National Bureau of Standards

Library, H.W. Bldg

AUG 8 1962

^ecltniccil vtote 99

A SURVEY OF THE TECHNIQUES

FOR MEASURING THE

I RADIO REFRACTIVE INDEX

R. E. MCGAVIN

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

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NATIONAL BUREAU OF STANDARDS

99

MAY, 1962

A SURVEY OF THE TECHNIQUES

FOR MEASURING THE

RADIO REFRACTION INDEX

R. E. McGavin

NBS Boulder Laboratories

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 25. D.C. - Price 30 cents

CONTENTS

Page

1. INTRODUCTION 1

2. THE RADIO REFRACTIVE INDEX 1

3. THE MEASUREMENT OF THE RADIO REFRACTIVE INDEX 2

3.1. The Indirect Method of Measuring the Radio Refractive Index 3

a. The Required Accuracy of Meteorological Sensors 3

b. Surface Measurements of Refractive Index 6

(1) Sources of Data 6

(a) Weather Services 6

(b) Automatic Recording Systems for Particular Investigations- 7

c. Measurement of Gradient of Refractive Index 10

(1) Low Level Measurement of the Radio Refractive Index 10

(2) High Altitude Measurement of the Radio Refractive Index 10

(a) Sensors for the Radiosonde 12

3.2. Direct Measurement of the Refractive Index 18

a. Radio Frequency Refractometers 18

(1) Microwave Refractometers 19

(a) The Crain Refractometer 20

(b) The Birnbaum Refractometer 23

(c) The Vetter Refractometer 25

(2) Light- Weight Refractometers 29

(a) The Deam Refractometer 29

(b) The Hay Refractometer 31

3.3. Summary 33

4. REFERENCES 35

iii
ABSTRACT

The radio refractive index can be measured either directly or

indirectly. The former method is utilized by radio frequency refractometers; the latter method involves measurement of temperature,

pressure and humidity and conversion to refractive index. In terms

of convenience and accuracy the direct method is superior; however,

lack of the universal use of refractometers requires the use of weather

service type of data for the bulk of refractive index structures. Meteor

ological sensing is limited mainly by the inaccuracy in measuring

humidity which under ideal conditions appears to limit the accuracy to

± 1.0 N. Gradient measurements utilizing radiosondes reflects an

accuracy no better than ± 3 N units. Radio frequency refractometers

are capable of accuracies as much as an order of magnitude better

than that achieved by meteorological sensors. Lightweight refractometers have been devised for balloon-borne and dropsonde measurements reflecting accuracies inferior to the conventional refractometer

but superior to the radiosonde.

iv
A SURVEY OF THE

TECHNIQUES FOR MEASURING THE RADIO

REFRACTIVE INDEX

by

R. E. Mc Gavin

1. INTRODUCTION

The radio refractive index has been measured extensively by many

experimenters, especially in recent years. Methods vary with the individuals

This review attempts to assemble and to discuss the different methods for

determining the radio refractive index of air with some analysis of the expected accuracies for the different methods.

2. THE RADIO REFRACTIVE INDEX

The radio refractive index is central to any study of radio wave

propagation. The gradient of the refractive index determines refraction

through the medium, its turbulence determines the scattering of radio

energy, sharp discontinuities in the refractive index profile produce

reflections. The results of many investigations yield an expression of

the refractive index as a function of the three parameters of the atmosphere. In the temperature range of -50 C to +40 C, the refractive index

can be expressed with negligible error as:

l k / k e ^ N = (n-l)10 = -f ( P + -|— ) (1)

where N = refractivity

n = refractive index

T = temperature

P = total atmospheric pressure

e = partial water vapor pressure,

1
The Smith and Weintraub constants [ 195 3] adopted by CCIR* in 1959

result in the following expression:

N = (n-l)10

6

= ^(P + ^) (2)

where T is measured in degrees absolute and P and e are in millibars.

This expression is sometimes written

, „ , / 4810 e(RH)

N = (n-D10

6

= ^(P* Y )

(3)

where e is the saturation vapor pressure in millibars at temperature

s T and RH is the relative humidity in per cent.

3. THE MEASUREMENT OF THE RADIO REFRACTIVE INDEX

The radio refractive index is defined as the ratio of the velocity

of propagation of radio energy in a vacuum to the velocity in a specified

medium. Hence the radio refractive index may be measured directly if

the measuring instrument is sensitive to the velocity of propagation. The

refractive index is measured indirectly by measuring temperature, pressure

and humidity with consequent conversion to refractive index by means of (3).

The direct method is employed by radio frequency refractometers ; the indirect method is utilized where standard weather observations are used to

determine the refractive index. It is apparent that the direct method

should be superior since the accuracy is a function of a single sensor

rather than three, and since the result's are in a form requiring no conversion. However refractometers are relatively complex and expensive

devices requiring some degree of skill to operate. Hence, as yet refractometers are not in general use or even in sufficient quantity to permit

large scale mapping of refractive index structures. The bulk of the

International Radio Consultative Committee
synoptic and climato logical mapping of refractive index is, as yet, based

on the indirect method of measurement [Bean, Horn, Ozanich, I960] .

It seems that although the refractometer is a superior device for such

investigation, indirect measurement of the refractive index will continue

to play the major role in producing information on large scale refractive

index structures.

One of the difficulties of indirect measurement is the laborious

task of conversion of the measured parameters to refractive index

especially for large quantities of data. This problem has been somewhat

alleviated by the development of special analogue computers [Johnson,

195 3] . In addition, digital computers have been used for such conversion.

3.1. The Indirect Method of Measuring the Radio Refractive Index .

a. The Required Accuracy of Meteorological Sensors.

