PLAGER, Circuit Judge.
This is an appeal from a district court judgment that Hawk Measurement Systems Pty. Limited (individually “Hawk Australia”) [1041]*1041and Hawk America, Inc., (collectively “defendants” or “Hawk”) infringed U.S. Patent No. 4,000,650 (“the ’650 patent”). The patent, now expired, was the property of Endress + Hauser GmbH & Co. (“E + H Germany”). Endress + Hauser, Inc. (“E + H U.S.”), the exclusive distributor for E -I- H Germany in the United States, is also a party to the suit. The plaintiffs will be referred to collectively as “plaintiffs” or “E + H”. After conducting a bench trial and having heard and considered the evidence, the District Court for the Southern District of Indiana found that defendants infringed plaintiffs’ patent, and awarded damages. Because the district court correctly construed the means-plus-function claims, correctly determined that they were infringed by the defendants’ accused device, and properly awarded damages, we affirm.
BACKGROUND
At issue in this case are devices that measure the height or level of a material enclosed in a bin or tank by using ultrasonic pulses to determine the distance from their source, the transducer, to the material enclosed in the bin or tank. After the transducer emits an ultrasonic pulse, the device calculates the time it takes the pulse to travel to the enclosed material and reflect back to the transducer. The device then converts this time measurement to a distance measurement. A particular problem with devices of this type lies in distinguishing the true return pulse from false echoes emanating from sources other than the enclosed material, sources such as ladders or other structures within the enclosure, and echoes from the walls or dust.
Beginning in about 1988, Hawk Australia began manufacturing ultrasonic level-measuring equipment. This equipment was subsequently sold to U.S. distributors. In mid-1991, Hawk America began selling the accused Hawk Australia products in the U.S. At least as early as 1990, Hawk Australia learned of the ’650 patent when plaintiffs notified Delavan, another U.S. distributor of Hawk Australia’s products, of their belief that the Hawk device infringed the ’650 patent.
After Hawk Australia learned of the ’650 patent, it modified its device, the prior “comparator device,” and instead incorporated an analog-to-digital converter. It modified its software accordingly to make it compatible with the new converter. The record indicates that the majority of the sales made in the U.S. were of the Hawk device as modified.
DISCUSSION
The claims at issue in this appeal, claims 43 and 44, are means-plus-function claims and come within 35 U.S.C. § 112 ¶ 6 (1994). Claims so written “shall be construed to cover the corresponding structure, material, or acts described in the specification and equivalents thereof.” Id. Claim 43 is an independent claim, from which claim 44 depends. Claim 43 states:
In a control system for use in monitoring the level of material in a storage tank including a transducer directing ultrasonic pulses toward and receiving echo response pulses reflected from the upper surface of said material, and a control circuit operatively connected to said transducer to provide an indication of material level on the basis of the round-trip transit time of an ultrasonic pulse from said transducer to said material surface and back again, the improvement wherein said control circuit comprises means converting said echo response pulses to digital signals having a numerical value indicative of the intensity of each of said echo pulses relative to one another, and level indicating means responsive to said converting means to provide said indication of material level on the basis of the relative numerical value of said digitized response pulses, (emphasis added).
The claim thus recites two improvements over the prior art, the converting means and the level indicating means responsive to the converting means. Much of the argument in the district court and again on appeal centered on the question of exactly what was encompassed in the limitation regarding the level indicating means, the limitation italicized above.
[1042]*1042The parties do not dispute that the accused Hawk device contains structure (material or acts not being applicable) that differs in certain respects from that described in the specification. Thus, as the district court correctly stated, “the only question is whether the Hawk device employs means that are the equivalent of the structures described in the [’650] patent’s specification.” Endress + Hauser, Inc. v. Hawk Measurement Sys., 32 USPQ2d 1768, 1776, 1994 WL 736442 (S.D.Ind.1994) (emphasis added).
