Note: Descriptions are shown in the official language in which they were submitted.
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TITLE OF THE INVENTION
MULTIPLE REFLECTION OPTICAL INSTRUMENT AND
REFLECTED LIGHT CATCHING METHOD USING THE SAME
BACKGROUND OF THE INVENTION
1. FIELD OF THE INVE;NTION:
The present invention relates to a multiple path
optical matrix: system and, more. particularly, to a
multiple reflection optical instrument used for the
component analysis of a gas or the like and a reflected
light catching method using the same.
2. DESCRIPTION OF THE PRIOR ART:
In a conventional technique of this type, a laser
light beam is caused to pass through the housing of a
cell, in which a gas to be analyzed is inserted, and the
wavelength intensity of the exit light beam is analyzed,
thereby performing the component analysis of the gas. In
order to perform this analysis, it is necessary to
realize an optical path (transmission path) as long as
possible in the housing.
In a classic system developed by White, ["Very Long
Optical Paths in Air", Journal of Optical Society of America;
May 1976, Vo1.61~, pp.~411-416] a plurality of mirrors are used
to prolong the optic: al path. However, this system cannot
provide a suffi~~iently long optical path.
A technique is recently disclosed in U.S. Patent
No. 4,626,078 i~o Chexnia et al. This technique relates
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to a multiple path. optical matrix system having an
arrangement schematically shown in Fig. 1 and an
operation to be described below with reference to Fig. 2.
Referring to Fig. 1, this system is constituted
by a cylindrical cell. having a housing 4. A main field
mirror 24 and an auxiliary field mirror 25 adjacent to
the main field mirror 24 are arranged at one longitudinal
end of the housing 4. On the other hand, a set of four
objective mirrors 39, 40, 41, and 42 having the
same radius of curvature are arranged on a mount 34
disposed at the other longitudinal end of the housing 4
opposite to the field. mirrors 24 and 25. The main field
mirror 24 has the same curvature as that of the objective
mirrors. The center of curvature of the main field
mirror 24 matches the center of symmetry of the four
objective mirrors along the longitudinal axis of the
housing 4. In the multiple reflection optical apparatus
having the abovE~ arrangement, a light beam from a light
source is incidlent in the housing 4 through an inlet
window 2 provided on the field mirror side. The light
beam is repeatedly reflected between one of the objective
mirrors 39, 40, 41, and 42 and one of the field mirrors
24 and 25 a plurality of times. The light beam finally
emerges through an outlet window 27 formed beside the
inlet window 2, and the wavelength intensity of the light
2
2 .~ ~. 9 'T1.~.
beam emerging from the outlet window 27 is measured. The
reflection operation in the housing 4 of the above
multiple reflection system will be described below in
relation to an image matrix shown in Fig. 2.
The light beam emitted from the light source
passes through the inlet window 2 formed at one
longitudinal end of the housing 4 formed in the cell. The
light beam is directed to the first objective mirror 39
of the four objective mirrors and reflected thereby to
the main field mirror 24 to perform the first coming and
going reflection in the housing 4. A first spot is
located at one corner of the image matrix focused on the
main field mirror 24. The light beam is directed from the
first spot on the main field mirror 24 to the second
objective mirror 40, reflected thereby, and reflected to
the first objective mirror 39 once more through the main
field mirror 24. The reflection between the first
objective mirror 39 and the field mirror 24 and the
reflection between the second objective mirror 40 and the
field mirror 24 are alternately repeated a plurality of
times until the reflected light beam reaches a
spot-column at one end of the image matrix which
includes the first spot. At this time, the light beam is
incident through the first objective mirror 39 on the
auxiliary field mirror 25 provided adjacent to the main
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field mirror 24 on the inlet window 2 side and having
the same curvature as in the objective mirrors and the
center of curva~.ture matching the point of symmetry of the
first and third objecaive mirrors 39 and 41. The light
beam reflected by the auxiliary field mirror 25 is
directed to the third objective mirror 41, incident on
the main field mirror 24 again through the third
objective mirror 41,. and directed to the last fourth
objective mirror 42.
