Visual detection of organic monomolecular films byinterference colors

Torbjorn Sandstrom, Manne Stenberg, and Hakan Nygren

Thin (<10-nm) adsorbed organic films are visible to the unaided eye, if the substrate is first covered witha dielectric film giving a strong interference color, a so-called sensitive color. It is found that a single low-index dielectric film on an absorbing substrate gives optimal sensitivity. A detection limit in the subna-nometer range is predicted and confirmed by experiments. Two practical designs using silicon and glasssubstrates are discussed. These slides can be produced by industrial methods and have proved to give goodvisualization of monomolecular protein films, e.g., antigen-antibody layers. They have a detection limitof 0.7 nm or 100 ng of protein/cm 2 surface.

1. Introduction

Changes in the reflection properties of surfaces dueto adsorption of thin organic films have been studiedsince the mid 1930s.1,2 Langmuir and co-workers notedthat the adsorption of a single monolayer of proteinproduced a very striking change in the interference colorof a polished chromium slide covered with a multilayerbarium stearate film. To give strong interference ef-fects, the slide had to be viewed in polarized light at alarge angle of incidence, and the barium stearate filmthickness had to be of the order of 100 nm. The aim ofthese early studies was to measure the thickness of lipidor protein layers on the surface, and the method wasdeveloped further using monochromatic light andphotoelectric detection. In 1945 this line of develop-ment matured into the ellipsometer, a new instrumentwith high sensitivity and high accuracy.3

Later it was realized that the influence on the inter-ference colors by thin organic layers could be used as aqualitative indication of an antigen-antibody reactionon a surface.47 Simple and sensitive immunoassayscould be based on such reflection phenomena. For areview, see Ref. 8. All slides used for this purposeconsist of a metal substrate with a dielectric layer ontop. Systems used are barium stearate on chromium,4

Hakan Nygren is with University of Gothenburg, Histology De-partment, S-400 22 Gothenburg, Sweden; the other authors are withChalmers University of Technology, Research Laboratory of Elec-tronics, S-412 96 Gothenburg, Sweden.

Received 30 May 1984.0003-6935/85/040472-08$02.00/0.( 1985 Optical Society of America.

tantalum oxide on tantalum, 5 and indium oxide on agold-indium alloy.6 A similarly functioning systemwith a semitransparent metal layer on top of a dielectriclayer on a metal has also been described.7

Although a number of groups have used dielectricfilms to enhance the contrast caused by a thin biolayeron a reflecting surface, there is no systematic study ofthe phenomenon. Likewise, there is no system pro-posed which promises both simple fabrication and goodbiochemical properties.

It is the purpose of this paper to discuss such contrastslides in general and to present two practical designs.These slides have silicon, glass, or plastic as substratematerial and have a top dielectric layer of silicon diox-ide, which has excellent mechanical and chemicalproperties (patent pending). By making the surfacehydrophobic, an even protein coating with strong ad-hesion to the surface is obtained. Protein layers thickerthan 0.7 nm are clearly seen as a change in the color ofthe slide.

II. Theory

A. Interference of Light in Thin Films

A dielectric surface layer, with a lower refractiveindex than the underlying substrate, changes the re-flecting properties of the substrate and produces in-terference colors. Within certain ranges the thicknessof such a film can be fairly well judged from the inter-ference color. Part of the light is reflected at the air-dielectric interface and part of it at the dielectric-sub-strate interface (Fig. 1). There are also successivelyweaker multiple reflections, which are neglected for themoment. The dielectric-substrate part of the light isdelayed relative to the air-dielectric part, and the twoparts interfere with each other. When light of one coloris attenuated in the reflection through destructive in-

472 APPLIED OPTICS / Vol. 24, No. 4 / 15 February 1985

I, = 2 (If 1 [1 + cos(ah)],

a = 4[(nf)/X].

(2)

(3)

The intensity difference for a thickness difference Ahis

Air = d Ah = -21,1 f a oa sin(ah)Ah.dh \ ~flf+l (4)

For photoelectric detection of a thickness difference,the thickness should be chosen to maximize Eq. (4).For detection with the unaided eye the situation is dif-ferent, however, since the eye is more sensitive to con-trast than to intensity level. The intensity contrast Sis

Fig. 1. Reflection from a surface with and without a dielectric surfacelayer. With the dielectric layer, the reflected beam is split into anumber of components. When the optical path is different for thecomponents, they can add up to a smaller amplitude than in the case

without the dielectric layer.