In arriving at her conclusion that the answer is “yes,” the district judge, in a detailed and thorough opinion, first construed the claims and their specific means-plus-function limitations, including the scope of equivalent structures those limitations encompassed, and then determined whether the accused devices infringed the claims so construed.
Defendants vigorously attack the district judge’s crediting of the testimony of Dr. Silva, a professor of electrical engineering at Purdue University, who testified as an expert on behalf of the plaintiffs. Defendants point out that the district judge arrived at many of the same conclusions as did Dr. Silva, and complain that had the district judge instead agreed with their expert witness, the interpretation issues would have been decided quite differently. Defendants attack Dr. Silva on the grounds that he is not “a person of ordinary skill in the art,” and that he at one point in the proceedings acknowledged that much. Of course that objection is meritless. The “person of ordinary skill in the art” is a theoretical construct used in determining obviousness under § 103, and is not descriptive of some particular individual. Custom Accessories, Inc. v. Jejfrey-Allan Indust., Inc., 807 F.2d 955, 963, 1 USPQ2d 1196, 1201 (Fed.Cir.1986) (“The person of ordinary skill is a hypothetical person who is presumed to be aware of all the pertinent prior art”); see also Kimberly-Clark v. Johnson & Johnson, 745 F.2d 1437, 1453 (Fed.Cir.1984). To suggest that the construct applies to particular individuals could mean that a person of exceptional skill in the art would be disqualified from testifying as an expert because not ordinary enough. To the extent that the gravamen of defendants’ complaint is that Dr. Silva was unqualified to testify as an expert witness at all, the record reflects his substantial credentials as an electrical engineer, and the decision to permit him to testify was well within the discretion of the trial judge. See, e.g., Kelsay v. Consol. Rail Corp., 749 F.2d 437, 448-49 (7th Cir.1984).
Defendants further argue that:
Dr. Silva had never attended law school, never practiced patent law and was not appearing as a lawyer.
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PLAGER, Circuit Judge.
This is an appeal from a district court judgment that Hawk Measurement Systems Pty. Limited (individually “Hawk Australia”) [1041]*1041and Hawk America, Inc., (collectively “defendants” or “Hawk”) infringed U.S. Patent No. 4,000,650 (“the ’650 patent”). The patent, now expired, was the property of Endress + Hauser GmbH & Co. (“E + H Germany”). Endress + Hauser, Inc. (“E + H U.S.”), the exclusive distributor for E -I- H Germany in the United States, is also a party to the suit. The plaintiffs will be referred to collectively as “plaintiffs” or “E + H”. After conducting a bench trial and having heard and considered the evidence, the District Court for the Southern District of Indiana found that defendants infringed plaintiffs’ patent, and awarded damages. Because the district court correctly construed the means-plus-function claims, correctly determined that they were infringed by the defendants’ accused device, and properly awarded damages, we affirm.
BACKGROUND
At issue in this case are devices that measure the height or level of a material enclosed in a bin or tank by using ultrasonic pulses to determine the distance from their source, the transducer, to the material enclosed in the bin or tank. After the transducer emits an ultrasonic pulse, the device calculates the time it takes the pulse to travel to the enclosed material and reflect back to the transducer. The device then converts this time measurement to a distance measurement. A particular problem with devices of this type lies in distinguishing the true return pulse from false echoes emanating from sources other than the enclosed material, sources such as ladders or other structures within the enclosure, and echoes from the walls or dust.
Beginning in about 1988, Hawk Australia began manufacturing ultrasonic level-measuring equipment. This equipment was subsequently sold to U.S. distributors. In mid-1991, Hawk America began selling the accused Hawk Australia products in the U.S. At least as early as 1990, Hawk Australia learned of the ’650 patent when plaintiffs notified Delavan, another U.S. distributor of Hawk Australia’s products, of their belief that the Hawk device infringed the ’650 patent.
