Optical properties of narrowband spectral filter coatings related to layer structure and preparation D. R. Gibson and P. H. Lissberger The optical properties of thirty-five all-dielectric spectral filter coatings for the visible spectrum have been investigated and correlated with the deposition conditions of the constituent layers of cryolite and zinc sul- fide and with the processes which occur when the coatings are exposed to atmosphere. It will be shown that the results of measurements of transmittance and reflectance over the passband wavelengths can be predict- ed theoretically only if account is taken of absorption in the layers and scattering at the rough boundaries and of changes in the refractive indices of the layers due to water penetration. 1. Introduction In the past few decades there has been a marked in- crease in the variety of applications of optical coatings and in the demands for greater and more reliable per- formance. Whereas this has stimulated research and brought about distinct improvements in their design and in methods of preparation, two common unsatis- factory features of optical coatingsremain. First, their optical performance falls short of predicted ideals by margins which range from tolerable to unacceptable; second, their properties are frequently unstable. The reasons for these problems are understood in general terms. It is argued' that the structures of the layers do not conform to those of the basic idealized model which is used to make predictions of optical properties of coatings and that these structural deviations or defects are attributable to insufficient understanding and hence control of the deposition process. The cross-sectional electron micrograph of Fig. 1 illustrates that the as- sumptions of the basic model, namely, that the layers of a coating consist of perfectly homogeneous materials with plane-parallel boundaries, are patently not tenable in the final analysis. Indeed, whenever coatings are required to operate near their limits of performance, as, for example, in the cases of mirrors for laser gyroscopes, spectral filters of very narrow bandwidth, and coatings of several types for use in high power laser systems, the The authors are with Queen's University of Belfast, Department of Pure & Applied Physics, Belfast BT7 NN, Northern Ireland, U.K. Received 6 August 1982. 0003-6935/83/020269-13$01.00/0. (D 1983 Optical Society of America. effects of structural imperfections are highlighted, and the need is clearly demonstrated for a still more detailed understanding of the relationhips between optical performance and layer structure on the one hand, and layer structure and deposition parameters on the other. The investigations described in this paper are designed to establish the former relationship quantitatively and to throw further light on the latter for coatings con- taining the common soft materials, zinc sulfide and cryolite. However, the experimental and theoretical techniques, as well as the conclusions, have features which are applicable to coatings generally. The modus operandi adopted in the investigations is as follows. Thirty-five optical coatings, designed as narrowband spectral filters for the visible spectrum and prepared on substrates at various temperatures, were subjected to a comprehensive set of optical measure- ments both in vacuo and on being exposed to the at- mosphere. Structural observations by optical micros- copy were also undertaken, but the structural obser- vations are not complete since the final analysis in- volving electron microscopy is destructive and can therefore be undertaken only when no further optical investigations are envisaged. To allow the optical measurements to be arranged in a logical pattern, errors associated with the monitoring of the thickness of the layers during deposition and systematic errors such as those related to the coherence of the radiation used for measurement were first reduced to negligible propor- tions. Values of the porosities of the layer materials and hence their refractive indices both in the vacuum- and air-stablized conditions were inferred from measure- ments of the drifts of the wavelengths of peak trans- mittance on exposure to atmosphere, i.e., as water penetrates the pores. These values together with ap- propriate values of the rms roughness at the spacer 15 January 1983 / Vol. 22, No. 2 / APPLIED OPTICS 269
Transcript
Optical properties of narrowband spectral filter coatingsrelated to layer structure and preparation
D. R. Gibson and P. H. Lissberger
The optical properties of thirty-five all-dielectric spectral filter coatings for the visible spectrum have beeninvestigated and correlated with the deposition conditions of the constituent layers of cryolite and zinc sul-fide and with the processes which occur when the coatings are exposed to atmosphere. It will be shown thatthe results of measurements of transmittance and reflectance over the passband wavelengths can be predict-ed theoretically only if account is taken of absorption in the layers and scattering at the rough boundariesand of changes in the refractive indices of the layers due to water penetration.
1. Introduction
In the past few decades there has been a marked in-crease in the variety of applications of optical coatingsand in the demands for greater and more reliable per-formance. Whereas this has stimulated research andbrought about distinct improvements in their designand in methods of preparation, two common unsatis-factory features of optical coatings remain. First, theiroptical performance falls short of predicted ideals bymargins which range from tolerable to unacceptable;second, their properties are frequently unstable. Thereasons for these problems are understood in generalterms. It is argued' that the structures of the layers donot conform to those of the basic idealized model whichis used to make predictions of optical properties ofcoatings and that these structural deviations or defectsare attributable to insufficient understanding and hencecontrol of the deposition process. The cross-sectionalelectron micrograph of Fig. 1 illustrates that the as-sumptions of the basic model, namely, that the layersof a coating consist of perfectly homogeneous materialswith plane-parallel boundaries, are patently not tenablein the final analysis. Indeed, whenever coatings arerequired to operate near their limits of performance, as,for example, in the cases of mirrors for laser gyroscopes,spectral filters of very narrow bandwidth, and coatingsof several types for use in high power laser systems, the
The authors are with Queen's University of Belfast, Departmentof Pure & Applied Physics, Belfast BT7 NN, Northern Ireland,U.K.
Received 6 August 1982.0003-6935/83/020269-13$01.00/0.(D 1983 Optical Society of America.
effects of structural imperfections are highlighted, andthe need is clearly demonstrated for a still more detailedunderstanding of the relationhips between opticalperformance and layer structure on the one hand, andlayer structure and deposition parameters on the other.The investigations described in this paper are designedto establish the former relationship quantitatively andto throw further light on the latter for coatings con-taining the common soft materials, zinc sulfide andcryolite. However, the experimental and theoreticaltechniques, as well as the conclusions, have featureswhich are applicable to coatings generally.
