J.F.S.S. COMMENTARY

Non-Destructive Identification of Textile Fibres by Interference Microscopy

0. HEUSE and F. P. ADOLF (Translation by M. A. Reichert)

Bundeskriminalamt, Posfach 1820, 6200 Wiesbaden, Federal Republic of Germany

Abstract The quantitative analysis of interferograms in connection

with the equirefractive immersion of the material to be studied has been demonstrated to be a simple and non-destructive method of classifying textile fibres. The two refractive indices rill and n l are measured in light polarized parallel, and perpendi- cular to the fibre axis. Frequently encountered fibres have been measured and their optical values shown in "standort" diagrams (locus diagrams). Some typical fringe patterns of fibres are shown. Journal of the Forensic Science Society 1982; 22: 103-122 Received 17 December 1980

Introduction The Problem

In forensic science, the examination of small single fibres plays an ever- increasing role (Culliford, 1963 ; Stratmann, 1969; Rouen and Reeve, 1970; Pohl, 1975; Grieve and Kotowski, 1977; Cook and Paterson, 1978).

Recently various new analytical approaches have been developed and those methods which are quick and leave the specimen undamaged so that it remains available for any further examination are preferred. Single fibres used here are fibre fragments of less than 0.5mm in length and lop-50p in diameter and weighing between 10-5g and 10-'g. They are transferred during any textile contact according to certain rules (Locard, 1928, 1930) and adhere to the recipient object for a longer or shorter period of time (Pounds and Smalldon, 1975). Microscopic methods of examination which fit the above category include the methods mentioned in Table 1.

TABLE 1

MICROSCOPIC METHODS OF EVALUATION OF FIBRES

Transmitted light microscopy and scanning electron microscopy Shape Inner structural elements Colour (Stratmann, 1969)

Microspectrophotometry and incident light fluorescence microscopy (Halonbrenner and Meier, 1973: Martin. 1978: Home and Dudley, 1980) . -

' co1our Presence of optical brighteners

Special optical microscopic methods for phase-structure analysis including phase-contrast microscopy, polarization microscopy, the Becke line method (Becke, 1893; McLean, 1965; Juda and Medenbach, 1967; Patzelt, 1974) and interference microscopy (Hannes, 1972; Schwenzer and Eckard, 1976; Kuhnle et al., 1978)

Refractive indices Birefringence of fibres

Of the optical methods for phase structure analysis, only polarization microscopy has become established in fibre analysis. The use of interference microscopy, however, which profitably comprises polarization microscopy and the Becke line method and in particular enables the worker to obtain detailed information specific to the material under examination, has so far been little used in the forensic analysis of fibres and is therefore worthy of study.

Structural Parameters and Optical Properties of Textile Fibres The fibre material submitted to the forensic examiner covers the whole

range of textile fibres. There are approximately 60 natural fibres and 4000 man-made fibres, and a chart of the most important types of textile fibres mentioned in this paper is shown in Table 2.

One of the main problems of forensic fibre analysis is the diversity of man- made fibres. The expert in general finds it relatively easy to differentiate natural fibres by means of their morphological features, although difficillties are sometimes encountered, e.g. distinguishing between hemp and flax (see below). I n the field of man-made fibres, however, certain morphological properties such as cross-sectional shape, diameter, surface structure and degree of delustring are not characteristic of individual types of fibre. With regard to external features, man-made fibres display no type-specificity whatsoever.

All textile fibres, however, have a common feature in that they consist of shorter or longer polymer chains, which are more or less oriented along the fibre axis. Length of polymer chains, and their orientation and partial crystal- linity are used here as internal features of textile fibres.

Light waves, when traversing a fibre, enter into interaction with the chemical bonds of the fibre substance. The phase of these light waves, therefore, contains information on the fibre substance, i.e. on the internal features of the fibre. This information is quantifiable where the optical characteristics are known, i.e. by means of the refractive indices. A prerequisite for their determination is transparency, a condition fulfilled by most textile fibres. Very thick fibres (filaments, wires) which are matted or dyed cause problems. Dyed fibres of normal size are transparent as seen from the microscopist's viewpoint. For instance the PP fibre 4 in Figure 9 seemed to be deep black to the naked eye.

