IMPROVED SCREEN FOR REAR PROJETION VIEWERS

• Document Type: CREST
• Collection: NGA Records (Formerly NIMA)
• Document Number (FOIA) /ESDN (CREST): CIA-RDP79B00873A001900010120-1
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 132
• Document Creation Date: December 28, 2016
• Document Release Date: September 6, 2012
• Sequence Number: 120
• Publication Date: April 26, 1966
• Content Type: REPORT

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CORNING GLASS WORKS
TECHNICAL STAFFS DIVISION
IMPROVED SCREEN
7 FOR
REAR PROJECTION VIEWERS
fl
PHASE II. THEORETICAL STUDIES
April 26, 1966
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J -44- P CORNING GLASS WORKS
REV. 2/63
NING
C ORNINO, NEW YORK
RESEARCH AND DEVELOPMENT LABORATORY
TECHNICAL STAFFS DIVISION
TITLE: IMPROVED SCREEN FOR REAR PROJECTION VIEWERS
PHASE.II: THEORETICAL STUDIES
AUTHOR
L_1
REPORT NO. P-19-9
PRINT NOS.
PROJECT NO. 89050
NO. OF PGS. 1 28.
NO. OF FIGS. 53
25X1
,DATE April 26, 1966
ABSTRACT: This constitutes the final report of4-41e second phase of the
government sponsored program, "Improved Screens for Rear Projection
Viewers". It summarizes six months of theoretical investigations
relating to the scattering of light by rear projection screens.
These investigations have been conducted toward determining the
relations between viewing properties and such physical characteristics
as particle diameter, their number density, and the relative index
of refraction between the scattering particles and the surrounding
medium. The results of this study have been used as specific materials
requirements for samples of the glass ceramics, Fotoform and the
sintered glasses.
The results of a study on the feasibility of using hollow optical
fibers with metallic coatings is given along with a discussion of
preliminary models of two dissimilar, novel, rear prOjection screens.
The last section discusses the instrumentation for,testing samples
of rear projection screens.
KEY WORDS: Rear View Screen, Projection Screens, Light Scattering,
Hollow Fibers, Instrumentation
25X1-1.
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TABLE OF CONTENTS
Page
I. Introduction 1
II. Conclusion 3
III. Background of the Problem
IV. Theoretical Investigations
A. Mie Scattering
1. Theory
2. Mie Scattering Theory Applied
to Rear Projection Screens
3. Specific Materials Requirements
Based on our Theoretical Studies
B. Rayleigh. Scattering
1: Theory
2. Feasibility of Using Rayleigh
Scattering Materials as Rear
Projection Screens
5
9
9
9
14
38
39
39
42
V. Corning Glass Works' Materials 51
A. Hollow Fibers 51
B. Other Approaches S 57
1. Ultraviolet Sensitive Screen 57
2. A Louvered Screen 58
VI. Instrumentation 61
A. Goniophotometer 61
1. Xenon Light Source 61
2. Collimator 64
3. Sample Holder S 66
4. Detector 66
5. Control and Display Electronics 70
B. Modulation'Transfer.Function'Analyzer 72
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VII. Data Appendices 84
A. Appendix A - Raw Data 85
B. Appendix B - Corrected Data 98
C. Appendix C - Computer Programs 117
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I
ABSTRACT
The analytical relations between the viewing properties of
rear projection screens and such physical characteristics
of the screens as particle diameter, number density, and
the particle's index of refraction relative to the surrounding
medium have been theoretically investigated. We have shown
how each of these parameters influences the scattering of
light by the screen material, and subsequently how they
determine the uniformity of screen brightness, efficiency,
and color fidelity. Specific material requirements for the
next phasp.of this program have been generated using the
results of this study.
Other approaches which do not depend upon light scattering
by a volume of material are also being investigated, The
feasibility of using hollow glass fibers with metallic
coatings is given along with a description of preliminary
models of a louvered screen and an ultravioldt'sensitive
screen.
Lastly, a goniophotometer.to measure the light scattering
.properties and a modulation transfer function analyzer to
measure the resolution of samples made of Corning Glass Works'
materials are described.
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I. Introduction
This constitutes the final report concluding the second
phase of the government-sponsored program, "Improved
Screens for Rear Projection Viewers." The main objective
of this program is the fabrication of improved rear pro-
jection screens from available Corning Glass Works'
materials.
This report summarizes the theoretical investigations
relating to light scattering by rear projection screens.
The conclusions of this study are presented in Section .
II. The major conclusion is that optimum rear projection
screens, for most applications, can be obtained by
properly choosing the correct size, number density, and
relative index of refraction of the scattering particles.
A background to the problems associated with rear pro-
jection systems is given in Section III, Projection and
viewing problems, some terminology, and constraints
. introduced by the screen are presented. The behavior of
a typical rear projection screen is illustrated as well
as how the light scattering property of the screen
material determines the viewing properties. Finally, the
influence of factors such as magnification, projection
and viewing distances, screen size, optics of the projector,
and the ambient light level are discussed.
The results of the Mie theory of light scattering are
covered in detail in Section IV. The equations based on
this theory were used to compute light scattering functions
for particles of different size and different relative
indices of refraction. These scattering functions are given
in Appendix A. Additional modification of these angular
scattering functions was required because of total internal
reflection and refraction at the air glass interface of the
screen. The corrected data are given in Appendix B. From
these data, parameters such as efficiency and axial gain
are correlated With particle size.
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Additional data are presented to illustrate how the
particle size influences the amount of light trapped
through total internal reflection, how this degrades
image contrast, and how this influences the sensitivity
of the material to ambient light. The influence of
particle size and refractive index on the color fidelity
of a material is covered in detail. Specific material
) requirements are formulated to give a rear projection
screen material that theoretically meets the contract
requirements. This section is concluded with a brief
discussion of Rayleigh scattering and why materials
consisting of particles much smaller than the wavelength
of illumination are unsuitable for use in rear projection
screens.
Alternate approaches directed toward other types of
rear projection screens and screen materials 'are dis-
cussed in Section V. The difficulty of 'using metallized,
hollow glass tubes is outlined and substantiated by
experimental data. Optical design and applications of
t ultraviolet sensitive screens and louvered screens are
also included.
Section VI is devoted to a description of the instrumenta-
tion to be used in evaluating samples of Corning Glass
Works' materials. Each of the five main sections of the
goniophotometer,yhich measures the angular scattering
properties, is discussed. The principles of operation
LJ of the modulation transfer function analyzer, and the
7- details of making the special'sine-wave resolution target
are then covered.
