Lctur 22 Principls of activ rmot snsing: Lidars Ojctivs: 1. Optical intractions of rlvanc to lasrs. 2. Gnral principls of lidars. 3. Lidar quation. quird rading: G: 8.4.1, 8.4.2 Additional/advancd rading:.m. Masurs, Lasr rmot snsing, 1984. 1. Optical intractions of rlvanc to lasrs. Lasr is a y componnt of th lidar. Lidar (LIght Dtction And anging) Lasr (Light Amplification y Stimulatd Emission of adiation) Basic principls of lasr: stimulatd mission in which atoms in an uppr nrgy lvl can triggrd or stimulatd in phas y an incoming photon of a spcific nrgy. Th mittd photons all possss th sam wavlngth and virat in phas with th incidnt photons (th light is said to COHEENT). Th mittd light is said to INCOHEENT in tim and spac if o th light is composd of many diffrnt wavlngths o th light is mittd in random dirctions o th light is mittd with diffrnt amplituds o thr is no phas corrspondnc twn any of th mittd photons 1
Proprtis of lasr light: Monochromaticity Cohrnc Bam divrgnc: All photons travl in th sam dirction; th light is containd in a vry narrow pncil (almost COLLIMATED), lasr light is low in divrgnc (usually). High irradianc: Lt s stimat th irradianc of a 1 mw lasr am with a diamtr of 1 mm. Th irradianc (powr pr unit ara incidnt on a surfac) is F = P/S = 1x10-3 W/( (1x10-3 m) 2 /4) = 1273 W/m 2 Elastic scattring is whn th scattring frquncy is th sam as th frquncy of th incidnt light (.g., ayligh scattring and Mi scattring). Inlastic scattring is whn thr is a chang in th frquncy. 2
Optical intractions of rlvanc to lasr nvironmntal snsing ayligh scattring: lasr radiation lastically scattrd from atoms or molculs with no chang of frquncy Mi scattring: lasr radiation lastically scattrd from particulats (arosols or clouds) of sizs comparal to th wavlngths of radiation with no chang of frquncy aman Scattring: lasr radiation inlastically scattrd from molculs with a frquncy shift charactristic of th molcul sonanc scattring: lasr radiation matchd in frquncy to that of a spcific atomic transition is scattrd y a larg cross sction and osrvd with no chang in frquncy Fluorscnc: lasr radiation matchd in frquncy to a spcific lctronic transition of an atom or molcul is asord with susqunt mission at th lowr frquncy Asorption: attnuation of lasr radiation whn th frquncy matchd to th asorption and of givn molcul Typs of lasr rlvant to rmot snsing : solid stat lasrs (.g., ruy lasr, 694.3 nm) gas lasrs (.g., CO2, 9-11 µm) smiconductor lasrs (GaAs, 820 nm) 2. Gnral principls of lidars. Thr ar svral main typs of lidars: Bacscattr lidars masur acscattrd radiation and polarization (oftn calld th Mi lidar) DIffrntial Asorption Lidar (DIAL) is usd to masur concntrations of chmical spcis (such as ozon, watr vapor, pollutants) in th atmosphr. 3
Principls: A DIAL lidar uss two diffrnt lasr wavlngths which ar slctd so that on of th wavlngths is asord y th molcul of intrst whilst th othr wavlngth is not. Th diffrnc in intnsity of th two rturn signals can usd to dduc th concntration of th molcul ing invstigatd (s lctur 23). aman (inlastic acscattring) Lidars: dtct slctd spcis y monitoring th wavlngth-shiftd molcular rturn producd y virational aman scattring from th chosn molculs (s lctur 23). High Spctral solution Lidar (HSL) masurs optical proprtis of th atmosphr y sparating th Dopplr-roadnd molcular acscattr rturn from th unroadnd arosol rturn. Th molcular signal is thn usd as a caliration targt which is availal at ach point in th lidar profil. This caliration allows unamiguous masurmnts of arosol scattring cross sction, optical dpth, and acscattr phas function (s G8.4.3). Dopplr lidar is usd to masur th vlocity