Scattering properties of nineteen single layer titania films are presented. These films are among thoseprepared for the 1986 Optical Society of America Annual Meeting and were made using six differentdeposition techniques. The properties are given in terms of total integrated scattering and the bidirectionalreflectance distribution function. We looked for a relationship between scattering properties and micro-structure. Our measurements indicate a strong influence by the substrate which greatly limits the conclu-sions that can be drawn. Measurements and theoretical analysis demonstrate that some samples have shortperiod defects incorporated in the film.
1. Introduction
This work presents a study of the scattering losses ofnineteen samples prepared for the 1986 OSA AnnualMeeting. The samples consist of thin films of titani-um oxide on fused silica. They are all of approximate-ly the same thickness and on similar substrates. How-ever, six different deposition techniques wereemployed [electron beam, ion assisted deposition(IAD), ion beam sputter deposition (IBSD), activatedreactive evaporation (ARE), and ion plating (IP)], andthe samples come from twelve different laboratories(including both industrial and research).
Several studies have been performed on these sam-ples. All addressed a common question: What arethe optical properties of titania thin films?' The firstpart of this answer centered on the refractive index.Our laboratory was among several to perform such ananalysis. Results of this characterization were notsufficient for a full disclosure of the film propertiesbecause they do not account for factors which are moreor less closely related to the film microstructure. Mi-crostructure unfortunately creates films which arenever strictly identical to the model, even a very de-tailed one, that is employed for refractive index calcu-lations. Thus, beyond a certain degree of precision,local index inhomogeneities cannot be neglected, and awide spread in refractive index values was found de-spite the similar substrates and thicknesses of the tita-
The authors are with Ecole Nationale Sup6rieure de Physique deMarseille, Laboratoire d'Optique des Surfaces et des CouchesMinces, CNRS U.A. 1120, Domaine Universitaire de St Jer6me,13397 Marseille CEDEX 13, France.
nia films examined. The second thrust of researchwas to examine characteristics other than the refrac-tive index to obtain complementary information to aidin our understanding of the thin film properties. Thiswork, as well as the refractive index work, is beingcoordinated by Bennett into a single publication.2 Wewould like to add to this bulk of information by pre-senting here results of scattering measurements ob-tained from our experimental setup in Marseilles.
When optimal optical performance is desired, lossesby absorption and scattering must be minimized.This implies that very careful precautions must bemade concerning both the substrates, which must beuniformly and rigorously clean and well polished, andthe deposition conditions, which must avoid contami-nation of the film by any impurity or parasitic ele-ments from inside the deposition chamber.
So long as these experimental conditions are ob-served, the amounts of scattered light will be very lowand generally not exceed some millionths of the inci-dent flux. This scattered light originates in roughnessdefects at the two interfaces of the transparent film,that which is in contact with the substrate and thatwhich is in contact with the ambient medium (in thiscase, air), and at the back surface of the substrate.Inhomogeneities in refractive index in the bulk of thefilm can also give rise to scattering. However, for wellformed titanium dioxide films, with little or no grossdefects (such as inclusions), there is typically a negligi-ble contribution to the scattering.
The apparatus for measuring the scattering diagramof a thin film surface in Marseilles is extremely sensi-tive to very small scattering losses. In addition, wehave theoretical tools at our disposal which enable usto analyze and interpret the information contained in ascattering diagram.3 4 This gives us indirect access tothe grain size of materials in thin film form, one of theessential characteristics of a thin film microstructure.
After a brief review of the samples and our measure-ment technique we present our results for the titaniafilms. One of the objectives which interests us is todiscover to what extent the scattering losses depend onthe particular deposition technique employed.Knowing that the different samples were not preparedin identical conditions, particular care must be takenin the interpretation of results.
