J. Exp. Biol. (1966), 45, 433-447 4 3 3With 2 plates and 8 text-figures

Printed in Great Britain

A MULTILAYER INTERFERENCE REFLECTOR IN THEEYE OF THE SCALLOP, PECTEN MAXIMUS

BY M. F. LAND

Department of Physiology, University College London

(Received 6 July 1966)

Animals frequently make use of highly reflecting surfaces, as for example in thetapeta of the eyes of many vertebrates, the iridophores and photophores of manymarine animals, and the scales of fish. Such surfaces raise the question: how are highreflectivities, often comparable with that of polished metal, achieved using biologicalmaterials?

Highly reflecting surfaces in which metals are not employed have recently beendeveloped industrially. The principle employed is that of the quarter-wavelengthfilm (Text-fig. 1), in which light reflected from the front surface of a transparent thinfilm is in phase with, and so interferes constructively with, light reflected from theback surface. Light reflected at a low to high refractive index interface (in this case theupper surface of the film) undergoes a phase change of £ wavelength. So, for construc-tive interference, light reflected from the lower interface must be retarded by \ wave-length. The optical thickness of the fihn (refractive index, n, x actual thickness, t)must therefore be J wavelength for maximum constructive interference to occur whenlight is reflected normally.

The reflectivity of such a film, although approximately four times that of a singleinterface, is still much less than that of a metallic surface. The reflectivity, however,may be increased by laying down a number of such films, of alternately high and lowrefractive index (Text-fig. 2). In such a system light reflected at each interface inter-feres constructively with light reflected from all others, resulting in a very high reflecti-vity for light of the ' ideal' wavelength. If materials with well-spaced refractive indicesare chosen, a reflectivity as high as that of a silver mirror (96-6 %) can be achievedusing as few as seven layers, and with more films surfaces reflecting more than 99 %of the incident light can be produced. The materials commonly used industrially inthese' all dielectric' reflectors are vapour-deposited ZnS (n = 2-4)andMgF2(n = i"36)(VaSfcek, i960).

In a system such as that shown in Text-fig. 2 the reflected light is coloured becauseconstructive interference only occurs for wavelengths close to the ideal wavelength.If the difference between the refractive indices n± and n% is increased, the ' bandwidth'of the reflected light increases, and the number of films required to achieve a givenreflectivity decreases, hence for most purposes it is desirable for nx and n^ to be as farapart as possible. Reflectors of this type are used as colour-selective mirrors, heat-reflecting filters, coatings for increasing the reflectivity of the ends of lasers, and in othersituations where both high reflectivity and wavelength specificity are required. Suchsystems are virtually non-absorbing, transmitting all hght that is not reflected. Hence

28-a

434 M. F. LAND

in the visible spectrum the light which is transmitted is complementary in colour tothe reflected light.

The colours of a number of biological surfaces have been attributed to thin filminterference. Mason (1927) produced evidence showing that thin film interference wasresponsible for the iridescent colours of the wings and bodies of many insects, andAnderson & Richards (1942), in an early electron microscope study, showed that the

Text-fig. 1 Text-fig. 2

Text-fig. 1. Thin film. Constructive interference occurs when nt = J A.Text-fig. z. Multiple quarter-wavelength film system, n ^ = «,£, = ± A.

blue colour of the wing scales of the butterfly Morpho cypris was due to reflexion froman array of appropriately spaced lamellae (see Fox & Vevers (i960) for further refer-ences). Only recently, however, has much attention been paid to interference pheno-mena associated with highly reflecting surfaces. Denton & Nicol (1965) have shownthat both the colours and high reflectivity of fish scales are due to multiple thin filmreflexion with constructive interference—the thin films in this case being stacks ofguanine crystals in the inner surfaces of the scales.

The argentea of the eye of Pecten, with which the present paper is concerned, is aparticularly interesting reflector. Unlike the situation in most other eyes, the opticalsystem is in this case based not upon a lens, but upon a reflecting system (Text-fig. 3){Land, 1965, 1966). The argentea, which is spherical, forms the visual image, muchas in a reflecting telescope.