The accuracy of the determination of the refractive index will be

limited by the accuracy of the individual sensors. The degree of accuracy

demanded of the sensors can be estimated by differentiation of (2).

«-(S)«*(£)—(S)«

which can be expressed for average conditions and for small changes in N:

AN = aAT + bAe + cAP. (5)

Typical values of the constants a, b, and c based on the ICAO atmosphere

and assuming a relative humidity of 60 percent can be expressed as a

function of the altitude. Table I expresses this function for several values

of the altitude.
4

Alt, in km Temp(°C) e (mb)

15.0 10.

2

1 8.2 6.5

10 -50.3 0.04

Table I

P(mb) a b c 1013 -1.27 4.50 0. 27

893 -1.09 4.72 0. 28

262 -0.50 7.52 0.30

It can be noted that the effect of pressure variation is relatively constant with altitude, and the effect of temperature variation decreases

with altitude but that the effect of water vapor pressure increases with

altitude. Hence the requirements for sensor accuracy increases for

humidity sensors as the altitude is increased.

Figure 1 illustrates the degree of accuracy to be expected in the

measurement of the refractive index as a function of the accuracies of

the sensors for sea level conditions. It is assumed that the errors are

additive; hence this should reflect the maximum error to be expected.

Planes of equal accuracy are shown for accuracies of ± 0. 1 N, ±0.5 N,

± 1.0N, and ± 2. N. It can be seen that a measurement error of ± 1. N

can be contributed by each sensor if the accuracy of the sensors are not

within; ± 0. 8 C for temperature, ±3.7 mb for total pressure and ± 0. 22

mb for vapor pressure measurements. Since the total error will be a combination of these errors considerably better accuracy than this is

required.

It is apparent that extreme accuracy is required in the measurement of the water vapor pressure. The temperature can be measured

easily to within several tenths of a degree, and the total atmospheric

pressure can be measured to within several millibars. If an Assman,

or wet and dry bulb, hygrometer is used to measure the humidity, the

Sprung [1888] psychrometric formula may be used to determine the water

vapor pressure:
CO<

CO

(r

o

CO

UJ

CO

> O

< _l

UJ q

o w

O UJ

^ o

q:

uj

i- w

uj y

<

ui en x z> l- o

o

u_ <

<

or

=>o

o

<

UJX

hLUX

UJ

<ru

x

Q_

(/) O

<

C><

Z>

Q ^ Q

2 d UJ O 5 b

—

UJ Q

UJ o

Q

< -z. uj —

en

u_

!N3lM3dnSV3IM 3dnSS3Hd dOdVA d31VM Nl d0dd3

(qui) 37
e _ e " C CLLL > \ b > s 566

•where

e = the water vapor pressure (mb);

e = the saturation, water vapor pressure at the temperatures

of the wet bulb (mb).

c = hygrometer constant (c = 50 for a water covered bulb;

c = 43 for an ice covered bulb).

AT = difference between the dry bulb and wet bulb temperatures (degrees centigrade).

P = barometric pressure corrected for temperature (mb).

The degree of accuracy becomes a function of temperature; at 35 C the

relative humidity must be accurate to within 0. 33 percent while at C

an accuracy of 3.0 percent is necessary. Experimenters at the National

Physical Laboratories [ I960] have shown that when an Assman hygrometer

is used with thermometers accurate to within 0. 1 C the optimum expected

accuracy in the determination of the water vapor pressure is 0. 2 mb,

and errors three times as great can be expected at extreme conditions.

Hence it would appear that the optimum measurement of water vapor

limits the accuracy of the determination of the refractive index to approximately ± 1. N unit.

b. Surface Measurements of Refractive Index.

(1) Sources of Data.

(a) Weather Services.

Surface observations of temperature, pressure, and humidity

are standard measurements of the weather services around the world.

Methods of measuring these parameters are somewhat standard with

all weather services. Usually the temperature is read from mercurial
or alcohol thermometers, the pressure from mercurial barometers,

and the humidity from a conversion of wet and dry bulb thermometers.

The degree of accuracy of these measurements is usually a function of

the care and exactitude of the observer. Thermometers protected by

radiation shields are usually accurate to within 0.1 C, barometers to

within ±1.0 millibars. Reading errors can easily be in excess of the

instrument error. Especially in the determination of humidity is care in

measurement essential. The measurement of the wet bulb depression is

subject to many sources of error. Contamination of the wick or water,

insufficient wetting, and inadequate aspiration are common sources of

error. The wet bulb determination can be used below freezing, if proper

precautions are observed. When the bulb is wetted, the water freezes

releasing the heat of fusion (80 calories/ gm) which tends to raise the

temperature of the wet bulb. Sufficient time must be permitted to elapse

before reading the thermometer to allow this heat to be totally dissipated.

The thermometer then must be observed when it arrives at its minimum

temperature, indicating the maximum effect of evaporation.

(b) Automatic Recording Systems for Particular

Investigations

.

Automatic recording systems have been devised for measurement

of temperature, pressure, and humidity. The simplest devices are the

hygrothermograph and the microbarograph. In these devices the sensors

are connected by mechanical linkages to pens on chart recorders. The

pressure is recorded by means of an aneroid capsule, the temperature

b'} means of a bimetal strip or a curved bourdon tube, the humidity by

means of a hair hygrometer. The accuracy of such devices is relatively

poor and the measurement of the refractive index should not be considered

accurate to more than two or three N units for long-term averages.
8

Sensors producing electrical outputs are used to measure meteorological parameters in a variety of automatic recording systems, such

as strip-chart recorders, punched-paper tape, and magnetic-tape

recorders. The common methods of measuring temperature include

sensors such as resistance thermometers, thermocouples, and thermistors. The platinum resistance thermometer, an international standard,

is capable of measuring temperature to within ± 0. 05 C if used in a well

compensated bridge circuit. However since significant current is

necessary to achieve accuracy and resolution the platinum resistance

thermometer is velocity sensitive in a moving air stream. Thermocouples avoid the problem of sensitivity to velocity and yield accuracies

of approximately ±0.1 C. Thermistors reflect accuracies equivalent

to the platinum thermometer for short-term measurements but the long

term drift is undesirable. The chief advantage of small bead thermistors

is the very fast response; time constants measured in milliseconds render

thermistors ideal for higher frequency variations.