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Three appendices follow which present the raw computer
data, the converted data, and a list of the three programs
used to compute the light scattering functions and perform
the necessary modifications discussed in Section IV.
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II. Conclusion
1. An analysis of the computer data indicates that
the angular gain functions of particles with
identical sizes but different refractive indices
are similar. The axial gain (0 = 0) differs at
most by 5 percent at a = 5 and by only 15 percent
at a = 10. The major difference being for M
which represents highly reflective particles.
The most obvious difference between the scattering
functions corrected for refraction at the air glass
interface and those which have not been corrected
is that the former are somewhat broader.
The contract requirements for uniformity of screen
brightness and efficiency are met by particles in -
the size range 1.75 s a s 2.25, where a is the ratio
of the particles' circumference to the wavelength
of illumination inside the medium. This dictates a
particle diameter from .2 to .3 micron. Thus it
can be expected that on axis these screens can only
be from 3.0 to 3.5 times brighter than a uniformly
diffusing screen.
The efficiency of the screens is strongly influenced
? by the particle size. For a value of a greater than
losses through backscattering are insignificant
compared to thosaproduc_ed by total internal reflec-
tions. Losses throughiinternal reflections become negligible
beyond a = 4, except for reflecting metallic particles.
The major factor limiting the use of large particles
is the resulting non-uniformity of the screen. Thus
the low efficiency materials are the most sensitive
to ambient light.
The refractive index of the particles is relatively
unimportant in determining the shape of the scattering
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function, but strongly influences the color char-
acteristics. The further the relative refractive
index is from unity, the better the color fidelity
of the material.
An expression relating the reduction of contrast
in an image to the fraction of light internally
trapped in a material has been derived. It shows
that if half of the trapped light eventually passes
through to the viewers, the reduction of contrast
is linear with the fraction of light trapped.
Rayleigh scattering theory has been considered and
the general scattering function investigated.
Separate terms in the scattering function have been
individually considered and numerically evaluated to
understand better how they contribute to the scattering
function. We have been able to show theoretically that
rear projection screens made from Rayleigh scattering
materials are unsatisfactory for a number of reasons.
First, although their scattering functions are very
broad and uniform, these screens are inefficient and
have low brightness gains. Second, the resolution
of such screens is correspondingly very low. Third,
the strong wavelength dependence of the scattering
function and scattering cross section impose nearly
? impossible constraints which, when not met, result in
screens which have very poor color characteristics.
Applications for these materials probably lie only in
low gain, low resolution, monochromatic screens.
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Backciround of the Problem
The function of a rear projection screen is to accept
an image from a projector on one side and present it
to viewers on the other. To do this it must diffuse
and re-radiate the incident illumination. The types
of projectors in use range from television screens to
conventional slide projectors. The effectiveness of ,
such a display system is governed by the light
scattering characteristics of the screen and by the
geometries under which it is illuminated and viewed.
The scattering properties of various screen materials
have been discussed in a number of good articles1-7
The viewing properties of rear projection screens are
determined by their light diffusing characteristics
and also by internal reflection and absorption. The
behavior of a typical rear projection screen is
illustrated in Figure 1. Two rays of light are shown
incident on the screen, one at point A, the other at B.
.1)
Figure 1. Typical Rear Projection Screen Geometry
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Continuation of the line representing the incident ray
through a point at the screen establishes the principal
axis.for that ray. The scattering function for that
point on the screen also has its axis colinear with this
principle axis. An observer at 0 will view point A along
its principle axis, but he will view point B at sone
angle off-axis. The intensity of point B is determined
by the angle DBO, at which the scattering function must
be evaluated. This angle, 0, termed the "bend angle,"
is a function of the size of the screen and the pro-
jection and viewing distances.
The scattering function of any material is obtained by
measuring, with a goniophotometer or comparable
instrument, the brightness of a narrow, parallel beam of
light as it is spread out by the screen. These intensities
are then normalized to a reference taken to be a perfect
isotropic diffusor where the intensity of the scattered
light is uniform and independent of the angle 6, These
data are called gain curves.
Screens which do not diffuse as uniformly as the isotropic
screen will appear brighter over a certain range of
viewing angles. The angular gain curve will have a value
greater than unity in this region. Because a diffusing
screen is a passive element which does not add energy to
the light passing through it, any increase in gain above
unity for one viewing position must necessarily result in
a gain less than unity at some other position, Figure 2.
It is important to note that viewing requirements
generally call for greater viewing angles in the horizontal
plane than in the vertical direction. This necessitates
a screen which is anisotropic, i. e., the gain curve should
be broad for the horizontal plane and relatively narrow for
the vertical plane.
The intensity ratio between the light incident on the
transparency and the screen is equal to the inverse square
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of the magnification. Thus, if the screen can be made
half as big, it will require only a fourth as much power
to illuminate, and the bend angles will be considerably
smaller. The closer the screen is to the audience, the
larger are the bend angles; hence, the difficulty of
maintaining a uniform picture increases. The width of
the screen also has a comparable effect. The wider
the screen, the greater the range of bend angles; hence,
the problem of projecting an acceptable picture is also
more difficult. Bend angles are increased by using
short focal length projection lenses placed closer to
the screen, or by increasing the f/No, at which the pro-
jection lens is operating. The faster the lens, the more
light can be projected on the screen; however, this also
increases the bend angle and may require a lower-gain
screen to maintain sufficient uniformity of illumination.
It is important to note that the screen may be brighter
overall for an observer at the center of the audience
than for one near the edge. It has been found, however,
that it is more important to view a uniformly illuminated
?image than a brighter non-uniform picture. In any case,
brightness must be sufficient for all to view the display
with comfort.
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IV. Theoretical Investigations
A. Mie Scattering
1. Theory
The light scattering characteristics of the
materials to be investigated are given by the
Mie theory of light scattering9. This theory
is founded on the general solution to the
boundary value problem of an isolated sphere
in an electromagnetic field. Although this
theory is very general, it finds primary
application when the size of the particle is
about the same size or larger than the wave-
length of the incident radiation.
