Atmospheric modulation transfer function in the infrared

Atmospheric modulation transfer function in theinfraredKobi Buskila,Shay Towito,Elad Shmuel,Ran Levi,Natan Kopeika,Keith Krapels,Ronald G.Driggers,Richard H.Vollmerhausen,and Carl E.HalfordIn high-resolution ultranarrowfield-of-view thermal imagers,image quality over relatively long pathlengths is typically limited by atmospheric degradation,especially atmospheric blur.We report ourresults and analyses of infrared images from two sites,Fort A.P.Hill and Aberdeen Proving Ground.The images are influenced by the various atmospheric phenomena:scattering,absorption,and turbu-lence.A series of experiments with high-resolution equipment in both the3–5-and8–13-␮m regions atthe two locations indicate that,as in the visible,image quality is limited much more by atmosphere thanby the instrumentation for ranges even of the order of only a few kilometers.For paths close to theground,turbulence is more dominant,whereas for paths involving higher average elevation,aerosolmodulation transfer function͑MTF͒is dominant.As wavelength increases,turbulence MTF also in-creases,thus permitting aerosol MTF to become more dominant.A critical role in aerosol MTF in thethermal infrared is attributed to absorption,which noticeably decreases atmospheric transmission muchmore than in the visible,thereby reducing high-spatial-frequency aerosol MTF.These measurementsindicate that atmospheric MTF should be a basic component in imaging system design and analysis evenin the infrared,especially as higher-resolution hardware becomes available.©2004Optical Society ofAmericaOCIS codes:110.3080,110.4100,010.1290,010.1330,010.1110,290.1310.1.IntroductionIn this paper we describefield experiments in which images of infrared test targets were collected to in-vestigate atmospheric modulation transfer function ͑MTF͒in the IR.Thefield experiments were held inAugust2000at two sites:Fort A.P.Hill͑APHill͒in Virginia and Aberdeen Proving Ground͑APG͒in Maryland.Both sites are near Washington,D.C. Whereas at the APG site the surface is planar and the path elevation was close to the surface,at site APHill the surface was irregular with hills and valleys.A preliminary paper on the APG experiments was published recently.1Here we present more detailed analysis and measurements at both locations.Thetargets used in this research were4ftϫ4ft͑1.3mϫ1.3m͒aluminum panels of0.25-in.͑0.64-cm͒thick-ness.The panels were set in stands4ft above theground.Panels were either bare polished metal orwere painted with high-emissivityflat black paint.The panels were set out in the following order:twobare aluminum panels,two black panels,and twobare aluminum panels.The target panels were ar-ranged this way so that multiple edges were availablein thefield of view that could be used to determineMTFs at different spatial locations.The measuringsensors were in the IR range.In the mid-IR window ͑3–5␮m͒the sensor is a Merlin midwave-IR͑MWIR͒system manufactured by Indigo.The sensor was a320ϫ256staring array cryocooled camera.This isa staring array with a maximum integration time of16.7ms.Thefield of view was0.36by0.27deg.Inthe far-IR window͑8–12␮m͒the sensor was an In-frametrics760radiometer with30ϫoptics.Heretoo,thefield of view was similarly ultranarrow.However,this is a scanning-type system with an in-tegration time per detector of the order of a microsec-ond.Additional details can be found in Ref.1.Inboth cases hardware MTFs including optics extendout beyond15cycles͞mradϪ1.The long-distanceK.Buskila,S.Towito,E.Shmuel,R.Levi,and N.Kopeika͑kopeika@ee.bgu.ac.il͒are with the Department of Electrical andComputer Engineering,Ben-Gurion University of the Negev,Beer-Sheva84105,Israel.K.Krapels,R.G.Driggers,and R.H.Vollmerhausen are with the U.S.Army Night Vision and Elec-tronic Sensors Directorate,Fort Belvoir,Virginia22060-5806.C.E.Halford is with the University of Memphis,Memphis,Ten-nessee38152.Received4April2003;revised manuscript received2September2003;accepted26September2003.0003-6935͞04͞020471-12$15.00͞0©2004Optical Society of America10January2004͞Vol.43,No.2͞APPLIED OPTICS471horizontal imaging͑3.6km at APG and4.2km at APHill͒of the passive target panels was sampled in 12bits,256frames