
723 F.Supp. 587 (1989)
T.D. WILLIAMSON, INC., Plaintiff,
v.
Dwane Odell LAYMON, and Electronic Pigging Systems, Inc., an Oklahoma corporation, Defendants.
No. 83-C-84-C.
United States District Court, N.D. Oklahoma.
September 21, 1989.
*588 *589 *590 James R. Head and Paul E. Johnson, Head, Johnson & Stevenson, and Claire V. Eagan, Hall, Estill, Hardwick, Gable, Golden & Nelson, Tulsa, Okl., and Alan T. McCollom, Sp. Master, Marger & Johnson, P.C., Portland, Or., for plaintiff.
William S. Dorman, Tulsa, Okl., and Duane Burton, Denver, Colo., for defendants.

ORDER
H. DALE COOK, Chief Judge.
Before the Court for its consideration are the parties' objections to the Special Master's Proposed Findings of Fact and Conclusions of Law. At a hearing on June 2, 1989, the parties presented arguments in support of their objections. Having heard these arguments, and reviewed the hearing transcripts, the parties' briefs and the applicable statutory and case law, the Court is now ready to rule upon those objections.
In its decision of April 30, 1986, the Court found the defendants had infringed plaintiff TDW's patent on a device known as a caliper pig, used for measuring and reporting on the internal geometry of pipelines. An injunction prohibiting the defendants from further use of defendant EPS' infringing version of a caliper pig was issued on May 8, 1986. After the appellate court affirmed the determination of liability against the defendants, the Court appointed a Special Master, pursuant to F.R. Cv.P. 53(a), to determine and report on damages due TDW as a result of defendants' infringement. In hearings, lasting ten days the Master received and considered evidence from the parties pertaining to the damages for infringement claimed by TDW. The Master issued proposed findings of fact and conclusions of law on July 28, 1988. TDW has objected to one finding of fact made by the Master. Defendants have lodged seventeen objections *591 to the Master's findings and conclusions.
The Court's scope of review concerning the Master's proposed findings of fact is limited. F.R.Cv.P. 53(e)(2) requires the Court to accept those findings "unless clearly erroneous". A factual finding cannot be deemed "clearly erroneous" unless it stems from a mistaken view of the law or unless, despite its support by substantial evidence, the Court is thoroughly convinced after a consideration of the evidence that a mistake has been made. McGraw Edison Company v. Central Transformer Corp., 196 F.Supp. 664, 666-67 (E.D.Ark.1961), aff'd 308 F.2d 70 (8th Cir.1962). The party objecting to the Master's findings carries the burden of proving them to be clearly erroneous. Oil, Chemical and Atomic Workers Intern. Union, AFL-CIO v. N.L. R.B., 547 F.2d 575, 580 (D.C.Cir.1976).
The Court will first consider TDW's single objection, and then turn to defendants' seventeen objections.

I. PLAINTIFF'S OBJECTION TO PROPOSED FINDING OF FACT.
TDW's only objection is to the Master's Finding of Fact 30, in which the Master concluded that TDW was not entitled to damages from jobs performed in Venezuela in 1986 by EPS' infringing pig embodiment. In support of his conclusion, the Master noted that the sensory "fingers" of the pig were manufactured in Venezuela, and that the pigs EPS shipped down to Venezuela were used for other types of pipeline operations, such as cleaning and batching jobs, as well as geometric surveys of the pipeline interiors.
TDW argues that the Master erred in not finding EPS' Venezuela jobs were infringing uses of TDW's patent under 35 U.S.C. § 271(f)(1). That statute, enacted in 1984, provides
Whoever without authority supplies or causes to be supplied in or from the United States all or a substantial portion of the components of a patented invention, where such components are uncombined in whole or in part, in such manner as to actively induce the combination of such components outside of the United States in a manner that would infringe the patent if such combination occurred within the United States, shall be liable as an infringer.
The Master recognized that this section imposed liability for infringement when the components of a patented invention are not combined in the United States, and concluded that the defendants were liable for damages under § 271(f)(1). See Conclusion of Law 17. TDW argues that that conclusion of law is at odds with the Master's Finding of Fact 30 and asks this Court to correct that Finding of Fact and award TDW damages for defendants' use of the infringing pig in Venezuela after 1984.
The caselaw interpreting 35 U.S.C. § 271(f) is limited, and no decisions were found that were dispositive of TDW's objection. The evidence supports the Master's finding that only the sensory fingers were manufactured in Venezuela, in order to meet a requirement of the Venezuelan government as a condition of the defendants performing jobs there. See Record, vol. III, p. 609, In. 7-21. The evidence is unrefuted that the majority of the components of defendants' pig bodies, minus the sensory fingers, were supplied from the defendants' offices and were shipped from Tulsa to the job sites in Venezuela. Defendant Laymon testified that defendants shipped their pigs sufficiently assembled so that EPS' technicians could complete the assembly at the job site in about two hour's time.
Defendants pin their argument for precluding the application of § 291(f)(1) to EPS' Venezuelan jobs upon the term "actively induce" in that subsection. Defendants reason that EPS escapes liability under that section because it did not "actively induce" some third party to combine the sensory fingers with the infringing pig body; according to defendants, they cannot "actively induce" themselves to combine the fingers with the infringing pig body. Defendants point to the legislative history of § 271(f) that states that the term "actively induce" was drawn from § 271(b), *592 which provides that whoever actively induces patent infringement is liable as an infringer. However, defendants ignore the preceding sentence in the legislative history, which states that
[i]n order to be liable as an infringer under paragraph (f)(1), one must supply or cause to be supplied "all or a substantial portion" of the components in a manner that would infringe the patent if such a combination occurred within the United States.
Patent Law Amendments, Pub.L. No. 98-622, 1984 U.S.Code Cong. & Admin. News (98 Stat.) at 5828.
The legislative history noted that § 271(f) was intended to prevent copiers from avoiding U.S. patents by supplying components of a patented product in this country so that the assembly of the components may be completed abroad. Id. This section of the patent law amendment was proposed in response to the U.S. Supreme Court's decision in Deepsouth Packing Co. v. Laitram Corp., 406 U.S. 518, 92 S.Ct. 1700, 32 L.Ed.2d 273 (1972), which created a loophole in prior patent law, allowing copiers to avoid liability for products patented in the United States, by shipping the patented components for combination in foreign countries.
Defendants' claim of required "active inducement" for liability under § 271(f)(1) is not supported by that subsection's legislative history. It is unreasonable that Congress, in attempting to close the loophole for infringement created by the Deepsouth decision, would create another loophole allowing infringers to eschew dealing with foreign parties in order to avoid liability for "active inducement", as defendants now claim. Rather than a limiting factor for liability under § 271(f)(1), the legislative history suggests the phrase, "actively induce" was intended to broaden the basis for liability, extending it to cover both those who actually supply the components as well as those (contributory infringers) who cause others to supply components.
Defendants contend that the Court's construction of § 271(f)(1) makes subsection (f)(2) superfluous. The legislative history of § 271(f) explains the difference between subsections (f)(1) and (f)(2):
Under paragraph (f)(1) the components may be staple articles or commodities of commerce which are also suitable for substantial noninfringing use, but under paragraph (f)(2) the components must be especially made or adapted for use in the invention. The passage in paragraph (f)(2) reading "especially made or especially adapted for use in an infringement of such patent, and not a staple article or commodity of commerce suitable for substantial non-infringing use" comes from existing section 271(c) of the patent law, which governs contributory infringement. Paragraph (f)(2), like existing subsection 271(c), requires the infringer to have knowledge that the component is specially made or adopted. Paragraph (f)(2) also contains a further requirement that infringers must have an intent that the components will be combined outside of the United States in a manner that would infringe if the combination occurred within the United States.
Although the Master did not reference Finding of Fact 30 to § 271(f), it appears that he may have misconstrued § 271(f)(1), in finding no infringement by the defendants on the Venezuelan jobs. The Master included in his finding that components of the defendants' pigs were used for other pipeline purposes, such as cleaning and batching jobs, and not solely for caliper surveys of the pipeline. Although the Master did not clarify the meaning he intended in making that finding, it is possible that he regarded defendants' components as staple articles or commodities of commerce, since they could be used for other pipeline uses, and thus excused defendants' infringing uses of those components in Venezuela. However, the legislative history quoted above makes clear that one can be liable as an infringer under § 271(f)(1), even if the components are staple articles or commodities of commerce suitable for noninfringing use. Thus, defendants' use of infringing pig components in cleaning and batching jobs in Venezuela does not excuse their liability under § 271(f)(1).
*593 Defendants admit that they shipped all components of their infringing pig, except the sensory fingers, from Tulsa to Venezuela in 1986 for a caliper pig survey of a pipeline there. The combination of these components in Venezuela with the sensory fingers, equally infringed TDW's patent as did defendants' use of those combined components in the United States. The Court finds that the law as stated in § 271(f)(1), and the evidence presented here, does not support the Master's finding of fact 30. That finding of non-infringement of TDW's patent and the denial of lost profits to TDW from defendants' 1986 Venezuelan job is clearly erroneous. The Court thus finds that TDW's objection to finding of fact 30 should be sustained.