A transparent solid has three principal refractive indices, which are perpen- dicular to one another and form the three main axes of the "index ellipsoid" known as "indicatrix" (Figure 1). When polarized light traverses a transparent solid, the refractive index applicable to the light is dependent upon the direction of vibration (electric vector) of the light relative to the index ellipsoid. I n the case where the index ellipsoid is a sphere, i.e. all three axes are of equal length, the index of refraction is independent of the direction of vibration of the light: the solid is optically "isotropic" e.g. like glass or water.

Fibres in general are, however, optically anisotropic, their index ellipsoid having rotational symmetry. Its main axis is aligned along the longitudinal axis of the fibre. I n order to quantify the internal features of a fibre it is there- fore necessary to determine two optical characteristics, from which, as will be shown, two further ones can be deduced. These four values are given in the caption to Figure 3.

Determination of Refractive Indices in Textile Fibres The Becke Line Method

Values for the two refractive indices n,, and 121 in fibres have repeatedly been given (Heyn, 1952 ; Koch, 1958; Morrison, 1963 ; Stratmann, 1969; Pohl, 1975). Mostly they were determined by the so-called Becke line method (1893) which had been developed in mineralogy. The fibre material is systematically embedded in various immersion media of known refractive indices until a medium is found which makes the optically conditioned white line on the fibre edge, the so-called Becke line, disappear. At the same time, the contour

TABLE 2

CLASSIFICATION OF TEXTILE FIBRES

MAN-MADE FIBRES (ca 4000 products, see Figure 4a)

SYNTHETIC POLYMERS (see Figure 4b) Polycondensation products

polyesters (PES) polyethylene terephthalate (PET) polybutylene terephthalate (PBT) polypropylene terephthalate (PPT) polycyclohexane-1.4-dimethylene

terephthalate (PCT) polyamides (PA) e.g. Perlon (PA6)

e.g. Nylon (PA66) e.g. Rilsan (PA1 1) e.g. Qiana

Polymerisation products polyfluorides polytetrafluoroethylene (PTF)

polyvinylidene fluoride (PVDF) polyalcohols polyvinyl alcohol (PVA) polychlorides polyvinyl chloride (PVC)

polyvinylidene chloride (PVD) polyacryls polyacrylonitrile (PAC)

polyacrylonitrile, modified (PAM) polyolefines polyethylene (PE)

polypropylene (PP) Polyaddition products

polyurethanes polyurethane (PUR) polyurethane elastomer (PUE)

Others e.g. biconstituent fibre (bico)

NATURAL POLYMERS OF VEGETABLE ORIGIN (see Figure 4c) Cellulose

regenerated cellulose cupro fibre (CC) viscose (CV)

cellulose ester 24 acetate (%A\ thacetate ~cT)'

Algae algeic acid

Latex polyisoprene

. ,

alginate (AL)

rubber (LA)

NATURAL POLYMERS OF ANIMAL AND VEGETABLE ORIGIN (see Figure 4c) Protein

regenerated protein zein (ZE) casein (KA)

NATURAL FIBRES (ca 60 products, see Figure 5)

CLASSIC TEXTILE FIBRES Vegetable fibres

cellulose

Animal fibres keratin

fibroin

fruit-hair fibres (fr) seed fibres (sd) stem fibres (st) leaf fibres (If)

wool (wo) human hair (mh) mulberry silk (ms) spider web (spw)

MINERAL FIBRES Asbestos

silicate chrysotile (chr) horniiendc (hbij

of the fibre disappears. When this occurs the refractive index of the fibre is equal to the refractive index of the immersion medium; "equirefractive" immersion has been achieved.

This method is of little accuracy. Only the refractive indices of the outer fibre layer are determined, whose submicroscopic structure frequently differs from the inner part of the fibre.

Determination Using the Mach-Xehnder Interference Microscope Phase structures of microscopic objects, e.g. the internal features of textile

fibres, cannot be observed directly by the human eye. Special optical aids are required, such as the phase-contrast microscope or the polarizing microscope. A universal microscopic method to render phase structures visible is interference microscopy. All interference methods (Hannes, 1972; Schwenzer and Eckard, 1976; Kiihnle et al., 1978) are based on the same principle. A beam of light is optically divided into two halves ("coherent beams of light"). These follow different ~ a t h s through the microsco~e and are then re-united. If the ~ a t h s travelled by the bear& differ slightlyA- for instance by + a wavelength 1 the resultant beam will produce a set of fringes - an interferogram. Where white light is used (a mixture of light of many wavelengths) a colour interferogram will result since interference depends upon wavelengths. Monochromatic light will produce an interferogram consisting of distinct black lines of interference. Frequently, monochromatic light from a mercury vapour lamp having a wavelength of 546nm (green) is used.

