()022- 1554/79/2701 THE

.25O$2()tJ/()

JOURNAL

Copyright

OF

HISTOCHEMISTRY

AND

© 1979 by the Histochemical

Light

and

H. CHEW,

2513-2631979

pp.

Printed

Inc.

Scattering

M. KERKER,

\#{248}l. 27. No. 1.

CYTOCHEMI5TRY

Society,

Fluorescence by Small Internal Structure’

P. J. McNULTY, Clarkson

J. P. KRATOHVIL,

College

of Technology,

Received

Particles

D. D. COOKE,

Potsdam,

for publication

Neu’

May

York

in U.S.A.

Having

M. SCULLEY

M.-P.

AND

LEE

13676

16, 1978

We consider two related, yet distinct queries: 1. How does the internal morphology of a small particle affect the elastic light scattering signals? We have devised an algorithm, presently accurate for particles comparable only to small biological spheres (diameter less than 1 tm), which suggests that light scattering is sensitive to internal morphology only in the backward directions. Accordingly, observations should be obtained in these directions when probing for internal morphology. 2. How are fluorescent signals affected when the active molecules are variously distributed within small particles? One cannot assume that the fluorescent signals are simply proportional to the number of active molecules contained in the particle because there may also be a dependence upon the geometrical and optical properties of the particle and upon the particular spatial distribution of these molecules within the particle. Indeed, even the measured emission spectrum may be affected by such morphological

features.

Here,

too,

these

calculations

are

mainly

restricted

to

small

particles

(diameter

less than 1 tm) in which the fluorescent molecules are isotropic and immobile. Under these conditions the effects are quite dramatic. These effects should be considered in quantitative procedures which utilize fluorescence for determining the concentration of specific molecules in small particles such as biological cells. They may provide a clue for discriminating among cells which differ morphologically or in which the spatial distribution ofthe fluorescent moiety differs. These effects may be minimized by utilizing a light source which is polarized perpendicularly to the scattering plane.

. . .

and

after

the

biologist

and

the

chemist

f irst Perhaps

the

microscopy

most

is that

appealing

these

of cellular morphology. from nonfocused light such

signals

light

scattering

tive,

continuous,

suspended possibilities

to

which

light

and

visual

been

contrived

advantages.

instantaneous,

It

remote

permits

sensing

their descriptions of the horse, the horse is a sphere. . . “

electron

That

elastically1

well

known

is

resolution

of comparable signals requires

have

have

of

recognizable

Recovery scattering

models does

aspect

provide

had completed assume that

scattered even

formulated only for some ently used in an empirical separate cell populations.

nondestruc-

There are Time-dependent ing of bodies,

in medium and it contains much information. for extracting this information may appear

cell

The forbid-

result

in Doppler-like

shifts

theory and techniques

the incident wavelength. light scattering. Inelastic

and

fundamental

limitations

the Raman effect, lated by radiation

computer

technology.

Yet

light beam irradiance, with

time,

13102 2

and ERDA We use the

geometrical

and in part

Supported

in the for

the

and

scattering

of a parallel

m(t,i,A) particle

which F; with

by particle may

its is

of the Science

in a general

chemical

sense

grant to

include

at other

small carry

particles information

tion

size,

within

occurs at the

of the

when incident

wavelengths. the

a small

3

In

Accordingly, elastic

unchanged

composition.

us

morphology

theory

cases. Such to discriminate

let

has

been

signals are presamong and to

scattered

molecular wavelength

When

signals at about particle

wavelength

any

from

quasielastic or dynamic such as fluorescence or transitions result

such

events

the shifted morphology.

stimuin emis-

arise

within

wavelengths

also

absorptive materials, the refractive index is a complex whose imaginary part measures the bulk optical abin accordance with the Beer-Lambert law. Absorp-

length.

CHE77-

upon

analytical

This is called scattering,

particle

is much

depends upon the morphology the complex refractive index,

of

particle. Foundation

sions

For number sorption

vary

wavelength

optically active or anisotropic of the radiation. The refractive description in a classical sense

history

by National

grant 77502-4361. term morphology

configuration

the

beam is characterized its wavelength. The index

position

A; and polarization a complete

morphology2 I

The and

by its refractive t; with

of the radiation materials with index provides the

1 depicts

by a particle. its polarization

characterized

the

simple way

depend

“Now

signals which convey similar information. phenomena within a particle such as streamBrownian motion of bodies or molecular motion

state of the experimental

hardly severe. The scheme in Figure

an

began:

other

ding because of the present primitive because of the severe demands upon are

signals

though

information matching apriori. Yet of a single

the physicist

scattering,

from

that

250

Downloaded from jhc.sagepub.com at KAI NAN UNIV on April 4, 2015

the the

more

complicated.

It

of the particle in addition to and this effect varies with wave-

absorption wavelength

of the incident

spectrum of the

radiation.

scattered

and,

for radiation

optiis

QUANTITATIVE

ANALYSIS

AND

PARTICLE

251

SIZES

I

I

/ 1. A light

FIG.

beam

entering

from

the

left

is scattered

by a particle.

Refractive

arbitrarily

complex

1 and

such

2, we

explore

Here,

the

cent tides.

internal

how

fluorescent

active

motivation

results

and

raise

A.

2.

Boundary value model of electromagnetic particle with refractive index m’ immersed index m, showing the incident (E0,H0),

scattered

cally

(E.,H.)

active

fields.

materials,

tatory dispersion Light scattering internal

the

circular

dichroism

structure

of particles,

and

tering and to calculate

inelastic scattering. Part elastically scattered require

This

that

when

the

paper

deals 1 utilizes signals

algorithm

be

with

as shown

in Figure

is to explore

the

extent

to which

index

obtained

here

as a mammalian remote goal. Yet

suggest

directions

questions

which

experimenters

1. Light

Scattering

by

Integral

classical problem refractive

a configuration and stifi

formulation

cell. That prelimi-

experiments

wish

Structured

of

the

for

will

fluoressmall paras large

to consider.