The total atmospheric pressure can be measured by a variety of

electrical sensors. The simplest device is the pressure potentiometer

where an aneroid capsule is mechanically linked to the wiper of a potentiometer. Inertia and friction as well as the resolution of the resistance

are limitations to its accuracy and time constant. One to two millibars

can be considered the limit of accuracy in a differential device operating

over a range of ± 100 millibars with reference to an average value. Time

constants of the order of five milliseconds are possible. The capacitive

microphone is capable of very good accuracy and resolution if used over

a restricted range. Accuracies of ± 0.01 mb and time constants of

several milliseconds have been achieved with capacitive microphones

measuring variations over several millibars. The resolution diminishes

as the range of operation increases, and a resolution of ± 0. 1 millibars
would be expected over the normal range of variations of atmospheric

pressure. Unfortunately unlike the pressure potentiometer, the capacitive microphone is temperature sensitive and requires correction for

temperature variations of 5 to 10 degrees. Strain gauge pressure transducers have approximately the same characteristics as capacitive microphones with some degradation in time constants. Differential strain

gauge transducers operating over a range of four to five millibars may

yield accuracies of several hundredths of a millibar. Fortunately

strain gauge transducers are relatively free of temperature effects over

the normally encountered ranges of the atmosphere.

The relative humidity which requires the most exactitude in

measurement is the one parameter most poorly measured. Sensors

for measuring the humidity directly do not produce the accuracy desired.

The common lithium chloride strip even under optimum conditions cannot

be expected to produce accuracies to within better than 5 percent in relative humidity. In general the time constant is of the order of 6 to 8 seconds

Other sensors show promise but are either in the developmental state or

have not been fully evaluated as yet. The Barium Fluoride strip [Jones

and Wexler, I960] yields accuracies, hysteresis effects, and response

times far superior to Lithium Chloride but has the disadvantage of calibration shift due to ageing. Phosphorous pentoxide sensors and aluminum

i oxide sensors have been used and appears to correct some of the deficiency

of the conventional sensor. The optimum method, at present, to measure

relative humidity is the wet-dry bulb technique using electrical thermometers. With care, accuracies of ± 0.02 millibars can be approached. The

lag coefficient will be relatively large being a function of the wick, the

rate of aspiration, and even the relative humidity itself. The limitation

of the wet-dry bulb technique is noted for extreme temperatures. Below

-24 C this method is inconclusive.
10

c. Measurement of the Gradient of Refractive Index.

(1) Low Level Measurement of the Radio

Refractive Index.

Low level measurements of the gradient of refractive index

can be accomplished utilizing towers. Towers up to 300 meters are

practical for such probing. Simultaneous sampling of the atmosphere

can be accomplished using many sensors along the tower. Using

electrical sensors permits a differential method of recording which

increases the accuracy and eliminates some of the necessary computations.

These, combined with a single measurement of the absolute surface

value, yields the profile of refractive index over the vertical interval.

Higher elevation measurements up to several thousand feet can

be made\using tethered balloons or wiresonde. It is necessary to send

aloft only the sensors with all other ancillary devices on the ground.

Long cables are used to transmit the information from the sensors to

the recording equipment.

(2) High Altitude Measurement of the Radio

Refractive Index.

For high altitude measurement of the meteorological parameters

influencing the refractivity, the radiosonde is in almost universal use. There are many models of the radiosonde, however, the principle of

operation for present American radiosondes is standard as illustrated

in figure 2. An aneroid capsule is used as the active element of a baroswitch. The temperature sensor, humidity sensor, and a reference resistance are alternately switched into the grid circuit of a blocking oscillator as the baroswitch wiper moves under the action of decreasing pressure.

The blocking oscillator controls the pulse rate of the RF transmitter.
11

RF

TRANSMITTER

BLOCKING

OSCILLATOR

i •—

*

<

T RH

i :rEF EF*EN

E

ICE

ANEROID

CAPSULE

BAROSWITCH

Figure 2 BLOCK DIAGRAM OF THE RADIOSONDE
12

Hence the pulse rate of the transmission is indicative of the value of the

sensor being sampled. The number of the contact energized is a measure

of the pressure; the switching sequence permits identification of temperature and humidity values. A constant rate of ascent of the balloon is

assumed hence the values of the parameters can be identified with the

proper altitude (the assumption of a constant ascent rate has proven to

be accurate especially at the higher altitudes).

(a) Sensors for the Radiosonde.

