. West and K. L. Churney, (To be published).

5. E. D. West and K. L. Churney, J. Appl. Physics 39, 4206(1968).

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UJ o u 1 bfl

CO fl1 fl s

•M

M

>s

u CD

r "\ rt ,fl VJ i—< Ph •M m

CD

flW)

20
3. Energy Measurements

3. 1. Introduction

Of the several methods one may use to measure pulsed laser

1 -8

energy, the calorimetric one is capable of yielding relatively high

accuracy. We have designed, built and calibrated calorimeters for

measuring the output energy of the pulsed ruby laser 694. 3 nm and the

pulsed neodymium laser 1060 nm. Input energy measurements 0. 1J to

100J, to calibrate laser energy detectors, have an estimated ± 2%

uncertainty. Energy measurements of our absorption cell calorimeters

agree within 1% of our own reflecting metal plate calorimeters which

absorb a known portion of the energy and reflect the rest.

Details are given in reference 8. They are reviewed here and

modified according to the additional work accomplished.

3. 2. The Calorimeter

The calorimeter is shown in figure 3-1. The calorimeter

absorption cell, filled with an energy absorbing solution, is supported

in an aluminum or brass heat sink by polystyrene foam. The heat sink

is also placed in low density polystyrene foam insulation and the entire

system enclosed in an aluminum box. One junction of a copper -constantan

thermocouple is attached with silver epoxy to the absorption cell, and

the other junction is attached to the heat sink. The cell junction should

have close thermal contact with the cell. When pulsed laser energy is

fired into the absorption cell, the cell rises in temperature and the

thermocouple generates a voltage proportional to the temperature

difference between the absorption cell and the heat sink. The decaying

output voltage of the thermocouple, logarithmically extrapolated to a reference time (see section 6 on calibration), is a measure of the energy

21
QUARTZ

WINDOW HEATER

3 mm

6 mm

Figure 3-2.

v^W5 THERMOCOUPLE

AG. HOUSING

Cross- sectional diagram of the calorimeter absorption

cell, showing the approximate size of components and

the position of the heater wire.

22
in the laser beam. The extrapolation is made when the decay is a single

logarithmical function. The voltage generated by the thermocouple is

measured with a nanovoltmeter whose output is amplified and fed into a

strip chart recorder.

A cross -sectional view of the absorption cell is shown in

figure 3-2. The cell wall is made of silver ~ 0. 5 mm thick. The cell

has a diameter ~ 3 cm and a depth of 3 mm at the edge and 6 mm at the

center. It has two or three small holes near the edge. One hole is

utilized for filling liquid and the other one or two is for the heater wires.

The latter has a Teflon coating, a resistivity of 16 ohms/foot and a total

resistance ~ 100 ohms. The entrance window is high optical quality

quartz. A cement, used to bond materials with dissimilar expansivities,

bonds the quartz window to the silver cell. A small amount of beeswax

and cement is used to seal the fill and heater wire holes. The cell is

filled with a one molal solution of CuSO / 5H ? 0. A 4 mm air bubble

between the heater leads relieves expansion of the heated liquid. The

addition of a few drops of Bendix purple ink into the solution extends

the useful range to < 500. nm. The absorption characteristic of the

solution is nearly the same at 694. 3 nm and 1060. nm, although there

is a large increase in it between these two wavelengths. The cell filled

with this solution will absorb >99. 9 percent of the laser beam, not

including the Fresnel reflection at the entrance window which is 3. 5%.

The index of refraction of the glass and liquid are approximately the

same.

The cell gives about 0. 1 C temperature rise for a 1 . 4 J input.

3.3. Methods of Calibration

Three independent methods of calorimeter calibration are used.

One calibration is based on the thermocouple calibration (/LtV/°C)

23
divided by the heat capacity of the absorption cell (J/° C) ; and the second,

on the thermocouple output (jLiV) divided by a dc electrical energy input (J)

into the absorption cell heater; and the third, inter comparing at 694.3 nm

to several reflecting metal plate calorimeters. A plate absorbs 43% of

the energy and reflects the rest at a 45 angle into a liquid cell calorimeter. A correction is made for Fresnel reflection at the entrance window

of the liquid cell and the absorption of some of this reflected energy by

the plate.

Other details are also given in section 6.

a. Heat Capacity Calibration

The heat capacity calibration (~ 3jiV/j) consists of the thermocouple calibration divided by the heat capacity of the absorption cell.

All the component parts of the absorption cell are weighed and the most

accurate obtainable values of the specific heats are used to calculate

the heat capacity of the absorption cell. The largest part of the heat

9 capacity is the heat capacity of the CuSCs solution . The thermocouple

sensitivity is determined (error ± 0. 2%) by a technique described by

Sparks and Powell . Correcting for Fresnel reflection, the corrected

specific heat calibration SHC compared to the calculated value SHC is

SHC = SHC (1-R) where R is the reflectivity of the window.

b. DC Electrical Energy Calibration

The dc electrical energy substitution calibration is accomplished

by applying energy J from a dc voltage V across the resistance r of the

V2

heater wire for a time t where J = t. Corrections are made for the

r voltage drop and resistance of the cable to the heater. The calibrated

value is obtained by making a logarithmical extrapolation of the thermal

decay to a reference time (see section 6). The thermal output (jiV) (1-R)

24
is divided by the J input. Calibration value R here is the reflectivity

of the window. The thermocouple output is normalized at 25° C. A

ribbon thermometer attached to the heat sink is used to measure the

temperature of the system. The thermocouple output is corrected for

this temperature.