Spheres

the

scattered

field:

The

treatment of light scattering as a boundary value is illustrated in Figure 2 for a uniform particle with index4 m’ immersed in a medium with refractive m,. Perturbation

by the

particle

of the

incident

electro-

optical

ro-

morphology. about

the

and the boundary

it is viewed

tamed

outlined above, considering not also quasielastic scattering, inelastic

scattering

We

absorption.

particularly

such

in biological cells. In Part scattered signals are affected by molecules within spherical particles.

magnetic field (E0,H0) gives rise to an internal field (E,H1) and a scattered field (E,,H,). Each of these fields satisfies Maxwell’s equations, usually expressed as differential equations,

and

also provide information about offers a plethora of information

in the broader perspective only elastic scattering but

spheres.

scattering by a in a medium with internal (E1,H) and

structure

of dots.

markers may be affected by inclusion within In neither case has it been possible to approach

nary

FIG.

to density

encountered

of the

and as complicated remains an ambitious

uniform refractive

is proportional

as is usually

embedment

m0

index

elastic

applicable

to

4

of

Hereafter, the

particle an

for simple

of spherical

scat-

a new algorithm from structured

fields bear particular relations of the particle. Analytical geometries

shells,

infinitely

all refractive

external

in Figure

biological particles 1.00 to 1.10.

medium,

Downloaded from jhc.sagepub.com at KAI NAN UNIV on April 4, 2015

as spheres,

long

cylinders

the

2 is m=m’/m,,. suspended

such

indexes e.g.

to one solutions

concentric (1),

will be expressed relative

Thus,

in aqueous

another at the have been oband

relative

refractive

the media

refractive may

layers ellipsoids

vary

to that

index

of

index

within

from

the

about

252 of revolution less symmetrical tational

(2).

effort

Although

Numerical configurations,

has

impeded

there

boundary refractive

their

seems

little

have been obtained for the considerable compu-

tory

widespread

prospect

use

for

AL for

(3).

treat

The

extension

of these

but may be of refractive

More can as

upon the optical properties of the need be neither homogeneous

specifically,

in the

be represented illustrated

of the

field the the

Figure

moment location internal

at each

integral

is determined and also electric

particular

by

field.

the

the

location

within

in the

particle, resultant outside internal of the

usual

fashion.

it is a simple field of the

and

at

direc-

Given

their

of the particle. However, before field must be known, and since boundary value problem in the

appear

that a full circle B. Field average integral representation fords for approximate leigh-Debye or Born precisely by the

to this formulation unperturbed incident

tide not be too particle be close

t #{163}

\

I

\

-#

-

3-’

&

‘

/

.-

I,

‘

\

I

I -.

-.-.8

a

the it aS-

uniform

particle

particle

(F)

is

-

-6

), H,(r’) ,

m

highly

-

[m2(?)

+ 2]

1] dv

(1)

sphere.

We

refer

inhomogeand th is

process.

although

th

the

electric

is conceived field

both

in

to

within

be

such

magnitude

and

the by

internal field with the actual index m(?’) within the structured

to this

as FA,

C.

Test

centric results

of

field

average

the

spheres: for a pair

upon

the

exact

We will of concentric

a field

average

approximation

has can

the be

same average envisaged as

The

(1) boundary

refractive using the

index same

value

model

system)

at 0

=

the 157

into mcident within

agreement

degrees.

On

the

FA

and

exact

range). AK

results

Thus, near

Downloaded from jhc.sagepub.com at KAI NAN UNIV on April 4, 2015

into a

is shown

m1,m2

the

in

represent

between at 9 the

=

other

whereas 180

degrees,

FA hand,

angle power

direction

per

with the electnc plane. The solid obtained dashed

and

130 degrees

FA

scattering radiant

indicated

irradiance the scattering

quite well for 8 < 120 degrees and 120 degrees < 0 < 150 degrees, this gives quite different results at the . degrees (RD gave much different angular

(AK)

have also (1) boundsphere

indexes. The optical sizes 2ira/A and a and fi, respectively. A single test case the advantages and the limitations.

scattered

maximum

solution

to test radii

line in Figure 5 represents the exact solution the dotted line was obtained by FA and the obtained by LMA as indicated above. is good

the based

It does not take m(i’). It represents

used the

con-

#{241}#{236} as used in FA. LMA internal field as FA to

of dipoles. structure,

represent

unit solid angle for umt vector linearly polarized

MKS

for

by comparing calculations

Rayleigh ratio, which is plotted against 180 degrees is backscatter), represents

=

(in

FA with

configuration. The results and with the Lorenz-Mie in which the homogeneous

a uniform distribution the discrete internal

the relative refractive 2ib/A are denoted by will suffice to illustrate

approximation

now test spheres

Aden-Kerker

for the concentric sphere been compared with RD ary value solution (LMA)

, m0

of the particle

(5).

/

,1

explicitly.

volume sphere

.

variable

the approximate of the refractive

(0

is denoted

the

field of an sphere is

the scattered field is obtained from which in turn has been constructed

a,b

FIG. 3. Integral model of electromagnetic scattering by a uniform particle with refractive index m’ immersed in a medium with refractive index m0 showing the incident (E0 lL) internal (E1(i’) I%(?’)) and scattered (E6,1L) fields. In this case, the dependence of the internal

the

internal

equal to the inhomogeneous

[m2(r’)

averaging sphere,

4 in which

‘-zk:s

within

J,

that, the

Finally, of dipoles

There

location

by this

Figure

-zZ’\ Z

v

noted

throughout

including

upon

be

process. sphere

I,

f

1

averaging concentric

4.-4.---,..-.--

field

i.e.;

simpler The

, /-. .-

f / I ? .-.-

“I-____\

4#{149}____ ,....*____4___

f //

to represent,

refractive index of the it is quite unsatisfac-

E (r

that

to approximate

by the internal This equivalent

polarizabiity of the

“pump” account

/,

particles of the

attempt

a uniform polarizabiity

field is replaced that the par-

-.

,

of

well-known Ray(1) corresponds

when the internal field. RD requires

large and that the to that of the medium;

E0 , H0

within

this can be done the this requires solution first place, it would

the (RD)

smaller

in estimation

sphere sphere.

2)

obtained

combining distribution

superposition the at any position

has been turned to little avail. approximation: The utility lies in the opportunities which solutions. Indeed, approximation

the

is the relative refractive index at each location ? within the

should

direction. assembly

“pumps”

distribution

value It

a uniform

electric

particle

matter to obtain by assembly of dipoles

it purports

m(?) sphere

the of

index

internal

the

lies

of a structured homogeneous

to have average

where neous

dipoles

direction

magnitude

for

an initial

\th2

particle

refractive

It is as if the

matter

explore

(m2_-_l

polarizable matter at that location, thereby stimulating local oscillating dipoles. Each of these dipoles radiates

energy

-.

by

and

or even

distri-

electric

magnitude

field

which

1.

the

ofradiating

3. The

we

particle. nor iso-

general in Figure

formulation

by an assembly in

each dipole the particular tion

described by a completely index such as indicated

of the

Here,

presumed weighted

cells

below.

crux

field.