each time.A Fourier analysis of the received images from those distances was per-formed to determine the overall system MTF,which includes both the camera and the atmosphere.As described in Ref.1,because of the low signal-to-noise ratio,a Gaussianfit was used.In addition,a Fou-rier analysis was made on imaging received from nearby target boards at a distance of130m.The MTF,as a result of that image,was considered the camera’s MTF without the influence of the atmo-sphere.The overall system MTF͑long-range mea-surement͒was divided by the camera’s MTF͑short-range measurement͒to obtain the MTF of the atmosphere.Analyses of long-distance images were made with regard to time and space.The model for turbulence MTF,which we used forthe implementation of this experiment,is summa-rized by Kopeika2and derived previously by Good-man.3The turbulence strength is characterized by the refractive-index strength coefficient C n2.The transfer function that is attributed to the turbulence is implemented as either a long-term exposure model or a short-term exposure.Short-term exposure is defined as a time short enough to stop temporal changes͑less than several milliseconds typically͒. The long-term exposure MTF is described by2,3 MTF LEϭexp͑Ϫ57.4a␰5͞3C n2␭Ϫ1͞3R͒,(1) where a is the waveform constant,3͞8for a spherical wave and1for a plane wave;␰is the spatial fre-quency in cycles per radian;C n2is the index of re-fraction structure parameter in metersϪ2͞3;␭is the wavelength in meters;and R is the distance from the target in meters.For a short-term exposure the MTF is2,3MTF SEϭexp͕Ϫ57.4a␰5͞3C n2␭Ϫ1͞3R͓1Ϫ␮͑␰␭͞D͒1͞3͔͖,(2) where D is the diameter of the optics in meters and␮is0.5for a farfield and1for the nearfiing these models we calculated turbulence MTF based on C n2.As described in Ref.1,the values of C n2were mea-sured by two independent techniques:angle of ar-rivalfluctuations2and scintillations.2There was good agreement between C n2measurements with both techniques.To avoid saturation,the scintil-lometer measurements were over only a1-km path of the propagation path,near the sensor.As discussed in Ref.1,a short-term exposure ver-sion of turbulence MTF is used.The MWIR system maximum detector integration time of16.7ms is much closer to the short-term than the long-term exposure criterion.The far-IR͓long-wave infrared ͑LWIR͔͒system integration time per detector of the order of a microsecond clearly justifies our using Eq.͑2͒to calculate turbulence MTF.For the mid-IR,the short-term exposure justification is somewhat less clear.However,if we consider the actual MTF cal-culation,the difference between short-and long-term exposure turbulence MTFs is not that great,as can be seen in Figs.1and2.Hence,because the exposure time for the staring array mid-IR system is much closer to the short-exposure than long-exposure cri-terion,the error in this approximation is limited. For the far IR,there is no such error.Previous investigations of atmospheric MTF in the IR2,4,5included aerosol size distribution measure-ments and involved equipment with approximately 1͞10the resolution in a dry climate with high aerosol concentration,with the imager at the top of a30-m-high building.The present experiments involve much higher-resolution equipment in a humid cli-mate with the receiver approximately1.5m above the ground.Hence,the present experiments including those in Ref.1are much more appropriate to detect effects of optical turbulence in the thermal IR. Motivation for this research is the need for a de-tailed image system analysis to improve system de-sign.Often identification of the weakest MTF can permit image restoration to correct from such blur, including atmospheric blur.The results thatwe Fig.1.Short-and long-term exposure turbulence MTFs from measurements of Cn2at APG at noon for3600-m line of sight at a 4-␮m wavelength on22August2000at14:00.Fig.2.Short-and long-term exposure turbulence MTFs frommeasurements of Cn2at APG for a3600-m line of sight at a4-␮m wavelength on22August2000at19:00.472APPLIED OPTICS͞Vol.43,No.2͞10January2004provide here indicate that atmospheric blur is so dominant over relatively long path lengths that the hardware resolution is far from being realized.This has adverse effects