The modus operandi adopted in the investigationsis as follows. Thirty-five optical coatings, designed asnarrowband spectral filters for the visible spectrum andprepared on substrates at various temperatures, weresubjected to a comprehensive set of optical measure-ments both in vacuo and on being exposed to the at-mosphere. Structural observations by optical micros-copy were also undertaken, but the structural obser-vations are not complete since the final analysis in-volving electron microscopy is destructive and cantherefore be undertaken only when no further opticalinvestigations are envisaged. To allow the opticalmeasurements to be arranged in a logical pattern, errorsassociated with the monitoring of the thickness of thelayers during deposition and systematic errors such asthose related to the coherence of the radiation used formeasurement were first reduced to negligible propor-tions.
Values of the porosities of the layer materials andhence their refractive indices both in the vacuum- andair-stablized conditions were inferred from measure-ments of the drifts of the wavelengths of peak trans-mittance on exposure to atmosphere, i.e., as waterpenetrates the pores. These values together with ap-propriate values of the rms roughness at the spacer
Fig. 1. Cross-sectional electron micrograph of a filter coating air:L(HL) 4 8H(LH) 4 glass. L is a quarterwave of cryolite (C), and H is
a quarterwave of zinc sulfide (Z).
boundaries and the imaginary part of the refractiveindex of zinc sulfide were used in a model 2 of totalscatter to fit measured values of the transmittances andreflectances of the filters at the wavelength of peaktransmittance. Finally, the calculations were extendedover the spectral range of the whole of the filter pass-band to obtain values of the filter half-bandwidths(HBW) which were then compared with the corre-sponding measured values.
IL. Filter Design and Preparation
All-dielectric filters of the simple Fabry-Perot design,i.e., with a single cavity or spacer, are convenient vehi-cles for the type of investigation outlined above for threemain reasons. First, they can be designed and preparedwith very small bandwidths, and their transmittancein the passband region, which can be measured easilyas functions of wavelength, time, and beam position, isvery sensitive to structural changes in the layers, par-ticularly to water penetration of defects and pores whenthe filters are exposed to atmosphere. Second, theoptical properties of such filters are well-known to theextent that various associated optical functions, suchas transmittance,3 absorptance,' 7 and phase changesat the boundaries of the spacer,4 8 are given in terms ofbasic parameters by simple analytical expressions,certainly if idealized layer structures are assumed. Andthird, narrowband spectral filters have prominent fea-tures2 4 9 in the spatial and spectral distributions of theirscattered radiation which must be predictable by vectormodels of radiation scattering due to roughness of thelayer boundaries. Whereas the testing of such a model9
Table I. Filter Types and Designs
Predicted HBW (nm)XD = XD =
Type Design 546.1 nm 589.0 nm
U-, C-, H- Air (HL)48H(LH)41 glass 0.70 0.82U+, C+, H+ Air (HL)48H(LH) 4 L I glass 0.60 0.70
Air l(HL)4H4LH(LH) 4 LI glass 0.58 0.64
NotationU, uncooled H, ZnS quarterwave layerC, cooled L, cryolite quarterwave layerH, heated+(superscript), with AR coating z(subscript), with ZnS spacer-(superscript), with AR coating c(subscript), with cryolite
spacer
was one of the objectives of a wider investigation, theresults of this particular aspect will not be reportedhere.
In accordance with the aims of the investigation, thethree basic filter designs shown in Table I were used,consisting of from seventeen to twenty layers. Theestimates of HBW are based on refractive-index valuesnL = 1.36 and nH = 2.239 + 4.52 X 104/X2 ( in nano-meters) appropriate to bulk cryolite10 and zinc sul-fide,11 12 respectively, dispersion being taken into ac-count in the latter case. Design wavelengths D, cor-responding to the ideal spectral location of the peak ofthe filter passband, were chosen at 546.1 or 589.0 nm,so that suitable discharge sources, for example, mercuryor sodium vapor emitting radiation in strong spectrallines, can be used in observations of the spatial distri-bution of transmittance during the water penetrationprocess.
Filters were prepared in a vacuum system at pressuresin the (1-5) X 10-4-Pa range. Both materials wereevaporated in howitzer sources consisting of aluminacrucibles packed with the materials in powdered formand heated by a central spiral of tungsten wire. Filmswere deposited at constant rates of -0.3 nm sec 1 ontorotating substrates of 1-mm thick soda glass. The layerthicknesses were monitored on the basis of monochro-matic (0.1-nm bandwidth) transmittance measurementsacquired and evaluated by a microprocessor,1 3 and thedepositions terminated automatically at the turningpoints by the operation of a shutter to cover the sub-strate. An experimental assessment of the performanceof the microprocessor monitoring system will be givenlater in terms of the precision with which the passbandwavelengths of the filters can be controlled.
When no steps are taken to control the temperatureof the substrate during the deposition process, it risessteadily from the beginning to the end because of theabsorption of radiant energy from the sources of evap-oration. Consequently, the later layers of a coating aredeposited on a significantly hotter substrate than theearlier layers, and this leads to differences in theirstructure. Filters prepared in such conditions willhenceforth be labeled U, denoting uncooled.
There are two ways of avoiding these differences instructure, both involving a measure of control over thesubstrate temperature. The simplest expedient in theabsence of a substrate heater is to introduce pauses intothe deposition process so that excursions of substratetemperature from the ambient are reduced. Therefore,for some filters, pauses, each of 2-h duration, were in-troduced at two stages of their deposition, one at the endof the third halfwave of the spacer, and the other half-way through the third zinc sulfide layer after the spacer.The strategy of pausing in the middle of a layer is de-signed to allow for simple compensation of the opticaleffects produced by the cooling during the pauses.Filters prepared in this way will be described as cooledand labeled C.