1, there is an alternative approach in which the scattered field is formulated as an integral. This formulation, derived directly from Maxwell’s equations (4), automatically incorporates the boundary conditions. There are no restrictions upon particle shape nor the particle

biological

we will

internal equivalent

tropic bution

solutions within the

ET

to include arbitrary variation of particle such as depicted in Figure

size and Indeed,

value index

solutions but

KERKER

AK and

although

by AK, line was

at all angles the

minimum

LMA

agrees

moderately well between simple averaging method backward angles, 9 > 150 results over the entire virtually LMA

differs

duplicates by

250%.

the

QUANTITATIVE

ANALYSIS

AND

PARTICLE

is better

when

SIZES the

not nearly equal. obtained for a = case

the

difference

was

so small.

relatively

small

in the

example

4. Concentric

FIG.

relative

sphere indexes.

refractive

2rra/A

and /3

model; a and Dimensionless

b are size

radii,

m1 and

parameters

are

the

of about particles that

and

for

results 1.02.

=

was

a somewhat Yet

FA

core

backscattered

gives

m2 = 1.06. for by a

larger

a small

are were In this

tolerated

which

7.00, m1 = 1.10 and of /3 is compensated

=

the

regions

m

example

of a and affects

refractive

m1

Another

value

of m2

such

as in this

signals.

We have

domain of validity of FA for the concentric over a wide range of size, refractive index and For biological particles [m(f’) = 1.00 to 1.10]

upper size that can 7, which, with visible

=

two

quite accurate = 1.10 and m2

between

example.

sensitively

a

2irb/A.

=

value

previous

explored the sphere model configuration.

m

are

of the

results is a = 1.75, $ case, the larger value

accurate In this than

volumes

For example, 1.5, fi = 3.0, m1

large

fi

because

253

1 m. such

be safely radiation,

Thus this as bacteria,

backscatter

technique may not to larger

alone

be expected

to hold

used appears corresponds

is sensitive

for larger

be applicable cells. Yet

to internal

particles

$

to be about to a diameter the

to small fmding

structure

as well

may

as those

studied

here. D.

Asymmetric

less

internal

symmetrical

structure:

configurations

may

unlike the case for concentric spheres, against which to check the accuracy. to retain all of the other conditions

0

strated to be “safe” and then of eccentricity. The question signals are sensitive to changes the response is affirmative is tive examples in Figures 6 to

x 0 -J

m1 the

1.10, center,

should which

100

120

140

SCATTERING FIG.

Rayleigh

5.

ratio

within the scattering 2ra/A = 2.5, fi = 2irb/A = (....)FA,(----)LMA. Expressed the

light

only

for

smaller

scattering 0

of having

two an

The

the

sensitive

Nearly the

different average

the

fluctuates fluctuation

value

solution

constraint comes

of

=

spheres 1.08;

this

to internal result

plane

with

size

for

is obtained

at

an

accurate

upon

the

technique extent

to

for which

severe

the

sphere.

magnitude the

larger

It

appears

of fluctuations the

particle.

Also

of the

in m(?)

be-

the

accuracy

because,

the inner practically

sphere identical

in those asymmetric by a boundary

touches is hardly

tering

9

increases

at

only

=

by two

180

degrees

more figures

than are

30 degrees angular

(a

intervals

first

so that is not

7, except

for curve

any

possible

= 0.75) is at results so FA

configurations value solution. inner sphere beam. The the Rayleigh curves desiga distance its radius. In

the outer affected, 38-fold

a factor of three. based on calculations

patterns

These fine

different previous Again,

from case

each other in which

it should

polated between results in scattering angle and the

curves

would

0 which

Downloaded from jhc.sagepub.com at KAI NAN UNIV on April 4, 2015

and

then

and obtained

the at

structure

in

corresponds

to a single displaced 1, the other Just as in sensitive to patterns

and they are also different from there is only a single internal

be noted obtained that for

probably

surface. the scat-

exhibited.

core at the center, there now are two cores, one 2 or 3 radial distances in the incident direction, displaced correspondingly in the opposite direction. the previous example, the backscattering is very the particular internal structure. The backscattering are the

to

to use FA to explore the effect is whether or not the scattering in the internal structure. That demonstrated by three illustra8 for which a = 0.75, f. = 3.00,

case the inner sphere the forward scattering

sphere.

that

of FA

there is no exact theory Yet, it seems reasonable which have been demon-

the latter Although

In Figure

regions or a uniform index. However, these

1.02. When and FA give

Extension precarious

Figure 6 shows the effect of displacing the from the center along the direction of the incident curve designated 0 gives the angular variation of ratio when the inner sphere is at the center. In nated 0.5, 1, 2, 3, the inner sphere has been moved equal to either one half, one, two or three times

the

sphere

=

be accurate even cannot be determined

decreases following

range,

results at the backward angles. scattering is very sensitive to

depends

a uniform

=

structure

is a structured

refractive refractive

a

(-)AK,

from its average value. Indeed, in the limit FA reduces exactly to the classical boundary

upon more

FA

irradiation

for

same

particle

model, FA provides scattered signals.

accuracy

m(?) zero

at least

are

models give quite different at these angles where the

the particular calculating

unit

for concentric m1 = 1.10, m2

5.0,

signals whether

for

plane

differently,

150 degrees.

>

angles

consisting sphere two Yet

somewhat

angle

180

,8

ANGLE

scattering

vs

polarized

160

m2 AK

=

be

that

these

curves

only at 30 degrees more closely spaced

exhibit

a fine

structure

are

inter-

intervals intervals, which

254

KERKER

ET

AL

tides

(diameters

comparable

to

aqueous

media

signals

obtained

changes

about

1 pin

those

of

(m

lateral

and

changes.

1.00 to 1.10)

=

in the

in internal

or less)

forward

indicate

directions

that

light are

scattering

are are

quite also

the

other

hand,

forward

0

signals of

and

Alternative

particles

are

capable

internal

should

lateral directions. algorithms which presently

being

may

sensitive

insensitive valid

for

be

to the

to

such

particles

as

light scattering among internal directions. On

of discriminating

structure

in

scattering

signallin

large as mammalian cells, they suggest that signals capable of identifying or discriminating structures should be sought in the backward independent

indexes

suspended

directions

whereas

conclusions

refractive

particles

backward

structure,

If these

having

biological

among be

sought

sizes, in

applicable

the

to larger

explored.

