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4? NBS TECHNICAL NOTE 678

*"»CAU O* *

U. S. DEPARTMENT OF COMMERCE/National Bureau of Standards

An Electrically Calibrated

Pyroelectric Radiometer System
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

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the Institute for Computer Sciences and Technology, and the Office for Information Programs.

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- Located at Boulder, Colorado 80302.
•ATIOMAL BDHKAf

Or STANDARDS

LE3RABY

APR 2 9 1976 a c zoo

Pyroelectric Radiometer System

*—

An Electrically Calibrated

C. A. Hamilton

G. W. Day

R. J. Phelan, Jr.

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

<*** 0F c°*

i/i

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

James A. Baker, III, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

- NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued March 1976
NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 678

Nat. Bur. Stand. (U.S.), Tech Note 678, 50 pages (Mar. 1976)

CODEN: NBTNAE
FOREWORD

The program to develop an Electrically Calibrated Pryoelectric Radiometer

began in 1972 when Robert Phelan, Jr. demonstrated the first electrically calibrated pyroelectric detector. The potential of this device as an absolute

radiometric standard was quickly realized, and a dual development effort began.

The first part of this effort was aimed at characterizing and improving the

detector itself while the second part involved the design of a complete

radiometric instrument. The result of these efforts is the instrument described in this Technical Note.

The authors are grateful to Paul Gruzensky for his contribution to the

understanding of pyroelectricity in PVF_, to Lou Mullen for fabrication of

detectors, to Gerry Klein and Kurt Pyatt for automating many of the characterization experiments and to Robert Peterson for his theoretical analysis

of heat flow in pyroelectric detectors. The suggestions of Bill Blevin of

the National Standards Laboratory, Australia, were crucial to our understanding and use of gold black absorbers. Finally we acknowledge the many

ideas and incentive resulting from our interaction with Jon Geist of the

Radiometry Section of NBS

.

111

Contents

Page

Foreword iii

1. Introduction 1 2. System Operation 3 3. Circuit Design 9 3.1 Chopper Speed Control 9 3.2 Calibration Power Driver 11

3.3 Auto Null Servo Loop 13

3.4 Calibration Power Measurement 19

4. Corrections and Error Analysis 21

4.1 Irradiance Distribution 21

4.2 Detector Uniformity 23

4.3 Detector Reflectance 25

4.4 Electrical-Optical Thermal Difference 27

4.5 Lead Resistance 31

4.6 Implementing Corrections 31

4.7 Electrical-Optical Duty Cycle Difference 32

4.8 Detector Noise Error • 32

4.9 Nonlinearity Error 33

4.10 Quantization Error 34

4.11 Power Calculation Error 34

4.12 Servo Gain Error 35

4.13 Error Summary 36

4.14 Failure Detection 36

5. Summary 40

Appendix A. Table of Symbols 41

References 44

List of Figures

Page

Figure 1.1 A schematic diagram of the pyroelectric detector shows

how the gold black functions as both optical absorber

and electrical heater 2 Figure 2.1 Block diagram of the Electrically Calibrated Pyroelectric Radiometer (ECPR) shows the null balance servo

loop (upper portion) and power computing circuitry

(lower portion) 4 Figure 2 . 2 Capacitive coupling from the heater to the detector

output can be corrected by (1) shielding or

(2) cancellation 6

v
List of Figures (Continued)

Page

Figure 2.3 A system diagram of the null balance servo loop. The

nonlinear behavior of the loop gives rise to a time

constant which continuously varies with power level 7 Figure 3.1 Chopper speed control schematic shows the derivation

of the calibration and demodulation reference square waves 10

Figure 3.2 The calibration driver uses two inputs, V and the calibration reference square wave to produce an alternating

push-pull drive for the detector heater (R ) 12

Figure 3.3 Schematic diagram of the detector, preamplifier and

the null balance servo loop 14

Figure 3.4 (a) Normalized system step response for power levels

— 8 —2 from 10 to 10 " watts and (b) system settling time

(99%) and small signal time constant as a function of

power level 16

Figure 3.5 Waveforms at the synchronous demodulator output (a) just

after a positive going step of optical power and

(b) just after a negative going step of optical power.

The last three waveforms are after the servo loop has

reached equilibrium with a narrow optical input beam

at the left edge of the chopper aperture (c) , aperture

center (d) and right edge (e) 18

Figure 3.6 The power calculation circuitry uses high accuracy

amplifiers and an analog multiplier to measure the

power dissipated in the detector heater (R ) 20

Figure 4.1 Analog and digital uniformity scans of the detector

response over its receiving surface 24

Figure 4.2 Spectral reflectance is determined by combining a point

reflectance measurement (a) and a spectral responsivity

measurement (b) 26

Figure 4.3 The spectral reflectance of a typical gold black 28

Figure 4.4 The thermal properties of the gold black are determined

by measuring the phase shift in the detector response

caused by the thermal delay through the black 2 9 Figure 4.5 A plot of the random errors as a function of power

level 3 8 Figure 4.6 A plot of the total fractional error as a function of

power level for three different types of measurement

(a) a typical 2 mm diameter He-Ne laser beam (b) uniform visible illumination, and (c) a 10.6 urn CO,, laser

beam 3 9

vi
AN ELECTRICALLY CALIBRATED PYROELECTRIC RADIOMETER SYSTEM

C.A. Hamilton, G.W. Day, and R.J. Phelan, Jr.

Abstract

A new type of radiometer based on an electrically calibrated

pyroelectric detector is described. Emphasis is placed on system

design and analysis with careful consideration of design tradeoffs. An evaluation of both systematic and random errors for

the complete system yields an expression for the accuracy relative to the electrical standards by which it is calibrated.

Throughout the paper the analysis should be sufficiently general

that it can be applied to any Electrically Calibrated Pyroelectric Radiometer which employs the same basic principals.

Key words: Detector; pyroelectric; radiometry.

1 . Introduction

Until recently, most low level radiometric measurements have been based

on standard sources such as blackbodies and standard lamps. The development

of electrically calibrated pyroelectric detectors for low level power measurements has made possible a new standard which is based on a detector

rather than on a source. This detector based standard uses a thermal detector whose response is nearly identical for optical power absorbed in its re- ceiving surface and electrical power dissipated in that same surface. Thus

optical power measurements can be translated directly into the units of

electrical power. Since electrical standards are highly accurate and readily

available in most laboratories, calibration is a simple and straightforward

procedure. The design and theory of operation of these detectors has been

described in numerous publications [1-8].

Figure 1.1 provides a brief review of the detector construction and

operation. A pyroelectric material is sandwiched between two conducting

electrodes. The front electrode is a gold black coating which is both highly

absorbing and electrically conductive. The pyroelectric material contains

an electric dipole moment which is a function of temperature . Thus , when it

is heated, the induced charge on the surface electrodes changes and a current

flows to the preamplifier. The heat input may come either from optical

radiation absorbed in the "black" or from electrical power dissipated in the

"black." The electrical power is used for calibration and is determined using

a four wire measurement of the voltage and current at the heater. The

detector produces an output only when its temperature is changing, thus the

input power must always be chopped.
Gold Black Absorber-Heater

Electrica

Power

Input

Optical Input

V

Pyroelectric

Signal

Contacting

Pads

Pyroelectric

Material

Figure 1.1 A schematic diagram of the pyroelectric detector

shows how the gold black functions as both optical

absorber and electrical heater.
This technical note will cover in detail the operation of a complete

Electrically Calibrated Pyroelectric Radiometer (ECPR) system based on one

of these detectors . The next section uses a block diagram approach to describe

the entire system. Section 3 provides an analysis of the circuits which make

up each block. Emphasis will be placed on identifying design trade offs

and justifying the particular design choices made. Section 4 is a careful

analysis of all the known sources of error. It takes into account the nonideal nature of all of the system components in order to arrive at a realistic

evaluation of the total system error.

2 . System Operation

Figure 2.1 is a block diagram of the complete system. The incident

radiation to be measured is chopped with a mechanical chopper and absorbed

in the detector surface. During the time the radiation is blocked, an electrical signal is synchronously applied across the heater on the detector

surface. The detector response to the optical and electrical heat input is

amplified and synchronously demodulated in such a way that the lock-in amplifier output is proportional to the difference between the optical and electrical inputs. This difference signal is fed back around a closed servo loop

to drive the electrical input thus reducing the difference signal to zero. Hence, the electrical input tracks the optical input and a continuous balance

is maintained.

