  United States Court of Appeals
      for the Federal Circuit
                ______________________

 FRANS NOOREN AFDICHTINGSSYSTEMEN B.V.,
            AND STOPAQ B.V.,
            Plaintiffs-Appellants,

                           v.

STOPAQ AMCORR INC., doing business as Amcorr
Products and Services, AND DOLPHIN SEALANTS,
                      LLC,
              Defendants-Appellees.
             ______________________

                      2013-1200
                ______________________

   Appeal from the United States District Court for the
Southern District of Texas in No. 10-CV-3150, Judge
Lynn N. Hughes.
                ______________________

              Decided: February 21, 2014
               ______________________

    GREGORY A. CASTANIAS, Jones Day, of Washington,
DC, argued for plaintiffs-appellants. With him on the
brief were JOSEPH M. BEAUCHAMP and H. ALBERT LIOU, of
Houston, Texas.

    JOHN R. KEVILLE, Winston & Strawn LLP, of Houston,
Texas, argued for defendants-appellees. With him on the
brief was DUSTIN J. EDWARDS. Of counsel on the brief was
RICHARD L. STANLEY, of Houston, Texas.
2     FRANS NOOREN AFDICHTINGSSYSTEM    v. STOPAQ AMCORR INC.



                   ______________________

    Before RADER, Chief Judge, TARANTO, and CHEN, Circuit
                           Judges.
TARANTO, Circuit Judge.
    The district court granted summary judgment of non-
infringement. We conclude that the district court
made errors in at least one claim construction underly-
ing its non-infringement judgment. We vacate the judg-
ment and remand for further proceedings.
                         BACKGROUND
    Frans Nooren Afdichtingssytemen B.V. owns U.S. Pa-
tent No. 5,898,044, entitled “Use of a Preparation for
Insulation/Sealing and Coating Purposes and Method for
Sealing Manhole Covers.” The ’044 patent discloses a
composition used for insulating and protecting sub-
strates—for example, manhole covers, underground
tanks, pipes, and cable sleeves—from corrosion, water
ingress, and mechanical stresses. ’044 patent, col. 1, lines
6-14; id., col. 4, line 63, through col. 5, line 2. Independ-
ent claim 1 of the ’044 patent reads:
      [a] shaped article comprising a substrate having
      on at least one portion of at least one surface a
      coating composition comprising an apolar, non-
      thermosetting fluid polymer having a glass tran-
      sition temperature lower than -20° C. and a sur-
      face tension of less than 40 mN/m at a
      temperature above its glass transition tempera-
      ture, and a filler comprising a plurality of frac-
      tions each comprising different size particles, and
      wherein said different fractions have different par-
      ticle size distributions.
’044 patent, col. 8, lines 10-18 (emphasis added). The ’044
patent specification explains the following about fillers:
FRANS NOOREN AFDICHTINGSSYSTEM      v. STOPAQ AMCORR INC.    3



    The preparation according to the invention can
    contain one or more fillers. Said fillers can be of
    organic or inorganic nature. Examples of inorgan-
    ic [sic] fillers are polyvinyl chloride, polyethene,
    polypropene, polyisoprene and rubber. Examples
    of inorganic fillers are inorganic minerals, salts
    and oxides, for example chalk, boron sulphate, al-
    uminium oxide, silicon dioxide, ground quartz,
    glass, talc, slate, bentonite and the like. Prefera-
    bly, a mixture of coarse and fine particles, in a
    specific mixing ratio, of one or more fillers is used.
    The rheological characteristics of the preparation
    according to the invention can be controlled by
    means of the amount of filler. According to the
    invention, it is therefore preferable that the fillers
    comprise one or more fractions, each fraction hav-
    ing a different particle size and a different particle
    size distribution. In particular, the fillers com-
    prise at least one fraction having a particle size of
    0.1 µm to 1500 µm.
Id., col. 3, line 55, through col. 4, line 4. The specification
adds that fillers can be “swellable or non-swellable” and
can have “a low or a high density.” Id., col. 4, lines 5-12.
    The ’044 patent is licensed exclusively to Stopaq B.V.,
a Dutch company that designs and manufactures coatings
and sealants that exhibit both viscous and elastic proper-
ties (i.e., visco-elasticity) and are designed for corrosion
protection and waterproofing. Kleiss & Co. B.V., a Dutch
company, manufactures similar products that prevent
corrosion and protect against leaks. One of these prod-
ucts, ViscoWrap, contains a mix of polybutene, polypro-
pylene, and aluminum trihydrate. EZ Wrap and Hippo
Patch, also manufactured by Kleiss, are products that
contain a mix of polybutene, polypropylene, and calcium
carbonate.
4   FRANS NOOREN AFDICHTINGSSYSTEM     v. STOPAQ AMCORR INC.



