Opinion by Judge O’SCANNLAIN; Concurrence by Judge BETTY B. FLETCHER.
OPINION
O’SCANNLAIN, Circuit Judge.We must decide whether the Fourth Amendment compels the suppression of the results of a series of searches set in motion by an application to scan a private residence and its outbuildings with a thermal imaging device.
I
In October 1998, DEA special agent Ronald Wright and IRS special agent Kurt Charlton interviewed a prisoner incarcerated on federal drug charges, seeking information on drug trafficking activity in southern Oregon. The informant gave them a tip that an individual variously known as Galen Maxwell, Courtney Maxwell, and Steve Huggins (“Huggins”) was involved in producing and distributing marijuana and LSD. The informant added that he had last spoken to Huggins three years before, that Huggins had then lived in the Eugene area but might have since moved to Ashland, and that at the time Huggins had had a girlfriend named “Rhonda.”
Wright proceeded to corroborate some of the details of the tip. He established that a Steve Huggins had listed 199 Mow-etza Drive, Ashland, Oregon, as his address on a still-current vehicle registration and on an Oregon driver’s license that had expired six months before; that Huggins had previously listed on his driver’s license an address in Veneta (near Eugene); that a Rhonda Taylor owned the Mowetza Drive property and maintained a personal address, a business address, and telephone service there; and that Rhonda Taylor also used the names Rhonda Jewell and Rhonda Huggins. A check of DEA files indicated that a Rhonda Jensen, also known as Rhonda Jewell, who had the same date of birth as Rhonda Taylor, had been arrested in Mexico in 1983 with 200 kilograms of marijuana.
Wright drove by the Mowetza Drive property and determined that it was a five-acre parcel with a single-story ranch house, two barns, and a riding ring. He also obtained the electrical records for that property and the two neighboring properties from Pacific Power and Light. Those records indicated that the combined electricity bills for the two meters in service at 199 Mowetza Drive had averaged $455.87 per month (with total power use averaging 7784 kWh per month) over the thirteen months that the electric service had been in Rhonda Taylor’s name. By comparison, electric consumption at the adjacent properties averaged 1583 and 1377 kWh per month, respectively, and their bills averaged $92.83 and $71.84. During the thirteen months before Rhonda Jensen took over the electric service at 199 Mowetza Drive, the combined bills for that property had averaged $133.69, with average usage of 2309 kWh/month.
Wright swore out an affidavit before a U.S. magistrate judge, reciting the above information about the tip (although with no details about the identity or background of the tipster,1 and with the caveat that the *1042tipster’s “reliability” was “untested”); the corroborated details of Huggins’s move from Veneta to Ashland and of his association with Rhonda Taylor; the information about Taylor’s past arrest; and the electricity consumption data. Wright stated that based on his past experience, he thought this information indicated that Huggins was engaged in marijuana production. In particular, he stated that “large indoor marijuana cultivation operations typically consume large quantities of electricity primarily to power large 1,000 watt lamps associated with the grow operation.” He therefore requested a warrant to examine 199 Mowetza Drive using a thermal imaging device,2 as well as to collect discarded trash from the property.
The magistrate judge issued the warrant, and the search was conducted overnight by Sgt. Ken Hauge of the Oregon National Guard, a trained operator of thermal imaging equipment. As Wright later reported, the scan indicated that the south side of the eastern barn “showed an excessive heat-loss signature” that was “greater than the heat loss on the north side of the same barn” and that “continued after 1:00 a.m., which is a time during which the solar heat loading that would have occurred during daylight hours would have dissipated.” The other barn also showed an excessive heat-loss signature on one wall. The heat-loss signatures, Hauge concluded, were “consistent with the signatures he ha[d] seen from other thermal images of structures from which indoor marijuana ‘grows’ were subsequently seized.”
Meanwhile, Charlton investigated Huggins’s and Taylor’s finances. Taylor had bought property in Veneta in 1993, sold that property in 1996, and bought the Mowetza Drive property the same month. Both properties were subject to mortgages. Huggins had never filed a federal income tax return; Taylor had filed returns, but they showed income insufficient or only barely sufficient to cover her mortgage interest payments, and they gave no indication of where she got the money for the two down payments.
Wright swore out a second affidavit, repeating the averments of the first affidavit and adding the details of the thermal imaging scan and the review of Huggins and Taylor’s finances. He requested a warrant to search 199 Mowetza Drive for evidence of marijuana cultivation and related offenses. The magistrate judge granted the warrant.