I 0

w 4

0

60

180

120

SCATTERING

I 0

ANGLE,9

w

Rayleigh polarized within the encased in a larger sphere moves from

ratio vs. scattering angle for unit irradiation scattering plane for a sphere (a = 0.75, m1 = sphere (/1 = 3.00, m2 = 1.02). Center of the center (0) along the direction of the incident so that its center is located 0.5, 1, 2 or 3 times its radial distance the center of the larger sphere. FIG.

would

provide

changes at

plane 1.10) inner beam from

6.

further

in internal

In the final the center

obtained

possibilities

for

discriminating

among

structure.

example (Fig. 8) the case with is denoted as 1.0. The other

when

4

this

spherical

core

the spherical three curves

is distorted

into

core are

equivolume

prolate spheroids with the figure axis (unequal axis) parallel to the incident beam. A similar effect is obtained as in the previous examples. There is no significant influence of the internal structure upon the forward scattering. However, the scattering at 180 degrees increases eightfold as the spheroid elongates and

until

fmally

0.125

configuration, and

back

the

length that

of the

ends

of the

prolate

outer

the spherical core results in a significant quently E.

a large Conclusion:

equal

times

the of the

of each

surface. to

axis

figure

is 0.50

axis.

spheroid

Interestingly,

an equivolume decrease of the

At touch

then this the

compression

oblate backscatter

spheroid and

latter front of first subse-

theoretical

studies

with

small

par-

120

SCATTERING

0.25

increase. These

60

180

ANGLE,

9

FIG. 7. Rayleigh ratio vs scattering angle for unit irradiation plane polarized within the scattering plane for two inner spheres (each with a 0.75, m1 = 1.10) encased in a larger sphere (6 = 3.00, m = 1.02). One of these spheres is displaced from the center along the direction

of the

incident

beam

so

that

its

center

is located

1, 2 or

3 times

its

radial distance from the center of the larger sphere; the second sphere is displaced in the opposite direction in each case. The curve labeled 0 corresponds to a single inner sphere at the center as in Figure 6.

Downloaded from jhc.sagepub.com at KAI NAN UNIV on April 4, 2015

QUANTITATIVE 2.

Fluorescence

A. rescent by

by Molecules

Model for fluorescent staining in the analysis

flow

ings,

techniques yet

is

an

work

such cases fluorescent active

need

there

quantitative

that, signal

molecules

quantitative particle

hardly

as

be

aspect

for the

in the specific

signal

well

as

the

E0(w0), E1 (w0) and

the

fields are not as a collection a molecule, the

incident

such

as one of

that

be

photons

active

In

fluorescent oscillating located

the

molecules

in

this

in small

steps the

case

of

molecules

two the

as

be raised

state is assumed to be proportional to the square electric field component at the incident frequency the number density of active molecules at this

to the

size,

and

by the

that the molecules

absorption are the with

addition

The excited

of the local and also to location. We

magnitude

of

emission

of this

of the

index

In what

local

of the active function of as well

of radiation

molecules.

exception.

dipole

field

There

at the

follows,

the

as of shifted

we assume

these

effect

associated

with

induced

conditions

emission

field

at

the

that

of in a geometrical-optics and

and

the

refractions

angular

of

occurring

distribution

its polarization,

is

surface

reflections

effects,

fluorescence

additional

be thought

with

active bulk

active molecules within medium; it is that, in

is a secondary boundary

might

is an

of the infinite

normally

there

This

Because

direction

distribution is a sensitive

of refractive

the inclusion than in an

sense as associated at the surface. scattered

direction

way with location site the excitation

and emission characteristics of the same in the particle as in a comparable

to satisfy

particle.

and

and

as upon the field, in turn,

active

molecules,

needed the

the

one

to the

the

magnitude

distribution

in

by

the

incident frequency. The second step is the

frequency

by

that

upon

shape

255

3) varies in a complicated Accordingly, at each

field as well The local

medium

magnetic

frequency.

depend

which arises from a particle rather

electric

?, is excited

position

noted

field (Fig. the particle.

exciting molecules. the

SIZES

of

are considered In the first step

incident will

with

morphology

represent

molecules dipoles.

at the at

the

of

viewed E,(o0)

frequency.

shown. The of induced

absorption

probability

can

problem

embedded by

distribution

Figure

at

The

molecules is affected

by

in

the strength of the to the number of

particle.

already

will

if

assume

PARTICLE

internal within

Proceed-

considered

always

AND have

Particles

these

be

cannot

just as in bulk media, is simply proportional

it. scattering

fields

in

should

One

interest within Fluorescent 9 where

stressed

which

contained

is that

in Small

spheres: The utility of fluoand sorting of biological cells

is to be done.

assay

particles the

Embedded

ANALYSIS

as well

of as the

fluorescent intensity, will depend upon: (a) particle and distribution of refractive index, i.e. morphology;

the total

size, shape (b) wave-

0 I-. 4 I C, -I

60

SCATTERING

120

ANGLE,

FIG. 8. Rayleigh ratio vs scattering angle for unit irradiation plane polarized encased in a larger sphere ($ = 3.00, mi = 1.02). This is denoted by curve 1. The into equivolume prolate spheroids with axial ratios 0.50, 0.25 and 0.125.

within other

9 the scattering curves

Downloaded from jhc.sagepub.com at KAI NAN UNIV on April 4, 2015

are

obtained

plane

for a sphere when

the

(a

spherical

=

0.75, core

m,

1.10)

is distorted

KERKER

256

ET

AL

molecules the

to the

fluorescent each

Certainly, E0(w0)

may

within

real into

biological the model

qualitative not include on

The

B.

value model for fluorescent scattering. Elastic is denoted by electric fields E0(co0), E(u) and E8(0) at incident frequency w,,. The arrow inside the particle denotes the emitting dipole at position ?‘. E1(t,,?) and E,(u,i’) denote the internal and the scattered fields at the shifted frequency w which arise from the dipole at i’. Ee(t,i’) is the sum of the dipole field plus a secondary field induced by the boundary. 9.

length

Boundary process

and

polarization

distribution Furthermore,

of active the

scattered

of

the

incident

molecules frequency

radiation

observed

and

these

effects

will

particle. By solving have derived observed

the

particle

outside

incoherently power over particle Here,

the

particle

be different

at each

and

original

the

presented.

emitted

and

emission.

along emitted

I-I

of

(6).

angles

0 and

incident 90

the internal the molecular

The

over

dipoles

the

distributed

of all to

Figure 10. The vector parallel to

There are two cases. is polarized parallel

boundary

field at the transitions,

at the shifted is spherically

main

the

due

frequency. symmetric

in that

and the is calculated the

value

incident and

there are no fluorescent

limitation

contributions within

.