During the electrical calibration the gate output from a preset

scaler, counting the line frequency (60 Hertz), is used to turn on a transistor switch. The transistor is powered by a constant current

source (constant to 0.01%), and the absorption cell heater wire is in the

collector circuit of the transistor. The voltage drop across the heater

is monitored by a digital voltmeter and a calibrated strip chart recorder.

A recorder event mark determines the starting time.

c. Reflecting Plate Calibration

Intercomparison of liquid cell calorimeters to reflecting metal

plate calorimeters yield energy values within 1 % f rom each other. The

reflecting plate is calibrated from the thermocouple calibration and the

heat capacity and reflectivity of the plate. It reaches a uniform temperature in 2 or 3 seconds. The laser energy is the /iV output divided by

the calibration value. A detailed discussion is given later.

3.4. Logarithmical Extrapolation

Logarithmical extrapolation of data may be accomplished as

follows. One may plot the fj,V output versus time on semilog paper. The

output coordinate is the log scale and the time is the linear scale. The

straight line portion of the curve when a single logarithmical decay

occurs, is extrapolated to find the fXV output y at a reference time (see

section 6). In a second method two points are selected from the portion

of the curve where a single logarithmical decay occurs. An extrapolated

25
output is calculated using the expression for y . If the same two points

are always used, precision is improved for those calorimeters whose

decay deviates slightly from a single logarithmical function. We have

for the output r y at t 3 r r

t'i/r

yr

= y 1 e (i)

' ln(y

1 /y 2

) (2)

where y, and y are the juV output at t and t . For the NBS calorimeters,

T?«1000 seconds, t, = 240 sec and t ? = 600 sec. The chart paper is

centimeter cross section with millimeter divisions and 25 centimeter

width. Chart speeds of 1.25 cm/minute or greater are used. To

maintain accuracy, half to full scale deflection of y is used. To

calculate y values, prefiring data at a constant or zero slope is used as

a baseline. All data are read to — of a division.

The upper bound on the percentage error of y for no error in

time is

yr Vz'h) \

2 ?i ' y z J

dy

r,

(3)

Using several output values on the decay curve, the value of y deviates

r (~ 0. 1%) from data using only y and y .

26
Let us briefly consider extrapolation in calibrating a calorimeter

with a relatively long time constant and large thermal capacity. Sometimes linear extrapolation to a reference time or a maximum of the output voltage of the unknown is used. This leads to errors which can be ~ 10% when the area of the beam's cross-section and/or the magnitude

of the beam changes. Logarithmic extrapolation to a reference time

gives a calibration independent of the beam area or intensity for the

range of the instrument. The maximum output voltage gives a precise

calibration factor for fast responding calorimeters.

3. 5. Intercomparisons Using Liquid Cell Calorimeter

To intercompare calorimeters and other detectors at 694.3 nm,

we use the apparatus arrangement shown in figures 3-3, 3-4, and 3-5.

We evaluate the energies received E and the reflectivities R. These

are approximately 4%, 20% and 40% for R , R _ and R _, respectively.

R. can be used for making measurements f rom ~ 20 to 100 J; R- n ,

5 to 20 J; and R ._., 1 to 5 J. R . and R„» can also be used for measuring

40 4 20 to energies < 1 J. To know the laser energy one might expect for measurements, the laser output is calibrated ~ 1 0%. R and R ?n are used

together because of the maximum energy limits of the NBS calorimeter.

The energy input to the unknown device, E , is evaluated after

determining the energies received and the reflectivities of the components in figure 3-3 and figure 3-4. The calorimeters and beam splitters

are 1 to 2 meters from the output mirror of the laser.

We have

_ |LlV(output laser energy) E N

is the energy of

N uV(output dc energy) (1-R)/J (dc energy) , IDC , . , r x r &j" v // \ &// an nbs calorimeter.

27
R40 0r

R 20

orU

Figure 3-3. Block diagram of apparatus arrangement used to intercompare pulsed laser energy measuring devices. Laser

L, demagnifier D, aluminum oxide porcelain aperture

A, NBS calorimeters 4, 5, 6 and device U, and beam

splitters R"4' R and R. n with reflectivities 4, 20, and

40%, respectively. D reduces the diameter of laser

beam to ~ 1/4 size. A= 3/8", etc., depending on devices to be calibrated.

A

U

Figure 3-4. Same as figure 3-3 with the second beam splitter

removed,

28
m!

0)u

-J GX)

•r-t _£

<+H "> o 6^ +J CO s

a>

+-> S o

0)

Q

flcd

u

^i <u ua

Cfj ao 2 ctf a u a>

tti T3

Oh

flj <+-! J ^ u a CD

rt CO ^ cd

&jO

J

r3

A

+>• i-l & £ , m

on

<U

?H3

cuo h

29
R

E c See figure 3-3 for laser

5

20 E c + E, output S. Calorimeter

5 6

6 used.

&' See figure 3-3 for laser

d _ 4 El output S . Device U

R „ 4 used.