Radiosondes are used throughout the world, however there

is no uniformity in the selection of sensors. Hence, it is difficult

to compare measurements from different countries. At one international comparison at Payerne, Switzerland in 1956, fourteen nations

participated. The results indicated significant differences. Temperature measurements corresponded to within ±1.5 for night flights but

corresponded only to within ±3.5 for day time flights. Pressure measurements agree well at low altitudes but indicated a dispersion of ± 1.5

mb above 9000 meters (29, 000 feet), and ±2.5 mb above 16, 000 meters

(50, 000 feet). Humidity comparisons were poor indicating that at best

15 percent would be the most optimistic estimate of the standard deviation from the mean for all flights. The American sonde in most cases

approached the mean value. On the average it is estimated that the

standard American temperature sensor indicated a value approximately

1.5 C below the mean for all sondes used in the test, the pressure

determination was below the mean by .5 mb, whereas the humidity sensor although approaching the mean cannot be quantitatively evaluated.
13

No attempt was made at these comparison trials to determine the

absolute accuracy of any radio sonde. Although the absolute accuracy

of the American sonde has not been determined, statistical evaluation

of the uniformity of American radiosondes have been conducted by both

the U. S. Air Force and the U. S. Army Signal Corps. Statistical evaluation of radiosondes sent aloft in groups have been conducted. Results

indicate a standard deviation for the temperature sensor of 0. 8 C to

6000 meters and 1.0 above that altitude. The standard deviation for

the pressure determination was 2. 2 mb below 9000 meters and 1. 1 mb

above 9000 meters. The humidity sensor (lithium chloride) exhibited

the poorest comparison. Under ideal conditions the standard deviation

was 5 percent. This accuracy is possible only if the element is not subjected to high humidity (95 to 100 percent) or saturation by liquid water

and only if the temperature is above C. The response of the element

is especially poor where both temperature and humidity is low. The evaluation means little if the relative humidity is below 15 percent at a temperature of 20 C, or 20 percent at a temperature of C, or 30 percent

at a temperature of -30 C. Hence "under ideal conditions" at sea level,

reflecting the accuracies as stated, the standard deviation in the determination of the refractivity from radiosonde data is approximately 3 N

units; at one kilometer the standard deviation would be approximately 2 N

units. This then would appear to b e the ultimate precision which the

present conventional radiosonde sensors can yield the refractivity in a

static condition.

In addition to the inherent accuracy, the time constant or lag

coefficient of the sensors are of importance. Since the sonde is rising

at a relatively rapid rate, it passes into regions of changing refractivity

before the sensors are aware of it. The lag coefficient associated with
14

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15

the radiosonde introduces an error in the estimation of the true gradient.

The lag coefficients of the sensors have been analyzed by Wexler [ 1949]

and by Bean and Dutton [ 1961] and there are indications that some correction can be made to the radiosonde data. Wexler, in figure 3, shows

that the lag coefficient of the lithium chloride strip is a function not only

of the temperature but also of the absolute value of the relative humidity

as well as the size and direction of the gradient.

One of the disadvantages of the radiosonde is the sampling process

whereby the temperature and humidity are measured in sequence rather

than simultaneously. Several experimenters devised means to correct

this deficiency in the radio sonde. Misme [ 1956] decreased the cycling

time in one refractometer such that many more samples of each parameter

were produced per unit time. Clinger and Straiton [ I960] developed a

radiosonde that combines the parameters such that the output signal is in

terms of the refractive index (see figure 4). Since the wet and dry terms

are additive, a parallel combination of independent conductances can be

used. The dry term sensor has a conductance proportional to temperature

and inversely proportional to pressure; the wet term sensor is such that

it not only yields a value proportional to the relative humidity but also

adjusts the relative magnitude of the two terms. Thiesen [ 1961] devised

a similar radiosonde utilizing two separate sondes on the same balloon.

(See figure 5). The temperature and humidity information are combined

at the ground station by means of an analogue computer. For captive

balloon application, Hirao and Akita [ 1957] and Crozier [ 1958] developed

similar systems using wet and dry bulb thermistors to produce direct

output in refractive index.

Hence it is apparent that the indirect method of determining the

refractive index is less than optimum. Not only is the absolute accuracy
16

TEMPERATURE

SENSOR

PRESSURE

SENSOR

R,

®EMPERATURE

HUMIDITY

SENSOR

BLOCKING OSCILLATOR

[AN /AMT-6(xa-l)

Figure 4 CLINGER- STRAITON RADIOSONDE

(TRANSMISSION IN N UNITS)
17

Tw 395 MC

300 GRAM

RADIOSONDE

BALLOON

RECEIVER

395 MC

T 405 MC P

FREQUENCY

METER

UNIT

FREQ a Tw

FREQ. a T

Figure 5 THE SCHEMATIC DIAGRAM OF THE NAVY

ELECTRONICS LABORATORY (THEISEN) SYSTEM

BUL. AM. MET. SOC. VOL.42 N9 4 APRIL, 1961
18

poor even under the most advantageous conditions (several N units) but

the necessity for conversion of parameters imposes additional computational work. The limitations are chiefly due to the lack of accuracy in

the measurement of humidity. The present work on the development of

new hygrometer elements indicates future improvement in the correction

of these deficiencies.

3.2. Direct Measurement of the Refractive Index.

a. Radio Frequency Refractometers

The development of radio frequency refractometers has eliminated

the necessity of measuring the several parameters influencing the refractive index of the atmosphere. Since the radio refractive index is a function

of the velocity of propagation, the resonance of tuned circuits can be used

as a measure of refractive index. A cavity resonator open to the atmosphere or a capacitor utilizing the atmosphere as a dielectric, have been

used as such a measure.

In either case the radio refractive index can be measured as a direct function of the contents of the measuring element. The relationship between the change of the resonant frequency and the change in

refractive index is

**="*£-

(7)

f n ' {7]

where f is the original resonant frequency of the element whose contents

has a refractive index of n. Since n is very close to one the following

approximation can be used with negligible error

Afy « -An . (8)
19

(1) Microwave RefTactometers .