    In the United States, ViscoWrap and EZ Wrap are
distributed by Amcorr Products and Services, Inc., and
Hippo Patch is distributed by Dolphin Sealants LLC (the
two companies collectively, “Amcorr”). On August 24,
2010, Kleiss and Amcorr filed a declaratory judgment
action against Nooren in the Netherlands seeking a
declaration that their products, including ViscoWrap, EZ
Wrap, and Hippo Patch, do not infringe the ’044 patent.
On August 31, 2010, Nooren brought the present action
against Amcorr in the United States District Court for the
Southern District of Texas, alleging infringement of the
’044 patent. Amcorr asserted no counterclaims but did
assert affirmative defenses of non-infringement and
invalidity.
    Upon the parties’ joint request, the district court pro-
ceeded directly to entertain cross-motions for summary
judgment on infringement. Accepting that the polybutene
in the accused products met the claim’s “fluid polymer”
requirements—the specification itself names poly(1-
butylene), or polybutene, as a suitable fluid polymer, ’044
patent, col. 3, lines 6-10—the parties agreed to focus on
the phrase “a filler comprising a plurality of fractions
each comprising different size particles, and wherein said
different fractions have different particle size distribu-
tions” in claim 1, which is the only independent claim in
the ’044 patent. The court did not conduct a separate
proceeding, or receive separate papers, on the proper
construction of that filler/fractions limitation.
    It is undisputed that, for a product to come within the
limitation, it must contain “a filler” that itself includes at
least two “fractions” (having certain properties). Nooren
contended that the limitation is met by the combination of
polypropylene and aluminum trihydrate (for one accused
product) and by the combination of polypropylene and
calcium carbonate (for the others). In arguing that the
polypropylene in the accused products is one of the frac-
tions of the “filler,” it noted that the specification identi-
FRANS NOOREN AFDICHTINGSSYSTEM     v. STOPAQ AMCORR INC.   5



fies polypropylene (“polypropene”) as a possible filler.
’044 patent, col. 3, line 58. As far as appears, Nooren has
not argued that the polypropylene in the accused products
itself contains the required plurality of “fractions”; thus,
even if polypropylene counts as a fraction, the other
claim-required “fraction” has to come from the aluminum
trihydrate (for one product) or calcium carbonate (for the
others). Nooren did contend, however, that the accused
products meet the filler/fractions limitation even if one
disregards the polypropylene. Specifically, Nooren argued
that each of the aluminum trihydrate and calcium car-
bonate in the accused products—each undisputedly a
“filler”—itself contains two or more “fractions” with the
required properties.
    Amcorr denied that polypropylene could help satisfy
the limitation. First, it argued, all of the “fractions” of
any given filler must be of the same material; as a result,
polypropylene—not itself containing more than one “frac-
tion”—could not supply a second “fraction” to add to the
aluminum trihydrate or calcium carbonate.          Second,
Amcorr argued, polypropylene in the accused products is
not a “filler” at all. Having thus sought to exclude poly-
propylene from relevance, Amcorr completed its non-
infringement argument by denying that either aluminum
trihydrate or calcium carbonate itself contains at least
two “fractions” having the specified properties.
    On January 4, 2013, the district court issued an opin-
ion and order granting summary judgment of non-
infringement in favor of Amcorr. Frans Nooren Afdicht-
ingssytemen BV v. Stopaq Amcorr Inc., No. H-10-3150
(S.D. Tex. Jan. 4, 2013), ECF No. 55 (“District Court
Opinion”). The opinion does not announce full construc-
tions of all of the significant terms of the filler/fractions
limitation. It does, however, rely on certain constructions
in agreeing with Amcorr. First, it adopts both of Amcorr’s
grounds for concluding that polypropylene cannot help
meet the limitation. Id. at 2, 3. Second, it adopts
6   FRANS NOOREN AFDICHTINGSSYSTEM     v. STOPAQ AMCORR INC.