And

E"s -

= : |E" = E" See figure 3-4 for laser -{-£)

fc^)*4

'4 output S'

Since E « 4E , the error of E is approximately the error of E,.

o 5 u b

When R„„ or R„_ are used to determine the energy E , we have

20 40 to/ u

:;= (^fH'I El , for R .

E E E

And E; = ^ E'

5

, where g* for R / ^ for R^

5 5 5

30
Again the error of E is approximately the error of E ,. Using R and R?n to calibrate a calorimeter gives values which

agree within 1%. Using R 9n and R. n to calibrate another calorimeter

gives similar agreement. The NBS calorimeters need to be recalibrated

occasionally to check the absorption cells for leakage.

At 1060 nm the same setups are used except the reflectivities

of the beam splitters R. A and R. are 44% and 6%. These are used

similarly to R ?n and R . in calibrating for measurements at relatively

high energies at 1060 nm.

If the position of the unknown and the NBS calorimeter are interchanged in figures 3-3 and 3-4 then energies below 1 J can be measured.

The estimated calibration uncertainty over the energy range is ±

± 2%o The energy E of an NBS calorimeter is

jLtV(output laser energy)

N ^V(output dc energy) (1-R)/J (dc energy)

lithe same nanovoltmeter and recorder are used with a given calorimeter without changing the instrument ranges, no error occurs in the

output voltage ratio above. Its precision is (~±0.Z%). The estimated

error in the dc energy J is (~±0. 1%). The estimated error from the

substitution of dc energy for laser energy is (~±0. 1%). The estimated

calibration error of the nanovoltmeter is (~±0. 1%), the recorder is

(~±0. 1%) and the reflectivity (R~40%) is (~±0. 2%). For reflectivity

(R~5%), it is (~±0. 5%). A Lindeck potentiometer made from NBS and

commercial components is used to calibrate the voltmeters and recorders,

3. 6. Intercomparisons Using Metal Reflecting Plate Calorimeter

Liquid cell and reflecting metal plate calorimeters are inter

compared at 694.3 nm. They agree with each other within 1% over an

31
(a) L D I

R40

Q

Q

(b)

R40

Q

H

Figure 3-6. Setup to calibrate R . Refer to figure 3-3 for identification of symbols.

32
input energy range of several joules. The plate absorbs 43% of plane

polarized light and reflects the rest at 45° angle into a liquid cell

calorimeter. The plate is a 99. 9% purity silver disk, diameter 1-1/2"

and thickness 0. 17". It is optically polished being relatively free of

-ft imperfections and plated with 99. 5% purity nickel 10-15 • 10 inch

thick. The purpose of the plating is to increase the sensitivity and

precision of measurements. The plate reaches a measured uniform

temperature in 2 or 3 seconds. Two calibrated thermocouples are

mounted at the center and edge of the back of the plate using a low

temperature Indium alloy solder. The plate is housed similarly to the

liquid cell calorimeter except there are both an entrance and an exit.

Laser energy E is determined from the absorbed energy of the

plate E , the reflectivity of the plate R (calibrated from measurements

P P

using the liquid cell calorimeters) and a correction for plate absorption

of some of the energy reflected from the liquid cell calorimeter. This

latter energy is two percent of the energy absorbed by the plate. E

equals the jiV rise in temperature at the time of energy input divided

by the heat capacity calibration of the plate (~3. 5jiV/j).

We have for the laser energy

E

e t =- -&

L (1-R ) (1 +R R,)

P P 6

where R R, = 0. 020 to a close approximation,

p 6

To make inter -comparisons of the two types of calorimeters the

following measurements are made.

The absolute value reflectivity of RAO is measured using the

setup shown in figure 3-6. Using setup (a), E and E are measured.

5 6

33
CD

c

u

»*-a> or V CO

o

r-l U

ft <D

CO

CD •—

I

O

s ? a "

•H C ti o fn 2

ti rt °

cu o <+H tH o

T)

CD

f] s rt o

rt .-H • H

ft +-> i-H rt i—

1

cu bo o

• p-l u • H m +> •H

T3 o 4->

• rH (1) W

3 1—1 cu a

1 m TJ •H CU • H

i-H u

Jh <u

ctf Jh <+H

rrt CO ft •r-l OO B Oh CO O

c> cu

CD

• CO

rH bO a

CU • H

+-> <-H o

cu o

Oh •H

fn O

I—

1

CU

CD Of cD CO o Pd

CO

cu

bO

•rH

34
Calorimeters 5 and 6 are the liquid cell type. Using setup (b), E' and

E/ are measured, where

6

E

5 + K

R

40

=

2

Averageto of several sets of data is used to find R.„.

40

The reflectivity R of the reflecting plate is measured using the

setup shown in figure 3-7. E r , E, and E are measured

5p 6p p E j- E , R = =— —— . Average of several sets of data is used to find R . P E

6

E

5p

P

To intercompare calorimeter 6 with calorimeter P, we use the

following expression

6p

And for calorimeter 5, we have

E. = lf^~ ^4C ]

^

5p I 1 - R

40 p^jpv^)'

The error of E is (±0. 5%). The error of the reflectivities are

P

approximately as given in the previous section*

35
3. 7. Other Parts of the System

Let us consider other parts of the system. The ruby rod has its

crystal axis aligned horizontal ~±1° . The outputs of the ruby and

neodymium rod lasers are plane polarized light. Polarizers are used

with the neodymium laser because its output is unpolarized without them.

