U.S. patent number 3,645,606 [Application Number 05/002,026] was granted by the patent office on 1972-02-29 for multifacet substantially paraboloidal collimator and method for making same.
This patent grant is currently assigned to TRW Inc.. Invention is credited to Allan D. La Vantine.
United States Patent |
3,645,606 |
La Vantine |
February 29, 1972 |
MULTIFACET SUBSTANTIALLY PARABOLOIDAL COLLIMATOR AND METHOD FOR
MAKING SAME
Abstract
A light reflecting collimator having a substantially
paraboloidal surface and being formed of a plurality of juxtaposed
facets each having a substantially paraboloidal surface. A method
for making such a collimator of a plurality of facets each having a
substantially paraboloidal surface on individual plates and each
facet formed on each plate being defined by two paraboloidal radii
lying in orthogonal planes.
Inventors: |
La Vantine; Allan D. (Tarzana,
CA) |
Assignee: |
TRW Inc. (Redondo Beach,
CA)
|
Family
ID: |
26669813 |
Appl.
No.: |
05/002,026 |
Filed: |
January 12, 1970 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
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656093 |
Jul 26, 1967 |
3494231 |
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Current U.S.
Class: |
359/853; 29/428;
359/900 |
Current CPC
Class: |
F21S
8/006 (20130101); G02B 5/09 (20130101); G02B
27/30 (20130101); Y10T 29/49826 (20150115); Y10S
359/90 (20130101) |
Current International
Class: |
G02B
27/00 (20060101); G02B 5/09 (20060101); G02b
005/10 (); B23p 019/00 () |
Field of
Search: |
;350/292,293,296,320
;29/407,428 |
References Cited
[Referenced By]
U.S. Patent Documents
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3009391 |
November 1961 |
Zagieboylo et al. |
|
Other References
Brunner "Process for Obtaining a Convex Surface" 1(1) IBM Tech.
Disclosure Bulletin p. 22 6-1958.
|
Primary Examiner: Schonberg; David
Assistant Examiner: Leonard; John W.
Parent Case Text
This application is a division of application Ser. No. 656,093, now
U.S. Pat. No. 3,494,231.
Claims
I claim:
1. A collimator having a substantially paraboloidal surface and
formed of a plurality of juxtaposed facets, each having a
substantially paraboloidal surface, comprising:
a. each facet surface being defined by two paraboloidal radii in
orthogonal planes;
b. the radii being calculated for a known paraboloid from the
equations:
where R.sub.s is the short radius, R.sub.c is the long radius, F is
the focal length of the paraboloid, and .theta. is an angle between
the parabolic axis and a line normal to a tangent through the
center point of each facet, said line and axis being in a first of
said orthogonal planes normal to a respective tangent: the angle
being determinable from the equation:
.theta. = tan.sup..sup.-1 (U/2F):
where U is the distance from the center point of each facet along a
line normal to the parabolic axis, the latter line and axis being
in the same plane:
c. each of said facets being predetermined squares when viewed
along lines parallel to said parabolic axis, each square having at
least one adjacent corner with another square;
d. at least one of said facets having a diagonal lying in its
second orthogonal plane;
e. the distance of the center point of said last facet from the
parabolic axis being predetermined;
f. the parabolic axis and the center point of each facet lying in
the second orthogonal plane of the respective facet;
g. the position of the second orthogonal plane in each facet other
than that second plane of said one facet being determinable by the
equation;
.phi. = tan .sup..sup.-1 (X/Y);
where .phi. is the angle between said second plane of said one
facet and the plane to be determined; X is the length of a line
normal to said second plane of said one facet to the center point
of the respective facet and along a diagonal thereof and Y is the
length of a line in said second plane from said parabolic axis to
and normal to said last line, X and Y being determinable as
diagonals or parts thereof of known squares.