The lower half of figure 2.1 shows how the electrical power is computed

and displayed. The voltage and current for the detector heater are measured

with a pair of differential amplifiers. The outputs of these amplifiers are multiplied together with a high accuracy analog .multiplier and the resulting

power is displayed in 3 1/2 digits

.

The null balance technique used in this system takes advantage of the

speed and sensitivity of pyroelectrics and yet is independent of changes in

detector responsivity or amplifier gain. Calibration does not depend on any

standard optical source but rather is based directly on readily available

electrical standards . The realization of such a system requires solutions to

a number of practical problems. Before going into the detailed design, we

shall consider four of the most important of these problems and the design

choices made to solve them.

The first problem results from the fact that the electrical and optical

waveforms and phase are not necessarily identical. The electrical waveform

is a square wave with finite rise and fall times. It is convenient to define

its phase to be zero. The waveform and phase of the optical signal, however,

are determined by the irradiance distribution over the chopper aperture . One

method of matching the electrical and optical signals is to equate the integrated power due to each signal. This approach requires the use of a 25%
GOLD BLACK ABSORBER AND HEATER

OPTICAL CHOPPER

-u^

PYROELECTRIC DETECTOR

PHASE REFER&NCE

LOCK IN AMPLIFIER I

NDARD /n\ ST.. ^J^S)

PHASE REFERENCE

J\y^ ELEC __U^ CHOPPER

4 QUADRANT

ANALOG MULTIPLIER

COMPUTED

POWER WAVEFORM

SAMPLE

& HOLD

3 1/2 DIGIT DISPLAY

Figure 2.1 Block diagram of the Electrically Calibrated Pyroelectric Radiometer (ECPR) shows the null balance

servo loop (upper portion) and power computing

circuitry (lower portion)
duty cycle and a wide band lock-in amplifier following the detector output

and is usually referred to as the waveform independent method [9] . In theory,

this method yields equivalence regardless of the optical waveform but it has

the disadvantage of requiring exactly matched electrical-optical duty cycles

and a complex wide-band front end amplifier with a very large dynamic range.

Our approach is to use a 50% duty cycle and a narrow band lock-in amplifier so that only the fundamental, in phase, components of the electrical and

optical signals are matched. This approach leads to a small dependence on

the irradiance distribution over the chopper aperture. With a proper chopper

design the resulting worst case error is easily held to less than a few tenths

of a percent. In addition to the advantages of simplicity, this method yields

a 2:1 improvement in signal-to-noise and is relatively insensitive to such

practical problems as the electrical power turn on transient and small deviations in the relative lengths of the electrical and optical duty cycles. A

quantitative evaluation of all of these error sources is made in Section 4

.

Another problem arises from the fact that the voltage across the detector

heater resistance is capacitively coupled directly into the detector output.

Two solutions are diagrammed in figure 2.2. The first is to introduce an insulating layer and a ground plane between the heater and the pyroelectric

material. The ground plane serves as the front electrode for the detector

and simultaneously shields the detector from the heater. Unfortunately, this

method has the disadvantage of complicating detector fabrication and making

it very difficult to achieve uniform response over the detector surface

.

The approach we are using is to drive opposite ends of the heater with

equal and opposite voltages, thus establishing a virtual ground at the center

of the heater. This causes the capacitively coupled signals to cancel. Any

residual error caused by the imprecise adjustment of this virtual ground is

further reduced by reversing the heater voltage every other cycle. Capacitively coupled signals are thus at one-half the chopper frequency and are re- jected by the lock-in amplifier.

This reversal of the heater voltage every other cycle has a further

important function in the calculation of the electrical power. Since the

voltage and current waveforms are maintained throughout the power calculation

circuitry, any zero offsets in either the drive or calculation circuits will,

to first order, cancel out in the final filter before the display. This

feature significantly improves the accuracy and temperature stability of the

power calculation. A detailed error calculation for the power computation

circuitry is given in section 4

.

The third design problem to be considered is the servo loop which automatically balances the electrical and optical power. This loop, shown in

figure 2.3, consists of the detector, whose output is proportional to the
CAPACITIVE COUPLING PROBLEM

SOLUTION #1

•HEATER

INSULATION

•GROUND PLANE

PYROELECTRIC

-ELECTRODE

^- TO LOCK IN AMP

SOLUTION #2

VIRTUAL

GROUND

v

TO LOCK IN AMP (fj

POWER

SIGNAL

CAPACITIVE

ERROR SIGNAL ^yy^yy^y

f=f

f=f II

Figure 2.2 Capacitive coupling from the heater to the detector

output can be corrected by (1) shielding or (2)

cancellation.
op

LOCK-IN

AMPLIFIER

COMPENSATION

(INTEGRATOR)

DRIVERHEATER

>

+ o - V

I "

G (P .-P , ) p opt elec

V

D

= el ec

< g dV 2

P , el ec DISPLAY

P

t \ el ec

p , -' i V

I V D

' el ec

Figure 2.3 A system diagram of the null balance servo loop.

The nonlinear behavior of the loop gives rise to a

time constant which continuously varies with power

level.
electrical-optical power difference, the lock-in amplifier, a compensation

element, and the electrical heater. Note that the driver-heater is a non- linear element because its output power is proportional to its input voltage

(Vrj) squared. The transfer function of the lock-in amplifier contains

several poles with characteristic frequencies on the order of ui — 15.

Consequently, if the compensation element is pure gain, the loop becomes

unstable long before the gain is high enough to accurately balance the electrical and optical power. However, the loop can be stabilized by using a pure integrator for the compensation element. If the time constant of the

integrator (x . ) is sufficiently large, it will completely dominate the frequency response of the loop and the poles associated with the lock-in amplifier can be ignored. The integrator stabilizes the loop with a very high dc

gain and also determines the system frequency response in a unique and

desirable way. To see how this comes about, we can use figure 2.3 to derive

an equation for the system response:

P , = (-2-E. / (P .-P , )dtl (2.1) elec I T i opt elec J i*»-»-j

After taking a square root and derivative on each side we have:

d/P , G^G^

P ° CP_-P^J (2.2) dt T.. opt elec

and finally this becomes:

d P . 2/P~ G_G_ elec _ elec P D . . . . dt t.

l opt elec' ^ ,J;

In the limit of small deviations from some equilibrium value of P . , /P , is approximately constant and the solution of eq. (2.3) is a simple

exponential with a time constant,

T =

* (2.4)

2/P~^elec GoGr. P D The time constant automatically and continuously increases as the power

decreases. Thus the system responds quickly at high power levels and achieves

good sensitivity at low levels by increasing the time response which is

equivalent to limiting the noise bandwidth. Since the loop gain is increasing

steadily with power, the poles of the lock-in amplifier will eventually become important and cause instability. However, the integrator time constant

can always be adjusted to put this instability threshold beyond the power

capability of the system.
Although this nonlinearity of the servo loop is useful in determining the

system time constant, it causes another problem when the system is operating

near zero power. If for some reason the optical input is negative (e.g., when

viewing a cold background) the system will attempt to drive negative electrical

power by reversing the polarity of the heater voltage. However, since the

heater output is proportional to V*, the power is actually positive. In effect,

the loop switches to positive feedback and will run away to saturation. This

is easily prevented by clamping the heater voltage when it attempts to go

negative. Then, however, when the optical input is negative the instrument

will read a false zero. Thus measurements against a cold background will

contain an offset which cannot be detected by making a zero measurement.

This problem is resolved by electronically offsetting the servo loop so that the electrical power always exceeds the optical power by some value

P _- . . P ff is then electronically subtracted from the display to make

o r i o c u o lib " l, the instrument read correctly. Thus the system reads negative inputs up to

the value of P , £ . . offset

3 . Circuit Design

Having outlined the major design decisions, we can now consider the

specific circuits adopted to implement each of the blocks in figure 2.1.

These circuits are intended to be a reasonable trade off between performance,

simplicity, and cost. As new components become available, improvements will

certainly be possible.

3 .1 Chopper Speed Control

Since the detector preamplifier is tuned to a specific frequency (- 17 Hz)

it is important that the chopper run at a precise speed. The circuit of fig- ure 3.1 provides this speed control as well as supplying calibration and

demodulation reference square waves

.

