U.S. patent number RE29,091 [Application Number 05/607,645] was granted by the patent office on 1976-12-28 for radiation-redistributive devices.
This patent grant is currently assigned to Eastman Kodak Company. Invention is credited to James J. De Palma, Harold F. Langworthy.
United States Patent |
RE29,091 |
De Palma , et al. |
December 28, 1976 |
Radiation-redistributive devices
Abstract
Devices for redistributing incident radiation in a prescribed
manner. Such devices comprise a multitude of contiguous optical
microelements, each of such microelements being contoured and
oriented to redistribute incident radiation, emanating from an
intended irradiating source, only throughout an angular field just
large enough to encompass a predefined region wherein the
redistributed radiation has particular utility. Moreover, the
contour and orientation of each microelement is such as to produce
substantially uniform radiance throughout such predefined region of
utility, and to redirect extraneous or undesirable radiation
incident thereon away from said predefined region. The
radiation-redistributive devices of the invention are particularly
useful as front or rear projection screens, lighting reflectors or
refractors, illumination aids for photographic prints, traffic
signs, advertisements, etc.
Inventors: |
De Palma; James J. (Pittsford,
NY), Langworthy; Harold F. (Rochester, NY) |
Assignee: |
Eastman Kodak Company
(Rochester, NY)
|
Family
ID: |
26901945 |
Appl.
No.: |
05/607,645 |
Filed: |
August 25, 1975 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
Reissue of: |
207082 |
Dec 13, 1971 |
03754813 |
Aug 28, 1973 |
|
|
Current U.S.
Class: |
359/454; 359/457;
359/451; 359/459 |
Current CPC
Class: |
G03B
21/602 (20130101); G03B 21/625 (20130101) |
Current International
Class: |
G03B
21/62 (20060101); G03B 21/60 (20060101); G03B
021/60 () |
Field of
Search: |
;350/117,126-129,125 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Wintercorn; Richard A.
Attorney, Agent or Firm: Husser; John D.
Claims
We claim:
1. A radiation-redistributive device having a surface defining a
plurality of parallel grooves, each of said grooves having a depth
which undulates along the groove length to define a row of
alternately concave and convex optical microelements, each of said
microelements being contoured to redistribute incident radiation in
such a manner as to produce substantially uniform radiance
throughout predefined vertical and horizontal field angles and
being disposed such that a plane which bisects one of its field
angles and which extends .[.perpendicular.]. .Iadd.transverse
.Iaddend.to the groove length intersects with similarly defined
planes of all other microelements substantially along a first line
which extends parallel to said surface and is in a plane
perpendicular to the groove length.
2. The invention according to claim 1 wherein said surface is
cylindrically curved about said first line.
3. The invention according to claim 1 wherein said grooves are
rectilinear.
4. The invention according to claim 3 wherein said grooves are
contiguously arranged to form cusp lines at the juncture of
adjacent grooves, said cusp lines undulating in a plane
perpendicular to said surface and extending substantially parallel
to the groove length.
5. The invention according to claim 1 wherein each of said
microelements is disposed such that the plane which bisects the
other of its field angles and which extends parallel to the groove
length intersects with similarly defined planes of all
microelements substantially along a second line which
perpendicularly intersects said first line and is in a plane
parallel to the screen surface.
6. The invention according to claim 5 wherein said grooves are
rectilinear.
7. The invention according to claim 5 wherein said surface is
cylindrically curved about said second line.
8. The invention according to claim 5 wherein said surface is
substantially reflective so as to reflect radiation emanating from
a source on one side of the screen to a field situated on the same
side of the screen as the source.
9. The invention according to claim 5 wherein the screen, including
said surface, is substantially transparent so as to refract
radiation emanating from a source on one side of the screen to a
field situated on the opposite side of the screen from the
source.
10. The invention according to claim 5 wherein said surface is
spherically curved about the intersection of said first and second
lines.
11. A projection screen for presenting a predefined field of
observation an image projected thereon by a projecting apparatus,
said screen having a surface defining a plurality of contiguous
grooves, each of said grooves having a depth which periodically
undulates along the groove length and thereby defines a row of
alternately concave and convex optical microelements, each of said
grooves having a transverse cross section which is substantially
defined by at least a segment of a first curve ##EQU3## where w and
u are the coordinates of said curve, w being measured in a
direction parallel to the path of incident image light, u being
measured in a direction perpendicular to w and in the plane of the
cross section; and n is the refractive index of the microelement (n
being -1 when the microelement is reflective); and w has a value
with the limits:
-.ltoreq. w.ltoreq.-cos.sup.2 (B + .theta.'), when g(w;n) is
positive and the microelement is refractive;
-1.ltoreq.w.ltoreq.-cos.sup.2 (A - .theta.'), when g(w;n) is
negative and the microelement is refractive;
-1.ltoreq.w.ltoreq.-cos.sup.2 (A - .theta.), when g(w;n) is
positive and the microelement is reflective; and
-1.ltoreq.w.ltoreq.-cos.sup.2 (B + .theta.), when g(w;n) is
negative and the microelement is reflective;
where .theta. is the projection in the u - w plane of the angle
formed by a line extending parallel to incident image light, and
the normal to the screen surface; n = sin .theta./sin .theta.'; and
A and B are the audience angles, measured from a normal to the
screen surface and in the plane of the cross section, through which
incident image light must be distributed to just encompass said
field of observation.