After repeating this reflection a plurality of
times, the light beam is finally reflected by the first
objective mirror 39 in the housing 4, emerges from the
housing 4 through the outlet window 27 including a spot
corresponding i.o an odd-numbered coming and going
reflection (45th coming and going reflection in Fig. 2)
in the housing 4" and is caught by a sensor or the like.
Practica7Lly, however, when the above conventional
system is used :in an environment, e.g., in a running car
or flying airplane, which produces a very strong
vibration, the cell of the multiple reflection optical
instrument is distorted to cause variation of the optical
path. This makes i_t impossible to stably catch the
transmitted light bE~am at the outlet window. This
phenomenon will be described below in relation to Fig. 3.
Assume that, during use of the above system,
4
~1 i.~'~ ~ 1
distortion of the cell by the vibration causes one
mirror M of the field mirrors or the objective mirrors to
tilt by an angle O a . At this time, a light beam 1
directed to the mirror M makes a light beam lb reflected
from the mirror M, which is shifted by an angle 2p a
with respect to a reflected light beam la in a normal
state. That is, the reflected light beam lb is shifted
by an angle twice the tilting angle of the mirror by
distortion of the cell. Therefore, the light beam finally
reflected in the housing can be greatly shifted from the
outlet window depending on the magnitude of distortion of
the cell and the length of the housing to make it
impossible to catch the light beam. It can be considered
to anticipate the maximum distortion of the cell and form
an outlet window having an opening area large enough to
cope with this shift. However, the size of the cell
itself is limited. In addition, when an optical sensor is
used in accordance with such a large opening area, the
accuracy of the sensor is greatly degraded, and the
object to perform the gas analysis or the like cannot
be achieved.
Further, when air is sampled in a flying airplane
while moving at a high speed, it is difficult to repeat
measuring in a specific spot. Therefore, the light beam
must be caught without any error.
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SUN~IAF;Y OF THE INVENTION
The present invention has been made in
consideration of the above situation, and has as its
object to provide a multiple reflection optical
apparatus capable of stably catching the light beam
without any shift of the finally reflected light beam
from a predetermined position even when the cell of the
multiple reflection optical instrument, in which a gas
to be measured, is distorted by a vibration, and a
reflected light: catching method using this apparatus.
In order to achieve the above object,
according to a first aspect of a multiple reflection
optical instrument o:E the present invention, there is
provided a multiple :reflection optical apparatus used
for a gas analysis, ~.ncluding
(a) a :housing formed in a cell,
(b) a main field mirror fixedly mounted on a mount
which is disposed at one longitudinal end of the housing and
is provided with a light beam inlet window for introducing
a light beam from a :Light source into an inside of the
housing and with an outlet window for causing a light beam
multiply refleci;ed in the housing to be directed to a
measuring equipment,
(c) an auxi7Liary field mirror having the same
radius of curvature as that of the main field mirror,
f fixedly mounted on the; mount so as to be adj scent to the
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main field mirror on the light beam inlet window side, and
(d) first to fourth objective mirrors arranged at
the other longitudinal end of the housing which is opposite
to the two fie:Ld mirrors, said objective mirrors being
freely rotated entirely through a holder and also
individually in every direction, having equal radii of
curvature each equal to that of the main field mirror, and
arranged such that a center of curvature of the auxiliary
field mirror becomes a point of symmetry between the first
and third objective mirrors,
wherein an image matrix is formed on the main and
auxiliary field mirrors by a plurality of reflection spots
of the light beam passing through the inlet window into the
housing, and a position of a center of curvature of each of
the first to fourth objective mirrors, which is projected
onto the main :Field mirror, is adjusted such that the
finally reflected light beam which is reflected toward the
outlet window is. a ma~:imum even-numbered coming and going
reflection reflected from the third objective mirror in the
image matrix, wherein a position of a center of curvature of
each of said form pieces of objective mirrors, which is
projected onto t:he main field mirror, is adjusted such that
a row of spots arrangE:d in a horizontal direction of the
image matrix contains an odd number of spots, said outlet
window being formed on said auxiliary field mirror, wherein
said first to fourth objective mirrors are arranged such
that a center of curvature of the first objective mirror is
a point of symmetry beaween a position of the inlet light
beam at the inlet window and a first spot focused through
the first objective mirror at a cross point of a left end
column of the image matrix on the main field mirror and a
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row thereof, t:hat a center of curvature of the second
objective mirror is a point of symmetry between the first
spot and second spot focused through the second objective