on target acquisition.Charac-terization of such limiting atmospheric MTF and im-plementation in image restoration can noticeably improve target acquisition.22.ResultsA.Modulation Transfer Function of the Aerosols: Dependence on Wavelength and Time of DayIn this subsection we consider the influence of the aerosols on the atmospheric MTF.To determine the influence of aerosols wefind the overall͑long-range͒system MTF,divide it by the͑short-range͒camera’s MTF,and compare the resulting atmospheric MTF with turbulence MTF.If they are identical then the aerosol MTF is negligible.If they are not,the ratio between them is the aerosol MTF.The scintillation measurements of turbulence strength and the overallatmospheric MTF measurements from the edge re-sponse were simultaneous.As described above,there were two edges that dis-tinguished between high-and low-emissivity por-tions of the bar chart.Edge responses were measured from each.The gradient of each yielded a line-spread function,a Fourier transform of which yielded overall MTF.As described in Ref.1,C n2 values measured by angle-of-arrivalfluctuations from the left and right edges were sometimes differ-ent near midday.This was attributed to emitted heat from the dark panels,caused by crossing winds, that appeared in front of a light panel,thus causing changes in turbulence strength.Because we want to concentrate here on atmo-spheric MTF rather than on the emissivities of ma-terials used in a target,we use the scintillometer measurements of C n2rather than the angle-of-arrival fluctuation.As described above,edge response mea-surements from the long-range and short-range bar charts were used to obtain overall system MTF and camera MTFs for each measurement.Both the long-range and short-range bar charts were imaged simultaneously so that we could minimize any possi-ble vibration effects caused by winds.The overall atmospheric MTFs measured this way from both the right-and left-edge response functions were gener-ally quite similar.The case of greatest difference is shown in Figs.3and4.In other cases,as in Figs.5 and6,the atmospheric MTFs measured from both edge response functions are almost identical. Figures3–7represent MWIR measurements and Figs.8–10represent LWIR measurements at APG. From Figs.5–7for MWIR wavelengths during the day,we can see that the influence of the aerosols was not significant at APG.However,in Figs.3and4we can see the presence of a noticeable aerosol MTF at that time,causing a knee in the overall atmospheric MTF.This is characteristic of aerosol MTF.2This happened because clouds at that time caused a sud-den decrease in C n2.It is clear that in all cases atmospheric MTF cannot be neglected,especially closer to midday when turbulence is maximum.It is clear from Figs.3–10that,without good image res-toration2from atmospheric blur,the high resolution of the hardware͑15cycles͞mrad͒will not be realized. At APHill significant aerosol MTFs are also mea-sured in the LWIR,as can be seen in Figs.11–13. However,they were also observed in the MWIR wavelengths as can be seen in Figs.14–17.In all these cases atmospheric MTF is noticeably lower than turbulence MTF.In summary,at APG,aerosol MTF was negligible for most of the MWIR measurements͑except for Figs. 3and4͒whereas aerosol MTF was significant for all the LWIR measurements.At APHill,aerosol MTF was significant for all measurements in both the MWIR and the LWIR bands.Indeed,the shape of the overall atmospheric MTF is dominated by that of aerosol MTF,with a clearly defined knee in the MTF curve.2We attribute the difference in MWIRmea-Fig.3.MTF right edge at APG for MWIR on22August2000at11:58.Fig.4.MTF left edge at APG for MWIR on22August2000at 11:58.10January2004͞Vol.43,No.2͞APPLIED OPTICS473surements to the differences in topography at both locations.At APHill the higher average elevation gives rise to a reduction in C n 2and therefore to a rise in turbulence MTF,reducing its signi ficance and thereby allowing aerosol MTF to become more dom-inant,so much so that overall atmospheric MTF there is dominated by an aerosol MTF shape with a sharp knee at the aerosol MTF spatial-frequency cut-off.2At APG overall atmospheric MTF does not ex-hibit such a sharp knee for MWIR imaging.We attribute the dominance of aerosol MTF at LWIR wavelengths in both locations to the wave-length dependence of Eq.