II. Sample History
The samples under study belong to two sets of filmsprepared for the 1986 Optical Society of America An-nual Meeting. The films are all nominally five quar-terwaves thick at X = 550 nm. Fused silica substrateswere provided for the depositions by ESCO Productsand were all grade A-1. The substrates of all thesamples studied here were 2.54 cm (1 in.) in diameter,1.58 mm (1/16 in.) thick, and presumably from thesame lot. Six different techniques were employed inthe depositions, and twelve separate laboratories pro-vided the films. The two sets were intended to consistof twin films; that is, each film in a given set was to havea corresponding film in the other set that was deposit-ed at the same time and, therefore, in essentially iden-tical conditions. One of the sets is currently at theENSPM for measurement of refractive index, and Ta-ble I lists the film samples belonging to this set. Thecorresponding twin numbers in the other set are alsogiven for comparison with other characterizations ifthe reader wishes.
Previous characterization of the films is describedelsewhere.2 Several laboratories performed measure-ments on this and the other set of films. The focus wasprimarily on the optical constants n and k, absorp-tance, and roughness (from a Talystep surface profil-er).
026 . bare substrate124 bare substrate125 --- bare substrate
The first column gives the sample set measured at E.N.S.P.M.. The secondcolumn gives the corresponding twin sample set numbers.
BRDF-cos(o)
0 30 60 90 120 150 180o (degrees)
Fig. 1. Measured BRDF cosO curves for the nineteen single layertitania films on silica substrates.
Ill. Measurement Technique
The scatterometer, which permits measurement oflight scattered into all directions of space, has beendescribed extensively elsewhere.3 4 Here we recall afew basic aspects of our experimental setup.
The quantity directly measured is the productBRDF cosO, where bidirectional reflection distribu-tion function (BRDF) is defined by Nicodemus.5 Thisquantity represents the flux scattered per unit solidangle into a direction 0 of space and normalized withrespect to the incident beam flux.
The light source is a 4-mW He-Ne laser. The beamis spatially filtered with a 50-Am pinhole and expand-ed. For these measurements, the quasiparallel beamis unpolarized and illuminates a 3.8-mm diam area onthe sample at near normal incidence (1030' from nor-mal). A photomultiplier tube measures scattered fluxin a solid angle of AQ = 6.8 X 10-5 sr. It is mounted ona detector arm that rotates about the sample in theplane of incidence. An angular range 3°20' 0 <176050' is covered by this arm, and measurements aremade at every 60.
We know that surface defects are often not isotropicand show instead preferential orientations. Thesecorrespond in turn to occasionally intense scattering incertain directions. This effect can be studied or aver-aged out by rotating the test sample in its own plane(i.e., about the mean surface normal). For this workwe rotated the sample about its normal at each value of0 and consequently made measurements for 250 sam-ple orientations. We then averaged the 250 values todetermine the mean BRDF * cosO value for each 0.
Figure 1 shows the BRDF -cosO curves for the nine-teen titania samples. The angular region 0° < 0 < 90°corresponds to the half-space containing the directionof specular reflection, and the region 900 < 0 < 1800corresponds to the half-space containing the directionof specular transmittance.
Comparison of the BRDF -cos0 curves is evidently acomplex matter. As a first step, we consider insteadthe integral of BRDF cos0 over the half-space con-
taining the specular reflected beam: DAV (totalamount of scattering by reflection). This quantityvaries sufficiently from one sample to another to per-mit comparison. Even so, care must be taken; sincethe films and substrates are transparent interpretationof experimental results is made difficult by the factthat scattering originates as well from the two inter-faces of the film, the back substrate surface, and vol-ume scattering.
(a)
MP1 IML20M Z
10 4 1 3
E-BEAMIV. Total Amount of Scattering for the TiO2 Films
Results are in Table II(A) where we have arrangedthe samples in order of increasing DAY (all data aregrouped in the table for convenience in comparison).The variation in DAV values is large: the ratio betweenthe minimum (1.5 X 10-4 for sample 135) and maxi-mum (25 X 10-4 for sample 120) is -17.
Can this difference be explained? In particular, canwe correlate the total scattering with the depositiontechnique? With respect to the latter, results are farfrom conclusive. For example, we can look in detail atthe DAv histogram (Fig. 2). This gives the statisticaldistribution of DAV values on a log1 0 scale. We haverepeated the histogram four times in this figure, show-ing where samples produced by different techniquesfall: electron beam deposition in Fig. 2(a); ion assisteddeposition in Fig. 2(b); ion beam sputter deposition inFig. 2(c); and the remaining three techniques groupedin Fig. 2(d).