Amcorr’s position that neither the aluminum trihydrate
nor the calcium carbonate meets the specific requirements
for a plurality of “fractions.” Id. at 2. Based on those
conclusions, the court found no infringement as a matter
of law. Id. at 3.
    The court entered an amended final judgment on
January 31, 2013. Nooren appeals. We have jurisdiction
under 28 U.S.C. § 1295(a)(1).
                        DISCUSSION
    Nooren challenges the district court’s conclusions and
the constructions on which they rest. We review the
district court’s claim constructions and its grant of sum-
mary judgment de novo. Cybor Corp. v. FAS Techs., Inc.,
138 F.3d 1448, 1451 (Fed. Cir. 1998); Honeywell Int’l, Inc.
v. ITT Indus., Inc., 452 F.3d 1312, 1317 (Fed. Cir. 2006).
                              A
                              1
     The district court’s principal ground for holding that
polypropylene in the accused products cannot help to meet
the limitation at issue is a claim construction—that “a
filler” in the ’044 patent can contain only “one material.”
District Court Opinion at 2; id. (“Nooren’s patent limits its
infringement claims to single-material mixtures.”); id. at
3 (“the patent does not cover fillers mixed from multiple
materials”); id. (“a mixed-material filler is outside the
patent’s scope”). Because there is no contention that
polypropylene itself contains more than one “fraction,” as
the filler/fractions limitation requires, the district court’s
construction means that polypropylene can play no role in
meeting the limitation—which, instead, must be met
solely by either the aluminum trihydrate or the calcium
carbonate.
    We disagree with the district court’s construction. We
see no basis in the language or specification for limiting “a
FRANS NOOREN AFDICHTINGSSYSTEM    v. STOPAQ AMCORR INC.   7



filler” to “one material.” We have been pointed to nothing
about a customary usage of the term itself, and nothing in
the specification’s use of it, that excludes from being “a
filler” a mixture of two different “materials” (whether that
word means a mixture of different molecules or something
else). The district court did not rely on the claim term or
the specification to draw its conclusion. Instead, the court
based its one-material construction entirely on its conclu-
sion that, during prosecution of the ’044 patent, “the
examiner rejected the claims and requested amendments,
citing the Nakano patent and other prior art indicating
that polymer-based coatings with two fillers have already
been patented.” District Court Opinion at 2. But we
think that the prosecution history does not support the
court’s adoption of its otherwise-unwarranted narrowing
of the term’s meaning.
    During prosecution, the examiner rejected claims 55-
57 of the application as obvious in light of five pieces of
prior art, including U.S. Patent No. 5,221,575 (Nakano),
which the examiner found “divulge[s] metal foil coated
with a silica and graphite filled organopolysiloxane.” J.A.
467. Based on a review of this prior art, the examiner
concluded that “[i]t would have been obvious to one hav-
ing ordinary skill in the art to apply known insulating
and waterproofing coatings to electrical equipment where
the kind of coatings are customarily used.” J.A. 468. The
examiner explained that claim 58, dependent on claim 56,
would actually be allowable if it were “rewritten in inde-
pendent form to include all of the limitations of the base
claim and any intervening claims.” J.A. 469. Applicants
did so, and that claim became claim 1 in the issued ’044
patent.
    This history does not establish exclusion of dual-
material fillers. Applicants never said anything that
states or implies such an exclusion. And even the exam-
iner’s language regarding Nakano does not clearly focus
on the number of materials in what constitutes a filler.
8   FRANS NOOREN AFDICHTINGSSYSTEM    v. STOPAQ AMCORR INC.



