REFLECTIVITY OF ELECTROMAGNET IC WAVES

AT AN AIR-WATER INTERFACE FOR PURE AND SEA WATER

by

Larry K. Lep ley

Will iam M. Adams

Technical Report No. 25

December 1968

No. 1 of 4 Reports in Completion

of

GEOPHYSICAL EXPLORATION FOR HAWAIIAN GROUNDWATER, PHASE II

OWRR Project No. B-008-HI, Grant Agreement No . 14-01-0001-1494

Principal Investigators: Doak C. Cox &Wi l l i am M. Adams

Project Period: July 1,1967 to October 31,1968

The programs and act ivities described herein were supported in part by fundsprovided by the United States Department of the Interior as authorized underthe Water Resources Act of 1964, Public Law 88-379 .

ABSTRACT

CompiLation of the opticaL properties of eLectromagnetic waves

incident on pure (chemicaLLy pure) or sea water shows an abrupt diver­

gence of behavior for the two water types at about the 3-centimeter

waveLength . From this point on to aLL Longer (radio) waveLengths3 sea

water behaves opticaLLy Like a metaL3 whereas pure water behaves Like

a semiconductor . At shorter waveLengths (be Low 3 centimeters) 3 both

fresh and pure water behave as dieLectrics with simiLar opticaL prop­

erties. OnLy at visibLe waveLengths are the optics of naturaL waters

of aLL saLinities weLL known. The refLectivity contrast (difference

in refLectivity divided by average refLectivity) between pure and sea

water to visibLe Li ght is approximateLy 3%. The refLectivity contrast

between sea and pure water at radio frequencies is approximateLy 44% .

iii

CONTENTS

LIST OF FIGURES v

INTRODUCTION 1

THEORY .

LABORATORY EXPERIMENTATION 8

SUMMARY AND CONCLUSIONS 11

REFERENCES 15

LIST OF FIGURES

Figure

Spectra of Refractive Index, n, Absorption Coefficient, ko' andReflectivity, R, of Pure and Sea Water as a Function of Electro-magnetic Wavelength in Air 3

2 Relation Between R, ko' and n for Pure and Sea Water TracedThrough Their Spectra; 3 cm. to 300 m 4

3 Relation Between R, ko' and n for Pure and Sea Water TracedThrough Their Spectra; 310 Microns to 3 cm. 6

4 Relation Between R, ko' and n for Pure and Sea Water TracedThrough Their Spectra; .18 to 310 Microns 7

5 Reflectivi~y to Visible Light and Density Vs. Salinity andTemperature 9

6 Optical Classification of Water by Reflectivity and Absorption. 10

7 Front View of the Laser Reflectance Comparator 12

8 Side View of the Laser Reflectance Comparator 13

v

INTRODUCTION

Present techniques for aerial detection of coastal springs or

estuarine outflows involve remote measurement of temperature or color.

At this time no aerial remote sensor is available for measurement of

salinity anomalies per se.

The purpose of this report is to provide some background for a

study to determine the feasibility of using surface reflectivity

as a measure of salinity. Graphs of reflectivity of an air-water

interface for both pure and ?ea water are plotted as a function of

electromagnetic wavelengths ranging from ultraviolet to radio waves.

The graphed values were taken from published tables (Dorsey, 1940) or

computed from other parameters (Corson and Lorrain, 1962;Liebermann,

1962) .

For the purposes of this report, a distinction between pure and

fresh water must be made. Chemically "pure water" does not exist in

nature but must be approximated by distillation, ion exchange, etc .

"Fresh water" refers to natural potable water such as rain water. Pure

and fresh water, as defined above, have different electromagnetic prop­

erties at radio frequencies and can therefore be expected to show

different ref1ectances.

"Sea water" refers to ocean water containing 32 parts per thou­

sand dissolved solids and can be approximated for electromagnetic

measurements by 0.5 molar NaCl.

THEORY

The reflectivity of plane electromagnetic waves from a smooth

water surface at normal incidence is related to the refractive index,

n, and the adsorption index, k, both of which depend on wavelength.