Roughly, both electron beam and ion assisted depo-sition techniques occupy a broad range of values in thecenter of the histogram. Ion beam sputter deposition
FL-
(c)
U
(d)
DA V
1 -4 3 1 4 1 - 3
I.B.S.D. E //A.R.E. R.F.S. I.P.
Fig. 2. DAV histogram for TiO 2 samples. Repeated 4 times, eachtime showing the position of samples produced by the indicateddeposition technique(s). DAV is the total amount of scattering byreflection with the light incident from the front, or film, side of thesample. The axis for this and all subsequent histograms is loglo
scale.
samples curiously occupy positions in both the ex-treme high and extreme low values of TISR. Giventhese disparate results, it is clear that one or both of thefollowing situations is probable: (1) The depositionconditions can be very different even when the same
Table II. Samples Arranged According to Increasing Scattering
Table A. Table B. Table C.TiO2 samples Aluminized front Aluminized back
surfaces surfaces
Sample No. DAV Defects Sample No. TAS Sample No. TAS
technique is being employed, and thus the resultingfilms will scatter differently. (2) The scattering prop-erties of the samples depend more on some other factor(such as substrate quality or surface cleanliness) thanthey do on the films themselves.
The question of substrate smoothness, cleaning, andpreparation may be of critical importance. The depo-sition conditions are also important to the growth of afilm having a microstructure that is as fine and regularas possible. Thus scattering losses can result directlyfrom the number of defects of all kinds in the film(such as cleaning imperfections, dust particles, spit-ting clusters, and slight variations in the microstruc-ture).
We observed each film under a Nomarski phasecontrast microscope (50OX magnification). It is rela-tively easy to establish the statistics for the observeddefects by compiling average counts per unit area foreach film [Table III(A)]. The majority of defects werein the size range of 2-7 um with <0.1% having largerdimensions. It is curious that for one of the films thedensity of defects observed under the microscope ismuch higher than for any of the other films; film 138has 200 counts/(0.1 mm2) compared with the nexthighest value of 30 counts/(0.1 mm2). Grouping thesamples according to several ranges of defect densitiesand locating their positions on the DAV histogram yieldFig. 3. Samples having the fewest defects often occu-py those places in the histogram which correspond tothe lowest scattering levels. However, this cannot besaid to be a general rule since there are many excep-tions. In particular, all the highest scattering levelsare occupied by samples with very low defect densities.These isolated defects are thus not the primary sourceof scattering.
Thus far, many questions remain unanswered.From the point of view of scattering losses, the nine-teen samples vary substantially one from the other,but these differences are not obviously due to thetechniques employed in the film preparation. Fur-thermore, we must conclude that the density of defectsdoes not explain the considerable variation in the mea-sured DAV-
In view of these results, we must ask up to what pointdoes characterization of the scattering losses yield in-formation on the titania films. The preceding analysiseffectively assumes that the fused silica substrates aresufficiently identical to not confuse the comparison ofDAV measurements. However, we do not know how
Table Ill. Calculated DAV of a Single TiO2 Layer for the Case ofUncorrelated Interfaces (a = 0) and Perfectly Correlated Surfaces (a =1); Influence of the Front Film Surface (Negligible Back Interface, 51 = 0)
and the Back Film Surface (Negligible Front Interface, 60 = 0)
0=1 C= =5 a = 0 6 0=0, 8 =0, 80
DAV (10-4) 4.50 0.53 1.86 2.62
Corresponding curves are displayed in figure 6.
DA V
.D-U
200,21-3011-20
400 defectsdefectsdefects
0-1 0 defects
10-4 10-3Fig. 3. DAv histogram showing different defect counts on a 0.1-mm 2
area. No dependence of the scattering level on defect density isseen. Uncoated substrates are indicated by white circles.
accurate this assumption is. We did not have theopportunity to check this point by measuring eachsubstrate prior to deposition.
V. Uncoated Substrates
A few of the substrates from the lot employed in thetitania depositions remained uncoated. These servedas reference samples in the refractive index character-ization.3 Precision in the spectrophotometric analysisis improved by normalizing the reflected and transmit-ted signals to the reflectance and transmittance of asample whose refractive index is well known.