The argentea is optically of very good quality, the law of reflexion being obeyedwith little or no scattering of the incident light. A simple examination of the eye showsthat the reflectivity of the argentea is comparable with that of a metallic reflector, andalso that the reflected light is not spectrally uniform, the apparent colour being a ratherunsaturated blue-green. Patten (1886) noticed that the argentea was a multilayeredstructure, consisting of several layers of thin, square crystals. These facts strongly

Scallop eye reflector 435

suggest that, optically, the argentea may be functioning as a multilayer quarter-wavelength reflector.

In the present study this suggestion has been followed up by four methods: lightmicroscopy, electron microscopy, interference microscopy and spectral analysis of thereflected light.

METHODS

Pecten maximus were obtained from Plymouth and kept in a recirculating sea-wateraquarium.

Interference microscopy

The instrument used for measuring the optical constants of individual argentealcrystals was the high-power interference microscope developed by Huxley (1954).This microscope enables one to measure the difference between the optical path

Text-fig. 3. Optical system of the eye of Pecten maximus.

lengths of light which has passed through a crystal, and light which has passed directlythrough the suspending medium. This path difference can be measured with a standarderror of less than 1 m/i over ten individual measurements. Path differences (p.d.) weremeasured in two suspending media with different refractive indices (in this case water,n = 1-333 a nd 50% sucrose (w/w solution), n = 1-420). From the two simultaneousequations:

P-°--water = '("crystal ~~ wwater)> P-°--sucrose = ^("crystal ~ nsucrose)>

the crystal thickness (i) and refractive index (n) were determined.The microscope produces two images, one in the main beam and one in the reference

beam. The most consistent results were obtained by matching the brightness of theimage of a crystal in the main beam against the background, and then moving thecompensator until the image of a crystal in the reference beam matched the back-ground; the amount by which the compensator has to be moved in performing this

436 M. F. LAND

operation gives the sum of the half path differences of the two crystals, i.e. the meanpath difference for the pair. After each series of ten measurements in water, the waterwas carefully removed and replaced by sucrose, and a further set of measurements wasmade on the same pair of crystals.

The measurements were made using approximately monochromatic light of wave-length 525 m/i. The microscope has an objective N.A. of 0-9, and was used with anilluminating cone of N.A. 0-7.

Spectral reflectivity measurements

An eye was removed from the mantle and mounted pupil upwards in a sea-waterchamber (Text-fig. 8a). It was illuminated with parallel light from a microscope lamp,whose horizontal beam was directed into the eye by a coverslip inclined at 32-5° to thehorizontal (not 450, to avoid reflections from another coverslip which covered the eyein its chamber). Light reflected from the back of the eye entered a microscope (16 mm.objective, N.A. 0-12) which was focused to give an image of the eye on a screen abovethe eyepiece. In the centre of this screen was a CdS photocell, which covered the imageof the light source produced by reflexion in the eye. The light which entered themicroscope was not reflected exactly normally from the argentea, but at an angle ofincidence and reflexion of about 9° ±8° (160 cone). The wavelength of the incidentlight could be varied using a set of seven Balzers interference filters with maximumtransmissions between 400 and 710 mfi, and half widths of 40-50 m/t. The resistanceof the photocell was measured at each wavelength using a microammeter and a 67 V.battery. The eye was then removed, and replaced by a white opal Perspex plate, andthe photocell was calibrated at each wavelength using a set of Wratten neutral densityfilters. The apparent optical density of the argentea relative to the white plate couldthus be found for each wavelength. CdS cells, although sensitive and simple to use,have the disadvantage of taking up to 2 min. before giving a steady reading at lowlight intensities, and each experiment thus took about 30 min. to complete. The eyesremained in perfect condition over this period, and there was almost no differencebetween readings made at the beginning and end of each experiment. Each point inText-fig. 7 is the mean of two measurements, one made with wavelength increasing,and the other decreasing.

RESULTS

Light microscopy

In the intact eye the argentea may be examined through the pupil. It is superficiallyperfectly smooth, the only visible defects being occasional hair-like cracks. By reflectedight it is blue-green (Amax usually about 530 m/i, although the exact maximum variesfrom eye to eye between 500 and 550 m/i). By transmitted light the reflector appearsred, but this colour is mainly due to underlying pigment cells.