12. The invention according to claim 11 wherein each of said
microelements has a longitudinal cross section, taken in a plane
parallel to the groove length and normal to said surface,
substantially defined by at least a segment of said first curve,
and A and B and u are measured in the plane of said longitudinal
cross section, and by at least a segment of a second curve ##EQU4##
where w has a value within the following limits: cos.sup.2 (A -
.theta.').ltoreq. w.ltoreq. 1, when f(w;n) is positive and the
microelement is refractive;
cos.sup. 2 (B + .theta.').ltoreq.w.ltoreq. 1, when f(w;n) is
negative and the microelement is refractive;
cos.sup.2 (B + .theta.).ltoreq.w.ltoreq. 1, when f(w;n) is positive
and the microelement is reflective;
cos.sup.2 (A - .theta.).ltoreq.w.ltoreq. 1 when f(w;n) is negative
and the microelement is reflective.
13. A rear projection screen for presenting an image projected
thereon to a predefined audience space, said screen comprising a
sheet of substantially transparent material having a first surface
comprising means defining a plurality of contiguous grooves each of
said grooves having a transverse cross section defined by at least
a segment of the curve ##EQU5## where w and u are the curve
coordinates, w being measured in a direction parallel to the path
of incident image light, u being measured in a direction
perpendicular to w and in the plane of the cross section; n is the
refractive index of said material, and w has a value within the
limits
-.ltoreq. w.ltoreq. -cos.sup.2 (B + .theta.'), when g(w;n) is
positive, and
-1.ltoreq.w.ltoreq. -cos.sup.2 (A - .theta.'), when g(w;n) is
negative;
where A and B are the angles, measured from the normal to said
first surface in the plane of the cross section, through which each
groove redistributes image light to just encompass said audience
space, and sin .theta.' = sin .theta./n, where .theta. is the
projection in the u - w plane of the angle formed by the line
extending parallel to incident image light and the normal to said
first surface.
14. The invention according to claim 13 wherein said first surface
is substantially planar, and said sheet of material has a second
surface, spaced from and extending substantially parallel to said
first surface, comprising means defining a Fresnel-type lens.
15. The invention according to claim 14 wherein each of said
grooves has a depth which periodically undulates along the groove
length to define a row of alternately concave and convex optical
microelements.
16. A rear projection screen for presenting an image projected
thereon to a predefined audience space, said screen comprising a
sheet of substantially transparent material having a first surface
comprising means defining a plurality of contiguous grooves, each
of said grooves having a transverse cross section defined by at
least a segment of the curve ##EQU6## where w and u are the curve
coordinates, w being measured in a direction parallel to the path
of incident image light and u being measured in a direction
perpendicular to w in the plane of the cross section; n is the
refractive index of said material, an w has a value within the
following limits;
cos.sup.2 (A - .theta.').ltoreq.w.ltoreq.1, when f(w;n) is
positive; and
cos.sup.2 (B + .theta.').ltoreq.w.ltoreq. 1, when f(w;n) is
negative;
where A and B are the angles, measured from the normal to said
first surface in the plane of the cross section, through which each
groove redistributes incident image light to just encompass said
audience space, and sin .theta.' = sin .theta./n, where .theta. is
the projection in the u - w plane of the angle formed by the line
extending parallel to incident image light and the normal to said
first surface.
17. The invention according to claim 16 wherein said first surface
is substantially planar, and said sheet of material has a second
surface, spaced from and extending substantially parallel to said
first surface, comprising means defining a Fresnel-type lens.
18. The invention according to claim 17 wherein each of said
grooves has a depth which periodically undulates along the groove
length to define a row of alternately concave and convex optical
microelements.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
References made to the commonly assigned copending application Ser.
No. 207,334 entitled "Method and Apparatus for Fabricating
Radiation-Redistributive Devices," filed concurrently herewith in
the names of Robert N. Wolfe, et al..Iadd., now U.S. Pat. No.
3,765,281 issued Oct. 16, 1973. .Iaddend.
BACKGROUND OF THE INVENTION
In general, the present invention relates to improvements in
projection screens and other radiation-redistributive devices, such
as lighting reflectors and refractors, illumination aids for
photographic prints, traffic signs, advertisements, etc.
Heretofore, a wide variety of radiation-redistributive devices
.[.has.]. .Iadd.have .Iaddend.been proposed to achieve such
features as a definitely controllable field through which incident
radiation is redistributed, uniform radiance throughout such field,
high efficiency due to a definite separation of the field of
redistribution from the environmental field and due to minimum
absorption losses at the redistributing surface of such devices,
and a favorable rejection of radiation impinging on the device from
sources other than those intended for irradiating the device.
In attempting to provide radiation-redistributive devices having
one or more of the features mentioned above, two approaches have
been taken. One approach is purely empirical in nature and involves
the evaluation of commercially available, inherently reflective,
refractive, or diffuse materials to determine the utility thereof
for a particular application. Exemplary of the projection screens
developed through such an empirical approach are the volume and
surface diffuser-type rear projection screens, and the aluminum
foil front projection screens disclosed in the commonly assigned
U.S. Pat. No. 3,408,132, high reflectance projection screens
commercially available under the trademark Kodak Ektalite
Projection Screen.
The second approach toward the provision of improved
radiation-redistributive devices is analytical in nature, involving
the derivation of mathematical expressions to define the contour
which each elemental area of the redistributing surface must
possess in order to achieve a desired redistribution of incident
radiation, and the fabrication of an optical surfaces in accordance
with such expressions. Lenticular projection screens and general
lighting refractors are exemplary of such an analytical
approach.
Notwithstanding the .[.approach.]. .Iadd.two different approaches
.Iaddend.taken, radiation-redistributive devices heretofore
proposed have not been totally satisfactory in all respects.