I. of two

the complicated programming tions. The scattered intensity summing

treated below. be encountered first

in

do

and the scattered intensity is desigdegrees, the incident radiation is to the scattering plane and the

scattered field the particle

particle.

the

for simplicity we should be cautioned

instructive

radiation

as yet been made. However, the spatial distribution of the

in

to

Only have

in at-

constraints molecules

connection

is

length of the calculaat a given angle by

to the

particle.

prob-

frequency second

various The

length

individual of

the

dipole

The

we the

the

and add

in these

have

is

theory

is

calculations

assumed

strength

reader

that

of the

the

exciting

and that the dipole is induced parallel to This implies that the active molecules are they are embedded in a solid matrix in rotation during the interval between exciIn

the

more

general

case,

radiation

a particular orientation of the molecule along a second orientation. Also, the

observation

the

tempts upon

radiating

5 The solution applies to other inelastic scattering as the Raman effect. The total power for spontaneous tering is obtained by superposition as for fluorescence. processes such as stimulated Raman scattering, the

point

by

the where

scattering

can be incorporated goal is to present

upon the particle of radius a along the The scattered radiation proceeds along

intensity is designated model requires solution first, to obtain stimulates

rotation

comparable

also be considered. to some degree

shown its electric

obtain cases

problem, we scattered fields,

power.5 results. used

to

i defined 0 degrees,

=

be

system, with

free are

of the cases here may not

also

classical, not radiation “senses” the

(6, 7) in which

treatment

features present

nature seen

the coordinate polarized radiation

4

must enter

aspects of the phenomenon, them here. And so the reader

to the scattering plane nated Ih. When q = polarized perpendicularly scattered The

they will

particles. These but since our

or

motions

to sum the time average of dipoles within the

equations

is proportional

field at its location this exciting field. isotropic and that which there is no absorbed may be

this

value

to a single

emitted numerical papers

relevant In

field

tation

due

so that it is necessary the particular distribution

to the

derived

boundary the fluorescent

times, effects

scatterwaveof the

? within uniform spheres (6) In fluorescence, the emissions

to obtain the total we present some

referred

power

(c)

direction When

restricted

if these

lems: which

will

as well as upon the at each particular by the properties

all of these effects are is the electromagnetic molecules which

the appropriate expressions for

at an arbitrary location concentric spheres (7).

the

and

particle. of the inelastically

decay of these

the x axis is incident positive z direction.

within

It should be noted that quantum-mechanical. It rather than the fluorescent

are

the

outside

depend upon the above quantities ing angle. This is because emission length will be affected differently particle angle.

radiation;

within spectrum

and

usual biological circumstances. Numerical results: It wifi

consider linearly FIG.

either

cell

the mainly illustrative more dramatic aspects

under

scattering

undergo

biological

must

be

added

before

is and it active

processes

such

Raman

scat-

For coherent

electric calculation

field at of the

x Coordinate system with particle of radius Radiation is incident along the positive z-direction, vector parallel to the x-axis. Radiant intensities are = 0 degrees and 90 degrees, respectively. FIG.

10.

Downloaded from jhc.sagepub.com at KAI NAN UNIV on April 4, 2015

a at the center. with electric Ih and I when

QUANTITATIVE calculation and also

increases with the

fluorescent larger the bution

with the within

molecules. The number of dipoles

of active

to

be obtained

All

a single here are

by

the

total the

greater needed

molecules.

been normalized intensities reported would

both volume

the

volume particle

ofthe particle occupied by

this latter to represent

volume, the the distri-

results

dipole proportional

same

ANALYSIS

in this

so

number

paper

will

be a sphere

for

which

wavelength

in the

a

SIZES

257

have

of fluorescent

2ira/A

=

PARTICLE

that the scattered to the signals that mole-

cules variously distributed within the dielectric sphere. In the calculations presented below, except when specified, the partide

AND

5 where

=

I(I)

A,, is the

z

incident will

be

A

1.5A,

=

wavelength index

will

which

pended for

and

the

be m

smaller

than

will

size.

shifted

wavelength

refractive presume

that

media

particle

the

relative 1.5. We

=

is larger

in aqueous

the

medium,

index that

this

of biological at least

This

ing

dipole.

a small6

Such

a dipole

aggregate

homogeneous dielectric curves represent the

may

because

be thought

z-axis.

UI II-

ofthe particle in the case of

0 (0

of as represent-

sphere. scattered

In Figure intensities

11, the two pairs of for each incident

The

exhibits nearly the an infinite medium,

in-

embedded

positive

the

internal with

molecules

0.Ola

along

0 UI

of active

and Ih) plotted versus scattering dipole is nearly at the center

positive

sus-

the both

polarization (I (1) the isotropic the

z

refractive compensate

electric field becomes more highly structured creasing refractive index and particle size. 1. Single dipole: The effect ofthe geometry upon fluorescence is most strikingly illustrated a single

UI I-

each

particles

partially

follows

at

z.axis)

and

(2) displaced

dipole

near

the

same i.e.,

center

within

a

angle (displaced

when by

by 0.7a

along

of the

particle7

0

pattern as an isotropic dipole within I remains constant with scattering

60

120

SCATTERING

ANGLE,e

angle 0 whereas I varies in proportion to cos29. The pattern for the off-center dipole is strikingly different. I oscillates with angle and the minimum in Ii has shifted to larger angles. Also, the scattering is mainly more intense, and the backward

1 1. Fluorescent scattered intensities angle for a dipole at x = y = 0; z = 0.Ola a 5.0, m = 1.5, A = 1.5 A,,.

fluorescent

fluorescent

The different

fluorescent

for dipoles

emission

emission. This is further intensity

at 0

of a single case four

I = orders

=

dipole

is greater

the square not exactly

dipole does the exciting emission

in Figure

12 where

is plotted

as a function

on the

z-axis

(shown

to the

E(?’,c,) with 12. Yet the

Ii

As

usual,

the

curve);

by

“turn on” and “turn is also a contribution

refractive

effects

field. The to refractive word

small

off’

of the

in this

by more than a comparable

position scattered

along the intensity strength that the

in response to upon the dipole

boundary.

This

12 which represents local exciting field by a uniform field

signal still varies considerably effects (m = 1.5). implies

small

compared

with

is

the inside equal in this

wave-

length. 7 Our computer where the angular infinite medium.

program pattern

will would

not operate be precisely

dipoles 11; the values

two pairs patterns

exactly at the center that of a dipole in an

of curves of scattered

variously

degrees and depolarized,

180 i.e.,

orthogonally arises because

to

quency

13 illustrate that may

in a sphere.

degrees and each they each contain the the

field.

again section

dipole

rigidly

from

somewhat be obtained

In these

cases

the

direction

particular than

fixed the

in to

biologically

in a fluid oscillatory in Figure

2. Pair

particle, patterns 1 1 would

of separating a pair of fluorescent

Downloaded from jhc.sagepub.com at KAI NAN UNIV on April 4, 2015

forward

They of

realistic

the

fre-

of the fluores-

fluorescent caveats are for

matrix.

inclusion more

the

backward

a solid the

and I,, is polarized

of polarization cases,

the

ih

The depolarization at the incident

we call attention to the 2A. These calculations due

tropic dipole minima and as exhibited

of the signals a component

radiation. electric field

the

is greater

perturbations In

incident internal

In these

emission

sion. Once end of

which

in Figure intensity

positioned

is twisted

incident cent

(----)

are no longer located on a coordinate axis as in Figure minimum is no longer as deep as in the prior case, the of Ih and I,, are no longer necessarily equal at 1) = 0

particle. the

I and Ih vs. scattering and z = 0.7a(-) for

FIG.