NORMALIZED THICKNESS (n h)

Fig. 2. Reflected monochromatic intensity I from an antireflectionlayer. The layer has a perfectly matching refractive index but avarying thickness. The reflectivity vanishes for a layer with an opticalpath length of 7r/4, curve a. The change of reflectivity dI/dh is largestat 7r/8 and vanishes at 7r/4, curve b. The contrast, dI/dh .1/I, tends

to infinity at Tr/4, curve c. Arbitrary units.

terference, i.e., when the interfering parts of the lightcancel each other, the reflected light appears to have thecomplementary color. An interference color is pro-duced. The interference colors are most saturatedwhen the reflected intensity in a narrow wavelengthband is totally extinguished. For a substrate with a realrefractive index n, and normal incidence, this occurswhen the film index nf is9

nf = v/S-. (1)

For monochromatic light with the vacuum wavelengthX and for moderate refractive indices, Eq. (1) gives anapproximate reflected intensity, which is a periodicfunction of the film thickness h:

Ar sin(ah) Ah.

Ir 1 + cos(ah)(5)

According to Eq. (5) S tends to infinity for values of hfor which the reflected intensity approaches zero (seeFig. 2). The conclusion is clear: a dielectric layer thatforms a perfect antireflection (AR) coating raises themonochromatic contrast to very high values. We shalluse this result only as a starting point for analysis of thewhite light case. A brief assessment of the monochro-matic interference for visualization of bioreactions willbe given in Sec. VI.

B. Color Contrast

The eye is more sensitive to a color change than to achange in intensity, and the use of white instead ofmonochromatic light gives higher sensitivity and moreconvenient viewing. White light consists of manywavelengths, and only a narrow band of wavelengths isextinguished by a single dielectric layer. A thin coatingattenuating the blue light gives a reddish reflection, anda slightly thicker coating makes the reflection bluish byextinguishing the red light. A thin organic layer on topof the AR layer makes it appear thicker and causes theinterference color to change toward blue.

The theory of interference colors has been reviewedby Kubota'0 : The strong thickness dependence of thefirst-order purple, known by the term sensitive color,has been studied for a long time. Since the purpose ofthese studies is somewhat different from the presentone, we shall make a new start by choosing an inde-pendent model and comment on previously relatedfindings in the concluding section of the paper.

How thin can biolayers be and still remain visible?For a quantitative treatment of the discrimination ofinterference colors, a mathematical model of the visualperception is needed. A number of models for theperception of color differences between adjacent areashave been proposed.1" None of the models is true in thesense that it gives a good description of the perceptionof color under all circumstances. Shape, size, and glossof the compared colored surfaces, background colors,lightness, and so on influence the sensitivity of the eye.We have compared three different models and chosenone of them on the basis of our subjective judgment ofthe agreement with experiments.

15 February 1985 / Vol. 24, No. 4 / APPLIED OPTICS 473

r1!-2

-CI

R

I--

I�tLI

jI i

a.-

6

4 -

2 -

0 50h (nm)

100

0.4

0.3

150

Fig. 3. White light reflection and color contrast of a n, = 2.25 sub-strate with a nf = 1.50 dielectric layer: a, reflected intensity vs thethickness of the dielectric layer; b, c, and d, color contrast for a 1-nmthick organic layer calculated by the CIELUV, CIELAB, and FMC

II models, respectively.

To find quantitative measures of the interferencecolors we have calculated the reflectivity of the surfacefor each wavelength using a computer program devel-oped for calculations in ellipsometry. The programfollows closely the S matrix theory in Ref. 12 and givesthe complex amplitude reflection coefficients of amultilayer structure for both polarization eigenstatesat any angle of incidence. Nonpolarized light was as-sumed, and the two reflection coefficients were squaredand added to give the unpolarized reflectivity of thesurface. Lightness and chromaticity coordinates, thenormal way to describe a color, were obtained using thestandard procedure found in most textbooks on color:the reflectivity was integrated with the weight functionsof the 1931 CIE Standard Observer.' 1 CIE ColorSource B representing noon sunlight was chosen as areasonable compromise between different light sourcesused in the laboratory.