II. DEFENDANTS' OBJECTIONS.

A. Defendants' claim that TDW did not show detailed computations of lost profits.
Defendants object to the Master's award of lost profits to TDW (finding of fact 34), claiming that TDW failed to carry its burden to show "detailed computations" of its lost profits. Defendants claim that TDW had to show both (1) an "established firm fixed price at which it actually sold its services during the relevant time period", and (2) the contribution margin percentage to be multiplied against that established firm, fixed price. Defendants' objections to Special Master's Proposed Findings of Fact and Conclusions of Law [hereinafter cited as Defendants' Objections], p. 2.
In Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152 (6th Cir.1978), under the test for damages in the form of lost profits, a plaintiff must show, among other elements, detailed computations as to the loss of profits. Id. at 1156. However, defendants cited no authority to support the rule they claim, and no such rule was located in the case or statutory law, mandating a showing of "established firm fixed prices" by the plaintiff. In contrast it has been stated that a "patent owner's burden of proof is not absolute, but one of reasonable probability." King Instrument Co. v. Otari Corp., 767 F.2d 853, 863 (Fed.Cir. 1985). "The determination of a damage award is not an exact science." Id. Nor must a plaintiff prove the amount of lost profits with "unerring precision". Bio-Rad Laboratories v. Nicolit Instrument Corp., 739 F.2d 604, 616 (Fed.Cir.1984). The patentee must show a reasonable probability that, but for the infringement, it would have made the sales that were made by the infringer. Milgo Electronic v. United Bus. Communications, 623 F.2d 645, 662 (10th Cir.1980).
TDW presented an expert witness and one of its employees to testify concerning the computations made regarding its loss of profits. The Master evidently considered these witnesses' calculations to be detailed enough to satisfy the Panduit test. Defendants do not appear to be challenging the detail of TDW's calculations as to their sufficiency. Rather, the substance of defendants' objections is their assertion that TDW did not present evidence of a fixed pricing system which it consistently followed in making its bids on pipeline calipering jobs. Defendants point to testimony indicating that TDW bid prices both higher and lower from those set forth on its price or cost lists. Defendants object to the Master's calculation of lost profits according to TDW's price quote list, in his finding of fact 33.
While a court's calculation of damages cannot be based upon speculation or guess, the court can use evidence which shows "the extent of damages as a matter of just and reasonable inference, although the result be only approximate." Story Parchment Co. v. Paterson Parchment Paper Co., 282 U.S. 555, 563, 51 S.Ct. 248, 250, 75 L.Ed. 544 (1931). "The wrongdoer is not entitled to complain that [the damages] cannot be measured with the exactness and precision that would be possible if the case, which he alone is responsible for making, were otherwise." Id. Once it has chosen an accounting method, the court has discretion in choosing the figures or charts from which to determine the amount of damages. Paper Converting Machine v. Magna-Graphics, 745 F.2d 11, 22 (Fed.Cir. 1984). The Court may thus fashion a *594 "yardstick" from evidence presented by the parties to measure the patentee's lost profits. See Kori Corp. v. Wilco Marsh Buggies & Draglines, 761 F.2d 649, 654 (Fed. Cir.1985) (infringer's profits used as "yardstick" for measurement of patentee's lost profits).
TDW put into evidence the price and cost lists it used during the relevant period to calculate its basis for caliper job quotes to customers; the lists were formatted according to such factors as the pipe diameter, length of pipeline to be calipered, the contents of the pipeline, and whether the job was in the U.S. or overseas, in order to estimate an initial, basic price. See Pl.E. 94, 95, and 96. TDW sometimes raised its quoted price from that basic price because of factors such as extra days required for some jobs. On other bids, TDW lowered its quoted bid from that provided on the applicable price or cost list in order to encourage use of the caliper pig service or because of competition from defendant EPS. In the damages hearing TDW only used the price and/or cost list to calculate what it would have bid for the domestic and foreign caliper jobs that EPS performed; TDW added no factors to raise or lower that basic price. The Master used the applicable price lists to compute TDW lost income from the 27 jobs in the United States and Canada that EPS performed. The Master's use of this "yardstick" does not appear to the Court to be clearly erroneous, and defendants have not convinced the Court of any clear error in the Master's reliance upon TDW's price lists.

B. Defendants' claim that TDW failed to show demand for its patented pig.
Defendants claim that TDW should not be awarded lost profits for the reason that TDW failed to show any demand for the caliper pig claimed in TDW's patent. Defendants base this argument upon testimony they elicited during the damages hearing, which they claim demonstrates that the commercially valuable feature of the patented pig was the ability to provide the customer with a written record of the defects located along the length of the pipeline. Defendants attribute this ability solely to the pig's odometer wheels, which they contend are covered by another TDW patent, and not the patent in issue here. Defendants argue that since the odometer wheel is not covered by the caliper pig patent, TDW cannot recover damages on that pig; TDW did not show a demand for a caliper pig constructed without odometer wheels to locate dents and other deviations along the pipeline. TDW admits that the odometer wheels are covered by a separate patent, but argues that the caliper pig patent indicated the odometer wheels in the patent drawings and describes the use of the odometer wheels as a means to move the recording tape in accordance with the pig's travel through the pipeline.
The patented pig's inventor testified that the caliper pig would not work without an odometer wheel, unless something else to track the location in the pipeline in correlation with the deviation measurement was substituted for the wheel. VerNooy, vol. I, p. 95, In. 15-25. TDW's witness, David Atwood, agreed with the statement that a pig could be designed to use something other than the dual odometer wheel method, used by TDW and EPS. Atwood, vol. VI, p. 1112, In. 6-13. Both Atwood and VerNooy stated that the earliest versions of the caliper pig used a clock driven mechanism which recorded that pig's travel through the pipeline in relation to time elapsed, rather than distance traveled. VerNooy, vol. I, p. 95, ln. 15-25; Atwood, vol. VI, p. 1112, In. 6-10.
In its drawings and descriptions thereof, TDW's patent refers to the use of an odometer wheel in the caliper pig in combination with a stepper motor, which drives the suggested recording means in the form of a strip chart. TDW's patent suggests the odometer wheel as a preferred embodiment in the caliper pig to correlate the measurement of deviations with their location in the pipeline, but as TDW's witnesses indicated, the odometer wheel is not the only possible embodiment by which this correlation could be made. Courts have been cautioned not to limit the claimed invention to preferred embodiments or specific examples in the specification. Lemelson v. United States, *595 752 F.2d 1538, 1552 (Fed.Cir.1985). Similarly, "an inventor's decision to manufacture and market one embodiment of his invention obviously does not limit the patent to that embodiment." Velo-Bind, Inc. v. Minn. Mining & Mfg. Co., 647 F.2d 965, 969 (9th Cir.1981). Defendants' arguments, crediting the separately-patented odometer wheel as giving the caliper pig commercial value and creating a demand for the pig's services does not create a justification for a denial of damages to TDW. Undoubtedly, a pig with odometer wheels, but none of the patented sensory apparatus to detect and measure pipeline defects, will not have much more demand for its services than as a dummy pig.
Additionally, the Master concluded it was appropriate to apply the "entire market value rule" and not attempt to apportion damages as resulting from the patented and unpatented portions of the infringing pig, since the patented portion was crucial to its operation. Conclusion of Law 12. That rule allows "the recovery of damages based upon the value of the entire apparatus containing several features, even though only one feature is patented." Paper Converting Machine Co. v. Magna Graphics Corp., 745 F.2d 11, 22 (Fed.Cir. 1984). The determining factor is whether the patentee or its licensee can normally anticipate the sale of the unpatented components together with the patented components. Id. at 23. Another court applied the rule even when only some of the elements of the infringing device were covered by the patent claims, since such unpatented elements would be routinely purchased by the accused infringer's customers when such customers purchased the infringing device which included elements of the claims of the patent in suit. ACF Industries v. Midway Fishing Tool Co., 2 USPQ2d 1767, 1770, 1986 WL 15706 (C.D. Cal.1986).
In Kori Corp. v. Wilco March Buggies and Draglines, 761 F.2d 649 (Fed.Cir. 1985), the defendants were found to have infringed the plaintiff's patent on a device called an Amphibious Marsh Craft, and described as an improved pontoon type, endless-track amphibious vehicle to be operated in swamps. The appellate court quoted with approval the trial court's conclusion that it found no evidence that the unpatented upper portions of the vehicle had been or could have been used independently of its patented pontoon structure. Id. at 656. From that, the appellate court concluded that the plaintiff would have normally anticipated the sale of an entire vehicle, including both the patented and unpatented components, and awarded damages based on the entire market value of the infringing machines. Id.
Applying the entire market value rule here, the fact that the odometer wheel is not specifically included in the claims of TDW's caliper pig patent, does not cause TDW to forfeit a showing of demand for its patented pig. TDW's patent envisioned in the patent drawings and description the use of the odometer wheel as one possible method to correlate the recording mechanism's record in relation with the pig's movement through the pipeline. Although the caliper pig patent focused its claims upon the unique, protected, full-circle caliper sensory devices of the pig, the odometer wheel was referred to in the patent as a means to provide a location track against which deviations detected by the sensory apparatus could be compared. While the separately-patented odometer wheel could have been used in another of TDW's pigs, TDW chose to include it as a preferred embodiment in tracking the distance traveled by its caliper pig. In selling the pig's services as being able to detect and provide a record of deviations in the pipeline, TDW could have normally anticipated its customers' use of its entire caliper pig, including both the patented sensory features and the separately-patented odometer wheel.
It was established in the liability phase of this lawsuit that defendants' infringing pig had a virtually identical sensory apparatus to TDW's caliper pig. Defendant Laymon has admitted the use of odometer wheels on the infringing pig. As in the ACF Industries decision above, the entire market value rules applies here, since defendants' customers, in using the services of the infringing pig, were using a device *596 which incorporated elements of the claims of the TDW caliper pig patent, as well as the separately-patented odometer wheels.

