Surface Roughness Measurement Using Terahertz Waves

Transcription

1 Procdings of th 3rd Intrnational Confrnc on Industrial Application Enginring 015 Surfac Roughnss Masurmnt Using Trahrtz Wavs Ttsuo Fukuchi a,*, Norikazu Fus a, Maya Mizuno b, Kaori Fukunaga b a Cntral Rsarch Institut of Elctric Powr Industry -6-1 Nagasaka, Yokosuka-shi, Kanagawa , Japan b National Institut of Information and Communications Tchnology 4--1, Nukui-Kitamachi, Kogani-shi, Tokyo, Japan *Corrsponding Author: fukuchi@cripi.dnkn.or.jp Abstract Surfac roughnss masurmnt is frquntly usd in industrial applications, such as assssmnt of th quality of coatings and paint layrs, arly dtction of corrosion and coating dgradation, and charactrization of matrials. Trahrtz (THz) wavs, which ar lctromagntic wavs in th frquncy rang 100 GHz - 10 THz, can b usd for noncontact masurmnt of th surfac roughnss of mtal or dilctric matrials in th ordr of 10 m. This rang of surfac roughnss is too larg for optical snsors, but too small for microwav snsors. Th surfac roughnss is obtaind from th ffctiv rflctivity of th surfac, which is th ratio of th spctral intnsity of wavs rflctd from th spcimn and from a rfrnc mtal plat, whos rflctivity can b assumd to b 1. In this work, th rlation btwn th frquncy of THz wavs, surfac roughnss, and ffctiv rflctivity was valuatd by an analytical modl and by simulation, and invstigatd by xprimnts using sandpapr spcimns of varying surfac roughnss. A broadband THz systm using photoconductiv antnnas for th transmittr and rcivr was usd in th xprimnt. Rasonabl agrmnt was obtaind btwn th xprimntal rsults and simulation rsults. Th ffctiv rflctivity could b dscribd by a Gaussian function of th surfac roughnss. Th xprimntal rsults wr compard with masurmnt rsults using a contact surfac roughnss gaug, and wr in rasonabl agrmnt. Th rsults showd that THz wavs ar usful for surfac roughnss masurmnt. Kywords: surfac roughnss, surfac profil, trahrtz wav, rflctivity, alumina 1. Introduction Surfac roughnss is an important paramtr in manufacturing (mainly machining), and various approachs hav bn mad to prdict in th machining procss (1). In addition, in arly stags of corrosion of th substrat mtal undr a paint layr, small blistrs appar on th paintd surfac, so surfac roughnss can b usd as a paramtr to monitor th formation of rust undr th paint layr (). Convntional surfac roughnss snsors us a stylus to follow th surfac profil, but ar inconvnint to covr larg surfac aras bcaus of its contact natur, and ar difficult to apply to vrtical or downward-facing surfacs. Noncontact snsors using lctromagntic wavs can solv ths problms. Optical tchniqus such as intrfromtry, spckl, scattring, diffusnss ar usd to masur th surfac roughnss with a rsolution in th ordr of nm (3). Howvr, for surfacs with surfac roughnss in th ordr of 10 m, lctromagntic wavs with longr wavlngth ar mor suitd. Trahrtz (THz) wavs ar lctromagntic wavs in th frquncy rgion btwn optical wavs and radio wavs (100 GHz - 10 THz). Sinc a frquncy of 1 THz corrsponds to a wavlngth of 300 m, THz wavs ar snsitiv to surfac roughnss in th ordr of 10 m, and can b usd for noncontact masurmnt of th surfac roughnss (4,5). Rcnt progrss in THz dvics has nabld dvlopmnt of THz snsors which can b usd in an industrial nvironmnt. In addition, sinc THz wavs pntrat through paint matrials, thy can b usd to dtct corrosion undr paint layrs (6). Thrfor, surfac roughnss masurmnt of th mtal substrat, which is hiddn undr th paint layr, is DOI: /icia Th Institut of Industrial Applications Enginrs, Japan.