Indeed, what distinguishes the claims rejected based on
Nakano and other prior art (claims 55-57) from the claim
approved if rewritten in independent form (claim 58) is
not, on its face, whether the filler contains one or more
“materials,” which is not a term in the claims. Moreover,
Nakano itself appears to disclose a product containing
graphite powder alone as a (single-material) filler. ’575
patent, col. 2, lines 38-44, and col. 3, lines 38-68. For all
of these reasons, there is no clear prosecution-history
narrowing of “a filler” to a single material.
    Amcorr makes a claim-differentiation argument that
the district court rightly did not embrace. Amcorr sug-
gests that claim 2’s requirement that the composition of
claim 1 “additionally comprises at least one filler” re-
quires that claim 1’s requirement of “a filler” be limited to
a single material. But there is no persuasive connection
between the claim 1/claim 2 difference and the number of
materials that can be in a filler. Indeed, the relation
between claim 1 and claim 2 is obscure on its face, and the
reason is evident: It results from a sloppy amendment
process that conveys nothing about intended scope.
     Issued claim 2 was original claim 56, which depended
on original claim 55, and original claim 58 (which became
issued claim 1) depended on claim 56. In that original
arrangement, the greater specificity of claim 58 than of
claim 56 made sense. When the examiner said that claim
58 would be approved if rewritten in independent form,
applicants did so by amending claim 55, so that the
unchanged claim 56 now depended on the substantive
claim that previously had depended on it. And the claims
issued in this peculiar form as claims 1 and 2. We have
often counseled care in drawing inferences from claim
differentiation. See, e.g., Marine Polymer Techs., Inc. v.
HemCon Inc., 672 F.3d 1350, 1359 (Fed. Cir. 2012) (en
banc). In the present circumstances, no inference about
the scope of claim 1 can fairly be drawn from claim 2.
FRANS NOOREN AFDICHTINGSSYSTEM     v. STOPAQ AMCORR INC.   9



                             2
     The district court’s second ground for holding that
polypropylene in the accused products plays no role in
meeting the filler/fractions limitation is the conclusion
that “[t]he polypropylene in Amcorr’s products is not a
filler” at all. District Court Opinion at 3; id. (“[p]olypro-
pylene [in the accused products] is not a filler”). The
court’s sole explanation is the statement that, in the
accused products, “[p]olypropylene mixes with polybutene
to form a homogenous polymer mixture.” Id.
    That reasoning, however, does not state a claim con-
struction of “a filler,” let alone justify a particular con-
struction by addressing the parties’ respective contentions
about the term’s meaning through the usual analysis.
Indeed, the claim-construction portion of the district
court’s opinion (id. at 2) includes nothing about “a filler”
except that it must consist of only one material. The
opinion thus does not explain the connection between its
finding about a “homogenous polymer mixture” and any
construction of “a filler.”
     Nooren has argued that “a filler” should be construed
to mean “one or more organic or inorganic components
other than the specific, ‘apolar, non-thermosetting fluid
polymer’ that assist in controlling rheological characteris-
tics of the preparation.” Brief for Plaintiffs-Appellants at
44; id. at 46 (“everything else in the composition, other
than the apolar, non-thermosetting fluid polymer, that
assists in controlling rheological characteristics of the
composition”). But it has barely developed that argu-
ment, instead focusing almost entirely on (successfully)
challenging the one-material construction of the district
court. Nooren’s only cited support for this construction is
the specification statement that “[t]he rheological charac-
teristics of the preparation . . . can be controlled by means
of the amount of filler.” ’044 patent, col. 3, lines 64-65.
That statement, however, does not mean that everything
10 FRANS NOOREN AFDICHTINGSSYSTEM v. STOPAQ AMCORR INC.