The true 'transmitted light' colour can be observed by carefully scraping theargentea from an eye on to a slide and removing the pigment cells. This processinvariably breaks up most of the structure, but some intact parts remain. These partsretain their high reflectivity and blue-green colour by reflexion, and by transmittedlight they continue to appear red (the complementary colour to blue-green). If theorganization of the intact piece of tissue is destroyed by pressing on the coverslip, both

Scallop eye reflector 437

the colours and the high reflectivity are lost. The colours are thus structural ratherthan pigmentary.

Examination of the less damaged parts under high-power shows the argentea to be arather regular mosaic of square crystals. Each crystal has sides 1-1-1-3 /* l°ng> aQd istoo thin for the thickness to be measured with the light microscope. Judging from thenumber of crystals liberated when an intact piece of tissue was broken up, many morecrystals were present than could be accounted for by a single layer, indicating a multi-layered structure. The surprising ease with which the crystals disperse indicates thatthey are not embedded in a rigid matrix, but are held loosely in the cytoplasm of thecells containing them. Individual crystals are colourless by transmitted light.

Electron microscopy

It is a pleasure to thank V. Barber for taking electron micrographs of the argentea.A full account of the ultrastructure of the eye of Pecten, including the argentea, is givenin Barber, Evans & Land (1966).

CytoplasmCrystals(guanlne)

1-1-13//-

Text-fig. 4. Reconstruction of part of the argentea. The crystals are drawn exactly one abovethe other. This situation is sometimes seen, but staggered arrangements are also found.

Eyes were removed from the animal, and opened with a small cut to allow penetra-tion of the fixative. They were fixed in phosphate-buffered osrnic acid (Millonig, 1961),Araldite embedded after dehydration, sectioned and examined under a Siemenselectron microscope. PI. 1 shows a typical section of the argenteal region, cut at rightangles to the surface. In all sections the crystals themselves have dissolved out duringpreparation of the tissue, leaving electron-transparent spaces. Where these spaces havea consistent parallel-sided appearance, they are considered to be accurate replicas ofthe crystals. Parts of the sections were clearly worse than others, the spaces beingdistorted like expanded aluminium mesh.

The argentea contains from 30-40 layers of crystals. Each crystal is rather less than100 m/i thick, and is separated from the next below it by a layer of cytoplasm ofslightly greater thickness—about 100 mft,. There are thus five to six 'repeat units' permicron, and the thickness of the whole structure is about 6 fi. The gaps between thecrystals laterally are very narrow, and the lateral dimension of the crystals, about I-I /i,is in close agreement with that obtained from light microscopy. A reconstruction ofpart of the argentea is shown in Text-fig. 4.

438 M. F. LAND

If the argentea is to function in the manner suggested, both the crystals and thespaces between them should have optical thicknesses of £Amax , i.e. ^f^m/i = 133111/4.The cytoplasmic interstices are unlikely to have a refractive index much different fromthat of water (1-33), so their optical thickness (n.t. = 133 m/i) is clearly compatiblewith the theory. So also is the slightly smaller thickness of the crystals, as these mightbe expected to have a higher refractive index. However, to obtain more exact informa-tion about the crystals, an interference microscope was used.

Interference microscopy

Crystals from a dissected argentea were dispersed in water, and allowed to settle ona microscope slide. The crystals were then examined under an interference microscope:their appearance is shown in PI. 2. The microscope was used to measure the pathdifference (p.d.) between individual crystals and two suspending media, water and50% sucrose. From these p.d.'s the thicknesses (t) and refractive indices (n) of thecrystals were calculated. The measurements were made on pairs of crystals (seeMethods) and the p.d.'s obtained are the mean p.d.'s of each pair. The results, forfive pairs of crystals, are given in Table 1.

Table 1. Optical properties of isolated crystals

Crystalpair

ABCDE

Means

P.d. inwater

(n = 1-333)

4 0 6

35-838637-835-437-6

(All dimensions

P.d. insucrose

(n = 1-420)

3i-92 9 930-93 0 52 9 8

3 0 6

Recalculated from mean path difference

(P

, P

,d.^,Xl-420)-

are in m/J.)

n

1-74i-861-771-78i-88

I-8 I

3 i-8o

f p H .iijjiTjn X

t

IOO

6 8 0

87-483964-48 0 7

80S

1-333)

nt

' 74126

I5S1491 2 1

145

145

("-1-333)'

The mean value of n.t. from Table 1 is 145 mfi, which is very close to the expectedvalue, iAmax =133 mfi, and the crystals may therefore be regarded as quarter-wavelength films.