The lightness and chromaticity coordinates must betransformed to new color coordinates in which the leastperceptible difference has the same magnitude for allcolors and intensities. Three different transformationswere tried: the CIELAB and CIELUV systems rec-ommended by the Commission Internationale de l'Ec-lairage and the Friele-MacAdam-Chickering II Sys-tem." The latter is based on a mathematical model ofthe neural processes in the eye and the signal condi-tioning performed by the brain, while the CIELAB andCIELUV are mathematically simple transformationsbased on color discrimination experiments. All threemodels give a single numerical value for the differencebetween two colors, but the values obtained by differentmodels cannot in any simple way be compared with eachother. The units in the three models are of the sameorder of magnitude, and the discrimination thresholdof the eye has a value of the order of 1 in all threemodels.

Figure 3 shows the color difference produced by a1-nm biolayer with index 1.5 on a perfect antireflection

X 1.0

Fig. 4. Chromaticity coordinates for interference colors of a nf = 1.50dielectric layer on a n, = 2.25 substrate and thicknesses from 0 to 600

nm.

coated slide with index 2.25. The dielectric film hasindex 1.5 equal to that of the biolayer. The threemodels give different color differences S and differentdependences of S on the thickness of the dielectric layer.To compare the models we have multiplied the colordifference obtained by the FMC II model by the nu-merical factor 0.41 to make all three models give ap-proximately the same sensitivity at 50 and 150 nm. Themost important difference between the models is thebehavior at low reflected intensities. On the basis ofour experiments we state simply that in this case theFMC II model describes the sensitivity best, althoughit may give too high sensitivity at very low intensities.The choice of the model will be more thoroughly dis-cussed later. At this point we only note that we con-sider FMC II to be the most realistic model in thiscontext, and it will be used in the following analysis.Note that the unit used here differs from that of thestandard FMC II model by the numerical factor 0.41.It corresponds to the units of CIELUV and CIELAB,which are more widely used.

C. Single Dielectric Layer

Curve d in Fig. 3 shows the calculated sensitivity Svs dielectric layer thickness for the 1.5 on 2.25 single-layer model system in the preceding paragraph. Thecolor contrast for a 1-nm thick biolayer rises slowly fromzero at zero thickness. At 80 nm it rises steeply and hasa narrow peak at 93 nm. Above 100 nm it is back at alow value.

Figure 4 shows the chromaticity coordinates of theinterference colors for different thicknesses of the di-electric layer. An illustration showing the chromaticitydiagram in color can be found in Ref. 13. The inter-ference color starts at white for a very thin layer, reachesa relatively saturated (close to the boundary) yellow at85 nm, and passes rapidly through orange, red, purpleto blue within a few nanometers. A comparison to theintensity curve in Fig. 3 shows that the transition fromred to purplish blue takes place when the intensity isvery low.

474 APPLIED OPTICS / Vol. 24, No. 4 / 15 February 1985

6

0 300 600h (nm)

Fig. 5. Same as Fig. 3 but showing only FMC II. The intensity,curve a, and the sensitivity, curve b, functions are shown for thick-

nesses up to 600 nm.

For thicker coatings the color returns almost to whiteand makes another turn through red, purple, and blue.The second turn has a much lower pace, and the sensi-tivity is expected to be lower than for the first order ofinterference colors. In Fig. 5 it is seen that the sensi-tivity function has another maximum at 280 nm but notas high as the first one. The intensity curve shows howthe interference of white light gets weaker with growingthickness. Only the first order gives an attenuationstrong enough to be used practically.

D. Angle of Incidence

It was mentioned above that Langmuir used polarizedlight at large angles of incidence. The reason is thatbarium stearate gives strong interference on chromiumonly at large angles of incidence. For oblique incidencethe reflection coefficients differ between light withpolarizations parallel and perpendicular to the plane ofincidence.9 The relationship between film and sub-strate index (1) holds only for perpendicular incidence,while for oblique incidence the optimal film index de-pends on the polarization of the light. For slides in-tended for use in simple visual immunological tests,viewing at a fixed angle or through polarizing filters isa major drawback. Near-normal incidence gives theleast critical viewing.

We have computed the dependence of the sensitivityon the angle of incidence for the 1.50 on 2.25 systemabove. For deviations up to 300 from perpendicularincidence the sensitivity is only slightly affected, whileat larger angles it falls rapidly. An interesting conse-quence is that the slides work well under the micro-scope. Optical resolution of small details requires thatdivergent light be used, the more divergent the smallerthe details to be resolved. Numerical simulation showsthat a marked deterioration of the performance sets inonly at numerical apertures of 0.4 or larger. This resultholds also for the physical implementations describedbelow. It is, however, important to use a high-qualitymicroscope with no stray light that reduces the contrast.