For a given wavelength in air, A , the reflectivity is:°

(n-1) 2 + (nk) 2R =

(n+1) 2 + (nk)2

The refractive index, n, is defined as the ratio of wavelength in

air, AO, to wavelength in water, A, at a given AO: n = AO/ A = c/v,

2

where c is the velocity in air and v is the velocity in water. The

refractive index, n, of water is a function of the angle of incidence for

some frequencies, but only normal incidence will be considered here.

The absorption index, k, is a measure of the rate of attenuation

of the radiation in the water in terms of wavelengths in air. It i s

defined as:

k ;:: KAo4 1T

where K, the more familiar absorption coefficient, is the length of

penetration through water required for the intensity of the radiation

to be attenuated to lie (~ 63%) of its initial value.

The spectra of the indices of refraction, n, absorption, k,

and reflectivity, R, of pure (p) and sea (s) water are shown in Figure

1 as traces labeled n , k p, n , k s, R , R , respectively.p 0 sop sA special relationship exists between nand k for both pure and

sea water at and near wavelengths of 3.0, 6.1, and 15.1 microns in the

infrared. At these wavelengths where n increases with increasing

wavelength, there are peaks in k (maxima in attenuation). At these

"anomalous dispersion" wavelengths, the polar (asymmetric) water mole­

cules resonate with the electromagnetic radiation. At wavelengths less

than but approaching those corresponding to anomalous dispersion, the

molecular oscillation increasingly lags behind the electromagnetic

excitation. At wavelengths greater than but approaching those corres­

ponding to anomalous dispersion, the molecular oscillation increasingly

leads the electromagnetic excitation. Associated with the anomalous

dispersion wavelengths there are changes of 1T radians in the phase

difference between the excitation and the induced oscillation.

At the resonant frequencies, the induced alteration of phase

causes destructive interference shown by high absorption index.

Figure 2 is a plot of refractive index, n, vs absorption index,

k . The reflectivity, R, coordinates are represented by circular arcs

on that same figure. The equation,

(n-l) 2 + (nk) 2R ;::

(n+l) 2 + (nk) 2

nCYCLES PER SECOND

108

108 107 108 10" 104 10' 10 2 10 ' 10°

..'

DATA COMPILED FROM:I. DORSEY, N.E. (1940)2. CORSON AND LORRAIN (1962)3. LIEBERMAN, L.N. (1962)4. McALISTER AND McLEISH (1965)

10"2 10" ' 10° 10 10 210 ' 104

10" 10810710810 8

IdO

x, (WAVELENGTH IN AIR , CENTIMETERS)

,-

~_;. ~ R•• I.O

° -- r'-----------------------..:...-_ c __ , '\

r-~\ .,.......... • ~ \. " \,I : ~--'""r-------------------n!.:.9-----I :: \ ,-- -------·· ••••••••••• • ··k"p·0063

::": \ /" "

V

- PHOT OGR APHIC IR

- PHOTOCONOUCTlv E IR

THERN AL "' ICReWAVESoR

;- ~HOTOGR A PHIC uv. -v iS IBLE

R ' 0.64 - ---l• p -..! ----"0 __-.. ---:i': _ _ _ _ I., -r:

:'., 1'l-/-'.) Q

.:.• -/ 3.:..:y ..... -.

-. -. :»-... U

e •••-. e.-. e.'.

00' ....-. -..: :.'. .,;. .-."/ 0 •

n. :: ::~~£'.,~.~~iJnp : ~ ,'-

I

kos

np PURE WATER -­

10" ~n, SEA WATER--

~KoI' PURE WATER -­

4 KOS SEA WATER -­10

IRp p.URE WATER -­R. SEA WATER -­

10'

102

10'

10°

10"'

.:l I02 f- 8 0.8

IO' f- 7 07

I04 f- 6 0.6

IO"f- 5 0 .5

lOaf- 4 0 .4

10"7 f- 3 0 .3

I08 f- 2 02

loer I 0 .1

n RR.

FIGURE 1: SPECTRA OF REFRACTIVE INDEX, n, ABSORPTION COEFFICIENT, kO I

AND REFLECTIVITY, R, OF PURE AND SEA WATER AS A FUNCTION OFELECTROMAGNETIC WAVELENGTH IN AIR. Vl

~,_~~J;; ;t:""':.~iEIii:i:;:;e:;'~.J1Ilfi:;;::;:;LiLftIiiji&_-'•.........,...;E',01= :=

.;:..