There is a negative correlation between the values of n and t in Table 1, which isdifficult to interpret; it might be caused by individual crystals showing different degreesof swelling and shrinkage, in which case n and t would not be expected to vary in-dependently. If, however, the assumption is made that all crystals are formed of thesame material, and have the same refractive index, a better estimate of the variationof thickness between crystals can be made. Taking n as i-8o, the thicknesses can berecalculated from the p.d.'s. The standard deviation of the thicknesses, recalculatedfrom the path differences in water, is only 4-6 mfi, i.e. about 6 % of the mean value(81 mfi). It seems likely that in the animal, crystal thickness is controlled with con-siderable precision.

Scallop eye reflector 439

Absolute reflectivity of the argenteaIt is possible to calculate the reflectivity of a quarter-wave assembly of the type

shown in Text-fig. 2, provided the refractive indices of the constituent films are known(see VaSffiek, i960, p. 234). For light incident normally on a single interface, separatingmaterials of refractive indices nx and n^, the reflectivity, i.e. the ratio of reflected toincident energy, is given by

r = JFor a system such as the argentea, consisting of a number of quarter-wavelengthfilms (wj) separated by quarter-wavelength spaces (%), and with the same material (r^)

100r

50

10No. of interfaces

20

Text-fig. 5. Reflectivity at the ideal wavelength of a multilayer system (Text-fig. 2)for different numbers of films, tti = i-34, n, = i-8o.

above the first and below the last n^ film, a very similar equation may be used to calculatethe reflectivity:

I - -

(2)

where k is the total number of interfaces. This may also be expressed in terms ofthe reflectivity of a single interface (r):

(3)

Equations (2) and (3) are only appropriate for light of the ideal wavelength, i.e. whenA = 4«i*i = 4«2'2' They can be used to calculate the reflectivity of the argentea by

44° M. F. LAND

taking nx as the refractive index of cytoplasm (about 1-34) and n% as that of the crystals(1 -8o), and k as twice the number of crystal layers. Text-fig. 5 shows the results of thecalculation.

It can be seen from Text-fig. 5 that with only ten layers of crystals the argenteawould be a 99 % efficient reflector for light of the appropriate wavelength. With thirtylayers its reflectivity would be undetectably different from 100%. Unfortunately, ithas not been possible to measure the absolute reflectivity, as the argentea cannot beremoved from the eye intact and laid flat, and in situ methods of measurement involvetoo many approximations for them to be of any use. There is, however, no reason tosuppose that the reflectivity departs far from the theoretical value; it has been shownin the context of interference-filter manufacturer that inaccuracies of up to 10 % infilm thickness, such as are likely to occur in the argentea, have a negligible effect onoverall reflectivity (Heavens, 1955).

Variation of reflectivity ztrith wavelength

Light reflected from single or multiple quarter-wavelength films is coloured. Withsingle films the colour is very unsaturated; a quarter-wavelength film of refractiveindex i-8, in water, reflects between 6 and 9% of the incident light over the wholevisible spectrum. However, in a multilayer structure, the variation of reflectivity withwavelength becomes more pronounced with increasing number of layers, the band-width becomes narrower and more sharply denned, and the colour correspondinglymore intense (Text-fig. 6 a).

100

so

-

i/ I

/ ! '

/I !

Jl ;1

k_=20

/<=10•" --.

K = 6

K ^ L

\

i\i ••

i '•

iii

t

1

(a)

*•. " i

; \ \* ~

1

1001—

400 500 600 700Wavelength (m/*)

600

Text-fig. 6. Reflectivity of multilayer systems (Text-fig. 2) at different wavelengthsnumber of interfaces, i.e. twice the number of crystals in an ideal argentea. The k =in Text-fig. 66 should correspond to an actual argentea with thirty layers of crystals. «n, = i-8o and A^., = 530 ny*.

700

k is the60 curve= 1-34,

The reflectivity of a thin-film system at any wavelength may be calculated using themethod given by Vasicek (i960, pp. 236-7), and other methods are given by Heavens(i960). These calculations, however, are laborious to perform by hand. In connexionwith the present study, Prof. A. F. Huxley has derived a much more convenientmethod (Huxley, 1966) which is given below.