The resonant frequency of a microwave cavity is a function of

its dimensions and the refractive index of its contents. Hence, if a cavity is open to the atmosphere, the resonant frequency changes as

the refractive index of the air passing through changes in accordance

with (8). If a sealed reference cavity is used for comparison, the difference between resonant frequencies becomes a convenient measure of

the refractive index variations in the sampling cavity. This method of

measurement was used in two different instruments; the Crain type

(University of Texas) and the Birnbaum type (NBS). The Crain refTactometer utilizes the cavities as frequency determining elements in

ultra-stable oscillators. The difference frequency is then the unit of

measure. The Birnbaum refractometer utilizes the cavities as passive

elements energized by a klystron oscillator swept across the different

resonance frequencies of the cavities. The time difference between

resonances is the unit of measure. A third refractometer to utilize

this principle is the Vetter refractometer. This instrument utilizes

servo techniques to achieve a null system, thus eliminating the necessity

for extreme electronic stability.

The cavities are the major components in any of these instruments

Of prime importance is the temperature coefficient of the cavity. Most

cavities today are made of invar having a temperature coefficient of

approximately one part per million per degree centigrade [ Lement,

Roberts, and Averback, 1951; Bussey and Birnbaum, 1933]. This is

equivalent to 1 N unit per degree centigrade. Further temperature compensation of the cavity has produced temperature coefficients of 0. 2 to

0. 1 N unit per degree centigrade [Crain and Williams, 1957]. The possibility of improving cavity performance by use of special ceramics have
20

been investigated [Thompson, Freethey, and Waters, 1958]. Similar

temperature coefficient without compensation were found, however the

frailty and porosity of the ceramic limits its use. The response time of the refractometer is a function of how much

of the end plates of the cavity can be opened to the air. Unless the cavity

is well ventilated, the flushing time will be excessive. Adey [ 1957]

found that by judicious design of the end plates 67 percent of the area could

be cut away without appreciable loss of Q. Thompson et al [Thompson,

Freethey, and Waters 1959] found that as much as 92 percent of the end

plate area could be eliminated without serious degradation of the Q of

the cavity. Hence, the flushing time of cavities with such end plates becomes a function of the linear dimensions of the cavity and the velocity of

the air flow.

The accuracy of the refractometer is in general several orders

of magnitude better than what can be achieved by indirect measurement.

With proper care these instruments are capable of discerning changes of

the refractive index that are less than a tenth of an N unit. As a relative

instrument, i. e. , used to measure variations about an undetermined mean,

the accuracy and time constant are such as to detect easily very small

changes in the refractive index at a rate of up to one hundred cycles per

second. Accurate measurement of the gradient of refractive index is now

possible using these devices.

(a) The Crain Refractometer.

The Crain Refractometer [Crain, 1950; 1955] as illustrated in

figure 6, utilizes one sealed cavity as a reference cavity and a ventilated

cavity as the sampling element. Each of these cavities is the frequency
21

c )

SAMPLING REFERENCE /

CAVITY CAVITY I )

OSCILLATOR OSCILLATOR

MIXER

AMP D C^Anru-n

DISCRIKIINATOR RECOnucn

Figure 6 THE CRAIN REFRACTOMETER
22

determining element of a stabilized microwave oscillator in the manner

devised by Pound [ 1946]. Hence for optimum operation relatively high

Q's are necessary, and thus the end plate opening is of importance with

the consequent limitation due to flushing time (operation has indicated

that even the earliest models had a sufficiently fast flushing time to discern discontinuities displaced by as little as two feet of atmosphere at

normal aircraft speed of 250 feet/ sec).

The Crain Refractometer is so designed that the cavity resonators

operating in the 9400 megacycle range are displaced in resonant frequency

for equal values of refractive index. The resultant difference frequency

is the center frequency from which departures due to changing refractive

index are measured. Recent models utilize a 43 megacycle center frequency. As the refractive index of the contents of the sampling cavity

changes, the difference frequency at the output of the mixer changes

according to

Then since

Af-=-An.

AN = An 10 ,

a change of 1 N unit, corresponds to a change in the resonant frequency

of the sampling cavity of approximately 9-4 kilocycles if the nominal

operating frequency is 9400 megacycles. The output of the mixer is applied through appropriate amplifiers, limiters and discriminators, and

the DC output is a function of the changes in the refractive index within

the sampling cavity. The linearity of the function will be determined

chiefly by the characteristics of the discriminator. A 400 N unit range

would require a discriminator having a linear range of 4 megacycles.
23

For the measurement of small scale variations of refractive

index a modified Crain refractometer utilizing a 10. 7 megacycle center

frequency with a 200 kilocycle linear range has been used. Scales of 1

to 20 N units for full scale deflections of a 1 milliampere chart recorder

have been used. Since this instrument is relative the position of the

zero point is of little consequence, hence the zero can be shifted by means

of a tuning slug in the reference cavity.

(b) The Birnbaum Refractometer.

The Birnbaum refractometer [Birnbaum, 1950], illustrated in

figure 7, applies the principle of resonance in a somewhat different

fashion. Both the reference or sealed cavity and the sampling or open

cavity are passive elements. The cavities are slightly different in dimensions and are of the transmission type having crystal detectors at the

output. A klystron is frequency modulated by a sawtooth voltage such that

the output frequency is linear with time. The one klystron excites each

cavity in sequence at its respective resonance frequency. During the frequency excursion of the klystron the resonance of each cavity is excited

and a pulse is formed at the crystal detector. Since the resonant frequency

of the cavities usually differ, the two output pulses will be displaced in

time. If the modulation on the klystron is periodic then the output pulses

are also displaced in phase. Then the two pulse trains coming from the

detectors are displaced in phase, the displacement being a function of the

klystron modulation. Any change in the refractive index of the contents

of the sampling cavity will alter the phase difference between two pulse

trains. The relative phase between the two outputs can then be measured

by an electronic phase meter. The phase meter in use is merely a multivibrator having a constant amplitude output. The pulse from each cavity
24 1 i i 4 = 9S

*«:

SAW GENE

orUl

hUlO<

ccU.