with a fluid-flow controlling effect is “a filler.” And the
specification says that, in addition to the fillers, the
product “can also contain” petroleum gel and wax (and
similar substances)—which, it is undisputed, can affect
the fluid-flow character of the overall preparation. ’044
patent, col. 4, lines 21-25; J.A. 993.
     Amcorr has offered evidence of the ordinary meaning
of the term “a filler” that appears to be uncontroverted by
Nooren and that appears to fit this patent. The Con-
densed Chemical Dictionary 383 (9th ed. 1977) defines
“filler” (in the relevant definition) as “[a]n inert mineral
powder of rather high specific gravity (2.00-4.50) used in
plastic products and rubber mixtures to provide a certain
degree of stiffness and hardness, and to decrease cost.”
J.A. 501. (It gives calcium carbonate as an example. Id.)
It adds that “[f]illers have neither reinforcing nor coloring
properties, and the term should not be applied to materi-
als that do, i.e., reinforcing agents or pigments.” Id. On
the present state of the record, “a filler” should be accord-
ed that meaning.
    But we are not prepared to affirm the district court’s
conclusion that, as a matter of law, the polypropylene in
the accused products is not serving as a filler. The court
did not recite the above construction or explain how its
observation about the “homogenous polymer mixture”—
and the evidence about glass transition temperatures on
which it was based, e.g., J.A. 617-18—connects to the
claim term’s scope, especially in light of the specification’s
express contemplation that polypropylene can, at least
sometimes, serve as a filler. See ’044 patent, col. 3, line
58. Moreover, the experts disagreed about whether poly-
propylene in the accused products is serving as a filler.
Compare J.A. 617-18 with J.A. 902-03. The district court,
not having articulated a construction, did not parse the
experts’ evidence for genuine disputes under the proper
construction, and we will not do so ourselves. Indeed, the
experts’ declarations are not focused on how the polypro-
FRANS NOOREN AFDICHTINGSSYSTEM     v. STOPAQ AMCORR INC. 11



pylene fits, does not fit, or might fit the claim requirement
of “a filler” as properly construed—the district court not
having provided the experts a construction. In these
circumstances, we vacate the district court’s summary-
judgment ruling that “[t]he prolypropylene in Amcorr’s
products is not a filler.” District Court Opinion at 3.
                             B
     For the foregoing reasons, it remains an open ques-
tion whether polypropylene can be a filler, and thus may
be considered as part of any analysis of whether the
accused products meet the filler/fractions claim limitation.
It is therefore at present unnecessary to decide whether
either the aluminum trihydrate or the calcium carbonate
in the accused products can by itself meet that limitation.
And we choose not to do so.
     If we agreed with the district court that each of those
two conceded “fillers” itself has only one “fraction” meet-
ing the limitation’s requirements, as a matter of law, we
still could not affirm the judgment of non-infringement,
because we leave open whether polypropylene might
supply a second such “fraction.” If we disagreed with the
district court, the ordinary course would be for us to
reverse the grant of summary judgment of non-
infringement and remand. It is true that we would have
the “authority” to consider the (implicit) denial of Noor-
en’s motion for summary judgment of infringement, i.e., to
decide if, as a matter of law, either the aluminum trihy-
drate or the calcium carbonate itself has at least two
fractions with the required properties. See, e.g., Dey L.P.
v. Sunovion Pharm. Inc., 715 F.3d 1351, 1360 n.5 (Fed.
Cir. 2013). But we are not required to do so, and here we
exercise our discretion not to proceed to the question of
infringement as a matter of law. There has been insuffi-
cient exploration in the record, both here and in the
district court, of too many questions of apparent relevance
to identifying a proper construction of the limitation,
12 FRANS NOOREN AFDICHTINGSSYSTEM v. STOPAQ AMCORR INC.