The search turned up 474 growing marijuana plants in the eastern barn, plus assorted growing paraphernalia, some dried marijuana, documents, and cash. It did not, however, turn up any drying equipment. Among the documents seized were some relating to a property at 16000 North Applegate Road in Ruch. Specifically, the agents found a bill made out to Rhonda Taylor for water testing at the North Ap-plegate Road property; receipts of payments to a title company, which bore the name D.W. Hagen; and a power bill for the North Applegate Road property addressed to Whip Hagen. They also found an envelope labeled “receipts 98 Apple-gate,” which contained a number of receipts from a hardware store for several items, including a water heater timer, temperature gauge, and humidity gauge, *1043that can be used in operating an indoor marijuana grow. In addition, they seized a “Property Inspection Sheet” relating to a property at 15333 Highway 238 in Grants Pass. The document listed Steve and Rhonda Huggins as tenants.
Further investigation, including questioning of Taylor at the scene of the search, verified that Dahcota Whip Hagen was Taylor’s son, that he owned the North Applegate Road property, and that there had been a number of phone calls from Taylor’s phone line to Hagen’s in July and August. In addition, an Oregon state trooper relayed an anonymous informant’s tip that he had seen a marijuana grow at 16000 North Applegate Road (and had provided a leaf that he said was from that grow), and a contractor working across the road said that he had seen Whip Hagen’s “parents” going in and out of Hagen’s property over the previous week. Finally, the agents discovered that the electrical service at the Highway 238 property was in Steve Huggins’s name and that Huggins’s electricity usage was higher than the previous tenant’s had been.
Based on the foregoing information, a Medford police officer working with the DEA and IRS agents sought and obtained a state search warrant for the North Ap-plegate Road and Highway 238 properties. Both properties were searched the day after the Mowetza Drive search. The North Applegate Road property was found to contain a marijuana grow with over 100 marijuana plants, and the Highway 238 property yielded over 300 marijuana plants and some bagged marijuana.
Hagen was arrested at the North Apple-gate Road property, and Vicki Jensen, who is Taylor’s sister, was arrested at the Highway 238 property. Jensen told the authorities that Huggins and Taylor had set her up as caretaker of the Highway 238 property.
All four defendants3 were indicted and charged with marijuana possession, cultivation, and distribution. All except Taylor were also charged with conspiracy to commit money laundering. The defendants filed various motions (with various cross-joinders) to suppress the evidence from the series of searches. In particular, the defendants challenged the affidavits’ failure to describe the Mowetza Drive property and to provide an adequate basis for evaluating the electricity usage; the failure to provide information about the tipster’s plea bargain and motive to lie; and the efficacy of the thermal imager, Hauge’s operation of the imager during the scan of 199 Mowetza, and Wright’s report of the scan results.
The district judge held a limited Franks hearing to examine whether the affiants had made material omissions or misstatements in obtaining the several search warrants. After testimony from both sides, including expert testimony on the operation and accuracy of the thermal imaging device, the district court denied the motions to suppress. The court concluded that “probable cause exist[ed,] but not by a wide margin,” and that the defendants had not carried their burden of establishing dishonesty or recklessness in the affidavit.
All four defendants subsequently reached conditional plea agreements under which they reserved their right to challenge the constitutionality of the various searches. They timely filed the instant appeals, which we consolidated.
II
The Supreme Court recently determined that the use of thermal imaging equipment or other devices “not in general *1044public use” to discern “details of the home that would previously have been unknowable without physical intrusion” is a search, unreasonable under the Fourth Amendment unless supported by probable cause and, presumptively, authorized by a warrant. Kyllo v. United States, 533 U.S. 27, 121 S.Ct. 2038, 2046, 150 L.Ed.2d 94 (2001). In this case, Wright obtained a facially valid warrant4 before performing the scan, so we initially ask only whether he conducted the search in good faith reliance on the magistrate judge’s determination that probable cause existed. The “good faith exception” applies, and suppression is unwarranted, unless the searching officers’ reliance on the warrant was not “objectively reasonable,” United States v. Leon, 468 U.S. 897, 922, 104 S.Ct. 3405, 82 L.Ed.2d 677 (1984), the magistrate judge “wholly abandoned his judicial role,” id. at 923, 104 S.Ct. 3405, or the officers acted in bad faith by misleading the magistrate judge, id. (citing Franks v. Delaware, 438 U.S. 154, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978)). In evaluating whether the officers could reasonably rely on the magistrate judge’s probable cause determination, we are mindful that although a thermal imaging search is less intrusive than a physical search, the degree of probable cause required is not diminished merely by virtue of that fact.5
A comparison with the warrant we considered in United States v. Clark, 31 F.3d 831 (9th Cir.1994), is instructive. In that case, we held that an anonymous tip, which did not specifically link Clark to criminal activity and which was only partially corroborated, and an assertion that the target’s electricity usage was “high,” which offered the issuing magistrate no basis for comparison, were together inadequate to support a finding of probable cause. Id. at 835. However, we went on to hold that the good faith exception nonetheless applied, because “[tjhere was enough information so that objectively rea*1045sonable officers were entitled to rely on the magistrate judge’s determination.” Id.