UJ

<r<

CD

orCO

UJx
25

after shaping alternately switches the multivibrator "on" and "off". The

width of the constant amplitude output pulse from the multivibrator is a measure of the time difference between trigger pulses. The resulting

train of constant amplitude variable width pulses is then applied to appropriate recording circuits where the time constant may vary from a minimum which is determined by the sweep rate of the modulating voltage on the

klystron to a value in excess of this depending upon the averaging time of the

recording circuit.

The accuracy of the instrument is dependent upon its ability to maintain a linear frequency sweep. The function of frequency versus time is the

determining factor in establishing the relative difference in refractive index.

Individual differences between klystrons, as well as different temperature

characteristics of individual klystrons, complicate the problem since the

sweep characteristics must be matched to the individual klystron. This

problem can be circumvented in the manner of Sargent [ 1959] , who modified

the Birnbaum refractometer to operate as a microwave hygrometer. A

servo system is used to tune the sampling cavity to the resonant frequency

of the reference cavity; hence, the instrument is essentially a null device.

The servo positions a tuning probe in the sampling cavity. The depth of

penetration is the measure of the refractive index of the contents of the sampling cavity. This technique minimizes the dependence on the sweep characteristics of the klystron.

(c) The Vetter Refractometer.

The problems associated with the Birnbaum refractometer led to the

development of the Vetter refractometer [Vetter, 1962]. This device, figure

8, virtually eliminates the dependence of the refractometer on electronic

characteristics and shifts the limitations to the cavities themselves. In addition, whereas the two previous instruments are primarily relative refractive

index indicators, the Vetter refractometer is an absolute refractive index

device.
26

PHASE SENSITIVE ERROR SIGNAL

AMPLIFIER

X

_/ SAMPLING \ i r V CAViiy j SERVO

AMPLIFIER

r^ v Ky i

r

i ' MODULATING

SINE WAVE /tunedy^^^-' SERVO

MOTOR

hi nrrrr H KU LrtENCE 1 \CAV TY/ ^--^^

READOUT

r ERROR SIGNAL

PHASE SENSITIVE

AUDI ICICD MMr L

Figure 8 THE VETTER REFRACTOMETER
27

If the cavity is a symmetrical filter driven by a klystron which is

modulated by a symmetrical signal such as a sine wave, then when the

center frequencies of the cavity and the klystron are identical, the output

of the cavity will contain only even harmonics of the modulating signal,

i.e., no fundamental or odd harmonics of the original modulating signal

will be present. If the center frequencies of the cavity and klystron

differ then some fundamental of the modulating signal appears at the

detector output. If the cavity is above the klystron then there will be an

output at fundamental modulating frequency; if the cavity is below the klystron there will again be an output but will be shifted 180 in phase from

the former condition. Hence, presence of the fundamental modulating

signal is a measure of lack of identity between center frequencies. Such an

output can be used as an error signal to tune the klystron to the same frequency as that of the cavity.

The Vetter refractometer utilizes this principle in a null system.

The reference cavity is excited by a klystron which is modulated by a small sine voltage on the repeller. Any output at the fundamental modulating

frequency at the detector of the reference cavity is compared in phase to the

original modulating signal and an error signal is applied to the repeller of

the klystron to lock the center frequency of the klystron to the reference

cavity. At coincidence, the fundamental disappears in the output of the

reference cavity. The same klystron excited the sampling cavity. Any

fundamental appearing at the output after phase comparison to the modulating

signal develops another error signal. This error signal is used to drive a

mechanical servo which tunes the reference cavity to the resonant frequency

of the sampling cavity with the concomitant shifting of the klystron center

frequency. This then is a double loop system: the reference cavity controls

the klystron; the sampling cavity controls the reference cavity.
28

The tuning of the reference cavity is accomplished by a motordriven probe that penetrates the reference cavity. The output of the

refractometer is in terms of probe penetration; associated circuitry

provides an electrical output in terms of probe positioning. The tuning

of the probe is accomplished over a 400 N unit range. Although the

range of variations experienced are more of the order of 100 N or less

this extended range permits a zero calibration point. The design of the

probe is such as to permit very nearly a linear function of AN versus

probe penetration over the range of operation. Once the probe is calibrated with the cavity the relative calibration is static and practically

independent of the contents of the cavity, which is usually dry air or an

inert gas. The reference cavity is sealed but does not require a vacuum

tight seal.

The absolute calibration is accomplished merely by determining

the zero point or the intercept where N = 0. This is done by evacuating

the sampling cavity. Experience has indicated that a simple vacuum

system can be adapted for calibration which will be both rapid and accurate.

It should be noted that the shape of the calibrating curve is independent of the intercept, and consequently the calibration curve of the probe

penetration versus AN can be moved to pass through the intercept. Also

it is not necessary that the calibration curve be linear over the range of

0-400 N units; the requirement for linearity is demanded only over the

range of operation.

Since the refractometer is mechanically tuned with a servo system

having considerable inertia, the high frequency response is relatively poor.

Above 10 cycles per second the validity of results is questionable. The

accuracy and simplicity of operation are the distinct advantages.
29

(2) Light- Weight Refractometers .