mirror at a cross point: of a right end column of the image
matrix on the main field mirror and an uppermost row
thereof, that a center of curvature of the third objective
mirror is a point of symmetry between a spot in a lowermost
row on the auxi7.iary field mirror and a spot focused through
the third objective mirror at a cross point of a left end
column of the image matrix on the main field mirror and a
second row from the tap thereof, that a center of curvature
of the fourth objective mirror is a point of symmetry
between the spot: focused through the third objective mirror
at the cross p~~int of the left end column of the image
matrix on the main field mirror and the second row from the
top thereof and a spot focused through the fourth objective
mirror at a cross point of the right end column of the image
matrix on the main field mirror and the lowermost row
thereof, that a distance between the centers of curvature of
the first and third objective mirrors or between the centers
of curvature of the second and fourth objective mirrors is
a half of a dis~~ance between two spots vertically adjacent
to each other, ~~nd that a distance between the centers of
curvature of the first and second objective mirrors is a
half of a distance between two spots horizontally adjacent
to each other.
According to a second aspect of the present
invention, thex-e is provided a reflected light receiving
method in a multiple path optical matrix system, including:
causing a light beam from a light source to pass through an
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inlet window formed at: a corner portion of one longitudinal
end of a housing provided in a cell and causing the light
beam to be incident on a first objective mirror of four
pieces of objective mirrors having equal radii of curvature
to one another send mechanically mounted on a holder which is
arranged at the other longitudinal end of the housing to be
freely rotated about vertical and horizontal axes with
respect to an image matrix,
reflecting t:he light beam by the first objective
mirror and causing the :Light beam to be incident on a first
spot of a lowermost row in a column on one end side of the
image matrix foamed on a main field mirror having the same
radius of curvature as that of the objective mirrors and
arranged at one longitudinal end of the housing such that a
center of curvature matches a center of symmetry of the four
pieces of objective mirrors along a longitudinal axis of the
housing,
directing the light beam reflected from the first
spot on the main field, mirror to a second objective mirror
placed at a diagonal position with respect to the first
objective mirror,
directing the light beam reflected from the
second objective mirror to the main field mirror, then
reflecting the light '.beam thereby to the first objective
mirror, alternately repeating a reflection between the first
objective mirror and tlae main field mirror and a reflection
between the second objective mirror and the main field
mirror a plurality of times, and causing the light beam to
reach the column vertically focused on one side of the image
matrix which includes the first spot,
causing the reflected light beam present on the
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spot at one side to be: incident, through the first objective
mirror, and an auxiliary field mirror arranged adjacent to
the main field mirror on the inlet window side, and having
the same curvai:ure as that of the obj ective mirrors and a
center of curvature matching a point of symmetry between the
first and third. objective mirrors,
subsequently reflecting the light beam by the
auxiliary field mir:rar to the third objective mirror
arranged at a position parallel to the second objective
mirror and perpendicular to the first objective mirror,
causing the light beam from the third objective
mirror to be incident: on the main field mirror again and
then reflecting the light beam thereby to a fourth objective
mirror placed at a diagonal position with respect to the
third objective mirror,
directing the light beam reflected by the fourth
objective mirror to t:he main field mirror, then reflecting
the light beam thereby to the third objective mirror, and
alternately re~~eatinc~ a reflection between the third
objective mirror and t:he main field mirror and a reflection
between the fourth objective mirror and the main field
mirror a plurality of times,
alternately repeating the reflections between the
first and second objective mirrors and the main field mirror
a plurality of times again,
alternately repeating the reflections between the
third and fourth objective mirrors and the main field mirror
a plurality of mimes again, and
causing the .light beam finally passing through the
housing to emerge fromv the housing through an outlet window
formed on one longitudinal side of and one end of the
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housing, wherein the finally passing light beam is a
reflected light beam toward a spot corresponding to a
maximum even-numbered coming and going reflection in the
image matrix, the reflected light beam toward the spot
corresponding t,o the even-numbered coming and going
reflection being a light beam finally reflected through the
third objective mirror, and the finally reflected light beam
being caused to emerge from the housing through the outlet
window formed at a crofas point of the other end side of the
image matrix including spots focused on the auxiliary field
mirror and the center :Line thereof.