1 0

0.3

0.2

Iin, le

0.04

.0.03

0.02

0.01

0 1 2 3 4 5nf

Fig. 6. Maximum sensitivity, curve a, and minimum reflectivity,curve b, for perfect single-layer antireflection coatings with differentfilm indices. In each case the substrate has the matching index nf.

It is also important to have a sharp edge between thedetected protein layer and the surrounding area, sincethe eye enhances the contrast of sharp edges and re-duces that of slow variations.

III. Optimization

Calculations performed using the computer modelshow that very little can be gained in optical perfor-mance from using a multilayer structure instead of asingle-layer perfect AR coating. Multilayer antire-flection coatings are often used to give wavelength-independent suppression of reflections. Our goal is theopposite: to find a coating with a strong wavelengthdependence. Other multilayer structures, e.g., inter-ference filters, do have strongly wavelength-dependentreflections, but a biolayer on the surface changes thereflection of such structures very little since the opticalproperties are determined mainly by the interfaces in-side the multilayer structure.

The biolayer changes the optical path difference be-tween interfering parts of the light. The greater thetotal path difference, i.e., the thicker and more com-plicated the interfering structure, the smaller is therelative change caused by the layer at the surface. Theconclusion is, somewhat surprisingly, that the mostsensitive system for detection of biolayers is a single-layer coating, while in most other applications perfor-mance can be improved by additional dielectriclayers.

A slide with a single layer with index 1.50 on a sub-strate with index 2.25 gives one unit of color differencefor a biolayer only 0.12 nm thick. The sensitivity S hasan approximate inverse dependence on the index of theAR layer, Fig. 6, provided that in each case the substratehas a matching index. The organic layer can be thoughtof as an added thickness to the underlying dielectriclayer. The effective thickness change is not equal to thegeometrical thickness but depends on the reflection

15 February 1985 / Vol. 24, No. 4 / APPLIED OPTICS 475

S...S

coefficients at the two surfaces of the biolayer and thuson the index difference between the biolayer and di-electric layer.

Low-index films give high S values, but they also havea low overall reflectivity, which makes more elaboratearrangements for viewing necessary. Curve b in Fig. 6gives the minimum reflectivity vs film index, a relevantmeasure since the reflectivity minimum corresponds tothe sensitivity maximum in Fig. 3. As will be discussed,viewing conditions can be made to compensate for lowreflectivity, but there is a practical limit where poorreflection becomes a restriction on the applications ofthe slides. We have found that films with indices in the1.5-2.0 range work well in practice.

The influence of deviations from optimal filmthickness and index of refraction for a given substratecan be found in Figs. 3 and 7. For the 1.50 on 2.25 sys-tem an index mismatch of more than 0.05 gives asmoother sensitivity curve with a considerably lowermaximum.

IV. Physical Implementation

It is difficult to find a single-layer system that com-bines good sensitivity, good chemical properties, me-chanical ruggedness, and simple production. Slideswith cryolite or magnesium fluoride on heavy glass andmetal oxides on metals, e.g., tantalum oxide on tanta-lum, can be produced in volume, but they have certaindrawbacks. Coatings with indices below 1.45 are me-chanically and chemically delicate, and they give weakreflections. Slides with metal substrates have a lowerthan optimal sensitivity, since they require high-indexcoatings. The presence of metal ions can also beharmful in many biochemical applications.

An ideal material for the top dielectric layer is silicondioxide, which has good mechanical strength, is chem-ically stable and inert, and has a relatively low index ofrefraction (1.46). We have designed and tested anumber of systems with SiO2 as the top layer. Two ofthese will be presented here:

The first system uses silicon as substrate material andhas a layer of silicon monoxide between the substrateand silicon dioxide layers. Polished silicon wafers areused in the semiconductor industry, and deposition ofSiO is a standard process. The refractive indices of thematerials are such that the thickness of the SiO2 layercan be very small. Such a thin (2-3-nm) SiO2 layer isformed spontaneously on the deposited SiO layer whenexposed to the ambient atmosphere. The opticalproperties are determined almost entirely by the mon-oxide layer, while the chemical properties of the surfaceare those of the dioxide. The calculated maximumsensitivity of a SiO on a Si slide is 5 units/nm.