of a targt. Whn th light transmittd from th lidar hits a targt moving towards or away from th lidar, th wavlngth of th light rflctd/scattrd off th targt will changd slightly. This is nown as a Dopplr shift - hnc Dopplr Lidar. If th targt is moving away from th lidar, th rturn light will hav a longr wavlngth (somtims rfrrd to as a rd shift), if moving towards th lidar th rturn light will at a shortr wavlngth (lu shiftd). Th targt can ithr a hard targt or an atmosphric targt - th atmosphr contains many microscopic dust and arosol particls which ar carrid y th wind. Lidars compard to radars: Lidar uss lasr radiation and a tlscop/scannr similar to th way radar uss radio frquncy missions and a dish antnna. 4
Optically thic cloud and prcipitation can attnuat th lidar am. On th othr hand, radar scattrrs may consist of clouds and hydromtors (.g., rain or frozn prcipitation, which hav a dfinit fall vlocity). In optically clar air, radar rturn signals may otaind from inscts and irds, and from radio rfractiv indx variations du to humidity, tmpratur, or prssur fluctuations. Lidar am divrgnc is two to thr ordrs of magnitud smallr compard to convntional 5 and 10 cm wavlngth radars. Th comination of th short puls (of th ordr of 10-8 s) and th small am divrgnc (aout 10-3 to 10-4 radiant) givs a small volum illuminatd y a lidar (aout a fw m 3 at rangs of tns of m). 3. Lidar quation. In gnral, th form of a lidar quation dpnds upon th ind of intraction invod y th lasr radiation. Lt s considr lastic scattring. Similar to th drivation of th radar quation, th lidar quation can writtn as C h Pr ( ) = xp( 2 ( r ) dr ) 2 2 4π whr C is th lidar constant (includs P t, rcivr cross-sction and othr instrumnt factors); κ /4π (in units of m -1 sr -1 ) is calld th acscattring factor or lidar acscattring cofficint or acscattring cofficint; κ is th volum xtinction cofficint; and t p is th lidar puls duration (h=ct p ) o [22.1] 5
Solutions of th lidar quation: In gnral, oth th volum xtinction cofficint κ and acscattring cofficint κ ar unnown (s Eq.[22.1]) it is ncssary to assum som ind of rlation twn κ and κ xtinction-to-acscattring ratio) (calld th EXAMPLE: ayligh scattring cas. Assuming no asorption at th lidar wavlngth, th volum xtinction cofficint is qual to th volum scattring cofficint On th othr hand, Eq.[ 21.9] givs = s = P s ( Θ = 180) Using th ayligh scattring phas function, w hav P Thus, for ayligh scattring ( Θ = 180) = 3 2 0 (1 + cos (180 )) = 1.5 4 sp ( Θ = 180) = 1.5s = 1. 5 = [22.2] To liminat systm constants, th rang-normalizd signal varial, S, is introducd as 2 S ( ) = ln( P ( )) [22.3] If S o is th signal at th rfrnc rang 0, from Eq.[22.1] w hav S( ) S( ) = ln 2 ( r) dr 0, o 0 or in th diffrntial form ds 1 d ( ) = 2 ( ) [22.4] d ( ) d r 6
Solution of th lidar quation asd on th slop mthod: assums that th scattrrs ar homognously distriutd along th lidar path so Thus d ( ) 0 d [22.5] ds = 2 [22.6] d and κ is stimatd from th slop of th plot S vs. Limitations: applical for a homognous path only. Tchniqus asd on th xtinction-to-acscattring ratio: us a priori rlationship twn and typically in th form n = [22.7] whr and n ar spcifid constants. Sustituting Eq.[22.7] in Eq.[22.4], w hav ds n d ( ) = 2 ( ) [22.8] d ( ) d with a gnral solution at th rang = 1 S S 0 xp n 2 S S n xp n o 0 dr [22.9] NOTE: Eq.[22.9] is drivd ignoring th multipl scattring Eq.[22.9] rquirs th assumption on th xtinction-to-acscattring ratio Eq.[22.9] is instal with rspct to (som modifications wr introducd to avoid this prolm. For instanc, us th rfrnc point at th prdtrmind nd rang, m, so th solution is gnratd for < m instad of > o 7