The important equations derived by Mie for
both polarizations of the scattered light are
? 2
Ill (0) = [E (Anif + an[xlin - (1 - x2)711']1 ], (1)
n=1
2
= [E (Pin[x7n - (1 x2)7111] + an7n1], (2)
-n=1
where rin and irn ' are the first and second derivatives,
? witherespeOt difithel."legeri'dre)rp;odynorni-aliP 1--(x)
ofiJOrder, nj?11) ,xr:F.--Tr.dos e1 and
(-1)n+1/2(2n+l)irsn(a) dp -
n (n+1) dSn(p)
0n (a)
dSn(O dSn(a)
M*Sn(p) da
d$ (a)3'
M*Sn(p)
( 3 )
dSn(p) dSn(a)
M*Sn(a) di3 - snco
Bn = n
(-1) n+3/2( 2n+1)
(4)
n (n+1) ][ ds co 0 (a) )
M*13n(a) dp SnW d:
where Sn(a) = Riccati Bessel function = (7()
2 '
1/2
J (a)
n+11n(a) = Riccati Hankel function =
ct]TinREEE
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Sn(a) + j (-1)n (navl j-n-1/2(a), and J11.01(a)
2'
and J(a) = Bessel functions of half integral
order.
Thus, the only physical parameters are:
? The angle 0, between the direction of propagation
of the light scattered and the direction of the
incident light, Figure 3,
and
_ np?
x '
(5)
M*a. = (M ? ik) (6)
where D = diameter of spherical particle
= wavelength of incident radiation
in surrounding media'
M = index of refraction of particle
relative to surrounding media
k = extinction coefficient of the
particle material
i = .
/No ovorr elm
5-orraegix:r
MTENSI7Y
Figure 3. Scattering Geometry
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To solve any given scattering problem requires
tables of the real and imaginary parts of An and
B' tables of the Legendre polynomials and their
n
first and second derivatives10-14. These are
then combined using a desk calculator .or prefer-
ably a large digital computer into values of
-IN (0) and 4(0) from which the angular distribution
function "I(0)" is obtained
n1(0)
(0) + I(B)
27aK
(7)
where the scattering coefficient, i. e., the ratio
of the scattering cross section to the geometrical
cross section is,
2
2 n=1
2n+
Hartel15 suggested that Equations (1) and (2) could
be simplified in form by the repeated use of
fl recurrence relationships between the derivatives
and, products of Legendre polynomials. Recently
Chu and Churchill succeeded in rearranging of
radiation scattered by nonabsorbing spheres in terns
of a series of Legendre polynomials16,
K =
1)2 q A4 2 +1 B4
fl
1
"I- (0)"= 47 E a 11 (ajp)P n 4 1 (cos0)= + 7, a P (cose),
n=0
(9)
-where the coefficients an, are functions of a and
p, but not of the angle, and are given by
an - (2)(-1)n j
(10)
a2K(a,o) j.E1 k=I + )((2n:+1)
[1(1+1) + k(k+1) - n(n+1)w12
2 -jkn"w
j VjknVjkl)
u;k1F-1 n p,
?
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Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
-12--
. 771
Vjkn -
::7
where
0 for j k
jk (1 for j = k ,
Wjk = Re(Aj) eRe(Ak) + Im(Aj),Im(Ak) + Re(Bj)-Re(Bk)
Vjk = Re(A .)*Re(8k
j
4-1m(3.)*Im(Bk) , (12)
+ Im(Aj)-Im(Bk) + Re(Bj)-Re(Ak)+
Im(Bj),Im(Ak), (13)
Wjkn = 0' if j + k - n 2r, r = 0,1,2...k, (14)
+k+n 2
(LjA-n_k)(Lk+n-j)(Lj+k-n)(L 2 )
2)(15)
Wjkn
(Lj+k+11+1)[(L) NL. f,k+n- )
2 xL.
r
Vjkn = 0' if .j + k n 2r +1, r = 01112...k(16),
and
(2n+1) (j+k-n) (j+n-k+1)(k+n-j+I) (Lj+n-k+1) (Lk+n-j+1) (Li+k-n-1)(L 2
1+1n+1)2
k+n-j, 2
4 (L j+k+n+1) 11k+11
, 2 ' (L +1
2 "Lj+k-n-1 2 )]
if. j+k-n = 2r +
where Im = Imaginary part,
Re =,Real part,
L = Factorial.
"n
PIFFIT Pr717
, Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
= 0,1,2...k) (17)
Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
tj kiLl,
The advantage of expressing the angular distri-
bution of intensity in the form of Equation (9)
rather than Equations (1) and (2) is obvious.
The intensity at any angle for which the Legendre
polynomials are available can be computed from a
set of coefficients for a given a and M. In
general, the number of significant terms in the
series is about equal to 2a. The Legendre poly-
nomials are available at one-degree intervals,
,and their behavior is better known; interpolation
with respect to 0 can be done more accurately
than with In (0), 14.(0), "1(0)", or the tabulated
derivatives of the polynomials. Interpolation with
respect to a and 0 is also easier with the
coefficients an,than with Ig (0), 11(0), or "1(0)",
and need be carried out but once for all angles.
Additional advantages of the representation of the
angular distribution of scattered radiation by
Equation (9) can be noted. The power scattered into
any region, and particularly into the forward and
backward hemisphere, can be obtained by simple
analytical integration. By assuming that a particle
receives power only from adjacent particles having
the same multiple-scattering distributions, Hartel
developed the following equation in terms of the same
coefficients an' for the angular distribution of the
k-th scattered radiation in a dense dispersion:
ank
1
"Ik(0)"= +n= t(2n + 1)k_j_lPn (cos 0)]. (18)
It is somewhat simpler to evaluate (9) than Equations
(1) and (2),because only values of An and Pn (cos 0)
are required and are easily availab1e17-19. However,
the tables of an and Pn (cos 0) are very limited,
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.7
Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
LA
while the tables of An and Bn are by far more
I ' complete, i. e., they have finer divisions of
fl
a and M and cover a larger range of particle sizes.
For these reasons, Equations (1) and (2) were used
for the single scattering investigations. The
angular coefficients approach will be utilized
if a study of multiple scattering is necessary.
2. Mie Scattering Theory Applied to Rear Projection
Screens
The screen must not only diffuse the incident
illumination but do it efficiently as well. The
efficiency EFF(M,a), is defined as the ratio of the
scattered light Is, forming the image which passes
through the screen, to that incident Io' thus,
EFF(M,a) =.231 rT1/2.
j I(M ,a00)sin 6 de
0 o
where Io is given by
10 =, ? I(mia,O)sin 0 de (19)
The angular gain of a scattering material is defined
as the ratio of intensity of the light scattered
at a given angle by any given material to that
scattered by an isotropic radiator.