Scallop eye reflector 441

If the wavelength under consideration is A, the phase change in each film (<f>) isgiven by

<f> =

where Amax is the ideal wavelength. When cos <p lies between /̂r and — ^jr, A is closeto Amax , and the reflectivity of the system is only slightly less than the reflectivity atthe ideal wavelength, given by equation (3). Under these circumstances the reflectivityis given by

w h e r e _ / s in <f> - ^ ( r - cos2 <f>)\ ky ~ [sin $+ <J(r-cos* $)) '

where r is the reflectivity of a single interface from equation (1) and k is the number ofinterfaces.

Outside this range, i.e. when cos <j> is greater than ^jr and less than — *Jr, equation (4)no longer applies, and the reflectivity is given by

R = [2(cos2 0-r)]/[r(i -cos k0)]

where a / co s2^ - r \cos 6 = I — I.

\ i-r )

\'

cos

The reflectivity fluctuates with wavelength between zero when cos kd = +1, and(r/cos2 (p) when cos kd = — 1. These fluctuations become closer together as the numberof films increases. When the number of films is large, these fluctuations may beaveraged to give a smooth curve; the reflectivity is then given simply by

In calculating theoretical reflectivity curves for the argentea (Text-fig. 6), thequarter-wavelength film model has been assumed, and the methods given above havebeen used. Equation (6) was used for the k = 00 curve in Text-fig. 6b.

It can be seen from Text-fig. 6 that apart from the rapid fluctuations the shape ofthe reflectivity curve changes very little when A>2O, i.e. when the argentea is 10 ormore crystal layers thick. If the quarter-wavelength film hypothesis is correct, theactual argentea ought to be a nearly perfect reflector for wavelengths up to 50 ra/i oneither side of Amax , and the reflectivity should fall to near zero at either end of thevisible spectrum.

Although it is difficult to measure the absolute reflectivity of the argentea, it iscomparatively easy to compare the reflectivities at different wavelengths; this can bedone with the eye intact. The method of illumination is shown in Text-fig. 8 a. A CdSphotocell was used to measure the reflected light, and the wavelength was varied witha set of interference filters (see Methods section). In Text-fig. 7, the ordinate is therelative reflectivity, i.e. reflected light intensity at wavelength A divided by reflectedintensity at Amax. Curves are given for two eyes; three other eyes gave curves very

442 M. F. LAND

similar to the right-hand curve. The eye which gave the left-hand curve was visiblybluer than the others.

The measured curves are similar in shape to the theoretical curves in Text-fig. 6b.Like the theoretical curves they show that most of the reflected light lies within awell-defined band of wavelengths, and that outside this band the reflectivity fallsmore steeply towards the blue end of the spectrum than towards the red. Both curveswere almost symmetrical when plotted against 4> o r XM- The bandwidth of the

100 r-

50

400 500 600Wavelength (m/t)

700

Text-fig. 7. Reflectivity relative to the reflectivity at A^.T for the argenteaeof two eyes from different animals.

Green Blue

(b)

White

A i r

Sea water

Text-fig. 8. (a) Method of illumination for reflectivity measurements. (6) Angles ofincidence and reflexion for singly and doubly reflected rays.

measured curves appears to be rather greater than that of the theoretical curves, evenafter making an allowance for the distorting effect of the broad band filters used inmaking the measurements, and this larger bandwidth may well be a consequence of' inaccuracies' in crystal thickness or spacing in the argentea itself. It is of interest thatinterference reflectors with a high (95 %) reflectivity over the whole visible spectrumhave been manufactured by deliberately varying the thicknesses of the constituentfilms (Heavens, i960). The rapid fluctuations predicted in Text-fig. 66 were sought

M. F. LAND

the light reaching the receptor cells will have a Amai appreciably shorter than thefigure of 530 m/i given here for angles of incidence close to zero. By estimating therelative amounts of light reflected at each angle of incidence one can form an estimateof Amax for the cone of light reaching the receptors; Amax thus obtained is approxi-mately 490 m/t. One would expect the argentea to be 'tuned' to reflect best in thepart of the spectrum containing the spectral sensitivity curve of the receptors. Cronly-Dillon (1966) found that the animal's shadow reflex, which is mediated by the receptorcells in question (Land, 1966), has a peak sensitivity in the range 475-480 rafi, whichis agreeably close to the maximum reflectivity.