For high-volume applications where the substratecost is important a glass or plastic substrate is preferableto silicon. The refractive index of these materials ismuch lower than the value 2.13 required to match asingle-layer iO2 . However, an auxiliary high-indexlayer between the substrate and SiO2 layer can be usedto raise the reflectivity of the glass to that of a n = 2.13material. If SiO is chosen for the auxiliary layer, both

S

1.0-

-

I I

I

t0 1 15 1. 6 17

Fig. 7. Influence of deviations from the perfect index for antire-flection, nf = 1.50, on a n, = 2.25 substrate. The upper graph, curvea, shows the value obtained after correction of the thickness, whilethe lower graph, curve b, gives the sensitivity at nominal thickness.

Fig. 8. Silicon slide with an SiO layer with varying thickness from0 to 150 nm that is covered with a 2-3-nm thick Si0 2 layer. A strip

in the middle of the slide is coated with a 7.5-nm thick biolayer.

layers can be deposited in one operation. With 70-95nm of SiO 2 on 40-60 nm of SiO an inexpensive glass orplastic (n = 1.50-1.70) substrate can be used. Thecalculated sensitivity is 5-7 units/nm.

For transparent substrates like glass the reflectionfrom the back surface must be suppressed since it isstronger than the attenuated front surface reflection.A simple remedy is to use a dark colored substrate, ei-ther homogeneously colored or with a dark layer withthe same real refractive index as the rest of the sub-strate. Silicon substrates absorb light strongly and donot have this problem.

V. Experimental

An antireflection layer with a wedgelike thicknessprofile, Fig. 8, was fabricated in the following way.Silicon monoxide was evaporated onto a 5-cm (2-in).polished silicon wafer (Wacker Chemie). The filmthickness and refractive index were measured using anellipsometer (Rudolph Research) and found to be 200.1nm and 2.10, respectively. The wafer was then slowlyimmersed in a dilute (1:10) HF etch. The dipping ratewas so chosen that the moment the entire wafer was

476 APPLIED OPTICS / Vol. 24, No. 4 / 15 February 1985

L , , . , ,nf

Fig. 9. Viewing arrangement to make specular reflection compensate

for low reflectivity. The lamp is seen reflected in the slide, while thebackground scatters light diffusely. The intensity of the background

can be varied at constant apparent slide lightness by changing thedistance between the lamp and table.

immersed in the etching solution, all SiO had beenetched away from the edge immersed initially. Whenexposed to ambient air after the etching, the siliconmonoxide surface was spontaneously covered with a2-3-nm thick silicon dioxide layer. The Si0 2 surfacewas made hydrophobic by treatment in a dilute solutionof dichlorodimethylsilane, and the wafer was scribedand cut to a rectangular shape. A biolayer of antigenand antibody was applied as a strip in the middle of theslide along the wedgelike thickness profile (BSA 100,ug/mliter in 0.15-M NaCl for 1 h and a-BSA diluted 1:10in 0.15-M NaCl for 2 h). Accurate film thicknessmeasurements were carried out in the ellipsometer.The biolayer was found to have a thickness of 7.5 nmwith an assumed refractive index of 1.50. A scaleshowing the silicon monoxide thickness was printed onthe slide.

Visual inspection of the slide showed that this ratherthick biolayer could be seen everywhere, except wherethe SiO thickness was below 5-10 nm. Comparison tocomputed results gives a detection limit of 1-1.5 unitsof color difference in the modified FMC II model. Thepractical limit should be set higher, -3 units, to allowfor differences between observers and different viewingconditions. The maximum contrast was found in theregion around 65 nm where the interference colorchanged from purple to blue. The theoretical sensi-tivity maximum is 4 units of color difference per 0.1-nmbiolayer at 66-nm thickness giving a maximum contrastof 30 units for 1 7.5-nm organic layer.

Figure 8 is a black and white photograph of the slide.It is seen that the maximum contrast in the photographbetween the strip and its surrounding is in the 50-60-and 70-80-nm regions. The discrepancy between thevisual and photographic interpretation comes from thecolor blindness and limited dynamic range of the pho-tographic material. The wedge was also viewed inmonochromatic light. Compared to white light a visiblecontrast was seen in a narrower thickness range.