Refractometers have been used to measure both the surface value

and the gradient of the refractive index. Although the aforementioned

units were designed originally as ground -based equipment, modifications

have been made to convert them to airborne use. However where vertical

gradients to high altitude are desired the airborne version of the refractometer has definite limitations. The turning radius of the aircraft, and

the angle and rate of climb or glide are factors influencing this type of

measurement. A considerable horizontal component is present which

can conceivably be more significant in the measurement than is the vertical

component. In addition the time involved in ascent or descent is relatively

long and the measurement is valid only under the assumption of relatively

static conditions for the total time of the measurement. Due to the expense

and weight, the conventional refractometers are not economical or practical to use in balloon ascent whether free or tethered. Hence, the need

for light-weight refractometers to be used either in wiresonde, radiosonde

or dropsonde applications led to the development of several refractometers

for such applications.

(a) The Deam Refractometer

.

Figure 9 is a block diagram of a light-weight (6 pounds), expendable

refractometer developed by Deam at the University of Texas, for use as a balloon-borne unit or as a drop sonde. The device is a Pound oscillator [ 1946]

operating at a nominal frequency of 403 megacycles; the actual frequency is

determined by a coaxial cavity. The refractive index is sampled by a cavity

and is reflected as a capacitance in the tuned circuit of the oscillator.

The RF oscillator utilizes a tuned transmission line as the resonant

circuit. The transmission line is terminated with a semiconductor to

allow for adjustment of its electrical length. The correction voltage which
30

CORRECTION

VOLTAGE

^

DETECTOR

HF

OSCILLATOR

AMP

PHASE

DETECTOR

4.5 MC

OSCILLATOR

CRYSTAL

MODULATOR

CAVITY

Figure 9 THE DEAM EXPENDABLE REFRACTOMETER

(MODIFIED POUND OSCILLATOR)
31

is proportional to the frequency difference between the RF oscillator and

the resonant frequency of the cavity, is used to bias the semiconductor

changing its capacitance and producing a change in the resonant frequency

of the oscillator.

Operational tests indicate that the electronics are sufficiently

stable to produce the desired accuracy. Due to the cavity size and mass

the time constant is less than desirable. Lag coefficients and temperature

coefficients are also characteristics which are not fully evaluated and optimized at this time. Since the expendability of this sonde was a principal

consideration in its development, extreme accuracy must be balanced with

economic factors. The present accuracy is estimated to be better than

± 5 N units for a complete profile.

(b) The Hay Refractometer

.

A refractometer was developed by D. R. Hay, as a compromise

between the microwave refractometer and the conventional radiosonde.

See figure 10. It lacks by an order of magnitude the accuracy of the

microwave refractometer but weighing only six pounds it incorporates the

light-weight feature of the radiosonde. Hence as an airborne instrument

it fulfills a need for more accurate, faster response, probing of the refractive index at high elevations.

Two Clapp oscillators, operating nominally at 5 megacycles, are

used as separate transmitters. They are designed to be identical with the

exception of the frequency determining capacitors. One oscillator is the

reference oscillator whose capacitor is unaffected by the atmosphere; the

other oscillator uses a parallel plate capacitor through which the atmosphere

is allowed to pass. Each oscillator or transmitter transmits an independent

signal to the ground station. At the ground station the two signals are detected and the audio difference frequency is used as the unit of measure.
32

REFERENCE

CAPACITOR

__r

, -i

<?

SWITCH OSCILLATOR

DOUBLER

AMPLIFIER

SENSING

CAPACITOR

Figure 10. THE HAY REFRACTOMETER
33

Considerable care is necessary to compensate the sensing capacitor

for temperature and to provide sufficient air flow over the plates of the

capacitor. The capacitor consists of forty-one parallel plates spaced oneeighth of an inch apart, each plate being ten inches long and 0. 28 inches

wide. A later model of the Hay refractometer utilizes a single oscillator

with a carefully designed rotating switch to sample alternately a reference

capacitor and the air sampling capacitor. The reference capacitor is

sampled for three seconds, the sensing capacitor for eleven seconds. The

transmitted signal is 10 megacycles per second. Tests on this device

reveal a remarkably fast time constant; a -52 N unit change was indicated

in 0. 6 seconds.

Temperature compensation is extremely important. Since a 3-cycle

change in frequency corresponds to one N unit, frequency drift due to temperature must be minimized by careful design.

3 . 3 Summary.

In comparison between the direct and indirect method of measurement absolute accuracy may not be the only consideration. Although

refractometers may be capable of superior accuracy, the factors of requirements, economics, and availability of competent technical personnel

may outweigh this advantage. Refractometers are relatively expensive,

hence availability in quantity requires a considerable investment. Refractometers are somewhat complex and require competent technical personnel

to maintain, calibrate, and operate them.

In many cases where average values or long term statistics are

adequate, the use of refractometers may not be indicated. The data on

refractive index structure derived from weather service data has been

used most successfully for the determination of average conditions. Errors

can be assumed to be normally distributed about a value proportional to the

true value; hence the average should approach this value. Gradient
34

measurements do not require the same absolute accuracy as do surface

measurements; the change in value with change in height is of chief interest.

This implies importance of lag coefficients especially where balloon ascents

are concerned. The chief limitation appears to be the lag coefficient of the

humidity sensor in the radiosonde, but the gravity of this limitation also

is relative. During ascent the lag coefficient introduces an error in the

determination of the boundary and height of elevated layers. Sharp discontinuities in the profile are smoothed, and the smoothed edges of the layer

appear to be higher. Well above C the lag coefficient of the lithium

chloride sensor is approximately 10 seconds or less. At a constant rate

of ascent of 300 meters per minute, this lag coefficient would cause the

sensor to move 50 meters beyond the layer boundary before 63 percent of

the change would be noted. At -40 the lag coefficient would be approximately 400 seconds. However at this temperature the saturation water

vapor pressure is of the order of 0. 1 mb and the contribution to the refractivity will be at most 0. 5 N units. At , where the contribution can be

as high as 25 N units, lag coefficients of 20 to 30 seconds introduce an

error of from 100 to 150 meters. These errors, depending upon the application, may or may not be significant.