Three such uncoated substrates at our disposal weresubjected to the same measurements as the nineteentitania samples. The measured DAV for the substratesare 1.99 X 10-4, 3.46 X 10-4, and 7.17 X 10-4 for samplenumbers 026, 124, and 125, respectively. It is interest-ing to compare these values with those obtained for thetitania coatings. The position of substrate measure-ments is, therefore, added to the DAv histogram of Fig.3. Table III(A) also includes the substrate measure-ments (in parentheses) within the overall ranking ofthe samples.
Clearly, these three uncoated substrates are not nec-essarily representative of the entire substrate lot.Firm conclusions cannot be drawn from such a smallsampling. Nonetheless two essential points are clear.First, scattering from the uncoated substrates fallswell within the films' DAV histogram. It is, therefore,certainly not negligible compared to the scatteringobserved from the films and so the titania layer is notnecessarily responsible for the differences in scatteringbetween samples. Second, microscope observationsindicate that some substrates are of particularly poor-er quality than others. Of the three samples, twoappeared smooth and clean, while the third possessedan exceedingly high number of point defects 400/(0.1mm2)] and many fine parallel scratches. These proba-bly result from incomplete polishing. Similar defectswere observed in a few of the coated samples as well.
Having seen DAV values for the substrates which arecomparable with those of the films, and knowing thatthere are differences in substrate quality, we can askourselves whether the scattering measurements reflectthe film properties or the substrate properties. Thespatial distribution of scattered light yields interestinginformation concerning the distribution of defects ator near the various surfaces in a coating. Therefore,the BRDF cos6 curves may assist in answering this
.question. Certainly, the validity of such an analysisneeds to be carefully examined, and this subject isaddressed in the following paragraphs. Aluminizingthe surfaces will provide interesting additional infor-mation. 6
VI. BRDF Curves and Discussion
It is possible to predict successfully DAV values andBRDF cos6 curves with theoretical calculations. 4 Adetailed analysis would be difficult in this study be-cause it requires simultaneous determination of manyparameters, some of which depend on the substratequality and so are not available to us. We, therefore,limit ourselves to only a few essential conclusions con-cerning this study.
One factor which may have an unexpected impor-tance is that the scattering measurements are made atX = 633 nm and not at the design wavelength X = 550nm. The optical thickness is, therefore, no longer anintegral number of quarterwaves. As a result of varia-tions in the film thickness, the reflectance of the filmsat the measurement wavelength varies between 8 and24%. We have clearly lost the benefit of stationaryoptical properties that is obtained near integral quar-terwave thicknesses. A certain number of parametersin the scattering theory is, therefore, more difficult todetermine, and calculations must be modified to ac-count for this shift away from the design wavelength.
When the BRDF * cosO curves of all the titania filmsare examined, they can be divided into two groupsaccording to the form of the curves. Figure 4 is ex-tracted from the set of samples. We have retainedsamples 093, 114, and 120, because their particularBRDF cos6 shape is relatively higher for larger angu-lar values ( in the 30-85° range). For these samplesthe BRDF cosO form is basically one where the curvedrops down steeply at low angles, and beyond 15° thereis an abrupt change to a near horizontal slope whichcontinues until almost 90°. In this figure we have alsoincluded, to permit comparison, more classicalsmoothly decreasing BRDF cosO curves (samples 036,052, and 138). With the help of theoretical techniquesavailable to us, we can easily interpret this differencebetween the two types of curve shape. We explain inthis way the origin of the highest scattering measure-ments and obtain results for the total integrated scat-tering.
The simplest approach is to consider the coating as asingle TiO2 surface (index equal to 2.35) with air as theincident medium. Roughness defects that are slightdepartures from a planar surface can be represented byan autocorrelation function r, which is the sum of anexponential and a Gaussian function:',7
r=r, +rg,
where re(X) = 3e exp(-4r/L,1) and rg(T) = 52 exp(-r 2 /LP). The exponential function models large spatialperiod defects and is assumed here to have a rmsroughness be = 1 nm and a correlation length Le = 4000nm. The Gaussian function describes short spatialperiods, and we assume Lg = 100 nm. The different
110
io-2
1-410-
BRDF-cos(0)
093
o 30 60 90 120 150 180o (degrees)
Fig. 4. Measured BRDF cosO curves of selected samples.