2 also a possibility. In this papr, th rlation btwn th ffctiv rflctivity of th masurd surfac and th surfac roughnss is stablishd basd on an analytical modl basd on th tim-of-flight mthod. Simulations ar prformd to vrify th calculations. Exprimntal masurmnt of abrasivs with diffrnt surfac roughnss is prformd, and th masurmnt rsults ar compard with thos using th convntional mthod (contact gaug)..1 Analytical Modl. Modl and Simulation Th modl for scattring from a rough surfac is shown in Fig. 1. Hr, z(x) is th surfac profil in th normal dirction. A plan THz wav with a uniform wavfront is incidnt in th z-dirction. Th rflctd wav consists of wavs rflctd from ach point x, for which th tim dlay rlativ to an arbitrary rfrnc tim is givn by z(x)/c. This tim dlay is simply th round-trip tim from th position corrsponding to th rfrnc tim to th actual surfac position. Th lctric fild of th rflctd wav x) from rang (x, x+dx) is givn by q.(1), which shows that th tim dlay rsults in a phas diffrnc dpndnt on th surfac profil. Hr, E 0 is th incidnt amplitud, is th angular frquncy, and r is th spcular rflction cofficint (th spcular rflctivity is r ). Th lctric fild of th rflctd wav, avragd ovr all positions x, is givn by q.(). x, re i[ tz( x) / c] 0 (1) it iz( x) / c re0 () If th surfac roughnss is zro, z(x)=z 0 =constant, so <>=re 0 xp[-it-z 0 /c)], which shows that th rflctd wav is a plan wav with a constant phas factor rlativ to th incidnt wav. If th surfac roughnss is not zro, thn th rflctd wav will b an nsmbl of a larg numbr of wavs with diffrnt phas factors. This rsults in intrfrnc btwn th wavs which rsults in th variation of th amplitud of. Th amplitud variation dpnds on th profil function z(x). If th spot siz of th incidnt wav is much largr than th latral dimnsion of th surfac profil (charactristic lngth of surfac profil variation), thn th numbr of positions which ar avragd in q.() is vry larg. In this cas, th surfac profil z(x) can b assumd to follow a normal distribution, with man z and varianc z. In fact, th rms (root-man-squar) valu of th surfac profil is frquntly usd to dfin th surfac roughnss. In calculating th nsmbl avrag of th phas factors in q.(), th momnt function, which is a standard mthod in statistics (7), is usd. For a randomly distributd variabl X, th momnt gnrating function is dfind as q.(3), whr < > dnots th xpctation valu. If X follows a normal distribution with man and varianc, th momnt gnrating function is givn by q.(4). M X For =1, on obtains X ( ) (3) 1 M X ( ) (4) 1 X (5) Substituting X=iz/c into q.(5), th nsmbl avrag is givn by q.(6), and bcoms q.(7). iz( x) / c iz / c z / c (6) i( tz / c) z / c 0 re (7) Th ffctiv rflctivity R is givn by th ratio of intnsitis of th rflctd and incidnt wavs, so that R (8) E 0 Fig. 1 Modl for rflction from a rough surfac S 4 z / c R R (9) whr R S =r is th spcular rflctivity (th rflctivity of a surfac with zro roughnss). In trms of th frquncy f, q.(9) bcoms 95