Let 1(0) and Ii(6) be the angular scattering
functions for an experimental sample of material
and an isotropic material respectively, and let
I'(0) and I' (e) be the angular scattering functions
normalized to the respective incident' intensities
I(M,a,O)
21117 I(M,a)din e'do
(20)
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r:
Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
Ii(M,a0) ?
Ij' (21)
27fIT I(M,ap)sin.0 do
Since the one diffuser is isotropic, we know that
I.1 (o)= C.?1 hence, (21) becomes
1
L 1
; L=7
?-?
Ci
L'AM,0,0) (22)
:C1 . 47('.
-
By definition, the angular gain function, Gain (0,
is
Gain (M,0) = I'(M,a,0)/Ii1(M,a,0) (23)
=4TTI (M, ,
ricm,a,0)84.ne de
0
To simplify the equations which depend upon M,a,
and 0 as much as possible throughout the remainder
of the paper, only the parameter 0 will be indicated;
and the other parameters will be implied.
A computer program titled "Mie III" to compute
in (0, 1.1(o), (In (o) + I.1.(0))/2, Gain (0),
EFF (M,a), and the per cent polarization has been
written and tested. (See program Appendic C.)
This program has been used to compute scattering
functions for M = .8, .9, 1.05, 1.20, l.30 and
infinite for values of a from 1 to 10. Since the
values of the angular gain function are the most
important parameters, they have been separated from
the other data by "Mie-Compressor" and have been
printed separately. They appear in data Appendix A
along with plots of these data.
C7Et F
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Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
bLik6i4IT d UML
The angular gain functions are very similar to
each other differing at most by only 5 per cent
at a = 5, and 15 per cent at a = 10 among the
different values of M at 0 = 0. This is not only
because curves of equal a have nearly equal gains
at 0 = 0, Figure 4, but because their shapes are
so similar. It must be concluded, then, that the
refractive index of the scattering particles,
relative to the surrounding material, is not a
significant design parameter when considering
only the uniformity of the scattering function.
The correlation between efficiency, the particle
- size a, and M is given in Table I, and Figlire 5: They
fl :show that little is gained in efficiency by increas-
L
(_J
fl
LJ
ing a beyond 2.
Figure 6 is a graph of efficiency versus gain at
0 = 0 and is redundant data to Figures 4 and 5,
.but it is useful for visualizing the relationship
between these two parameters. It can be seen that
the efficiency remains constant for all values of
M beyond a gain of about 3.75 which corresponds to
an a of about 2.
The only major difference in any of these curves
is for M = cx, which represents highly reflective
metallic particles. Screens containing metallic
particles are by far less efficient than those with
finite values of refractive index. The scattering
function shows many lobes, but in terms of the gain
function, little detail can be seen. Because of
the lower 'efficiencies, the gain curves are much
different than those for corresponding a at finite
values of M.
This analysis is only valid inside the diffusing
material because, in general', there will be a medium
, ? 121FEEE-71
J1:4\11 .
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=- =1. :111 1E`: r.."n1 111- IA 10 --"-71P2 ;1=-R IU I 1-141 `11-111.M4, '-1=I /=-
? Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1 /
ItUtItL tbb LA".
trmil
1 II
011 111111111
11 ion
Ill,
3 44
7 k 9 /0
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ninr 7 7 1 7-7 n r 1 1 1 7
-I Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
Table I. The Efficiency EFF as a Function of a and M
cc/m
.8
.9
1.05
1.20
1.30
M=00
1
.6413
.6432
.6472
.4554
.6580
.3371
2
.9186
.9351
.9596
.9766
.9784
.7621
3
.9945
.9942
.9853
.9821
.9825
.8281
4
.9922
.9940
.9957
.9895
.9787
.8500
5
.9975
.9977
.9978
.9945
.9884
.8710
.,
6
.9972
.9988
.9981
.9966
.9908
.8848
.9988
.9987
.9994
.0000
.9911
.9010
.7.
8
.9982
.9995
.9993
.9973
.9903
.9109
9
.9991
.9994
.9994
.0000
.9864
.9202
10
.9988
.9996
.9996
.9976
.9803
.9255
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CDeclassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
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/ Declassified in Part :Sanitized 6 '-
Copy Approved for Re ease 2012/079/06 : CIA-IDP79B00873A00190/6)010120-1
T
Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
of different refractive index around the screen,
and light emerging from the screen will be
refracted at this interface. The correspondence
between 0 the angle inside the medium and 0'
outside is given by Snell's law.
0' = sin (n sin 0) 3
( 24)
7 where n is the relative index of refraction
Li between the screen material and the surrounding
medium, usually air.
P.
This refractive index boundary also modifies the
intensity of light passing through, depending upon
its polarization. The reflection coefficients for
the parallel and normal components are given by
RN(0) - (sin (e 91)2
sin (0 + ))i
17
Rp(e) (tan (0 - 0')
' 'tan (0 + 0')
4.71
L
L.7J
( 25)
(26)
where parallel and normal refer to the angle between
the electric field vector, and the plane formed by
the incident beam and the reflected and refracted
components, Figure 7.
NciDarr U'RePedeid
$sAft com9.1.wor
TeAuSairra
410114MENr
DirtflDaaPDOVV.co/d.
Pini0e of A.ficAieit
P Figure 7. Refraction Geometry
q_1.4
1,Mr[Pri7P71717:
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Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
LLJAtt-AXHAP-4,
171
1-1
.1
!
'rn
t
If there is no absorption, then all the other
light must be transmitted and the two transmission
coefficients are
and
TN(0) = 1 RN(0)
T (0) = 1 R (0) ?
(27)
(28)
Figure 8 shows TN(0) and Tp(0) as a function of
the angle O. They both must be zero beyond 0 =
sin (l/n) as this is the critical angle ec inside
the medium.
This refraction of the scattered light for n > 1
acts to broaden the scattering function which helps
to make the screen illumination more uniform. Any
pencil of light making an angle with the normal to
the boundary greater than 0c, will be totally
internally reflected regardless of its polarization.
For n = 1.5, 0c is about 42?. The resulting intensity
l'(g), taking into account these losses, is
II(0) = TN ? IN(0) Tp ? Ip(0) (29)
where IN(0) and I (0) are the two polarized com-
ponents of the scattered intensity. Therefore, a
new effiCiency function, EFU, must now be defined aso
2r ec
EFU =-F- [Ip(0)*Tp(0) + IN(0) *TN(0)3(iined0(30)
o o
Correspondingly, the fraction backscattered EBU is
EBU = iL sir [Ip(0).Tp(0) + IN(0)*TN(0)]dinZd0(31)
0 r-Oc
Clearly, the light which is scattered between Oc
and r - gc is internally trapped by total internal
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Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
loxK C.1E01. Tel0E 1sT E. CC OM.. v 5,49, 4A
4TT-7=7. ? ?-?-?-: , ? ?
