Copyright 2004 by the Society of Photo-Optical Instrumentation Engineers.

Transcription

1 Copyrght 004 by the Socety of Photo-Optcal Instrumentaton Engneers. Ths paper was publshed n the proceedngs of Optcal Mcrolthography XVII, SPIE Vol. 5377, pp It s made avalable as an electronc reprnt wth permsson of SPIE. One prnt or electronc copy may be made for personal use only. Systematc or multple reproducton, dstrbuton to multple locatons va electronc or other means, duplcaton of any materal n ths paper for a fee or for commercal purposes, or modfcaton of the content of the paper are prohbted.

2 Explorng the Capabltes of Immerson Lthography Through Smulaton Chrs A. Mack * and Jeffrey D. Byers KLA-Tencor ABSTRACT Immerson lthography has recently emerged as the leadng canddate for extendng 93nm lthography to the 45nm lthography node and beyond. By mmersng the wafer n a hgh ndex flud, lens desgns wth numercal apertures (NAs) approachng the refractve ndex of the flud are possble. Whle such a hgh numercal aperture s normally accompaned by an extreme decrease n the depth of focus at the resoluton lmt, an advantage of the mmerson approach to ncreasng the numercal aperture s that the depth of focus s ncreased by at least a factor of the refractve ndex, mtgatng some of the DOF loss due to the hgher NA and smaller feature. Though ths technque for resoluton enhancement s recevng sgnfcant attenton, useful expermental data on the subtle effects of such hgh NA magng s one to two years away. Thus, smulaton s expected to brdge the gap n mmerson lthography research. In ths paper, the fundamental magng physcs of mmerson lthography wll be descrbed. The mpact of resoluton and depth of focus wll be explored, as well as the subtle though sgnfcant nfluence of hyper NAs on polarzaton related thn flm effects and the defnton of ntensty. Wth a rgorous model n place, the use of mmerson lthography for extendng 93nm towards ts ultmate lmts wll be explored. Keywords: Immerson Lthography, Lthography Smulaton, PROLITH. Introducton and Theory Although the scentfc prncples underlyng mmerson lthography have been know for well over 00 years, only recently has ths technology attracted wdespread attenton n the semconductor ndustry. Despte ths rather late start, the potental of mmerson lthography for mproved resoluton and depth of focus s changng the ndustry s roadmap and seems destned to extend the lfe of optcal lthography to new, smaller lmts. The story of mmerson lthography begns wth Snell s Law. Lght travelng through materal wth refractve ndex n strkes a surface wth angle θ relatve to the normal to that surface. The lght transmtted nto materal (wth ndex n ) wll have an angle θ relatve to that same normal as gven by Snell s law. n = θ () snθ n sn * chrs.a.mack@kla-tencor.com, KLA-Tencor, 8834 N. Captal of Texas Hghway, Sute 30, Austn, TX USA

3 Now pcture ths smple law appled to a flm stack made of up any number of thn parallel layers (Fgure a). As lght travels through each layer Snell s law can be repeatedly appled: n snθ n snθ = n3 snθ3 = n4 snθ4 =... = n k = snθ () Thanks to Snell s law, the quantty nsnθ s nvarant as a ray of lght travels through ths stack of parallel flms. Interestngly, the presence or absence of any flm n the flm stack n no way affects the angle of the lght n other flms of the stack. If flms and 3 were removed from the stack n Fgure a, for example, the angle of the lght n flm 4 would be exactly the same. We fnd another, related nvarant when lookng at how an magng lens works. A well made magng lens (wth low levels of aberratons) wll have a Lagrange nvarant (often just called the optcal nvarant) that relates the angles enterng and extng the lens to the magnfcaton m of that lens. no snθ m = o (3) n snθ where n o s the refractve ndex of the meda on the object sde of the lens, θ o s the angle of a ray of lght enterng the lens relatve to the optcal axs, n s the refractve ndex of the meda on the mage sde of the lens, and θ s the angle of a ray of lght extng the lens relatve to the optcal axs (Fgure b). Note that, other than a scale factor gven by the magnfcaton of the magng lens and a change n the sgn of the angle to account for the focusng property of the lens, the Lagrange nvarant makes a lens seem lke a thn flm obeyng Snell s law. (It s often convenent to magne the magng lens as X, scalng all the object dmensons by the magnfcaton, thus allowng m = and makng the Lagrange nvarant look just lke Snell s law). k θ n n θ n θ θ o θ n 3 n 4 Entrance Pupl Aperture Stop Ext Pupl (a) (b) Fgure. Two examples of an optcal nvarant, a) Snell s law of refracton through a flm stack, and b) the Lagrange nvarant of angles propagatng through an magng lens. These two nvarants can be combned when thnkng about how a photolthographc magng system works. Lght dffracts from the mask (the object of the magng lens) at a partcular angle. Ths dffracted order propagates through the lens and emerges at an angle gven by the Lagrange nvarant. Ths lght then