Usually, certain desirable features are severely compromised to
achieve other features which are deemed more desirable for a
particular application. For instance, in the case of projection
screens, several screens have been proposed having reflecting or
refracting surfaces which, at least in theory, are capable of
redistributing incident-image light in such a manner that the
luminance of every elemental area on the screen surface is
substantially constant throughout a predefined angular field of
observation. Such screens, however, often suffer the disadvantages
of being inefficient or wasteful of available image light and of
being difficult, if not, for all practical purposes, totally
impractical to manufacture in large quantities. See, for instance,
the screens disclosed in U.S. Pat. No. 3,257,900 and U.S. Pat. No.
2,870,673. On the other hand, projection screens having highly
efficient and readily manufacturable surfaces are often incapable
of distributing incident image light uniformly and in a controlled
manner, such surfaces commonly exhibiting "hot spots" or regions of
non-uniform luminance.
SUMMARY OF THE INVENTION
Accordingly, one of the objects of the present invention is to
provide a radiation-redistributive device which not only makes
maximum utilization of radiation emanating from an intended
irradiating source by redistributing substantially all of such
radiation only throughout a region wherein the redistributed
radiation has utility, but also redistributes incident radiation in
such a manner that substantially uniform radiance is produced
throughout such region of utility.
Another object of the invention is to provide a
radiation-redistributive device of the above type which, upon being
irradiated by extraneous or nondesirable radiation emanating from a
source other than that intended for irradiating the device,
redistributes or redirects such nondesirable radiation away from
said region of utility, thereby maximizing the signal-to-noise
ratio for any environmental light condition.
A further object of this inventon is to provide
radiation-redistributive devices of the above type which are
readily manufacturable in large quantities.
In accordance with the present invention, the above objects are
achieved by the provision of a radiation-redistributive device
which comprises a plurality of contiguous optical microelements,
each being contoured substantially in accordance with a
mathematical expression requiring that all radiation incident
thereon be redistributed therefrom such as to produce uniform
radiance throughout a predefined angular field and substantially
zero radiance outside such field. Preferably, the
radiation-redistributing surface of such device is planar and each
of said microelements comprising said surface is uniquely contoured
and arranged, depending upon its respective position on the
surface, to redistribute incident radiation only throughout a solid
angle just large enough to encompass a region which is intended to
receive radiation from said device. Alternately, the redistributing
surface of the device is substantially spherically or cylindrically
curved and all of the microelements contoured substantially alike,
the screen curvature assisting in redistributing incident radiation
into the desired region.
In addition to the objects of the invention set forth herein above,
other objects and advantages of the invention will become apparent
to those skilled in the art from the ensuing description, reference
being made to the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1 and 2 are, respectively, diagrammatical representations of
rear and front projection systems, respectively, illustrating the
radiation-redistributing properties of rear and front projection
screens embodying the invention;
FIG. 3 shows the ideal radiance curve for a
radiation-redistributive device;
FIGS. 4-6 illustrate a reflective radiation-redistributive device,
structured in accordance with a preferred embodiment of the
invention, in plan view and sections taken along lines 5--5 and
6--6, respectively;
FIG. 7 is a side elevational view of apparatus used in fabricating
the radiation-redistributive devices of the invention, such
apparatus including a stereo sound-recording head;
FIG. 8 is a constructional diagram of the mechanism used to drive
the cutting stylus of the sound recording head illustrated in FIG.
7;
FIG. 9 is a side elevational view of the cutting stylus and support
therefor;
FIG. 10 is a front elevation of the cutting stylus illustrating the
cutting profile thereof;
FIG. 11 is a perspective view of apparatus for translating a master
from which the radiation-redistributive devices can be subsequently
replicated relative to the cutting apparatus illustrated in FIG.
7;
FIG. 12 illustrates the manner in which the waveform applied to the
cutting stylus differs from the stylus motion produced thereby;
FIG. 13 is an electrical schematic of circuitry for driving the
cutting stylus to produce one side of the radiation-redistributive
surface illustrated in FIGS. 4-6;
FIG. 14 illustrates the additional logic circuitry required to
modify the circuit of FIG. 13 so as to produce the entire surface
illustrated in FIGS. 4-6;
FIG. 15 illustrates the manner in which the positive-going ramp of
a sawtooth waveform is shaped to a desired stylus-driving
waveform;
FIG. 16 illustrates the input signal to the cutting stylus when in
a cutting position displaced from center of the master;
FIGS. 17-19 illustrate a radiation-redistributive device structured
in accordance with another preferred embodiment of the invention,
in plan view and in section taken along lines 18--18 and 19--19,
respectively; and
FIGS. 18a and 19a illustrate alternative cross sections for the
devices illustrated in FIG. 17.
FIG. 20 is an electrical schematic of circuitry adapted to drive
the cutting stylus in a manner such as to produce a master from
which radiation-redistributive devices, such as that illustrated in
FIGS. 17-19, can be fabricated.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
As indicated above, the radiation-redistributive devices of the
invention have utility in any situation wherein it is desirable or
necessary to precisely control the redistribution or redirection of
radiant energy from a surface which is irradiated by a source which
occupies a predictable position relative to such surface. Such
devices have been found to have particular utility as projection
screens, both of the front and rear projection variety, being
capable of presenting to a precisely definable audience area or
field of observation a projected image of substantially uniform
luminance, regardless of the viewing position within such audience
area. Accordingly, projection screens represent a preferred
embodiment of the invention and the invention will be described
hereinafter with particular reference thereto; however, it should
be borne in mind that projection screens are merely exemplary of
the uses for the invention, and all such uses, including those
previously mentioned, are considered within the spirit and scope of
the invention.