Osmotically induced colour changes

If an eye is placed in distilled water, the colour of the light reflected by the argenteachanges from blue-green through yellow to orange, over a period of about 2 min. Thisprocess is reversible, the colour returning slowly to blue-green when the eye isreplaced in sea water. In hypertonic sucrose the colour becomes bluer. These changesare presumably caused by swelling and shrinking of the spaces between the argentealcrystals, brought about by osmotic entry of water. They give further support to theassumption that the crystals are not held rigidly in position, but are free to moverelative to each other. This raises the problem of how the crystals are normally main-tained at the 'correct' distance apart; at present, no explanation of this spacingmechanism can be offered.

Chemical nature of the crystals

Purines have been identified as the main constituents of reflecting structures inmany marine animals. The reflecting material in the scales of fish is guanine; hypoxan-thine is also present in some scales. Guanine forms the reflecting tapetum in bothteleosts and in crocodiles (see Fox & Vevers, i960). Kleinholz (1959) showed that fivedifferent purines and pterins are present in the reflecting layers of the lobster eye, andalso that the reflecting material in the eye of Limulus is guanine. Uric acid has beenfound in the lobster eye, and in iridocytes of the sea anemone Metridium senile.

The argenteal crystals from Pecten have properties compatible with those of purines.They are insoluble in water, but soluble in both N/IO HC1 and N/IO NaOH. They areslightly soluble in alcohol, but not in either acetone or ether. Isolated argenteae gavemurexide reactions, although the quantity of material was too small for the colour ofthe residue to be used to identify the particular purine. The crystals are not uric acid,as they failed to give a reaction with Folin's reagent.

When crystals from the argentea were dissolved in N/IO NCI, which was then allowedto evaporate, needle-like crystals were formed which were indistinguishable fromthose of British Drug Houses' guanine recrystallized in the same way.

The argenteae dissected from two eyes were dissolved in N/IO HC1, and chromato-graphed using water-saturated n-butanol as the solvent. The standards used wereguanine and uric acid (5 fig. each). The chromatograms were developed by the descend-ing method, and when dry were examined under ultraviolet light. The argenteae gavea blue-fluorescent spot, of the same colour, and with the same Rf value as the guaninestandard. A green fluorescent spot which had remained on the origin was probablycaused by pigment from the cells behind the argentea, as this spot occupied the same

Scallop eye reflector 445

area as the red mark on the paper. The argenteal material gave only these two spots,and the crystals are therefore taken to be made of guanine.

It is interesting that the refractive index found by interference microscopy for thecrystals of the argentea (i-8o) is close to that found by Denton & Nicol (1965) for therefractive index of guanine crystals from the scales of the herring—18 to 1-9. Themethod they used was an immersion method, crystals being examined in liquids ofdifferent refractive index until a match was obtained, the crystals becoming invisible.Similarly, Schmidt (1949), using polarization microscopy and comparison liquids,found that guanine plates from the copepod Sapphirina were strongly birefringent,having an ordinary refractive index of 1-79 (for rays normal to the plate surface—theindex relevant here) and an extraordinary index of 1-55 (for rays parallel to the platesurface).

A 'good' material for use in a reflecting system would be one which is insoluble inwater, which can be crystallized as parallel-sided plates, and which has a high refractiveindex in this form. The popularity of purines as reflecting substances may well resultfrom their ability to fulfil these conditions particularly well.

DISCUSSION

There are two ways, besides thin-film interference, in which highly reflecting non-metallic surfaces may be produced. First, the amount of light reflected at a singleinterface between two media may be increased by increasing the refractive indexdifference between the media. Thus when light is incident from air on to a singlesurface of refractive index (n) 1-5, the reflectivity is 4%; this increases to 11 % whenn = 2, 25 % when n = 3, and 36% when n = 4. Transparent materials are knownwith refractive indices as high as 3 (e.g. SbjSa, n = 3-0), but it is unlikely that therefractive indices of biological materials much exceed 2, which would limit single-surface reflectivity to 11 %.