The calibration reference is 180° out of phase with the optical signal and

is used to turn the electrical calibration power on and off. The demodulation

reference has an adjustable phase with respect to the optical signal and is used

to synchronously rectify the output of the detector preamplifier.

The reference square waves are derived from an LED-phototransistor pick

off which is intersected by the chopper wheel. The phase of this pick off is

adjusted mechanically to be exactly 180° from the center of the optical aperture, thus providing the calibration reference. The demodulation reference

is produced by delaying the calibration reference with a pair of one-shots.

The pick off is also used in the speed control to trigger a pulsing circuit. This circuit creates a stable 3 ms pulse whose height and width are independent of frequency. Thus, when the pulses are averaged, the resulting

dc level is proportional to the chopper speed. This level is compared to a reference and the amplified difference signal drives the motor. This servo

loop controls the chopper speed to better than 0.1 Hz.

9
CALIBRATION

REFERENCE

680jjF

HI3BI

^

+ 15

IOK

2N3906 3.9K

2N3904.

.047>jFf|UAA^-K047AiF

i5Kj '^rHh

SI5KS390

I—wvww 15

50K

=" SPEED

CONTROL

IK

DEMODULATION

REFERENCE

47K

20KFT 1 fr.

PERIOD PHASE

Figure 3.1 Chopper speed control schematic shows the derivation of the calibration and demodulation reference

square waves

10
3 .2 Calibration Power Driver

Next we consider the circuit which produces the electrical calibration

power. As was mentioned in section 2, the electrical calibration .power is

driven by applying a voltage waveform like that shown in figure 2.2 across

the detector heater. The circuit of figure 3.2 uses two inputs, a dc level,

Vn

, and the calibration reference square wave to produce the desired waveform.

The operation is as follows : The reference square wave drives a flip flop

producing a square wave at one half the reference frequency. This half frequency wave drives analog switch SI which in turn switches the gain of amplifier Al between +1 and -1. The output of Al is thus a square wave varying

between +Vn and -V_. at one half the chopper frequency. The reference square wave is also inverted and used to drive analog switch S2 . S2 chops the output of Al producing the desired waveform. Finally, the signal is amplified

by two driver amplifiers which produce equal voltages of opposite polarity.

These voltages are applied through an attenuator and standard resistor network

to either end of the detector heater. The result is a symmetrical heater

drive in which there is a virtual ground established at the center of the

heater. The symmetrical drive, together with the alternating drive polarity, causes cancellation of any signals which are capacitively coupled from the

heater to the detector output.

The 1000 pF capacitor in the drive circuit slows both drivers to a 0.2 ms rise time in order to eliminate switching transients. The effect of this

slowed rise time on the electrical optical equivalence is examined in section

4 and shown to be negligible.

The gain of the driver-heater (G ) can be calculated directly from

figure 3.2. Beginning with the definition of G

n in figure 2.3 we have

' 2 %

Vl v DlRr,+R f 4 V*RT V. <w 2 - w - - ^^ — ».d

*D "D <VRa> where R = RT + R, + R_ . Solving for G_, we have

a I 1 2

J D

2/i£

Gn

= (3.2)

*D + R

a

Jjn. order to match dynamic ranges, it is desirable that when the system is

reading full scale on the top range (P ), the driver input voltage, V , should also be at its maximum value (V^ ) . Therefore Dm

4 R

n

P „ = ( Gr^ ) 2 = V* — (3.3) em D Dm Dm (RD+R

a>

11
lOOOpF

Figure 3.2 The calibration driver uses two inputs, VD and

calibration reference square wave to produce an

alternating push-pull drive for the detector heater

12
This equation is easily solved for R after which R , R.. and R

2 can be selected

to satisfy the virtual ground condition, i.e., R_ = R, + R_.

Finally, eq. (3.3) can be used to define a more general form of G_,

namely

G

D

= ^

(3.4)

V

Dm

3 .3 Auto Null Servo Loop

Having examined the operation of the mechanical chopper which modulates

the optical input and the drive circuitry which modulates the calibration

power, we can now consider the servo loop which automatically matches these

two power levels. Figure 3.3 shows the detailed circuitry which makes up the servo loop shown as a block diagram in figures 2.1 and 2.3.

Before describing the circuit aspects of the loop, we must consider

briefly the physics of the detector. Since the detector is a pyroelectric,

its output current is proportional to the time rate of change of its temperature

1 " at (3 - 5)

Using an approximation appropriate for the low chopping frequencies in our

system, the temperature derivative can be written as two terms, a positive

term resulting from the power input and a negative term representing losses

to the environment.

dT _ P T

3t " C~J " 7

(3 ' 6)

P

Here C v (heat capacity x volume) represents the thermal mass of the detector

and t is the inherent thermal time constant — typically about one second.

Since the chopping frequency (17 Hz) is considerably greater than 1/t , the

second term in eq. (3.6) can be considered constant and represents the average

loss. Further, since the average power input must equal the average loss

f - cTv"

(P-Pave } (3 ' 7)

P

Thus the detector output is proportional to the difference between the instantaneous power and the average power. In the ideal case where the electrical

and optical power inputs are square waves, 180° out of phase, the amplitude

of the square wave detector output is exactly proportional to the power difference. Since the system normally nulls this difference, the lock in amplifier connected to the detector can have a very high gain and a considerably

smaller dynamic range than the system as a whole. This is possible because

the power difference is taken in the detector rather than in the lock in

amplifier.

13
FET AMPLIFIER

INTEGRATOR

CALIBRATION

REFERENCE

Figure 3.3 Schematic diagram of the detector, preamplifier and

the null balance loop.

14
Returning now to figure 3.3, the detector output is amplified by a band

limited current mode, FET, operational amplifier. The second stage is tuned

to the chopper frequency, f , and selects only the fundamental component of

the detector output. Finally the signal is synchronously rectified and

averaged by the integrating amplifier. The overall gain of the preamplifier including the detector is given by

G

P

= ^ r

i

Z fG

t

(V/W) {3 ' 8)

P

where r. = current responsivity of the detector in A/W,

Z = FET amplifier feedback impedance at f , G. = center frequency gain of tuned amplifier.

The constant factor 4/tt 2 results from averaging the rectified fundamental

component of the detector output. Typical values are R. = 10 A/W,

Z £ = 2 x 10

9

fi, G,_ = 6, and G = 5 x 10 3 V/W.

f t p

' The phase for the synchronous rectifier is adjusted to 180° for the calibration signal and to 0° for an optical signal centered on the chopper aperture. The integrator output feeds the calibration power driver thus closing

the loop. As mentioned in section 2, the integrator output is clamped to

positive values and its input is offset by the equivalent of about a microwatt

of optical power in order to allow the system to view negative background

radiation

.

In section 2 we showed that the system time constant, x , is given by

T i and thus varies continuously in such a way that the S/N ratio is

2/P n G^G^ elec P D

enhanced at low power levels. However, because of the heater nonlinearity

,

the system does not respond with a simple time constant to large changes in

the input power. Consider the response to a large step function of optical

power. In this case, both the system nonlinearity and the saturation level

of the preamplifier become important. If the step function is large enough to

saturate the preamplifier (P , ), it will apply a constant voltage V to the

s at pm

integrator. The integrator output then rises linearly causing the calibration

power to rise parabolically . This continues until the preamplifier comes out

of saturation after which the system approaches equilibrium exponentially with

a time constant (t ) determined by the power level . These results are sum- marized in figure 3.4(a) which shows the system step response to a number of

power levels and in figure 3.4(b) which shows x and the system settling time

(99%) as a function of power level. Both curves in figure 3.4(b) level out

when the applied power level becomes small compared to the offset power.

(See section 2 .)

15
o

Q.

Q.

o

1.0

0.8

0.6

0.4

0.2

10 20 30

TIME (SECONDS

40 50

la I

60

200

160

2 120

o

o

80

40

10

Figure 3.4

;ettling time

•TIME CONSTANT

10 10 " 10 ' 10"

INPUT POWER (WATTS)

10'

(b)

10

(a) Normalized system step response for power

— 8 —2 levels from 10 ' to 10 watts and (b) system

settling time (99%) and small signal time constant

as a function of power level.

16
The settling time decreases to a minimum at an input power equal to P . . S St

For values above P , , saturation of the preamplifier in effect reduces the

S 3. t loop gain causing the settling time to increase.