For the work leading to the present paper, a Mach-Zehnder interference microscope, manufactured by Leitz, was used. This particular instrument is no longer in production but it is possible to work with other types of interference microscopes. Good results were achieved with a Jamin-Lebedeff set manu- factured by Carl Zeiss, Oberkochen, and a Peraval interphako for transmission work, marked by the manufacturer "aus Jena". (In both cases the so-called "shearing method" was used).

Figure 2 shows the path of light in the Leitz instrument. Prism TI splits the beam of light into two coherent beams, whose paths are adjusted by means of the pairs of plane-parallel plates PI-P, and which are then re-united by prism T, to produce interference. Analyzer A enables the interferogram of the light polarized parallel or perpendicular to the fibre to be interpreted. The em- bedded fibre is inserted, on a microscope slide and with a cover glass, into the left-hand beam. Into the right-hand beam (reference) is inserted an optically matched miscroscope slide without a fibre as a reference object. Condensers K and objectives 0 are of the same design as in other microscopes and identical on both sides.

If the fibre has a refractive index (nfihre) different from that of the immersion medium (no) the fringes in the microscopic image of the fibre will be displaced. Some typical fringe patterns are shown in Figures 6 to 9 and 11.

If the fibre is round and its substance homogenous as the one in Figure 6c, the fringes will for geometric reasons take the shape of a semi-ellipse with its vertex to be found where the optical path through the fibre is the longest, in the

a x centre. If the readily measurable -q = - is defined as the "relative phase X

difference" (as shown in Figure 6c), then, according to the laws of interference optics, the difference between the refractive index of the immersion medium (no) and the refractive index of the fibre (nfihre) is determined by the equation

where nfibre may be either 1211 or n l , depending on the position of the analyzer, and h is the wavelength of the light used and d the fibre diameter.

If q = 0, "equirefractive" immersion is present. I n this case, the fringes will go through the fibre image without displacement, as in Figure 7a. Where

equlrefractive immersion is achieved, the refractive index of the immersion medium will yield the identical refractive index of the fibre. If, however, as in the case of the instrument used here, the fringes are displaced to the right (Figure 7b), nfibre > no; if they are displaced to the left (Figure 7c), nfibre < no.

Using equation (I), a single immersion will suffice to determine the refractive indices rill and n l by simply positioning the analyzer of the microscope first parallel, and then perpendicular, to the fibre axis, determining the two relative phase differences r j l l and -ql (according to Figure 6c) and calculating the refractive indices on that basis.

In practice, however, working with just one immersion is possible only in special cases, for instance where there is very little birefringence or where accuracy is not important. As a rule, two "nearly" equirefractive immersions for rill and n l are required, which have to be determined in a preliminary test using the reference material and equation (1). The refractive index liquids of Cargille company (R. P. Cargille Lab. Inc., 55 Commerce Road, Cedar Grove, N. J. 07009, U.S.A.) have been found to be efficient immersion media.

Standort Diagram Using the method described above, numerous types of fibre and fibre

products have been measured. The values obtained for rill and n l , entered into a co-ordinate system in which n l is shown as the abscissa and rill as the ordinate, identify the optical "standort" (locus) of a fibre.

The co-ordinate system has, therefore, been described as "standort diagram". This diagram also contains An and niso, since both can be deduced, as shown in Figure 3, from n,, and n l . Figure 3 is a small-scale standort diagram pro- viding a summary view. The commercially important fibre materials are concentrated in a relatively small area. This area is shown in more detail in Figures 4a, 4b and 4c, and it is found that individual types of fibre occupy what may be termed "standort districts".

Figure 4a shows the standort districts of the most important man-made fibres. A further subdivision is given in Figures 4b and 4c, which show the standort districts of individual fibre products made from synthetic polymers and on the basis of natural polymers, respectively, whereas Figure 5 shows the standort districts of natural fibres with their individual loci.

The district borderlines in Figures 4 and 5 have been drawn to encircle all fibres measured so far. The standort borderlines in the detailed diagrams 4b, 4c and 5 are determined by the "standard deviation from the mean" of the individual measurements.