The second method of controlling the substratetemperature is to heat it with an electrical heater to atemperature which is so high that absorption of radia-tion from the sources of evaporation has a negligibleeffect. As will be mentioned later, this procedure is alsoadvantageous in that it results in layer structures whichlead to better stability of filter properties. The corre-sponding filters are labeled H for heated.
The design14 of heater and substrate holder ensuresthat the temperature is uniform over the substrate.Moreover, reliable values of the temperature are ob-tained from the changes of optical thickness of thesubstrate by observations on fringes of equal inclinationwith radiation from a He-Ne laser reflected from thesubstrate surfaces. This techniques avoids the ne-cessity of attaching a thermometer to the substrate andthe consequent sources of systematic error.
Ill. Measurement of Filters
Table II shows the main consequences of varioustypes of defect in narrowband interference filters andpoints to the need for a comprehensive set of optical andstructural measurements if the effects of individualdefects are to be isolated and quantified. Moreover, ashas been mentioned already, errors in monitoring thethickness of the layers during deposition and errors dueto lack of coherence of the radiation used for measure-ment must be reduced to negligible proportions. To
Table I. Defects in Narrowband Filters
Type Result References
Thickness errors 5X 16-18Refractive-index errors
symmetric i tB 19asymmetricJ w.r.t. the spacer B, T(R)post deposition 5X +
Notation5X, wavelength shift of peak 6T, transmittance loss into:
transmittance (R) reflectance,eB, increase in bandwidth (H) heat, (S) scatter
SPECIMEN HOLDER
Fig. 2. Schematic diagram of the automatic normal incidence pho-tometer used for measurments of reflectance and transmittance of
narrowband filters.
meet the former requirement the optical thicknesses ofthe layers were controlled by means of a microprocessorsystem13 programmed to predict the turning points inthe transmittance of a coating from measurementstaken at 0.1-sec intervals during deposition. In theoptimum conditions the wavelength of peak transmit-tance of a filter can be located to within a 0.04-nmstandard deviation of the desired value by the use of thissystem. The control of thickness of individual layersis correspondingly precise, as confirmed by simulta-neous measurements of the mass of the layers by meansof a quartz-crystal monitor. Significant errors ofmeasurement are avoided in that the convergence of thebeams used in the spectrophotometer (Fig. 2) for themeasurement of transmittance and reflectance is neverallowed to exceed f/20, and the spectral bandwidth ofthe monochromator was always kept below 0.1 nm, itslimiting resolution being 0.02 nm in the visible spec-trum. Since the same monochromator is used in theoptical thickness monitor, the same coherence condi-tions apply during the deposition of the layers.
The optical measurements performed on the thirty-five narrowband filter coatings are listed in Table III.The results of a comprehensive set of measurements onthe angular and spectral distribution of radiation
Table Ill. Optical Measurements on Narrowband Filters
Measured optical Filter stabilizedfunction In vacuo In air Instrument
Transmittance V / SpectrophotometerReflectance V SpectrophotometerAbsorptance * Tunable laser calorimeterScatter * Tunable laser scatterometerWavelength shift of i V Spectrophotometer
Notation0, shutter out of beam H @ V = 1, specimen in, comparator out1, shutter in beam H e V = 0, specimen out, comparator inA change from 0 to 1 or vice versa in H or V represents a r rotationof the specimen holder about the horizontal or vertical axis, respec-tively.
scattered from the filter coatings will be reported else-where,2 5 as will those of absorptance which are as yetincomplete. Since the automatic spectrophotometershown schematically in Fig. 2 is the main source of theresults to be presented in this paper, some of its prom-inent features are enumerated briefly below.
(1) The optical system consists of mirrors to obviatethe effects of dispersion in transmitting componentsand hence to make the instrument operable over anextended spectral range.
(2) There are two water-cooled tungsten-halidesources and the optical system is fixed, with the ex-ception of the specimen itself. The latter is reversiblewith respect to the sources since it is mounted on aholder capable of being rotated by motors about hori-zontal (H) and vertical (V) axes.
(3) At a given wavelength, values of the transmit-tances and reflectances of the specimen can be obtainedin the two normal directions in terms of the normaltransmittance of a comparator from eight readings ofthe DVM corresponding to the states given in Table IV.To avoid defocusing problems, the comparator consistsof an uncoated substrate of the same material andthickness (1.0 mm) as the coated specimen. Its normaltransmittance is evaluated from the known opticalconstants of the soda glass, and since this transmittanceis close to unity, uncertainties in the constants do notintroduce significant errors into the measured reflec-tance and transmittance of the coated specimen.
For convenient comparison with theoretical predic-tions, the transmittance and reflectance of the coatingare separated 9 from the effects of the uncoated surfaceof the specimen, again by the use of the known substrateconstants.
(4) The optical system is aligned by means of aHe-Ne laser, and the equality of the transmittances ofthe specimen in the two opposite normal directions, asrequired by the second law of thermodynamics, is usedas a sensitive test of the effectiveness of the alignmentprocedure.
(5) The sequence of readings, the operation of theshutters, the wavelength drive of the monochromator,
"2 514 546 548 550 552 554WAVELENGTH (NM )
Fig. 3. Reflectance (R), transmittance (T), and loss (1 - T - R) fromthe air side in the passband region of a narrowband filter coating (C+)
measured by the photometer.
and the storage of data on a floppy disk are all controlledby a microprocessor.
A typical output from the processing of the spectro-photometer data is shown in Fig. 3 for the passbandregion of a narrowband filter.
As well as the measurements listed in Table III whichrefer to the properties of filters stabilized either in vacuoor in air, other measurements were also taken to eluci-date the changes which occur when a filter is first ex-posed to atmosphere. In particular, the evolution of thetransmittance in the filter passband is observed atregular intervals by means of a Carey spectrophotom-eter until stabilization occurs (Fig. 4). The same pro-cess is also observed with good spatial resolution (Fig.5) by means of an optical transmission microscope (N.A.= 0.15) using a monochromatic source of appropriatewavelength.