OJ"ot-

OJ1ot-~

REFLECTIVITY

':lot­OJ"·

PURE WATER --­SEA WATER --

100

90

~oBO

70

60

50

40111// 9~'"

30

o 10 20 30 40 . 50 60 70 BO 90 100 110 120 130 140 150 160 170 IBO 190 200

n

FIGURE 2: RELATION BETWEEN R, ko, AND n FOR PURE AND SEA WATERTRACED THROUGH THEIR SPECTRA; 3 em. TO 300 m.

5

may be written as,

k2 + [(n-l + R)(1-R)]2 = 4R/(1-R)2

which represents a family of circles with 21iR/(1-R) radii and centers

at (n-l + R)/(l-R). The same relationship is replotted at increasingly

larger scales in Figures 3 and 4 to show the trace in detail at various

wavelengths. As the trace progresses through increasing wavelength,

from 2.3 to 15.0 microns, each major band of molecular resonance

absorption is represented by a clockwise loop in Figure 3.

Whereas in Figure 4, the optical properties of pure and sea water

do not differ enough to be shown as separate traces, in Figures 2 and

3 a very significant divergence is shown. The long wave reflectivities

are better shown in Figure 1 where the reflectivity values of both pure

and sea water are shown increasing sharply with wavelength. There is

a major divergence beginning at about 3 centimeters: sea water becomes

nearly 100% reflective and pure water 64% reflective.

T. 5. Moss (1961) has shown a relationship between refraction and

absorption that can be used to fill in the data gaps for natural fresh

and brackish water. In terms of the absorption coefficient, K,

The computations are beyond the scope of this paper, but since Ko = 4nk/AQ'

an examination of the k trace of Figure 1 indicates that the refractive

index, and thus the reflectivity of sea water, can be expected to be

higher than that of fresh water at most wavelengths.

L. N. Liebermann (1962) states that, although sea water is perfectly

reflecting at radio frequencies at normal incidence, its reflectivity

can be somewhat l ess at other angles; hence,

(5-1)R = (5+1) ,

where

~ l+i5 = 2a cos Q

6

PURE WATER --­SEA WATER ---

REFLECTIVITY

0\

5

4o~

:3

2

10"·

o 2 :3 4

n5 6 7 8 9

R. =64%

". =9

10

FIGURE 3: RELATION BETWEENR, ko, AND n FOR PURE AND SEA WATERTRACED THROUGH THEIR SPECTRA; 310 MICRONS TO 3 em.

II

~lIL

I

f

rI

2.2 2.3 2.4 2.51.9 2.0 2.11.8

80 IL

l·...·;~ ..-..-

63.:':.,- <,

1.6 1.7

18

1.2 26 2.3 2:6 .21L 1.5\ " I

If! VIS UV n

10% -

REFLECTIVITY

\5"10- -

1.11.0.9.8.7.6

.3 -1 I r ;'

2%--........

"~---{ ~ \ \ \ \ l21 / / / / /' . , ~ ::::----- \\r 5

%--------..:::

. 14 I I I I I I I II~ X

8

.7

9 ~

1.0

FIGURE 4: RELATION BETWEEN R, ko, AND n FOR PURE AND SEA WATERTRACED THROUGH THEIR SPECTRAj .18 TO 310 MICRONS.

-...I

~' 1 ;': ·~~.\,;'". ;:· l~ ,j;;~~t?-~::;~~~:,c -. "S;"'i~:"""-=ir -;:;;;- ;:k~ ,"~ . 1;<.._ ,,_ £:... . .1.

8

Q is the angle of incidence measured from the vertical, a is the conduc­

tivity, £: is the permittivity of free space (£: = 8.85 x 10- 12 farad/meter),

and w is the angular phase velocity.

Since reflectivity is dependent upon conductivity, which in turn

depends on temperature and salinity, in areas of great variations of

salinity, such as areas of stream discharge, e.g., estuaries and the

vicinities of submarine springs, salinity may be the most significant

factor . Reflectivity dependence upon salinity in visible light, where

all natural waters are dielectrics, are an order of magnitude smaller

than at radio frequencies, where sea water is a good conductor. At

optical frequencies, reflectivity is closely related to salinity and

density, rather than to temperature (Fig. 5). The probable range of

coastal springs on Hawaii is shown on the plot by the shaded pseudo­

ellipse.