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? ? ?
; erwl' ? ?
, I
? ?
_ _ --
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Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
reflection until --it-i-S scattered at an angle
less than oc or greater than ri -c The
_J
,.I
In
fraction of the light trapped is
ETU = 1 - (EFU EBU) . (32)
A second computer program, "MIE-S3", has been
written which adjusts the angular gain functions
for refraction and losses owing to reflection at
the screen-air interface. The data on the corrected
angular gain functions are given in both tabular
and graphical form in data Appendix B. Tabular
values of the functions EEF, ETU, and EBU are
also given.
The data, Gain (8), is not strictly valid beyond
a = 5; however, for a greater than 5 the shape of
the Gain (0) curves still give some measure of .the
_J increase in the directivity with the particle size
parameter a.
L,
The most obvious differences between the data of
Appendix A and B, are the broadening of the gain
functions because of refracion at the air-screen
interface. This can be seen by comparing the angular
gain functions for different M and equal a. Even
through the gain functions are more uniform, the gain
at 0 = 0 is not significantly different from the
uncorrected data. This was to be expected as there
is no refraction and the reflection losses amount to
only about 4 per cent. There are considerable differences
between the old and new efficiency functions, EFF and
EFU respectively, particularly at the smaller.values of
a. Figure 9 shows the distribution of intensity
between the three functions, EFU, ETU, and EBU as a
function of a, for six different values of M. The back-
scattered fraction, EBU, is very small compared with
the fraction ETU which is internally trapped and is
responsible for the major portion of the losses.
Backscattering is only significant for values of
a less than 2, except where M is infinite.
7,
L, Declassified in Part - Sanitized Copy Approved for RelWa-sce26-1-2/09/06 : CIA-RDP79B00873A001900010120-1
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L Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
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The fraction EFU contributes directly to the
image, while the fraction ETU adds an ambient
light level which degrades the image by lowering
contrasts. Generally, less than half of ETU is
effective in terms of directing trapped light out
of the front of the screen to viewers.
To see how ETU effects the contrast of the pro-
jected image, let the contrast y of an image be
defined as
I 1
max min C - 1
(33)
Imax + I . C + 1 )
min
where Imax and Imin are the maximum and minimum
intensities of some type Of bar pattern; C is
called the contrast ratio, C = I /I . . When
max min
a screen is illuminated with a pattern of a given
contrast ratio, energy from all parts of the .
pattern contributes to the total amount of light
trapped. Of the total amount trapped, only a
given fraction V will pass through to the viewers.
Thus,thecontrasty.of the final image can be
shown to be
where
EFU
YT EFU (1 - 2V) + 2V '
(34)
(35)
and where yo is the contrast of the pattern for
ETU = 0. The contrast, yT, being a function of the
efficiency EFU, acts to reduce the contrast of detail
on the screen.
For V = 1/2, (34) simplifies to
. EFU (36)
?
n Li ,117-7.7 ,'ri`61-1,F;, 7-
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7
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?27?
where the contrast falls linearly with the
efficiency, EFU. The backscattered component
only decreases the overall, efficiency and has
little affect on image quality.
The sum of ETU and EBU is a measure of the
screen's sensitivity to front lighting. This
is because only the light which enters the screen
from the viewing side, and is either backscattered
or trapped, is of concern. The amount which passes
completely through the screen has no direct effect
on the quality of the projected image. Ideally,
all of the light from the viewing side should pass
through the screen. In general, the more trans-
mitting, i. e., the less diffusing the screen, the
less sensitive it is to ambient light. ,This is
impc)rtant because in many applicaticns the display
will be viewed with a certain amount of room light
present. The greater the difference between the
ambient intensity and the screen brightness, the
better will be the conditions for obtaining good
quality on the projection screen.
An unsatisfactory solution to this problem often
used is to put a light absorbing material into
the screen. The absorption tends to reduce the
sensitivity to ambient light by absorbing a large
fraction of it. However, it also reduces the
overall efficiency of the projection system by the
same amount, and in many applications where total
power is of utmost importance such losses cannot
be tolerated. The light which passes through the
screen should not illuminate any highly reflecting
objects behind it, as rear projection screens are
very sensitive to stray back illumination.
L Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
Along with parameters such as particle size and
relative refractive index, a given material can
be characterized by the particle number density
and its associated thickness. Thus far we have
considered scattering only by a single particle,
whereas practically, we are concerned with the
combined scattering of billions of particles. One
of the most important parameters is the scattering
cross section Gs, of the scattering particles.
This has units of area and represents the effective
cross-sectional area of the patticle which produces
scattering.
Another parameter closely related to the scatter-
ing cross section is the efficiency factor K,
which is defined as the ratio of the scattering
cross section to the geometrical cross section
Gg# also called the scattering coefficient.
K = Gs/Gg (37)
For a sphere G = ma2. Therefore, K is a measure
of how efficiently the area Gg produces scattering.
The total scattered intensity Is', per geometrical
cross section is
Is' = Io ? K
Using (37) in (38) we get
Is'
c5s
Io ag
(38)
(39)
This takes into account only the light which falls
on a geometrical cross section rather than on a
unit of the material containing scatterers. The
Ca
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L Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
?
-29-
fraction F of the incident light being scattered
in terms of the number of'particles N, the area
A of the material being illuminated, and the
scattering cross section are
F- s _NGS
Io A
?
( 40)
The ratio N/A in (40) can be written in terms of
the particle number density pi and the thickness
T of the material as
N _
T .
A -
Thus, (40) becomes
Is
F = = pT Gs .
0
( 41)
( 4 2 )
This assumes that each particle is completely
illuminated, which actually never occurs as the
particles nearer the front side of the material
shadow other particles which lie further into it.
From theoretical considerations, it can be shown
that
-Kr,
= Io (1 sra2pT) .
( 4 3 )
,7 Thus, for F = 1, the per cent of the incident light
scattered is IS/IO = 63 per cent; for F = 2, I /I
s o
86.4 per cent; and for F = 3, Is/I0 = 95 per cent.