The radiation-redistributing surface of the invention devices was
derived mathematically based upon the theorems of geometrical
optics and upon the following postulates which are believed to
define a radiation-redistribution device having ideal
radiation-redistributive properties:
I. Every elemental area on the redistributing surface of the device
shall redistribute all radiation incident thereon from an intended
irradiating source throughout a solid angle just large enough to
encompass a predefined field wherein the redistributed radiation
has utility. (A radiation-redistributing surface satisfying this
postulate is one of maximum efficiency, utilizing all available
radiation).
II. Every elemental area on the radiation-redistributing surface of
the device shall redistribute incident radiation in such a manner
that the radiance of every such area will be constant, no matter
where measured within the solid angle through which radiation is
redistributed. (With respect to projection screens, a surface
satisfying this postulate is one which will present an image of
uniform brightness everywhere within the intended audience area,
and no image whatsoever outside such audience area).
In FIGS. 1 and 2, projection systems comprising projectors P and
rear and front projection screens S and S', respectively, are shown
in two dimensions. Image light or flux emanating from the projector
is focused upon the surfaces 10 of the projection screens, rear
projection screen S being fabricated from a transparent material.
As shown, each surface comprises a plurality of contoured optical
microelements 11, shown, for purposes of illustration, greatly
magnified and of concave shape. Actually, each microelement is
preferably of a size so as to be unresolvable by the closest
intended viewer and can be either concave or convex in shape. The
contour of each microelement is such that image flux incident
thereon at an angle .theta., measured from a line connecting the
projector lens 15 to the screen center C, is redistributed
throughout a viewing angle H which is just large enough to
encompass the predefined audience volume V. Viewing angle H
consists of left and right viewing angles A and B, respectively,
each being measured from a normal N to the screen surface. All
angles are considered positive when measured in a counterclockwise
direction from a normal to the screen surface. Because the size of
the microelement is quite small relative to the distance separating
the microelement from the projector, all light rays striking a
particular microelement are assumed to be parallel.
It can be shown mathematically that to satisfy Postulates I and II
above wherein the intended audience volume is bounded in either a
transverse or longitudinal plane by audience angles A and B, every
convex optical microelement comprising the radiation-redistributing
surface must have transverse and longitudinal cross sections
defined by at least a segment of the curve ##EQU1## where n is the
refractive index of the microelement (n being -1 when the
microelement is reflective); u and w are the microelement
coordinates, w being measured in a direction parallel to the path
of the rays of radiation incident on the microelement and u being
measured in the plane of the cross section, perpendicular to w; and
w has a value within the following limits;
cos.sup.2 (A - .theta.').ltoreq.w.ltoreq. 1, when f(w;n) is
positive and the microelement refractive;
cos.sup.2 (B + .theta.'j.ltoreq. w.ltoreq. 1, when f(w;n) is
negative and and microelement refractive;
cos.sup.2 (B + .theta.).ltoreq. w.ltoreq. 1, when f(w;n) is
positive and the microelement reflective;
cos.sup.2 (A - .theta.).ltoreq.w.ltoreq.1, when f(w;n) is negative
and the microelement reflective;
where .theta. is the projection in the u - w plane of the angles
formed by a line connecting the microelement and projector, and the
normal to the screen surface, and .[.n surface, sin .theta./sin
.theta.'.]. .Iadd..theta.' = sin.sup..sup.-1 [sin
.theta./n].Iaddend..
Similarly, it can be shown that every concave optical microelement
comprising the projection screen surface must have transverse and
longitudinal cross sections defined by at least a portion of the
curve ##EQU2## wherein w has a value within the following limits:
-1 .ltoreq.w.ltoreq.-cos.sup.2 (B + .theta.'), when g(w;n) is
positive and the microelement is refractive;
-1 .ltoreq.w.ltoreq.-cos.sup.2 (A - .theta.'), when g(w;n) is
negative and the microelement is refractive;
-1.ltoreq.w.ltoreq.-cos.sup.2 (A - .theta.), when g(w;n) is
positive and the microelement is reflective; and
-1.ltoreq.w.ltoreq.-cos.sup.2 (B + .theta.), when g(w;n) is
negative and the microelement is reflective
Equations (1) and (2) above define the contour required for a
microelement to provide an ideal goniphotometric response (i.e.,
constant radiance, between horizontal audience angles A and B, and
vertical audience angles A' and B'. (See FIG. 3). As is apparent
from these equations, screen performance is independent of the size
and sense (concave or convex) of each microelement relative to
adjacent ones. Thus, the microelements could be of random sizes and
randomly sensed over the entire screen surface so long as the
contours defined by Equations (1) and/or (2) are substantially met,
such contours being dependent only on the angle at which incident
light impinges the microelement surface, the horizontal and
vertical audience angles through which such light must be
distributed to encompass the intended audience area, and, in the
case of rear projection screens, the refractive index of the
material from which the microelements are formed. However, to
facilitate the manufacture of such screen, it is preferred that
microelements be substantially the same in size and be arranged in
contiguous linear rows, each microelement having a transverse cross
section which is everywhere curved in the same sense, preferably
concave, and a longitudinal cross section which is shaped in an
opposite sense from that of adjacent microelements in the same row.
Thus, the preferred longitudinal cross section of each row of
microelements is one which undulates from concave to convex, etc.
Such a surface is illustrated in FIGS. 4 through 6.
As shown in FIGS. 4 through 6, a screen structured in accordance
with the present invention comprises a surface which defines a
plurality of contiguous linear grooves 16 shown running in a
vertical direction from the top to the bottom edges of the screens.