The results presented here were mostly obtained from undyed fibres. When measuring bleached, macerated and dyed fibres etc., it was found that the various processes of textile finishing produce little, if measurable, change in the interferometric standort of fibres.

Discussion General Remarks

First of all, the tests show that it is possible to identify, to a large degree, specific differences between textile fibre materials by measuring refractive indices with an interference microscope using refractive index liquids, and entering the values obtained in standort diagrams.

This is especially true for man-made fibres, which are differentiated both by their chemical properties and by their physical properties, which are a result of the production process. This is exemplified most clearly in PET (Figure 4b) where already various extrusion speeds (up to 5000m/min) cause differences in optical standort. The structural modification deliberately brought about by further processing, drawing and thermal treatment, finally lead to a long-drawn district of individual optical positions of PET fibres, each of which represents specific use of the given fibre.

The size of the standort district of PET as compared with wool, for instance, further shows that the variation of the production parameter may have a considerably greater impact than the variation of parameters which determine the growth of' natural fibres.

On the other hand, the example of PA 6 (perlon) and PA 6.6 (nylon) (Figure 4b) shows that fibre substances which are chemically and structurally very similar cannot be distinguished as unambiguously as would be desirable. In this particular case, determining the melting point by means of a hot-stage microscope is a helpful, if destructive, method.

An and nl,, have already been incorporated into the diagrams. Of significance in this respect is the straight line An = + 0. Fibres displaying positive bire- fringence are located above this line and those having negative birefringence below it. Amorphous textile fibres, e.g. alginate, are to be found on it (Eigure 4c). The relation between the optical parameters and the conditions of pro- duction resides in the fact that increased drawing will augment An and move the optical standort of the fibre to the upper left. Higher temperature during processing, however, will increase niso = degree of crystallization and move the fibre standort to the upper right. ( I t is further to be noted that the first of the previously mentioned "internal features", the length of molecular chains ("degree of polymerizatian"), is not reflected in the optical characteristics).

Differeerztiation of Various Fibre Products within the Sam. Type of Fibre Figures 6a to 6c show the interferograms of three different "PET wool

types". The same immersion medium was used for all three fibre products so that direct comparison is possible and clearly the three fibres produce different interferograms.

This is similar for the cotton-type PET fibre products in Figure 7a to 7c, all of which originate from the same manufacturer but are used for different purposes. By means of interference microscopy they, also, can be clearly differentiated. I t is noted that the immersion medium used for the cotton types had a greater refractive index (no = 1.709) than that used for the wool types. (no = 1.694). PET cotton types are subjected to a greater amount of drawing than PET wool types (cf. Figure 4b). Practice shows that, even by means of interferograms, products are not unambiguously identifiable to a particular manufacturer. Firstly a certain degree of change occurs within the same product of a particular manufacturer over a period of time and secondly, the product parameters are not manufacturer-specific.

Determining Cross-Sectional Shape The shape of the fibre's cros-section is an important inorphological feature

for differentiation purposes in fibre analysis. So far, only sections enabled the worker to obtain exact information thereon. The present study has shown that the resulting fringe pattern can be interpreted to provide qualitative information on the cross-section with mostly sufficient accuracy. A prerequisite for this is that there be no equirefractive immersion since this would make the fringes run through the fibre undisplaced, regardless of its shape. Figure 8a shows, for instance, the interferogram obtained from a trilobal PET fibre; fibre 1 in Figure 9 shows a fringe pattern exemplifying the "dog-bone" cross-section frequently encountered in dry-spun PAC fibres and fibre 3 in Figure 9 is again a trilohal shape.

Irl?~o.mogeneities in Fibres Generally, the structure of a fibre is not homogeneous throughout its cross-

section. These structural inhomogeneities may constitute a batch-specific characteristic, especially in thick fibres, and therefore are of interest in forensic fibre analysis. When present in fibres having a circular cross-section, such inhomogeneities will cause the fringes to present a not quite semi-elliptical pattern. This can be seen in Figure 8b. Identifying such detail in interference

fringes requires nearly equirefractive immersion for measuring both rill and nl (cf. Figure 8c).