They must thoroughly polarize the light so that the reflectivity will not

vary as a function of the intensity of the laser beam. Both lasers are

aligned with their beams parallel to the optical bench at a constant

elevation above it. The demagnifier reduces the beam to about l/3 to

l/4 size. It is adjusted to give a beam with approximately parallel rays.

If the rays converge, they will yield destruction where they are most

concentrated. The beam splitter is sensitive to change in its angle with

respect to the laser. If any part of the system moves, the calibration

of the beam splitter changes. Consequently, the reflectivities of the

beam splitters need frequent calibration. Movement of the calorimeters

will affect the accuracy of measurements if not all the energy is

captured.

To assure proper alinement of a calorimeter, an aluminum plug

with cross hairs is placed in its entrance with a piece of photographic

paper over it which burns a clear image. Glass covers are placed

between the target and the beam splitter. The glass protects the latter

from a searing heat wave. The calorimeters are aligned so that the

burned area is close to the center of each entrance.

The beam splitters are 2" diameter, l/2" thick and 30 minutes

of arc wedge. A reflective coating is on the front surface and an antireflective coating on the back surface from the laser. The beam

splitters can withstand higher energy if they are used this way because

the front surface needs to be able to yield when the laser pulse strikes

it. The laser light is plane polarized in the horizontal direction. The

36
o beam splitters are mounted vertically at a 45 angle. The same

orientation is used in the reflecting metal plate calorimeter. The

wedge of the beam splitter is adjusted for minimum horizontal deflection

of the transmitted beam and for discarding the reflection from the back

surface of the beam splitter. Energy data using several beam splitters

indicate that the energy lost by absorption or scatter from them is

negligible.

References

1. G. Birnbaum and M. Birnbaum, Proc. IEEE, 55, No. 6, 1026

(1967).

2. D. E. Killick, D. A. Batemen, D. R. Brown, T. S. Moss and

E. T. DeLaPerrelle, Infrared Phys. 6, 85 (1966).

3. A. J. Schmidt and R. C. Greenhow, J. Sci. Instr. 44, 468 (1967).

4. J. G. Edwards, J. Sci. Instr. 44, 835 (1967).

5. H. S. Heard, "Laser Parameter Handbook, " (John Wiley & Sons,

New York, 1968), p 480.

6. R. A. Valitov, Yu. A. Kalinin and V. M. Kuz'michev, Translated

from Izmeritel'naya Tekhnika, No. 5, 37 (May 1965).

7. A. V. Kubarev, A. S. Obukhov, A. Ya. Leikin, Y. S. Solov'ev and

V. P. Koronkevich, Translated from Izmeritelhaya Tekhnika,

No. 11, 20 (Nov. 1967).

8. D. A. Jennings, IEEE Trans, on Instr. & Meas. IM-15, No. 4,

161 (Dec. 1966).

9. A. F. Kapustinskii, B. M. Yakushevskii and S. L Drakin, Zhur.

Fiz. Khim. , 27_, 588(1953).

10. L. L. Sparks and R. L. Powell, Measurements and Data, 1_, 82

(1967). '

37
CD +>

CO

!>N (0

flO• H

+J

tti fH ^•H

i-Hrto

J-( <D

+-><ua

vi

<uzo

CXM

<u

COa

1- <—*

^^ <u e> J

_JCO +» < V

fti o

COI

<uu

60 • i-i

38
4. CW Power Measurements

4. 1. General Description

The need often arises while working with CW lasers for measuring the absolute power in the laser beams. The calorimeter used

for pulsed laser energy measurements as described earlier lends itself

to the task of absolute power calibration of power meters. Since the

calorimeter and its associated equipment have already been calibrated,

it can be used as a device to integrate the power of a CW laser beam

for a measured period of time from which the average power can be

determined. However, due to the necessity of using long integration

times, on the order of 1 to 2 minutes, the heat losses from the calorimeter cell during the initial temperature rise are not the same as for

pulse laser energy measurement. It is necessary therefore to use an

electrical calibration pulse of the same power level and same time

duration as the CW laser pulse.

A schematic representation of the CW laser power meter calibration used in this laboratory is shown in figure 4-1. The function of

each component is as follows: the time- shutter control actuates the

shutter and precisely controls the time during which the laser beam

enters the unit. In addition it provides a time reference for the two

chart recorders. The beam splitter, B, divides the beam into two

parts; one part is directed towards the transfer detector and the other

part illuminates the calorimeter cell, C. A diffusing screen is placed

before the silicon photovoltaic cell in the transfer detector to provide

more even illumination and to prevent damage of the photocell surface.

Two recorders record separately the output of the transfer detector

and the calorimeter as a function of time. The time reference is re- corded on the second channel in each. R, which terminates the output

39
LASER BEAM

SHUTTER fTER/

u U

TIMER

2-

SHUTTER

CONTROL

T~

i

g

MILLIVOLTS

TIME

TRANSFER DETECTOR

CHART

MV

TIME

CALORIMETER CHART

Figure 4-2. Diagram showing the basic calibration procedure.

40
of the transfer detector, is chosen such that the maximum illumination

of the transfer detector will not produce a nonlinear output of the photocell. The achromatic lens, L , provides a divergent beam to accommodate power meter sensing heads with different diameter apertures.

