U.S. patent number RE41,744 [Application Number 11/732,827] was granted by the patent office on 2010-09-21 for raman probe having a small diameter immersion tip.
This patent grant is currently assigned to Axiom Analytical, Inc.. Invention is credited to Walter M. Doyle.
United States Patent |
RE41,744 |
Doyle |
September 21, 2010 |
Raman probe having a small diameter immersion tip
Abstract
A probe for use in Raman spectroscopy that can be inserted into
a chemical vessel through a small diameter fitting while maximizing
the amount of Raman shifted radiation collected and minimizing
spurious effects.
Inventors: |
Doyle; Walter M. (Laguna
Niguel, CA) |
Assignee: |
Axiom Analytical, Inc. (Tustin,
CA)
|
Family
ID: |
31891250 |
Appl.
No.: |
11/732,827 |
Filed: |
April 4, 2007 |
Related U.S. Patent Documents
|
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
|
60387521 |
Jun 10, 2002 |
|
|
|
Reissue of: |
10459004 |
Jun 10, 2003 |
06876801 |
Apr 5, 2005 |
|
|
Current U.S.
Class: |
385/117; 600/473;
385/39; 385/115; 356/301 |
Current CPC
Class: |
G01N
21/65 (20130101); G02B 6/4206 (20130101); G02B
6/4246 (20130101); G01N 21/8507 (20130101); G01N
2201/08 (20130101); G02B 6/4214 (20130101); G01N
2021/656 (20130101); G02B 6/29361 (20130101); G02B
6/3624 (20130101); G02B 6/32 (20130101) |
Current International
Class: |
G02B
6/06 (20060101); G01J 3/44 (20060101) |
Field of
Search: |
;385/12,39,115-120
;600/407,473,476,478,326 ;356/301,328 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Sanghavi; Hemang
Attorney, Agent or Firm: Myers Andras Sherman LLP Andras;
Joseph C.
Parent Case Text
This patent application claims the benefit of provisional patent
application No. 60/387,521, filed on Jun. 10, 2002.
Claims
I claim:
1. An immersion probe for use in Raman spectroscopy .[.which
includes.]. .Iadd.comprising.Iaddend.: an extended immersion tip
that includes an internally reflecting lightguide; first optical
element for collecting laser radiation emerging from a first
optical fiber and directing it, after subsequent reflections, into
the end of said internally reflecting lightguide in such a way that
it is as nearly collimated as possible consistent with
substantially all of the radiation entering the lightguide; second
optical element for collecting Raman shifted radiation emerging
from said internally reflecting light guide and focusing it on a
second optical fiber in such a way that the size and shape of the
image of the end of the lightguide matches the size and shape of
said second optical fiber; .Iadd.and .Iaddend. reflecting means for
redirecting the beam formed by said first optical element so that
its axis is anti-parallel to and coaxial with the axis of the Raman
shifted radiation emerging from said lightguide.
2. The immersion probe of claim 1 wherein the numeric apertures
corresponding to the diameter and longitudinal positions of said
first and second optical elements are at least as great as the
numeric apertures of the associated optical fibers.
3. The immersion probe of claim 2 wherein the diameter of said
second optical fiber is substantially greater than the diameter of
said first optical fiber.
4. The immersion probe of claim 3 wherein the distance from said
first optical element to said first optical fiber is set so that
the image of said first optical fiber is falls at the end or within
said lightguide and is no greater in diameter than said
lightguide.
5. The immersion probe of claim 4 wherein the ratio of the distance
from said first optical element to said first optical fiber to the
distance from said first optical element to said lightguide is
approximately equal to the diameter of said first optical fiber to
the internal diameter of said lightguide, and Wherein the ratio of
the distance from said second optical element to said second
optical fiber to the distance from said second optical element to
said lightguide is approximately equal to the diameter of said
second optical fiber to the internal diameter of said
lightguide.
6. The immersion probe of claim 2 in which said reflecting means
comprises two totally reflecting, parallel surfaces.
7. The immersion probe of claim 6 in which the area of the
reflecting surface which overlaps the collected radiation is small
compared to the cross section of said collected radiation in the
vicinity of said reflecting surface.
8. The immersion probe of claim 7 in which said reflecting means is
an internally reflecting rhomboid.
9. The immersion probe of claim 1 wherein the diameter of said
second optical fiber is substantially greater than the diameter of
said first optical fiber.