Water can be classified into optical types as a function of its

salinity and the electromagnetic wavelength. Figure 6 is a diagram of

the type originated by McMahon (1950) and relating optical types to re­

flectivity, R, and absorption, K. The optical properties of water are

traced through the spectrum in the diagram. At this scale, pure and sea

water can be separated at ultraviolet frequencies by differences in

transparency . With respect to ultraviolet light, sea water behaves as

a more effective black body than does fresh water. As the trace progresses

through the visible range, it takes a brief sharp excursion to the opti­

cally transparent region of the diagram (the visible window) and then

returns abruptly to the black body region at infrared frequencies. As

the wavelength progresses farther into the infrared toward microwaves,

the trace remains at the opaque side of the diagram, but moves toward the

metallic corner owing to an increase in reflectivity. When 64% reflec­

tivity is reached at around 3 centimeters, the sea water and pure water

traces separate abruptly. The sea-water trace goes to 100% reflectivity,

whereas the pure water trace turns abruptly parallel to the 64% reflec­

tivity contour and remains at 64% reflectivity as it progresses toward

the radio wi ndow at 1 meter, above which it becomes a transparent body.

LABORATORY EXPERIMENTATION

Experiments of reflectance of water as a function of salinity to

9

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II

II

II

II ~

I ­I,

~~.

II

II

II

I1III,II

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//

//

//

//

o.....~.

II

1I

III

C\I I~ I- I

IIIII

/O'?"'./

/ // / /

/ I I II I

o / ~. I I ~9

~ / I I I II I If I /

I I I II I I I

I I I I II I I I II I I I II I I 1 1I I 1- I 1I I I 3 I II I I I I, , I I I

, I I I, I I II , , II , I ,I I , ,

5 15 25SALINITY, PER MIL

35

Reflect ivity (%) - -­Density (om/c .c) -­Pseudo ellipse ffffffff

FIGURE 5: REFLECTIVITY TO VISIBLE LIGHT AND DENSITY VB SALINITYAND TEMPERATURE. SHADED PSEUDO-ELLIPSE SHOWS THE REGIONIN WHICH THE NATURAL FRESH WATERS OCCUR.

ULTRAVIOLET, PURE WATER

PERFECT (GOOD REFLECTOR'lMETAL ~OOR EMITTE~

\~ oJo

(~O~~..q~.sA..q1!J.sO':4~~~7"

:l?1!J/.A.'rG)

BODYCXl5.0 .....4.0

03.0

2.3

2.0

1.5

1.2

- ~ 'It l.OULTRAVIOLET- O.l8I' t I .....

SEA WATER __ I cnC)0.9 O:::Zw-08

1-1-1-°., _w

~~...JoWu..

:.::: WcO:::06Oz00

0.5 C)z--0 .4

03

It:• UJ... ...

0.2 aUJ~

::i~etUJll.UJ..J ena1J: o

0 .1 !abz>a1et

~0 .26-0.21 "J 0

OPTICAL VACUUMWINDOW

FIGURE 6: OPTICAL CLASSI FICATION OF WATER BY REFLECTIVITY AND ABSORPTION.(FO~T AFTER MCMAHON, 1950)

11

confirm the theoretical conclusions expressed in this report are not

complete. The reflectance comparator now used utilizes visible light

at 632.8 nanometers . One justification for continued optical experi­

ments in the visible or near-visible range, in spite of the smaller

optical contrasts with salinity, is the possible application of the

results to the development of photographic techniques for airborne map­

ping of fresh or brackish water as it flows into the sea.

A helium-neon (Optics Technology, Inc.) laser was chosen as a

light source because its narrow, collimated, monochromatic beam and ease

of operation simplified the optics of the system. Silicon solar cells

were used as sensors. Figure 7 shows the laser mounted on the right arm

of the adjustable rack. The left arm contains two photovoltaic sensors,

each in an aluminum tube. At the entrance of each tube is a pair of

small diaphrams to pass the laser beam (less than 2 mm) and to block out

the extraneous light. The beam-splitting prism and the front-surface

mirror, which together split the laser beam into two equal parallel beams,

can be seen at the exit of the laser head. These two beams are reflected,

one each from the surfaces of the water placed in the two halves of the

water tank. The problem of polari zation of light by the beam-splitting

optics (the O. T. laser does not polarize light) is avoided in one of

two ways: the projector and sensors are rotated 45° or they are at near

normal incidence.