Following this, the material must be infinitely
thick for all of the light to be scattered. The
question is: for what value of F is enough of the
light scattered so the specular component is
unnoticeable? There can be no definite theoretical
answer to this; however, this limiting value will be
determined experimentally.
-7 n. Frpfr:ITTTnt
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Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
-30= ? ? "--1
This can be done simply by measuring the intensity
? of the specular component for several different ,
thicknesses and evaluating the exponent of (43)
for the thickness which has the optimum amount of
scattering.
? To ensure color fidelity of the projected image,
the scattering coefficient should not change
rapidly with a. For example, if a particle is
illuminated by two different wavelengths, X1 =
.45 micron and X2-= .65 micron, the ratio of the
two a's is
al . X2
(44)
a2 X1
The scattering function for Xi and x2 is determined
by the scattering functions evaluated at al and
a2 respectively. Therefore; if the angular
scattering functions are significantly different,
as in Figure 10, and the power spectral density is
uniform, the center of the screen would have an
excess of blue while the edges would have an excess
of red. A good color balance would only occur around
00._
16_1
4
Figure 10. Poor Color Balance Resulting from
? Differences in the Shapes of the Angular
-- GgilifiFtifidtiOITS".1gti Two Wavelenaths .
?
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Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
Llk4.3?
The .scattering coefficients are plotted as a
function of a for different values of M, Figure
-11. The important parameter is Kr,,-the ratio
of the scattering coefficientat the two values
of a
K(M,a1)
K(M,a2)
(45)
This ratio is plotted as a function of al in
Figure 12. The limit of Kr(M,a1), for small alpha;
is, (1.445)4 = 4.36,which is.the limiting case of
Rayleigh scattering. Kr(M,a1) = 1 implies the
scattering Cross section at al and a2 are equal,
and the intensities of the scattered light are
the same. When Kr(M,a1) = 2 the Scattering cross
section at al is twice that at a2.
Using Equation (43). and denoting the.scattering
coefficient for al by K2.and for a2 by K21)we have
and
Isl
- 1 e-K1 ra2p T
Io
Is2-K a2pT
? e 2 r
Io
The ratio R,of the scattered intensities is
Ii e -K1 fla2p T
= R -
Is2 e-K2 Tra2p T
ECOFEDEE1111%1
(46)
(47)
? (48)
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I
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-34-
or
,K1 ra2pT = U
2
7a pT =
1\1
( 49)
U is referred to as the "optical density" of the
scattering material. For an optical density of
unity, U = 1, the intensity of the unscattered
1
beam has fallen to ;- its initial value after
passing through a. thickness T.
Using (49) in (48), we have
1 - e-U
R =
1 -e -UK2/K1
(50)
Solving for the ratio of scattering doefficients
at the two different wavelengths, we have
K1
K2 = loge[ - 1 -177T71
(51)
The ratio K1/K2 is plotted for U = 1 as a function
of R, Figure 13. Thus, by specifying the maximum
tolerable ratio of the scattered light at two
different wavelengths and the "optical density"
of the material, we have defined the maximum per-
missable ratio of the scattering coefficients. As
an example for U = 1 and 11/12 = 1.5, we see that
K /K must not be more than 1.85.
1 2
Clearly, values of R and K1/K2 near unity are the
most desirable, because the degree of scattering
is then independent of wavelength and only differences
between the two gain functions for al and a2 are
responsible for any residual color. When
_ Declassified in Part - Sanitized Copy Approved for Release 2012/99/06: CIA-RDP79B00873A001900010120-1
Declassified in Part - Sanitized Copy Approved for Release 2012/09/06 CIA-RDP79B00873A001900010120-1
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? Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
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Declassified in Part - Sanitized Copy Approved for Release 2012/09/06: CIA-RDP79B00873A001900010120-1
-35-
Kr1) > 1, a greater fraction of blue light
is scattered, making the color characteristics
of the material more undesirable.
The refractive index is therefore a significant
design parameter, but in an unexpected way it
can be seen from Figures 12 and 13, that the
most promising materials have refractive indices
as far from unity as possible but not infinite,
i. e., the best values of M are .8, .9, and
particularly 1.30.
Requirements in the contract specify the angular
gain function should not change by more than
?15 per cent over a viewing angle of ?45?. This
requirement, in terms of the gain function
already computed, is shown in Figure 14. The
ordinate is the variation in intensity from 00 to
?45?, 00 to ?35?, and 00 to ?25? plotted against
particle size a for different values of M. It is
desirable to use the largest particle size practical
because of the higher efficiencies and less
degradation of the projected image by light which
is trapped. Clearly, the major factor limiting
the use of large particles is the resulting non-
uniformity of the screen. As can be seen from
Figure 14, the uniformity is a very critical
function of the angular limits and a.
To strictly meet the requirements set forth; the
particles must be no larger than a = 2, which
means the gain at 0 = 0 will not exceed 3.5; the
overall efficiency will be somewhere near 65
per cent with the remaining 35 per cent of the
light being trapped. This trapped light will
reduce ?the contrast of the image by almost one-third.
L Declassified in Part - Sanitized Copy Approved for Release 2012/09/06 r: CIA-RDP79B00873A001900010120-1
70
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Declassified in Part - Sanitized Copy Approved for Release 2012/09/06 : CIA-RDP79B00873A001900010120-1
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in
? E-1
If, on the other hand, the limits of uniformity
are chosen to be ?15 per cent over ?350, we see
the particle size now moves up to a = 2.75; the
gain at 0 = 0 moves up to a value of 4.75; the
efficiency significantly improves to a value of
near 80 per cent. The contrast is lowered by only
20 per cent rather than 33 per cent, and the color
fidelity is better. The second screen would be
34 Per cent brighter than the first in the center
and 11.5 per cent brighter at the edge. This
second criterion is only used as an example to
show the improvements in efficiency and contrast
by using slightly larger particles which give a
higher gain, higher brightness screen. This type
of analysis can be easily carried out rapidly for
any given set of criteria using only the graphical
data.
The particle densities required are governed
primarily by the thickness of the samples. The
thinner the sample, the higher the density of
scatterers required to maintain the same amount
of scattering.
Thickness and shape of the gain function are the
main parameters limiting resolution. We are
working toward an initial resolution of 10 lines/mm,
and the desired goal is 20 lines/mm with the MTF
.down only 10 per cent to .9. This will require
a very thin scattering layer which may possibly
have to be bonded to a thicker transparent sheet
for structural support. Initially in our
materials program, relatively thick samples will
be requested to facilitate handling and slabbing
into thinner sections.