In this case, Wright’s affidavit did not present the current power consumption data for the target property in isolation; it also offered comparative data, both from neighboring properties during the same period and from the Mowetza Drive property during the prior owner’s residency. The defendants argue that the affidavit should have spelled out in more detail the relative sizes of the neighboring properties and any differences in the way the previous owners used the property (such as not using the barn for livestock). We agree that such additional comparative data—especially if it had shown the usage from neighboring properties with bams— would have aided the magistrate judge in his determination. However, we do not think that the magistrate judge’s decision to issue the warrant without the benefit of such information evinces objective unreasonableness, particularly as the affidavit did provide a breakdown between usage from the residential meter and the barn meter, as well as some information on the size of the buildings on the 199 Mowetza property. We conclude that these additional details reduced the dangers of an apples-and-oranges comparison sufficiently to distinguish this affidavit from that in Clark, at least on its face,6 and that an officer with “a reasonable knowledge of what the law prohibits,” Leon, 468 U.S. at 919 n. 20, 104 S.Ct. 3405, could therefore give credence to the magistrate judge’s finding of probable cause even in light of our Clark precedent. See United States v. Fowlie, 24 F.3d 1059, 1067 (9th Cir.1994) (distinguishing a warrant affidavit from a less detailed affidavit offered in an earlier, factually similar case, and holding that reliance on the latter affidavit was objectively reasonable).
Additionally, the tip that Wright recounted was more specific and was supported by more corroborating detail than was the bare assertion we confronted in Clark. Although the informant did not directly implicate Huggins in ongoing marijuana production, as the information he possessed was several years old, the corroboration of other details of the tip (such as Huggins’s relationship with Taylor and his move from Veneta to Ashland) lent credence to the tipster’s assertion that Huggins had previously been involved in growing marijuana—and that he had done so while involved with Taylor and living on property she owned.
Finally, Huggins’s still-current vehicle registration gave reason to believe he might still be found at the electricity-hungry Mowetza Drive property. (Although the Oregon driver’s license on which he listed 199 Mowetza as his address had expired, that did not establish with any certainty that he had moved elsewhere.) Thus, the magistrate judge had before him information suggesting that Huggins had previously been involved in marijuana production while living on property owned by his girlfriend, that he and his girlfriend had moved together to a new location, and that their new home displayed patterns of electricity consumption consistent with an indoor marijuana grow.
In light of Wright’s recitation of all of these facts, we cannot say that his affidavit was “so lacking in indicia of probable cause as to render official belief in its existence *1046entirely unreasonable.” Leon, 468 U.S. at 923, 104 S.Ct. 3405 (quoting Brown v. Illinois, 422 U.S. 590, 611, 95 S.Ct. 2254, 45 L.Ed.2d 416 (1975) (Powell, J., concurring in part)) (internal quotation marks omitted). An objectively reasonable officer could rely on the magistrate judge’s determination that Wright’s affidavit sufficed to make out probable cause to conduct the thermal imaging scan.
The defendants also argue that the good faith exception is inapplicable because, they contend, the officers misled the issuing magistrate. See id. (citing Franks). Specifically, they assert that had the agents surveilled the Mowetza Drive property over a longer period, they would have discovered information — e.g., that the occupants kept horses and dogs, that the house was equipped with a heat pump for air conditioning, or that the occupants made “extensive use of power tools” — that could and would have provided an innocent explanation for the comparatively high usage, and that the failure to undertake such extended observation was reckless. However, even assuming without deciding that such a “duty of further inquiry” may exist in some cases and that, as the defendants argue, a more thorough surveillance of Mowetza Drive would have uncovered information that would have undermined a finding of probable cause,7 we think that the agents’ decision not to conduct prolonged surveillance certainly was not made with the degree of recklessness necessary to warrant suppression. See United States v. Young Buffalo, 591 F.2d 506, 510 (9th Cir.1979) (“Even if we were to find that the information possessed by [the attesting agent] was enough to create a duty of further inquiry, these assertions at best raise the possibility of negligence on his part.... ‘Allegations of negligence or innocent mistake are insufficient’ to [justify a hearing].” (quoting Franks, 438 U.S. at 171, 98 S.Ct. 2674) (alteration omitted)).