which requires, among other things, that the construction
itself supply “a meaningfully precise claim scope.” Halli-
burton Energy Servs., Inc. v. M–I LLC, 514 F.3d 1244,
1251 (Fed. Cir. 2008); see MeadWestVaco Corp. v. Rexam
Beauty and Closures, Inc., 731 F.3d 1258, 1270 n.8 (Fed.
Cir. 2013).
    Regarding claim construction, the district court said
the following:
   3. Single Material, Multiple Fractions
   ...
   The filler must include multiple fractions, each
   with a distinct particle size distribution. For the
   filler limitation to be meaningful, each fraction
   must have both a discrete range of particle sizes
   as well as a high number of particles in that
   range. Without this threshold, any variation in
   size would be a different fraction, and infringe-
   ment would be unavoidable.
   On a size-distribution graph, a different fraction
   would be represented by a distinct peak. A minor
   bump does not distinguish a separate fraction. A
   graph representing multiple fractions would re-
   quire at least a bimodal distribution with two or
   more predominate peaks.
District Court Opinion at 2. Applying this construction,
the court then added the following:
   4. Amcorr’s Fillers.
   Amcorr’s filler materials—calcium carbonate and
   aluminum trihydrate—have unimodal particle
   distributions and are not covered by Nooren’s pa-
   tent. The distribution graph for each filler has a
   single peak. The minor protrusions and changes
   in slope are not peaks. They show multiple parti-
   cle sizes but not multiple fractions.
FRANS NOOREN AFDICHTINGSSYSTEM      v. STOPAQ AMCORR INC. 13



Id. This reasoning leaves us with a host of questions,
which we think would be better addressed initially by
more focused analysis—and, if necessary, more focused
record development—on remand.
     The claim limitation at issue requires a filler that in-
cludes “a plurality of fractions each comprising different
size particles, and wherein said different fractions have
different particle size distributions.” ’044 patent, col. 8,
lines 16-18. It is the usual (though not invariable) rule
that, in patent claims as elsewhere, the construction of a
clause as a whole requires construction of the parts, with
meaning to be given to each part so as to avoid rendering
any part superfluous. See 3M Innovative Props. Co. v.
Tredegar Corp., 725 F.3d 1315, 1329 (Fed. Cir. 2013); see
also Duncan v. Walker, 533 U.S. 167, 174 (2001); Medlin
Constr. Grp., Ltd. v. Harvey, 449 F.3d 1195, 1200-01 (Fed.
Cir. 2006). Terms generally carry their ordinary and
customary meaning in the relevant field at the relevant
time, as shown by reliable sources such as dictionaries,
but they always must be understood in the context of the
whole document—in particular, the specification (along
with the prosecution history, if pertinent). See Phillips v.
AWH Corp., 415 F.3d 1303, 1312-18 (Fed. Cir. 2005) (en
banc); see also Sandifer v. United States Steel Corp., 134
S. Ct. 870, 876-77 (2014) (statute construed by discerning
ordinary meaning at relevant time, relying on dictionar-
ies).
     The district court did not separately construe “frac-
tion,” “different size particles,” and “different particle size
distributions.” It is not clear that the court gave “differ-
ent size particles” a meaning that avoids redundancy with
“different particle size distributions.” And it is not clear
whether, in saying that “each fraction must have both a
discrete range of particle sizes as well as a high number of
particles in that range,” the court was construing “frac-
tion” or instead was stating a conclusion about some
combination of “fraction” with one or the other of the two
14 FRANS NOOREN AFDICHTINGSSYSTEM v. STOPAQ AMCORR INC.