10. The immersion probe of claim 9 wherein the distance from said
first optical element to said first optical fiber is set so that
the image of said first optical fiber is falls at the end or within
said lightguide and is no greater in diameter than said
lightguide.
11. The immersion probe of claim 10 wherein the ratio of the
distance from said first optical element to said first optical
fiber to the distance from said first optical element to said
lightguide is approximately equal to the diameter of said first
optical fiber to the internal diameter of said lightguide, and
Wherein the ratio of the distance from said second optical element
to said second optical fiber to the distance from said second
optical element to said lightguide is approximately equal to the
diameter of said second optical fiber to the internal diameter of
said lightguide.
12. The immersion probe of claim 1 in which said reflecting means
comprises two totally reflecting, parallel surfaces.
13. The immersion probe of claim 12 in which the area of the
reflecting surface which overlaps the collected radiation is small
compared to the cross section of said collected radiation in the
vicinity of said reflecting surface.
14. The immersion probe of claim 13 in which said reflecting means
is an internally reflecting rhomboid.
15. An immersion probe for use in Raman spectroscopy .[.which
includes.]. .Iadd.comprising.Iaddend.: an extended immersion tip
that includes an internally reflecting lightguide; first optical
element for collecting laser radiation emerging from a first
optical fiber and directing it.[., after subsequent reflections,.].
into the end of said internally reflecting lightguide in such a way
that it is as nearly collimated as possible consistent with
substantially all of the radiation entering the lightguide; second
optical element for collecting Raman shifted radiation emerging
from said internally reflecting light guide and focusing it on a
second optical fiber in such a way that the size and shape of the
image of the end of the lightguide matches the size and shape of
said second optical fiber; .Iadd.and .Iaddend. reflecting means for
redirecting the .[.beam formed by.]. .Iadd.Raman shifted radiation
to .Iaddend.said second optical element so that its axis is
anti-parallel to and coaxial with the axis of the .[.Raman
shifted.]. .Iadd.laser .Iaddend.radiation .[.emerging from said
lightguide..]. .Iadd.; wherein the ratio of the distance from said
first optical element to said first optical fiber to the distance
from said first optical element to said lightguide is approximately
equal to the diameter of said first optical fiber to the internal
diameter of said lightguide, and wherein the ratio of the distance
from said second optical element to said second optical fiber to
the distance from said second optical element to said lightguide is
approximately equal to the diameter of said second optical fiber to
the internal diameter of said lightguide. .Iaddend.
16. The immersion probe of claim 15 wherein the numeric apertures
corresponding to the diameter and longitudinal positions of said
first and second optical elements are at least as great as the
numeric apertures of the associated optical fibers.
17. The immersion probe of claim 16 wherein the diameter of said
second optical fiber is substantially greater than the diameter of
said first optical fiber.
18. The immersion probe of claim 17 wherein the distance from said
first optical element to said first optical fiber is set so that
the image of said first optical fiber is falls at the end or within
said lightguide and is no greater in diameter than said
lightguide.
.[.19. The immersion probe of claim 18 wherein the ratio of the
distance from said first optical element to said first optical
fiber to the distance from said first optical element to said
lightguide is approximately equal to the diameter of said first
optical fiber to the internal diameter of said lightguide, and
Wherein the ratio of the distance from said second optical element
to said second optical fiber to the distance from said second
optical element to said lightguide is approximately equal to the
diameter of said second optical fiber to the internal diameter of
said lightguide..].
20. The immersion probe of claim 16 in which said reflecting means
comprises two totally reflecting, parallel surfaces.
.[.21. The immersion probe of claim 20 is which the area of the
reflecting surface which overlaps the collected radiation is small
compared to the cross section of said collected radiation in the
vicinity of said reflecting surface..].
.[.22. The immersion probe of claim 21 in which said reflecting
means is an internally reflecting rhomboid..].
23. The immersion probe of claim 15 wherein the diameter of said
second optical fiber is substantially greater than the diameter of
said first optical fiber.
24. The immersion probe of claim 23 wherein the distance from said
first optical element to said first optical fiber is set so that
the image of said first optical fiber is falls at the end or within
said lightguide and is no greater in diameter than said
lightguide.
.[.25. The immersion probe of claim 24 wherein the ratio of the
distance from said first optical element to said first optical
fiber to the distance from said first optical element to said
lightguide is approximately equal to the diameter of said first
optical fiber to the internal diameter of said lightguide, and
Wherein the ratio of the distance from said second optical element
to said second optical fiber to the distance from said second
optical element to said lightguide is approximately equal to the
diameter of said second optical fiber to the internal diameter of
said lightguide..].