IV. Stabilization Processes
A. In Vacuo
When filters of the type discussed here are allowedto cool in vacuo, the wavelengths of peak transmittanceinvariably drift to lower values by amounts 5X, (TableV). Clearly these wavelength changes depend on thechanges of optical thicknesses of all the layers in thefilter but most strongly on the change in the spacinglayer. At the first sight therefore, the direction of theobserved wavelength change is surprising since, if therefractive index of a material is considered to be pro-portional to its density, the refractive index would beexpected to decrease with increasing temperature andthis would more than compensate the correspondingincrease in geometrical thickness of a layer whenchanges in the optical thickness of the spacer and hencethe wavelength of peak transmittance are being evalu-ated. However, such a prima facie argument does nottake into account the effect of temperature on the po-larizabilities of the molecules and the experimental factthat the temperature coefficients of the refractive in-dices of materials are generally not equal to minus threetimes their linear expansion coefficients. Indeed, the
WAVELENGTH (nm)Fig. 4. Evolution of transmittance in the spectral passband region .,
of a filter coating (CZ) on exposure to atmosphere.
temperature coefficients of the refractive indices ofmaterials are not always negative.
On the basis of the formalism described by Lissbergerand Wilcock,2 2 it is easily shown that changes in theoptical thicknesses, X, of the layers of a filter due to anyeffect other than dispersion lead to a change 5X in thewavelength of peak transmittance given by
(A) = [MI(fb), (1)where
( Xaxi. 1 ] (0 [(b/)L 1(5X/Xmax)H]
mL + m2 ml
[M = L + O + ML ML + MO + ML
ml mH+m2
mH + mO + mH mH + mO + mHm = c/(1 - c), ml = c/(1 - c 2 ), m2 = c2/(1 -),
c = nL/nH,
A2LD XnL + D (DnH]nL a nH aXI
6mH = - ml -- + (MH + M2) - ._nL A nH AI
In the expression for bX, the subscripts L and H referto filters with spacer or cavity layers of cryolite and zincsulfide, respectively, the corresponding optical thick-nesses of those layers being mL XD/2 and mHXD/2.
The following two important points should be notedabout Eq. (1).
(1) Dispersion, i.e., change of refractive indices withwavelength, has been taken into account and shows upin the denominators of the elements of the matrix [M].The result is effectively to increase the orders of thespacers by 5m, that is, in addition to mO which repre-sents the order of the phase changes at the spacerboundaries. The amounts 3m are not insignificant, andneglect of dispersion leads to underestimates of the ef-fects on the refractive indices of temperature and waterpenetration, as well as to overestimates of the filterbandwidths; both miscalculations would be serious inthe context of the arguments to be presented in thispaper. In the calculations to follow, dispersion incryolite is neglected, but the value of -(XD/nH)(OnH/A) in the appropriate spectral region is -0.1.
(2) Since the components of (fx) are the measurablequantities from which the values of the components of(f4) are to be deduced, it is convenient to invert Eq. (1)so that
(f/)= [M= 'V0)
l J1 0 0 Pum
Fig. 5. Optical micrograph of the water penetration pattern in a C-filter observed with radiation from a sodium source in the initial stages
of the stabilization process in air.
(2)
If the components of (fx) are the changes per unittemperature rise, those of (4o) become material con-stants whose values may be reasonably compared withcorresponding ones measured elsewhere.26 With anambient temperature of 18'C the mean value of
(max dO H (0 D)H
obtained from the measured properties given in TableV for all filters (U', C+, and H') with zinc sulfide
spacers, is (2.15 ± 0.11) X 10-5 K- 1, and that for filterswith cryolite spacers (C+) is
(1 Omax'1 = (3.39 ± 0.73) X 10-' K-1.\Xmax 00 IL
When these values are used in Eq. (2) as the componentsof (fx), the values of the components of (f4) are
(!-) =O (2.02 0.13) x 10- K-'
and
Ia) L CO (4.00 0.56) X 10-5 K-1
which may be compared with{1 ap\l = (4.8 1.0) X 10-5 K-1
and
(-a-)L =(3.1 0.7) X 10- K-'
obtained by Roche et al.2 6 The following points shouldbe noted in relation to this comparison.
(1) The value of (4b) obtained from measurementsof X, (Table V) corresponds to the layer materials offilters before they are exposed to atmosphere, i.e., beforethe second stabilization process involving water pene-tration, to be discussed in the next section, has takenplace. As a consequence, no hysteresis effects wereobserved on temperature cycling. On the other hand,Roche et al.2 6 did observe marked hysteresis of thewavelength of peak transmittance as a function oftemperature, which suggests that their measurementswere taken on filters after removal from the vacuumchamber in which they were prepared. In that case,since the removal of water with increasing temperaturesleads to lower values of X, their values of (60/0) wouldbe expected to be lower than for filters not exposed toatmosphere, the greatest difference occurring forcryolite which is usually much more porous than zincsulfide. Thus, the two comparative values of [(I/O)a0/d0]& are clearly not in accord.
(2) Persin et al.2 7 measured a value of
00 H -5 K-1.
(ma X - 0.8 X 10
Since this measurement was made on a filter with a veryhigh-order zinc sulfide spacer (mH = 32), it can be takenwithout significant error as a measure of [(1/1k) &k/aO]H.A correction for the effects of dispersion by a factor
1 - XD anH
nH axleads to a value of -0.9 X 10-5 K- 1 , which is at leastqualitatively in accord with the argument outlinedabove, since the measurement was made on a filterpreviously exposed to atmosphere.