of position

as a solid

of the fluorescence is caused mainly

illustrated by a third curve in Figure scattered intensity at 180#{176} when the the particle is replaced at all locations to the incident case due only

the

of the modulus of the internal field proportional to each other indicating

not merely field. There due

forward

illustrated

variation of the internal field z-axis as also shown in Figure and are

the

180 degrees

The variation of magnitude

‘h.

than

180

emis-

noted at the an isotropic illustrate

dipole case

the

within of an

one anticipates that the in the angular patterns be partially washed out.

dipoles: We now consider dipoles separate along

a

anisodeep such

a case in an axis

258

KERKER

ET

AL

thirds

its

angular

initial

value.

distribution

the flattened It, the

signal

broad change

range of angles. Finally, to positions +0.7a, there

has

fluorescence at greater change curves between

IU)

z z

0 UI I-

(I)

against

0

0

POSITION

distance

from

the

(case

1) and

along

the

sphere.

Once

of isotropic more nearly

particle size are chosen.

(a = 50) It would

of a biological

tagged

with have

dye

more

THE

we call

dipoles with to simulate

model

and be

10_2

cell

in

which

a pair

by much

larger

scattered

15) is plotted

along the y axis. Curve located at a distance The dipole,

the

dipoles

the

center

an order

angular i.e.

‘h

for

over

a

with just a small additional are still further decreases

of

It is interesting that horizontal polarization

to

for vertical polarization larger distances from

different

of separating 1.05). Here

aspect

for

dipoles

the

x-axis

(case

the

curves).

a dielectric is plotted

separating

along

2, scale multiplied AlS#{228}plotted (as

changes

fluorescent

occur.

(curve

2) I, at 90 degrees whereas

sharply

to a separation beyond

of 0.8a.

0.4a,

goes

field

However,

through

is

Ih itself

a maximum

at

I,. has

I-. U) z

UI Iz

UI I-. 0

regions.

intensities

(Fig.

‘h

of a pair

similar and

At a distance has

>-

capabilities. Yet in the biological

at 90 degrees

of magnitude

off

out

associ-

U)

figure corresponds and -0.05a, from

is quite

to zero

constant

is the

of fluorescent

dipoles within I,, at 30 degrees

center

separate

while the between

chromosomes

separations

1 in each of +0.05a

distribution is close

separate,

Such

present computational given here might appear

four

free

order

of magnitude

and for

0 UI

contin-

of chromosomes

mitosis.

14) and

Ic (Fig.

to the

refractive index (m = 1.05) to suggest that this is a

during

to be modeled

attention

case, albeit not as dramatically. The angular dependence of the

center.

in

the 3. For

Z AXIS

the effects noted just above. biological conditions, a larger

a smaller far-fetched

fluoresces

is beyond our of the features

dipoles dipoles

=

a pair 50, m

0.65a

+0

ALONG

FIG. 12. Fluorescent scattered intensity at 9 = 180 degrees (-) for a dipole as a function of position along the z-axis. In this case Ih = I. Also plotted is the power associated with the internal field at the exciting frequency, I E1(i0,i’) 2 ) and the fluorescent scattered intensity when E(w0,i’) is replaced by the incident field E,,(w0) (----). Each of the latter curves has been appropriately scaled for convenience.

That some

by

z-axis

drops

would

orders

a somewhat

(a

quite

ued use In order

16 depicts

at

as curve

the signal has decreased 30 and 150 degrees while

two

90 degrees. occurs for

are

shown

dashed curves) are corresponding values of the power ated with the exciting field at each pair of sites. For case I, the power associated with the internal

U

within

by

scattering sphere the by

UI

fallen

molecules

shapes

1 and 2, the greatest change curves 2 to 4, i.e. at the

center. Figure

UI I.-.

the the

trend has reversed and considerably between

Ih,

>.-

When takes

increased

decreased

of to the

to that

60

of a

I is flat.

As

of 0.2a

from

more

than

to about

0

two

SCATTERING FIG.

13.

Fluorescent

angle

scattered

ANGLE,I intensities

for a dipole at r = 0.25a, 0 = (----) and r = 0.55a, 0 = 195 degrees for a = 5.0, m = 1.50, A = 1.5 A0.

Downloaded from jhc.sagepub.com at KAI NAN UNIV on April 4, 2015

180

120

I,, and

lb vs.

105 degrees and 111 and 4 = 126 degrees

=

scattering 66 degrees (-)

and

QUANTITATIVE

ANALYSIS

AND

PARTICLE

surface

to a spherical

radius,

the

that

shell

scattering

of a dipole

of these

259

SIZES

located

must

at the

arise

center.

the from

incident

the

the

particle

becomes

at the

arrangements,

terns

within

pattern

asymmetry

of

may

be obtained

Accordingly,

>-

1-

18 for

U)

minimum

z

the

a

=

Li I-

z

ble component zation. The

0

angle.

Li

about with

Li

is

scattering

U,

tions,

0

Each

signal,

significant

much

rays of

field

is about ‘h

and

course,

more be

intense.

attributed

reflected are

all such

absent

external in the

the

value

an appreciaincident polariwith scattering

the

backscatter

is

scatter. This contrasts for which the forward effect

to contributions

by the

third

I, contains

is that

This

surfaces. in Figure

a characteristic one

from the somewhat

aspect

case can be for assemshells since

I shown

Ih exhibits

which

which is depolarized depolarization varies

can

by

pat-

internal

for by

surface. fluorescent

Lorenz-Mie

diffracted

Such

rays

contribu-

emission.

180

120

60

SCATTERING

angle.

over

of Ih and

surprising.

90 degrees

A quite

scatter

and

pattern

twice as intense as the forward Lorenz-Mie elastic scattering

I4 0

scattering the

This observed spherical

by averaging

angular

5 is hardly near

of I,, at this

like

symmetry

frequency.

distribution of dipoles: anticipated from what has already been blies of dipoles located within concentric result

more

of the

of the

nonuniformity

a smaller

and

In view

4. Uniform

the

having

more

ANGLE,e >-

14.

FIG.

Fluorescent

two dipoles

scattered

separating

1.5 A... Distance 0.65a, (4) 0.70a.

along

of each

intensity

the y axis for a

dipole

from

the

scattering 50, m = (1) 0.05a,

vs.

Ih

=

origin:

angle 1.05 and (2) 0.20a,

for A = (3)

(1)

z LI

Iand

0.75a

power effect

then

beyond this of refraction

fluorescent

drops

maximum. in this is

not

off

parallel

Obviously, intermediate

to the there region

proportional

to

the

z

incident

is a decided where the power

of

the

field.

For

case

II there

magnitude

of

position.