26. The immersion probe of claim 15 in which said reflecting means
comprises two totally reflecting, parallel surfaces.
.[.27. The immersion probe of claim 26 in which the area of the
reflecting surface which overlaps the collected radiation is small
compared to the cross section of said collected radiation in the
vicinity of said reflecting surface..].
.[.28. The immersion probe of claim 27 in which said reflecting
means is an internally reflecting rhomboid..].
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates generally to spectroscopy and, more
particularly, to a Raman probe having a small diameter immersion
tip.
2. Description of the Related Art
Molecular spectroscopy is a family on analytical techniques that
provide information about molecular structure by studying the
interaction of electromagnetic radiation with the materials of
interest. In most of these techniques, the information is generally
obtained by studying the absorption of radiation as a function of
optical frequency. Raman spectroscopy is unique in that it analyzes
the radiation that is emitted (or scattered) when the sample is
irradiated by an intense optical signal consisting of a single
frequency, or a narrow range of frequencies. In this case the
"Raman scattering" signal is essentially an emission spectrum with
frequency dependent intensities. The individual bands in this
spectrum are shifted from the frequency of the excitation signal by
amounts that are related to the structure of the molecules present
in the sample.
Many different probe designs have been proposed for use in Raman
spectroscopy. Some examples are given in I. R. Lewis & P. R.
Griffiths, "Raman Spectroscopy with Fiber-Optic Sampling", Applied
Spectroscopy. Vol. 50, pg. 12A, 1996, FIGS. 3 through 11. These
fall into two general categories. The first category includes
probes that use separate optical fibers to transmit radiation to
and from the sample. Such "internal fiber probes" can be made quite
small in diameter. However, they are deficient in that their design
generally does not allow the use of optical filtering between the
sample and the fibers to filter out the spurious Raman signals
produced in the fiber. The second category includes probes which do
not use internal fibers but which employ optical means to
superimpose the path of the laser excitation beam and the receiving
path for transmission two and from the sample. Although these
probes are often employ optical fibers for coupling to the laser
source and the spectrometer, their design allows for the use of
filtering between these fibers and the sample. They are often
referred to as "externally filtered" or "fully filtered" probes. A
specific purpose of my invention is thus the design and
construction of a fully filtered probe which is suitable for
insertion into small volume chemical reaction vessels. I have been
told verbally that previous attempts to design small diameter,
fully filtered probes have been unsuccessful. This may be due to
the fact that most previous probe designs have superimposed the
transmitted and received paths in such a way that they are both
collimated and have approximately the same diameters at the point
where they are combined. This turns out to be a poor choice of
conditions for a small diameter probe.
Model RFP-480 Raman Probe introduced in the year 2000 by my
company, Axiom Analytical, employs a unique design in which a
collimated laser beam is injected into the center of the receiving
beam area by means of a rhomboid prism (see FIG. 1). This approach
provides ease of optical alignment by taking advantage of the fact
that the rhomboid can be fabricated with its two reflecting
surfaces highly parallel. However, in order to avoid blocking a
significant portion of the received signal, the areas of both the
rhomboid and the injected laser beam are made quite small. As will
be seen below, the use of a small diameter laser excitation beam
provides the first step toward the successful design of a probe
with an extended-length small diameter immersion tip. However, in
the standard RFP-480, both the transmitted and received beams are
nominally collimated in the beam-combining plane and inner diameter
of the lightguide in the immersion tip is necessarily set
approximately equal to the diameter of the lens which focuses the
Raman shifted radiation onto the receiving optical fiber. I will
show below that different considerations apply when it is necessary
for the probe to have a small diameter immersion tip that can be
inserted a substantial distance into a chemical mixture.
SUMMARY OF THE INVENTION
The purpose of this invention is to provide a probe for use in
Raman spectroscopy that can be inserted into a chemical vessel
through a small diameter fitting while maximizing the amount of
Raman shifted radiation collected and minimizing spurious
effects.