According to the method of the present invention,
there is provided a reflected light receiving method,
wherein a position of .a center of curvature of each of the
four pieces of objective mirrors, which is projected onto
the main field mirror, is adjusted such that a row of spots
arranged in a horizontal direction of the image matrix
contains an odd number of spots.
According to the present invention having the
above aspects, the light beam is reflected between the
objective mirrors arid the opposing field mirrors
even-numbered mimes at maximum. With this operation,
the shift of tlxe reflected light beam at the outlet
window can be prevented, and an optical path having a
sufficient length ca,n be ensured in a gas detection
housing. For this reason, even in an environment, e.g,
in a running car or flying airplane, which produces a
strong vibration, t:he reflected light beam can be
certainly caught. Therefore, a stable gas analysis can
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be effectively performed.
The above and other objects, aspects, and
advantages of the invention will be apparent to one
skilled in the art from the explanation in relation to
the following dnscript:ion and the accompanying drawings,
in which the preferred detailed examples according with
the principle of the present invention are illustrated as
embodiments.
HRIE~F DESCRIPTION OF THE DRAWINGS
Fig. 1 is a :schematic perspective view showing a
conventional multiple reflection optical instrument;
Fig. 2 is an image matrix by a conventional
reflected light catching method;
Fig. 3 is an. explanatory view related to the
shift of a r~aflected light beam in the multiple
reflection optical instrument;
Fig. 4 ~~s a ;schematic perspective view showing a
multiple reflection optical instrument of the present
invention;
Fig. 5 i.~ a s~~hematic perspective view showing a
holder on which four objective mirrors are mechanically
mounted to be adjustable in angles;
Fig. 6 is a view showing an image matrix
representing the spots of a light beam focused on a field
mirror and an auxiliary field mirror;
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Fig. 7 is an explanatory view showing the image
matrix in a method of catching the reflected light
emerging from a spot corresponding to the 78th
coming and going reflect=ion;
Fig. 8 is an explanatory view showing the
relationship between the shift of the center of
curvature of each objective mirror and the shift of each
spot on the field mirror; and
Figs. 9A and 9B are explanatory views showing an image
matrix having an even number of lines when an outlet window of
the light beam is set at the position of a spot corresponding
to a maximum even-numbered coming and going reflection and an
image matrix having an odd number of lines of spots, which are
one line lesser tlhan the even number of lines, respectively.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
The present invention will be described below in
more detail in relation to some preferred embodiments
shown in the accompanying drawings (Figs. 4 to 9B).
Fig. 4 ins a schematic perspective view showing a
detailed examples of a multiple reflection optical
instrument of thE: present invention. This instrument has
almost the sames arrangement as in the conventional
instrument shown in Fig. 1 except for the position where
an outlet opening (out:let window) of the reflected light
beam is formed and the position of the center of
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curvature of each objective mirror on a main field
mirror. Therefore, a detailed description of the
instrument will 1~e omitted.
A main :Field mirror 111 is fixedly mounted on a
mount 110, at or,~e end of a housing 120 provided in a cell
of instrument. An auxiliary field mirror 112 is fixedly
mounted on the mount 110 so as to be adjacent to one
side of the main field mirror 111 and has the same
curvature as that: of the: main field mirror 111.