B. On Exposure to Atmosphere
The processes which take place when optical coatingsare exposed to atmosphere, specifically the effects ofwater penetration, are most readily observable in in-
defect
I I -1 - e -t / Uz-Ie-t/lc ,L 1 - eIt /xc JI I
Fig. 6. Schematic diagram illustrating the water penetration processin the cryolite and zinc sulfide layers of a coating.
terference filters. Although Koppelmann28 did notrecognize them as such, as early as 1960 he showed mi-crographs and corresponding transmission spectra ofdefects on simple metal-dielectric-metal (MDM)Fabry-Perot filters which quite clearly exhibit patternsattributable to water penetration. He observed thesame effects in all-dielectric filters consisting of zincsulfide and cryolite layers in the design:air(LH) 3 H2LH(LH) 3 glass. Such patterns were ob-served again by Pulker 10 in MDM filters and were ex-plained by him in terms of the penetration of water fromthe atmosphere.
A structural model of the water penetration processis shown schematically in Fig. 6 for a multilayer systemof cryolite and zinc sulfide. Liquid water collects atgross defects (shown at the right of Fig. 6) such as pin-holes which generally extend from the air to the sub-strate. The water then penetrates laterally into thelayers by capillary condensations via the porousstructure, and, as will be shown, the water penetrationis appreciably more rapid in the cryolite layers than inthe layers of zinc sulfide, because of the lower porosityof the latter material. Thus, in Fig. 5 the outer circlesshow the penetration fronts in the cryolite layers of afilter with a zinc sulfide spacer. In the initial stagesthese fronts advance at a rate of -1 mm h-1 outwardfrom the central defect. This fact leads to speculationas to why the atmospheric water does not penetrate thewhole layer in a direction normal to the layer boundariesin a matter of seconds, since the whole structure is onlya few micrometers thick. Macleod and Richmond 2 9
attempted to explain the observed lateral penetrationaway from gross defects by postulating that the zincsulfide layers and the layer boundaries act as barriersto penetration normal to the layer boundaries.Whereas the former is plausible, the latter conflicts withobservations of the cross-sectional structures of opticalcoatings which indicate very strongly that layerboundaries are regions with defect densities muchhigher than in the materials themselves. It is for thatreason that the process of exposing the cross section of
Fig. 7. Transmittance changes at the design wavelength in a C7 filterdue to relative refractive-index changes bnL/nL = 1.72 X 10-2 andbnH/nH = 1.32 X 10-3 in individual layers of cryolite and zinc sulfide,
respectively.
a coating quite frequently leads to a stepwise fracturewhich runs normal to the layer boundaries across thelayers themselves and then along the boundaries (forexample, Fig. 1). Consequently, the layer boundarieswould not be expected to act as barriers to water pene-tration. Thus, in the model depicted in Fig. 6, thepenetration of a zinc sulfide layer is shown to proceedfrom the gross defect as well as at various points in thelayer across the boundaries from saturated regions ofthe cryolite layers on either side. Such a mechanismwould explain the irregular darker patches (Fig. 5)within the circular regions, the darker patches beingidentified (Fig. 7) with penetration of the ZnS spacerlayer. The irregular nature of the water penetrationfronts in zinc sulfide compared with the markedly cir-cular fronts in cryolite is not necessarily attributable tofundamentally different mechanisms of penetration inthe two materials but merely to the different penetra-tion rates and densities of defects acting as sources ofwater. Irregular penetration fronts are not observedin Fig. 8 which corresponds to a filter with a cryolitespacer. Whereas seven grey levels are easily distin-guishable and identifiable (Fig. 9) with the variouscryolite layers in the filter, the sensitivity of the trans-mittance to changes of refractive index of the zinc sul-fide layers is very low in this case. The central blackcircle corresponds to penetration of the spacer.
At this stage a digression is necessary to consider apoint of practical importance. The detail observablein transmission micrographs such as those of Figs. 5 and8 obviously depends on the type of objective that is usedin the (Reichert) microscope. To obtain high lateralresolution, objectives of relatively high N.A. must beused. However, the collection of light over the corre-spondingly large angles leads to an effective deteriora-tion22 of the filter properties, specifically to a broad-ening of the passband, which reduces the contrast pro-duced by refractive-index changes in the various layersof the filter and hence the depth resolution of thetechnique. A satisfactory compromise must thereforebe reached between the usual, lateral, and depth reso-lutions.
I . I
100 m
Fig. 8. Optical micrograph of the water penetration pattern in a C+filter observed with radiation from the sodium source in the initial
stages of the stabilization process in air.
xto
9:
a) d-01
o 7
U 6
2
1 :0:-5
1-1: l . . . . . . . . . ._ . . . . I I I
77 Tn1nn E 1 7 X X nnnr-i:H L H L H L H L H 4L H L H L H L H L H
Fig. 9. Transmittance changes at the design wavelength in a Cc filterdue to relative refractive-index changes nL/nL = 1.72 X 10-2 and
nH/nH = 1.32 X 10-3 in individual layers of cryolite and zinc sulfide,respectively.
In interpreting Figs. 7 and 9 it should be noted thatthe calculated changes of transmittance for the givenchanges of refractive index relate to normally incidentmonochromatic radiation. Moreover, the results referto a change in a single layer at a time, whereas in mi-crographs such as those in Figs. 5 and 8, the effects inthe various layers are superposed. Thus, Figs. 7 and 9serve only as approximate guides in identifying thelayers affected by water penetration from the micro-graph patterns.