͑2͒,which causes turbu-lence MTF to be less signi ficant at longer wavelengths.B.Atmospheric Modulation Transfer FunctionIn this subsection we compare the atmospheric MTF from both experimented sites.Figure 18shows the MTFs of the images for all measurements.We can clearly distinguish the MTFs at APHill because theyare wider than those at APG despite the shorter path length at APG ͑3600m at APG,4235m at APHill ͒.The explanation is that the APG site is closer to the ground than the APHill site,which causes C n 2to increase and MTF to decrease ͑see Table 1͒.1.Spatial EffectsAnother comparison that can be performed between the areas is to look at the whole image rather than only at the target boards,as can be seen in Figs.19͑a ͒and 19͑b ͒.At site APG we can see the whole target board,but it is blurry with gradual edge spread func-tion transitions ͑and a correspondingly narrow MTF function ͒.At site APHill we can see interference on the right side of the target and a water puddle or a different element that blocks transitions from the ground to the atmosphere ͑in front of the target im-age ͒.The white target boards on the left side have vanished from the image because of equal energy emission of the surroundings.In spite of that,the right-edge transition is still sharp andimmediate.Fig.5.MTF left edge at APG for MWIR on 22August 2000at14:08.Fig.6.MTF right edge at APG for MWIR on 22August 2000at14:08.Fig.7.MTF left edge at APG for MWIR on 22August 200at16:04.Fig.8.MTF left edge at APG for LWIR on 22August 2000at 12:10.474APPLIED OPTICS ͞Vol.43,No.2͞10January 2004Fig.9.MTF left edge at APG for LWIR on22August2000at15:04.Fig.10.MTF right edge at APG for LWIR on22August2000at18:00.10January2004͞Vol.43,No.2͞APPLIED OPTICS475Fig.11.MTF atmospheric left edge at APHill for LWIR on16August2000at13:01.Fig.12.MTF atmospheric right edge at APHill for LWIR on16August2000at15:19. 476APPLIED OPTICS͞Vol.43,No.2͞10January2004Fig.13.MTF atmospheric right edge at APHill for LWIR on16August2000at17:53.Fig.14.MTF atmospheric left edge at APHill for MWIR on16August2000at12:49.10January2004͞Vol.43,No.2͞APPLIED OPTICS477Fig.15.MTF atmospheric right edge at APHill for MWIR on16August2000at12:49.Fig.16.MTF atmospheric right edge at APHill for MWIR on16August2000at14:31. 478APPLIED OPTICS͞Vol.43,No.2͞10January2004The conclusions for the overall system MTF of the image are also relevant to the atmospheric MTF be-cause the atmospheric MTF can be obtained when we divide the overall system MTF by the camera ’s MTF ͑that is constant ͒.In some of the images that we have analyzed,from both sides of the image we found a difference between the MTF of the right side compared with that of the left side.We can see this difference in the LWIR images in Figs.14and 15and 20and 21.The con-trast between the high-and low-emissivity boards is usually better on the right side than on the left,con-forming to the wider and higher MTFs for the rightedge on most graphs in which MTFs for both edges are displayed.Exceptions are Figs.3and 4for MWIR at APG.2.Temporal EffectsTemporal effects are also shown in Figs.20and 21.The worst images are those near midday when tur-bulence is strongest.C.ErrorsSources of error include the short-term exposure as-sumption for MWIR turbulence MTF that,as shown in Figs.1and 2,is usually small compared to the difference between turbulence and atmospheric MTFs for the MWIR measurements,and even more so for the LWIR measurements.This error is small because the time exposure for the MWIR equipment is much closer to that required for small exposure than for long exposure.For the LWIR equipment,the exposure is so short that there is no error intheFig.17.MTF atmospheric left edge at APHill for MWIR on 16August 2000at17:51.Fig.18.MTF comparison at APHill and APG for LWIR.Table 1.C n 2Data at APG on 22August 2000and APHill on16August 2000Time ͑h ͒APG ͑10Ϫ14͒APHill ͑10Ϫ14͒11:009 1.9713:0015 1.6514:0014 1.916:0011 2.618:00 4.4 1.2320:001.20.8610January 2004͞Vol.43,No.2͞APPLIED OPTICS 479short exposure modeled here,as described at the end of Section 1.Another source of error