Lens L produces an image, I, on the alignment screen of the beam

spot on the transfer detector. This provides a convenient means of

checking the alignment of the calibration unit with respect to the incoming laser beam throughout the entire calibration.

The calibration procedure consists of two parts. In the first

part the output of the transfer detector is calibrated in terms of absolute power in the laser beam as seen by the calorimeter. Schematically this is shown in figure 4-2. After the calibration unit has been

aligned with the laser beam, the time is set for a time T and the shutter

is activated. The output of the transfer detector in millivolts is re- corded on one chart recorder as a function of time. Simultaneously the

output of the calorimeter is recorded on the other recorder as a function

of time. The reference time pulse on the transfer detector recorder

provides a check of zero time and on the other it determines zero time.

The output of the calorimeter begins to rise with the onset of

the laser beam and the light energy is converted to heat energy. It continues to rise after the shutter is closed until an equilibrium is

reached after which the cooling is predominantly that due to Newton's

law of cooling and hence fits an exponential decrease. Thus by using

data points to fit an exponential and knowing the calibration constant

(determined as described earlier) in microvolts per joule of the calorimeter, the total electromagnetic energy incident on the calorimeter

for the time, T, can be determined.

41
S3! nor 'A9U3N3

nJ

(D £>u

CU

CO ^ a cu i-H 4-> £

u CO rt T>

cu •M s

u •H

cu +J

•(-> cd CUB

M T3

CU i-H +> o 3

i-H Jh i—

<

Sh cu CU CJ +J T> •|H •H

EJ CO cr «J r—

1

£

CU a

+» cti m

O

cu

cu ^

CO CU

CO a

i-H

CO

cu £

Jh u

cu <u ^1 ^

H Eh

CO

<u

H42
The average power then leaving lens L is known for one power

level input. Repeating this procedure for other power levels into the

calibration unit yields a straight line graph of millivolts output of the

transfer detector as a function of the laser beam power leaving lens

L for one wavelength.

La The second and last part of the calibration is performed by re- placing the calorimeter with the sensing head of the power meter to be

calibrated. Since the output of the transfer detector is now calibrated

in terms of the power incident on the power meter sensing head, it is

merely necessary to compare outputs and the calibration is complete.

Figures 4-3 and 4 show data obtained during a power meter

calibration. The three wavelengths used were 514. 5 nm and 488. nm

lines from an argon ion laser and the 63 2. 8 nm line from a helium neon

laser. Various power levels in the beam were obtained by varying the

input power to the laser.

One of the calorimeter output recordings is shown in figure 4-3.

The illumination was the 488. nm line. The two points shown are ex- amples of the points used to determine the constants of the exponential

cooling curve; the equation of which is also shown. The average power

seen by the calorimeter in this case was 1 0. 9 milliwatts as determined

by the method discussed in section 6. (See section 6). Also indicated

by the event marker is the time, 104 seconds, that the laser beam

illuminated the calorimeter.

The results of the first part of the calibration procedure, namely

calibration of the transfer detector are shown in figure 4-4. The values

of the ordirates for the plotted points shown were obtained from curves

like figure 4-3. Values for these data point abscissas were obtained

from the output of the transfer detector as measured across a five ohm

terminating resistor with a calibrated chart recorder. The chart re -

43
1000

5

E

UJ

ha:

3

<

100-

I 10 100

TRANSFER DETECTOR OUTPUT (mv)

Figure 4-4. Transfer detector calibration as a function of laser power.

44
corder also provided a monitor of the laser beam during the time of

illumination. Since the curve for the 488. nm line was linear, it was

assumed the curves for 514. 5 and 632. 8 nm lines would also be linear

and only two data points were used.

The last part of the calibration was completed by replacing the

calorimeter with the sensing head of the power meter and comparing

the power meter readings with the curves of figure 4-4.

The estimated error in a single point on the curves of figure 4-4

is approximately ± 4%. This value was determined as follows. An

estimated error of 1% is associated with the calorimeter- -nanovoltmeter- chart recorder calibration. In fitting the exponential curve of

figure 4-3, it is estimated that the coefficient of the exponential which

is the energy into the calorimeter is determined to within ± 1. 3%. The

timer used here has an uncertainty for the shortest time of ± 0. 8% plus

a ± 1% uncertainty in the shutter activation.

45
ALL PARTS ALUMINUM UNLESS

OTHERWISE STATED

Figure 5-1. Schematic of the copper disc calorimeter showing

construction details.

46
5. CW Power Measurements in Excess of 1 Watt

5 1. Introduction

The advent of lasers capable of producing many watts of power

(notably the CO laser) has produced a demand for methods of measuring these powers.

A simple method of measuring powers in excess of 1 watt consists of absorbing the laser beam in a calorimeter and measuring the

heat produced. Several different types of calorimeters were tried and

will be discussed. The most recent design will measure from 1 watt

to 5 kilowatts with an accuracy of better than 3% at 100 watts. Although

the calorimeter was used at a wavelength of 10. 6(j, it should work well

throughout the visible spectrum.