Four objective mirrors 113, 114, 115, and 116 are
identical to each other and have the same curvature as
that of the fie:Ld mirrors 111 and 112. These objective
mirrors are arranged, through a holder 125, at the other
longitudinal end of the housing 120 which is opposite to
the field mirrors 111 and 112 and be movable together and
also individually. An outlet window 118 is formed in the
auxiliary field mirror 112.
The holder 125 for mechanically mounting the
objective mirrors 113., 114, 115, and 116 will be
described below in detail with reference to Fig. 5.
The holder 125 includes a first mount 125a
having the four objective mirrors 113, 114, 115, and 116
arranged to be movable and a second mount 125b for
rotating the first mount 125a about a central vertical
axis 124. The first mount 125a is rotated about a central
1 4
,,~ ~.L1~71~
horizontal axis 123 byan adjusting knob 121 and rotated
by another adjusting knob 122 about the vertical axis 124
through the second mount 125b. The angular position of
each of the objective mirrors 113, 114, 115, and 116 can
be adjusted by an adjusting knob (not shown). Adjustment
by these adjusting knobs determines the direction of a
light beam reflected to the field mirror 111 and the
auxiliary field mirror 112.
When the adjusting knob 122 is fixed and the
adjusting knob 121 is adjusted, the four objective
mirrors are rotated about the horizontal axis 123.
When the adjusting knob 121 is fixed and the
adjusting knob 122 is adjusted, the four objective
mirrors are rotated about the vertical axis 124.
The center of curvature of the auxiliary field
mirror I12 is located at the point of symmetry of the
first and third objective mirrors 113 and 115.
When the reflection angles of the objective
mirrors 113, 114, 115, and 116 are respectively adjusted
by the adjusting knobs (none are shown), the number of
lines and columns of an image matrix formed on the field
mirrors 111 and 112 is determined.
When the four objective mirrors are rotated about
the horizontal axis 123, the reflection angle of the
light beam to the field mirrors 111 and 112 along the
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horizontal direction is changed. The number of lines of
the image matrix along the horizontal direction is thus
increased/decreasEsd. ~n the other hand, when the four
objective mirrors are rotated about the vertical axis
124, the reflection angle of the light beam to the field
mirrors 111 and 112 along the vertical direction is
changed. Therefore, t:he number of columns of the image
matrix along the vertical direction is
increased/decrease:d.
Fig. 6 is a view showing an image matrix
representing the spots of the light beam focused on the
main field mirror 111 and the auxiliary field mirror
112. The reflec tion operation of the light beam in the
multiple reflection optical apparatus of the present
invention will be described with reference to Fig. 6.
( 1 ) Re:ferenc:e numeral 0 denotes an inlet
position of the light beam passing through an incident
window 117. ThE~ light beam is reflected through the
first objective mirror 113 and incident on a first spat 1
of the image matrix focused on the main field mirror 111.
(2) The light: beam is reflected by the first
spot 1 focused on the main field mirror 111, directed to
the second objective mirror 114, reflected through the
objective mirror J~14, a.nd incident on a second spot 2 on
the main field mirror 111.
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(3) The: light beam reflected by the second spot
2 is incident on a third spot 3 on the main field mirror
111 through the i:irst objective mirror 113 again.
(4) The light= beam reflected by the third spot 3
is incident on a. fourth spot on the main field mirror 111
through the second objective mirror 114 again.
(5) The light beam reflected by the fourth spot
4 is incident on 'the next spot through the first
objective mirror 113 again. Such a reflection between
the first objective mirror 113 and the main field mirror
111 and a reflecaion between the second objective mirror
114 and the main field mirror 111 are alternately
repeated a plur~ility of times until the light beam is
incident on a spot 7 in the right end column and the
lowermost line. The light beam is then moved through the
second objective mirror 114 to a spot 8 in the left end
column and the upi~ermost line.
(6) The light beam reflected by the spot 8 is
incident on a spot 9 in the lowermost line the auxiliary
field mirror 112 i~hroug:h the first objective mirror 113.
(7) The lighi= beam reflected by the spot 9 is
directed to the third objective mirror 115 and incident
on a spot 10 on the main field mirror 111.