Identifying Fibre Blends Mixtures of fibres are used in textile products, for example where it is

desirable to obtain certain properties of use. In a practical case, two carpet specimens had to be compared which consisted of a blend of PAC, PA, PET and PP fibres. An important parameter to be studied in such comparative work is the match in blend ratio of the fibre types present. Since the standort districts of the four types of fibre are clearly separate from each other in different directions of the standort diagram, an attempt was made to work with one single immersion medium having a refractive index no = 1.534, and thus to determine the blend ratio just by counting, since no was intermediate.

Interpretation is exemplified by Figures 9a and 9b. Figure 9a shows an interferogram obtained with the analyzer in "para" position. The fibres were studied in top-to-bottom order and the result has been entered in large letters in Figure 10, using Figure 4a as a matrix. I n fibre 1, rill and n l are almost equal. The fringes are always displaced to the left, viz. rill m n l < no. Exact measurements reveal that the fringes of fibre 1 in Figure 9a are displaced slightly more to the left than in Figure 9b; i.e. negative birefringence. Accord- ingly, a broken arrow in Figure 10 points from the standort of the immersion liquid to PAC. In fibre 2 in Figure 9a, there is marked fringe displacement to the right, viz. n, , > no; in Figure 9b, slight displacement to the left is present; therefore n l < no. The entry in Figure 10 identifies this specimen as a PA fibre. For fibre 3, Figure 9a shows extreme displacement to the right, meaning n l $ no. In Figure 9b, however, there is only slight displacement to the right, meaning n.L > no. This is a PET fibre, as shown in Figure 10. A.ccordingly fibre 4 was identified as a PP fibre since rill < no and n l < no.

Since with some practice a good qualitative estimate can be made of the displacement of the fringes, it was possible to make a count of the required number of samples within a short period of time. I t is an advantage of this analytical method that the cross-sectional shape of the fibre is obtained as a "by-product" as well. As far as discernible, hatched drawings of the cross- sections of the fibres are shown on the left-hand margin of Figure 9.

Difirentiating Hem@ and Flax When examining natural fibres it is in certain cases not sufficient to study

the morphological characteristics alone, especially where various types of leaf fibres or stem fibres are to be differentiated within the same group of fibres; if in addition only a few fibres are available, determination is difficult.

A recurrent problem in this field as far as stem fibres are concerned is dis- tinguishing between hemp and flax. In the literature, much attention has centred oh just these two types of fibre. Herzog (1926) for example notes that separation by determining the refractive index using the Becke line method is not possible. As the interference-frinqe method is more accurate, the question was studied again and it has been found that the aids and methods described here allow optical separation to be made. Differentiating these two stem fibres also reveals, however, that because of natural scatter in the fibre material the limit of the method has been reached.

As shown in Figure 5, the refractive indices are as follows: for hemp, n l = 1.524, rill = 1.580, and for flax, n l = 1.525, rill = 1.585. A scatter of 0.002 applies to all values. Although the values found for n l are virtually identical, the difference between those found for n, , is sufficient to allow differentiation.

An example of this is shown in Figure 1 1, where a bundle of flax fibres and a bundle of hemp fibres have been positioned parallel to each other. In light polarized parallel to the fibre axes, the fringes can therefore be observed simultaneously in the same immersion medium. The refractive index of the

immersion medium (no) is 1-583 which is between the two mean tzll of the two types of fibre. It is clearly visible that in the flax fibres the fringes are displaced to the right and in the hemp fibres to the left.

Analyzer in ortho position for measurinq 1 1 ~

Analyzer in para position for measuring rill

Figure 1. Index ellipsoid of revolution in the fibre. Usually n r < all.

Figure 2. Mach-Zehnder double-beam interference microscope (by courtesy of Leitz Company, Wetzlar).

TI-splitting prism, PI - P,-compensators, K-condensers, 0-objective, T,-reuniting prism, A--analyzer

Figure 3. Optical "standorte" (loci) of fibres. Small-scale overview; the outlined area is shown in greater detail in Figures 4a, 4b and 4c.

t Refractive index rill in light polarized parallel to fibre axis + Refractive index n l in light polarized perpendicular to fibre axis R, Birefringence A n = rill - n s , inter alia a measure of molecular orientation f Isomorphic index of refraction niso = b (2n r + rill), inter alia a measure of crystallization

(see text) (For classification of fibres see Table 2).

Figure 4a. Optical "standorte" (loci) of man-made fibres (see Table 2). Overview of "standort' ' districts. Go-ordinates as in Figure 3.