If the water penetration fronts are considered to ad-vance approximately according to exponential functionsof time, with different time constants TC and T2 for
Fig. 10. Computed simulation of the evolution of the transmittancein the spectral passband of a C. filter coating on exposure to atmo-
sphere; to be compared directly with Fig. 4.
cryolite and zinc sulfide, respectively (Fig. 6), the areaof the filter can be divided for simplicity into three re-gions. In the first region none of the layers is pene-trated by water, in the second only the cryolite layersare penetrated, and in the third all the layers are pen-etrated. Consequently, the observed evolution of thetransmittance in the passband (Fig. 4) can be simulatedby the summation of three Airy functions weighted bythe appropriate exponential functions of time. EachAiry function corresponds to one of the specified regionsof the filter, the main distinguishing feature of eachbeing the wavelength of peak transmittance which isstrongly dependent on the refractive indices of thelayers and hence on the state of water penetration. Thethree wavelengths can be identified from Fig. 4, corre-sponding to a Cp filter with XD = 546.1 nm, at 545.6,546.2, and 547.5 nm, the first corresponding to a wave-length close to the wavelength of peak transmittance ofthe filter stabilized in vacuo, and the third, after 33days, to the air-stabilized condition. From a knowledgeof the values of these wavelengths and values of the peaktransmittance and bandwidth in vacuo, the evolutionof the filter passband can be simulated, as shown in Fig.10. A more sophisticated model would embody dif-ferent water penetration rates in each layer, certainlyfor the zinc sulfide layers.
The change of wavelength from the vacuum-stabi-lized state of a filter to the air-stabilized state, i.e., 5ANin Table V, can obviously be used to provide informa-tion about the changes of refractive indices of the layermaterials brought about by water penetration. Inparticular, if measurements are taken of 3 AN for filters(C+) with zinc sulfide spacers as well as for ones (C+)with cryolite spacers, Eq. (2) can be used to infer thechanges of refractive indices of both cryolite and zincsulfide, since, if the layer thicknesses are assumed toremain constant during the water penetration pro-cess,
(fb) =nL/nL )(3)~bn/lnJ
With the values of 3X, for C' and C+ filters from TableV substituted into Eqs. (2) and (3), values for the com-
ponents of (fn) are bnL/nL = (1.72 ± 0.08) X 10-2 andbnH/nH = (1.32 ± 0.20) X 10-3. When these values areused to evaluate Xu, for U' filters on the assumptionthat in the latter type of filter only the layers near thesubstrate up to and including the spacer are porous, atheoretical value 5X, = 1.21 (Table V) is obtained,which is in reasonable agreement with the measuredvalue, bearing in mind the crudity of the assumptionsabout the porosity of the layer materials in the uncooledfilters. The assumptions are based on the observationsthat in such filters the substrate temperature increasessteadily as the deposition proceeds and that the layersdeposited at higher temperatures have a predominantlycolumnar structure with a lower porosity than theearlier layers. Indeed, in the heated filters (Hi) theporosity is so low that no changes in properties occur onexposure to atmosphere.
From the components of (fn) it is useful to infer thedegree of porosity of the two materials by the use of theMaxwell-Garnett30 relationship:
K - KB
K + 2KB(4)
where
A= K, -KB K = n2.K, + 2KB
K, KB, and KI are the dielectric constants of the porousmaterial, the corresponding bulk material, and theimpurity in the pores, respectively, and q is the volumefraction of the bulk material. A simple transformationof Eq. (4) leads to K = KB(1 + 2qA)/(1 - qA).Therefore,
n = nB(l + 1.5qA), (5)
if qA << 1. From Eq. (5) the change of refractive indexon water penetration of the pores is given by
1n n -n n_1= = qG,n nB
(6)
where G = 1.5(A - Av), and A, and A, are the valuesof A [Eq. (4)] with KI = (1.33)2 and 1.00, respectively.The values of q corresponding to the values of (n)quoted above are qL = (6.8 ± 0.3) X 10-2 and qH = (1.04± 0.16) X 10-2 which are in good agreement withpacking fractions (1 - q) quoted elsewhere.29 More-over, these values show that the cryolite layers are ap-preciably more porous than those of zinc sulfide.
Whereas the values of q are interesting in themselves,the main purpose of deducing them is to enable thevalues of refractive indices of the layers to be obtainedvia Eq. (5) for both vacuum and air-stabilized porouslayers. These values then enable the optical propertiesof the filters to be predicted in both stabilized states.
It should be noted, however, that Eq. (4) refers tospherical inclusions of impurities in the bulk material,a structure probably not closely related to the columnarmorphology of the materials in question. On the otherhand, the departures of the refractive indices of thelayer materials from their bulk values brought about byporosity are relatively small, so that the adoption of amore realistic structure model31 is not likely to affect
the issues significantly, certainly not sufficiently towarrant the additional complexities.
V. Precision of the Optical Thickness MonitorAs has already been emphasized, the precision with
which the optical thicknesses of the individual layersbeing controlled during deposition is a factor whichshould be negligible in the process of assigning less thanperfect performance in multilayer filters to the variouspossible defects of layer structure (Table II); it istherefore important to obtain estimates of this preci-sion. This is achieved most conveniently in terms of thereproducibility of the wavelength of peak transmittance,which is simply related to the errors of thickness of theindividual layers. In fact, for a filter consisting of 2N+ 1 layers, the departure ClXmax of the wavelength ofpeak transmittance from the design wavelength D isrelated to errors Adi in the layer thickness by
N4 E liniLAdi
AXmax = i=l (7)
(= ni )according to the formalism of Lissberger and Wilcock,2 2
where i are the first N integers starting at i = 1 for thespacer. Also,
11 = 1/2, P1 = mL ormH,
i Pi = ci- 1 for i 1 and c = nL/nH.
If the errors are distributed randomly about corre-sponding means in the various filters in a group and therandom rms error aUd in the thickness is assumed to bethe same for each layer, Eq. (7) leads to a value for therms error Cx in the wavelength of peak transmittancegiven by
4 (ini)21 1/2xJ;< = * ~~~~~~~~~(8)N X n,) (5)
APi 1 _ aiil ni /
Thus, the random error in the spectral location of thefilter passband is determined predominantly by that ofthe spacer thickness. Moreover, since Cd (ax, thereproducibility of the wavelength of peak transmittancegiven by a is a measure of the precision with which thethicknesses of the layers are being monitored duringdeposition, subject to the following reservations.