C. Defendants' claim that TDW failed to show that the Kopp pig was not an acceptable, noninfringing substitute in the Western Hemisphere.
Defendants object to the Master's Findings of Fact 13, 14, and 15, in which the Master concluded that Kopp A.G. or Kopp International did not perform any caliper survey jobs with the Kopp pig in North or South America prior to June, 1987, and that the Kopp pig was not an acceptable, noninfringing substitute for TDW's caliper pig during the relevant period in those two continents. Defendants' objection focuses upon the application of the term "acceptable substitute" to a caliper pig manufactured by the Kopp A.G. Company, headquartered in West Germany. Defendants contend that the Kopp pig was "available" in that Kopp could have bid on and performed caliper survey jobs in North and South America during the relevant period. Defendants' contention is based upon their claim that the Kopp pig was used elsewhere in the world during the relevant period, and thus could have been as easily shipped for use in North and South America as well. According to defendants, such "availability" of the Kopp pig makes it an "acceptable substitute" for TDW's caliper pig.
Defendants cite the decision in Hughes Tool Company v. G.W. Murphy Industries, Inc., 491 F.2d 923 (5th Cir.1973), as support for their contention that an "acceptable substitute" does not have to be actually used, as long as it is available for use. In the portion of Hughes, relied upon by the defendants, the Fifth Circuit stated that
the noninfringing Reed two-piece seal was available as a viable alternative. To be sure, the two-piece seal was less efficient than the one-piece seal and cost more to manufacture and install. Moreover, the two-piece seal was never put into actual production. Nevertheless, Reed's two-piece seals were marketable; Reed sold approximately 40 bits containing the two-piece seals made in its research department.

Id. at 930-31.
The subsequent decision in Panduit Corp. v. Stahlin Bros. Fibre Works, 575 F.2d 1152 (6th Cir.1978), required a plaintiff to demonstrate an absence of "acceptable, noninfringing substitutes" as one element to recover damages, rather than the lack of an available, "viable alternative" of the Hughes decision. Id. at 1156. The Panduit test appears to require actual use of the substitute product and not merely its "availability"; the court there identified an "acceptable substitute" as one which customers in general were "willing to buy in place of the infringing product" and stated that "[a] product lacking the advantages of that patented can hardly be termed a substitute `acceptable' to the customer who wants these advantages." Id. at 1162.
Further review of the case law does not convince the Court that a product's mere "availability" qualifies it as an "acceptable substitute". In Radio Steel & Mfg. Co. v. MTD Products, Inc., 788 F.2d 1554 (Fed. Cir.1986), the patented product was described by the court as "a new and improved complete wheelbarrow", having advantages superior to other wheelbarrows available on the market. The appellate court rejected the infringer's argument that other available wheelbarrows on the market were acceptable substitutes, when those had none of the advantages of the patented product. Id. at 1556.
The Court is unpersuaded by the defendants' argument that the Kopp pig's "availability" suffices for "acceptability" as a substitute under the Panduit test. More than speculation that the Kopp pig "could have been used" in North or South America during the relevant period must be shown to overturn the Master's finding of fact on the Kopp pig as an acceptable substitute. From its review of the evidence, the Court finds no reason to disturb the Master's finding of fact on this point. The deposition testimony of the Kopp Americas International president showed that that corporation was first incorporated in mid- *597 1984, and ran its first caliper pig survey in June, 1987 in Venezuela and in September, 1987 in North America, more than a year after the relevant period. See Wells, V. III, p. 446, lines 11-12; p. 447, lines 1-25; p. 449, lines 1-8. That same testimony did not indicate whether Kopp Americas' bids for caliper survey work were made within the relevant period. No evidence affirmatively established Kopp's performance of jobs in North or South America during the relevant period to contradict the Master's findings.

D. Defendants' claim that TDW failed to show that defendants' "External Finger" Pig design was not available during the relevant period.
Although the Master did not make a specific finding concerning the availability of defendants' "external finger" pig design during the relevant period, defendants contend that they had the design for that variation of a caliper pig as early as 1982, before they made their first caliper pig survey with the infringing pig. According to defendants, the fact that this alternate design for a caliper pig was available to them before their use of the infringing pig, causes their conversion to that alternate design a few days after being enjoined from using the infringing pig to be strong evidence that the alternate design was an acceptable, noninfringing substitute for TDW's patented pig.
No statutory or case law was located which supported defendants' position. In leading up to their statement of the above "rule", defendants cite the decision of Smith International, Inc. v. Hughes Tool Co., 229 USPQ2d 81 (C.D.Cal.1986). That case does not support the defendants' argument, but rather, undermines it, by reference to the decision in Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152 (6th Cir.1978).[1] In Panduit, the court stated that
[t]he post-hoc circumstances that Stahlin, when finally forced to obey the court's injunction, was successful in "switching" customers to a noninfringing product, does not destroy the advantage-recognition attributable to the patent over the prior 15 years. * * * That Stahlin's customers, no longer able to buy the patented product from Stahlin, were able to buy something else from Stahlin, does not establish that there was on the market during the period of infringement a product which customers in general were, in the master's words, "willing to buy in place of the infringing product". Moreover, Stahlin's "switching" occurred years after the date on which the determination of available substitutes must focus, i.e. the date of first infringement.

Id. at 1162 [emphasis original].
That defendants could easily switch to their alternate pig design because that design was drawn up before they infringed TDW's patent, has little significance. The date of defendants' "switching" to the "external finger" pig design occurred in May, 1986, four years after 1982, when defendants began infringing TDW's patent.
Further, defendants' argument that their "external finger" pig is a noninfringing substitute ignores the fact that this Court has not yet decided whether that pig infringes TDW's patent. That question is before the Court on TDW's Citation for Contempt.