The

refraction

3. Dipoles face: In molecules ingly

again

emission

internal

ingly,

once

is not

signal two

nor curves

plays uniformly

as great

a variation

internal

field

the

follow

somewhat

a lesser role. distributed

some cases are located

be instructive

nearly of

to explore

this

closely.

on

of biological on the surface

in the

power

with

Li II4 U U)

Accord-

a spherical

sur-

interest, the fluorescing of the cell. It will accordeffect.

The

scattered

inten-

and I are shown in Figure 17 for an assembly of dipoles distributed just within the surface of a small particle and also for dipoles located within thin spherical shells inside the particle at distances 0.166a and 0.5a from the center. As indicated earlier, these curves for arrays of dipoles and those sities

0 Li

1

‘h

that

are

to follow

the

distribution

have of

been

dipoles

normalized

to a single

is

from

changed

dipole.

a shell

at

0

60

the

120

SCATTERING

As FIG.

15. Same

Downloaded from jhc.sagepub.com at KAI NAN UNIV on April 4, 2015

as Figure

ANGLES9 14 except

L.

180

260

KERKER

ET

AL

the fluorescent hazard of utilizing differences

emission upon particle size fluorescence for quantitative

in particle

size

5. Nonspherical shows

the

effect

respectively.

0

ing

1)

of

0.4a into which

increase

with

‘p..

the

is elongated

I-

tive analysis of spatial

U)

z

signal

UI I-

of the

appears For

elongation.

At and

must take distribution

forward

90 degrees,

then

Figure from

prolate z axis,

to have

Ih, the

dipoles: dipoles

equivolume lie on the

Elongation

the when

considered.

redistributing

I,, in all directions. core

not

distribution

core with radius figure semi-axes, 0

are

illustrates analysis

increases.

spheroids are 0.7a,

the

effect

and

whose and a,

of increas-

backscattering

ih first Here

into consideration of the fluorescent

19

a central

decreases also

as

quantita-

the possible effect moiety upon the

strength.

6. Spectral

effects: Still another effect resulting from the inclusion of the active molecules within a small particle is a distortion of the fluorescent emission spectrum from that observed in the bulk medium. The fluorescent intensity at any particular wavelength de-

z 0

UI

UI p.-

pends upon wavelength

U

U)

the distribution and upon the

sion as it exits the wavelength eases, there wifi molecules within wavelength

O.4o

0

DISTANCE

with

of the internal field at the “refraction” of the fluorescent

from the particle. Accordingly, dependence intrinsic to the be an effect the particle scattering

exciting emis-

in addition to molecular proc-

due to the inclusion of the active which will vary at each emission angle

as well

as with

particle

size,

O.8o

FROM

THE

ORIGIN

FIG. 16. Fluorescent scattered intensity It, at scattering angle 0 = 30 degrees for two dipoles vs. distance of each dipole from the origin for a = 50, m = 1.05, A = 1.5 A,,. (1) separation along z axis, (2) separation along x axis. Dashed curves represent power associated with exciting field at each pair of sites.

‘p.-

IU)

z

The effect of particle size is also intensity is much less for a = 1.0, symmetrical with a deep minimum consequence ized internal

dipolar

scattered smaller, pattern

chosen

resembles

medium. Since

each

a

=

strength

of

curves

molecule,

the

a

as in Figure

11 which

molecules

embedded

the

Li II-

As the particle the character. for

the in

different

wavelength.

particular separately. in a

normalized

model

the

4

bulk

0

magnitudes to

to correspond ofthe

values

which

equal numbers within spheres

scattering cross section of the much stronger

exciting

illustrated a = 1 and

been

when distributed

The much greater a consequence at

has

5 correspond

=

experimentally are uniformly

scattering, the be investigated is also between

such that

of the

1 and

anticipated molecules sizes. mainly

signals are very small. pattern approaches

z

U)

to a single for

the

UI F0 Li

of the more nearly uniform and hardly depolarfield. Also, as expected for such an internal field,

the depolarized becomes still istic

shown in this figure. The and the pattern is nearly in ‘h at 90 degrees as a

=

detailed Thus

Just

as for

intensities might

be

of active of these

for a internal

=

5 is field

merely intermediate of the strength

60

SCATTERING

behavior for each case must the pattern for a = 3 which

Figure 17 is not 5. This dependence

0

Lorenz-Mie

180

ANGLE,O

Fluorescent scattered intensities L and I vs. scattering angle for an assembly of dipoles uniformly distributed over the outer surface (-), within a spherical shell at 0.5a ( . . . . ), and within a spherical shell at 0.166a (----) for a = 5, m = 1.5, A = 1.5 A,,. FIG.

of

120

17.

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QUANTITATIVE

ANALYSIS

AND

PARTICLE

dependence

SIZES

upon

and (d) changing illustrated

particle

U)

z

is illustrated

in curves

results:

We

have

verified

aspects of fluorescent scattering by small touch upon these experiments only briefly.

results,

which

by

(b),

some

qualitative We will reference Aqueous

I-

size

(c)

for a = 3, 5 and 6, respectively. Also the effect the excitation wavelength from 300 nm to 250 nn by comparison of curve (b) with curve (e).

C. Experimental

‘p.-

261

will

be

surfactant-free

Li

thacrylate

I-

z

Appropriate Mie)

and

0

each

other.

Li

conventional

Li IF4 0

tion. The variation

published

(8). dispersions

elsewhere,

of monodispersed emulsion

with

monomer,

were

to isolate

inelastically The

used

theory was fluorescent

signals

then used scattering

prepared methylme-

elastically

scattered the

in

dansylallylamine.

viz

scattered

(1) to determine

present of the

were of

the

(fluorescent)

elastically

way

latex

of the

particles. Detailed be found

copolymerization

a fluorescent

filters

may

of is

(Lorenzsignals

were

from

utilized

particle

size

in a

distribu-

to predict the angular with the measured

values. The emission wavelength selected for the calculation was taken to be the peak in the emission spectrum (vacuum wavelength 500 mn) even though in the measurements all wavelengths passed by a sharp cut-off filter were accepted.

