Determination of light-scattering properties of glass surfaces

Journal of NonCrystalline Solids 19 (1975) 105-113 © North-Holland Publishing Company

DETERMINATION OF LIGHT-SCATTERING PROPERTIES OF GLASS SURFACES G. T O M A N D L

lnstitut ffir lCerkstoffwissenschaften III, University of Erlangen, Federal Republic of Germany

Glass surfaces were damaged in a defined manner by sandblasting with an adjustable sandblasting machine and subsequent etching with HF. Investigations with the scanning electron microscope (SEM) showed surface defects with an ellipsoidal shape. A quantitative evaluation of the exact profile of these defects was made using mathematical evaluation of stereographic pairs. A new method is described for characterizing surfaces with optical light scattering. In contrast to the usual method of a fixed specimen and a photocell moving on a circle around it, here the specimen revolves on an axis perpendicular to a laser beam and rotates on an axis parallel to it in order to average the scattering over a large area of the surface, thus preventing interferences of the coherent laser beam with "surface defects. A theory is described which enables a numerical estimation of roughness parameters using a distribution function of angles of small mirrors to the average surface. In this special case the theory was extended for the special type of defects having an ellipsoidal shape. The results are discussed with respect to creation of surface defects by sandblasting, which are accompanied by subsurface cracks.

1. Introduction The aim o f this w o r k was to d a m a g e surfaces o f glasses in a d e f i n e d m a n n e r and to c h a r a c t e r i z e these surfaces. The surfaces o f the samples were a b r a d e d w i t h SiC powder in an a d j u s t a b l e s a n d b l a s t i n g m a c h i n e * . A f t e r w a r d s surface defects were altered in a c h a r a c t e r i s t i c m a n n e r b y e t c h i n g w i t h H F acid (10%). Individual d e f e c t s could be o b s e r v e d easily w i t h a SEM a n d e v a l u a t e d stereographically. In o r d e r to evaluate regions o f defects, a new a p p a r a t u s was b u i l t for a q u a n t i t a t i v e d e t e r m i n a t i o n o f the lightscattering characteristics.

2. I n v e s t i g a t i o n s w i t h the SEM

using stereography

S t e r e o g r a p h i c pairs were o b t a i n e d b y the SEM f r o m the surfaces o f the s p e c i m e n s (fig. l). The tilt angles were usually 3 0 a n d 45 ° in o r d e r to o b t a i n the r e q u i r e d contrast. The resulting perspective s h o r t e n i n g was e l e c t r o n i c a l l y rectified. * Airbrasive machine, S.S. White. 105

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G. Tomandl ~Light-scattering properties of glass surfaces

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Fig. 1. Stereographic pair of a damaged surface. 15 s sandblasting, A = i0, B = 30 and C = 60 min etching. Tilt angles are 30 and 45 ° . The pictures are electronically rectified.

2.1. Evaluation of stereographic pairs An object (fig. 2) consisting of the points OPQ gives a plane image OP'Q' with the tilt angle a. The electronic rectification has the effect that the distance OQ will be kept constant for every angle a. The point P lying below the plane OQ with the image P' becomes point P" by the correction of the distortion. The correction of the distortion follows the equation

d ''= d'/cosa.

(1)

G. Tomandl / Light-scattering properties of glass surfaces

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i Fig. 3. Stereographic pair of one defect on a damaged glass surface. 5 s sandblasting, 10 min etching.

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G. Tomandl /Light-scattering properties of glass surfaces

According to fig. 2 the equations for the calculation of the coordinates of the object point P can be derived easily: h = (d~ 1 [ A tt

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d = ~ ' 1 + d 2 ) + ~h (tanal + tana2). The subscripts 1 and 2 represent pictures l and 2 of the stereographic pair having two different angles a 1 and a 2. The equations are valid only for points P along a horizontal line. The term in the equation for d which contains h results in the stereographic pair showing a depth-dependent distortion during viewing. This term is omitted only for the case when a 1 = - a l , in the case of very small h, or very small angles a 1 and a 2. In the present case this term cannot be neglected because of the large tilt angles, 30 and 45 °. This was a deliberate choice which permitted a better resolution for the mathematical evaluation. Fig. 3 shows steoreographic pair of a single defect; in fig. 4, the corresponding profile along the line is shown.