Another experiment to confirm the predicted sub-nanometer sensitivity was performed. A nonstoi-chiometric film Si Oy, was evaporated onto a siliconwafer to a thickness giving a saturated brown-violetinterference color. The thickness and refractive indexwere measured to be 75 nm and 1.83, respectively. A0.5-nm high step was etched in the film. The step wasclearly visible to the unaided eye. Since the step wasetched in a n = 1.83 material, it corresponds to asomewhat thicker biolayer, -0.7 nm.

Experiments were also performed on a black coloredglass substrate by evaporation of a 60-nm thick siliconmonoxide layer and then a 95-nm silicon dioxide layer.Like the silicon system this slide showed saturated in-terference colors and good sensitivity.

These two types of slide have been used for immu-nological experiments, the details of which will be givenelsewhere. The sensitivity has proved to be highenough not only for simple visual detection of antibodiesbut also of protein antigen.14

VI. Discussion

The choice of the FMC II model for the subjectivediscrimination of color differences can be discussed andcriticized. All three models agree well with each otherand with empirical data at high and moderate intensi-ties, and the differences are important only at low in-tensities. The low intensity dependence of FMC IIresembles that of less complicated models used in otherstudies where only the difference in chromaticitycoordinates have been considered.10

The discrimination of colors of dark surfaces dependsvery much on the viewing conditions. In the CIELABand CIELUV models the surfaces compared are as-sumed to be relatively small and viewed against a mid-dle gray background. When seen against this middlegrey background, dark surfaces appear black by con-trast, while they would appear colored against a darkbackground. By the simple choice of a dark back-ground the discrimination of dark colors can be madebetter than in CIELAB and CIELUV.

The slides discussed in this paper have specular, i.e.,mirrorlike, reflection. While in most cases specularreflection makes discrimination of colors more diffi-cult," it can be used here to compensate for the lowreflectivity of the slides. If a slide is made to reflect thelight of a luminous surface, it appears to be much lighterthan a diffuse background (Fig. 9). In this way aspecularly reflecting surface with very low reflection canappear to have a color of medium lightness. The FMCII model, with a weak dependence of the color dis-crimination on the intensity, can be justified underthese conditions.

Admittedly there is a reflectivity limit below whichthe visible contrast vanishes, and surfaces with very lowreflectivity should be avoided. Ideally use of the slideshould require no special instruments. The experi-mental slides described in this paper have good contrastand visibility when reflecting the surface of a fluorescenttube, a matte incandescent bulb, or a lightly overcastsky. To achieve the highest possible sensitivity a

15 February 1985 / Vol. 24, No. 4 / APPLIED OPTICS 477

viewing instrument, preferably binocular, with a colli-mating lens, can be used to provide an intense lightsource. However, during our experiments with theslides we have not felt the need for such an instrumentto enhance the sensitivity. On the contrary we havefound the very uncritical viewing against a lamp or thesky both convenient and adequate.

It was shown above that very high contrast could beobtained in monochromatic light. However, the highcontrast depends on the fact that monochromatic lightcan be more totally extinguished by an antireflectionlayer than white light. At equal lightness the visibilityis better in white light due to the color sensitivity of theeye. The sensitivity function in white light is smootherand less sensitive to the angle of incidence. In conclu-sion, white light gives higher sensitivity and more con-venient viewing and does not require a special lightsource.

The shape of curve d in Fig. 3 is subjectively con-firmed by our experiments with a high and narrow peaknear the intensity minimum. The calculated sensitivityshown is high, one unit of color difference for a 0.12-nmorganic layer. The experiments indicate a usable de-tection limit of three units. Thus the sensitivity is 0.4nm in the ideal case and 0.7 nm for the two implemen-tations given. We have also confirmed that the sensi-tivity is high enough for the detection of protein antigenby immobilized antibodies.14

It is interesting to compare this sensitivity to otherinvestigations of the sensitive color. A development ofstain on glass surfaces by deposition of a nonreflectinglayer on top of the stained surface was found to have asensitivity of 1 nm.10 The film-covered reflectingsurface has a close resemblence to a two-beam inter-ferometer, where 2nfh corresponds to the path differ-ence of the interferometer. Using the interferometerdata from Ingelstam and Johansson15 the least per-ceptible thickness step with a perfect n = 1.5 should be0.2 nm. A usable detection limit should be set higher,-0.4-0.6 nm, in reasonable agreement with the exper-imental results.