4 propagates through the meda between the lens and the wafer and strkes the photoresst. Snell s law dctates the angle of that ray n the resst, or any other layers that mght be coated on the wafer. Takng nto account the magnfcaton scale factor, the quantty nsnθ for a dffracted order s constant from the tme t leaves the mask to the tme t combnes nsde the resst wth other dffracton orders to form an mage of the mask. So how does ths optcal nvarant affect our understandng of mmerson lthography? If we replace the ar between the lens and the wafer wth water, the optcal nvarant says that the angles of lght nsde the resst wll be the same, presumably creatng the exact same mage. Is there then no mpact of mmerson lthography? There s, from two sources: the maxmum possble angle of lght that can reach the resst, and the phase of that lght. Consder agan the chan of angles through multple materals as gven by equaton (). Trgonometry wll never allow the sne of an angle to be greater than one. Thus, the maxmum value of the nvarant wll be lmted by the materal n the stack wth the smallest refractve ndex. If one of the layers s ar (wth a refractve ndex of.0), ths wll become the materal wth the smallest refractve ndex and the maxmum possble value of the nvarant wll be.0. If we look then at the angles possble nsde of the photoresst, the maxmum angle possble would be snθ max, resst =/ nresst. Now suppose that the ar s replaced wth a flud of a hgher refractve ndex, but stll smaller than the ndex of the photoresst. In ths case, the maxmum possble angle of lght nsde the resst wll be greater: snθ max, resst = n flud / nresst. At a wavelength of 93nm, ressts have refractve ndces of about.7 and water has a refractve ndex of about.44. The flud does not make the angles of lght larger, but t enables those angles to be larger. If one were to desgn a lens to emt larger angles, mmerson lthography wll allow those angles to propagate nto the resst. The numercal aperture of the lens (defned as the maxmum value of the nvarant nsnθ that can pass through the lens) can be made to be much larger usng mmerson lthography, wth the resultng mprovements n resoluton one would expect. The second way that an mmerson flud changes the results of magng comes from the how the flud affects the phase of the lght as t reaches the wafer. Lght, beng a wave, undergoes a phase change as t travels. If lght of (vacuum) wavelength λ travels some dstance z through some materal of refractve ndex n, t wll undergo a phase change φ gven by ϕ = π n z / λ (4) A phase change of 360º wll result whenever the optcal path length (the refractve ndex tmes the dstance traveled) reaches one wavelength. Ths s mportant n magng when lght from many dfferent angles combne to form one mage. All of these rays of lght wll be n phase only at one pont the plane of best focus. When out of focus, rays travelng at larger angles wll undergo a larger phase change than rays travelng at smaller angles. As a result, the phase dfference between these rays wll result n a blurred mage. How does mmerson lthography affect ths pcture? For a gven dffracton order (and thus a gven angle of the lght nsde the resst), the angle of the lght nsde an mmerson flud wll be less than f ar were used. These smaller angles wll result n smaller optcal path dfferences between the varous dffracted orders when out of focus, and thus a smaller degradaton of the mage for a gven amount of defocus. In other words, for a gven feature beng prnted and a gven numercal aperture, mmerson lthography wll provde a greater depth of focus (DOF). A more thorough descrpton of the mpact of mmerson on DOF wll be gven n the followng secton.