5. 2. Calorimeters

Three different calorimeters were used to measure the power of a CW 200 watt CO laser. All three devices utilized standard calorimetric techniques to measure the heat produced by the absorption of the

laser beam. The three devices, the disc, cone- disc, and cone-flow

power meters will be described separately.

a. Disc Power Meter

A copper disc blackened with flat black spray paint served as the

absorber in the disc power meter shown in figure 5-1. The reflectivities

of various materials was measured by using a beam splitter arrangement and comparing the reflected intensities with that from a polished

copper surface. The results are summarized in table 5-1. The heat

absorbed in the central region of the disc flowed to the periphery of the

disc and was dissipated by the cooling fins. The thermal gradient

47
Table 5-1.

Reflectivities of various materials at 1 0. 6 microns compared

with polished copper. (Accuracy about 10%).

Surface Direct Total Reflection

Reflection (Direct & Diffuse)

Heavily anodized aluminum (undyed) 0. 45% 3.5%

11 " " (dyed black) 0. 55% 3.7%

3-M velvet coating #101 -CIO black 0.2% 6. 0%

Aluminum anodized cone < 0.2% < 1%

Velvet coated cone < 0. 2% < 1%

Aluminum oxide disc 0. 94% 9.0%

48
cr

UJ<

(r 2 1 UJ < CO UJ < CD

_l

0)O• Ho

•M

COOuwao

CO

140)

+->Uo

fto

(0

0)oo

CD 3o• r-l 3

COo

CON

ID

<DU

•H

49
on the disc was measured with a copper- constantan thermocouple with

one junction at the center and one on the periphery. The device proved

very useful and convenient for relative power measurements, partly

because it had a shorter time constant than the other two calorimeters

used (about 0. 1 second). However, the disc became excessively warm

during operation, and the output varied by several percent as the beam

diameter and its position on the disc was changed, therefore no attempts

were made at accurate calibrations of the disc power meter and it is

presently used as a convenient relative power indicator.

b. Cone- Disc Power Meter

In the cone- disc power meter shown in figure 5-2, a blackened

cone absorbs the laser beam and the heat then flows radially through a

disc attached to the apex of the cone as in the disc power meter. The

periphery of the disc is water cooled to lower the temperature of the

device and thus lower the loss of heat due to radiation and convection.

The cone serves to reduce reflection losses which may amount to 1 percent from the disc-power meter and to reduce the dependency on

beam position and area. To calibrate this power meter, an insulated

heater wire was wound on the outer surface of the cone and coated with

conducting epoxy to distribute the heat. The electrical heat dissipation

was plotted versus the thermocouple voltage from 25 to 150 watts.

Three major flaws were noted early in the use of this power meter; the

thermocouple output varied with the flow of cooling water, and the cone

became warm enough to heat up the outer shield of the meter, and the

response time was excessively long (several minutes). In spite of these

drawbacks good agreement (2%) was obtained at 75 watts of laser power

with the cone-flow meter to be described next. The cone- disc power

50
<0

tio

•I-l +>ouM

cooU

Miaomu

CDOo

r—) i <D

flOo

+-> o

nio

ro

<L>

•H

51
meter was abandoned in favor of the cone-flow power meter, since the

cone-flow power meter had none of the mentioned defects of the conedisc meter.

c. The Cone- Flow Power Meter

The cone-flow power meter shown in figure 5-3 has proved to be

the most useful and accurate one which we have used thus far. The

laser power is used to increase the temperature of water flowing

through the double cone. The flowing water in contact with the inner,

heat absorbing cone, maintains its temperature near room temperature

so that radiation and convection are negligible. The reflection from the

blackened cone was measured to be less than 0. 2%. The water flow

rate was maintained by a pressure regulator and metered with a calibrated differential flow meter. The flow rate was measured to an ac- curacy of 1%. The thermocouples were fastened on 3 cm pieces of 5. 3

mm o. d. , 4. 6 mm i. d. copper tubing separated 1 to 12 cm, from the

cone by tygon tubing. Electrically insulating epoxy held the junction on

the tube, and a layer of conducting epoxy over coated the entire junction

to maintain its temperature

In order to assure a "mixed flow", the tube was crimped twice

to an inner dimension of about 2mm; the two crimps were at right angles

and were about 1 cm apart. The junction was located between the

crimps. The cone and junctions were all isolated by an insulating plastic

shield and an aluminum box. The usual water temperature was about

o o

8 C and 75 watts of power produced a 1. 25 C temperature rise with a flow rate of about 1 L/min. The overall response time was about 8

seconds with this flow rate. Since one could obtain the same accuracy

o with a 20 temperature rise and could also quadruple the above flowrate, one could easily measure 5 kilowatts with the same 3% accuracy.

52
A flow-cone of similar design has been used to measure 8. 8 kilowatts

Cones were constructed from both black dyed anodized aluminum and

black painted copper. With the copper cone, the recorded thermocouple

voltage had fluctuations of about 1% while with the aluminum cone the

fluctuations were nearly 5%. Therefore, the copper cone was adopted

for this power meter.

To check the accuracy of this power meter a teflon insulated

resistance wire was wound outside a 1 mm thick copper cone about 6 cm

long which was inserted snugly into the calorimeter cone. In this way

the electrical power could be compared with the power measured by the

calorimeter. Agreement within 2% was achieved; this agreement confirms our independent accuracy estimation of 3%. Thus, it is felt that

the power meter is a reasonable choice for measurement from 1 watt

to 5 kilowatts of CW laser power with accuracies of about 3%.

References

1. Technical Report. High Power Gas Laser Research. Raytheon

Research Division, September 1968. Prepared for U. S. Army

Missile Command, Redstone Arsenal, Huntsville, Alabama.