The defendants also contend that the failure to disclose that the informant was in custody and trying to secure a plea bargain was a material omission that justifies suppression. However, the informant was detained on charges that did not bear on his credibility, and even if Wright had known about the plea bargain,8 the informant’s desire for favorable treatment does not seem material in light of the partial corroboration of his statement. See United States v. Meling, 47 F.3d 1546, 1555 (9th Cir.1995) (holding immaterial “the fact that an informant ha[d] an ulterior or impure motive in coming forward”). We do not think that the affidavit’s failure to state that the informant offered his information in exchange for leniency evinces bad faith or demands the suppression of the evidence. We also note that the affidavit did state, forthrightly, that the reliability of the informant was untested.
Finally, there is no evidence that the magistrate judge acted with partiality or in any way compromised the “neutrality and detachment demanded of a judicial officer when presented with a warrant application.” Leon, 468 U.S. at 914, 104 S.Ct. 3405 (quoting Lo-Ji Sales, Inc. v. New York, 442 U.S. 319, 326-27, 99 S.Ct. 2319, 60 L.Ed.2d 920 (1979)) (internal quotation marks omitted).
For the foregoing reasons, we conclude that the government conducted the ther*1047mal imaging search in good faith reliance on the facially valid warrant, and that the Fourth Amendment therefore does not require the suppression of the images recovered during that search. Therefore, we need not decide whether the magistrate judge’s probable cause determination was clearly erroneous, and we express no opinion on that question. See id. at 924-25, 104 S.Ct. 3405 (indicating that reviewing courts may, in their discretion, inquire into probable cause before good faith or vice versa); accord, e.g., United States v. Cavazos, 288 F.3d 706, 709 (5th Cir.2002); United States v. Lindsey, 284 F.3d 874, 877-78 (8th Cir.2002); United States v. Owens, 167 F.3d 739, 744-45 (1st Cir.1999); United States v. Chaar, 137 F.3d 359, 363 (6th Cir.1998); United States v. Cancelmo, 64 F.3d 804, 807 (2d Cir.1995); United States v. Clutchette, 24 F.3d 577, 581 n. 4 (4th Cir.1994); United States v. McKneely, 6 F.3d 1447, 1453-54 (10th Cir.1993). “Application of the good faith exception is particularly appropriate in the instant case because the legal question of whether probable cause existed is a close one,” while the objective reasonableness of the officers’ reliance on the warrant is more straightforward. Cancelmo, 64 F.3d at 808.
Ill
Next, we must examine whether probable cause existed to justify the physical search of 199 Mowetza Drive. In light of our conclusion that the fruits of the thermal imaging search were admissible, we consider the second warrant affidavit in its entirety, including the report of the scan results.
A
The thermal imaging data served to remove some innocent explanations for the comparatively high electricity usage at 199 Mowetza. Accordingly, the second warrant was much less dependent on establishing Huggins’s connection to the property; even if he no longer lived there, the electricity consumption data, the thermal imaging scan, Taylor’s recent association with Huggins, the partially corroborated tip that Huggins was involved in marijuana cultivation, and her apparent ability to purchase Mowetza Drive on only a small reported income9 were all factors supporting the notion that Taylor herself might be maintaining a marijuana grow on the premises, with or without Huggins’s involvement.10
*1048In considering this issue, we are guided by pre-Kyllo caselaw discussing the weight that thermal imaging results bear in probable cause analysis.11 Several of our sister circuits and multiple other courts have noted that although thermal imaging does not reveal direct evidence of crime, it can serve as a means of corroborating direct but weak evidence of criminal activity— such as the informant’s tip that triggered the investigation in this case.12 Thermal imaging can also bolster the probative value of comparative electrical data by indi-eating that whatever power-intensive activity is occurring on the premises under surveillance is also one that generates significant heat; this information rules out some, albeit not all, innocent explanations for the target location’s relatively high power bills.13 The thermal scan performed both functions in this case: Sgt. Hauge’s expert interpretation of the scan results indicated that the surplus electricity was likely being put to a heat-generating use, and that the thermal energy thus *1049generated was consistent with the presence of a marijuana grow.