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1-1 3. Specific Materials Requirements Based on our
Theoretical Studies
Specifically, we have already requested samples
Of glass-ceramic materials, Fotofor0, and
sintered glasses which have the properties listed
? in. Table II. The numbers on the left side of the
? Table II. Mat&tiais/Requirements
a = 2 a = 3 m = 4
fl
M/D .28 ? .42 p, .55 ?
fl
.8 8.9 x 1010
1.6 x 1010
5.2 x 109
:9 3.3 x 1011
5.8 x 1010
1.7 x 1010
r 1
1.3 2.9 x 1010
5.1 x 109
1.7 x 109
table are relative refractive indices between
the particle and the surrounding medium, those
across the top are the required diameters of the
particles, corresponding to values of a of 2, 3,
and.4 respectively, for .X = .65 microns. In
the body of the table are the required number
density of particles in number/cm3. The diameter
and the nuMber density are to be held to within
Li ?10 per cent of the values specified.
It is essential to know exactly the physical
f properties of the samples of materials if these
data are to be correlated with the theoretical
'71 work already completed. To aid in this, electron
Li photomicrographs will be made of each sample for
determining particle size, size distribution, and
the particle density.
It is hoped there will be enough glass from each
small melt to yield, after cutting, at least eight
r
pieces measuring 40 mm x 18 mm and 5 to 7 mm thick.
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Any two pieces cut from the same melt will be
expected to have identical properties. To
ensure the shortest turn around time from one
set of melts to another, at least one-half of
every melt will be directly forwarded to us for
preliminary optical evaluation. Detailed
evaluation will begin later, after electron
microscope data have been obtained and the
physical properties of the melt determined.
Thus, we have started the third phase of this
program, which is the evaluation of Corning Glass
Works' materials for applications in rear pro-
jection,screens.
B. Rayleigh Scattering
The mathematical formulations of Mie scattering theory,
although elegant, are correspondingly involved and
time consuming to carry out. Further, it is difficult/
if not impossible, to examine separate terms relating
to different parameters. However, when the size of
the particles are small compared to the wavelength of
illumination, their scattering properties can be
described by a much simpler theory first proposed by
Lord Rayleigh20.
1. Theory
Consider an incident electromagnetic wave perfectly
monochromatic and linearly polarized, with the
electric vector along the x axis, and moving in
the +z direction and is incident on a particle
at the origin, Figure 15. Let the amplitude be
unity and the phase angle be such that in complex
representation the field at the origin is
Ex =
-itut
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Figure 15. Coordinate System to Which the
Scattering Geometry is Referred
The result of the particles being subjected to
this field is that each of its elastically
bound electrons is set into sinusoidal oscill-
ation with frequency w, and with the same phase
angle. Since the particle is small compared
with the wavelength, the net scattered wave is
just that which would be radiated by a single
dipole oscillator' with some dipole moment P.
It is this property of the scattered wave,
guaranteed by the smallness of the particle
compared with the wavelength, that characterizes
Rayleigh scattering. Throughout this discussion,
it will be assumed that only scattering is
responsible for removal of light from, the incident,
collimated, unpolarized beam, i. e., no absorption
nor reflection will be considered.
The scattering cross section for these particles
is given as
r
L:\L _LI t1L-, 1-7
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?
in
,,/a, 4 2
A.
(52)
where 3 is the polarizability of the scattering
material. In general, 0 is a complex vector.
because of absorption and anisotropy of the
particles. This can be written
, 2. . 2 . 2 + + k 2 2 , 2
= .13xi
where i, j, and k are the direction cosines of the
incident electric field with respect to the three
main axes of the polarizability tensor.
Assuming independent spherical particles,
has been found to be 21
2 .6 M2 - 1,
=a
M2 +2
(53)
where a is the radius of the particle and M is the
index of refraction of the particles relative to
the surrounding supporting medium. M is real, only
when there is no absorption. The scattering cross
section for small spherical particles using (52)
and (53) is
2
128 175a6 M2 - 1
a s -
3 4 I 2 I
M + 2
( 5 4)
The angular intensity distribution of scattered
light is
(1 + cos2 e) 8 7 6 M2 - 1
4
I(e) - r2 ? a ? 1 ? Io (55)
4
M2 + 2
where r is the distance from the scattering center.
The gain function is, therefore,
Gain (e) = (1 + cos2 e) ? (56)
4
rk
rinT;NIT
t
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tI
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w F11,
-42
2. Feasibility of Using Rayleigh Scattering Materials
as Rear Projection Screens
We now wish to determine the feasibility of these
materials as rear projection screens using the
equationS given in the preceeding section. The
various terms will be studied to better understand
how each contributes to the overall properties of
Rayleigh scattering.
a. Dependence on the Relative Refractive Index M
Consider first the dependence of the scattering
function and scattering cross section on the
refractive index M
v
=
n"
(57)
where n and n' are the refractive indices of
the particles and medium respectively and are
assumed to be real. The function ?(M),
expresses this dependence, is
M2 - 1
T (
M2 + 1
2
which
(58)
The behavior of T(M), as a function of M, can
be seen from Figure 16. As M approaches
infinity, i. e., reflecting metallic spheres,
?(M) approaches unity. For practical purposes
.6 s M s 1.7. It seems pointless to consider
values of M less than .6 as this requires a
very high refractive index for the matrix
material, and a metallic matrix is implied for
M = 0. Therefore, to have as large a scattering
cross section as possible, M should be as far
from unity as possible. Clearly for M = 0 the
glass As "homogeneous" and transparent.
unfriEmDF-7717;\. rl ?
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, n(TH 'T
b. Wavelength Dependence
Consider next the influence of wavelength
on the relative size of the scattering
cross sections at two different wavelengths,
and the associated scattering function.
'Choosing xi = .45 microns, and X2 = .65
microns, we have as the ratio of scattering
cross sections and intensities of scattered
light
,O) a X 2
1 _ s _ (--) = 4.3
I(X.2,O) as2 X1
4
(59)
This means if we illuminate a screen composed
of Rayleigh scatterers with light from .45_
to .65 microns, there will be 4.3 times as much
light scattered at .45 microns as at .65 microns,
assuming only single scattering at microns.