The invention resides in an immersion probe for use in Raman
spectroscopy which includes an extended immersion tip that includes
an internally reflecting lightguide, first optical element for
collecting laser radiation emerging from a first optical fiber and
directing it, after subsequent reflections, into the end of said
internally reflecting lightguide in such a way that it is as nearly
collimated as possible consistent with substantially all of the
radiation entering the lightguide, second optical element for
collecting Raman shifted radiation emerging from said internally
reflecting light guide and focusing it on a second optical fiber in
such a way that the size and shape of the image of the end of the
lightguide matches the size and shape of said second optical fiber,
and reflecting means for redirecting the beam formed by said first
optical element so that its axis is anti-parallel to and coaxial
with the axis of the Raman shifted radiation emerging from said
lightguide. In an alternative embodiment, the received beam is
redirected rather than the transmitted beam.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a cross-sectional view of a prior art Raman Probe in
which a collimated laser beam is injected into the center of the
receiving beam area by means of a rhomboid prism;
FIG. 2 is a cross-sectional view of an immersion probe of
Raman-Spectroscopy immersion probe in accordance with a preferred
embodiment of the invention;
FIG. 3 is a diagram illustrating the laser excitation path in the
case where the distance from the end of the laser excitation fiber
to the rear of the collimating lens is set equal to the back focal
length of the lens;
FIG. 4a illustrates the condition in which the end of the optical
fiber core is imaged on the input end of the lightguide;
FIG. 4b illustrates the condition at the output of the
lightguide;
FIG. 5 is an enlargement of the objective region of FIG. 4b,
showing the central in extreme rays that determine the size the
focus spot;
FIG. 6 is an illustration of the objective region wherein three
planes within the illuminated region are indicated by the letters
A, B, and C;
FIG. 7 illustrates a preferred embodiment for an "optical head"
used in a preferred embodiment of the invention; and
FIG. 8 illustrates an alternative embodiment of the invention in
which the distances d.sub.1 and d.sub.4 are set equal to the focal
lens of the two lenses so that both the laser beam to the right of
the collimating lens and the receive field of view to the right of
the collection lens are nominally collimated.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
A specific embodiment of my invention is shown in FIG. 2, an
assembly drawing of the Axiom Analytical RFP-420 immersion probe,
introduced during 2001. In this design, the laser radiation
emerging from the excitation optical fiber is formed into an
approximately collimated beam by a lens that has a short enough
focal length so that the collimated beam is no more than about 3 mm
in diameter. A small rhomboid doubly reflecting prism is then used
to displace this beam to the axis of the probe and to direct it
along this axis to the small diameter lightguide which is contained
within the probe immersion tip. The received Raman-shifted
radiation that has been collected by the objective lens at the end
of the immersion tip has a substantially greater range of
divergence angles than the nearly collimated laser beam as it
travels through the lightguide. A typical ray is thus reflected one
or more times by the lightguide wall. Such a ray will emerge from
the lightguide at a sufficient angle from the axis so that it
misses the angled reflecting surface of the rhomboid a passes on
toward the receiving optical fiber. A collection lens, which is
significantly larger in diameter than laser beam, is then used to
focus this radiation on the receiving fiber. A key element of the
invention is the fact that the collection lens images the end of
the lightguide on the optical fiber. In contrast, the laser beam
collimating lens is configured to produce a small diameter beam
which is nearly collimated as is consistent with all of the
radiation entering the lightguide. The various elements of this
design will be discussed below.
In developing my invention, my specific objective was first to
optimize the transfer of radiation from the laser excitation fiber
to the sample contained in a small vessel and second to optimize
both the collection of Raman shifted radiation from the sample and
the transfer of this radiation to the receiving fiber. To see how
this is done, we need to consider the interaction of the various
requirements. First, we will consider the transfer of radiation to
the sample through a small diameter lightguide.
FIG. 3 illustrates the laser excitation path in the case where the
distance from the end of the laser excitation fiber to the rear of
the collimating lens is set equal to the back focal length of the
lens. For simplicity, I have shown this path in a straight line,
without the rhomboid element. The radius of the laser beam when it
reaches the entrance to the lightguide will be equal to
r.sub.2=r.sub.3+d.sub.2 tan .alpha., where tan
.alpha.=r.sub.1/f.sub.1, and r.sub.3=f.sub.1 tan .theta..sub.1. Eq.
1
Here, r.sub.1 is radius of the fiber core, sin .theta..sub.1 is the
numeric aperture of the fiber, f.sub.1 is the focal length of the
collimating lens, r.sub.3 is the radius of the beam as it leaves
the lens, and d.sub.2 is distance from the lens to the lightguide
entrance.