Since the detector preamplifier is tuned to the chopper frequency and the

synchronous rectifier has its phase set to zero (the phase of the electrical

calibration power), the servo loop matches the fundamental, zero phase components of the optical and electrical signals. If the optical distribution over

the chopper aperture is assymmetric, the optical signal will have a component

which is 90° out of phase. Although this signal is rejected by the synchronous

rectifier, it must not be allowed to saturate the preamplifier if the servo

loop is to be effective. Since the in phase component is normally nulled, the

out of phase component is the main cause of saturation and is thus the primary

consideration in choosing the preamplifier gain. We can analyze this situation

by taking the worst case optical distribution, i.e., a narrow beam at the

aperture edge. This gives a square wave signal with a fundamental frequency

component given by

P 2 P 2 -2— sin(co .+0) = -2— {cos 6 sin to . + sin 6 cos w . } (3.9)

where P is the optical power and 2 is the width of the aperture relative to

° P 2 the chopper center. The out of phase component has a value sin 0. If

the saturation value of the preamplifier output voltage is V , then

P emsin °i7t= Psat < 3 - 10 > p

For example, in a system with a 12 cm diameter chopper blade and a 1.25 cm

aperture (0 = 6°, sin - 0.1), P . cannot be less than 0.1 times the Sdt

maximum allowable input power P . This condition defines the maximum preamplifier f gain. ^ For typical Jf values of P =20 mW and V . = 10 volts, G em sat p

must be less than or equal to 5000 v/w.

Figure 3.5 shows the output of the synchronous demodulator for several

different conditions at the detector input. The first two waveforms (1 volt/

div) are the nonequilibrium saturated output just after a positive going and

a negative going step of optical power. The last three (0.1 volt/div) are the equilibrium waveforms for a narrow beam at the left edge, center and

right edge of the chopper aperture. Since the zero phase component is nulled,

the last three waveforms show only the component which is 90° out of phase

together with a small residual component at f /2 . The f /2 component arises

from a slight misadjustment of the virtual ground. See section 3.2.

17
fA)

(B)

MM m^

rc)

W)

CF.1

Figure 3 .

Waveforms at the synchronous demodulator output (a)

just after a positive going step of optical power

and (b) just after a negative going step of optical

power. The last three waveforms are after the

servo loop has reached equilibrium with a narrow

optical input beam at the left edge of the chopper

aperture (c) , aperture center (d) and right edge

(e) .

18
3 .4 Calibration Power Measurement

Figure 3.6 shows how the calibration power is measured. Two pairs of

wires are connected to the detector heater, one to carry the current and the

other to measure the voltage. A standard resistor in series with the detector

heater current leads is used to measure the heater current. The voltage and

current signals are amplified first with a pair of differential amplifiers

and then by a pair of amplifiers which can be range switched between gain

values of 1, /To, 10, and /1000 . The two signals are then applied to a high

precision, four quadrant, analog multiplier. The output of the multiplier is

proportional to the instantaneous power dissipated in the detector heater.

A filter after the multiplier samples the power during each heating cycle.

This sampling is controlled by the calibration reference square wave. The

sample time begins after the heater turn on transient has died out and ends

before the heater is turned off.

The filtering between the multiplier output and the digital display is

designed to provide at least 80 dB of attenuation at the chopper frequency,

about 40 dB of attenuation at one half the chopper frequency, and yet still

have a response time of less than a second. The 40 dB of attenuation at one half the chopper frequency, together with the alternating calibration drive

voltage, has the effect of making zero offsets in the power drive and measure- ment circuits cancel out

.

In order to compute the power correctly, the gains of the various stages

in figure 3.6 must satisfy the following equation

_^4 y m V

DPm(max)

(3>11)

R. + R.

v j. x p

3 4 em

where y = multiplier constant = .1,

G^ = differential voltage amplifier gain = R^/R,,

G = differential "current" amplifier gain = R_/Rq , Rj = standard cUrrent measuring resistor,

V f max } = maximum voltage displayed on digital panel meter, and

P = maximum power displayed by system.

One additional constraint is necessary in order to match the voltage and

current inputs to the multiplier:

R

I G

I

~ ^V ( within ±20%) (3.12)

where R

D

is the detector resistance. When this condition is satisfied, the

multiplier operates with maximum accuracy.

19
OFFSET

DIFFERENTIAL AMPLIFIERSGAIN SWITCHING

AMPLIFIERS

G = 1, /To", 10, /1000

Figure 3.6 The power calculation circuitry uses high accuracy

amplifiers and an analog multiplier to measure the

power dissipated in the detector heater (Rn

) •

20
In practice, eqs . (3.11) and (3.12) are used to select the various gains

such that y - 0.1. y is then adjusted experimentally to achieve calibration.

This is accomplished by substituting a precision resistor for the detector

heater and an on-off switch for the chopper. With the chopper switch in the

"on" position, the displayed power (minus P ff ) is compared with V^/R as measured with local laboratory standards . This comparison is made as an average over the positive and negative heater drive cycles. The accuracy and

linearity of the power calculation circuitry are discussed in section 4.5.

4 . Corrections and Error Analysis

The fundamental limitation on the accuracy of the ECPR is the extent

to which the equivalence between electrical and optical power can be characterized. Although considerable effort has been devoted to producing equivalence,

several small sources of inequivalence remain. Experimental procedures have

been developed for estimating the magnitude of each of these sources of inequivalence. The total estimated inequivalence is used to internally correct

the instrument reading. The uncertainty of these corrections is included in

the error analysis. This section first describes the various corrections and

then presents an error analysis of the complete system. It will be shown how

each error source depends on the parameters of the system as well as the mea- surement conditions including power level , wavelength and irradiance distribution. The error estimates should be interpreted as one sigma values. Addition of errors is done in an rms fashion

.

The final result is a curve of the total system uncertainty as a function

of power level. It will be seen that the system accuracy is limited at the

high power end by detector nonlinearity and at the low end by detector noise.

4 .1 Irradiance Distribution

The previous sections have shown how the servo loop nulls the zero phase

fundamental component of the electrical -optical power difference. In order

to evaluate inequivalence which may result from this mode of operation, we must compare the fundamental component of the optical signal relative to its

CW value, with the fundamental component of the calibration power relative to

the value displayed on the digital panel meter. The waveform of the optical

signal and therefore its fundamental component will depend on the irradiance

distribution over the chopper aperture. For example, a narrow beam, when

chopped, produces a square wave whereas uniform illumination of the chopper

aperture produces a trapezoidal-like wave.

The results of a simple Fourier analysis for the electrical power waveform

and for four different optical irradiance distributions are given in table 4.1.

As before, 20 is the angular width of the chopper aperture relative to the

blade center, cj is the radian chopper frequency, and t is the calibration

driver risetime.

21
Xio

-p

M 1 rH n

id

u o w

•HU

H

•P <d u o

<u

H

H -P w ao

dP

dp dp dP V£> in ro O H o H ID • o

mh

rH

IdO

•H

4J

(0 tf o

M-l

0)3

rH

id >

ido

•H

>i

CM|t=

in oooo

CN|t=

oo

in

cslt= V

MH >V

<Mlt=

00

VO

<T\

(0O

•rlM

-PO

0)gou

MHc

•H

•PH

100)u

0)oc

0) rH

(0>H3V

<ucH

mh rH >

id ~

•P

&4

0)o%ouc

<u o O -H C +J

<d 3

•h xi

(d ^ H P

)H CO H -HQ

CM

CM 0) H

<s

O3+

rH

MH >

«* ^-s

to rH

d) -P id

i-l •H

O

a

•HH

En

9? •P

15 >i

O

cu S

0) rH

n

w S p — U -H

X) o M o

<u •

cnI t=

mh

XIouu

to

a

ti id

<do

•H

-p8*oo

CDc

M-l o

all)M

-P

M-l •Hu

-H

-P&Oo

M-l P

<d a)

0)

d) XI 0)u £ 3

-P

<d ft

fi id

rH

<do

•H

•Pft Ooo

cnI t= v

M-l >V

U dP

d)

O

ftm

id +i

-H

si

-P 13 4J

CO d) -H •H H £

TJ d) -p dJ >i c C d)

id o p

ido

•H

-Pft ooo

rHN

id

a o

•rl in H •

rH c • rH o

d)g 1 d) .ego o CO -P o 0) 3. o (0 P in o o

<d CM • o o • CN rH <N

d) rH rH rH rH > II •rl || || II II u c u a u a u H

id d) 3

rl +J (0 d) W <D Cn g P C g C >i •H

d) id •HO -P T) S "rl c c d)

d) -rl TJ 0) a) 10

10 T3 ft 3 •rl 3 Q) D1 >H

d) TJ d) in M id d) M

U

M 3 rH TJ MH <D

d) P ,Q id >

-p

M

H

C •H

d) d)

M ^a id Sh

g ft d) •H Tl

id <d ftMH t3 u ft o <d

C

idM o M

ft d) x!M •H ftU d) U 4->

G ft

A d) id Cn 1 ft u

•H si 3 ft XI

(0

U 2 •H

d) XI rH Q c_> id u

22
The worst case inequivalence occurs when the system views a narrow beam

at the aperture edge. However, it is more reasonable to assume at least a crude alignment (±50%) and the last entry of table 4.1 shows the range of

inequivalence which can occur based on this assumption. We shall use this

value (-0.0011 ± 0.0016) for the analysis. Thus we have a required correction

of +0.0011 with an uncertainty of ± 0.0016.