3 4f z R RS xp (10) c Thrfor, th modl basd on th tim-of-flight diffrnc for ach point in th x-dirction rsults in an ffctiv rflctivity which is a Gaussian function of th standard dviation z of th surfac profil, which can b tratd as th surfac roughnss. Th rsult q.(10) can b undrstood from th concpt of impuls rspons. For a surfac profil which follows a Gaussian distribution in th normal dirction, th impuls rspons (rflction of an xtrmly short puls) also follows a Gaussian distribution in th tmporal rgim. Sinc any function can b xprssd as a summation of impulss, th total rspons will b a suprposition of impuls rsponss, ach following a Gaussian distribution. Sinc th tmporal variation of th rflction is dirctly proportional to th variation in th surfac profil, with a proportionality factor of /c, th spatial varianc z of th surfac profil will rsult in a tmporal varianc T =4 z /c in th rflction. For an incidnt wav of frquncy f, th corrsponding nondimnsional quantity will b T =(4f z /c), which appars in th argumnt of th xponntial function in q.(10).. Simulation Using Continuous Wav Simulations basd on th modl shown in Fig. 1 wr prformd. Th incidnt wav is assumd to b a continuous wav with constant frquncy f as in q.(11). Normal incidnc is assumd. E ( i ift E0 (11) A surfac profil z(x) was constructd, for a total of 1000 points in th x-dirction. Th variabl z was normally distributd with an avrag valu of 0 and a standard dviation of. Th lctric fild x, for ach point was calculatd using q.(1), and numrically avragd ovr all points (without using th analysis in q.(3)-(10)). Th rsult was substitutd into q.(8) to yild th ffctiv rflctivity. R S was st to 1 for simplicity. Th procss was rpatd for diffrnt valus of f and, to obtain th dpndnc of R on th frquncy and surfac roughnss. An xampl of th simulation rsult of, for th cass of f=1 THz and =0, 0, 40 m is shown in Fig.. Th calculatd rsults of R for f=0.5, 1.0, 1.5,.0 THz for th rang =0-50 m ar shown in Fig. 3 as solid lins. Th rsults wr in agrmnt with th dpndnc givn by q.(10), shown as brokn lins. Fig. Simulation rsult for continuous wav Fig. 3 Effctiv rflctivity for continuous wav obtaind from simulation (solid lins) and from analytical modl (brokn lins).3 Simulation Using Broadband Wav Th simulation was also prformd for a broadband wav gnratd by a photoconductiv antnna. An xprimntally masurd signal (rflction from a mtal plat, using th THz masurmnt dvic dscribd in 3.1) was usd as th incidnt wav. Th charactristics of th broadband wav ar shown in Fig. 4. Th rflctd wavform was calculatd in th sam mannr as for th continuous wav. In ordr to compar th rsults with th cas of th continuous wav, rflctd wavforms wr rconstructd aftr applying squar frquncy filtrs cntrd at 0.5, 1.0, 1.5,.0 THz with widths of 0. THz. Th simulation rsult of R is shown as solid lins in Fig. 5. Th brokn lins show th dpndnc basd on q.(10). Sinc th solid and brokn lins ar in agrmnt, th rsults showd that th width 0. THz of th frquncy filtr was sufficintly narrow so that th rconstructd wavform could b approximatd by a continuous wav of th corrsponding cntr frquncy. 96

4 Fig. 4 Tmporal and frquncy charactristics of broadband wav gnratd by a photoconductiv antnna As shown in Fig. 5, th rlation btwn th ffctiv rflctivity and th surfac roughnss dpnds on th cntr frquncy of th frquncy filtr applid to th broadband wav. Thrfor, in ordr to obtain good snsitivity on th surfac roughnss, th cntr frquncy should b chosn so that th ffctiv rflctivity variation is larg in th rgion of surfac roughnss in qustion. A masur of th snsitivity is th frquncy at which th ffctiv rflctivity dcrass to 0.5, which is givn by q.