We think that this information sufficed to justify the search of 199 Mowetza even without a firm connection between Huggins and the property. We therefore conclude that the magistrate judge did not clearly err in granting the second warrant.
B
The defendants maintain that even if the second affidavit was on its face sufficient to support the magistrate judge’s probable cause finding, the affidavit suffered from material misrepresentations or omissions that justify suppressing the fruits of the physical search under Franks.
First, the defendants assert that the second affidavit misrepresented what took place during the thermal imaging search. The affidavit stated that the scan showed excessive heat loss, consistent with the presence of a marijuana grow, on both barns, whereas Hauge testified at the Franks hearing that he had observed such a heat signature “only on the one [barn].” However, the district court did not clearly err in finding that this error was not reckless or calculated to mislead; Hauge did report observing some heat loss on the other barn.
Second, the defendants contend that the affidavit failed to disclose facts indicating that the thermal imaging search itself was fatally flawed. Relying on the expert testimony of Carlos Ghigliotty, the president of a company that uses infrared inspection technology, the defendants assert that the camera model used was substandard, the specific camera used was defective, and the camera permitted manipulation by the operator to allow for deceptive results. Specifically, Ghigliotty testified that the camera model used cannot sense temperature, only relative temperature, and an operator can manipulate the gain or the contrast so as to make hotter objects look much hotter and colder objects look much colder. Ghigliotty reviewed the videotape of Sgt. Hauge’s thermal imaging search of Mowetza Drive and concluded that “[i]n essence he fabricated the evidence to support his claim.”
The government presented expert testimony that partially refuted the claims about the camera’s alleged limitations and defects. Hauge also testified that he was not manipulating the controls during the taping, and that he had put the camera onto an automatic setting that locked in the focus and gain.
The district court did not consider Ghi-gliotty credible. Indeed, he found Ghi-gliotty’s testimony “biased,” “totally irresponsible,” and “useless to the Court.” Specifically, he pointed to Ghigliotty’s statement that “I’ve been doing this for about 10 years now, and I haven’t found one case that they haven’t fabricated the evidence in it, by that manipulating the controls in the camera.” This statement, together with other indications of bias and possible misrepresentation that the government brought out on cross-examination,14 offers adequate support for the district court’s determination that Ghigliotty lacked credibility. Likewise, we cannot say that the district court clearly erred in concluding that the thermal imager was sufficiently functional or that Hauge did not manipulate the camera to produce a misleading result. We thus conclude that the defendants have not shown that the affidavit left out or distorted any material fact.
*1050C
Because the second affidavit was sufficient to support a finding of probable cause, and because it neither omitted nor misrepresented material facts, the district court properly denied the motion to suppress the fruits of the physical search of 199 Mowetza Drive.
IV
Having concluded that the evidence from the two searches of ’199 Mowetza Drive was admissible,15 we have less difficulty in upholding the derivative searches of the North Applegate Road and Highway 238 properties.
A
Hagen strenuously challenges the search of his property as having been justified on a theory of “like mother, like son.” Although we agree that such a rationale would not by itself suffice to sustain a search, we disagree with the contention that that rationale was the only reason for searching the North Applegate Road property. Evidence recovered from Mowetza Drive directly supported the state judge’s conclusion that probable cause existed to search Hagen’s property; the affidavit did not merely invite the judge to infer from Taylor’s criminal activity that Hagen was a participant. And the mere fact of filiation did not immunize Hagen’s property from search in the face of probable cause to believe that it was being put to illicit use.
The most important evidence was the envelope labeled “receipts 98 Applegate.” The receipts in the envelope reflected the purchase of a number of items that could be used in growing or drying marijuana indoors. This evidence would, of course, mean little for Fourth Amendment purposes standing alone. However, as the investigators had confirmed in the search of Mowetza Drive that Huggins and Taylor were engaged in growing marijuana indoors, the presence of an envelope full of receipts with a label indicating that they might be growing marijuana elsewhere takes on a different cast. Additionally, the search had turned up some dried marijuana at the Mowetza Drive property, but no facilities for drying the marijuana, which further supported the conclusion that Huggins and Taylor might be maintaining other sites for cultivation, drying, or both.