4 .2 Detector Uniformity

For any thermal input, either electrical or optical, the detector output

is proportional to the integrated product of the input power spatial distribution and the detector responsivity distribution. If the responsivity is

nonuniform there may be an inequivalence between electrical and optical inputs . The magnitude of the inequivalence is given by

e =

// {Pelec (X ' Y) "

popt(X ' Y)}r

i

(X ' Y)dx dy

where r. (X,Y) is the spatial distribution of responsivity. The electrical

power distribution P .. (X,Y) is determined by the electrode geometry (see

figure 1.1) and P (X,Y) may be any optical distribution within the input

aperture. The inequivalence clearly depends on the size and position of the

input beam as well as the uniformity of r. (X,Y) . Figure 4.1(a) shows an analog uniformity scan of a typical detector. Such scans give a rapid but

qualitative measure of the detector uniformity. A more quantitative value can be obtained by establishing a beam diameter consistent with the expected

use of the instrument and measuring the responsivity at a large number of

points on the detector surface. The results of such a determination on the

same detector are shown in figure 4.1(b). The grid spacing is 0.75 mm and the

2 beam diameter is approximately 1.0 mm (1/e points). The results show a peak to peak deviation from the average of +.031 and -.026. These worst

case points, however, are well away from the center of the detector. If

the distribution of the input beam were known, the data of figure 4.1(b)

could be used to calculate a correction factor. However, this is" usually

impractical and the nonuniformity is thus treated as a random error. The

value of this error should be assigned based on the input beam characteristics and the uniformity data. In lieu of such a determination, a reasonable

estimate is just the standard deviation of all of the points of figure 4.1(b).

For this particular detector the value is + 0.0125.

Another source of nonuniformity which must be considered is a depression

of the responsivity around the whole perimeter of the active detector area.

(The active area is that area of the pyroelectric material with both front

and back electrodes.) This is caused by heat which is dissipated in the active

area diffusing laterally into the inactive area. The diffusion distance is

typically 30 urn in detectors made of PVF

?

. Inequivalence from this source is

avoided by preventing either electrical or optical power from being dissipated

near the edges. The aperture performs this task for the optical power. The

23
ANALOG

UNIFORMITY

SCAN

no

DIGITAL UNIFORMITY SCAN

1.008 1.008 1.008 1.002 0.991 0.984

1.016 1.007 1.009 1.003 1.000 0.993 0.992 0.974

1.019 1.016 1.005 1.004 0.999 0.994 0.991 0.988 0.974 0.980

1.018 1.012 1.007 1.010 1.001 0.996 0.991 0.986 0.978 0.985

1.022 1.017 1.013 1.015 1.006 1.001 0.996 0.992 0.988 0.988

1.031 1.023 1.011 1.006 1.003 1.002 0.997 0.993 0.998 0.993

1.027 1.020 1.014 1.007 1.002 1.004 0.996 0.996 0.998 0.990

1.019 1.016 1.014 1.002 0.993 0.986 0.990 1.001 0.991 0.988

1.011 1.006 0.997 0.992 0.990 0.989 0.998 0.983

1.005 0.999 0.993 0.988 0.991 0.994

Figure 4.1 Analog and digital uniformity scans of the detector

response over its receiving surface.

24
problem is more difficult for the electrical power but can be solved for

the most part by selecting an electrode geometry which concentrates the

dissipation in the center of the detector. If this requirement was ignored

2 and electrical power was dissipated uniformly over a 1 cm detector, there

would be an edge loss equal to the ratio of the 30 ym wide perimeter area to

the total detector area or about 1%. The instrument would therefore read

high by this amount and a correction would be required.

4 .3 Detector Reflectance

Any optical power which is reflected from the gold black on the detector

surface represents a direct inequivalence in the measurement. There are two

methods of handling this. The first is to place the detector in a light

trap which collects the reflected beam and returns it to the detector [7]

.

The second is to determine the total reflected power as a function of wavelength and make a correction. This determination can be made by measuring

the spectral response of the detector versus a spectrally flat detector and

then calibrating this response curve with one or more point measurements of

reflectivity. The experimental setups used in these two determinations are shown in figure 4.2(a) and (b) . The point reflectivity measurement (figure

4.2(a)) is made at a wavelength of 632.8 nm where the reflection is almost

entirely diffuse. This diffuse reflection is detected with a large area annular pyroelectric detector of outside radius r„ and a small center hole of

radius r,

.

If the reflection is assumed to be Lambertian then the fraction of the

reflected light which is intercepted by the annular detector is

.«J~ .„ ^X _ ...... [.„_.- r

l Y = sin {arctan -*— ) - sin jarctan -s— \ (4.2)

The separation distance d is chosen to maximize y. Typical values are

r, = 0.075 cm, r- = 2.5 cm, d = 0.6 cm and y = 0.94. The reflectivity of the

sample is determined by recording the annular detector output first with the

sample in place (V,) and then with a mirror of reflectivity n directing the

entire beam back into the reflectometer (V„) . The reflectivity is then

given by

V n Reflectivity = -±- (4.3) V

Typical gold blacks show a reflectivity of about 0.0085 at X = 632.8 nm when

measured with this technique. The uncertainty in the reflectivity results

mostly from nonuniformity and noise in the reflectometer and is estimated to

be about + 0.002.

The spectral response measurements are made using the system shown in

figure 4.2(b). The output of the double prism monochromator is divided

between the flat spectral response detector [7] (D#l) and the ECPR sample

25
d « 0. 6cm

SAMPLE

1S> MIRROR

Cs REFLECTIVITY

§

LARGE AREA ANNULAR

PYROELECTRIC DETECTOR

SIGNAL

READOUT

CHOPPER

SOURCE

« » -»

DOUBLE PRISM

MONOCHROMATOR

x

-A

? 0,20^—!-

LOCKIN LOCKIN

#2

CONTROL ELECTRON If

POSH ION

V V \i AUTOMATIC

DATA RECORDING

Figure 4.2 Spectral reflectance is .determined by combining a

point reflectance measurement (a) and a spectral

responsivity measurement (b)

26
detector (D#2) with a rotating mirror chopper. The path lengths and time

constants in the two channels are balanced. The output of the two detectors

as well as the monochromator position are recorded on paper tape and processed

with a minicomputer.

Spectral reflectance is determined by combining the spectral response

and point reflectance measurements. Figure 4.3 shows a spectral reflectance

curve for a typical gold black used on ECPR detectors . By changing the gold

black deposition procedure, it is possible to achieve lower reflectance in

the infrared. However, this usually results in a black which is more susceptible to damage and has a greater thermal resistance

.

For an instrument which is to be used for visible light measurements,

it is appropriate to make a fixed correction based on the relatively flat

response over the visisble range. In the case of figure 4.3 the correction

is +0.0085 with an uncertainty of ± 0.002.