Where extreme accuracy is required, the use of refractometers is

indicated. Radar and radio navigation are several examples where accurate . estimates of both surface values and gradient are necessary to determine

the refraction through the atmosphere. The necessity for true vertical

gradients would demand the use of balloon-borne or dropsonde type of

refractometer . In many applications the indirect method may be sufficient,

however, an accurate determination of the fine structure of the refractive

index can be accomplished only with some type of radio frequency refractometer.
35

4. REFERENCES

Adey, A. W. , Microwave refractometer cavity design, Can. J. of Tech.

34, 519-521 (1957).

I Bean, B. R. , J. D. Horn, and A. M. Ozanich Jr., Climatic charts and

data of the radio refractive index for the United States and the

world, NBS Monograph 22 (November 25, I960).

Bean, B. R. , and E. J. Dutton, Concerning radiosondes, lag constants,

and refractive index profiles, J. Geophys. Research 66, No. 11,

3717-3722 (November, 1961).

Birnbaum, G. , A recording microwave refractometer, Rev. Sci. Instr.

2J., No. 2, 169-176 (February, 1950).

Bussey, H. E. , and G. Birnbaum, Measurement of variation in atmospheric

refractive index with an airborne microwave refractometer, J. Research of NBS 51, No. 4, 17 1- 178 (October, 1953) =

C.C.I.R. Documents of IXth Plenary Assembly (Los Angeles, 1959), Vol.

II, Study Programme No. 138(v); p. 138 (Geneva, 1959).

Clinger, A. H. , and A. W. Straiton, Adaptation of the radiosonde for direct

measurement of radio refractive index, Bull. Am. Met. Soc. 41 , No. 5, 250-252 (May, I960).

Crain, C. M. , Apparatus for recording fluctuations in the refractive index

of the atmosphere at 3.2 centimeter wave length, Rev. Sci. Instr.

2l_, No. 5, 456-457 (May, 1950).

Crain, C. M. , Survey of airborne microwave refractometer measurements,

Proc. IRE 43, No. 10, 1405-1411 (October, 1955).

Crain, C. M. , and C. E. Williams, Method of obtaining pressure and

temperature insensitive microwave cavity resonators, Rev. Sci.

Instr. ,28, No. 8, 620-623 (August, 1957).

Crozier, A. L. , Captive balloon refractovariometer, Rev. Sci. Instr. 29 , No. 4, 276-279 (April, 1958).

Hirao, K. , and K. I. Akita, A new type refractive index variometer, J. Radio Research Lab. 4, No. 18, 423-437 (October, 1957).
36

Johnson, Walter E. , An analogue computer for the solution of the radio

refractive index equation, J. Research of NBS 51, No. 6, 335-342

(December, 1953).

Jones, F. E. , and A. Wexler, A barium fluoride film hygrometer element,

J. Geophys. Research ^5, No. 7, 2087-2095 (July, I960).

Lement, B. S., C. S. Roberts, and B. L. Averbach, Determination of

small thermal expansion coefficients by a micrometric dilatometer

method, Rev. Sci. Instr. 2_2, No. 3, 194-196 (March, 1951).

Misme, P. , Methode de mesure thermodynamique de l'indice de refraction

de l'air-Description de la radiosonde MDI. Annales des Telecommunications, 1_1_, 81-84 (1956).

National Physical Laboratory, Dept. of Scientific Research, (Teddington

Middlesex, I960), The refractive index of air for radio waves and

microwaves

.

Pound, R. B., Electronic frequency stabilization of microwave oscillators,

Rev. Sci. Instr. 17, No. 11, 490-505 (November, 1946).

Sargent, J. A., Recording microwave hygrometer, Rev. Sci. Instr. 30,

348 (1959).

Smith, E. K. , and S. Weintraub, The constants in the equation for atmospheric refractive index at radio frequencies, Proc IRE 41, 1035-

1037 (1953).

Sprung, A.W.F., Bestimm. d. Luftf euchtigk mit Hulfe d. Assman'schen

Aspirationspsychometer, Das Wetter 5, 105-108 (1888).

Thiesen, J. F. , Direct measurement of the refractive index by radiosonde,

Bull. Am. Met. Soc . 42, No. 4, 282 (April, 1961).

Thompson, M. C. Jr., F. E. Freethey, and D. M. Waters, Fabrication

X techniques for ceramic X-band cavity resonator, Rev. Sci. Instr.

29, No. 10, 865-868 (October, 1958).

Thompson, M. C. Jr., F. E. Freethey, and D. M. Waters, End plate modification of X-band TEq,, cavity resonators, IRE Trans. MTT-7,

No. 3, (July, 1959).
37

Vetter, M. J. , and M. C. Thompson Jr. , An absolute microwave

refractometer, Rev. Sci. Instr. 33, (June, 1962).

Wexler, A, , Low temperature performance of radiosonde electric

hygrometer elements, J. Res. of NBS 43, 49-56 (July, 1949).

U. S. GOVERNMENT PRINTING OFFICE : 1 162 O -

DEPARTMENT OF COMMERCE

Luther H. Hodges, Secretary

U.S.]

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director

The sc THE NATIONAL BUREAU OF STANDARDS

e scope of activities of the National Bureau of Standards at its major laboratories in Washington, D.C., and

Boulder, Colorado, is suggested in the following listing of the divisions and sections engaged in technical work.

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