5 . Immerson and the Depth of Focus Lord Raylegh, more than 00 years ago, gave us a smple approach to estmatng depth of focus n an magng system. Here we ll expressng hs method and results n modern lthographc terms, as well as extend them to numercal apertures approprate to mmerson lthography. A common way of thnkng about the effect of defocus on an mage s to consder the defocusng of a wafer as equvalent to causng an aberraton an error n curvature of the actual wavefront relatve to the desred wavefront (.e., the one that focuses on the wafer). The dstance from the desred to the defocused wavefront goes from zero at the center of the ext pupl and ncreases as we approach the edge of the pupl. Ths dstance between wavefronts s called the optcal path dfference (OPD). The OPD s a functon of the defocus dstance δ and the poston wthn the pupl and can be obtaned from the geometry of a convergng sphercal wave. Descrbng the poston wthn the ext pupl by an angle θ, the optcal path dfference s gven (after a bt of geometry and algebra) by OPD = δ ( cosθ ) (5) Depth of focus (DOF) s defned genercally as the range of focus that can be tolerated. Whle an exact crteron for tolerated s applcaton dependent, a smple example can be used to gude a basc descrpton of DOF. Consder the magng of an array of small lnes and spaces. The dffracton pattern for such a mask s a set of dscrete dffracton orders, ponts of lght enterng the lens spaced regularly dependng only on the wavelength of the lght λ and the ptch p of the mask pattern. The angles at whch these dffracton orders wll emerge from the lens are gven by Bragg s condton: mλ sn θ = (6) p where m s an nteger. Usng ths nteger to name the dffracton orders, a hgh resoluton pattern of lnes and spaces wll result n only the zero and the plus and mnus frst dffracton orders passng through the lens to formng the mage. Combnng equatons (5) and (6) we can see how much OPD wll exst between the zero and frst orders of our dffracton pattern. Unfortunately, some trgonometrc manpulatons wll be requred to convert the cosne of equaton (5) nto the more convenent sne of equaton (6). One such manpulaton uses a Taylor seres: sn sn = ( cos ) = 4 6 θ OPD δ θ δ sn θ + + θ + K (7) 4 8 At the tme of Lord Raylegh, lens numercal apertures were relatvely small. Thus, the largest angles gong through the lens were also qute small and the hgher order terms n the Taylor seres could be safely gnored, gvng OPD δ sn θ (8) How much OPD can our lne/space pattern tolerate? Consder the extreme case. If the OPD were set to a quarter of the wavelength, the zero and frst dffracted orders would be exactly 90º out of phase wth

6 each other. At ths much OPD, the zero order would not nterfere wth the frst orders at all and no pattern would be formed. The true amount of tolerable OPD must be less than ths amount. λ OPDmax = k, where k < 4 (9) Substtutng ths maxmum permssble OPD nto equaton (8), we can fnd the DOF. λ DOF = δ max = k (0) sn θ At ths pont Lord Raylegh made a crucal applcaton of ths formula that s often forgotten. Whle equaton (0) would apply to any small pattern of lnes and spaces (that s, any ptch appled to equaton (6) so that only the zero and frst orders go through the lens), Lord Raylegh essentally looked at the extreme case of the smallest ptch that could be maged the resoluton lmt. The smallest ptch that can be prnted would put the frst dffracted order at the largest angle that could pass through the lens, defned by the numercal aperture, NA. For ths one pattern, the general expresson (0) becomes the more famlar and specfc Raylegh DOF crteron: λ DOF = k () NA From the above dervaton we can state the restrctons on ths conventonal expresson of the Raylegh DOF: relatvely low numercal apertures magng a bnary mask pattern of lnes and spaces at the resoluton lmt. To lft some of these restrctons we smply use the exact OPD expresson and leave the angle to be defned by equaton (6) []. k = λ k = λ DOF () ( cosθ ) 4 θ sn Ths hgh NA verson of the Ralyegh DOF crteron stll assumes we are magng a small bnary pattern of lnes and spaces, but s approprate at any numercal aperture. It can also be modfed to account for mmerson lthography qute easly. When the space between the lens and the wafer s flled wth a flud of refractve ndex n flud, the optcal path dfference becomes the physcal path dfferent multpled by ths refractve ndex. Thus equaton (5) becomes and the hgh NA verson of the Raylegh crteron becomes OPD = n flud δ ( cosθ ) (3) k λ DOF = (4) ( cosθ ) n flud Lkewse, the angle θ can be related to the ptch by the modfcaton of equaton (6) to account for mmerson.