4 .4 Electrical-Optical Thermal Difference

The fact that the electrical and optical power are not dissipated at

exactly the same position through the thickness of the black may lead to a slightly different detector response to the two inputs. A worst case analysis

assumes that the optical power is absorbed at the front surface of the black

and that the electrical power is dissipated under the black at the surface of

the active detector material. Several experimental and theoretical analyses

[10,11] have shown that for this worst case, the thermal conductance and

capacitance of the black can lead to both a phase and amplitude difference

between the electrical and optical signals. For typical blacks and chopping

frequencies the dominant error mechanism is conduction to the air at the

surface of the black. The optical input has a greater loss to the air be- cause it is not impeded by the thermal resistance of the black. The magnitude

of the difference varies from a few tenths percent to greater than one percent

depending on the particular properties of the gold black used. Since these

properties may vary widely from one black to the next, it is desirable to

make a measurement for each black which is to be used in a calibrated system.

The theoretical analyses [10,11] show that by measuring the phase difference

in the detector output between heat applied at the front and back surface of

the black, both the thermal resistance and capacitance of the black can be obtained. These parameters, together with the known thermal properties of air, can be used to determine the difference in detector response to the two

different heat inputs.

The apparatus of figure 4.4 is used to measure the phase difference as a function of frequency. The chopped laser beam is applied first to the black

and then to an area where the black has been removed. In each case, the chopper is mechanically positioned with a micrometer mount to null the lock-in

27
0.3

0.2 -

<_)

<c

hUJ

_J

u_UJ

0.1 -

f

0.6328

4 6 8

WAVELENGTH ym

12

Figure 4.3 The spectral reflectance of a typical gold black.

28
BLACK REMOVED

DETECT

MICROMET

POSITIO

. CHOPP

LASER

LOCK IN

AMPLIFIER /

Figure 4.4 The thermal properties of the gold black are determined by measuring the phase shift in the detector

response caused by the thermal delay through the

black.

29
output. The difference in micrometer readings together with some simple

geometry yields the phase difference. The phase resolution of this method is

better than 0.1 degree.

The data obtained in this way are then fitted to an equation of the form

A<f> = aj^/f + a

2 f (4.4)

The approximate values [12] of the thermal resistance and capacitance of the

black are given by

R, = — = 0.1 a. (W

_1Km2

) (4.5)

a

2 -2 -1

C. - —— (J m K ) (4.6)

'b

TT P^

where K = air thermal conductivity = .026 Wm K , a -5 2-1

k = air thermal diffusivity = 2.1x10 m S

Finally, the ratio of the detector response to the heat at the front versus

the back surface of the black is given by

back

front

1 + R, (H +K a ) d a a a (4.7) cos A<{> -2 -1

where H = radiation loss (near 300 K ambient) = 5 . 7 Wm K , a

a = reciprocal of thermal diffusion distance of air = vArf /< , A* = a

x/r'+ a

2 fc

. The precision of the phase shift measurements and curve fitting suggest an overall accuracy2 for the determination of i, . /i, of about ±0.4%. The back front

results obtained on our typical black are

R. =270 yK W

_1m

2

C

fa = 0.147 J m~

2 K

-1

A<{>(17.5 Hz) = 0.8°

i, ./i, . = 1.013 + .004 back' front

This black was deposited at a nitrogen pressure of 230 P (1.73 torr)

,

a

8 cm from the source, and had a surface resistance of approximately 50 ft/square.

Unfortunately, this method does not quite fit the actual situation in our electrically calibrated detector because the electrical power is dissipated more or less uniformly through the thickness of the black rather than

all at the back surface. One would therefore expect the inequivalence to be

only about one half as great. We therefore make a correction of +0.007 with

an uncertainty of + 0.004.

30
Another method of measuring the thermal inequivalence is to place the

detector in a vacuum thus eliminating the heat loss to the air. However, the

thermal resistance, R,, of the diffuse gold black layer is highly dependent on

the gas in which it is immersed. In a vacuum, R, will increase resulting in an unknown increase in the radiation loss.

4 .5 Lead Resistance

Resistance in the leads attached to the detector heater can cause two

types of inequivalence . The first results from the heat caused by power dissipation in the current lead resistance . Some of this heat may reach an active area of the detector and add to the pyroelectric signal. The second

type of inequivalence results from the fact that the voltage leads may not measure precisely the "effective" voltage across the heater. This effective

voltage, V, , is the difference of the average voltage distributions across either edge of the heater. It can be measured by applying a steady current

through the heater and probing the voltage at about ten equally spaced points

along either edge of the heater. The inequivalence resulting from the voltage

measurement then is

-^ *

(4.8)

V

he

A typical value for this ratio is -.004 ± .001. It can be reduced considerably

by making the gold film on the lead pad area thicker.

The inequivalence resulting from lead heating can be determined by probing

the voltage difference between the detector heater current leads, V., , and by lh 2 measuring optically the responsivity of the lead pad area r. (see figure 1.1).

The lead heating inequivalence then is

(V.,-V, ) r. lh he ip

he i

(4.9)

Typical values are r. /ri

< 0.1 and (

V

±hV

he ) /Vhe = .008 which yields an inequivalence of +0.0008 + 0.0008. The correction for both the voltage measure- ment and the lead heating inequivalence then is +0.0032 with an uncertainty

(rms addition) of ± 0.0013.

4 .6 Implementing Corrections

A summary of the principal corrections together with typical values is

shown below:

31
Correction

Irradiance Distribution +0.0011 + 0.0016

Detector Uniformity + 0.0125

Reflectivity (Visible Spectrum) +0.0085 ± 0.002

E/0 Thermal Difference +0.0070 ± 0.004

Lead Resistance +0.0032 ± 0.0013

Total Correction z = +0.0198

c A simple method of making the correction is to add a resistor, R , in parallel

with the detector heater terminals. Some of the measured electrical power

will be diverted to this resistor causing the instrument to read high.

Precise compensation is achieved by choosing R such that R = -R /e where

e is the total correction to be made. The correction resistor is placed

c c in parallel with the 50 K pot of figure 3.3 such that the combination yields

the desired value.

4 .7 Electrical-Optical Duty Cycle Difference

Although the electrical calibration power is switched by an LEDphototransistor pick off on the chopper blade, it may not have precisely the same duty cycle as the optical signal. This difference in duty cycles arises

because the LED emits a beam which is several degrees wide relative to the

chopper blade center. The actual switch point may occur anywhere in this

several degree wide region and it is generally not symmetrical between the

turn-on and turn-off points. For a typical chopper the difference may be as much as ±7° . Fortunately, the fact that the system responds only to the fundamental

component of the electrical and optical signals greatly reduces the effect of

a duty cycle difference. Using Fourier analysis, we find that a duty cycle

difference between the electrical and optical signals of 8 degrees results in

a difference in fundamental components of 1 - cos 8/2. Thus, assuming a worst case duty cycle difference of 8 = ±7° , the resulting fractional system error is ± 0.00187.

4 . 8 Detector Noise Error

All of the remaining errors are a function of the applied power level.

The first of these is the fluctuation in the displayed power level which

results from detector noise. The rms fluctuation, AP, of the displayed power

from its expected value, P, is a function of the detector noise power spectral

density at the chopper frequency, PN(f )/ and the small signal system time

constant t . x in turn is a function of the applied power (see eq. (2.4))

32
Detector noise results from acoustic disturbances together with the

Johnson noise in the pyroelectric material . It can be modeled as a white

noise current source i (amps//Hz) in parallel with an ideal detector. It is

convenient to express the noise in terms of power by dividing i by the

current responsivity . Thus

i PN

=

r2" (watts//Hz) (4.10)

i

If we think of PM

as an input to the servo loop, then the resulting

system error is just the rms fluctuation at the output caused by the noise

at the input. The effect of the lock in amplifier and servo loop is to

translate the detector noise in a narrow band around the chopper frequency

down to zero frequency. The bandwidth is determined by the small signal system

time constant x . The rms fluctuation AP is thus given by

AP =

o

1 2 -,1/2

/ pN< fc > —V; df

|

(4 - 11)

1 + j2lTfX J s which reduces to

PN

(fc

} AP = ——

(4.12)

2/T~

s Substituting eq. (2.4) for x and expressing AP as a fractional error we

have

P

w c " 2 x.l

Typical values are PN

(17 Hz) = 1 x 10~7 W Hz

1 /2

, G = 5000 v/w,

G

D

= .014 W

1/2 V

-1

and x ± = 5 s which yields ^- = ± 2.6 x 10~7 p~3/4

4 .9 Nonlinearity Error

Measurements of responsivity vs. temperature show that PVF_ pyroelectric

detectors may have a temperature coefficient of as much as +0.5%/K at room temperature. Thus when the applied power level is sufficient to raise the

temperature of the PVF

2 more than a few degrees, the response becomes nonlinear. The null balance method of equating electrical and optical powers will

cancel the nonlinear effect only if the power density of the optical signal

matches the power density of the electrical signal. Since this is generally

not the case, the nonlinearity error must be considered.