In light of the discovery of the envelope and the dried marijuana, the documents detailing Taylor’s involvement in making mortgage payments and paying for water testing on the North Applegate Road property also bolster the finding of probable cause. Absent any other evidence, they might plausibly have been chalked up to a mother’s efforts to assist her son financially;16 however, in conjunction with the knowledge that the mother was engaged in growing marijuana, they established that she had some personal involvement in another nearby property where she might be engaging in similar activity. (They also lent some specificity to the *1051notation “Applegate” on the envelope.) Further, before obtaining the warrant to search Hagen’s property, the investigating officers investigated the property and verified that it was in fact entirely compatible with the existence of marijuana cultivation or drying operations, as it contained a 1500-square-foot metal out-building.
Further, we cannot discount the second informant’s tip. Although the affidavit presented no evidence in support of the source’s credibility,17 the informant purported to have firsthand knowledge of illegal activity, and the evidence recovered at 199 Mowetza Drive directly supported that allegation. See United States v. Angulo-Lopez, 791 F.2d 1394, 1397 (9th Cir.1986) (“A citizen informant’s veracity may be established by the absence of an apparent motive to falsify and independent police corroboration of the details provided by the informant.”).
We conclude that the envelope of receipts, the mortgage and water testing payments by Taylor, and the informant’s tip are, in combination with Huggins and Taylor’s confirmed involvement in marijuana cultivation, enough to support the judge’s finding of probable cause.18
B
The propriety of the Highway 238 search turned almost entirely on the evidence that Huggins and Taylor were the lessees of that property. Even before either of the Mowetza Drive searches took place, there was evidence to believe that Huggins had been involved in marijuana cultivation; the uncertainty was over whether he was still so engaged and, if so, where. The search of the Mowetza Drive property that Huggins and Taylor jointly occupied revealed that Huggins was definitely involved in marijuana cultivation and that Taylor was similarly involved. The discovery of dried marijuana but no drying equipment at Mowetza Drive also suggested that Huggins and Taylor might have more than one base of operations. We think that the revelation that the pair had, within the previous two months, rented another nearby property afforded a reasonable basis to suspect that they had expanded their drug operations to the second property.19 See, e.g., Angulo-Lopez, 791 F.2d at 1399; United States v. Poland, 659 F.2d 884, 897 (9th Cir.1981) (per curiam) (upholding a search of premises under suspects’ control, including “warehouse space leased by them,” based on “normal inferences about where criminals would be likely to hide property ..., taking into account the type of crime, the nature of the items, and the opportunity for concealment”).
*1052Because these facts sufficed to justify the warrant, the affidavit’s other aver-ments about the Highway 238 property are largely immaterial. Thus, we need not consider whether, as Huggins argues, the affidavit presented information about the jump in electricity usage once the service was put in Huggins’s name without also providing adequate comparative data by which to evaluate that information. Whether or not the alleged spike in power consumption can itself bear any weight in the probable cause analysis, it does not detract from the conclusion to which the other evidence leads us.
V
For the foregoing reasons, we conclude that the district court properly denied the motions to suppress the evidence from all four searches. Because the reasonableness of the searches was the only issue that the defendants’ conditional guilty pleas reserved, we affirm all four convictions.
AFFIRMED.
. The government later inadvertently revealed the tipster’s identity when it turned over an inadequately redacted document. The defendants subsequently obtained the details of the *1042informant's incarceration and plea agreement.
. "Thermal imagers detect infrared radiation, which virtually all objects emit but which is not visible to the naked eye. The imager converts radiation into images based on relative warmth — black is cool, white is hot, shades of gray connote relative differences; in that respect, it operates somewhat like a video camera showing heat images.” Kyllo v. United States, 533 U.S. 27, 121 S.Ct. 2038, 2041, 150 L.Ed.2d 94(2001).
. Vicki Jensen’s daughter, Selicia Sol Jensen, was found with her mother at the Highway 238 property and was also indicted, but the government later voluntarily dismissed the charges.
. Facial invalidity most commonly refers to a warrant's unconstitutional overbreadth. United States v. Towne, 997 F.2d 537, 549 (9th Cir.1993) (holding that a warrant is "so facially deficient that it precludes reasonable reliance" if it " 'fails to offer sufficiently detailed instruction’ " to the officers charged with executing it " 'and instead leaves them guessing as to their task' ” (quoting Ortiz v. Van Auken, 887 F.2d 1366, 1370 (9th Cir.1989))); see also United States V. Leon, 468 U.S. 897, 923, 104 S.Ct. 3430, 82 L.Ed.2d 677 (1984). In this case, the warrant's facial validity is not seriously in question, as the warrant "particularly describ[ed] the place to be searched, and the ... things to be seized.” U.S. Const, amend. IV. It identified the Mow-etza Drive property with specificity, and it contained none of the "catchall phrase[s]” that, we have held, render warrants facially overbroad. United States v. Clark, 31 F.3d 831, 836 (9th Cir.1994) (citing cases).