0 30 60 0 120 X 6O Im 6
0 (degrees)
Fig. 5. Calculated BRDF * cosO curves for a single interface betweenair and TiO2 (nh = 2.35). Each curve corresponds to a different rms
roughness g.
shapes of the BRDF * cosO curves are explained accord-ing to the value for 59, As an example, Fig. 5 givesvarious BRDF cosO curves for different values of g(0.5, 1.0, 2.0, and 3.0 nm). The corresponding DAVvalues are 0.35, 0.41, 0.65, and 1.04 X 10-4, respective-ly. A plateau (higher scattering at large angles) is seento appear for increasing rms roughnesses.
Having considered the importance of 3g in determin-ing the shape of the BRDF cosO curve, we can proceedfurther in the theoretical interpretation. Rather thantreating the TiO2 surface as a semi-infinite medium,we will take into account the rear surface of the film(which interfaces with the substrate). We define 61 asthe roughness at the substrate-film interface and 6 asthe roughness at the film-air interface. Assumingthat the two surfaces have identical roughness, o = = 1.5 nm, and that the correlation lengths are Le =4000 nm and Lg = 100 nm, we can predict the scatteringlosses. For the case where the two surface profiles arecompletely uncorrelated (a = 0) the order of magni-
Fig. 6. Calculated BRDF - cosO curves for a five-quarterwave thickTiO 2 layer (X = 550 nm) on fused silica illuminated with X = 633 nm.
tude of the DAV (Table III) and the BRDF cosO curveshape (Fig. 6) are in agreement with experiment. Thisresult applies to substrates of medium poor quality.
It is important to recall in this brief presentation ofthe parameters involved in the theory that the rough-ness of the surfaces and the correlation between thetwo surfaces have a strong effect on the total amount ofscattered light.8 1 0 A summary of calculated DAV val-ues and BRDF cosO curves for two identical interfacesis presented in Table III and Fig. 6. The two cases ofcorrelated (a = 1) and uncorrelated (a = 0) interfacesare described. We also show the results for when oneof the interfaces has a very small roughness (essentiallynegligible compared with that of the other surface).
What can be retained from this theoretical analysis?An essential point concerns the relative importance ofthe Gaussian in the roughness spectrum. A secondpoint is the relative importance of having two surfacesonce we take into account the fact that the titania filmis transparent. The most plausible hypothesis for thenineteen films is that the roughness of the two inter-faces is uncorrelated. Table III demonstrates that therelative importance of the substrate-film interface is1.86/4.50 = 42%, and that of the film-air interface is2.62/4.50 = 58%. Thus the two surfaces play practical-ly identical roles in the sample scattering.
The representation for the film roughness presentedabove may be tested by comparing it to results ob-tained for the films after an opaque layer of aluminumis deposited on them.6 With regard to the calcula-tions, the same parameters ( Le, g, and Lg) areretained, but we account for the different refractiveindex of aluminum (nh = 0.83, kh = 6.1). The resultyields 4.57 X 10-4 for the DAV, and the BRDF cosOcurve is given in Fig. 7.
If we now compare the calculated integrated scatter-ing of the titania layer before and after aluminization,we see that it goes from 4.50 to 4.57 X 10-4 (for a = 0).It remains essentially unchanged. By contrast, if per-fect correlation is assumed between the interfaces, the
lo-.1_ _ _ _ _0 30 60 SO
0 (degrees)
Fig. 7. Calculated BRDF * cosO curve for a single interface betweenair and aluminum (nh = 0.83, kh = 6.1).
TAS
10-3 10-2 10-3 10-2 1O-3 10.2
E-beam _ I.A.D. _ I.B.S.D.
TAS
13 02 103 1 0-2-111 1 Ed1 Acm uncoated
A.R.E. R.F.S. I.P. substrate
Fig. 8. TAS histogram for the front (or film side) aluminized sur-face. Repeated 4 times, each time showing the position of samplesproduced by the indicated deposition technique(s). A supplemen-tary histogram including the substrates and indicating their position
is included.
integrated scattering would go from 0.50 to 4.57 X 10-4.There would thus be a factor of 9 difference if theinterfaces were correlated.