3. Measurement of the light-scattering charactedstics of a rough surface In ref. [ 1] an apparatus for measuring the light-scattering characteristics of surfaces is given. The present author [2] has markedly improved this measuring method by using a He Ne laser as the light source, and a logarithmic amplifier which allows recording of the scattered light over a range of up to eight decades. In this apparatus the specimen is fixed and the photocell is moved around the specimen. For this investigation a new apparatus was built in which the specimen revolves on its axis, while the laser and the photocell are fixed at a constant angle/3 (see fig. 5). In addition, the specimen is rotated on an axis parallel to the laser beam in order to average tire scattering over a large area of the surface, thus preventing the disturbing influence of interferences within the laser beam at the surface defects (see fig. 8). 3.1. Theory

There exists a very extensive theory for light-scattering at surfaces [3], which is based on wave optics. In refs. [4] and [5] applications of this theory are shown;

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G. Tomandl /Light-scattering properties of glass surfaces

109

however, these are valid only for a roughness "< 0,5/~m and have relatively large inaccuracies. In ref. [2] a theory is described which relates the scattered intensity to the surface profile. This theory is described briefly and the equations modified for the new measuring arrangement The theory starts with geometric optics. In principle, therefore, it only allows statements about relations of angles, not of depths of defects. It is valid only for defects which are larger than the light-wave length. The surface (fig. 6) is described as a distribution of small mirrors

W(a) = dx/da,

(3)

where W(a) gives the length portion in the angular interval da, projected on the base area. W(a) should be equal for all section lines through the specimen. The scattered intensity as a function of the angle a (see fig. 5) will be evaluated according to the equation c~

I(a) ,x cos/3FR(/3) W(a) f W(a')da', sin2a 0

(4)

where FR(/3) is the reflected intensity ratio of unpolarized light with angle of incidence/3 calculated according to Fresnel's formula. The integral takes into consideration the light-scattering perpendicular to the plane laser beam -- specimen - photocell. For this particular investigation, owing to the fact that the surface defects have an ellipsoidal shape (as can be seen in the SEM micrographs), a special formula for I(a) was derived which is valid for rotational ellipsoidal defectS"

I(a) = W0 f2FR (/3)[1 + (f2 _ 1) sin 2 ct]--2 ,

(5)

where W0 is proportional to the area of these defects having a sha~e factor f ( = ratio of half diameter to depth). The maximum intensity is I(0) cc WOfL Fig. 7 shows schematically the resulting light-scattering curve and its individual components for those specimens measured most often. Range I is due to the amount of the undamaged surface. The ranges II and III are assigned to two different types of eltipsoidal defects having two shape factors (f2 >/'3). The area ratio of both types G

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Fig. 6. Idealized surface profile.

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of defects is evaluated as WO2/WO 3 = (102/103) f 2 / f 2 .

(6)

The amount of the damaged part of the surface is

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(7)

where f l is an effective shape factor depending on the kind of apparatus, and describes the resolution limit of the apparatus. 3.2. Measurements Figure 8 shows the influence of rotation of the specimen on the measured curves. The rotation frequency was ~ 20 Hz. Measurements were obtained with black welding safety glasses and with transparent window glasses. When measuring transparent specimens, a vapor deposited silver layer (fig. 9) is necessary to eliminate interference from the scattered light coming from the backside and interior of the specimen. Figs. 10 and 11 show the influence of sandblasting and subsequent etching on the light-scattering curves. The thin lines are calculated theoretical curves determined with different f factors using an iteration method. A quantitative evaluation with respect to area ratios, for defects with different fvalues, was treated in ref. [2]. Because of limited space it is omitted here.

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Fig. 8. Comparison of light-scattering curves without (left) and with (right) specimen rotation.

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4. Discussion of results The large cavities, visible in the stereographic pairs, yield f v a l u e s of a p p r o x i m a t e l y 3. Therefore, they can be assigned to range III of the scattering curve (according to

G. Tomandl / Light-scattering properties of glass sur]aces

113

fig. 7). The f v a l u e s for range II are limited to the range 2 0 - 7 0 . These defects are apparently the small craters visible in the SEM pictures. The following consideration may serve as an explanation for both sorts of defects. Small surface defects will be created by blasting with SiC particles on the glass surface and may be accompanied by subsurface cracks. These cracks will first be broadened by the subsequent etching, thus creating the deep craters. Successive etching leads to a further enlargement of these defects; however, the half-diameter/depth ratio remains approximately constant. The small flat cavities result from the etching of those defects which have no associated subsurface cracks. These considerations are in agreement with results reported in refs. [6] and [7], which were obtained during investigations of the influence of surface defects on the strength of glasses.

Acknowledgement I wish to thank Mr. H.-P. I-ioheisel for carrying out the experimental work and Dr. J.R. Varner for help in translation.

References [1] K. Doerbecker and H.J. Oel, Ber. Deut. Keram. Ges. 45 (1968) 116,478. [21 G. Tomandl, Glastechn. Ber. 47 (1974) 90. [3] P. Beckmann and A. Spizzichino, Scattering of electromagnetic waves from rough surfaces (McMillan, New York, 1964) ch. 5. [4] D.H. Hensler, Appl. Opt. 11 (1972) 2522. [5] D.H. Hensler, N.A. Soos, E.H. Hass, et al., Am. Ceram. Soc. Bull. 52 (1973) 191. [6] J.R. Varner and H.J. Oel, Surface defects: their origin, characterization and effects on strength, this volume, p. 321. [7] J.R. Varner and H.J. Oel, Einfluss von Oberflfichenbesch~idigungen auf die Festigkeit von Glasstfiben, Glastechn. Ber. 48 (1975), to be published.