A second method of achieving high reflectivities would be to use a series of alter-nating thick films. A thick film is one whose optical thickness is sufficiently great forinterference colours to be no longer visible, i.e. when successive interference maximafor different wavelengths become so close together that the film appears white. This isempirically taken to occur when znt > 5A, i.e. when the film thickness is greater thanabout a micron. The reflectivity of a system Eke that shown in Text-fig. 2, but withthick instead of thin films, is given by

where r is the reflectivity of a single interface, and k the number of interfaces.In Table 2 the reflectivities of a thin-film system (with constructive interference),

and a thick-film system using the same materials, are compared.It can be seen from this table that any thin-film system (k > 1) requires fewer inter-

faces than a thick-film system for the same reflectivity to be achieved. Nevertheless,thick-film systems using biological materials would be effective reflectors, and theyprobably do occur in situations where all that is required is a white reflecting patch ofindifferent optical quality. A serious drawback of thick-film systems is that, whenlight is not incident normally, light reflected from every interface follows a separate

446 M. F. LAND

path: thus one sees multiple reflexions from a pile of microscope slides. This meansthat as an optical mirror, a thick-film system would be useless. In a thin-film systemlike the Pecten argentea, where nearly all the light is reflected in the first 2/1 of thestructure, this scattering effect would be negligible.

The spectral dependence of the light reflected from thin film systems may limit theirapplicability as mirrors. However, in the case of Pecten, which lives at depths down to100 m., where what light there is lies in the blue-green part of the spectrum, this isclearly no disadvantage.

Table 2. Reflectivities of thin and thick film systems of alternating films

("1 = 1'34. n% = i-8o.)

Number ofinterfaces

(*)

1

2

41 0

2 0

4 01 0 0

R thin film(equation (2))

(%)

2-2

8-4298299

1 0 0

1 0 0

R thick film(equation (7))

(%)

2 - 2

4-48 4

193i4770

Reflectors with structures very similar to that of Pecten have been found in the eyesof the cockle, Cardium edule (V. Barber, unpublished) and the median eyes of thecrustacean Macrocyclops albidus (Fahrenbach, 1964). In both cases the dimensions ofthe crystals are compatible with their being quarter-wavelength films. Some vertebratetapeta are often of good optical quality. The tapetum of the bush-baby Galago crassi-caudatus, for example, is a brilliant reflector, and it, too, has a similar structure to thePecten argentea (Dartnall et al. 1965). The reflecting crystals in this case are made notof guanine but of riboflavin (Pirie, 1959). The tapetum of the cat contains a system oforientated rod-like structures, arranged in 'lattice planes' 450 m/i apart, and Pedler(1963) has given grounds for believing that the green colour and high reflectivity aredue to constructive interference.

SUMMARY

1. The physical mechanism responsible for the high reflectivity of the argentea ofthe eye of Pecten maximus has been investigated by light microscopy, electron micro-scopy, interference microscopy and spectral analysis of the reflected light.

2. The argentea consists of 30—40 layers of high refractive index material (guaninecrystals) separated by layers of low refractive index material (cytoplasm). Both highand low refractive index layers have optical thicknesses of approximately one-quarterof the wavelength of the light that the argentea reflects best (blue-green, A = 530 m/i).

3. The reflecting properties of such a system have been investigated theoretically,and the results compared with the measured reflectivity of the argentea at differentwavelengths.

4. The refractive index of the guanine crystals is i-8o.

Journal of Experimental Biology, Vol. 45, No. 3 Plate 1

Light

M. F. LAND (Facing p. 446)

Journal of Experimental Biology, Vol. 45, No. 3 Plate 2

. 10/tandV

M. F. LAND

Scallop eye reflector 447

My special thanks are due to Prof. A. F. Huxley for detailed advice on opticalproblems, and in particular for deriving several of the formulae given here. I shouldalso like to thank Dr B. E. C. Banks for chromatographing argenteal material, mysupervisor, Prof. J. A. B. Gray, for advice and discussion, and the Medical ResearchCouncil for a research training scholarship.

REFERENCES

ANDERSON, T. F. & RICHARDS, A. G. (1942). An electron microscope study of some structural colors ofinsects. J. Appl. Pkys. 13, 748-58.

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EXPLANATION OF PLATES

PLATE I

Electron micrograph of a complete vertical section through the argentea. The ' holes' are the sites of theguanine crystals. A pigment cell can be seen below the argentea. Stained lead citrate.

PLATE 2

Interference micrograph of isolated crystals. Crystals from the image formed by the main beam appearlight, those from the comparison beam appear dark. Part of a pigment cell can be seen top left.

Exp. Biol. 45, 3