7 n flud mλ sn θ = (5) p Combnng equatons (4) and (5) one can see how mmerson wll mprove the depth of focus of a gven feature: ( λ / p) DOF( mmerson) = (6) DOF( dry) n flud ( n ) ( λ / p) As Fgure shows, the mprovement n DOF s at least the refractve ndex of the flud, and grows larger from there for the smallest ptches. It s no wonder mmerson lthography s attractng so much attenton. flud.0.9 DOF(mmerson)/DOF(dry) Ptch (nm) Fgure. For a gven pattern of small lnes and spaces, usng mmerson mproves the depth of focus by at least the refractve ndex of the flud (n ths example, λ = 93nm, n flud =.46). 3. Polarzaton, Reflectvty, and the Defnton of Intensty The hgh angle propagaton and nterference of lght that results from very hgh numercal apertures presents several challenges, both n descrbng and calculatng the nature of ths lght, and n controllng the lght to acheve desred lthographc results. When two planes nterfere, the amount of nterference s determned by the amount the two electrc felds overlap (.e., by the dot product of the electrc feld vectors). When the angle between the two plane waves s small, the electrc feld overlap s nearly 00% and the vector sum of the electrc felds s nearly equal to the scalar sum (Fgure 3). However, as the angle ncreases the amount of overlap becomes dependent on the drecton of the electrc feld vector. Although unpolarzed lght contans

8 all possble electrc feld vector drectons that are perpendcular to the drecton of travel, mathematcally we can decompose an unpolarzed wave nto the ncoherent sum of any two orthogonal polarzatons. Snce we wll be nterested n how a plane wave propagates nto a resst coated wafer, the two most convenent drectons are those parallel and perpendcular to the plane of ntersecton of the waves wth the flm, as descrbed n more detal below. Thus, a descrpton of the polarzaton drecton of the lght becomes an ntegral part of how mages form nsde of a photoresst flm. p s Small Angles Large Angles Fgure 3. The overlap of s-polarzed (TE) lght s always perfect, regardless of the angle between the waves. For p-polarzed (TM) lght, the amount of overlap (and thus nterference) decreases as the angle ncreases. Whle seemngly smple n concept, the defnton of lght ntensty s more complcated than expected. In partcular, a comparson of ntensty values when the lght s n dfferent materals and travelng at dfferent angles requres careful consderaton. One case where these dffcultes become apparent s the smple refracton of a plane wave travelng from one medum to another. Thus, our dscusson wll begn wth a look at electrc feld and ntensty reflecton and transmsson coeffcents. The followng dervatons are based on the standard treatment gven by Born and Wolf []. (Note, however, that many modern authors do not follow Born and Wolf s use of the words ntensty and rradance, though few would dspute the correctness of the physcs that they present.) Consder lght ntersectng the plane nterface between two materals, numbered and as shown n Fgure 4. For the moment we wll consder normal ncdence of the lght on ths nterface, wth an ncdent electrc feld E, a reflected electrc feld E r, and a transmtted electrc feld E t. The electrc feld reflecton and transmsson coeffcents at normal ncdence are gven by ρ = E E r = n n n + n where n j = n j + κ j = the complex ndex of refracton of materal j. E n τ = t = (7) E n + n

9 The transmsson and reflecton coeffcents are also functons of the angle of ncdence and the polarzaton of the ncdent lght. If θ s the ncdent (and reflected) angle and θ t s the transmtted angle, then the electrc feld reflecton and transmsson coeffcents are gven by the Fresnel formulae. ρ τ ρ τ ncos( θ ) n = n cos( θ ) + n = n cos( θt ) cos( θ ) ncos( θ ) cos( θ ) + n cos( θ ) ncos( θt ) n = n cos( θ ) + n t t t cos( θ ) cos( θ ) ncos( θ ) = (8) n cos( θ ) + n cos( θ ) t Here, represents an electrc feld vector whch les parallel to the plane defned by the drecton of the ncdent lght and a normal to the materal nterface (.e., n the plane of the paper n Fgure 4). Other names for polarzaton nclude p polarzaton and TM (transverse magnetc) polarzaton. The polarzaton denoted by represents an electrc feld vector whch les n a plane perpendcular to that defned by the drecton of the ncdent lght and a normal to the surface (.e., perpendcular to the plane of the paper n Fgure 4). Other names for polarzaton nclude s polarzaton and TE (transverse electrc) polarzaton. Note that for lght normally ncdent on the resst surface, both s and p polarzaton result n electrc felds whch le along the resst surface and the four Fresnel formulae revert to the two standard defntons of normal ncdence reflecton and transmsson coeffcents gven n equaton (7). E r Et θ t θ E n n Fgure 4. Geometry used for the defnton of Snell s law and reflecton and transmsson coeffcents. It s nterestng to look at the mpact of the drecton that the lght s travelng on the defntons of equaton (7). Completely reversng the drecton of the lght n Fgure 4, f lght approaches the nterface through materal at an angle θ t, the resultng reflecton and transmsson coeffcents become