properties the limitation requires for the fractions: each
fraction must have “different particle sizes,” and different
fractions must have “different particle size distributions.”
    Nooren proposes in this court that “fractions” means
any “part of a whole.” Brief for Plaintiffs-Appellants at
26. But it does not cite any reliable source for that usage
being the ordinary meaning in the relevant field. And
because Nooren’s proposal (“part,” with no further clarifi-
cation whatever) seems to cover any proper subset of any
collection of particles, without regard to size ranges or any
other characteristic, it is not clear that this proposed
meaning would, once the other terms were properly
construed, leave the limitation as a whole with a sensible
and definite meaning. 1 The district court’s reference to
the need for “the filler limitation to be meaningful” may
reflect this concern. District Court Opinion at 2. Amcorr,
for its part, relied on two portions of the definition of
“fraction” in the McGraw-Hill Dictionary of Scientific and
Technical Terms 799 (5th ed. 1994): “[MET] In powder
metallurgy, that portion of sample that lies between two
stated particle sizes. Also known as cut. [SCI TECH] A
portion of a mixture which represents a discrete unit and
can be isolated from the whole system.” J.A. 505. The
district court’s “discrete range” language, if it means to
define “fractions” (rather than one of the other terms of



    1    In Nooren’s apparent proper-subset sense, a col-
lection of 1,000,000 particles would have 21,000,000 - 2
distinct “parts.” The limitation at issue would require
only that there be two “parts” (e.g., one subset consisting
of a 1 µm particle and a 3 µm particle, another consisting
of a 2 µm, 5 µm, and 10 µm particle) that would be tested
for meeting the size and size-distribution requirements.
Depending on what those two requirements mean, the
requirements might be met for practically any real-world
collection of particles.
FRANS NOOREN AFDICHTINGSSYSTEM    v. STOPAQ AMCORR INC. 15



the limitation), may be based on combining selected
portions of this definition.
    The claim language requires that each fraction (how-
ever defined) have two features. It must have “different
particle sizes”—which suggests simply that the particles
in that fraction must not all be of the same size. And its
“particle size distribution” must differ from that of the
other fractions that make up the required plurality.
Given the terms used and the presumptive need to avoid
redundancy with the first requirement, that requirement
suggests that the mix of different-size particles within a
fraction must show a pattern that differs from the pattern
shown by the mix of different-size particles within the
other fractions making up the claimed plurality. For
example, perhaps one pattern would be accurately repre-
sented by a bell curve, another by an asymmetrical curve,
in an apples-to-apples comparison after choosing one from
among the several options for graphing distributions
(discussed infra).
    But it is by no means clear that these understandings
are ultimately the right ones. In particular, the specifica-
tion, in contrast to the claim’s requirement that an indi-
vidual fraction have “different particle sizes” (a plural
phrase), speaks of “each fraction having a different parti-
cle size” (a singular phrase) “and a different particle size
distribution.” ’044 patent, col. 4, lines 1-2. The singular
phrase used for “different particle size” suggests, contrary
to the claim language, a comparison of the particle sizes
between fractions rather than within a fraction—so that
there is no overlap in size (e.g., diameter) between parti-
cles in one fraction and particles in another. A proper
claim-construction analysis would have to consider
whether this disparity affects the proper construction,
which depends on, among other things, the clarity of the
claim language and whether a specification statement
rises to the level of redefinition or disclaimer.
16 FRANS NOOREN AFDICHTINGSSYSTEM v. STOPAQ AMCORR INC.



    The district court, like the parties, turned to various
graphical representations of collections of particles in
discussing (and then applying) its claim construction.
District Court Opinion at 2. There are at least two prob-
lems with this discussion. First, there are a number of
different possible graphs involving particle size used in
the field: one cannot speak of “[t]he distribution graph.”
Id. (emphasis added). For example, a text submitted to
the district court explained that there are varying tech-
niques for measuring the size of particles (e.g., sieving,
sedimentation, light scattering); the x-axis, showing
particle size, can be linear or logarithmic; the y-axis can
show the number (frequency) or volume or mass of parti-
cles of any given size, often normalized by using percent-
ages; and the resulting graphs can be quite different. See
H.     MERKUS,       PARTICLE     SIZE     MEASUREMENTS:
FUNDAMENTALS, PRACTICE, QUALITY 13, 15, 18, 20, 23
(2009), available at Frans Nooren Afdichtingssytemen, No.
H-10-3150, ECF 24-3. The parties here relied on graphs
of varying methods—using particle numbers (J.A. 934),
mass (J.A. 411, 412), and volume (J.A. 413, 903). The
differences cannot be ignored: it seems that “peaks”
appearing on one graph can disappear on another, for the
very same particle collection. 2 If the claim scope turned