E. Defendants claim that TDW, as a nonmanufacturing patent holder, failed to join its licensee in the law-suit, which thus precludes TDW's recovery of lost profits.
Defendants object to Findings of Fact 5, 6 and 7, in which the Master found that TDW owned the patent in suit and was empowered to sue for damages resulting from infringement of the patent in suit. The Master also found that TDW had two wholly owned subsidiaries, TDW Services and TDW U.K., Ltd., and that TDW's and *598 its two wholly owned subsidiaries' financial statement were and are reported on a consolidated financial basis. Finding of fact 8.
A review of the hearing transcript shows that the Master's findings of fact 5-8 were supported by the evidence offered by TDW's president, A.B. Steen, as well as by other TDW witnesses who testified about TDW's and its subsidiaries' structure, consolidation of financial statements and TDW's reasons for entering into license agreements only with its foreign-based subsidiaries for use of TDW's patents. A.B. Steen, vol. I, p. 198, ln. 6-25; p. 199, ln. 10-25; p. 200, ln. 5-11; p. 202, ln. 1-21.
In support of their argument, defendants mischaracterize finding of fact 8, in the following manner:
the Special Master found that Plaintiff (TDW), a nonmanufacturing patent holder, was entitled to recover lost profits without joining in this litigation its (oral) licensee because under the federal and state tax laws, the financial statements of Plaintiff and its licensee were reported on a consolidated basis and the profits and losses of Plaintiff's licensees affected the profits and losses of Plaintiff on a dollar-for-dollar basis.
Defendants' Objections, p. 22.
Finding of fact 8 only addresses the consolidated nature of the financial statements reported by TDW and two subsidiaries, TDW Services, Inc. (an Oklahoma corporation) and TDW U.K., Ltd. (a London-based subsidiary), and the fact that the losses and profits of those two subsidiaries affected the profits and losses of TDW on a dollar-for-dollar basis. Contrary to defendants' characterization, the Master did not find that TDW was a nonmanufacturing patent holder or that tax laws allowed TDW to recover lost profits without joining an oral licensee. The Master did not address the licensee status of any of TDW's subsidiaries in his proposed findings and conclusions. Defendants thus impute findings to the Master which he did not make, and then attempt to persuade the Court of the error of that imputed finding.
Defendants also base their objection upon "rules" governing whether lost profits should be awarded to nonmanufacturing patent holders and their licensees, which have been developed through certain decisions. Defendants cite the following "rules" as applicable to the present case:
1. Where the patentee did not himself manufacture the patented product, he is not entitled to recover lost profits. [emphasis added] (citing Hanson v. Alpine Valley Ski Area, Inc., 718 F.2d 1075, 219 USPQ 679 (Fed.Cir.1983)).
2. Lost profits are available only to a manufacturing patentee. [emphasis added] (citing Kori Corp. v. Wilco Marsh Buggies, 561 F.Supp. 512, 217 USPQ 1302, 1305 (E.D.La.1982), aff'd 761 F.2d 649 (Fed.Cir.1985)).
3. A nonmanufacturing patent holder is entitled to recover only a reasonable royalty unless the patent holder joins his exclusive licensee in the litigation. (citing Del Mar Avionics v. Quinton Instrument Co., 836 F.2d 1320 (Fed.Cir. 1987)).
4. A nonmanufacturing patentee is entitled to recover lost profits if it joins its exclusive licensee under the patent. (citing Bott v. Four Star Corp., 807 F.2d 1567 (Fed.Cir.1986)).
5. Where the patentee did not himself manufacture the patented product and granted nonexclusive licenses, he was not entitled to recover lost profits. (citing Hanson, supra).
In reviewing the case law cited by the defendants, it appears that defendants have in some cases stretched a factual circumstance into some of the above "rules", without a supporting legal conclusion by the courts. In the other cases cited by defendants, no such rule was suggested by the court and no applicable factual or legal circumstance in the cited decision was readily apparent as the source of defendants' quoted "rule". Additionally, in characterizing TDW as a nonmanufacturing patent holder, defendants apparently overlooked testimony by TDW's president, A.B. Steen, indicating TDW's ownership of a manufacturing plant in Tulsa, which makes at least some of the components comprising the caliper pig. Steen admitted that *599 TDW farms out the manufacture of certain electronic components of the caliper pig. See Steen, vol. II, p. 289, ln. 7-25; p. 290, ln. 11-12; p. 303, ln. 13.25.
In the Hanson decision, cited by defendants as support for "rules" 1 and 5, the court there did not state such a "rule of law", nor did the facts of Hanson obviously lead one to conclusions such as those stated by defendants in their objection. Likewise, no support for "rule" 2 was found in the trial and appellate courts' decisions in Kori. As to defendants' "rule" 3, the DelMar court noted that "[t]he general rule for determining actual damages to a patentee that is itself producing the patented item is to determine the sales and profits lost to the patentee because of the infringement." 836 F.2d at 1326. Defendants evidently construe the quoted sentence as the basis for a rule that nonmanufacturing patentees can only recover a reasonable royalty. The DelMar decision does not make any reference to nonmanufacturing patentees or to licensees, and does not state any rules on a restriction of patentees to reasonable royalties instead of lost profits. Similarly, no such "rule" as cited by defendants appears in the Bott decision. There, the appellate court remanded the issue of whether the patentee's exclusive licensee would have competed for the infringer's business. 807 F.2d at 1570-71. The Bott decision makes no reference to an issue of proper joinder of the exclusive licensee to the patent holder's claim for lost profits.
Defendants point to TDW's lack of a license with its subsidiary, TDW Services, and characterize that subsidiary as an oral, nonexclusive licensee. In arguing that TDW is not entitled to lost profits because of TDW Services' lack of a written exclusive license, defendants place reliance on the decision in Baumstimler v. Rankin, 677 F.2d 1061 (5th Cir.1982) as being on "all fours" with the facts in the present case. Baumstimler was the patent holder and the president of a company which manufactured the patented device and exploited the patents assigned to Baumstimler. Baumstimler and his wife were the only shareholders in his company. The company was dismissed as a party before trial for lack of a property interest in the patents, which Baumstimler had not assigned to the company, and had not entered into a licensing agreement. After a jury awarded damages for lost profits, the appellate court questioned the award of damages to Baumstimler when his company, which had used the patent but had no property interest in it, was not a party to the decision. The appellate court noted that since Baumstimler did not manufacture, sell or use the patented invention, which was exploited instead by his company, Baumstimler technically had no lost profits.
The precedential effect claimed for the Baumstimler decision is weakened, however, by the appellate court's remand for determination of, among other issues, the effect, if any, of the company's lack of a license with Baumstimler and its relationship to Baumstimler had on the determination of damages. To date, no decision on remand has been reported, leaving this issue open. However, even if that issue had been decided by now, the Court questions whether the fact of TDW's manufacturing of components for its patented pig would place this case on "all fours" with the Baumstimler facts.

F. Defendants claim that TDW failed to show that gauging pigs and dummy pigs are not acceptable noninfringing substitutes.
Defendants object to the Master's finding of fact 12(a)(1)(3), in which the Master found that gauging pigs and dummy pigs were not acceptable noninfringing substitutes for TDW's patented caliper pig. Defendants complain that the Master's findings are a result of his attributing values accruing solely from the use of odometer wheels on the patented pig. According to defendants, the absence of the separately patented odometer wheels would render the patented device to be essentially performing the same function as the dummy pig or gauging pig. This argument is based on the same premise argued by defendants in section B. above, and which the Court did not find persuasive.
*600 As noted previously, a patent holder must prove the absence of acceptable noninfringing substitutes. Panduit, 575 F.2d at 1156. However, the "[m]ere existence of a competing device does not make that device an acceptable substitute." TWM Mfg. Co., Inc. v. Dura Corp., 789 F.2d 895, 901 (Fed.Cir.1986). When none of the alleged substitutes have all the beneficial characteristics of the patented device, it is reasonable to determine that there are no acceptable substitutes. Id. The "acceptable substitute" element should be considered, but viewed of limited influence where the infringer knowingly made and sold the patented product for years while ignoring the substitute. Panduit, 575 F.2d at 1162 n. 9.
The evidence at the damages hearing showed that gauging pigs and dummy pigs were non-infringing, but were not clearly acceptable substitutes for the patented pig. Testimony indicated that gauging plates were still being used in newly constructed pipelines, but witnesses noted that pipelines were indicating a preference for using caliper pigs to run in newly constructed pipelines. Kinnear, vol. IX, p. 1738, In. 17-21; Fears, v. IX, p. 1681, In. 8-9. Unlike gauging pigs, caliper pigs could be used in operating pipelines, without having to empty the pipeline contents. Gauging pigs were also likely to become stuck in the line; some pipeline companies considered it cheaper to use caliper pigs, considering the costs of excavating the pipeline to retrieve the gauging pig.
Dummy pigs are shaped like a corrosion detection tool, and are run with the purpose of ensuring that the expensive corrosion detection tool will not become stuck in the pipeline. The only location tracking ability to identify defects possessed by a gauging or dummy pig is if the pig becomes stuck in the pipeline, which must be then excavated to recover the pig and investigate that cause of the pig stopping. The presence and location of smaller defects which the gauging and dummy pigs were able to pass by are not located by these two types of pigs. The evidence thus showed that gauging pigs and dummy pigs, while used for some purposes in pipelines, do not offer all of the advantages or perform the same functions as the patented caliper pig.
Defendants assert the existence of newly discovered evidence regarding, in part, the acceptability of gauging pigs as a substitute for the caliper pig. Defendants' claimed evidence is a paper, published in 1987 in a collection of essays on pipeline pigging, written by TDW employee Geoffrey Guy Trenchard Blanford. In that paper, Blanford stated the "most serious competitor" to TDW's caliper pig "is the simple gauging plate". See Def.E.A. to Motion and Brief to Receive Newly Discovered Evidence. Defendants construe this single sentence in Blanford's paper as an impeachment of Blanford's testimony given at the damages hearing regarding the limitations in using a gauging pig.
The Court, however, does not view that single sentence, taken out of context, to impeach Blanford's testimony at the hearing to warrant reversing the Master's findings on gauging pigs. The remainder of that paragraph and the following one indicate again the limited knowledge and the hazards that are provided in running a gauging pig through a pipeline. Even if that single sentence afforded sufficient impeachment value against Blanford's testimony, there was ample testimony and other evidence, presented at trial and the damages hearing, concerning the inadequacies of the gauging pigs for the purposes for which caliper pigs are used, to support the Master's findings. Having reviewed the defendants' "new" evidence, against the hearing transcripts and exhibits concerning gauging pigs, the Court finds no clear error in the Master's finding that gauging pigs are not acceptable substitutes for TDW's caliper pigs.

G. Defendants' claim that the AMSI, Vetco, Rosen and Transcanada tools were acceptable, noninfringing substitutes for TDW's caliper pig.
Defendants object to Findings of Fact 12(b), 18 and 19 in which the Master found that certain tools offered by other pipeline service companies were not acceptable, *601 noninfringing substitutes for the patented caliper pig. Defendants complain that the Master mischaracterized the use of these tools as primarily corrosion detectors, rather than as caliper survey instruments.
Defendants' argument depends, again in part, on their equation of "availability" to acceptability as a noninfringing substitute under the Panduit test. Defendants thus contend that these tools were "available" on the market during the relevant period and had the ability, similar to that of the TDW caliper pig, to detect and provide a location record of dents and other deformations in a pipeline. As discussed above, the Court is not convinced that mere "availability" of a device is tantamount to its "acceptability" as a substitute for the patented device. Nor can a product be considered an acceptable substitute when it does not possess all the beneficial characteristics of the patented device, but is either different or inferior to that device. TWM Mfg. Co., Inc. v. Dura Corp., 789 F.2d 895, 901 (Fed.Cir.1986); Central Soya Co. Inc. v. Geo. A. Hormel & Co., 723 F.2d 1573, 1579 n. 4 (Fed.Cir.1983). Devices which may indicate distortions in a pipeline's geometry, but are not the equivalent of the caliper pig, are deemed to be outside the relevant "minimarket" for caliper survey services in determining TDW's lost profits. See Yarway Corp. v. Eur-Control USA, Inc., 775 F.2d 268, 276 (Fed.Cir. 1985). Further, the "acceptability" of the alleged substitutes must be questioned when the defendants ignored the "availability" of those substitutes in "designing around" the TDW patent. See Panduit, 575 F.2d at 1152 n. 9.
The patentee's burden in demonstrating an absence of acceptable substitutes is not stringent.
The patent holder does not need to negate all possibilities that a purchaser might have bought a different product or might have foregone the purchase altogether. The "but for" rule only requires the patentee to provide proof to a reasonable probability that the sale would have been made but for the infringement.