(8) The light beam reflected by the spot 10 is
directed to the fourth objective mirror 116 and once more
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incident on a spot 11 in the right end column and the
lowermost line ~~f the image matrix on the main field
mirror 111. This spot 11 is equal to the spot 7 of the
fourth preceding coming and going reflection and these
two spots are superposed. This superposition of spots
also occurs in other spots except in the uppermost line,
in the line including the outlet window and in spots formed
on the auxiliary field mirror 112. Such a reflection
between the third. obje~~tive mirror 115 and the main field
mirror 111 and a reflection between the fourth objective
mirror 116 and the main. field mirror 111 are alternately
repeated a plurality of times. Then again, the
reflections between the first and second objective
mirrors 113 and 114 and the main field mirror 111 are
alternately repeated a plurality of times. Thereafter,
the reflections between the third and fourth objective
mirrors 115 and 116 and the main field mirror 111 are
alternately repeaited a plurality of times. With this
operation, the spot of the image matrix is moved near the
horizontal axis ai: the central portion of the main field
mirror 111 while increasing the number of spots formed on
the surfaces of the: field mirrors 111 and 112.
(9) Finally, the light beam is reflected by the
third objective m.Lrror 115 and caused to emerge through
the outlet window 118 (Fig. 4) including the spot of the
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reflected light beam corresponding to an even-numbered
coming and going :reflect.ion.
In the :reflected light catching method of the
present invention, the finally reflected light beam is
caused to emerge through the outlet window including the
spot of the rei=lected light beam corresponding to an
even-numbered coning and going reflection. The reason
for this is as follows. When the relative position of
the incident light beans and the field mirrors 111 and 112
and the relative position of the centers of curvature of
the objective mirrors 113 to 116 projected onto the main
field mirror 111 are :not changed by a vibration or the
like, the spot oi= the reflected light beam on the field
mirror corresponding to~ an even-numbered coming and going
reflection is not shifted although the spot of the
reflected light bE'am on the field mirror corresponding to
an odd-numbered coming and going reflection is shifted.
The reason for this will be described with reference to
Fig. 8.
Referring to Fig. 8, the light beam passing
through the inlet window 117 is reflected by the first
objective mirror 113 (not shown) and forms the spot 1
(odd-numbered) on the main field mirror 111. Assume
that, for example, the apparatus is distorted by a
vibration in the horizontal direction, and the position
1 9
X119711
of a center A of curvature of the objective mirror 113
projected onto the main field mirror 111 is shifted by
D a to the right to become a position A'. At this time,
the position of the spot 1 focused on the main field
mirror 111 is shifted by 2p a to the right to become a
position 1'. Subsequently, the light beam from the spot
1' shifted by 2p a is reflected by the second objective
mirror 114 (not shown) which projects a center H of
curvature onto the main field mirror 111 to form the spot
2 (even-numbered) on the main field mirror 111 again.
Since the center B of curvature is also shifted by O a
in advance, the shift is offset. Thus, the position of
the spot 2 is not shifted regardless of the distortion of
the apparatus by a vibration. In the subsequent
reflections, the odd-numbered and even-numbered coming
and going reflections are alternately repeated. This can
also be applied when reflections by the third and fourth
objective mirrors are started.
In the multiple reflection optical instrument of
the present invention, the arrangement of columns and
lines of the image matrix shown in Fig. 6 is determined
such that the following conditions are satisfied.
(a) The point A of symmetry between the
position 0 of the inlet light beam at the incident window
117 and the first spot 1 focused on the main field mirror
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111 through the first objective mirror 113 becomes the
center of curvature of: the first objective mirror 113.
(b) Tree point B of symmetry between the first
spot 1 and the second spot 2 focused in the right end
column and the uppermost row on the main field mirror
111 through the. second objective mirror 114 becomes the
center of curvature of the second objective mirror 114.
(c) A point C of symmetry between the spot 9 in
the lowermost lane on the auxiliary field mirror 112 and
the spot 10 foamed in the left end column and the second
line from the i~op on the main field mirror 111 through
the third obje~~tive mirror 115 becomes the center of
curvature of the third objective mirror 115.