2. A method for making a collimator having a substantially
paraboloidal surface formed of a plurality of substantially
paraboloidal facets on individual plates, each facet being defined
by two paraboloidal radii in orthogonal planes, comprising:
a. determining the location of each facet to form said collimator
having a predetermined paraboloidal surface;
b. determining the shape and dimensions of each facet plate along
its edges viewed parallel to the parabolic axis;
c. determining the angles between the parabolic axis and lines
normal to tangents through center points of each respective facet,
each of said lines being in a first orthogonal plane normal to said
tangent for each facet;
d. determining the position of the second orthogonal plane for each
facet;
e. determining the respective radii for each facet;
f. preparing a respective jig face for each of said facets by
putting steps on a jig plate from a central axial apex downwardly
toward opposite sides symmetrically to nadir outer edge
positions,
g. said steps extending in an axial position relative to the axis
of a cylindrical curve adapted to extend transversely on the edges
of said steps;
h. the depth of each step from the apex being determined from the
equation;
where dh is the depth of each step; C is the transverse distance
normal to said cylindrical axis from the axial apex to each step
edge, arbitrarily selected; R.sub.c is one of said respective radii
for each facet to be used as a cutting radius to cut a spherical
face as a part of a respective facet in each facet plate and which
is in said second orthogonal plane; and R.sub.s is the other of
said respective radii which defines the finished facet and which is
in said first orthogonal plane:
i. tilting each plate at an angle with the horizontal equal to the
respective angle formed by the parabolic axis and the line normal
to the tangent at the respective center point of each respective
facet and positioning the plate in accordance with the respective
orthogonal planes of the facet in relationship to a reference plane
in the collimator so that the orthogonal planes will be in the
proper positions in relation to the position of the facet in the
collimator, then cutting the edges of each plate vertically to
shape and dimension it according to the predetermined shape and
dimensions viewed parallel to the parabolic axis:
j. placing each facet plate on a corresponding jig depending upon
the radii of the respective facet;
k. positioning and securing each facet plate on its respective jig
in accordance with the respective orthogonal planes of the facet in
relationship to the cylindrical axis of the jig with respect to
said reference plane so that the plate is deformed within its
elastic limit on the curve of said steps and so that the planes
will be in the proper positions in relation to the position of the
facet in the collimator;
l. cutting said spherical surface on each facet using a respective
R.sub.c radius;
m. releasing each facet plate from its jig to permit the plate to
return to its undeformed shape and thereby forming a second curved
surface having the R.sub.s radius in the first orthogonal plane,
the R.sub.c radius being in the second orthogonal plane;
n. finishing each facet to produce a highly reflective surface;
and
o. securing said facets together to form said collimator in
accordance with the predetermined location of each facet, and to
have a substantially paraboloidal reflective surface.
Description
BACKGROUND OF THE INVENTION
In the prior art paraboloidal collimators have been generally small
and formed as a single element. In a solar simulator, for example,
where a relatively large reflecting collimator is required, it
would be vary expensive to form the structure of a single element
in that the material used is relatively rigid and heavy, and the
paraboloidal surface would have to be ground into it. This would be
an obviously difficult and time-consuming effort. By forming a
substantially paraboloidal surface on a plurality of relatively
small sections, great savings of time and expense have been
accomplished. The invention provides a substantial simplification
over that which would normally be used for grinding and polishing a
surface of the required contour. This is especially true for
producing the required surface upon a metal plate, such as aluminum
which is used in solar simulators. In the manufacture of four
collimators for a solar simulator, using the present invention,
approximately three-fourths of a million dollars was saved over
what the cost of grinding true paraboloidal surfaces would have
been.
SUMMARY OF THE INVENTION
It is the object of the invention to provide a method for producing
a surface on a flat metal or other relatively rigid plate, such as
glass, defined by two radii of curvature in orthogonal planes.
Another object of the invention is to provide a jig for making a
facet of a substantially paraboloidal collimator.
It is still another object of the invention to provide a method for
making a collimator having a substantially paraboloidal surface
formed of a plurality of paraboloidal facets upon individual
plates, each facet being defined by two paraboloidal radii in
orthogonal planes.
It is a further object of the invention to provide a collimator
having a substantially paraboloidal surface and formed of a
plurality of juxtaposed facets each having a paraboloidal
surface.
Further objects and advantages of the invention may be brought out
in the following part of the specification wherein small details
have been described for the competence of disclosure, without
intending to limit the scope of the invention which is set forth in
the appended claims.