We have performed numerical calculations of thesensitivity of the other systems for biolayer detectionmentioned in Sec. I. The sensitivities were in each caselower than those of our designs, mainly because of thehigh refractive index of the dielectric films used. Forthe system in Ref. 7 we assumed a semitransparent buthomogeneous metal film on top of the dielectric layer.Strong interference could be achieved by the properchoice of parameters, and dielectric layers with low in-dices could be used. The sensitivity was, however,lower than optimal since the semitransparent metallayer isolates the biolayer from the dielectric layer andreduces its influence on the interference.

The subnanometer sensitivity of the slides viewed bythe unaided eye compares favorably with optical in-struments like ellipsometers. A typical routine ellip-someter has a specified accuracy of 1 nm. But an el-lipsometer only gives the thickness at one point on thesurface or rather the average thickness of a small spot.It cannot directly measure the geometrical extension of

a protein-covered spot. Nor can it detect the very smallamounts of organic matter that can be seen through amicroscope on the slides described here. The only in-strument that can at the same time visualize thin bio-layers on surfaces and give a quantitative measure of thethickness is the comparison ellipsometer.16

The high sensitivity of the method can only be usedwhen two adjacent areas with and without the layer tobe detected are viewed simultaneously. Many experi-ments can be conceived where physical or chemicalparameters, e.g., concentration, can be translated to athickness difference between two such areas.

It is still better if the measured quantity is not thethickness but the geometrical dimensions of the areas.Then quantitative measurements can be performed bya simple geometrical measurement, and the differencebetween observers is reduced to a minimum. One wayto do this is to let the measured substance move in a gelalong the surface until it is all bound to the surface. Forbiospecific reactions and thin gels the result is a well-defined zone with homogeneous thickness. Examplesare diffusion-in-gel 7 and electrophoresis-in-gel.18

The quantity of organic substance that can be de-tected on the slides by microscopy is worth mentioning.A 3-nm thick spot with a 10- X 10-Arm area contains only0.5 pg of organic substance. This is a conservative es-timation to be used until an empirical detection limithas been established. It indicates the possibility ofusing the slides together with a microscope for verysensitive immunoassays. The critical factor, which hasnot yet been studied, is the collection of the detectedsubstance to such small areas as 100 ,um 2. On the otherhand, the possibility of seeing microstructures in bio-layers should be immediately interesting in many ap-plications.

The optimal design of the slides depends on the ap-plication. The narrow peak in Fig. 3 produces a sharpcolor change at a particular thickness of the organic film.This is suitable for most applications, but slides for thecontinuous monitoring of a growing layer must have asmoother sensitivity function. This can be accom-plished using a slight index mismatch or for the two-layer coatings by a slightly too thin intermediatelayer.

In conclusion, the designs given are sensitive enoughfor a wide range of applications. The materials, i.e.,glass, silicon, and silicon oxides, are chemically inert anddo not affect the biochemical reactions studied. Usingthe computations above it is possible to design slidesthat are optimized for different applications. Theslides can be manufactured and their quality ensuredby industrial methods, and two designs are now com-mercially available.' 9 It is our hope that these sensitive,versatile, and inexpensive tools will further develop-ment of simplified methods in immunology and bio-chemistry.

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Proteins and their Properties," Science 85, No. 2194, 76(1937).

478 APPLIED OPTICS / Vol. 24, No. 4 / 15 February 1985

2. K. B. Blodgett and I. Langmuir, "Built-up Films of BariumStearate and their Optical Properties," Phys. Rev. 51, 964(1937).

3. A. Rothen, "The Ellipsometer, an Apparatus to MeasureThickness of Thin Surface Films," Rev. Sci. Instrum. 16, No. 2,26 (1945).

4. M. F. Shaffer and J. H. Dingle, "A Study of Antigens and Anti-bodies by the Monolayer Film Technique of Langmuir," Proc.Soc. Exp. Biol. Med. 38, 528 (1938).

5. A. L. Adams, M. Klings, G. C. Fischer, and L. Vroman, "ThreeSimple Ways to Detect Antibody-Antigen Complex on FlatSurfaces," J. Immunol. Methods 3, 227 (1973).

6. I. Giaever and R. J. Laffin, "Visual Detection of Hepatitis BAntigen," Proc. Natl. Acad. Sci. USA 71, 4533 (1974).

7. I. Giaever, "Diagnostic Device for Visually Detecting Presence

of Biological Particles," U.S. Patent 3,979,184.8. R. J. Laffin, "Visual Detection of Hepatitis B Surface Antigen

and Antibody," in Biomedical Applications of ImmobilizedEnzymes and Proteins, Vol. 2 (Plenum, New York, 1977), p.147.