The above equation can be written r.sub.2=f.sub.1 tan
.theta..sub.1+d.sub.2r.sub.1/f.sub.1. Eq. 2
It can be seen from Eq. 2 that either a large or a small value of
f.sub.1 will produce a large value of r.sub.2. Since we wish to
minimize r.sub.2, consistent with a reasonably small value of
r.sub.3, we wish to find the value of f.sub.1 that minimizes
r.sub.2. This can be done by taking the derivative of r.sub.2 as a
function of f.sub.1 and setting this equal to zero. The yields:
f.sub.1=(d.sub.2r.sub.1/tan .theta..sub.1).sup.1/2. Eq. 3
Substituting Equation 3 into Equation 2 yields the minimum value of
r.sub.2, r.sub.2=2(d.sub.2r.sub.1 tan .theta..sub.1).sup.1/2. Eq.
4
As a practical example, we will take r.sub.1=0.05 mm, d.sub.2=100
mm, and sin .theta..sub.1=0.22 (or tan .theta..sub.1=0.226).
Substituting these values into Equations 3 and 4 yields f.sub.1=4.7
mm and r.sub.2=2.1 mm. It can also be seen that the radius of the
beam at the collimating lens is r3=1.06 mm.
For the nominally collimated case just discussed, the angular
divergence of the beam is equal to .alpha., where tan
.alpha.=r.sub.1/f.sub.1. Eq. 5
This value can be reduced by increasing the focal length of the
collimating lens. This may be desirable in cases where the internal
diameter of the lightguide is larger than the initially calculated
beam diameter at its entrance. However, if the internal diameter of
the lightguide is smaller than the initially calculated beam
diameter, it may be necessary to change the design to one in which
the end of the fiber-optic core is imaged on the entrance to the
lightguide. This will increase the beam divergence in the
lightguide in the interest of enabling all of the radiation to
enter it. This compromise is discussed below.
FIG. 4 illustrates the condition in which the end of the optical
fiber core is imaged on the input end of the lightguide. Here, the
relationship between d1 and d2 is given by
1/d.sub.1+1/d.sub.2=1/f.sub.1, Eq. 6 and the image radius is given
by r.sub.2=r.sub.1d.sub.2/d.sub.1. Eq. 7
Here we see that the first term of Equation 2 has vanished. For a
given value of d.sub.2, we must select d.sub.1 (and hence f.sub.1)
to satisfy Equation 7. The radius of the beam at the lens will then
be equal to r.sub.3=d.sub.1 tan .theta..sub.1. Eq. 8
The maximum divergence of rays entering the lightguide will now be
given by tan
.beta.=(r.sub.3+r.sub.2)/d.sub.2=r.sub.3/d.sub.2+r.sub.1/f.sub.1.
Eq. 9
Comparing Equation 7 to Equation 3 and Equation 9 to Equation 5, we
see that by imaging the optical fiber core on the input to the
lightguide, we have decreased the beam diameter at the expense of
increased beam divergence. Under some conditions, it may be
possible to achieve a better compromise between beam diameter and
divergence angle by forming the imagine within the lightguide
rather than at the entrance.
We now consider the conditions at the output of the lightguide.
(See FIG. 4b.) The maximum divergence of the laser beam will still
be given by .beta. even if the individual rays have been reflected
by the walls of the lightguide. In the preferred embodiment of the
invention, an objective lens will be located adjacent to the output
of the lightguide. If the focal length of this lens (in the
surrounding medium) is given by d.sub.3, the focused laser spot
will have a radius of r.sub.4=d.sub.3 tan .beta.. Eq. 10
FIG. 5 is an enlargement of the objective region of FIG. 4b showing
the central and extreme rays that determine the size of the focused
spot.
FIG. 6 is a further illustration of the objective region in which I
have shown three planes in the illuminated region, indicated by the
letters A, B, and C. Plane A is the focal plane, i.e. the plane
where the illuminating beam has the least diameter. Raman shifted
radiation which originates in this plane and is collected by the
objective lens will have a maximum divergence angle of .beta. in
within the lightguide. After emerging from the far end of the
lightguide, this radiation would be confined to the same volume as
the laser illumination and thus would strike the injection element.
In the case where this element is a rhomboid--or other fully
reflecting element--all of the radiation would be blocked from
reaching the lens that focuses on the collection optical fiber.
However Raman shifted radiation is produced throughout the volume
that is illuminated by laser radiation. For example, in plane
.beta., a substantial part of the radiation arising from the two
regions indicated by the circles will strike the objective lens at
incidence angle larger than those corresponding to any of the laser
rays passing through the same regions. As a result, such radiation
will travel through the lightguide at angles such as .gamma..sub.1
and .gamma..sub.2 that are greater than the maximum divergence of
the incident laser radiation. On emerging from the far end of the
lightguide, most of this radiation will miss the injection element.