BRIEF DESCRIPTION OF THE DRAWINGS
Referring to the accompanying drawings, which are for illustrative
purposes:
FIG. 1 is a diagrammatic view of portions of a solar simulator
employing paraboloidal collimators made according to the
invention;
FIG. 2 is a side cross-sectional and diagrammatic view of a central
row of facets of a collimator illustrating portions of the parabola
geometry as they relate to the invention;
FIG. 2A is an enlarged view of the center facet shown in FIG.
2;
FIG. 3A is a side diagrammatic view illustrating the geometry of a
paraboloid as it relates to the center point of a specific
offcenter facet of the collimator according to the invention;
FIG. 3B is a plan view of a collimator, viewed along lines parallel
to the axis of the parabola, projected from FIG. 3A;
FIG. 3C is a true view of the facet whose center point and a
tangent thereto is illustrated in FIG. 3A, viewed normal to the
tangent plane;
FIG. 4 is a side-elevational view of a jig for forming a facet
according to the invention;
FIG. 5 is a diagrammatic view illustrating the geometry from which
the jig calculations are determined for a single facet of a known
parabola;
FIG. 6 is a plan view of the jig shown in FIG. 4 with the facet
plate, shown in FIG. 3C, positioned thereon;
FIG. 7 is a plan view of the jig and plate shown in FIG. 6 with
fill-in pieces arranged around the plate for obtaining a continuous
mill cut on the face of the plate;
FIG. 8 is a side-elevational view of the facet plate, shown in FIG.
3C, in position for cutting the edges of the plate; and
FIG. 9 is a fragmentary view of a collimator illustrating means for
securing the various facets together.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Referring to FIG. 1, there are shown portions of a solar simulator,
generally indicated as 10, diagrammatically illustrated. The solar
simulator is comprised of a plurality of light sources and their
collectors, generally indicated at 11, in optical alignment with an
input mosaic lens 12, output mosaic lens 13 and an aligning lens
14. The beams produced by the light sources, after passing through
the lenses, are reflected by an off-axis, substantially
paraboloidal collimator 17, comprised of nine substantially
paraboloidal facets 18, each defined by two radii of curvature in
orthogonal planes. The parallel light rays 19 are reflected
downwardly from the collimator parallel to a centerline 20 of a
test chamber, not shown. The test chamber has three other
collimators 23, 24 and 25, forming reflective portions of a total
solar simulator apparatus.
The facets 18 are made from aluminum alloy plates and are suspended
in a nearly horizontal position from a rigid thermally stabilized
rack, generally indicated as 26 in FIG. 9. The rack is constructed
of tubular members running generally horizontally with respect to
the collimator and fluid is circulated through the tubular members
to thermally stabilize the structure. The tubular members are
adjustable to provide means to properly align each facet so as to
form the substantially paraboloidal collimator. Thermal
stabilization of the rack eliminates the possibility of any
movement of aligned facets when the space simulation chamber is
under a vacuum and having liquid nitrogen in the panels lining the
walls of the chamber.
In FIG. 2 there is shown a cross-sectional view of the collimator
17 illustrating the reflective faces of the facets 18A, 18B and 18C
on a predetermined parabolic curve 29. The parabola 29 has an axis
30 and a focus point F. In designing the solar simulator, it was
determined that the center point 31 of the collimator should be
off-axis, an angle equal to 20, specifically 26.degree., the angle
being formed by the parabolic axis and the line 33 from the focus
to the center point 31. As is known, in a parabola a line 32 drawn
normal to a tangent 35, as shown in FIG. 2A, to the point 31,
intersects the parabolic axis at an angle .theta., half of
2.theta.. Similarly, the lines 32 and 33 also form an angle equal
to .theta..
In any paraboloid a line, such as 32, has the length of a radius
R.sub.s in a plane perpendicular to the face of the drawing. The
radius R.sub.s defines the curvature of the paraboloid at point 31
in the aforesaid plane. A second radius R.sub.c, longer then
R.sub.s as indicated by the extension 32B of the line 32, is in the
plane of the face of the drawing, normal to the plane of the radius
R.sub.s, and together the two radii in the respective orthogonal
planes determine the surface of a facet as 18B at the point 31.