Paper Converting Machine, 745 F.2d at 21 [emphasis original].
The AMSI tool, for example, was developed to detect pipeline corrosion, and only incidentally may detect dents and other deformations in the pipeline geometry. The testimony of AMSI's president indicated the tool's main use was for corrosion detection, rather than its caliper survey abilities. No recognition of AMSI's caliper capabilities over its corrosion detection uses in the pipeline field was evident from testimony presented at the damages hearing.
Similarly, the use of a Rosen geometric pig during the relevant period was not clearly established by the evidence. An employee of the U.S. company with rights to use the Rosen technology testified that the first use of the Rosen pig in the United States was made in 1987, a year after the relevant period. See Lewis, vol. VIII, p. 1569, ln. 1-11. That same witness noted that the Rosen geometric pig had been used in pipelines in the North Sea, Europe and the Middle East, but did not say when those jobs were performed. Id. p. 1568, In. 20-25. Although Rosen's pig was first shown at trade shows in 1982, and Rosen advertised its geometric pig in the United States, Lewis also testified that he would not include Rosen as among the companies performing caliper survey work before 1987. Id. p. 1569, ln. 14-20; p. 1585, In. 13-21. Defendant Laymon admitted that he had no knowledge of any caliper jobs performed by a Rosen pig during the relevant period. See Laymon, vol. III, p. 631.
Testimony indicated that the Transcanada tool was first used in 1972 to detect construction damage on new pipelines such as dents and deformations, as well as detecting internal corrosion of the pipeline. See French, vol. VIII, p. 1374. The Transcanada ID tool worked on a magnetic flux principle. A former employee of Transcanada testified that the ID tool was used for caliper work within Transcanada's own pipeline system, and was used on one yearly U.S. pipeline job from 1981-85. Id. p. 1388, 1412. However, one drawback to the use of the ID tool was that it cost nearly twice as much as a caliper survey offered *602 by TDW. Id. p. 1404, 1420-21. One of defendants' witnesses questioned whether a tool using flux leakage principles to detect and locate dents was acceptable to a pipeline customer wanting to locate dents, when the flux leakage tools cost so much more to run than a caliper pig. See Casey, vol. VIII, p. 1467, ln. 20-25.
Evidence from the damages hearing clearly demonstrated that C.E. Vetco had performed only one caliper survey job during the relevant period, on the Aliesco pipeline job in Alaska. See Atwood, vol. V, p. 817, ln. 14-18. C.E. Vetco developed its caliper pig for the 48" diameter Aliesco line. Id. C.E. Vetco has not developed that caliper tool in other sizes for use in other pipelines, because its engineers have determined that the design of that caliper pig is not economically feasible to be used in any other pipeline. Id. vol. VI, p. 1121, ln. 12-21. C.E. Vetco has called both TDW and EPS to bid on caliper survey jobs. Id. p. 1123, In. 10-13.
Testimony from several pipeline industry witnesses indicated that they considered only TDW and defendant EPS to offer a caliper pig survey services during the relevant period. See Wells, vol. III, p. 452; Dunham, vol. VIII, p. 1601, ln. 20-25; Bateman, vol. VIII, p. 1646-47; Griffin, vol. IX, p. 1715, In. 16-17.
Defendants also claim the existence of newly discovered evidence which allegedly impeaches the testimony of one of TDW's witnesses concerning acceptable substitute devices in the relevant period. Defendants point to a paper in a collection of essays on pipeline pigging, published in 1987, and written by a TDW employee, Geoffrey Guy Trenchard Blanford. In his paper, Blanford stated that six companies were known competitors in that they offered a form of pipeline inspection device "competing" with TDW's caliper pig. Among the companies Blanford named as "competitors" with TDW were C.E. Vetco, Kopp, Rosen and Transcanada. Defendants contend that Blanford's statements regarding TDW's competition in caliper surveys contradicts Blanford's testimony given at the damages hearing regarding the lack of acceptable substitutes for TDW's caliper pig during the relevant period.
From its review of Blanford's testimony and the defendants' "new" evidence, the Court is not persuaded that the "new" evidence constitutes an impeachment of Blanford's previous testimony. Blanford's paper points out drawbacks and inadequacies of the "competing" devices as compared to TDW's caliper pig. The Court finds no obvious inconsistencies between Blanford's paper and his hearing testimony to cast doubt upon that testimony. However, even if Blanford's testimony were thus discredited, the Court finds ample evidence from the testimonies of pipeline company representatives and representatives from the Kopp, Rosen, Transcanada and C.E. Vetco companies to support the Master's finding that the devices contended to be in "competition" with TDW's caliper pig were not "acceptable substitutes" for that device during the relevant period.

H. Defendants claim that TDW did not show a demand in the marketplace for their patented pig as commercialized.
Defendants object to the Master's finding that TDW had shown a demand for its caliper pig services. Finding of Fact 9. Defendants contend that the evidence demonstrated that TDW's pig was held in low repute in the pipeline industry, and cite several instances in which the TDW pig performed unsatisfactorily, giving inaccurate results and requiring that the pig be run through the line twice. Defendants assert the poor reputation and unreliability in results of the TDW pig are reasons why there was no demand for TDW's services during the relevant period.
Under Panduit, the demand element "concerns only the manufacturing/marketing capability of the patentee to meet the demand. The demand which a patentee must have the capacity to meet is measured by the total sales, by the patentee and the infringer, of the patented product." Datascope Corp. v. SMEC, Inc., 879 F.2d 820, 11 USPQ2d 1321, 1324 (Fed.Cir.1989) [emphasis original]. From the Court's review *603 of the evidence, the Master's finding as to demand for the patented pig was factually supported and without error. That evidence showed the need for the patented caliper pig was perceived nearly twenty years ago by the inventor, an employee of TDW, and TDW promoted the pig's use by the pipeline industry. The evidence also showed that TDW was recognized in the pipeline service field for its caliper surveys. When defendant Laymon left TDW's employ, he apparently realized the demand created by the patented pig, since in "designing around" the TDW patent, he retained essentially the same features in his infringing device. The number of defendants' jobs using the infringing devices containing the patented feature is compelling evidence of the demand for the product. See Gyromat Corp. v. Champion Spark Plug Co., 735 F.2d 549, 552 (Fed.Cir.1984). Defendants presented no evidence of specially designed features on their infringing device which would overcome the problems defendants allege caused TDW's customers or potential customers to turn to EPS for better caliper services.

I. Defendants claim TDW did not show that the Green caliper pig was not an acceptable noninfringing substitute for the patented pig.
Defendants complain that TDW put on no evidence, and the Master made no finding of fact regarding Green's patented caliper pig as an acceptable noninfringing substitute for TDW's patent caliper pig. Defendants admit that the Green pig was never actually commercially produced, but contend that its design was similar to TDW's pig. Green's patent having expired during the relevant period, defendants argue that that pig design was available for other companies' competing use in the caliper pig services market.
Once again, defendants' "availability" argument in finding an "acceptable substitute" must be rejected. In the case of Green's pig design, defendants' contentions of "availability" are unconvincing, as there apparently was no commercial embodiment of Green's design advertised or available and put in use during the relevant period. None of the pipeline customer witnesses called by the defendants mentioned their consideration of the Green pig design in the general area of pipeline caliper survey services or in contracting for such services.
Additionally, the fact that Green's patent expired a year before the defendants built their first pig weakens their argument of the design's acceptability as a substitute for TDW's caliper pig, when defendants "designed around" TDW's patented product rather than the "available" Green pig design.

III. DEFENDANTS' OBJECTIONS AS TO AWARDS OF LOST PROFITS FOR PARTICULAR JOBS.

A. Defendants' claim that TDW is not entitled to lost profits on any survey jobs defendants performed for Laurel Pipeline.
Defendants object to Finding of Fact 21, in which the Master found, by implication, that each of the four caliper survey jobs defendants performed for the Laurel Pipeline Company would have been performed by TDW, but for the infringement of the defendants. In support of this objection, defendants claim the applicability of a rule denying the patentee lost profits on jobs where the customer would not have used the patentee or the patented product, regardless of the infringer's activity. Defendants point to the testimony of Laurel Pipeline representatives, who, after experiencing unsatisfactory survey results from TDW's caliper pig, refused to use TDW's or any similar caliper pig to survey their lines.
Defendants cite the district court decision in Datascope Corp. v. SMEC, Inc., 678 F.Supp. 457, 5 USPQ2d 1963 (D.N.J.1988), as support for the rule that a customer's preference for the infringing device denies to the patentee lost profits attributable to that customer. The recent reversal of that decision precisely on the point argued by defendants has been noted by this Court. In reversing the lower court, the Federal Circuit stated

*604 We note, first, the logical error in considering the preference of customers for the infringer as a source of supply. That preference, if it exists, bears no relevance to element three of the Panduit test, which concerns only the manufacturing/marketing capability of the patentee to meet the demand. The demand which a patentee must have the capacity to meet is measured by the total sales, by the patentee and the infringer, of the patented product.