This is also true of a proportion of the radiation originating in
regions past the focal plane, as indicated by the dashed ray from
the circled region of plane C. However, the collection solid angle
will be greater for regions between the focal plane and the
objective lens. I would thus expect these regions to contribute
predominately to the collected Raman signal.
It should be noted that, for embodiments of the invention which use
a dichroic beam splitter rather than a fully reflecting injection
element, all illuminated regions--including the focal plane--will
contribute to the detected Raman shifted signal.
FIG. 7 illustrates a preferred embodiment of the "optical head" of
the probe, i.e. that portion of the probe which contains the
fiber-optic terminations and both the collimating and the
collecting optics. Also included in the region, but not shown in
FIG. 7, are the optical filters that are generally imposed in both
optical paths. As the figure illustrates, reflecting devices--which
may include one or more mirrors, a dichroic beamsplitter, or a
fully reflecting rhomboid--are used to superimpose the axis of the
laser beam on the axis of the receiving optical path. As discussed
above, the laser path will be nearly collimated and as small in
diameter as is consistent with the other requirements of the
design.
In order to collect as much of the Raman shifted radiation as is
practical, it is important to maximize the field of view of the
optical element which collects the radiation emerging from the
lightguide. In other words, we wish to maximize the collection
angle, .gamma..sub.m, as illustrated in FIG. 7. This angle is
determined by the numeric aperture of the optical fiber (NA=sin
.theta..sub.4), and by the two distances, d.sub.4 and d.sub.5.
i.e., tan .gamma..sub.m=(d.sub.4/d.sub.5)tan .theta..sub.4. Eq.
11
Since we have imaged the end of the lightguide on the collection
fiber, we have d.sub.4/d.sub.5=r.sub.4/r.sub.2, and we can write
the above equation as tan .gamma..sub.m=(r.sub.4/r.sub.2)tan
.theta..sub.4. Eq. 12
From Equation 12, we see that, for a given fiber numeric aperture
and lightguide diameter, the collected signal can be maximized by
maximizing the core radius of the receiving optical fiber. In the
case where the laser injection element is a rhomboid or other fully
reflecting device, it is also important that .gamma..sub.m be great
enough so that a large proportion of the collection field of view
misses this element. The size of the injection element should be at
least as large as the laser beam striking it. In the imaging case,
the radius of this beam is determined by the beam radius at the
collimating lens, by the radius of the lightguide, and by the
position of the element along the optical path. As a reasonable
approximation, we can assume that the beam radius at the injection
element is equal to the radius at the lens. i.e. r.sub.3=d.sub.1
tan .theta..sub.1.
In FIG. 7, I have indicated the radius of the collection field of
view to be r.sub.6 in the plane containing the injection element.
The maximum value of r.sub.6 will occur when the injection element
is quite close to the collection lens, in which case we can use the
approximation r.sub.6=r.sub.5. It can be shown that the maximum
value of the ratio of r.sub.6 to r.sub.3 will be
(r.sub.6/r.sub.3).sub.max=r.sub.4d.sub.5/r.sub.1d.sub.2. Eq. 13
For the assumed conditions, d.sub.2 will always be larger than
d.sub.5. However, this equation again indicates the benefit of
maximizing the radius of the core of the collection fiber relative
to that of the excitation fiber.
FIG. 8 illustrates an alternative embodiment in which the distances
d.sub.1 and d.sub.4 are set equal to the focal lengths of the two
lenses so that both the laser beam to the right of the collimating
lens and the received field of view to the right of the collection
lens are nominally collimated. A separate lens is then used for
coupling to the end of the light guide. Ideally, the distance
d.sub.0 would be set so that the image of the collection lightguide
core is matched to the lightguide. The radius of the laser beam at
the entrance to the lightguide, r.sub.2, could then be either
matched to the lightguide inner diameter or smaller than this,
depending on the following relationships:
r.sub.2/d.sub.0=r.sub.1/d.sub.1 and
r.sub.2/d.sub.0=r.sub.4/d.sub.4. Eq. 14
The advantage of this design is that it allows the obstruction due
to the injection element to minimized even if this element is some
distance from the collection lens. However, it does have a
disadvantage in that the additional lens used to the match the
lightguide is a source of potentially undesirable reflection of the
incident laser beam.
* * * * *