That is, at each such point, there are two radii in orthogonal
planes that define that portion of the surface of a paraboloid. At
locations off the point 31 in the facet 18B, the radii vary
slightly from R.sub.s and R.sub.c, but the size of 18B, as well as
that of the other facets, is selected so that the deviation is
minor so as not to be of any consequence for purposes for the
invention.
At the center 31 of the facet, the two radii defining the
paraboloid can be defined as R.sub.so = 2 F/cos O.sub.o, where F is
the focal length and .theta. is the angle as indicated above; and
R.sub.co =2 F/cos.sup.3 O.sub.o. The angle .theta. is determined by
the equation, .theta..sub.o = tan.sup..sup.-1 (U.sub.o /2 F), where
U.sub.o is the distance to the center of the facet from the
paraboloid axis. At any other location the two radii of the
paraboloid are:
where U is the distance of another point from the paraboloid axis.
Each collimator facet, according to the invention, is defined by
the two radii R.sub.so and R.sub.co at all points on the facet
surface and the size of the facet must be chosen so that the
deviation in the radii of curvature of the facet from those of a
paraboloid or any location will be small and insignificant.
For example, a typical computation for these variations is
indicated in the following, where F = 19.3 feet, U.sub.o = 10.3
feet, and U = 11.7 feet, then .theta..sub.o = 14.9.degree.,
R.sub.so = 39.9 feet, R.sub.co = 42.75 feet, .theta. =
16.9.degree., R.sub.s = 40.35 feet, and R.sub.c = 44.15 feet.
However, the difference in illumination from that of the true
paraboloid and the collimator made according to the invention is
0.043 which is insignificant for the illumination purposes
required. Thus, as a matter of practice for the collimator
according to the invention, it is sufficiently accurate to treat
the radii of each facet for all points thereon as R.sub.s and
R.sub.c, determined at each center point, the distance from the
parabolic axis to the respective center points being considered to
have a value equal to a respective U. It should be noted that
U.sub.max, as shown in FIGS. 2 and 3B, is predetermined for the
collimator in accordance with the area to be illuminated and is
measured from the axis to the center point of the space simulator
above the area illuminated.
Further, it should be noted that the intersection of the collimator
facets are visible from the test zone of the simulator, the area to
be illuminated, and these intersections block some of the light
coming from the source image, the image appearing across the
intersections on the collimator. This results in a local decrease
of illumination in the test zone, but this decrease is made
insignificant by closely butting the facets.
For each facet, F of the paraboloid being known, in order to
determine the two radii, it is necessary to determine the angle
.theta. from the equation, .theta. = tan.sup..sup.-1 U/2F. The
distance U for each center point may be determined in reference to
FIGS. 3A, 3B, and 3C. In FIG. 3B, the axis 30 of the parabola is
shown as a point, the axis being perpendicular to the surface of
the drawing. The position of a vertical plane or line 36 is
determined with respect to its position to the test zone or area to
be illuminated by the collimator 17. That is, the line 36 extends
from the axis of the parabola to the point U.sub.max, which is
determined to be at the center of a test chamber having a solar
simulator. Stated differently, the collimator is positioned so that
it will provide the proper illumination upon the test zone or
target. Thus, by using the line 36 as a diagonal through the center
of the rectangular collimator its length and angular position are
known.
The collimator in FIG. 3B is shown to be comprised of nine facets,
each 2 square feet, for example. The individual facets, as well as
the collimator, are square only when viewed along lines parallel to
the parabolic axis. In such an arrangement the center points of
each facet are easily determined as being at the intersection of
the diagnosis of known squares. To determine the distance, U.sub.p,
from the point P, the center of the facet 18D, to the axis in the
vertical plane 37 in FIG. 3B and on the drawing surface in FIG. 3A,
it is necessary to determine the length of the lines indicated as X
and Y, the two sides of the right triangle of which U.sub.p, is the
hypotenuse. The line X is equal to the length of the diagonal of
two foot square and Y is equal to U.sub.max minus the length of a
diagonal and half of the 2 foot squares. Thus, the angle .theta.
for the point P, shown in FIG. 3A, for the known parabola and the
radii R.sub.s and R.sub.c for the point P may be calculated from
the equations above.