. So long as thermal imagers are "not in general public use,” employing those devices to read the heat emissions from a property in which the target has a reasonable expectation of privacy will constitute a search within the meaning of the Fourth Amendment. Kyllo, 121 S.Ct. at 2043. And "[a] search is a search,” Arizona v. Hicks, 480 U.S. 321, 325, 107 S.Ct. 1149, 94 L.Ed.2d 347 (1987), meaning that whenever an intrusion upon a legitimate, undiminished privacy interest — such as "the Fourth Amendment sanctity of the home,” Kyllo, 121 S.Ct. at 2045 — is substantial enough to trigger the probable cause requirement, the substance of that requirement generally does not wax and wane with the degree of intrusiveness beyond the threshold level necessary to deem it a search. “The Fourth Amendment's protection of the home has never been tied to measurement of the quality or quantity of information obtained.” Id. To be sure, we recognize that probable cause is a protean concept fundamentally dependent on all the individual facts of each case. See, e.g., Illinois v. Gates, 462 U.S. 213, 238, 103 S.Ct. 2317, 76 L.Ed.2d 527 (1983). We note only that under otherwise identical circumstances, the quantum of probable cause necessary to justify a thermal imaging search does not differ from that necessary to justify a physical search.
. Evidence demonstrating that the affidavit had failed to state, for example, that the neighboring houses were much smaller than Taylor's might well have made out a material omission that would preclude reliance on the good faith exception. See Leon, 468 U.S. at 922, 104 S.Ct. 3430 (citing Franks). The defendants have made no such factual showing with respect to the electricity usage comparisons. (We address their other Franks claims in more detail below.)
. "The government need not include all of the information in its possession to obtain a search warrant.... The omission of facts rises to the level of misrepresentation onty if the omitted facts ‘cast doubt on the existence of probable cause.' ” United States v. Johns, 948 F.2d 599, 606-07 (9th Cir.1991) (quoting United States v. Dennis, 625 F.2d 782, 791 (8th Cir.1980)).
. The district court stated that "the record [was] uncontradicted'' that Wright had no knowledge of the plea bargain.
. To be sure, Taylor could conceivably live quite well without paying income tax — for example, if her entire income were from gifts, bequests, and tax-free interest, see I.R.C. §§ 102(a), 103(a) (1994), or if she subsisted on existing savings (albeit savings that generated no taxable interest). And the difference between the $135,000 she realized on the sale of her previous home and the $170,000 down payment on 199 Mowetza was not jaw-dropping. However, in 1997, she reported an adjusted gross income of about $12,100, and her mortgage interest payments alone totaled $11,445. The presence of significant assets together with the absence of apparent means of support may at least plausibly be included in the probable cause determination. See, e.g., United States v. Robinson, 62 F.3d 1325, 1331 (11th Cir.1995).
. The government urges that Taylor's past arrest for marijuana trafficking be considered as additional evidence in support of this conclusion. It is true that some of our cases indicate that relevant previous arrests may be considered in a probable cause analysis even if no conviction ensued. See United States v. U.S. Currency, $83,310.78, 851 F.2d 1231, 1236 (9th Cir.1988) (considering a 1973 conviction, a 1983 conviction, and a 1984 arrest); see also Greenstreet v. County of San Bernardino, 41 F.3d 1306, 1309 (9th Cir.1994) ("[T]he use of prior arrests and convictions can be helpful in establishing probable cause, especially where the previous arrest or conviction involves a crime of the same general nature as the one the warrant is seeking to uncover ....” (emphasis added)). At least three other circuits have held as much. United States v. *1048Jakobetz, 955 F.2d 786, 803 (2d Cir.1992) ("[T]he magistrate surely appreciated the difference between arrest and conviction. Moreover, the fact that, in determining probable cause, a judicial officer may take into account a prior similar arrest is not error.''); accord United States v. McSween, 53 F.3d 684, 686 (5th Cir.1995); United States v. Thomas, 913 F.2d 1111, 1116 (4th Cir.1990). Nonetheless, because there is adequate support for the probable cause finding without the fact of the prior arrest, and because in any event the age of that datum reduces its reliability, we do not consider it in our analysis.