is the fact that the scintil-lometer measurements of C n 2were only over a por-tion of the line of sight ͑from a camera extending 1km toward the distant target ͒rather than the entire line of sight.However,it is the turbulence in the region closer to the camera that dominates the image plane turbulence.2Therefore differences between C n 2at distances longer than a kilometer and those mea-sured within a kilometer from the cameras have a relatively small effect on the value of C n 2affecting the images.Another source of error is the noise or uncertainty in measuring turbulence MTF,especially at high spa-tial frequencies where noise can become a problem.Examination of Table 2and Fig.10in Ref.1indicates that,at low values of the turbulence MTF at high spatial frequencies,such errors were limited to ap-proximately 20%,or approximately Ϯ10%of the tur-bulence MTF values plotted here.Another source of error is the validity of the as-sumption that turbulence and aerosol MTFs are in-dependent of one another.A statistical regression coef ficient model with which to predict the refractive-index structure coef ficient according to weather was carried out in Ref.6.Indeed,it was found that high aerosol loading of the atmosphere is associated with noticeably increased turbulence strength,attributed to increased atmospheric warming derived from ab-sorption of light by aerosols.This means that,strictly speaking,aerosol and turbulence phenomena are not completely independent of one another.However,it was found that this occurs infrequently and when it does,the statistical signi ficance is small,being of the order of 10–15%.This means that to a first approximation the multiplication of turbulence MTF by aerosol MTF to compose atmospheric MTF is reasonable.Accordingly,designating aerosol MTF as MTF A and overall atmospheric MTF by M A ,MTF SE MTF A ϭM A .(3)The errors in measuring overall atmospheric MTF are rather small,being based on direct measurement of the line-spread function rather than time-varying scintillations.Therefore differentiating Eq.͑3͒yields⌬MTF A ͞MTF A ϭϪ⌬MTF SE ͞MTF SE ,(4)where ⌬designates the errors.The minus sign in-dicates that if turbulence MTF is underestimated then aerosol MTF is overestimated,and vice versa.Because the turbulence MTF error magnitude is es-timated at Ϯ10%,then the same holds for the aerosol MTF error magnitude as well.The above errors are too small to change the conclusions here,described in Section3.Fig.19.͑a ͒Image from APG,LWIR on 22August 2000at 15:03.͑b ͒Image from APHill,LWIR on 16August 2000at14:12.Fig.20.Images from ͑a ͒APG on 22August 2000and ͑b ͒APHill on 16August 2000for LWIR for different hours of theday.Fig.21.͑a ͒APG for LWIR on 24August 2000at 09:05.͑b ͒APG for LWIR on 23August 2000at 12:07.͑c ͒APG for LWIR on 22August 2000at 19:04.͑d ͒APHill for LWIR on 22August 2000at 11:00.480APPLIED OPTICS ͞Vol.43,No.2͞10January 20043.Discussion and ConclusionsWith the advent of high-resolution IR equipment,these experiments indicate that,for ranges of the order of even a few kilometers,image resolution is dominated much more by the atmosphere than by the equipment,even in the thermal IR.Atmospheric MTF should therefore become a basic component in thermal imaging system design and analysis.Both wavelength and elevation have critical roles.In Fig.18we can see that the MTF graphs at APHill are wider than those at APG despite the longer distance at APHill ͑4235m as compared with 3600m ͒.The explanation is that the APG site is at a lower eleva-tion ͑1.5m ͒than the APHill site,which causes C n 2to increase and the MTF to narrow.Data for C n 2are presented in Table 1and Fig.22.The smaller values of C n 2at APHill give rise to more noticeable aerosol MTFs in both the MWIR and the LWIR spectral regions,whereas at APG aerosol MTF is noticeable primarily at LWIR and less so at MWIR.The reason for the latter is probably that,for the same value of C n 2,the wavelength dependence of turbulence MTF ͓Eqs.