Where the edges of each groove intersect with those of adjacent
grooves, cusp lines 17 are formed. The transverse cross section of
each groove, as depicted in FIG. 5, is everywhere concave and is
defined by Equation (2) above. The depth profile or longitudinal
cross section of each groove, as illustrated in FIG. 6,
alternatively varies or undulates in shape from convex to concave,
the convex and concave portions being defined by Equations (1) and
(2), respectively. Thus, for each full wavelength of depth
undulation, two microelements are formed, one concave and one
convex. The longitudinal boundaries of each microelement are the
lines 18 along which the sense of the depth profile changes from
concave to convex, or vice versa. The lateral boundaries of each
microelement are, of course, provided by cusp lines 17. As best
shown in the sectional views of FIGS. 5 and 6, the microelements
are gradually "tilted" as their respective displacement from screen
center C increases. The degree of such tilt is determined by the
size and shape of the viewing area and, hence, the values of
viewing angles A and B. The sense of such tilt (i.e., toward or
away from the screen center) depends on whether the screen is
reflective or refractive, reflective microelements being tilted
toward the screen center, as shown in FIGS. 5a, 5c, 6a, and 6c, and
refractive microelements being tilted away from the screen center.
Generally, the microelements are oriented with respect to each
other such that the lines, formed by intersecting planes which
bisect the horizontal and vertical angles through which each
element distributes image light to the .[.the.]. audience,
substantially intersect at a common point in the audience area.
To fabricate the radiation-redistributive devices of the invention,
it has been found that various equipment and techniques
conventionally employed in the sound recording industry can be used
directly or in a modified form. In FIG. 7, apparatus used for
cutting the radiation-redistributive microelements is illustrated
in a side elevational view, being shown in a cutting position
relative to a blank workpiece 20 wherein microelements are to be
formed. While the microelements could be cut directly in any
readily workable material which itself could be used as the
radiation-redistributive device, the preferred method of
manufacture comprises the fabrication of a master in some workable
material, such as acetate or wax, from which a negative matrix or
press tool of correct contour can be subsequently made. The
negative matrix can then be used to produce a multitude of positive
radiation-redistributive devices by such well-known economical
duplicating processes as stamping or embossing. Preferred methods
of replicating radiation-redistributive devices from masters are
described subsequently herein.
As shown in FIG. 7, the cutting apparatus comprises a conventional
stereo sound recording head 30 which includes a cutting stylus S.
While a monaural sound recording head could be used, a stereo head
is preferred due to the high quality of conventional stereo heads
and the auxiliary equipment available for such stereo heads. As in
all sound recordings heads, the cutting position of the stylus is
determined by the waveform of an electrical signal applied to the
recording head, such as through input cables 31. The recording head
is mounted on a milling machine tool holder 32 by a cylindrical
fitting 33. Means are provided for controlling the vertical
position of fitting 33 in the tool holder 32 so as to provide a
coarse, vertical adjustment of the recording head 30 above the
workpiece. The workpiece may comprise, for instance, an aluminum
plate 36 having an acetate coating 37, the thickness of which is
sufficient to receive the contours of the microelements being cut.
Recording head 30 comprises a cutting assembly 40 having a
horizontally extending support arm 41 which is slidably mounted on
precision ways disposed in a saddle 42. By this arrangement, the
horizontal position of cutting assembly 40 can be varied. Set
screws 43a and 43b serve to lock arm 41 in a desired horizontal
position. Saddle 42 is pivotally mounted about pin 44 disposed on
recording head 30 so that the cutting stylus S, which forms a part
of cutting assembly 40, can be moved into engagement with coating
37. The rotational movement of a cam 46 serves to raise and lower
the stylus relative to the upper surface of coating 37 by
contacting an arm 47 which is rigidly coupled with saddle 42. The
downward force applied to the cutting assembly is controlled by
screw 48 which serves to adjust the tension in spring 49. The
precise depth of cut is controlled by adjustment screw 50 which
varies the vertical distance of the stylus tip from a small glass
ball follower 51 which rides on the uncut surface of coating 37 a
short, horizontal distance away from the stylus.
A sound recording head which has been found particularly well
adapted for cutting projection screen masters is the Westrex
Corporation, Model 3D Stereo Disc. As illustrated in FIG. 8 wherein
a simplified constructional diagram of the mechanism which controls
stylus movement is shown, each recording channel of the stereo
recording head contains a magnetic coil form assembly 60, each of
which contains a driving coil 62 located in separate pole pieces 64
and 65 which are attached to a single magnet 66.
The coil assmeblies are attached to the stylus holder through links
68 which are stiff longitudinally, but flexible laterally. These
links are braced in the center to prevent excessive lateral
compliance. This structure results in a stiff, forward driving
system with a high compliance in the lateral direction.
The supporting member for the stylus is shown in FIG. 9. The use of
a cantilever spring 70 permits the stylus to present a uniform
impedance to complex motions in any direction in the vertical plane
perpendicular to the drawing.
The cutting tip 72 of stylus S is preferably fabricated from
sapphire or diamond, and is heated by heating coil 73 to a
temperature such as to soften the acetate surface of the workpiece.
If the surface described by the above equations were to be produced
exactly, it would be necessary to use a stylus having a different
cutting profile for each groove cut. However, it has been found
that when the intended audience area can be encompassed by audience
angles of less than approximately .+-.40 degrees measured from the
normal, the ideal screen surface can be satisfactorily approximated
by using a single cutting stylus having a cutting profile defined
by Equation (1) at .theta. = 0, and by tilting the stylus axis
during the cutting operation so as always to be parallel to the
plane which bisects the audience angle through which the groove
being cut must distribute image flux to encompass the intended
viewing area. The required curve is illustrated by the cutting
profile of the stylus cutting tip 72 in FIG. 10, such curve being
somewhat flattened relative to a half sinusoid.