Datascope Corp. v. SMEC Inc., 879 F.2d 820, 11 USPQ2d 1321, 1324 (Fed. Cir.1989) [emphasis original].
Contrary to defendants' assertions, the evidence supports the implication in the Master's Finding of Fact 21 that, but for the defendants' infringement, TDW would have performed the four caliper survey jobs for Laurel Pipeline. The representative for Laurel testified that the decision to use EPS instead of TDW was made without his knowledge, and defendants' pigs were run in Laurel's lines despite his objections to using any caliper survey device similar to TDW's patented pig. See Kinnear, vol. IX, p. 1734, ln. 6-25; p. 1735, In. 1-9. This same witness testified that he saw no particular characteristic of EPS' infringing pig to cause it to perform more accurately that TDW's patented device. Id. at p. 1749, In. 7-10. The evidence demonstrates that Laurel, as a previous customer of TDW, in seeking caliper survey services, was thus able to turn to defendants' infringing device as an immediate alternative to TDW's pig. From this it can only be concluded that but for the defendants' infringement, TDW would have performed the caliper survey jobs for Laurel Pipeline Company, who sought those services during the relevant period.

B. Defendants claim that the Master mistakenly included a bend detector job as an internal geometry survey in calculating TDW's lost profits.
Defendants object to the Master's inclusion of what they allege is primarily a bend detector job they performed in Canada in 1986, in the calculation of lost profits to TDW. See Pl.E. 32. Because the Master excluded defendants' bend detector jobs from the calculation of lost profits (Finding of Fact 29), defendants argue that the inclusion of the one bend detector job in TDW's lost profits is error.
The testimony of Defendant Laymon at the damages hearing was contradictory as to the nature of the job described in Pl.E. 32. Defendant Laymon at one point in his testimony admitted that Exh. 32 pertained to an internal assembly job in Canada with total revenues of $26,616.80. Laymon, vol. III, p. 591, In. 8-12. Later, defendant Laymon testified that Exh. 32 pertained to a bend detector job performed after another company's dummy tool had been bent in the customer's pipeline. Id. p. 707, In. 11-17.
Def.E. 238A contains two spread sheets entitled "What TDW would have bid on EPS jobs." A special category, entitled "Bend Detector Jobs" is included in those two charts. Pl.E. 32 is not claimed by the defendants as a bend detector job on Def.E. 238A, although other jobs are claimed as such.
Pl.E. 32 is an invoice from EPS and other related paperwork dated April 1986, and shows that both bend location and a geometric survey were offered and billed in April, 1986. The description of work performed on the invoice is stated to be to "bend locate & gauge 133 Miles × 20 inch diameter pipeline". Defendant Laymon's letter dated April 4, 1986 to the pipeline customer explains the work performed:
EPS performed an internal geometry inspection of this line segment on March 25, 1986. Along with this service a bend detection survey was also run. Due to a miscalculation in supply, the geometric gauging chart was short and did not provide full line data. This information will be provided from another inspection after repair and relocation work has been completed.
Laymon then provided the customer with a report of four unlisted bends that had been detected. At the end of the letter, Laymon closed with the promise that a complete *605 geometric survey would be enclosed with the final report.
Defendants' inconsistent characterization of the nature of the survey job represented by Pl.E. 32 could have accounted for the Master's decision to find in favor of TDW in awarding lost profits to TDW on that job.[2] If defendants erred in characterizing the job as a caliper survey, rather than a bend location job, the burden of that error must fall upon the defendants, rather than upon TDW. See Story Parchment Co. v. Paterson Parchment Paper Co., 282 U.S. 555, 51 S.Ct. 248, 75 L.Ed. 544 (1931) ("the risk of the uncertainty should be thrown upon the wrongdoers instead of upon the injured party"); Milgo, 623 F.2d at 664 (doubts concerning the calculations of profits must be resolved against the infringer).
Given defendants' inconsistency in characterizing that particular job, the Court cannot say that the Master clearly erred in his inclusion of that job in his calculation of lost profits. The Master had the benefit of observing defendant Laymon's testimony and thus was in a better position to determine the credibility of his testimony on this point. See McGraw Edison Company v. Central Transformer Corp., 196 F.Supp. 664 (E.D.Ark.1961), aff'd 308 F.2d 70 (8th Cir.1962) ("the Court is more reluctant to overturn the Master's findings where such findings are based upon conflicting testimony of witnesses who have been seen and heard by the Master ...").

C. Defendants claim TDW cannot recover damages on two Canadian jobs performed in 1982, before TDW actually charged defendants with infringement.
Defendants' objection to the Master's inclusion of lost profits for two jobs performed in Canada in 1982, is based on defendants' argument that TDW failed to mark its caliper pig with the word, "Patented" or the abbreviation "Pat." as required by statute, and thus failed to give notice to defendants and the public about the patented status of the caliper pig. Defendants maintain that TDW's failure to mark its pig excludes any damages for patent infringement occurring before an actual charge of infringement to defendants was made by TDW. Defendants contend that the actual charge of notification from TDW was not provided to defendants until November 30, 1982, and thus the two Canadian jobs defendants performed prior to November, 1982 should not be included in the calculation of lost profits to TDW.
TDW offered into evidence three letters sent between its counsel and defendants and defendants' counsel. Pl.E. 161-163. On June 18, 1982, TDW counsel Johnson sent letters to defendant Laymon and former EPS partner Lanny Potts, informing them of TDW's awareness of EPS' contract with a Canadian pipeline for a caliper survey, using a device similar to TDW's caliper pig. Johnson's letter specifically informed the EPS partners of the patent numbers of TDW's caliper pig patents in Canada and the U.S., and that use of EPS' device would be an unauthorized use of devices covered by those patents. Johnson closed the letters by warning of TDW's intent to seek an injunction and damages for any past or potential infringements. Counsel for EPS, Dorman, responded to Johnson's letter on June 23, on behalf of Laymon and Potts, stating that EPS had avoided infringement by designing around TDW's patent.
In his finding of fact 31, the Master concluded that TDW counsel's letter of June 15 and 18, 1982 to Potts and Laymon constituted a notice of infringement of TDW's patent. The Master also held Johnson's letters constituted a notice of infringement within the meaning of 35 U.S.C. § 287. The Master's conclusion of a sufficient notice of infringement was based upon his finding that Dorman's letter of June 23, 1982 responded to Johnson's earlier letters by asserting that EPS had not infringed TDW's patent. The Master drew the inference from Dorman's response that *606 EPS regarded Johnson's letters of June 15 and 18 as charges of infringement.
It is undisputed that TDW did not mark the patented pig as required by § 287 (although TDW argues that since only TDW handles the caliper pigs in providing survey services, no member of the public can be misled by the lack of a "patent" marking on each of its pigs). The issue then is the sufficiency of notice of infringement provided defendants by TDW counsel on June 15 and 18, 1982. Dorman's letter of June 23, 1982 responds to the two letters, by offering assurances that the defendants had avoided infringement by designing around TDW's patent. "When one acknowledges for his adversary that the adversary is claiming infringement, the law most certainly does not compel the patent owner to repeat it any more explicitly." Livesay Window Company v. Livesay Industries, 251 F.2d 469, 475 (5th Cir.1958).
Defendants characterize Johnson's two letters as "cautionary" and therefore not an actual notice of infringement. That the two letters may be phrased in terms of defendants' future infringement is explained in the letters' first paragraph, where Johnson states his learning of a future pipeline survey with devices which had been described as similar to that covered by TDW's patent. The effect of TDW's warning of infringement is not lessened because the act of infringement has not yet occurred; no law requires an infringement to have taken place prior to an effective notice of infringement. 35 U.S.C. § 287 only requires proof that the infringer was notified of infringement and continued to infringe thereafter. Armstrong v. Motorola, 374 F.2d 764 (7th Cir.1967). The notice provision of § 287 is satisfied if the infringer was given the same information as the statute requires for patent marking, which need only contain the word "patent" or its abbreviation, and the patent number. Id. The second paragraph of Johnson's June 1982 letters clearly recites the word "patent" in connection with the patent numbers for TDW's Canadian and U.S. patents on the caliper pig. Additionally, TDW warned defendants in its intention to "aggressively" seek legal remedies against them. A charge of infringement, as was recognized in Dorman's response, would seem readily apparent in TDW's threat of court action.
Defendants contend the recent decision in Refac Electronics Corp. v. A & B Beacon Business Machines Corp., 695 F.Supp. 753, 8 USPQ2d 2028 (S.D.N.Y.1988), supports their argument that Johnson's letters were an insufficient notice of infringement. However, the Court's review of that decision reveals differences in the letters sent in Refac and those at issue here. The letters sent by Refac omitted mention of the particular infringing device sued upon; the eleven devices listed in the Refac letters were wholly different in nature from that sued upon so that the accused infringer could not be said to have had notice of the patentee's intent to include that device among those listed in the letters charging infringement. Id. 695 F.Supp. 753, 8 USPQ2d at 2030. The accused infringer's response letter requested further information about the devices alleged to be infringing, and did not acknowledge Refac's accusation of infringement. Id. 695 F.Supp. 753, 8 USPQ2d at 2029. In contrast, Johnson's June 18, 1982 letters to Laymon and Potts specifically mentioned defendants' proposed use of a device to perform pipeline caliper surveys in Canada, and warned of the likelihood for infringement of TDW's caliper pig patents in Canada and the U.S. upon the use of defendants' device. No possibility thus existed here for confusion by the defendants about which devices Johnson's letters intended to cover. This was evidenced by Dorman's June 23 response letter, which did not request further information from Johnson about what devices he meant, but instead denied infringement and asserted defendants' intentional avoidance of infringement by designing around the TDW caliper pig patent.