The radius R.sub.c lies in the plane 37. The radiuS R.sub.s is in a
plane indicated by the line 38, the latter plane being normal to
the plane 37, the two being the orthogonal planes having the two
radii which define the curvature of the facet 18D. In FIG. 3A, the
tangent line or plane 35' is perpendicular to the line 38 and is
analogous to the tangent 35 in FIG. 2. The facet 18D is projected
in FIG. 3C, as viewed normal to the tangent plane 35'. In this view
the facet 18D is a parallelogram having two long sides and two
short sides and is not a rectangle, the lengths of the sides being
24.5297 and 24.1379 inches, for example.
To determine the values of U and the radii for the other facets,
other than those on the line 36 where the distances to the center
points are either known or obvious by subtracting diagonals or
diagonal portions from U.sub.max, the same method may be used as
that for determining the value of U.sub.p and the radii in the
facet 18D. Thus, for example, to determine the value of U for the
facet 18E, the value of X' is that of half of a diagonal and that
the value of Y' is equal to U.sub.max minus the length of two
diagonals of squares. Thus, the length of the hypotenuse 41 is the
value for U in the facet 18E and it is in a vertical plane in FIG.
3B in which its radius R.sub.c extends. For this value of U, the
angle .theta. may be determined in the vertical plane 41 so as to
determine the respective values of R.sub.s and R.sub.c.
From the foregoing, it is clear how the value of U may be obtained
for the other center points of the nine facets. It should be noted
that each of the vertical planes in FIG. 3B, passing through the
axis and a center point, is at a corresponding angle .phi. with the
plane represented by the line 36.
After the radii for the facets are determined, they are used to
determine the configuration of a facet jig 42, shown in FIGS. 4 and
6, on which facet surfaces are formed. There is a separate jig for
each facet depending upon its radii, but the same jig may be used
for corresponding left- and right-hand facets with respect to line
36. Each jig is generally circular and has a flat bottom 43. The
upper face of the jig is formed so that a facet plate secured
thereon by bolts, extending through holes 44 and 45 and threadedly
engaged in tapped wells in the bottom of the plate, can be deformed
within its elastic limit to mate with a cylindrical arc generally
designated as 47, the arc being formed by the flat bottom base of
the facet when it is secured against the outer edges of each of the
steps as 48 and 49. That is, the arc 47 could be drawn so as to
pass over each of the steps and the apex 50 as well as the opposite
laterally outside nadirs as 51. The steps are spaced at equal
intervals on both sides of the axis of the cylindrical arc 47 or of
the apex of the jig.
The arc 47 is determined for each facet according to its radii
R.sub.s and R.sub.c. Each substantially paraboloidal face on the
facet is formed by cutting a spherical contour on the facet face 53
on a facet as 18D positioned on the jig. The spherical curvature is
determined by the long radius, R.sub.c. That is, the shape of the
concave spherical cut into the facet face has a radius equal to
R.sub.c. When that has been accomplished, the facet is removed from
the jig and it returns to its undeformed shape due to the energy
stored therein when it was deformed on the jig within its elastic
limit. The facet face 53, after being removed from the jig, is no
longer spherical but has a substantially paraboloidal face, defined
by two radii in orthogonal planes. When the facet plate springs
back to its undeformed shape, the second curvature is formed in the
face 53 and its radius is equal to R.sub.s. When the facet is
removed from the jig, its bottom should be flat and if it is not,
it must be cut to be flat. It is then put back on the jig and the
spherical cut is made again. The jig is of sufficient thickness so
that its deflection relative to that of the facet is
insignificant.
The jig is prepared so that the proper radii and the orthogonal
planes will define its substantially paraboloidal surface. The
configuration of the jig is determined in reference to FIG. 5.
There the large arc 54 has a radius R.sub.c and the small arc 55
has a radius R.sub.s. The distance C is the distance laterally
outwardly from the apex 50 for any step edge on the jig, or stated
differently, the distance out from the apex at which a point on the
cylindrical curve 47 will be formed so as to deform the facet
plate. The distance h.sub.s indicates the deformation that is
required to form the arc 55 on the jig at a point C and the
distance h.sub.c indicates the deformation that is required on the
jig to form the arc 54 at a point C on the jig. The distance dh is
the difference in deformation required between the two arcs, or
determined from the right angle triangles in FIG. 5.