The sensors are in a Wheatstone bridge nulling system. Thus what

is measured is only the difference in intensity of the twin beams reflec­

ted from the water samples. Asymmetries in the system can be detected

by rotating the projector and sensor assemblies 180° and by elec­

trically reversing the sensor positions with a double pole-double throw

switch. The output of the bridge is ampljfied and the signal read oh

a microammeter. The laser apparatus can also be used to measure the

statistics of surface roughness due to ripples which affects the apparent

or effective reflectance. It may also be modified by the "slicking"

caused by a salinity gradient (fresh water on sea water).

SUMMARY AND CONCLUSIONS

Published values of electromagnetic properties of sea water with

respect to wavelengths ranging from 200 nanometers in the ultraviolet

12

FIGURE 7: FRONT VIEW OF THE LASER REFLECTANCE COMPARATOR.

_.

...( .:

.~

~6uLUU

~ULU...JLLLUCl!

Cl!LU

~LUIl-

LLo

~......>LU£:)......(f)

co

LUCl![5......LL

13

14

frequencies to 30,000 kilometers in the radio frequencies have been com­

piled and plotted on graphs. The resulting curves of measured and com­

puted absorption index, k, refraction index, n, and reflectivity, R, VB

wavelength, A, show that the greatest optical contrasts between pure (p)

and sea (s) water are at radio wavelengths longer than 3 centimeters.

Whereas the computed average percentage reflectivity contrast for visible

light (6 x 10- 5 cm) is 100 x (R - R )/~ (R + R ) = 3.7%, the computeds p s p

reflectivity contrast at long radio wavelengths is 44.0%. (R is normals

incidence reflectivity of sea water; R is normal incidence reflectivityp

of pure water.)

The reflectivity contrast increases at wavelengths greater than

about 3 centimeters because k and n achieve constant values or decrease

in pure water, whereas in sea water, k and n continue to increase as the

wavelength increases. At any given wavelength,

R =(n-l)2 + (nk)2

(n+l)2 + (nk)2

The reflectivity contrast at optical wavelengths is almost linear with

salinity contrast for waters intermediate between fresh and sea water.

To electromagnetic wavelengths over about 3 centimeters, the

reflectivities of sea water and pure water are effectively 100% and 64%,

respectively. Hence, the reflectivity contrast to radio waves is an

order of magnitude greater than to light.

At optical frequencies, both fresh and sea water are dielectrics,

but at radio frequencies, fresh water is a semiconductor whereas sea

water has the reflective properties of a liquid metal.

This study indicates that the most effective part of the electro­

magnetic spectrum for use in the remote detection of large salinity

anomalies from aircraft would be that of wavelengths of 3 centimeters or

longer. Further study is needed to determine the optical contrasts of

the waters intermediate in salinity between pure and sea water.

Studies might also be undertaken to determine the feasibility of

exploiting the difference in transparency between fresh and sea water to

ultraviolet light at 2,000 to 2,500 angstroms by ~ltraviolet photography.

15

REFERENCES

Andrews, C. L. Optias of the Eleatromagnetia Speatrum. Prentice-Hall.1960.

Corson, D. and P. Lorrain. Introduation of Eleatromagnetia Fields andWaves. 1962. (See Table 10.1)

Dorsey. N. E. Properties of Ordinary Water-Substanae. Reinhold. 1940.

Liebermann, L. N. In The Sea~ Volume 1~ Physiaal Oaeanography. WileyInterscience. pp. 469-473. 1962.

McAlister, E. D. and W. L. McLeish. In Proaeeding of Conferenae onOaeanography from Spaae. Woods Hole Ocn. Inst. Ref. No. 65-10.Woods Hole, Mass. pp. 189-214. 1965.

McMahon, H. O. "Thermal Radiation from Partially Transparent ReflectingBodies." Journal of the Optiaal Soaiety of Ameriaa. Vol. 40,No.6. pp. 376-380. 1950.

Moss, T. A. Optiaal Properties of Semiaonduators. Butterworth, London.1961.