D. Defendants' claim that TDW cannot recover damages for foreign jobs performed prior to November 8, 1984.
Defendants object to the Master's inclusion of lost profits for jobs defendants performed in Canada and Italy prior to *607 November 8, 1984. The Master's inclusion of lost profits for these jobs was based upon his Finding of Fact 24 that defendants shipped their infringing pig components from the United States to the foreign job site. The Master also found that after completing these foreign jobs, defendants shipped the pig's disassembled components back to Tulsa for use on subsequent foreign or U.S. jobs.
In their assertions of error, defendants place much emphasis in their argument regarding the unassembled state in which their pigs were shipped to foreign job sites. Defendants contend that their pigs were not assembled in the United States before July, 1983. Defendants do not cite any evidentiary support for this contention and the Court's review of the record found no evidence indicating when defendants first assembled their infringing pigs in the United States. Likewise, defendants' contention that their first two jobs were performed in 1982 in Canada, without assembling their pig anywhere but at the Canadian job site, is also without evidentiary support in the record, as reviewed by the Court. After reviewing the record, the Court finds no clear error in the Master's Finding of Fact 24.
In their reply brief, defendants also apparently object to the Master's Conclusion of Law 16. There, the Master held the defendants' reliance upon Deepsouth Packing Co. v. Laitram Corp., 406 U.S. 518, 92 S.Ct. 1700, 32 L.Ed.2d 273 (1972), was misplaced, in that Deepsouth's products were never assembled in the U.S. and thus avoided infringement. Defendants point out that in Deepsouth, there were sales and assembly in the United States of devices which were held to infringe, but that the unassembled components sold in foreign countries were held not to infringe. Defendants may be correct in this characterization of the Deepsouth decision; however, the Court finds their reliance upon Deepsouth is misplaced for reasons in addition to that stated by the Master.
The facts surrounding the defendants' operation of their caliper survey business distinguish the instant case sufficiently from that of the infringer in Deepsouth to cause this Court to question Deepsouth's applicability. In Deepsouth, the infringing units remained unassembled for shipment to foreign purchasers, who assembled and used the infringing device overseas. The Deepsouth defendant apparently had no further involvement with an infringing unit, once it was shipped to the foreign purchaser. In Deepsouth, the Supreme Court noted that the return of the foreign-purchased infringing devices for subsequent use in the U.S. would not allow the defendant to escape liability for infringement: "[c]ertainly if Deepsouth's conduct were intended to lead to use of patented deveiners inside the United States its production and sales activity would be subject to injunction as an induced or contributory infringement." Id. at 526, 92 S.Ct. at 1706.
In the present case, however, defendants' conduct in shipping their pigs overseas in less than operable condition was intended to lead to defendants' continued use of their infringing devices within the United States. Defendant Laymon established that after performing caliper survey jobs in Canada and Italy, defendants brought the pigs back to the U.S. for future survey jobs in the U.S. and overseas. See Laymon, vol. III, p. 605, ln. 13-24; vol. X, p. 1947, ln. 2-7. Defendant Laymon also testified that in the first years of EPS' operation, EPS had only three recording instruments, and thus could not perform caliper survey jobs in the U.S. if the recorders were shipped overseas with the pigs; therefore the EPS technicians hand-carried the recorders to foreign job sites and then back to the U.S. Id. at p. 1883, ln. 1-6. Laymon also noted that the same pig components are used in defendants' pigs to perform survey jobs in both the U.S. and foreign countries. Id. vol. III, p. 605, ln. 17-24; vol. X, p. 1945, ln. 16-17. Components of the infringing pig are maintained and stored unassembled at defendants' offices in Tulsa; defendants compile pig components as needed for a particular job. Id. p. 1960, ln. 1-6. For both U.S. and foreign survey jobs, defendants basically ship their pigs in the same manner, reserving final, albeit minor, assembly and adjustments to *608 the pig to be done at the job site. Id. p. 1889, ln. 12-22; p. 1884, ln. 15-23.
Unlike the defendant in Deepsouth, defendants did not intend to make a one-time sale to foreign purchasers of their infringing device; defendants instead sold their use of the infringing devices to pipeline customers in the U.S. and in foreign countries. Defendants' rotation of the infringing devices between foreign and U.S. survey jobs as needed enabled defendants to exploit opportunities for survey jobs in the U.S. as well as overseas. Defendants' overseas use of their infringing pigs thus cannot be as neatly separated from their infringing activities in the U.S. as was the case in Deepsouth. While perhaps not following the same reasoning as used by the Master in proposed Conclusion of Law 16, the Court, after de novo review of that Conclusion, is nevertheless unpersuaded by the defendants' arguments of Deepsouth's applicability to the facts of this case.

E. Defendants' claim that TDW cannot recover lost profits on survey jobs lost to defendants unless TDW can show that it was the second lowest bidder.
No decision or statute was located which cited such a rule requiring a showing of a second lowest bidder. The decision cited by defendants as support for the stated "rule", Leesona Corp. v. U.S., 220 Ct.Cl. 234, 599 F.2d 958 (1979), does not set forth such a rule. Leesona also is distinguishable on its facts from this case or any other case involving damages assessment against a private infringer, rather than the United States. The federal government issued to Leesona a negotiated contract letter for procurement of batteries, on which Leesona had a patent. The government soon thereafter withdrew the letter contract and sought bids from Leesona and several other companies for the batteries. The lowest bidder received the contract, and began manufacturing the batteries under Leesona's patent, furnished by the government. Leesona was the second lowest bidder, and sued the government for infringement of its patent.
As the Court of Claims pointed out, the theory for recovery against the government for patent infringement is not analogous to that in litigation between private parties; the government's infringement is deemed a "taking" of the patent license under an eminent domain theory, rather than under patent infringement damages statutes. Id. 599 F.2d at 964. The federal government procurement and contract bid procedures also cannot be compared to the contract dealings between private companies.
Defendants also suggest that the Master did not consider the rule that where a patent owner and the accused infringer had a number of competitors bidding for jobs, the patent holder must show that he bid on all lost sales he claims to have lost. See Defendants' Objections, p. 64 (citing Milgo Electronic v. United Bus. Communication, 623 F.2d 645 (10th Cir.1980)).
However, as the Milgo decision indicated, [n]either the trial court nor the appellate court can demand absolute proof that purchasers of the infringing product would have bought the patent-holder's product instead. It is impossible and therefore unnecessary for the patent-holder to negate every possibility that the purchasers might not have bought another product. The plaintiff's burden of proof is not absolute, but rather one of reasonable probability.

Id. at 663.
In Milgo, the patentee and the infringer were deemed to be the only "viable" competitors in the marketplace, and the court there held it "unnecessary for the [patentee] to prove that he bid or at least solicited bids on every infringing sale in order to recover lost profits for these sales." Id. at 664. The evidence here does not support defendants' contention that "important" competitors existed during the relevant period who bid against defendants and TDW for caliper survey jobs during the relevant period. Instead, the evidence indicates that TDW and defendant EPS were considered to be the primary "viable" competitors offering pipeline internal geometry caliper surveys during the relevant *609 period. For many of the same reasons that the Court has found these other alleged "important" bidders to have non-acceptable substitutes for the patented device, the Court finds that the presence of the alleged bidding competition was negligible, and thus does not require TDW to show that it bid on all jobs in order to receive lost profits on the jobs performed by the defendants.