33
We shall define a worst case in which the optical input is a narrow

2 Gaussian beam of 2 mm diameter (1/e points). This beam diameter is typical

of the output of many HeNe lasers. Previous experimental studies [13] have

shown that in this case the fractional error is given by

AP

2f = +*P (4.14)

where I has a value of about 10 W . Thus a narrow beam at 1 mW results in an error of about +1%. If the beam is larger or if uniform illumination is used

the error is considerably smaller.

4 .10 Quantization Error

Since the instrument uses a digital readout, there is always an uncertainty of ± 1/2 least significant digit. The fractional error resulting from

this uncertainty depends on the power level being displayed. This fractional error for a 3 1/2 digit meter is given as a function of power level in eq.

(4.15). These results assume that the decade range switch is always set to

read the maximum number of significant figures.

AP 10 -3 -2 ^ = l^p- where R = 0.1, for 2x10 < P < 2x10

R = 1.0, for 2xl0~ 4

< P < 2xl0~ 3

R = 10.0, for 2xl0~ 5

< P < 2xl0~ 4

R = 100, for P < 2x10

(4.15)

4.11 Power Calculation Error

Once the auto null servo loop has matched the electrical and optical

powers, the electrical power must be computed and displayed. The circuitry

for accomplishing this is described in section 3.4. There are three principal

sources of error in the computation: 1) zero drift in the various amplifiers

before the multiplier, 2) gain inaccuracy in the range switching amplifiers,

and 3) nonlinearity in the multiplier module. The gain of the range switching amplifiers is determined by selected precision resistors and is accurate

to 0.2%. The multiplier has a nonlinearity specification of 0.04% of full

scale. Since the multiplier output is not normally less than an eighth of full

scale we can assign a conservative error of 0.3% to the multiplier nonlinearity,

The errors caused by zero offsets are greatly reduced by the alternate

polarity drive method (see Section 3.3). We can see how this comes about by

evaluating the error resulting from a cumulative zero offset (referred to the

output) of AV volts. The displayed power is the average over a positive and

negative drive cycle, i.e.,

P (V+AV) 2 + (V-AV) 2 P,. , = -£B (4.16) display V

2 2 max

34
where V is the voltage appearing at the multiplier terminals and V

max

is the

value of V when the e-lectrical power is at its maximum value P . If we define AP as the difference between the actual power (P = PQm V

2 /V2

) and

the displayed power, eq. (4.16) reduces to

AP AV2 AV2 Pem- (4.17)

P V

2 V

2 P max

The numerical value of AV is the rms summation of eight different potential

offsets in the driver and calculation circuitry. Each of these offsets is

individually adjusted to less than 1 mV throughout the operating temperature

range of the instrument. We therefore choose a value of AV of /8 mV. P is ^ em

typically 20 mW and V is typically 7 volts.

The total power calculation error then is the rms summation over the

three previously defined errors:

£|- ±{(.002) 2 + (.003) 2 +

(3xl0C!.] 2 }V2 (4>18)

If the total offset should become excessive, it is easily observed as a significant (greater than 2%) difference between the power during positive and

negative heater drive cycles during calibration. (See section 3.4 on the computation circuitry calibration procedure.)

4. 12 Servo Gain Error

In any servo system the input-output error is the reciprocal of the loop

gain. The ECPR is a so called type I system because the loop gain contains a single integration. Such systems in theory have infinite DC loop gain and

therefore zero steady state input-output error. In fact, however, the integrator DC gain is limited by the leakage resistance of the feedback capacitor.

The RC time defined by this leakage resistance is typically t, a 5000 seconds.

Thus the dc gain of the integrator G = t./t. or in our case GT

- 1000.

The input-output error due to finite loop gain can now be computed by

rewriting the loop eq. (2.1) with the integration operation replaced by G .

Pelec

= {G

PG

DG

I (PoPt-Pelec )}2 (4.19)

Rearranging and substituting our typical values we have

Popt

~ Pelec 1 _ 1.4 x 10~5

Pelec G

PG

D

G

I /Pelec /Pelec

(4.20)

35
4.13 Error Summary

All of the previously described errors are summarized in table 4.2 and

plotted as a function of power level in figure 4.5. The total system error

is an RMS sum over all of these components. Two of the power dependent

errors, the servo gain error and the nonlinearity error, have a known sign

and are therefore added arithmetically and then put into the RMS summation.

At the high power end, the accuracy is limited by detector nonlinearity

while at the low end it is limited by detector noise. The best accuracy is

achieved between 10 yW and 1 mW in a region where the error is dominated by

detector nonuniformity

As a result of the way the most significant errors have been evaluated,

the total system error should be interpreted as a one sigma value, i.e., any

given measurement has a 67% probability (confidence interval) of being

within the stated accuracy. A 99% confidence interval can be obtained by

multiplying the values of figure 4.5 by three. Thus, at a power level of

100 yW, the 99% confidence interval is ± 4%.

The nominal error values used for figure 4.5 correspond to the measurement of a 2 mm diameter Helium Neon laser beam at A = 632.8 nm. Other types

of measurements will lead to a different overall error. Two examples are compared with our nominal case in figure 4.6. Curve (b) corresponds to an irradiance measurement of visible light which uniformly illuminates the

detector aperture. In this case the nonlinearity, nonuniformity and waveform

errors are reduced and an error due to the uncertainty in the detector aperture

area must be added. We have not considered the aperture area error in detail

because it is not a fundamental part of the ECPR system. When applicable,

this error must be determined for the aperture in use and added into the

overall error. Curve (c) shows the result for the measurement of power in a 2 mm beam

from a 10.6 ym laser. In this case the uncertainty of the spectral response

curve raises the overall error.

4 .14 Failure Detection

In addition to all of the errors described so far, there are numerous

failure modes which can cause abnormally large errors. In many cases the

failure is obvious. For those failures which are not obvious, three simple

tests will discover the problem in almost every case.

1) The use of the detector check button applies a preset current to

the detector heater and displays the resulting power. Readings

which are not consistent with the preset value (±5%) indicate a problem with the detector or power measurement circuitry.

36
a

o

•H

-PU

OJ COO

•Pn

QJ m

OJ Pi

O rH CN rHCMco-^inr^oocrirHrHrH

^j* ^3* ^3* ^J* ^sf ^3* *^J* ^J* ^S1 ^f ^3*

to Q) u 3

iH U fd U >

0) rH g td

aj C

•p •H

01 £

>i O

01 J3

(N

QJ rH

fd

E-i

<N

oj -P —

rH •H CM J3

tn .- fd •H CM o

•0 \ •H

vo rH

• 1 a

^r tn o a. \ H rH CM fd n

1

CO X\CO H c

CM -p -^ CM Q)

f

to + m

fd co I V£> in o O n ro o <D iH o

iH CN <N "tf iH rH iH rH —' rH rH O iH O o o O X CM en X o

O o O o o O \D

o

CM I -* \ o

o• o o O o o O CM i-H rH rH rH o

+1 +1 +1 +1 +1 +1 +1 + +1 +1 | +1

>1

rH

rH

fdo

•H

co

OJ H

•H +J OJ •P 3 >i 0)

• C A -P c u CO •H •H •H fd c -p

td 5-1 e P CD + -p

-p -P u u rH QJ a td

5-1 CO QJ fd U £

CD •H m rH > C + •H O Q •H m -H fd QJ •P c

C C OJ 3 •p CO + fd fd H

D CU D c< CJ1 CO •H >i c rH OJ O H •H o -P 3 + a

5-1 C c 5h 5h CO OJ s H H o G Q

fd rH QJ rH 5-1 P rH H £

•H •H -P p fd C< u 5-1 fd fd fd fd QJ •P TS U o e >1 QJ N u O U a

O td OJ OJ r-t 'd u 4-> CJ -H 3

0J n -P p ^

fd U •H 4-» 5-1 o -P CO u 5-1 QJ OJ £ QJ >i OJ rH C OJ > 5-1 •H u H Q Q Eh ^ -p •p C fd fc 5-1 QJ 3 QJ 3 QJ C^ CM u Q Q z a Cm CO < +

37
o

on

<

o

10"" 10 " 10"

INPUT POWER (WATTS)

10

Figure 4.5 A plot of the random errors as a function of power

level

38
.09

.08

ozo .0/

cc

ccUJ .06 _J

<c

z.o .05

1—o

•a: .04

U. .03

\—

o1— .02

.01

10 10 10" u 10 " 10

INPUT POWER (WATTS)

10

-3

10

Figure 4 .