Thus, the scattered light will have an excess
of blue light, while the specular component
will have an excess of red. On the other hand,
if we require all of the incident light at .65
microns to be singly scattered we must accept
mixed higher order scattering over the whole
spectral region. Much of the light at shorter
wavelengths has been scattered so much that, at
best, 50 per cent of it has been scattered in
the forward direction, and only a fraction of
this will come through the screen to the viewers
because of total internal reflection.
It is instructive to compute the scattering
coefficient K1 and K 2 for the two extreme
wavelengths, X1 and x2, which after the evaluation
of the constants in (54) simplifies to,
= 415 ?(1L)4 ?
xi
t 'r
CI 1
(60)
PT
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n
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,
(-1
r
r
FT
?
; L_I
FT
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-45-
The value of the refractive index term T(M),
was chosen as .1 from Figure 16, which
corresponds to M = 1.55. Thus, using a
particle radius of a = .02 microns, which
is near the upper limit of particle size for
'Rayleigh scattering at visual wavelengths,
gives
and
K1 = 1.62 x 10-3
K2 = 3.74 x 10-4
(61)
This is to say the effective cross sections
which produce scattering are about 1000 times
smaller than the geometrical cross section.
Therefore, large particle concentrations
(number/cm3) are required to sufficiently
diffuse the incident light. -
' One of the major disadvantages of Rayleigh
scattering is the strong wavelength dependence
-of the scattering function. The blue excess
in the scattered light can be corrected by ?
using a filter with a spectral transmittance
T(X), of
T(x) = KX4 (62)
If such a filter can be used, the screen will
have a maximum efficiency of 23 per cent,
assuming all the light passes through to the
viewers. This approach will serve to improve
the balance color, but efficency will be
severely reduced.
H
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Consider the projection screen consisting of
Rayleigh scatterers, Figure 17. Light
reaching an observer, 0', outside the solid
angle,-(1., will consist only of scattered
light and no specular component. This light
will contain an excess of blue which could be
balanced by using the spectral filter previously
described. Inside41.., most of the screen will
be seen by scattered light. Unfortunately, for
single scattering at .45 microns, an observer,
0, will be able to see through the screen at
wavelengths less than this and see the source
by the specular component which will have an
excess of red light. Thus, it seems impossible
to compensate simultaneously for the excess of
blue in the scattered component and the excess
of red in the specular component. Since it is
undesirable to have any specular transmission,
from efficiency and viewing considerations, one
might suggest increasing the scattering in the
,screen until all of the light is at least singly.
scattered. This approach is impractical because
of the low efficiencies.
SOCIlle.lt
Figure 17; Two Viewing Geometries, with
and without a Specular Component
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-47-
c. Angular Dependence
The angular dependence of the scattering
function given by (55) is valid only for
single scattering of unpolarized light.
Therefore, when a range of wavelengths is used
and mixed scattering occurs, one can expect
the shape of the scattering function to be
significantly different at different wave-
lengths. From the symmetry of the scattering
function, Figrure 18, it is clear that only
half of the incident light is scattered through
the material and the other half is back-
scattered toward the projector. Thus, under
the best possible conditions, i. e., monochro-
matic illumination and complete single scat-
tering, the efficiency of the material cannot
exceed .5. It is important to remember that
since the efficiency is based on scattered
light only, any specular transmission results
in a decrease in the efficiency.
Figure 18. The Normalized Polar and Rect-
angular Forms of the Scattering
Diagram for Rayleigh Scattering
from a Monochromatic Unpolarized
Beam
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-48-
After considering only total internal reflec-
tion, less than 19 per cent of the light
scattered comes through the screen to form
an image, and an equal amount is backscattered.
The fraction of this trapped exceeds 61 per
cent which degrades the contrast of the image
by a factor of 1.7.
d. Polarization Considerations
Another effect. of the angular scattering is
that the scattered light ?is polarized to a
degree depending on the angle 0. The frac-
tional polarization P(0) is given as
p(o) = sin2
1 + cos 20
(63)
and its behavior is shown in Figure 19. The
cos2 term, in the parentheses of Equation
(55), gives the relative intensity of the
scattered component whose electric vector lies
In the plane defined by the incident beam and
the observed scattered beam. The term corres-
ponding to the factor unity in the parentheses
refers to the scattered component whose electric
vector is perpendicular to the plane of
observation. When 0 = 90?, it is seen that
the scattered light is plane polarized with
its electric vector perpendicular to the incident
beam, a well-known result.
e. Conclusion
Rayleigh scattering theory has been considered
and the general scattering function investigated.
Separate terms in the scattering function were
considered individually and numerically evaluated.
to better understand how they contribute to the
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11,
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-50-
'scattering function. We have been able to
show theoretically tha, rear projection
screens made from Rayleigh scattering
materials are unsatisfactory for a number
of reasons. They are inefficient although
the scattering function is very broad and
uniform. Correspondingly, the resolution
of such screens is very low. The strong wave-
length dependence of the scattering function
and scattering cross section impose nearly .
impossible constraints which, when not met,
result in screens which have very poor Color
characteristics. Applications for these
? materials probably .lie only in low gain;
low resolution; monochromatic screens.
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fl
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7-1
isi,.D.J2 u!,-13,?;71
V. Corning Glass Works' Materials
Some effort has been directed toward other types of rear
projection screen materials which do not depend upon
volume scattering. .It is expected that these alternate
approaches will depend as strongly upon available Corning
Glass Works' technologies as upon specific materials.
Only those approaches which have been considered in some
detail are reported.
A. Hollow Fibers
We have been investigating the feasibility of using
hollow optical fibers with highly reflective coatings
as a rear vew projection screen material. Conventional,.
optical fibers consist of an inner glass core and a
surrounding outer cladding of a lower refractive index
material. The attenuation of light in ?a fiber is a.
complex phenomena, but for practical purposes the
internal losses are due to inherent properties of the
dielectric core and not to imperfect total internal
reflection.
A modified concept is proposed here. This proposes the
use of hollow tubes with highly reflective inside walls
where losses are now governed only by the reflective
properties of the coating and not by the loss tangent
of the core. These can be manufactured more easily
than the cladded solid core fibers, thereby making them
less expensive. This type of optical fiber is fabric-
ated by Corning (without reflective coatings) and is
illustrated in Figure 20. Such hollow tubes have been
fabricated down to 10 microns in inside diameter with
good control of open area to wall area. In the 10-20
micron diameter region this ratio can be 'as much as 70/30.
At smaller diameters, wall thickness remains constant,
but the hole gets smaller and smaller until it becomes
?a solid fiber. The two major problems associated with
f1:1(7,nLr=r-i---??
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