(1) Clearly the random error in the thickness of aparticular layer due to the monitoring process dependson the shot noise in the detector photocurrent which,in turn, depends on the transmittance of the depositedsystem at the end of the deposition of that layer. Thus,a:d is not, in fact, the same for each layer of a filter.
(2) The rms error in the wavelength of peak trans-mittance may well depend on factors other than thoseattributable to the monitor. For example, the stabili-zation processes will be shown to be subject to randomvariations.
(3) The systematic variation of temperature, par-ticularly for uncooled filters, is likely to be subject to
fluctuations which contribute to a-.Values of A are given in Table V as errors in 6 X, and
6 XA for filters stabilized in vacuo and in air. The valuesdenoted by M refer to eight filters of the group UPprepared by manual control, whereas all other quotedvalues are for filters prepared by automatic controlusing a microprocessor system. 13 The following con-clusion can be drawn from the measurements of 6 Xv and6 XA.
(a) The values of oa for filters prepared by use of amicroprocessor system are invariably lower than forfilters prepared manually, pointing to significant im-provements in the precision of the control of thicknessof layers during deposition. The figures mean that, forU' filters prepared by manual control, 67% of the filterscould be prepared and stabilized in vacuo with wave-lengths of peak transmittance within 0.14 nm of thedesired value. With microprocessor control, the cor-responding proportion of filters rises to 95%, and, in thecase of HA filters, to 99.95%.
(b) On stabilization in air, the values of A increasemarkedly, to some extent obscuring the benefits of theuse of the microprocessor system. This means that thestabilization process itself is subject to random fluctu-ations. Significantly, because of the more compactstructure of layers deposited on heated substrates, nochange of wavelength occurs for the Hi filters on ex-posure to atmosphere. Therefore, the benefits of theuse of microprocessors are maintained for such filterseven on exposure to air. Filters with cryolite spacerssuffer the worst effects on exposure to air because notonly does the water penetrate the layers but also it leadsto fissures in the layers (Fig. 11).
L I
1.0 mm
Fig. 11. Optical micrograph of a C+ filter observed in transmissionwith radiation from a sodium source 25 days after the filter was ex-posed to atmosphere; the development of fissures which accompany
(c) As expected, the HA filters have the lowest valueof a-x because the temperature of the substrate is undercontrol during the deposition of the layers and is littleaffected by radiation from vapor sources. In the caseof all other types of filter, variation in changes of tem-perature during deposition can contribute to ax.
VI. Analysis of the Measured Optical Properties ofFilters
The optical properties of narrowband filters that areusually of direct practical interest are the passbandwavelength of peak transmittance, the peak transmit-tance itself, and the half-bandwidth, all in the air-sta-bilized condition. However, from the standpoint of aninvestigation of the causes of less than ideal perfor-mance, the reflectance at the wavelength of peaktransmittance is also an important optical function,since combined with the corresponding transmittance,it leads to a value of the total loss, L = 1- T-R. It iswell-known that the latter bears a close relationship 3 2
to the half-bandwidth.When the values of the refractive indices of the air-
stabilized layer materials, deduced as indicated in Sec.IV, are used to calculate the transmittance losses (1 -T) and reflectances R at the wavelengths of peaktransmittance, as well as the half-bandwidths, theagreement between the measured (Table V) and cal-culated values is poor, even when the effects of ab-sorption in zinc sulfide are taken into account by as-signing 10-4 to the imaginary part of its complex re-fractive index, this particular value being justified bythe preliminary results of laser calorimeter measure-ments 1 5 of the absorptance of filters with zinc sulfidespacers. Indeed, the difficulty of reconciling the mea-sured and theoretical performances of the filters canonly be overcome when scattering due to interfacialroughness is also considered, the necessity for thishaving been pointed out in 1956 by Giacomo3 3 to ex-plain the appreciable radiant flux scattered out of thedirect and specular beams when radiation interacts withnarrowband spectral filters.
The procedure for including the effects of surfaceroughness in the evaluation of normal transmittanceand reflectance is first to assume that only uncorrelatedroughness at the boundaries of the spacer is of impor-tance for filters with zinc sulfide spacers and at thesecond boundaries from the spacer for filters withcryolite spacers. These assumptions are justified bynoting the relatively very high electric field amplitudesat the chosen pair of boundaries (Figs. 12 and 13).Moreover, because of the symmetry of the electric fielddistribution about the spacer of a given filter, the scat-tering at each of the two important boundaries is thesame, and consequently uncorrelated roughness at onlyone of these boundaries needs to be considered inevaluating the total scattered radiant flux and its effectson filter performance. That identical roughness (i.e.,perfectly correlated and with the same rms values) atthe spacer boundaries produces no scattering, andtherefore no deterioration of filter properties is note-worthy.
LATER
GEOMETRICAL DISTANCE
Fig. 12. Electric field distribution in filters with zinc sulfide spacers(8H) but no AR layer.
GEOMETRICAL DISTANCE
Fig. 13. Electric field distribution in filters with cryolite spacers (4L)but no AR layer.
With these assumptions and the refractive indices,including dispersion and absorption, appropriate to agiven type of air-stabilized filter, the transmittance lossand reflectance can be calculated for normally incidentradiation and a range of values of the rms surfaceroughness using a previously described' 2 model for totalscatter. Figure 14 represents a typical result of thisprocedure, the random fluctuations of the theoreticalresults about mean curves reflecting the statistical na-ture of the calculation. To obtain an estimate of therms roughness a- for a particular filter, two values areread from the curves, one, T, corresponding to themeasured value of 1 - T and the other, R, to themeasured value of R. is taken as the mean of UT andaR. This procedure is repeated for each filter in agroup, and the group means quoted in Table V are thenused to obtain the theoretical values of (1 - T) and R.Finally, the calculations, using the group values of a, areextended over the whole spectral range of the filterpassbands to obtain the theoretical values of the half-bandwidth which are compared (Table V) with themeasured values of both the vacuum- and air-stabilizedconditions of the filters.