6

A plot of the total fractional error as a function

of power level for three different types of measurement (a) a typical 2 mm diameter He-Ne laser

beam (b) uniform visible illumination, and (c) a

10.6 ym C02 laser beam.

39
2) The electrical calibration procedure described in Section 3.4 should

hold its accuracy to better than ± 0.3%. A difference of greater

than 2% in the power reading between negative and positive drive

cycles indicates a zero offset problem.

3) Using a beam diameter of about 2 mm, move the chopper aperture

across the beam. The ECPR reading should peak with the beam cen- tered and not decrease more than about 0.5% at either edge. A

greater variation in the reading indicates a phase or chopper speed

control problem.

5 . Summary

The purpose of this Technical Note has been to describe in detail the

design and analysis of an Electrically Calibrated Pyroelectric Radiometer.

The results are sufficiently general that they can be applied not only to our particular instrument, but to a wide range of measurements involving

electrically calibrated pyroelectric detectors.

In the error analysis we have tried to address all those errors which

contribute in a significant way to the overall error in our system. The

values which are given for the various errors are by no means a limitation but

rather are examples of what has been achieved at this writing. Present

systems are limited almost entirely by detector based errors. As improved

technology reduces these errors, we can expect significant improvements in

both accuracy and dynamic range

The ECPR offers many advantages over more conventional radiometric

measurement techniques involving standard sources. It is faster and

simpler to use, and, most importantly, it results in a shorter and more direct

measurement chain between the user and the basic standards. As these

advantages are recognized, we believe the ECPR will become a widely accepted

tool for accurate radiometric measurements

40
Appendix A. Table of Symbols

elec em

offset

opt

AP

;}

heat capacity of gold black

heat capacity of pyroelectric material

chopper frequency

transfer function of calibration driver

current measuring amplifier gain

integrator dc gain

detector preamplifier gain

center frequency gain of tuned amplifier

voltage measuring amplifier gain

differential radiation loss at gold black surface

pyroelectric current from detector

thermal conductivity of air

linearity error factor

number of chopper blade openings

optical and electrical power in system equilibrium

electrical power dissipated in the "black"

maximum power to be measured by system

detector noise power spectral density

built in offset power c P » - P , elec opt

optical power dissipated in the "black"

a power uncertainty

attenuation resistors calibration driver output

t -2„-l J m K

t -3„-l J m K

17.5 Hz

.014 WVV

* 1000

5000 VW

- 6

-1

5.7 Wm~2 K~1

10

-14

to 10" 8 A

0.26 Wm~1K~

1

10 w" 1

n = 1 W

W

0.02 W

2xl0

-7

W//Hz

1 yW

W

W

voltage divider between multiplier output and

digital panel meter

differential voltage amplifier input and feedback

resistors G^ = R^/R^

differential current measuring amplifier input and

feedback resistors G = R-/R

I 7 8

41
\

IP

T

t

V

I

V.V

V,

Dm

DPm(max)

he

V

ih

sat

AV

= R

x + R

x + R

2 thermal resistance of gold black

error compensation resistor

detector heater resistance

standard resistor for current measurement

detector responsivity

responsivity of detector pad area temperature of pyroelectric material

time

voltage at input to calibration driver

maximum voltage at input to calibration driver

full scale input voltage of digital panel meter

voltage across detector heater voltage sensing leads

effective voltage across detector heater

voltage at input to integrator

voltage across detector heater current input leads

saturation output voltage of preamplifier

cumulative offset voltage of driver measurement

circuit

volume of pyroelectric material

spatial position over detector receiving surface

feedback impedance on FET amplifier

reciprocal of thermal diffusion distance in air

angular difference between the electrical and

optical duty cycles

total fixed error electronic multiplier constant

angular half width of chopper aperture relative to

the blade center

phase difference between heat applied on front and

back surface of black

detector thermal time constant

w~ h

2 m

ft

20 -60 ft

ft

= 10" AW

< 0.1 r

i

K

S

to 10 V

1C V

1. 999 V

V

V

V

V

~ 10 V

m

m

m

9 10 ft -1

0.1

1 s

42
t calibration driver rise time (63%) - 0.2 ms

e -

t . integrator RC time -5s

t- capacitor leakage time constant > 5000 s

t small signal system constant s

a) radian frequency s

a) radian chopper frequency s -5 2 -1

k air thermal dif fusivity 2.1x10 m s a

-1

43
References

[I] R.J. Phelan, Jr. and A.R. Cook, "Electrically Calibrated Pyroelectric

Optical-Radiation Detector," Applied Optics , 12 , 2494 (1973)

[2] Jon Geist and W.R. Blevin, "Chopper-Stabilized Null Radiometer Based

Upon an Electrically Calibrated Pyroelectric Detector," Applied Optics , 12, 2532 (1973)

[3] R.J. Phelan, Jr., R.L. Peterson, G.P. Klein, C.A. Hamilton and G.W. Day,

"Absolute, Pyroelectric Radiometers and Two Dimensional Arrays," Proceedings of the Electro-Optical System Design Conference, Sept. 18-20,

1973, New York, pp. 117-123.

[4] Jon Geist, "Fundamental Principals of Absolute Radiometry and the

Philosophy of This NBS Program (1968 to 1971)," National Bureau of

Standards Technical Note 5 94-1.

[5] Jon Geist, Bruce Steiner, Russell Schaefer, Edward Zalewski and

Antonio Corrons , "Electrically Based Spectral Power Measurements Through

the Use of a Tunable CW Laser," Applied Physics Letters , 26 , 309 (1975).

[6] R.J. Phelan, Jr., "Electrically Calibrated Detectors Versus Black Body

Sources," Proceedings of the IRIS Specialty Group on Infrared Detectors

(March 1975)

[7] G.W. Day, C.A. Hamilton, and K.W. Pyatt, "A Flat Spectral Response

Detector for the Visible to 12 pm Region," Proceedings of the IRIS

Specialty Group on Infrared Detectors (March 1975) . [8] C.A. Hamilton and G.W. Day, "An Absolute Pyroelectric Radiometer (A

Reference for Detector Responsivities) , " Proceedings of the IRIS Specialty

Group on Infrared Detectors (March 1975).

[9] Jon Geist, "Waveform-Independent Lock-In Detection," Review of Scientific

Instruments , 43, 1704 (1972) . [10] W.R. Blevin and Jon Geist, "Influence of Black Coatings on Pyroelectric

Detectors," Applied Optics , 13 , 1171 (1974).

[II] R.L. Peterson, G.W. Day, P.M. Gruzensky and R.J. Phelan, Jr., "Analysis

of Response of Pyroelectric Optical Detectors," Journal of Applied

Physics , 45, 3296 (1974) . [12] Equations (4. 3) -(4. 5) are a simplification of eq. (32) from reference [10]

based on the assumption of small error.

[13] C.A. Hamilton and G.W. Day, "A Pyroelectric Power Meter for the Measurement of Low Level Laser Radiation," National Bureau of Standards Technical

Note 665.

44
N£S 114A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS TN 678

2. Gov't Accession

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3. Recipient's Accession No.

4. TITLE AND SUBTITLE

An Electrically Calibrated Pyroelectric

Radiometer System

5. Publication Date March 1976

6. Performing Organization Code

276.04

7. AUTHOR(S) 8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

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

bibliography or literature survey, mention it here.) A new type of radiometer based on an electrically calibrated pyroelectric

detector is described„ Emphasis is placed on system design and analysis with

careful consideration of design trade-offs. An evaluation of both systematic

and random errors for the complete system yields an expression for the accuracy

relative to the electrical standards by which it is calibrated. Throughout the paper

the analysis should be sufficiently general that it can be applied to any Electrically

Calibrated Pyroelectric Radiometer which employs the same basic principals.

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)

Detector; pyroelectric; radi ometry

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