.E.g., Robinson, 62 F.3d at 1331 (finding probable cause based on infrared imaging results, the homeowner's purchase of thirty high-pressure sodium lights, his comparatively high electricity consumption, and the apparently expensive house he owned despite having filed no state income tax returns); United States v. Ishmael, 48 F.3d 850, 857 (5th Cir.1995) (finding probable cause based on high electricity consumption, a continuously running exhaust fan, phone calls to horticulture shops, and, "perhaps most importantly,” thermal imaging results); United States v. Robertson, 39 F.3d 891, 893-94 (8th Cir.1994) (finding probable cause based on infrared imaging results, foil-covered windows, and a credible anonymous tip allegedly based on the tipster's personal knowledge); State v. Siegel, 679 So.2d 1201, 1205 (Fla.Dist.Ct.App.1996) (finding probable cause based on thermal imaging results, comparatively high electricity consumption, two arrests for drug manufacturing many years before, and an informant’s tip that was "short on detail but ... substantially corroborated”); LaFollette v. Commonwealth, 915 S.W.2d 747, 750 (Ky.1996) (finding probable cause based on infrared imaging results buttressed by an anonymous tip and stating that the thermal imaging results alone would have been sufficient to support probable cause); Garrettson v. State, 114 Nev. 1064, 967 P.2d 428, 431-32 (1998) (finding probable cause based on thermal imaging results, "high power bills,” and an anonymous tip); State v. Norris, 47 S.W.3d 457, 469-70 (Tenn.Crim.App.2000) (finding no probable cause where the affidavit offered only "conclusoiy statements” about the results of a thermal imaging scan and analysis of electricity records, plus evidence that the defendants' windows were painted black and that they were arrested for growing marijuana six months before); see also United States v. Pinson, 24 F.3d 1056, 1057-59 (8th Cir.1994) (upholding a search based on infrared imaging results, comparatively high electricity consumption, and the receipt of packages from a manufacturer of hydroponic growing equipment); United States v. Zimmer, 14 F.3d 286, 288 (6th Cir.1994) (stating, in dicta, that thermal imaging results, comparatively high electric bills, and the smell of marijuana on a prior visit by a police officer "were enough to establish probable cause”).
. E.g., Ishmael, 48 F.3d at 857; Robertson, 39 F.3d at 894; Siegel, 679 So.2d at 1204; Garrettson, 967 P.2d at 431.
. Analogously, in Clark, although we deemed it insufficient to sustain the finding of probable cause, we noted with approval the search warrant affidavit's attempt to "negate one innocent use[of large amounts of electricity]— heating — by noting the alternative sources of heat at the residence.” Clark, 31 F.3d at 835.
. For example, the government suggested on cross-examination (but did not affirmatively demonstrate, see Fed.R.Evid. 608(b)) that Ghi-gliotty might have exaggerated his experience with infrared equipment in his declaration.
. In light o£ this conclusion, we need not decide whether Hagen or Jensen has standing to challenge the admissibility of that evidence, or whether the government waived that issue by failing to raise it in the district court. (Standing to challenge a search or seizure is a matter of substantive Fourth Amendment law rather than of Article III jurisdiction, Rakas v. Illinois, 439 U.S. 128, 139-40, 99 S.Ct. 421, 58 L.Ed.2d 387 (1978), meaning that the government can waive the standing defense by not asserting it, United States v. Taketa, 923 F.2d 665, 670 (9th Cir.1991), and that we may assume standing when denying an unreasonable-search claim on the merits.)
. Of course, in light of the financial information recited in the second search warrant application, this assistance would necessarily have to have come from savings or nontaxable income.
. According to the affidavit, the source had turned over a marijuana leaf ostensibly from Hagen’s operation, but there is no indication that the leaf itself gave any clue as to its provenance.
. We might be more skeptical if instead of presenting the aforementioned evidence, the government had relied only on six mother-son phone calls over a six-week period, or on the contractor's bare assertion that "Whip's parents” had been visiting Hagen's property with "unusual” frequency (with nothing to establish what was "usual”). However, those facts certainly do not detract from the government’s other evidence, and their inclusion in the affidavit does not undermine the existence of probable cause based on the other information.
.That the Highway 238 property turned out to be occupied by Taylor’s sister and niece does not affect the affidavit's facial sufficiency. See sources cited supra note 7. Although demonstrating that the affiant knew that Huggins and Taylor did not occupy the property and intentionally or recklessly omitted that fact from the affidavit might make out a valid Franks claim, the defendants do not press such an argument on appeal, and we accordingly do not consider it.