After Hawk Australia learned of the ’650 patent, it modified its device, the prior “comparator device,” and instead incorporated an analog-to-digital converter. It modified its software accordingly to make it compatible with the new converter. The record indicates that the majority of the sales made in the U.S. were of the Hawk device as modified.
DISCUSSION
The claims at issue in this appeal, claims 43 and 44, are means-plus-function claims and come within 35 U.S.C. § 112 ¶ 6 (1994). Claims so written “shall be construed to cover the corresponding structure, material, or acts described in the specification and equivalents thereof.” Id. Claim 43 is an independent claim, from which claim 44 depends. Claim 43 states:
In a control system for use in monitoring the level of material in a storage tank including a transducer directing ultrasonic pulses toward and receiving echo response pulses reflected from the upper surface of said material, and a control circuit operatively connected to said transducer to provide an indication of material level on the basis of the round-trip transit time of an ultrasonic pulse from said transducer to said material surface and back again, the improvement wherein said control circuit comprises means converting said echo response pulses to digital signals having a numerical value indicative of the intensity of each of said echo pulses relative to one another, and level indicating means responsive to said converting means to provide said indication of material level on the basis of the relative numerical value of said digitized response pulses, (emphasis added).
The claim thus recites two improvements over the prior art, the converting means and the level indicating means responsive to the converting means. Much of the argument in the district court and again on appeal centered on the question of exactly what was encompassed in the limitation regarding the level indicating means, the limitation italicized above.
[1042]*1042The parties do not dispute that the accused Hawk device contains structure (material or acts not being applicable) that differs in certain respects from that described in the specification. Thus, as the district court correctly stated, “the only question is whether the Hawk device employs means that are the equivalent of the structures described in the [’650] patent’s specification.” Endress + Hauser, Inc. v. Hawk Measurement Sys., 32 USPQ2d 1768, 1776, 1994 WL 736442 (S.D.Ind.1994) (emphasis added).
In arriving at her conclusion that the answer is “yes,” the district judge, in a detailed and thorough opinion, first construed the claims and their specific means-plus-function limitations, including the scope of equivalent structures those limitations encompassed, and then determined whether the accused devices infringed the claims so construed.
Defendants vigorously attack the district judge’s crediting of the testimony of Dr. Silva, a professor of electrical engineering at Purdue University, who testified as an expert on behalf of the plaintiffs. Defendants point out that the district judge arrived at many of the same conclusions as did Dr. Silva, and complain that had the district judge instead agreed with their expert witness, the interpretation issues would have been decided quite differently. Defendants attack Dr. Silva on the grounds that he is not “a person of ordinary skill in the art,” and that he at one point in the proceedings acknowledged that much. Of course that objection is meritless. The “person of ordinary skill in the art” is a theoretical construct used in determining obviousness under § 103, and is not descriptive of some particular individual. Custom Accessories, Inc. v. Jejfrey-Allan Indust., Inc., 807 F.2d 955, 963, 1 USPQ2d 1196, 1201 (Fed.Cir.1986) (“The person of ordinary skill is a hypothetical person who is presumed to be aware of all the pertinent prior art”); see also Kimberly-Clark v. Johnson & Johnson, 745 F.2d 1437, 1453 (Fed.Cir.1984). To suggest that the construct applies to particular individuals could mean that a person of exceptional skill in the art would be disqualified from testifying as an expert because not ordinary enough. To the extent that the gravamen of defendants’ complaint is that Dr. Silva was unqualified to testify as an expert witness at all, the record reflects his substantial credentials as an electrical engineer, and the decision to permit him to testify was well within the discretion of the trial judge. See, e.g., Kelsay v. Consol. Rail Corp., 749 F.2d 437, 448-49 (7th Cir.1984).
Defendants further argue that:
Dr. Silva had never attended law school, never practiced patent law and was not appearing as a lawyer. Nevertheless, the Court based virtually every claim interpretation and claim application finding on the testimony of Endress’ unqualified expert witness as confirmed by the transcript citations appended to each paragraph of the Court’s Opinion.