In fabricating projection screen masters by use of the apparatus
described above, the workpiece is moved relative to the heated
cutting stylus in a series of equally spaced, parallel traverses.
At the same time, the cutting position of the stylus is
electronically varied relative to the workpiece surface to produce
the desired longitudinal cross section or depth profile. Apparatus
for moving the workpiece relative to the stylus is depicted in FIG.
11. As shown, such apparatus comprises a table 80 for supporting
the workpiece during the cutting operation. Table 80 is preferably
fabricated from a non-magnetic metal, such as aluminum, so as not
to interfere with the magnetic cutting assembly 40. In the upper
surface of table 80, a circular groove 85 is provided. At the base
of groove 85 is an opening (not shown) which communicates with a
nozzle 86 located on the edge of the table. Attached to nozzle 86
via hose 87 is a vacuum source (not shown). By this arrangement,
the workpiece is securely fastened to the surface of table 80 by a
vacuum coupling. Table 80 is mechanically secured to a movable
workbed 88 comprising the x-y table 89 of a milling machine.
Workbed 88 is movable in the x direction and its position is
controlled with precision by a conventional stepping motor 90 which
acts through lead screw 91. Workbed 88 itself rides atop a carriage
93, also forming a part of the x-y table of the milling machine.
Carriage 93 is movable in the y direction by a hydraulic pneumatic
motor 95 which precisely controls the rate which the table moves
via piston rod 96.
To fabricate projection screen masters having transverse and
longitudinal cross sections such as depicted in FIGS. 5 and 6,
respectively, it is necessary to drive the cutting stylus with a
signal, the waveform of which varies in accordance with the
y-position of the stylus on the screen blank surface. Moreover, as
mentioned above, it is also necessary to vary the angle at which
the stylus contacts the screen blank in accordance with the
x-position of the stylus on the workpiece surface.
To maintain the proper orientation between the cutting stylus and
the workpiece during movement of the workpiece in the x direction,
the milling machine tool holder is motorized so as to be capable of
tilting the recording head in the x-z plane in accordance with an
electrical input signal. The x-z position of the stylus is changed
after each groove is cut so that at all times during the cutting
operation the angle t between the longitudinal axis of the stylus
and the work surface is:
where x is measured from the workpiece center, and p is the
projection in the x-z plane of the distance from the workpiece,
center to the line at which the planes which bisect the requisite
audience angles of the cut grooves substantially intersect. The
motorized tool holder of the milling machine is controlled by the
output of stepping motor 90.
To move the cutting stylus in a vertical plane and at a rate which,
when the workpiece is moved at a constant rate relative thereto,
results in the longitudinal cross section or depth profile desired,
the same signal must be applied, 180.degree. out of phase, to both
drive coils 62. Moreover, since the stylus is not mounted for pure
vertical movement, but rather for pivotal movement on the
cantilever spring 70, so as to traverse an arcuate path as shown in
phantom lines, it is necessary to drive the stylus with a somewhat
different waveform than that which corresponds to the longitudinal
cross section desired. Referring to FIG. 12, when a waveform 101 is
applied to the cutting stylus, the resulting groove has a depth
profile as shown by the asymmetrical waveform 102. To compensate
for the asymmetry, it is necessary to drive the cutting stylus with
a counterbalancing asymmetrical waveform 103 which the arcuate
stylus movement converts to the depth profile desired (e.g.,
waveform 101). It is interesting to note that in the sound
recording art, such asymmetry is automatically compensated for
during playback by the pickup stylus, which is also pivotally
mounted and moves along an arcuate path similar to that along which
the stylus which cut the original master moved. In achieving a
desired profile in projection screens, however, such asymmetry must
be compensated for by circuitry for modifying the desired waveform
accordingly.
Circuitry for driving the cutting stylus to produce a depth profile
such as illustrated in FIG. 5 is illustrated in FIGS. 13 and 14. To
facilitate an understanding of the circuitry, only that portion
which is used to cut half of the screen master, either the upper or
lower half, is initially described. The additional logic circuits
required to cut the entire screen surface are illustrated in FIG.
14.
In FIG. 13, circuitry is disclosed for generating the electrical
waveform whereby the cutting stylus can be modulated to produce
microelements having depth profiles similar to those illustrated in
FIGS. 5a and 5b. It has been found that the required electrical
waveform can be achieved by adding a sawtooth waveform, in varying
amounts depending upon the y-position of the cutting stylus, to the
asymmetrical waveform required for producing the desired depth
profile at the screen center (y = 0). To generate the necessary
sawtooth waveform, a sawtooth generator 130 is provided, such
generator comprising a flip-flop 131, a limit detector 132,
resistors R.sub.1 and R.sub.2, diode D1, capacitor C1 and
operational amplifier A1. Amplifier A1 is connected as an
integrator to give a linear ramp while the voltage at q, V.sub.q,
is constant. When V.sub.q is negative, the ramp output V.sub.s of
the sawtooth generator is positive-going. When V.sub.s exceeds the
positive threshold of limit detector 132, flip-flop 131 is switched
to make V.sub.q positive, at which time V.sub.s becomes
negative-going. When V.sub.s reaches a negative limit, the
flip-flop is again switched, to make V.sub.q negative again.