When the radii are known, dh, the depth of any step downwardly from
the apex 50 on the jig, is determined by selecting an arbitrary
value for C, the distance laterally outwardly perpendicular to the
axis of the jig or cylindrical surface to be formed. The values for
dh are relatively small in the making of a 2-foot square facet. For
example, where the radii are 482 and 525 inches, and C is 4 inches,
dh is equal to 0.0014 inch, and where C is 15.5 inches, dh equals
0.0204 inch. The jigs also could be made to be concave, in which
the spherical cut would be for the short radius R.sub.s and the
plate would be deflected into the concavity for the spherical
cut.
The various facets are positioned on their respective jigs in
accordance with the relationship of the central plane or line 36
which forms diagonals for the facets 18 A, B and C, and the angle
.phi. for a respective facet. For the facets 18A, B and C, the
angle .phi. is 0. and they are positioned on a jig with their
diagonals, along a plane 36, directly above and parallel to the
axis of the cylindrical arc 47.
The other plates from which the facets are to be made are
positioned on the jigs so that their center points are crossed by
the axis of the arc of the cylinder. In FIG. 6, for example, the
plate 18D is rotated on the jig so that the diagonal 36', parallel
to the reference plane 3B, through its center P forms the angle
.phi. with the cylindrical axis of the jig arc which is in the
position of the line 37 in FIG. 3B. The angle .phi. is determined
for the facet 18D, for example, as indicated in FIG. 3B, by the
equation:
.phi. = tan.sup..sup.-1 X/Y.
For facet 18E, X' and Y' are used to solve for .phi.. In this
situation, as shown in FIG. 6, the angle .phi. is to the left of
the cylindrical axis at the lower part of the drawing whereas for
the facets on the left of the line 36 in FIG. 3B, the angle .phi.
would be formed to the right of the cylindrical axis.
Prior to fastening the plates to the jigs, the plates being
somewhat larger than a 2 foot square, they must be milled along
their edges to form a 2 foot square when viewed along a line
parallel to the parabolic axis. As shown in FIG. 8, this is
accomplished by placing the plate on a support 59 having an upper
surface 60 slanted at an angle .theta. equal to that for the
respective facet as determined by the value of U. Further, the
plate is rotated or positioned with respect to its angle .phi. in
the same manner as it is on the jig with reference to the plane 36
and its corresponding plane, as 37 for facet 18D. A milling cutter
58 is then applied to the outer edges as 61 and 63 of the plate,
and moved to cut a 2 foot square, the cutter being in a position to
make a vertical cut, or stated differently, in a position parallel
to the axis of the parabola. This then makes a 2 foot square when
viewed from a position parallel to the parabolic axis. When viewed
as indicated in FIG. 3C, the plate, having finished edges, has the
appearance of a parallelogram and not a square. Two of the sides of
the facets as they would be viewed in FIG. 3C, except for the
facets 18A, 18B and 18C, are slightly longer than the other two
sides. The facets 18A, 18B and 18C have respective equal sides, as
24.5297, 24.3026 and 24.5297, 24.1379 inches.
After the edges of a facet plate are cut, the facet is positioned
on its jig as indicated above, and sectors 65 are placed on the
facet as shown in FIG. 7 so that when the spherical surface is cut,
the cut across and around the facet will be continuous as the
cutting tool passes back and forth over the outer edge of the facet
plate.
After the surfaces of the nine facets have been cut and polished
for reflective purposes, they are assembled in their specific
locations as indicated in FIG. 3B and put together to form the
collimator as shown in FIGS. 1 and 9.
It is clear that the foregoing method for making a substantially
paraboloidal collimator from substantially paraboloidal facets is
considerably less expensive in both time and money than the
manufacture of a collimator in one piece formed to have a
paraboloidal or a substantially paraboloidal face.
The invention and its attendant advantages will be understood from
the foregoing description and it will be apparent that various
changes may be made in the form, construction and arrangement of
the parts of the invention without departing from the spirit and
scope thereof or sacrificing its material advantages, the
arrangement hereinbefore described being merely by way of example.
I do not wish to be restricted to the specific forms shown or uses
mentioned except as defined in the accompanying claims, wherein
various portions have been separated for clarity of reading, not
for emphasis.
* * * * *