53
6. Data Reduction for the Liquid Cell Calorimeter

The measurement of the amount of energy in a laser pulse or

the average power in a CW laser beam would be a simple matter if an

ideal calorimeter could be employed. The calorimeter would consist

of a cell which would convert all of the incident electromagnetic energy

to heat energy. The heat energy in turn would raise the temperature of

the cell from a temperature that represented the initial thermodynamic

equilibrium state T. to a higher temperature T which represents a

final equilibrium state. If C represents the known heat capacity of the

cell, the amount of electromagnetic energy incident could be determined

from

Q= C (T. - T.) . i 1 (1)

In this case the response time of the cell as well as the time duration of

the input energy is immaterial since no energy is lost. Only the temperatures of the initial and final equilibrium states are relevant. A

temperature time- curve would be as shown:

Vf

V, jjlV

V(

Time

54
Where v is the temperature measured with a thermocouple and t., t

1 p

and t are times for the onset of the incident energy, the time the incident energy is turned off and the time the final equilibrium state is

reached, respectively.

A real calorimeter inherently possesses two problems which

prevent a simple determination of the injected energy as done above.

Heat loss mechanisms exist during the time of and after the injection

of the energy and the cell never reaches exactly a uniform temperature

after the energy injection. However, for the calorimeter used here

tests show that all of the electromagnetic energy entering the liquid

cell is absorbed and that the absorbing properties of the liquid do not

change with time for the energy levels and power levels used. In

principle, it should be possible to set up the heat flow problem for the

absorbing cell, from which the temperature distribution as a function

of time and position could be determined and consequently predict the

heat losses. The assumptions made in order to fit boundary conditions

and to compensate for the complexities in the geometry of the absorbing

cell make it difficult, if not impossible, to determine the heat losses to

within the desired accuracy. Another alternative approach is to develop

a technique of calibrating the calorimeter in such a way that when it is

used to measure electromagnetic energy, the results can be stated with

a confident accuracy.

The basic method of calorimeter calibration adopted here is to

inject a known amount of joule heat energy into the calorimeter cell

and measure the temperature rise with a calibrated thermocouple. Thus

determining a calorimeter calibration constant in the units of microvolts

(temperature rise) per joule (heat energy input). However, the calorimeter cell never reaches a uniform temperature and hence the problem

55
is to develop a technique of determining an effective temperature rise

of the cell that will give an accurate calibration constant. Once the

technique has been developed it can be applied to the measurement of

electromagnetic energy.

The technique of measuring the temperature rise of the calorimeter cell is a result of an understanding of the calorimeter behavior

under conditions of both measuring electromagnetic energy and that of

calibration. Consider e. g. a typical temperature- time curve of the

calorimeter cell under calibration condition:

v.M'

An accurately measured amount of joule heat is injected into the calorimeter for a time t . The measured temperature rises almost linearly

p

to v after which a slight overshoot with a maximum v at t takes

p mm

place. Then the temperature decreases to v at a time t and beyond

this point the temperature decreases at an exponential rate as a result

of the heat loss mechanisms. It has been determined without exception

and regardless of the source of heat, that the temperature decrease

after the time t fits a simple exponential within the accuracy of measurement. With the aid of the temperature-time curve and a knowledge

of the heat capacities and heat conductivities of the components of the

56
(61.6 sec, 9.32 ^.V)

(150 sec, 7.80 ^.V)

Time, sec.

(I64sec, 7.70 /xV)

Time, sec. Figure 6-1. Response of calorimeter to a DC electrical energy pulse.

Top trace shows the response of the silver surface and

bottom trace shows the response of the quartz window.

57
calorimeter cell (quartz window, liquid absorbing medium and silver

container), much can be inferred about the dynamics of the cell.

The temperature-time curve is a measure of the temperature

of the silver container and this temperature is uniform over the silver

surface compared to the rest of the cell. With the onset of the injected

heat, the temperature of the silver rises directly as the heat is added

until v is reached. Here, as a result of the relative heat capacities

P

and heat conductivities of the three main elements of the cell, temperature gradients exist between the silver container and the absorbing

liquid and the window (the former being the hottest). Between t and

P

t , heat flows from the silver container into the liquid and the window

eto alleviate these temperature gradients until the point (t , v ) is e e reached where the cell reaches a semi-isothermal state. For times

after t , the loss mechanism is the predominant influence. Since the

e time constant of the heat losses is large compared to the response time

of the cell, the gradients that exist within the cell are very small.

There are only two surfaces of the absorbing cell from which

heat can be lost to its surroundings; the front surface of the window

and the outside surface of the silver container. From the fact that a

simple exponential function will fit the temperature-time curve, the

predominant heat loss mechanism from the silver surface must be

that which follows Newtons law of cooling and the heat loss correction

can be evaluated on this basis. Figure 6-1 is a representation of the

temperature-time curves of the center of the window and the silver

container recorded simultaneously. Duration of the DC electrical input

energy pulse was sixty seconds. The data from these curves are given

in table 6-1.