Operational amplifier A1 preferably has complementary outputs, and
the limit detector 132 acts by detecting the negative limit of
first one output and then the other. The slopes of the positive-
and negative-going ramps of the sawtooth are controlled by diode D1
and resistors R1 and R2, the latter being variable. Diode D1 is
non-conducting when V.sub.q is negative, and conducts only when
V.sub.q is positive. Therefore, the positive-going ramp is slower
than the negative-going ramp because the slope of the former is
determined by the current flowing through resistor R1 only, whereas
the slope of the latter is determined by the current flowing
through both resistors R1 and R2. By varying the value of resistor
R2, the slope of the negative-going ramp can be varied.
The sawtooth output of generator 130 is then fed through a
non-linear shaping circuit 140 which, as shown in FIG. 15, acts to
convert the linear ramp 141 to the asymmetrical waveform 142
required to drive the cutting stylus to achieve the desired shape
of the microelements at the screen center. To prevent that portion
of the shaping circuit output which occurs during the flyback
(fast-sloped negative-going ramp) of the sawtooth from being
applied to the cutting stylus, a blanking gate 143 is provided
which transmits the input signal from the shaping circuit only when
V.sub.q is negative (i.e., during the slow ramp). The output of the
shaping circuit 140 produces a depth profile for the screen
elements at y = 0. To produce the required depth profile as the
y-position of the cutting stylus gradually increases, it is
necessary to gradually "tilt" the y = 0 depth profile. Such gradual
tilting is accomplished by gradually adding, as the y-position of
the cutting stylus gradually increases, the sawtooth waveform
V.sub.s to the output of the shaping circuit 140. Such addition is
accomplished by operational amplifier A2. To vary the contribution
of the sawtooth waveform, resistor R3 is mechanically varied by the
y-position of the milling machine carriage. In FIG. 16, the output
f of the amplifier A2 is illustrated when the cutting stylus is in
a position displaced along the y axis from screen center.
To provide an electrical waveform whereby the cutting stylus can be
modulated in such a manner as to properly vary the groove depth on
both sides of the screen center, it is necessary to provide
circuitry for interchanging the direction of the fast and slow
slopes of the sawtooth (i.e., change the sense of the sawtooth) as
the cutting stylus passes through the center of the screen.
Moreover, it is necessry to switch the shape-blanking so that gate
143 operates during the fast-sloped portion of the sawtooth,
whether positive or negative-going. The required circuitry is
illustrated in FIG. 14. To switch the sense of the sawtooth at y =
0, the fast-sloped diode D1 of FIG. 13 is replaced by an "exclusive
OR" gate 150, the output of which is controlled by a flip-flop 151.
The output of flip-flop 151 is controlled by a switch on the
milling machine carriage, switching from one state to another as
the screen center (y = 0) passes the cutting stylus. To properly
cut both sides of the screen surface, it cut. necessary to provide
an additional shaping circuit 152 since the asymmetry caused by the
arcuate movement of the cutting stylus does not depend on the
particular portion of the screen being cut. The output of the
proper shaping circuit is supplied to amplifier A2, during the slow
ramp portion of the output of the sawtooth generator, through
blanking gates 143 and 153 which are controlled respectively by
NAND gate 155 and OR gate 156.
To initiate the cutting operation, a start button is pressed which
pivots the cutting assembly 40 about pin 44 into a cutting
position, causes the hydraulic-pneumatic motor 95 to move the
milling machine carriage in the y direction and causes the
above-described electronic circuitry to drive the cutting stylus
according to the waveform of the electrical signal applied thereto.
After cutting a groove of predetermined length, a microswitch (not
shown) is actuated by carriage 93 which serves to stop pneumatic
motor 95, activate a solenoid which moves cam 46 of the recording
head clockwise into a position to pivot the cutting assembly into
an inoperative position, and actuate stepping motor 90 so as to
move workbed 88 a predetermined distance in the x direction. The
microswitch also returns the milling machine carriage to its
starting position on the y-axis which, in turn, actuates a second
microswitch. When actuated, the second microswitch rotates cam 46
counterclockwise to permit the recording head to pivot into an
operable cutting position, and the cutting process is repeated.
This process continues without interruption until the entire screen
master has been cut.
As the heater stylus S cuts a groove in the acetate coating, a
continuous .[.silver.]. .Iadd.sliver .Iaddend.or chip is extricated
from the workpiece surface. To continuously draw this .[.silver.].
.Iadd.sliver .Iaddend.away from the workpiece, a vacuum nozzle 162
(shown in FIG. 7) connected to a vacuum source through hose 163, is
positioned adjacent stylus S during the cutting operation. The
maximum depth of cut produced by the stylus in the acetate coating
is controlled by ball follower 51 which, as mentioned hereinabove,
rides on an uncut portion of the coating, near the stylus. The
recording head includes a mechanism for maintaining the distance
between the stylus tip and the base of the ball constant.
Preferably, the groove spacing and minimum groove depth are set
such that no "land" or flat areas exist between adjacent
grooves.
Another projection screen embodying the present invention is
illustrated in FIGS. 17-19 and is generally designated by the
reference numeral 200. Like the aforedescribed screen, the surface
of screen 200 comprises a plurality of contiguous microelements
having boundaries defined in a transverse direction by cusp lines
201 formed by the intersecting edges of adjacent linear grooves
202, and in a longitudinal direction by periodic shifts occurring
along lines 203 in the groove depth profile from concave to convex.
However, unlike the aforedescribed screen, the contour of all
microelements comprising the surface of screen 200 is substantially
identical, each being contoured such as to uniformly distribute
(i.e., distribute with constant luminance) normally incident image
light throughout the same horizontal and vertical audience angles.