Figure 4b. Optical "standorte" (loci) of man-made fibres from synthetic polymers (see Table 2). Detailed view of loci shown in Figure 4a. The size of the "standorte" (black) indicates the standard deviation of individual measurements from the mean. Go-ordinates as in Figure 3.

Figure 4c. Optical "standorte" (loci) of man-made fibres from natural polymers (see Table 2). Detailed view of loci shown in Figure 4a. The size of the "standorte" (black) indicates the standard deviation of individual measurements from the mean. Co-ordinates as in Figure 3.

Cellulose Fibres Fibroin Filaments

Figure 5. Optical "standorte" (loci) of natural fibres (see Table 2) . Combined overview of the three "standort" districts and detailed views of loci. The size of the "standorte" (black) indicates the standard deviation of individual measurements from the mean. Co-ordinates as in Figure 3.

Figure 6. PET (see Table 2). Interferograms of various "wool types" (flakes). All pictures taken in light polarized parallel to fibre axis.

a. Trevira 2 10. 3.3 tex, (Hoechst AG). rill = 1.690, no = 1.694 b. Trevira 220. 3.3 tex, (Hoechst AG). rill = 1.699, no = 1.694 r. Tergal T900. 3.3 tex, (Rhodiaceta SA), rill = 1.688, no = 1.694

n x Relative phase difference r ) = -

X

Figure 7. PET (see Table 2). Interferograms of various "cotton types" from yarns. All pictures taken in light polarized parallel to fibre axis.

a. Diolen 42. 1.7 tex, (Enka Glanzstoff AG). rill = 1.709, no = 1.709 b. Diolen 12. 1.7 tex, (Enka Glanzstoff AG). rill = 1.7 18, no = 1.709 c . Diolen 11. 1.7 tex, (Enka Glanzstoff AG). nl, = 1.700, no = 1.709

Exarnplc of the impact of cross-src-tionnl shapr

Iluamplr of an inl~nmogeneolts fiibrc: nl, is smaller outside than inqidr

m m .m . F,xan~l)l(. 01 non-equlrrf~active immcr\~on. Disad\nlltage:

Fringe\ cannot bc counted

Figure 8. Three typical interferograms. a. Trevira 813 (PET) trilobal, (Hoechst AG). nil = 1.688, no = 1-718. Light polarized parallel to fibre axis; example of the impact of cross-sectional shape. b. Perlon (PA6) round, (Enka Glanzstoff AG). rill = 1.568, no - 1.568. Light polarized parallel to fibre axis; example of an inhomogeneous fibre, n l i is smaller outside than inside. c. Perlon (PA6) round, (Enka Glanzstoff AG). n~ = 1.522, no = 1.568. Light polarized perpendicular to fibre axis; example of non-equirefractive immersion. Disadvantage: fringes cannot be counted.

1:ibr~ 2

1:ibre 3 PET

Fibre 4 PI'

Fibre I PAC

Fihrc 2 1'11

Fibrr 3 PET

Fihrr 4 Pf'

Figure 9. Interferograms of a fibre blend of synthetic polymers PAC, PA, PET and PP (see Table 2) . no = 1.534.

a. Light polarized parallel to fibre axis. Fibre 1 -PAC rill < n o : Fibre 2-PA n , , ;- n o : Fibre 3-PET rill > n o : Fibre 4-PP rill < no. Analyzer in para position. b. Light polarized Perpendicular to fibre axis. Fibre I-PAC n < no : Fibre 2-PA n , no : Fibre 3-PET n I > n o : Fibre 4--~PP n L < nu. Analyzer in ortho position.

>

1.45 7.50 '" 7.55 1.66 n,

Figure 10. Identification of the fibre blend of synthetic polymers PAC, PA, PET and PP (see Table 2 and Figure 9), by means of one immersion. Figure 4a is used as a matrix. no = 1.534. Fibre 1-PAC rill m n L < no: Fibre 2-PA rill > no and n l < no: Fibre 3-PET rill no and n l > no: Fibre 4-PP rill < no and n l 4 no.

Figure 11. Interferogranl of a bundle of flax fibres (a) and a bundle of hemp fibres (b). Light polarized parallel to fibre axis.

a. Flax rill = 1.585, no = 1.583 b. Hemp rill = 1.580, no = 1.583

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