It is of course nonsense to contend that only lawyers or patent lawyers can be expert witnesses in a patent suit. Indeed, this court has on numerous occasions noted the impropriety of patent lawyers testifying as expert witnesses and giving their opinion regarding the proper interpretation of a claim as a matter of law, the ultimate issue for the court to decide. Dr. Silva’s credentials clearly entitled him to be heard regarding the technical aspects of the patented invention and the accused devices.
Defendants conclude this point with the argument that “[t]he Federal Circuit noted that extrinsic evidence including expert testimony ‘amounts to no more than legal opinion’ and is entitled to no weight,” citing this court’s opinion in Markman. This court concluded no such thing, and, as we made abundantly clear in Markman, the trial court has wide latitude in the kinds of aids, including testimony of witnesses, employed to assist in the job of claim interpretation as a matter of law. Markman, 52 F.3d at 979, 34 USPQ2d at 1329.
By disposing of the attack on Dr. Silva, and by our finding unremarkable the decision by the trial judge to credit his expert testimony as she construed the meaning and scope of the means-plus-function claims, we dispose of much of defendants’ case on appeal. The other major issue attacked by defendants relates to the question of how [1043]*1043“corresponding structure ... and equivalents thereof’ is to be understood in the context of this case. Defendants argue that their accused devices perform the function of level indicating through the use of a noise thresholding process to define a series of spaced-apart echo caps each of which represents a closed geometric figure, a process not described in the patent specification, and that their devices do not contain the digital integrator and the digital peak detector that are described in the ’650 patent. They also emphasize that the patent contemplates the use in short-range measuring (2 to 21 feet) of a single pulse, but in long range measuring (14 to 158 feet) the patent describes the use of multiple pulses. The Hawk system generates a level indication in response to a single transmitted pulse in both modes.
The district judge, in an extensive series of carefully organized findings of fact and conclusions of law, analyzed the claims and concluded that the Hawk system on these facts comes within the means-plus-function limitations by containing the equivalent of the structure described in the specification. As noted earlier, the issue before the trial court was not whether the accused device incorporated the structure literally described in the patent, but whether the “level indicating means” of claim 43 was equivalently present in the accused device. Though it is well understood that “equivalents” under § 112 ¶ 6 is a different concept from “equivalents” under the judicially created doctrine of equivalents, the district judge correctly recognized that the statutorily required construction under § 112 ¶ 6 must proceed on a limitation-by-limitation basis, not dissimilar to the analysis under the doctrine of equivalents. See Wamer-Jenkinson Co. v. Hilton Davis Chem. Co.,—U.S.-, 117 S.Ct. 1040, 137 L.Ed.2d 146 (1997).
In this case, the trial court carefully identified the key structural elements of the claimed invention, and, to the extent these elements were not literally present in the accused device, she identified equivalent structure in the accused device that constituted the means for performing the claimed function. Appellants have failed to demonstrate error in regard to this aspect of the trial court’s analysis.
Damages
Finally, with regard to the damages issue, the district court decided on a reasonable royalty owed by defendant to plaintiff, hypothesizing licensing negotiations between the parties. The court assessed damages consisting of a $100,000 up-front licensing payment plus a 15% royalty on products sold by Hawk America in the United States, plus pre-judgment interest. Hawk objects to the lump sum payment, and to the court’s basing the accrual date on the date the complaint was filed. There is more than sufficient evidence in the record to sustain the trial judge’s exercise of the broad discretion under which such contested damages determinations are made. We have fully considered Hawk’s objections, and its argument that the determination was inconsistent with the provisions of 35 U.S.C. § 287 (1994), and we find them without merit.
CONCLUSION
Finding no basis in the appeal on which to overturn the judgment of the district court, it is in all respects
AFFIRMED.