(1). ln c c f1/ (1) 4 z z Th rlation btwn f 1/ and th surfac roughnss is shown in Fig. 6. For xampl, for z =0 m, th corrsponding valu is f 1/ =1.0 THz. Thrfor, in ordr to masur surfac roughnss around 0 m, a frquncy filtr cntrd at 1 THz will b appropriat. 3. Exprimnt 3.1 Procdur Fig. 5 Simulation rsult for broadband wav (solid lins) and dpndnc xpctd from th analytical modl (brokn lins) Fig. 6 Dpndnc of f 1/, th frquncy corrsponding to ffctiv rflctivity 0.5, on th surfac roughnss z (th dashd lin indicats that f 1/ =1.0 THz for z =0 m) Exprimnts wr carrid out to masur th surfac roughnss of sandpapr spcimns. Th abrasiv usd in th sandpapr consists of alumina particls. A THz masurmnt dvic (Picomtrix, T-Ray 4000), which uss photoconductiv antnnas for th transmittr and rcivr, was usd to obtain tmporal wavforms of THz wavs rflctd from sandpapr and Al tap surfacs, th lattr usd as a rfrnc in calculating th ffctiv rflctivity. Th THz wav pulss mittd from th transmittr had a typical tim width of 1 ps, and th usabl frquncy rang was THz. Th THz wav pulss wr focusd onto th surfac by a polythyln lns of focal lngth 5 mm, and th rsultant spot siz was about 0.6 mm. A schmatic diagram of th masurmnt is shown in Fig. 7. Sinc th surfac roughnss in qustion is in th ordr of 10 m, th charactristic lngth of th surfac profil in th latral (in-plan) dirction is in th sam ordr. This is much smallr than th spot siz, so a larg numbr (in th ordr of ) of local maxima and minima in th surfac profil ar covrd. Thrfor, it is saf to assum that th surfac profil within th spot follows a normal distribution. In this cas, th rms surfac roughnss is th standard dviation of th surfac profil variation. Th rfractiv indx of alumina in th THz rgion is n=3.0 (8). Thrfor, th spcular rflctivity for normal incidnc is R S =[(1-n)/(1+n)] =

5 Fig. 7 Schmatic diagram of THz wav masurmnt 3. Masurmnt Rsults Tmporal wavforms y( of THz wavs rflctd from th sandpapr spcimns ar shown in Fig. 8(a). Th wavform of rflction from Al tap y a ( is also shown. Th frquncy charactristics ar shown in Fig. 8(b). In obtaining th ffctiv rflctivity R, a squar frquncy filtr with cntr frquncy f=1.0 THz and width 0. THz was applid to y( and y a (, to obtain th filtrd wavforms y F ( and y af (. R was thn calculatd from q.(13), which is th ratio of th maxima of th rflctd intnsitis from th sandpapr spcimns and Al tap. maxyf ( R (13) maxyaf ( An xampl of th filtrd wavforms is shown in Fig. 9, for sandpapr spcimn #40 and Al tap. Th amplitud ratio was max[y F (]/max[y af (]=0.37, and th intnsity ratio was R=0.13. Th surfac roughnss was obtaind by substituting this valu into q.(10). Fig. 9 Exampl of filtrd wavforms (squar filtr, cntr frquncy 1.0 THz, width 0. THz) Fig. 10 Dtrmination of th surfac roughnss (solid curv: analytical modl, brokn lins: masurd rsults) Th rlation in q.(10) for R S =0.5 and f=1.0 THz is plottd as a solid curv in Fig. 10. Th brokn lins show th obtaind valus of R for ach spcimn. Th surfac roughnss of ach spcimn, which is th surfac roughnss corrsponding to th intrsctions of th solid curv and th dottd lins, is summarizd in Tabl 1. Th rrors indicat th standard dviation for 3 masurmnts. In viw of q.(1), f 1/ =1.0 THz corrsponds to z =0 m, so th rlativ accuracy of th valus for #40, #180, and #150 is xpctd to b highr. Fig. 8 (a) Tmporal wavforms and (b) frquncy charactristics of THz wavs rflctd from sandpapr spcimns and Al tap Tabl 1 Masurmnt rsult of surfac roughnss spcimn R z [m] # ± ±5 # ± ±5 # ±0.04 4±4 # ± ±3 # ± ±4 98