10 where these relatonshps hold for ether polarzaton. τ ρ = ρ ncos( θt ) = τ (9) n cos( θ ) The dfference between ntensty and rradance s a subtle one, and notwthstandng the dfferent defntons of these terms n use today, when determnng the ntensty or rradance transmtted nto a materal at an oblque angle t s very mportant to dfferentate between the two. I wll defne the ntensty of lght as the magntude of the (tme averaged) Poyntng vector, the energy per second crossng a unt area perpendcular to the drecton of propagaton of the lght. It s gven by I = n E (0) where n s the real part of the refractve ndex of the meda. Note that the defnton gven n equaton (0) may dffer by a constant multplcatve factor dependng on the unts used. The rradance s the projecton of the ntensty onto a surface whch may not be normal to the drecton that the lght s travelng. The ntensty reflectvty and transmsson, for ether polarzaton, are derved by consderng a unt area on the nterface between the two materals. Consder the rradance, J, of the ncdent lght along the surface of the nterface between the materals. J = cos( θ ) () I Lkewse, the rradances of the reflected and transmtted lght along ths surface are J J = cos( θ ) = cos( θ t ) () r I r t I t Now the rradance reflectvty and transmsson coeffcents can be defned R r = R = R = = ρ J J Jt n cos( θt ) T = T = T = = τ (3) J n cos( θ ) From these two equatons t s easy to show that R + T = for each polarzaton, whch s a consequence of conservaton of energy. Fgure 5 shows how the rradance reflectvty vares wth ncdent angle for both s and p polarzed llumnaton. An alternate form for equatons (3), makng use of the reverse drecton defntons of reflecton and transmsson coeffcents n equaton (9), are R = ρ ρ

11 T = τ τ (4) s-polarzaton Irradance Reflectvty Incdent Angle (degrees) p-polarzaton Fgure 5. Reflectvty (square of the reflecton coeffcent) as a functon of the angle of ncdence showng the dfference between s and p polarzaton (n =.0, n =.5). Consder a unt ntensty plane wave ncdent on the plane boundary between materal and at an ncdent angle θ and wth ntensty I. From equaton (0) the magntude of the ncdent electrc feld must be I E = (5) n The transmtted electrc feld s then E t I = τ E = τ (6) n The transmtted ntensty (.e., the ntensty n materal ) s found by applyng the defnton of ntensty to equaton (6). n I = n I (7) t Et = τ n

12 By comparng equaton (7) wth equaton (3), the non-ntutve result below s obtaned. I cos( θ ) = (8) t T I cos( θ) As can be seen n equaton (8), the transmttance T s not the rato of the ntenstes I t and I (see Fgure 6). The dfference comes from the change n the drecton of the energy flow caused by refracton. Thus, one mght ask the queston, whch s more mportant to know nsde flm, the ntensty of the plane wave, or ts rradance along a surface parallel to the materal nterface? The answer to ths queston depends on the task at hand. For lthography smulaton (and, n fact, most physcs problems) t s the absorbed energy that determnes the effects of exposure to lght. The absorbed energy s calculated by the Lambert law of absorpton, usng a defnton of ntensty as gven above, that s, the energy flow through an area perpendcular to the drecton of travel. Thus, for lthography smulaton, the ntensty as defned n equaton (0) s the quantty that matters T, s-pol. T, p-pol. T or It/I I t /I, p-pol. I t /I, s-pol Incdent Angle (degrees) Fgure 6. Intensty transmtted nto layer relatve to the ncdent ntensty (sold lnes) and the transmttance T (dashed lnes) as a functon of the angle of ncdence for both s and p polarzaton (n =.0, n =.5). Note, however, that although the rradance transmttance T s not an accurate predctor of the fracton of the ntensty of lght makng t n to the flm, the rato T s /T p s the same as the rato of s and p ntenstes nsde the flm for an unpolarzed ncdent wave.