Each microelement has transverse and longitudinal cross sections
defined by the above equations. In order to satisfy Postulate I set
forth above, namely that each elemental area on the screen surface
distribute image light only throughout an angle just large enough
to encompass a predefined viewing area, it is necessary to orient
each microelement on the screen surface such that the planes which
bisects its vertical and horizontal audience angles intersects with
similar bisecting planes of all other microelements at a point
remote from the screen surface. Preferably, such orientation is
accomplished by giving the screen surface a substantially spherical
shape, the center of spherical curvature corresponding to the
desired point of intersection of the optical axes of the
microelements.
Rather than curving the screen surface to effectively adjust the
orientation of each microelement, Postulate I could be satisfied by
adjusting the angle at which image light impinges upon each
microelement. Such adjustment could be accomplished in the case of
a rear projection screen by providing the rear surface 205 of the
projection screen, that is, the surface closest to the projector,
with a Fresnel-like lens See FIGS. 18a and 19a. Obviously,
combinations of Fresnel lenses and other screen curvatures, such as
cylindrical, could be used.
To fabricate screens of the type illustrated in FIGS. 17-19, a flat
master is initially made using the techniques and apparatus
described above. From the master, a flexible negative matrix is
made, which may be subsequently curved and used to generate
correspondingly curved positive projection screens by the molding
techniques described hereinbelow.
In fabricating the master, both channels of the above-described
stereo sound recording head are fed electrical waveforms defined by
Equations (1) and (2) above, at .theta. = 0. In FIG. 20, electronic
circuitry is schematically illustrated for generating the required
waveform. As previously indicated, such waveform differs from a
true sine wave in that the peaks are flattened, relative to the
lower-amplitude portions of the wave. Moreover, as also mentioned
hereinabove, to produce a groove depth profile in accordance with a
desired waveform, it is necessary to drive the cutting stylus with
an asymmetrical waveform which is converted to the desired waveform
by the arcuate stylus movement. To produce the waveform required,
the output (sin x) of a conventional sinewave generator 209 is
first asymmetrically distorted by asymmetrical circuit 210 to
compensate for the arcuate stylus movement, and then shaped by
shaping circuit 211 to produce the waveform required for
appropriately driving the cutting stylus S. It has been found that
by adding to the sine waveform a small amount of its second
harmonic, the requisite asymmetrical distortion can be achieved. A
squaring circuit 212, such as an analog multiplier module, is used
to generate the second harmonic waveform (sin 2x) from the
fundamental. Capacitor C2 is used to eliminate the dc component of
the squaring circuit output so as to produce a positive- and
negative-going signal. Since the midpoint of the resulting waveform
lags the sin x waveform by 45.degree., it is necessary to feed the
output of the sine wave generator through a simple RC phase-lagging
circuit 213. In this manner, the two waves are added while in phase
by operational amplifier A3. The amount of asymmetry in the output
of amplifier A3 depends, of course, on the peak-to-peak amplitude
of the added second harmonic. Potentiometer P1 serves to vary the
second harmonic amplitude prior to being added to the
fundamental.
To produce the desired waveform from the asymmetrically distorted
sine wave output of circuit 210, such output is fed to the shaping
circuit 211. The input signal to shaping circuit 211 is segmented
by reason of having to overcome successively the forward voltage
drops across diodes D3-D12. Diodes D3-D7 and D8-D12 serve to
segment the positive- and negative-going portions of the input
signal, respectively. Operational amplifier A4 serves to sum the
contributions of the various segments to produce a difference
signal .DELTA.x having a waveform representing the difference by
which the desired waveform differs from the asymmetrically
distorted sine wave input. The contributions of the individual
segments to the output of amplifier A4 are adjusted by varying the
values of resistors R5-R9. The output of amplifier A4 is adjustable
in amplitude by potentiometer P2. Resistors R10 and R11 and
potentiometer P2 serve to control the gain of amplifier A5. By
simply adding the difference signal .DELTA.x, which is of a
polarity opposite that of the unshaped signal due to the polarity
reversing affect of amplifier A4, to the unshaped signal, the
desired waveform for driving the cutting stylus is achieved. Such
addition is performed by operational amplifier A5. Resistors R10
and R11 and potentiometer P3 serve to control the gain provided by
the summing amplifier A5. The output of amplifier A5 is then used
as the inputs to both driving coils of the stereo recording head to
drive the cutting stylus.
After making the projection screen master in accordance with the
aforedescribed method and apparatus, projection screens can be
produced therefrom by making a negative matrix or master from the
original, and casting positive screens, in a resinous material,
from the negative master. Preferably, the negative master is made
from General Electric RTV-60 silicone rubber which is prepared by
adding 3 grams of dibutyl tin dilaurate RTV curing catalyst to 2
pounds of the RTV-60 rubber, agitating the mixture with an electric
stirrer for 5 minutes and then placing it in a bell jar which is
then evacuated to a pressure of 150 microns of mercury for about 20
minutes. Upon fixing sidewalls to the edge of the original master,
the RTV rubber mixture can then be poured into this mold so that no
air is entrapped. After curing, the rubber mold can then be used to
cast projection screens.
To fabricate spherically or otherwise curved front projection
screens of the type depicted in FIGS. 17-19, the rubber negative
mold is disposed on an appropriately curved support prior to
casting. A maraglas resin, after being degassed, is then poured
into the mold. After heating in an oven at 200.degree. F for
several hours to harden the resin, the casting can be coated with
an aluminum coating to form a front projection screen. Refractive
or rear projection screens can be made from a planar master by
incorporating a Fresnel-like lens on the castings replicated
therefrom.
As indicated above front and rear projection screens merely
constitute a preferred embodiment of the invention and it should be
understood that other radiation-redistributive devices, such as
those already mentioned, as well as the many obvious variations and
modifications of the invention as described, are considered within
the spirit and scope of the invention.
* * * * *