6 Dvlopmnt of mthods to liminat th ffct of th paint layr, optimization of frquncy filtring of th broadband wav, wavform analysis mthods ar of furthr study. Applications such as surfac roughnss masurmnt of plasma-sprayd coatings can b xpctd in th nar futur. Rfrncs Fig. 11 Comparison of surfac roughnss masurmnt rsult using THz wavs and using roughnss gaug 3.3 Vrification Th rms surfac roughnss of th sandpapr spcimns was masurd using a contact surfac roughnss gaug (Mitsutoyo, Surftst SJ-01). Th masurmnt was prformd for 3 positions on ach spcimn. Comparison of th THz wav and surfac roughnss gaug masurmnt rsults is shown in Fig. 11. Rasonabl agrmnt (within th rang of masurmnt rror) was obtaind for spcimns #40, #180, and #150. For spcimns #100 and #60, th valus obtaind by THz masurmnt wr significantly largr than thos obtaind by th roughnss gaug. A possibl caus of this discrpancy is th fact that th cntr frquncy of th frquncy filtr (1 THz) did not match f 1/, which is 0.5 THz for z =40 m. Th surfac roughnss valus obtaind by THz wavs wr consistntly highr than thos masurd by th surfac roughnss gaug, suggsting th prsnc of a systmatic rror. A possibl caus is th ffct of th paint layr which coats th abrasiv. In Fig. 8(b), dips in th frquncy spctra ar sn, which rsult from th étalon ffct of th thin paint layr. Ths may hav rsultd in lowr ffctiv rflctivity and highr surfac roughnss valus. 4. Conclusion Surfac roughnss masurmnt using THz wavs was invstigatd. An analytical modl using th tim-of-flight mthod and simulation showd that th ffctiv rflctivity of th surfac followd a Gaussian function of th surfac roughnss. Th surfac roughnss of sandpapr spcimns masurd by a THz masurmnt dvic wr in rasonabl agrmnt with th rms surfac roughnss masurd by a contact roughnss gaug, for surfac roughnss 15-5 m. (1) P. Bnardos and G. Vosniakos: "Prdicting surfac roughnss in machining: a rviw", Intrnational Journal of Machin Tools & Manufactur, Vol. 43, pp , 003 () P. Schwitzr: "Paint and coatings: applications and corrosion rsistanc", Taylor & Francis, Boca Raton, 006 (3) T. Vorburgr and E. Tagu: "Optical tchniqus for on-lin masurmnt of surfac topography", Prcision Enginring, Vol. 3, pp , 1981 (4) R. Anastasi and E. Madaras: "Trahrtz NDE for mtallic surfac roughnss valuation", Th 4th Intrnational Workshop on Ultrasonic and Advancd Mthods for Nondstructiv Tsting and Matrial Charactrization, Jun 19, 006, U. Mass. Dartmouth, N. Dartmouth, MA, procdings publishd in pp. 57-6, 006 (5) M. Hrmann, C. Wigand, J. Jonuschit and R. Bigang: "Th influnc of surfac roughnss on THz rflction masurmnts", Th 34th Intrnational Confrnc on Infrard, Millimtr, and Trahrtz Wavs (IRMMW-THz 009), Spt. 1-5, 009, Busan, Kora, 009 (6) R. Anastasi and E. Madaras: "Trahrtz NDE for undr paint corrosion dtction and valuation", Rviw of Progrss in Quantitativ Nondstructiv Evaluation, Vol. 5, AIP Confrnc Procdings, Vol. 80, pp , Amrican Institut of Physics, Nw York, 006 (7) M. Ahsanullah, B. Golam Kibria, M. Shakil: "Normal and Studnt's t distributions and thir applications", pp. 7-50, Atlantis Prss, Amstrdam, 014 (8) K. Rajab, M. Naftaly, E. Linfild, J.Nino, D. Arnas, D. Tannr, R. Mittra, and M. Lanagan: "Broadband dilctric charactrization of aluminum oxid (Al O 3 )", Journal of Microlctronics and Elctronic Packaging, Vol. 5, pp ,