13 4. Smulatons Vector smulatons that accurately track the polarzaton vectors of the electrc felds that propagate from the lens to and through the flm stack on the wafer allow the hyper-nas of future mmerson lthography systems to be accurately modeled. For the smulatons presented below, PROLITH v8. from KLA-Tencor was used. Fgure 7 shows how the use of mmerson can greatly mprove the process wndow and depth of focus when prntng the same features at the same numercal aperture. Fgures 8 and 9 shows how, for the case of mmerson wth dpole llumnaton, pckng an optmum polarzaton drecton for the llumnaton can mprove the process wndow. Dose Focus (a) Dose Focus (b) Fgure 7. For a gven NA, mmerson lthography can greatly mprove the depth of focus (93nm, NA = 0.9, σ = 0.7 (unpolarzed), 90nm lnes, 50nm ptch): a) mmerson, and b) dry. Although Fgures 8 and 9 show clearly the benefts of avodng the wrong polarzaton, the polarzaton drecton that results n p-polarzaton at the wafer, these examples make use of an extreme case: dpole llumnaton when only one orentaton of lnes and spaces occurs on the mask. To avod a double exposure process, some form of quadrupole or annular llumnaton must be used. One opton s the socalled double dpole or cross quad as show n Fgure 0. By makng the llumnaton azmuthally polarzed, each pole can have the optmum polarzaton for the orentaton of lnes and spaces that t s ntended for. As can be seen n Fgure 0, the use of azmuthal polarzaton sgnfcantly mproves the exposure lattude and somewhat mproves the depth of focus for these 0nm ptch patterns.

14 Dose Unpolarzed Focus Dose Y-polarzed Focus Fgure 8. Polarzaton affects reduce the sze of the process wndow (mmerson, 93nm, NA = 0.9, Dpole σ = 0.6/0., 90nm lnes, 80nm ptch). When the optmum polarzaton drecton for the llumnaton s chosen, the best process wndow s obtaned. Dose 4 Dose 4 3 Unpolarzed 3 Y-polarzed Focus Focus Fgure 9. Polarzaton affects reduce the sze of the process wndow (mmerson, 93nm, NA =., Dpole σ = 0.6/0., 50nm lnes, 30nm ptch). When the optmum polarzaton drecton for the llumnaton s chosen, the best process wndow s obtaned. 5. Conclusons Immerson lthography shows great potental for ncreasng the depth of focus of a process at a gven resoluton. An ncrease n DOF of at least the refractve ndex of the flud can be obtaned, though up to a

15 doublng of the DOF s possble at the smallest ptches. Further, the use of mmerson enables the desgn and constructon of hyper NA lens, lens wth numercal apertures greater than. Immerson, however, wll not stop the progresson of complexty and cost that the trend to hgher NAs has always followed. These hyper- NA lens wll requred contnued dramatc mprovements n lens desgn and manufacturng technology. These mprovements seem lkely, though, and numercal apertures up to. seem lkely, and NAs of.3 seem possble wth water mmerson at 93nm. The hyper NAs enabled by mmerson lthography pose another challenge to the lthographc system developer. The full resoluton benefts of these hgher NAs can only be realzed when the optmum polarzaton of the llumnaton s used. Thus, llumnaton polarzaton control (IPC) wll become a necessary component of a hyper NA mmerson tool. Azmuthal polarzaton may be a good compromse for cross quad and annular llumnaton systems, though polarzaton may need to be optmzed more fully for the wde varety of source shapes that may be used for the extreme lthographc magng condtons of the future Unpolarzed Azmuthal %Exposure Lattude DOF (mcrons) Fgure 0. Azmuthal polarzaton s one opton for mnmzng the detrmental affects of the wrong polarzaton when dpole llumnaton s not an opton (93nm, NA =., Cross-quad σ = 0.73/0., 50nm lnes, 0nm ptch). References. B. J. Ln, The k 3 Coeffcent n Nonparaxal λ/na Scalng Equatons for Resoluton, Depth of Focus, and Immerson Lthography, Journal of Mcrolthography, Mcrofabrcaton, and Mcrosystems, Vol., No. (Aprl 00) pp M. Born and E. Wolf, Prncples of Optcs, 6th edton, Pergamon Press, (Oxford, 980) pp. 4.