Fig. 14. Theoretical variation oftransmittance loss (1 - T), reflec-tance (R), and total loss (L = 1 - T- R) as a function of the rmsroughness on one of the spacerboundaries for a CZ filter with XD
= 589 nm.
r.m.s. Roughness (nm)
The following important features of the comparisonbetween the experimentally determined and theoreti-cally predicted values of transmittance loss, reflectance,and bandwidth are worth noting.
(1) The differences between the measured and cor-responding theoretical values are mainly less than theerrors in the mean experimental values. This generallygood agreement supports the validity of the theoreticalmodel and the assumptions on which it is based, par-ticularly that the optical performance of narrowbandspectral filters cannot be described satisfactorily unlessboth absorption and scattering are taken into account.It should be emphasized that the quoted errors in themeans. represent mainly the lack of reproducibility ofthe stabilized filter properties. Random errors inmeasurement make only a small contribution to thequoted errors.
. (2) The fact that all the experimental results in eachmajor group (Us, C, H, and Cc) of filters can be ex-plained on the basis of a single value of rms surfaceroughness a- suggests that its value depends predomi-nantly on the substrate temperature. Clearly, the valueof a increases with substrate temperature, consistentlywith the expectation that crystallite size in the layermaterials, with which the value of a- is closely related,also increases with temperature. At first sight thevalues of a- are surprisingly small by the practicalstandards of very smooth surfaces despite the fact thatthey correspond to the effects of roughness at a singleboundary only. The implied inconsistency is resolvedwhen it is remembered that the roughness to which relates may be superimposed on significantly greater('--nm rms) identical roughness at the spacerboundaries, which cannot be detected by optical ob-servations in the spectral passband region of the filter.The figure of 1 nm for the rms identical roughness isbased on Talystep measurements2 at the air interface
of the coating and is consistent with photometric datain the spectral stopband region of the filter, where it actsas a reflector.
(3) With the exception of the C, filters with a designwavelength of XD = 546.1 nm, the inclusion of a quar-terwave antireflection layer of cryolite increases thetransmittance loss, contrary to prima facie expecta-tions. The introduction of such an AR layer would leadto a 3% reduction in the reflectance and hence in thetransmittance loss in filters free from absorption andscattering. At the same time it leads to a reduction inthe bandwidth (Table I) of -45%; and it is this factorwhich explains the transmittance loss in real filters,subject as they are to absorption and scattering. Inother words, the effect on the transmittance loss due tothe reduction in reflectance is more than compensatedby increases in absorptance and scattering. Absorp-tance and scattering are also responsible for the fact thatthe observed reduction of reflectance due to the ARlayer is not quite as great as calculated for perfect fil-ters.
(4) On stabilization in air, the filter bandwidths in-crease by a few percent, HA filters being the exceptionsto the rule. These increases of bandwidth are due tochanges in the refractive indices of the layer materialson being penetrated by water.
(5) The advantageous properties of filters (Hr)prepared on heated substrates have already beenmentioned in connection with the problems of precisemonitoring of the optical thicknesses of layers duringdeposition. However, it is clear that freedom fromsignificant temperature changes of the substrate duringdeposition of the layers and stability of filter propertieson exposure to atmosphere are obtained, as yet, at theexpense of a marked deterioration of performance at-tributable to a significant increase in interfacial
roughness and hence in the scattered radiant flux andtransmittance loss.
(6) Filters (C: with cryolite spacers have by far thebest performance in vacuo of all types investigated.This is achieved by virtue of the low absorptance incryolite and the low interfacial roughness at the secondboundaries from the spacer (Fig. 13), the latter beingbrought about by the low substrate temperature duringdeposition. Unfortunately, C filters suffer cata-strophic changes on exposure to atmosphere (Fig.11).
VIl. Conclusions
The foregoing discussion of filter properties has takenaccount of the various physical processes involved in thepreparation, stabilization, and measurement of nar-rowband filters. In particular, the effects of substratetemperature, water penetration, interfacial roughness,dispersion, and absorption have been considered in theireffects on the optical properties of filter coatings. Thefact that the results of detailed measurements of theperformance of such coatings can be predicted theo-retically gives confidence in the validity of the modelsused for their interpretation.
More specific conclusions are:(1) The main obstacles to a closer approach to ideal
performance in narrowband filters are the absorptanceof the layer materials and the interfacial roughness.
(2) Freedom from the effects of water penetrationon exposure to atmosphere is achieved in multilayersof cryolite and zinc sulfide by deposition onto heatedsubstrates. However, at present, this stability is ob-tained at the expense of a deterioration in optical per-formance attributable to an increase in interfacialroughness and hence in scattering.
(3) Appreciably smaller bandwidths can be achievedin narrowband spectral filters by the use of a singleadditional quarterwave layer of cryolite as an antire-flection coating for the substrate. The improvementof bandwidth is accompanied by a marginal decrease inpeak transmittance.
Evidently, further improvements in the performanceand stability of optical coatings will follow from theacquisition of more detailed knowledge of the mecha-nism of film growth to a point where the structure of alayer can be controlled with adequate precision to allowthe ideals of amorphous or single crystal materials withsmooth boundaries to be approached.
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This work was presented as an invited paper34 at theSpring Meeting of the Optical Society of America(Rochester, May 1982).
One of the authors (D.R.G.) is grateful to the de-partment of Education (Northern Ireland) for the fi-nancial support of a Research Studentship.