58
Table 6-1. Data for Electrical Input

Energy 2. 733 Joules

Pulse Duration 60 seconds

(v , t ) glass (7. 70 |iV, 164 sec. )

(v , t ) silver (7.79 u V, 150 sec.)

e e

(vm

, t ) glass (7.87 uV, 129 sec. ) m

(v , t ) silver (9.326 uV, 62 sec.) m m

These curves show that the heat flows as described above during the

heating period. Also, it can be seen that the window and the silver

reach the same temperature at t and remain at the same relative

e temperature during the cooling period (t>t ) and hence to semiisothermal condition. The difference between t for the glass and the

silver can be explained by the difference in the response of the respective thermocouples as a result of difference in physical contact.

Establishing a procedure to determine an accurate calorimeter

calibration constant essentially involves a procedure for determining a meaningful temperature rise of the calorimeter cell with which the

known injected energy can be associated. The accuracy of the technique

can be determined by comparing the electrically measured calorimeter

calibration constant with one which is obtained from the known heat

capacity (sum of the heat capacities of the components) of the calorimeter cell and the calibration of the thermocouple. The latter constant

being that value which would be obtained from the results of calibrating

a lossless calorimeter using eq (1).

59
A technique of fitting the cooling curve with an exponential and

projecting the resulting equation back to zero time to obtain meaningful

temperature rise, v., was first used. This procedure gives reliable

results for calibration and laser energy measurements provided the

ninety second dc electrical energy pulse length is used for calibration.

In Section 6 the "reference time" is t = 0. However, it was later

found that if the amount of injected heat energy was kept the same, but

the time of injection was changed and of duration from fifteen seconds

to three minutes, the value of v. obtained from fitting the measured

curves and hence the calibration constant, k., varied linearly with the

duration of the injected energy pulse; with the lowest value determined

for the shortest pulse. This phenomenon presents a problem when the

same technique is used to determine the temperature rise of the cell

while measuring power in a CW laser beam when the integration times

are long compared to the cell response time.

The procedure that has been adopted is a result of two experimental facts (1) the cell does reach a nearly uniform temperature

sometime after the injection of an electrical dc calibration pulse or

energy injection from any other source and (2) the cooling curve is

always that of a simple exponential.

Since the cell goes from an initial isothermal condition (before

the onset of the injected energy) to a final nearly uniform temperature,

a true temperature rise can be found if the temperature decrease due

to the heat lost during the heating period (0<t<t ) can be found.

During the cooling period (t>t ), the rate at which the temperae ture decreases as a result of the heat loss mechanisms is

dv l

i<>\

dT =

" t

v

• (2)

60
sinoAoaoiiAi *a

y %

3 -M T3

<u

<u 5 w

Jh

*""' o. . g CD _.

^ ^

W3 v

CU m

<u

cti

m w> ^ o •S w» LU to h

3 5) CO

O

m <+H

CO LU 4-> ^

3 £

co 3

CU H

u

£

cu nt •S

+j mCU

**

„> so

Rj 8

X M

CU CU

_. -t-> ti cu <J TJ

tvj

1

CUu3

W)

•I-l h

61
Where v is the measured temperature difference between the cell and

its surroundings and 1/t is determined from the cooling curve. This

indicates that the losses are a function only of the v. Then the decrease

in temperature due to heat losses during the heating period should be

Av = - v dt (3)

J n

the true temperature rise then would be the temperature v plus A v. The quantity Av can be found since v is measured during the heating

period and T is known. The point (t , v ) can be determined by comparing the function v e with the measured curve.

The main problem is encountered when it is assumed that the

temperature-time curve during the heating period as measured by the

thermocouple attached to the silver container is the true temperature

of the surfaces of the cell that can lose heat to their surroundings. It can be seen from figure 6-1 that during this time the temperature of

the window center follows a similar curve, but it is not exactly the

same and hence the error in this method.

When this procedure is used to determine the calibration constant from the injection of dc electrical energy, consistent results are

obtained that are independent of the time duration of the injected energy

and in addition that are consistently 3. 5% below the thermocouple

sensitivity divided by the heat capacity. The error may result from

the departure from a uniform temperature condition in the cell during

the heating period and the delay in the response of the thermocouple.

An example of the results of using the integration procedure in

determining the amount of energy in a laser pulse are shown in figure

6-2, and given below.

62
H

v = 3. 51 n v

e

t e vdt = 0. 43 jjv

v. = 3. 94 W v

true

The calibration constant as determined by the same procedure is

2. 932 UV// , . Consequently, the energy contained in the laser

' Joules n ° pulse is 1. 34 Joules. The energy measurement made by the plate

described in Section 6 gives a value of 1. 36 Joules. The agreement

is- 1%.

An example of the application of the integration method to the

measurement of the average power in a CW laser beam is shown in

figure 4-3. The experimental data from the curve are as follows:

/

v= (3.19 Liv)e t^t curve fitting e

vdt = 347. 5 y, v sec

T= 1200 sec

Av= 0. 29 gv

(t , v ) = (211 sec, 2. 67 uv)

e e

The approach here has been to rely on experimental data rather

than theoretical analysis to suggest a technique for determining the

energy seen by the calorimeter. Results thus far indicate that the

integration procedure yields values for the calorimeter constant with

63
acceptable precision. Although the measured constants are lower than

the heat capacity value by 3. 5%, the error is always in the same direction. Since the same procedure is used for measuring the temperature

rise during the laser power and energy measurements, the effect is a partial cancellation of the error. Consequently, the integration procedure possesses a high degree of precision and allows the measurement of laser power and energy with an accuracy of better than 2%.

64 GPO 854 - 26 1
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