To further verify these predictions, we have deposit-ed a barely opaque layer of aluminum on the titaniafilms. Previous work6 has shown that, in appropriateproduction conditions, such a layer reproduces theessential scattering characteristics of the surface itcovers. Few conclusions can be drawn from the tableof measured TAS values for the aluminized samples[see Table II(B)]. The TAS histograms of these alu-minized films (Fig. 8), showing the position of samplesproduced by different techniques, do not modify ourconclusions concerning the wide variance of results foreach technique. Selected BRDF * cosO are displayed inFig. 9. Concerning the curves for samples 093, 114,and 120, we find the same sort of shape as in Fig. 4 with
e uncoated substrateFig. 10. TAS histogram for the aluminized back surface.
0 30 60 900 (degrees)
Fig. 9. Measured BRDF cosO curves for the aluminized front (orfilm) surface of the selected samples shown in Fig. 5.
only a slight increase in slope for the plateau. Wemust, therefore, attribute this shape to short spatialperiod defects (which are related to the Gaussian de-scription given above) that are present in the filmsurface.
With regard to the ratio of a total amount of scatter-ing before and after aluminum, we see that aluminiza-tion causes on the average a factor of 3 increase. Thiscannot be explained without admitting that the sam-ples had high scattering from the back surface andwidely varying substrate surface profiles. Moreover,the calculation was performed assuming identical filmand substrate roughness (0 = 61), which may not be thecase. Apart from a noticeable increase in short perioddefects in a few of the titania samples, virtually noconclusions can be drawn on the scattering propertiesof the films.
Vil. Verifying Surface Roughness of UncoatedSubstrates
We wished to verify our conclusions concerning thewide variance in substrate surface quality. The idealwould have been to measure the substrate roughnessbefore deposition. However, as this characterizationwas not made, and as only three uncoated sampleswere available to us, we also measured the aluminizedback surface of the coated samples. This analysisgives an idea of the statistical distribution of scatteringdue uniquely to the substrate surface.
The histogram obtained is shown in Fig. 10. Themost remarkable feature of this histogram is that thespread in TAS values is practically as large as seen inthe preceding histograms. The minimum and maxi-mum are 2.7 and 36.0 X 10-4, respectively [see TableII(C)], giving a factor of 13 difference. The meanscattering level is somewhat lower than that observedfor the aluminized front surfaces. This lower meanseems to indicate that the uncoated substrate surfaceis slightly less rough than the TiO2 surface. However,the cleaning quality of the film side of the substratemay be different from that of the back side of the
0 10
-4
0
1C-
10o6
-410
0-5
10~
Fig. 11. Measured BRDF cosO curves for the aluminized backsurface of the selected samples shown in Fig. 4.
substrate. Note also that for some samples the alumi-nized titania film scatters less than the aluminizedback surface.
The BRDF cos6 curves for the aluminized backsurfaces all have similar smoothly decreasing shapes.To illustrate this, measured curves for the same select-ed samples in Fig. 9 are displayed in Fig. 11. Thisconfirms that the plateau shape must be due to shortspatial period defects in the titania film and not in thesubstrate. It is interesting to notice that the sampleswith short period defects are related only to the higherenergy techniques (IAD, IBSD, and IP). The natureof these defects cannot be known from this study. Itwould be interesting to pursue this question through asystematic study similar to this one, however, per-formed with more care and a larger number of samples.In particular, it is essential to characterize the sub-strates before deposition so that their contributionmay be accounted for.
VilI. Conclusion
Scattering measurements were performed on thenineteen titania films prepared for OSA by severaldifferent techniques and in several different laborato-ries. The shape of the BRDF cosG curve and the totalamount of scattering for each curve vary considerably
from one sample to another. Theoretical analysis ofthese samples is delicate. However, for the most dis-tinctive titania film (with plateau-shaped BRDF cosOcurves), we have been able to explain their characteris-tics by the presence of short spatial period defects.These defects originate in the films and are not acharacteristic of the substrate. It is intriguing to notethat this phenomenon is observed only for films pro-duced by IAD, IBSD, and IP. However, other filmsproduced by these techniques do not show short periodscatter. Apart from these exceptional films, it is notpossible for us to derive any dependence of the micro-structure on the technique employed. We can onlyconclude that the different deposition techniques givesimilar results from the point of view of scattering. Itwould have been necessary to choose only the sub-strates that have very low scattering to conclude whichtechnique (e-beam, IAD, IBSD, IP, RFS, and ARE) ispreferred for producing films with the finest TiO2grain size.