   2    Solely for illustrative purposes, consider the graph
at J.A. 935, which Nooren relies on as showing (at least)
two peaks even under the district court’s construction:
FRANS NOOREN AFDICHTINGSSYSTEM     v. STOPAQ AMCORR INC. 17



on numbers of peaks, it may matter considerably which
graph is used. Moreover, where results can dramatically
differ according to which of several quantitative tech-
niques for applying a claim term is chosen, and the patent
does not make clear which technique is meant, an indefi-
niteness problem may arise. See Honeywell Int’l, Inc. v.
ITC, 341 F.3d 1332, 1338-40 (Fed. Cir. 2003).




The graph, using a logarithmic scale for particle size,
shows the percent of overall volume made up by particles
of a given size. Nooren has identified as a second “peak”
the local maximum on the right as the curve goes from
particles of about 12 µm diameter to particles of about 18
µm diameter. The heights at those points appear to be
about 1.1 and 1.3 (on the y-axis scale, measuring percent
of total volume). The curve at 18 µm is higher than at 12
µm—about 18% higher (1.3/1.1 is about 1.18).
     A frequency curve for the same particle collection
(showing the number of particles, in absolute or percent-
age terms) would seem to erase the volume-curve peak at
18 µm. If the volume is proportional to the cube of the
particle radius, as is true for a sphere, then a graph
showing the frequency of particles by number would be
lower at 18 µm than at 12 µm: the height at 18 µm diame-
ter (9 µm radius) would be only about one-third the height
at 12 µm diameter (6 µm radius). (Assuming away pack-
ing, the ratio of the volumes of the particles at those two
diameters is 729/216 [93/63] times the ratio of the numbers
of such particles; i.e., the ratio of the numbers of particles
at those two diameters is 216/729 times the ratio of the
volumes of particles at those two diameters. A volume
ratio of 1.18, times 216/729, is a number-of-particles ratio
of about .35, i.e., roughly one-third.) On these assump-
tions, simply changing from a volume graph to a frequen-
cy graph replaces a curve that is higher at 18 µm than at
12 µm with one that is lower at 18 µm than at 12 µm.
18 FRANS NOOREN AFDICHTINGSSYSTEM v. STOPAQ AMCORR INC.



    Second, the district court, in describing what it
thought a graph must show to satisfy the limitation
requiring at least two fractions with certain properties,
spoke of “a high number of particles” in a “discrete range,”
a “distinct peak,” and a “bimodal distribution with two or
more predominate peaks,” contrasting a “minor bump,”
“minor protrusions,” and “changes in slope.” District
Court Opinion at 2. At least some of these terms raise
evident questions of precision as to their boundaries.
(Although “changes in slope” has a precise mathematical
meaning, covering any curve without a constant slope,
Nooren, in using the term, evidently means something
else, since it seems to view a smooth bell curve as lacking
such changes, even though its slope is always changing.)
Again, such terms can raise an indefiniteness problem.
See Halliburton Energy, 514 F.3d at 1251.
    In enumerating problems relevant to arriving at a
proper construction, we do not mean to be exhaustive or
to suggest the absence of solutions. Nor do we address
the consequences for infringement or invalidity, including
what questions have to be answered (given the potential
availability of polypropylene as part of a filler) in order to
arrive at a final judgment. Rather, we are identifying at
least some of the problems that require attention in a
more focused and systematic claim-construction analysis
than the parties and the record currently supply.
                        CONCLUSION
    For the foregoing reasons, the judgment of the district
court is vacated, and the case is remanded for further
proceedings consistent with this opinion.
    No costs.
                VACATED AND REMANDED