(d) A point D of symmetry between the spot 10
and the spot 11 formed in the right end column and the
lowermost row on the: main field mirror 111 through the
fourth objective mirror 116 becomes the center of
curvature of the fourth objective mirror 116.
However, since the size of the housing 120
formed in the multiple reflection optical apparatus is
limited in advance, the maximum size of the image matrix
formed on the field mirrors 111 and 112 arranged in the
housing 120 is a~~parently limited accordingly. With this
limit, in order to cause the reflected light beam from a
spot corresponding to an even-numbered coming and going
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reflection to emerge from the housing 120, and at the
same time, realize an optical path as long as possible
for the purpose of stable catching of the reflected light
beam, the intervals oi: spots must be set larger than the
diameter of the light beam on the main field mirror
including an aberration. In addition, the centers A,B,
C, and D of curvature of the four objective mirrors,
which are projected onto the main field mirrors 111, must
be determined such that the number of columns of spots in
the image matrix is a. maximum natural number of two or
more which can be set :in the field mirrors 111 and 112,
and the number of: lines of spots is a maximum odd number
of three of more which can be set in the field mirrors
111 and 112. The reason for this will be described below
on the basis of Figs. 9A and 9B.
Fig. 9A shows an image matrix when the number of
columns of spots focused on the field mirrors 111 and 112
are represented by n, the number of lines are an even
number represented by 2m, and the outlet window of the
light beam is a spot ~of a maximum even number. As is
apparent from thi:~ example, when the number of lines are
an even number, no spot; is focused in the second line
from the top. In the uppermost row and the second row
from the bottom, the light beam is reflected only once.
The number of spots in this example are calculated as
2 2
~11~7~1
follows.
{2 x (2m - 2) x (n - 1) - (n - 1)~ ...(number in area X)
+ (2m - 2).........................-....(number in area Y)
+ (n - 1)...-..-........................(number in area Z)
- (2m - 2) x (2n - 1) (1)
Fig. 9H shows an image matrix when the number of
lines are an odd number (2m - 1) which are one line
smaller than the even number in Fig. 9A, and the finally
reflected light beam gotten out from the outlet window
118 is a spot of a maximum even number. As is apparent
from this example, when the number of lines are an odd
number, in the uppermost and central lines, the light
beam is reflected only once. The number of spots in this
case are calculated in accordance with the following
equation.
{2 x (2m - 2) x (n - 1) - (n - 1)~...(number in area X')
+ (2m - 2).............................(number in area Y')
+ (n - 1).......-....-.--......------..(number in area Z')
- (2m - 2) x (2n - 1) (
As is apparent from the above equations (1) and
(2), when the light beam reflected from a spot of a
maximum even number is caught, the number of spots of the
image matrix having an even number of lines are the same
2 3
CA 02119711 1999-06-16
as that in the matrix ruaving an odd number of lines, which are
one line smaller than the even number. Therefore, when the
matrix having an odd number of lines shown in Fig. 9B is used,
the field mirrors can be effectively used rather than use of
the matrix having an .even number of lines shown in Fig. 9A
because the second co:Lumn from the top is of no use in the
latter case.
Fig. 7 is ;~ view showing an image matrix when the above
reflections are repeated a plurality of times, and the light
beam is caused to emerge from a spot corresponding to the 78th
coming and going reflection.
As is clearly un<ierstood from this figure, in the first
embodiment of th,e multiple reflection optical instrument of
the present invention, t:he respective centers of curvature A,
B, C and D of the four pieces of objective mirrors 113, 114,
115 and 116 focused on, the surface of the main field mirror
111 has the following additional definitions in addition to
the foregoing definii:i.ons in addition to the foregoing
definitions (a) to (d). Namely, the vertical distance d2
between the centers of: curvature A and C (or B and D) is a
half of the distance d~. between two spots vertically adjacent
to each other, ~~nd the horizontal distance d4 between the
centers of curvature p. and B (or C and D) is a half of the
distance d3 between two spots horizontally adjacent to each
other.
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