͑1͒and ͑2͔͒causes it to be higher at longer wavelengths,thus permitting a more noticeable role for aerosol blur at longer wavelengths.It is interest-ing to consider the clear signi ficance of aerosol MTF at both locations for LWIR radiation.Because of the long wavelengths,scattering is diminished in this wavelength region.However,aerosol MTF is also strongly dependent on absorption by aerosols and at-mospheric molecules,which are also particulates.2,7The idea is that image transmission through particu-lates involves both a sharp unscattered light image and a blurred scattered light image.By conservation of energy,interaction of a photon with a particulate can involve either scattering or absorption,but not both.Hence it is the clear unscattered image that is more likely to be attenuated by absorption rather than the blurred scattered image because the latter has been scattered.2,7Therefore it cannot be absorbed.This implies that aerosol MTF amplitude is decreasedso that its high-spatial-frequency asymptotic value is approximately equal to atmospheric transmission where atmospheric transmission is governed by both absorption and scattering,as derived in detail else-where.7In this way absorption degrades image qual-ity.In the LWIR region,there is signi ficant absorption especially by both H 2O and CO 2,so the aerosol MTF is affected strongly by absorption.The weather during these experiments in August in the Washington,D.C.area was rather humid at times.For example,at APG on 22August,the relative hu-midity until 8a.m.was close to 100%.It decreased to around 59%at 3p.m.,remained around there until approximately 6:30p.m.,rose to approximately 85%by 8p.m.,and then rose to approximately 95%by 3a.m.23August.Relative humidity began to decrease again to approximately 64%around noon 23August.Periods of high humidity tend to increase aerosol MTF more in the LWIR wavelength area because of the effects of atmospheric absorption on aerosol MTF,in addition to the increase in aerosol size generated by an increase in humidity because of adsorption and ab-sorption of moisture by the aerosols.Temperatures during the night of 22August were of the order of 16°–17°C,rising to 30°C around 3–4p.m.They decreased to around 21°C early in the morning of 23August,and then rose to around 31°C around mid-day.Higher temperatures tend to increase optical turbulence.2The weather data for APHill showed similar tendencies,only the numbers were slightly dif-ferent.The figures shown here are consistent with the weather,with turbulence MTFs being narrowest in the midafternoons when temperature was at a maxi-mum and aerosol MTFs being least prominent at that time ͑when humidity was at its lowest ͒.This is con-sistent with the measurements of thermal imaging turbulence MTF by Watkins et al .8It is assumed that atmospheric MTF is the product of turbulence and aerosol MTFs,and therefore aero-sol MTF is obtained when atmospheric MTF is di-vided by turbulence MTF.The difference in aerosol MTFs between the right and left edges stems from the assumption that aerosol and turbulence MTFs are independent of one another.However,this is not completely true.The refractive-index structure coef ficient C n 2generally increases with increased aerosol loading,which is attributed to slightly in-creased atmospheric absorption and heating by the aerosols.2,6As seen in Ref.1,cross winds cause dif-ferences in air temperature at the two edges,which causes differences in C n 2.However,temperature differences also affect aerosol concentrations 9be-cause of convection,as well as aerosol sizes because of temperature effects on evaporation of water vapor adsorbed to aerosols.9Hence it is not surprising to see different aerosol MTFs as well as turbulence 1MTFs sometimes at the right and left edges.How-ever,such differences are small.References1.K.Krapels,R.G.Driggers,R.H.Vollmerhausen,N.S.Kopeika,and C.E.Halford,“Atmospheric turbulence modulationtrans-Fig.22.C n 2comparison as a function of the time of day at APG and APHill.10January 2004͞Vol.43,No.2͞APPLIED OPTICS481fer function for infrared target acquisition modeling,”Opt.Eng.40,1906–1913͑2001͒.2.N.S.Kopeika,A System Engineering Approach to Imaging,Vol.38of the SPIE Press Monographs͑SPIE,Bellingham,Wash., 1998͒.3.J.W.Goodman,Statistical Optics͑Wiley,New York,1985͒.4.D.Sadot,G.Kitron,N.Kitron,and N.S.Kopeika,“Thermalimaging through the atmosphere:atmospheric MTF theory and 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