U)

A typical

0

60

120

SCATTERING 18. Fluorescent

FIG.

angle witha=

for

intensities

an assembly of dipoles 1 (----),a=3(....)anda=5(----)andm=

uniformly

is shown

in Figure

21 where

the

scattered

180

ANGLE

scattered

result

e

,

Ih and

I

scattering

vs.

distributed

within

spheres 1.5,A= 1.5

A,,. particle within ally is

refractive the particle.

depend

index and Fluorescent

upon

below

the

excitation

a particular

internal

field,

which

is the

are

embedded

normalized in

polarizabiity. bulk emission of the length The tions

the

bulk

source

once the other also depend illustrated a “flat”

media

particle, i.e. the emission must be multiplied by ordinates of the curves to Ih at 0 = 0 degrees

have

However,

immediate

are to

provided

value.

in Figure spectrum

already

The nm,

noted

for

are fixed, excitation the

molecules

to

a constant

perturbation of the due to the effect

in Figure 20 represent for spheres uniformly

that

the

20 where

from the bulk corresponding

correction, is quite small

this

from

corresponding

the

that since

of excitation,

conditions upon the

Thus they represent the spectrum at each wavelength

active molecules. wavelength 300 We

will

of active molecules spectra do not usu-

wavelength

threshold

depends upon wavelength, the emission spectrum wavelength. Some of these effects curves

distribution emission

at each value

waveof I,,.

the correcfilled with

for a = 1 and excitation as indicated by curve (a). such

internal field is nearly uniform and hardly the angular distribution of the emission dipole except near 90 degrees. Accordingly, the effect in this case is not surprising.

a small

particle

0

60

SCATTERING

the

depolarized so that is close to that of a the smallness of However, a striking

FIG.

radius

19.

Fluorescent

a with

dipoles

scattered uniformly

180

120 P

intensities distributed

Ih and

I for sphere

within

a core

of

of

radius

0.4a and with this core deformed into equivolume prolate spheroids with figure axis on the z axis equal to 0.7a (----) and equal to a ( . . . . ); a 5, m = 1.5, A = 1.5 A,,. Upper curve in each pair is Ih.

Downloaded from jhc.sagepub.com at KAI NAN UNIV on April 4, 2015

262 intensities of

ET

KERKER

the

Hh and

and

‘h

V now

I,, which

same

plane

radiation.

are

as the

The

slightly ues

V.

backward steep

not

at

scattered between both

failure

to isolate

a narrow

fact

fluorochromes. with theory,

that

these the

the

do this

in

incident for

to

V, on values

each

they

show

the

(8). can

errors

though there experiments

and

also

spectrum)

isotropic

and

molecules

orientation

of

is qualitative are required

the

UI Iz

0 UI

(primarily

source

IU) z

same dispersions and calculations

emission

for and

exceedingly by

monochromatic of the

‘p..

the

exhibited

experimental

part

val-

towards

range

the

the

the other vary only

experimental trend

angular

calculations

anisotropy

Even further

vectors

results

upward

signals from experiment

a perfectly

consider

theoretical

slight

over

to utilize

to the

polarized

Although

the

failure

not

of the

For

neither

attributed

components

electric

90 degrees. and theoretical

angle.

trend

the elastically The differences be

vectors and

follow

directions,

polarized their

made to coincide at 90 degrees. and theoretical values of Hh display

scattering do

downward

easily

eltric

minimum experimental

with of

been

those with

experimental

polarization have Both experimental characteristic hand, both

denote

polarized

AL

do

UI II-

4

U U)

actual

agreement in order

to

40

80

120

SCATTERING FIG.

‘-I

angle

21. Fluorescent for

scattered

ANGLE,i

intensities

Hh and

polymethylmethacrylate-dansylallylamine;

V,, vs. scattering modal

diameter = 1.13, 376 nm. Hh and are polarized in component. Experi-

304 nm, standard deviation 18 nm, relative refractive wavelengths in the aqueous medium A,, = 277 nm, A v,, are the polarized components of Ih and I,, which

0

U-

the

0

ments

F-

same planes as the corresponding shown by 0, U. Calculations

incident

shown

index

m

by LV.

U resolve the above differences. In particular, measurements on bulk samples are desirable in order to ascertain the intrinsic depolarization and to incorporate this into the theory.

z 0

F-

D. Discussion: The theoretical studies in this section illustrate the dependence of the angular distribution of fluorescent intensity and polarization upon particle morphology and upon the distribution of the fluorescent moiety within the

U Li 0 U

particle. when

They the

demonstrate

active

molecules

that the fluorescent active molecules.

400

500

EMISSION FIG.

20.

Correction

600

WAVELENGTH, factor

nm

for Ih at scattering

emission wavelength A for a uniform spheres with m = 1.5 and (a) a 1, A,, nm,(c)a=5,A,,300nm,(d)a6,A,,300amand(e)a3,A,, = 250 nm. vs.

700

angle

distribution

300 nm,

(b) a

0 = 0 degrees of dipoles in =

3, A,,

=

300

it

cannot

biological cells and the effects would

biological cells of anisotropic

be

embedded

which are molecules.

assumed,

in a bulk

signals are proportional These calculations are

tides smaller than molecules. Certainly dramatic for and comprised

that are

to the number carried out for

for immobile be expected larger, Yet

of par-

isotropic to be less

somewhat

the

as

medium,

fluid

phenomenon

should be noted. It may play a role in the quantitative estimation of the amount of active species. It may provide a clue for discriminating among cells which differ morphologically or in which the spatial distribution of the fluorescent moiety differs. It may be possible to minimize the effect by utilizing a light tering

source

which

plane.

Downloaded from jhc.sagepub.com at KAI NAN UNIV on April 4, 2015

is polarized

perpendicularly

to the

scat-

QUANTITATIVE

LITERATURE 1. Kerker

M: The

Radiation. Academic 2. Asano S, Yamamota

Scattering

ANALYSIS

CITED

of Light

Press, New York, G: Light scattering

and

other

Electromagnetic

1969 by a spheroidal

particle.

PARTICLE

263

SIZES

5. Kerker M, Cooke DD, Chew H, McNulty PJ: Light structured spheres. J. Opt. Soc. Am. 68:592, 1978 6. Chew H, McNulty PJ, Kerker M: Model for Raman cent

Appl. Opt. 14:29, 1975 3. Barber PW, Yeh C: Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies. Appl. Opt. 14:2864, 1975 4. Saxon DS: Lectures on the Scattering of Light. Department of Meteorology, University of California, Los Angeles, California, 1955. See also, Newton RG: Scattering Theory of Waves and Particles, McGraw-Hill Book Co., New York, 1966 and reference 1, p. 480

AND

scattering

by

molecules

Rev. 13A: 396, 1976 7. Chew H, Kerker M, McNulty ing

by

molecules 66:440, 1976

Am. 8. Lee MP: ymer

embedded

Preparation

Colloids.

Ph.D. N.Y. (1977). distribution

Potsdam, Angular Opt. 17: 1978,

1978

Downloaded from jhc.sagepub.com at KAI NAN UNIV on April 4, 2015

and

embedded

in small

PJ: Raman in

Optical

concentric

Properties

scattering and

fluores-

particles.

Phys.

and fluorescent spheres.

J.

scatterOpt.

of Fluorescent

Thesis, Clarkson College See also Kratohvil JP, Lee of fluorescence from small

by

Soc.

Pol-

of Technology, MP, Kerker M: particles. Appl.