F. Defendants' claim that TDW cannot recover lost profits on 6" diameter pipeline surveys.
Defendants object to the Master's inclusion in his calculation of lost profits of three survey jobs EPS performed on 6" diameter pipelines. Defendants' objection is based upon their contention that TDW took its 6" caliper pig off the market in 1981 and instituted a company policy forbidding further use of the 6" pig, because of customer complaints and dissatisfaction with the results obtained from that particular size of pig. Despite the alleged company policy, defendants also contend that TDW used its 6" pig on a pipeline survey job in Australia in 1983, with such poor results that TDW was "thrown off" that job. According to defendants' witness, TDW then reinstated its policy of not providing 6" caliper pig surveys. See Beach, vol. XI, p. 2005, In. 1-11.
At the damages hearing, TDW presented evidence showing that it had used its 6" caliper pig to perform several caliper survey jobs during the relevant period when defendants contended that TDW had withdrawn the 6" pig. See Pl.E. 159. In response, defendants charge that TDW used its 6" pig on those several jobs in violation of its own company policy, without approval of TDW management, and with knowledge of the 6" pig's faulty design, thereby perpetrating a fraud upon the public. According to defendants, "principles of equity" should prevent TDW from recovering lost profits on EPS' 6" survey jobs in view of TDW's practice of a "fraud" upon the public and TDW's customers with its 6" pig.
Defendants did not specify the "principles of equity" supporting their argument. The Court must therefore infer that defendants' reliance is upon the "clean hands" doctrine, which bars relief sought by a plaintiff whose prior conduct had violated some legal or equitable principle.
If the Court's inference is correct, several problems are apparent in defendants' assertion of the "clean hands" doctrine to deny TDW lost profits on the three 6" jobs. It is questionable whether TDW's use of its 6" pig was even a "violation" of its own company policy and without the knowledge of its management; no evidence clearly established such alleged "nefariousness" within TDW's operations. See Nike, Inc. v. Rubber Mfrs. Ass'n., Inc., 509 F.Supp. 919, 926 (S.D.N.Y.1981) ("clear, unequivocal, and convincing evidence" required to establish the defense of unclean hands). Even if such intracorporate "infractions" were established, the Court fails to see how such can be labeled as a violation of a legal or equitable principle serious enough to invoke penalties against TDW under the "clean hands" doctrine. The evidence does not show a "bad intent" on the part of TDW, which is necessary to invoke the doctrine. See Wells Fargo & Co. v. Stagecoach Properties, Inc., 685 F.2d 302, 308 (9th Cir.1982) (bad intent is the essence of unclean hands defense). Finally, the Court questions whether defendants can invoke that doctrine here, as defendants assert damage to TDW's customers and the public, but not to themselves, from TDW's alleged "fraudulent" use of its 6" pig. "The maxim of unclean hands is not applied where plaintiff's misconduct is not directly related to the merits of the controversy between the parties, but only where the wrongful act in some measure affects the equitable relations between the parties in respect of something brought before the court for adjudication. The alleged wrongdoing of the plaintiff does not bar relief unless the defendant can show he has personally been injured by the plaintiff's conduct." Mitchell Bros. Film Group v. Cinema Adult Theater, 604 F.2d 852, 863 (5th Cir.1979).
*610 The Court, from its examination of the evidence, finds no evidence of a "fraud on the public" practiced by TDW with regard to its 6" caliper pig, nor clear error on the part of the Master in awarding TDW lost profits on the defendants' three 6" survey jobs. TDW's evidence demonstrated that it had the ability to perform 6" caliper survey jobs during the relevant period.

G. Defendants' claim that TDW should not recover damages for a job performed after the relevant period with EPS' "external finger assembly" pig.
Defendants complain of the Master's inclusion in the lost profits calculations of a job[3] they contend was performed after the relevant time period with their other caliper pig embodiment. That embodiment used an "external finger assembly" instead of the "internal finger assembly" found to be an infringement by this Court on April 30, 1986.
Defendant EPS' invoices and job paperwork on this one job clearly indicate that part of the caliper survey work performed by defendants took place between April 21 through May 2, 1986. Defendant Laymon has conceded that this part of the job was performed with the infringing "internal finger assembly" caliper pig. See Laymon, vol. III, p. 570, ln. 16-25.
However, defendants claim that the second part of the job, covering the period from May 3-14, 1986, was performed with the "external finger assembly" pig after the relevant period. The EPS invoice and job paperwork covering this part of the job do not indicate whether an internal or external finger assembly was used after April 30, 1986. Defendant Laymon testified that that job was performed with the "external finger assembly". See Id. vol. III, p. 659, ln. 14-21. Defendant Laymon also testified that he was advised of the Court's infringement finding on May 1, 1986, and that he immediately made arrangements to have a new finger assembly manufactured for the pig on this job. Laymon testified that he also spent that day and the next looking for casters or rollers to attach to the ends of the modified finger assembly; however, he was unsuccessful in finding anything in stock and readily available for use on the pig on the job in progress. Id. vol. III, p. 578-79. Laymon's testimony was not definite as to when the "external finger assembly" was actually put on the pig in use on the job and no documentation was available to pinpoint when Laymon sent the finished "external finger assembly" to be used on that job. See Id. vol. III, p. 571-72.
Defendants produced the job file to TDW, identifying it as a job using the infringing internal finger assembly. See Id. vol. III, p. 564, 657. Defendants now claim it inequitable for the Master to penalize them for their inadvertent production of their mislabeled file. However inadvertent defendants' mislabeling may have been, any penalty created by that mistake should not be assessed against TDW, since "any adverse consequences must rest on the infringer when the ability to ascertain lost profits is due to the infringer's own failure to keep accurate or complete records." Lam, Inc. v. Johns-Manville Corp., 718 F.2d 1056, 1065 (Fed.Cir.1983) (citing Milgo, 623 F.2d at 665). Aside from that question, the Court does not find the Master's identification of both parts of this particular job as performed by the infringing internal finger assembly to be clearly erroneous. Defendants could not furnish evidence, either by testimony or by document, of a precise date to prove if and when they switched to the external finger assembly on this job. Lacking such evidence, the Master could not apportion the damages between the usage of the infringing finger assembly and the alleged use of the external finger assembly.

H. Defendants' claim that TDW's conduct during lawsuit justifies a denial of prejudgment interest to TDW.
Defendants complain that the Master's award of prejudgment interest to *611 TDW is an abuse of discretion. Defendants contend that many of TDW's actions taken during this litigation were contrary to what TDW knew or should have known of the "actual" or "true" facts, and were taken intending to "punish" defendants by forcing them to incur increased time and expenses to defend against TDW's claim for damages.
In 1983, the Supreme Court set forth the standard for the award of prejudgment interest under 35 U.S.C. § 284, noting that such interest should ordinarily be awarded where necessary to afford a plaintiff full compensation for infringement of the patent. General Motors Corp. v. Devex Corp., 461 U.S. 648, 655, 103 S.Ct. 2058, 2062, 76 L.Ed.2d 211 (1983). However, the Court also indicated that prejudgment interest is not required to be awarded on every determination of infringement, but may be limited or denied, in circumstances such as when a patent owner is responsible for undue delay in prosecuting the lawsuit, or in "other circumstances". Id. at 656-57, 103 S.Ct. at 2062-63.
Defendants contend the "other circumstances" language of Devex applies to TDW's prosecution of its damages claim. This contention is premised on defendants' conclusion that TDW pursued its claim for damages, despite knowing (or that it should have known) that it could not prevail on such a claim. Defendants essentially impute to TDW the "knowledge" that each of defendants' sixteen objections, discussed above, would be sustained.
No court has yet given definition to the term "other circumstances" to illustrate situations justifying denials of prejudgment interest. In Devex, the Supreme Court found no unnecessary delay on the part of the plaintiff there, indicating that the plaintiff "had done no worse than fully litigate its claims, achieving a large judgment in its favor." Id. at 657, 103 S.Ct. at 2063. The Court here similarly finds TDW's prosecution of its claim for damages to be "no worse" than was that of the plaintiff in Devex, in seeking to prove its damages from defendants' infringement of TDW's patent. The record does not demonstrate TDW's possession of "knowledge" or an intent to "punish" defendants through their expenditure of time and money, as alleged by defendants. Defendants have not supplied the Court with any evidence to support their allegations of TDW's "knowledge" and intent to punish them, to warrant a finding that the Master's award of prejudgment interest is an abuse of discretion.

Conclusion
In summary, then, the Court finds as follows:
1. Plaintiff TDW's objection to the Special Master's Proposed Finding of Fact 30 is hereby SUSTAINED.
In calculating lost profits due TDW for defendants' 1986 caliper survey job in Venezuela, the Court has attempted to use the same methodology used by the Master. Using Pl.E. 96, TDW's Cost List, and referring to the third page, headed "Foreign-Products/New Construction", the Court noted from Pl.E. 33 that the 1986 Venezuela survey was for 119 miles of 26" diameter pipeline carrying natural gas. Using the chart on page three of Pl.E. 96, the amount for that length and size of pipeline and product is listed at $14,392. Multiplying that amount by the 51% contribution margin as set out by the Master for 1986, the Court arrived at an amount of $7,339.00 to represent lost profits to TDW on the 1986 Venezuelan job represented in Pl.E. 33.
Plaintiff TDW and defendants shall have ten days after the date of this Order to submit to the Court any correction to its calculations of lost profits as set forth above. Such correction must be substantiated with appropriate documentation, evidence, and applicable legal authority, if any.
2. Defendants' seventeen objections to the Special Master's Proposed Findings of Fact and Conclusions of Law are hereby OVERRULED.
3. All Proposed Findings of Fact and Conclusions of Law submitted by the Special Master, with the exception of Finding of Fact 30 as noted above, have been reviewed *612 by the Court and are hereby ACCEPTED AND ADOPTED by the Court, pursuant to F.R.Cv.P. 53(e)(2).
IT IS SO ORDERED.
NOTES
[1]  Additionally, the Court notes that the district court's judgment in that case was vacated and the case was remanded with instructions to dismiss the complaint because the case became moot on appeal. See Smith International Inc. v. Hughes Tool Co., 839 F.2d 663, 664 (Fed.Cir. 1988).
[2]  The Master excluded jobs claimed by defendants to be primarily bend location surveys from his calculation of lost profits. See Findings of Fact 25-29. TDW did not object to these findings, and the Court does not here assess their correctness.
[3]  Defendants' objection was actually directed toward the inclusion of two EPS jobs files, corresponding to Pl.E. 15 & 16, in the Master's calculations of lost profits to TDW. However, in Finding of Fact 26, the Master excluded the job in Pl.E. 16 from the lost profits calculations as a bend detector job.