The results of this study indicate clearly that- forscattering measurements to provide new informationbeyond what is established with other techniques, it isessential to take certain experimental precautions.The data here indicate that the substrates employed inthis study did not possess a surface polish of adequatequality for such a sensitive analysis. In any case,knowing that the initial roughness of the substratecontributes a large part (perhaps as much as 40%) tothe level of light scattered by the film, it is impossibleto consider deriving the TiO2 grain size without care-fully characterizing the substrates prior to deposition.The ideal would not only be to measure the substratessystematically before deposition but to choose sub-strates with approximately identical characteristics.It is also essential to insist on a prescribed substratecleaning and on precautions which must be observed instorage and transport procedures for the samples.With such precautions, the relationship between scat-tering and microstructure of the films could, therefore,be investigated.
References
1. C. Carniglia, Chairperson, Optical Materials and Thin FilmsTechnical Group Meeting, 1986 Optical Society of America An-nual Meeting; U. J. Gibson, Chairperson, Optical Materials andThin Films Technical Group Meeting, 1987 Optical Society ofAmerica Annual Meeting.
2. J. M. Bennett, C. Carniglia, K. M. Guenther, E. Pelletier et al.,"Comparison of the Properties of Titanium Dioxide Films Pre-pared Using Different Techniques," to be published.
3. P. Roche and E. Pelletier, "Characterizations of Optical Sur-faces by Measurement of Scattering Distribution," Appl. Opt.23, 3561-3566 (1984).
4. P. Bousquet, F. Flory, and P. Roche, "Scattering from Multilay-er Thin Films: Theory and Experiment," J. Opt. Soc. Am. 71,1115-1123 (1981).
5. F. E. Nicodemus, "Directional Reflectance and Emissivity of anOpaque Surface," Appl. Opt. 4, 767-773 (1965).
6. P. Roche, C. Amra, and E. Pelletier, "Measurement of Scatter-ing Distribution for Characterization of the Roughness of Coat-ed or Uncoated Substrates," Proc. Soc. Photo-Opt. Instrum.Eng. 652, 256-263 (1986).
7. J. M. Elson and J. M. Bennett, "Relation Between the AngularDependence of Scattering and the Statistical Properties of Opti-cal Surfaces," J. Opt. Soc. Am. 69, 31-47 (1979); C. Amra, C.Grezes-Besset, P. Roche, and E. Pelletier, "Description of a Scat-tering Apparatus-Application to the Problems of Characteriza-tion of Opaque Surfaces," in Technical Digest, Topical Meetingon Optical Interference Coatings (Optical Society of America,Washington, DC, 1988); Appl. Opt. 28, 2723-2730 (1989).
8. C. Amra, P. Roche, and E. Pelletier, "Interface RoughnessCross-Correlation Laws Deduced from Scattering DiagramMeasurements on Optical Multilayers: Effect of the MaterialGrain Size," J. Opt. Soc. Am. B 4, 1087-1093 (1987).
9. C. Amra, G. Albrand, and P. Roche, "Theory and Application ofAntiscattering Single Layers; Antiscattering AntireflectionCoatings," Appl. Opt. 25, 2695-2702 (1986).
10. P. Roche, P. Bousquet, F. Flory, J. Garcin, E. Pelletier, and G.Albrand, "Determination of Interface Roughness Cross-Corre-lation Properties of an Optical Coating from Measurements ofthe Angular Scattering," J. Opt. Soc. Am. A 1,1028-1031 (1984).
The authors would like to thank Jean M. Bennett formany helpful discussions concerning the experimentalresults and theoretical analysis. This paper is basedon one presented at the Fourth Topical Meeting onOptical Interference Coatings, Tucson, 12-15 Apr.,1988.