9. M. Born and E. Wolf, Principles of Optics (Pergamon, New York,1980).

10. H. Kubota, "Interference Color," Prog. Opt. 1, 211 (1961).11. D. B. Judd and G. Wyszecki, Color in Business, Science and In-

dustry (Wiley, New York, 1975), pp. 17, 19, 20.12. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized

Light (North-Holland, New York, 1977), p. 6.13. G. J. Chamberlin and D. G. Chamberlin, Colour (Heyden, Lon-

don, 1980).14. H. Nygren, T. Sandstrom, and M. Stenberg, "Direct Visual De-

tection of a Protein Antigen-Importance of Surface Concen-tration," J. Immunol. Methods 59, 145 (1983).

15. E. Ingelstam and L. Johansson, "Sur la sensibilite diff6rentiellede l'oeil aux couleurs dans l'6chelle de Newton notamment pourles teintes sensible," Opt. Acta 2, 139 (1955).

16. M. Stenberg, T. Sandstrom, and L. Stiblert, "A New EllipsometricMethod for Measurements on Surfaces and Surface Layers,"Mater. Sci. Eng. 42, 65 (1980).

17. H. Elwing and L.-A. Nilsson, "Diffusion-in-Gel Thin Layer Im-munoassay (DIG:TIA): Optimal Conditions for Quantitationof Antibodies," J. Immunol. Methods 38, 257 (1980).

18. H. Nygren and M. Stenberg, "Electrophoresis of Ligands overa Surface Coated with a Binding Receptor-a Novel Method-ological Principle for Electroimmunoassays," FEBS Lett. 135,73 (1981).

19. Slides of the two types described in the text are available underthe tradename Sagax slides. Sagax is a registered trademark ofSAGAX Instrument AB, Box 7003, S-172 07 Sundbyberg,Sweden.

Positions Open in NSF(NSF is an Equal Opportunity Employer)

Applicants for the following positions should submitresumes including current salary to NSF, Personnel Ad-ministration Branch, Room 212, 1800 G Street, N.W.,Wash. DC 20550. Attn: Catherine Handle (357-7840).Hearing impaired individuals should call: TDD(357-7492).

These positions will be filled on a one- or two-yearrotational or temporary basis and are excepted from thecompetitive civil service. Normally, the candidate se-lected receives a leave of absence from his/her employerand salary is set in accordance with NSF Circular 167,Rotator Program. Otherwise, salaries for temporary em-ployees are set at NSF's GG/GH schedule (equivalent tothe GS schedule). Specific years of successful scientificresearch experience beyond the Ph.D. are required forthe following positions in all fields:

Program Director, six to eight years, per annum salaryranges from $40,000 to $66,400.

Associate Program Director, four to six years, per annumsalary ranges from $35,000 to $55,000.

Assistant Program Director, three to four years, per an-num salary ranges from $30,000 to $45,000.

* NSF's Division of Biotic Systems and Resources isseeking qualified applicants for the position of pro-gram director for the Population Biology and 'Phys-iological Ecology program. The incumbent to thisposition will administer a program for basic re-search grant support, including advising applicants,reviewing proposals and other administrative du-ties. Applicants should have a background in popu-lation biology and physiological ecology or equiv-alent research experience.

* NSF's Division of Information Science and Tech-nology is seeking qualified applicants for the posi-tion of program director for Information Impact.This position will be filled on a permanent, rota-tional, or temporary basis. Responsibilities includeall aspects of proposal development, review andevaluation, grants and program administration, andrepresentation of Information Science within theNSF and to the research community. Applicantsshould have a background in behavioral, social orinformation sciences with emphasis on informationsystems, technology, processes, economics or infor-mation. Some administrative experience is desired.

* NSF's Division of Cellular Biosciences is seekingqualified applicants for two positions as assistant orassociate program directors for the Prokaryotic andEukaryotic Genetics programs. Responsibilities in-clude proposal review and evaluation, advising ap-plicants and providing technical expertise to theNSF in their particular science areas. Applicantsshould have a background in genetics. A broad gen-eral knowledge of the field and experience in theadministration of grants as a principal investigatorare desirable.

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15 February 1985 / Vol. 24, No. 4 / APPLIED OPTICS 479