- Email: [email protected]
Quantitative photoacoustic spectroscopy of cataractous human lenses
Journal of Photochemistry
QUANTITATIVE CATARACTOUS UMBERTO ALFONSO
BERNINIa, SCALAb
and Photobiology,
B: Biology,
PHOTOACOUSTIC HUMAN LENSES RAFFAELE
RECCIAb,
4 (1990)
407 - 417
407
SPECTROSCOPY OF
PAOLO
RUSSOa
and
aDipartimento di Scienze Fisiche, Universito’ di Napoli (Italy) bClinica Oculistica, II Facoltci di Medicina e Chirurgia, Universita’ di Napoli (Italy) (Received
January
21, 1989;
accepted
June 17,1989)
Cataract, lens nucleus, photoacoustic spectroscopy, extracapsular cataract extraction, UV absorption.
Keywords.
Summary Quantitative photoacoustic spectra of the nuclei of cataractous human lenses with various degrees of colouration and opacification were measured in the spectral range 250 - 600 nm. The lens nuclei were obtained from 20 cataractous patients through extracapsular cataract extraction. These measurements yield the light loss per unit path length in the nucleus of cataractous lenses.
1. Introduction The increased light absorption in the nuclei of human lenses which occurs during the process of aging has been associated with the development of pigments in the lens nucleus whereby it develops a yellow colouration [l]. These pigments are fluorogen compounds which accumulate in the water-insoluble fraction of lens proteins [2 - 51, and are thought to be photodegradation products of UV-absorbing molecules [ 1,2,6]. The light absorption due to pigment deposition in the nucleus is not large at wavelengths greater than 400 nm except for extreme pigmentation (brown or black nuclei). However, this is not the only cause of light loss in the nucleus. Light scattering also contributes to light loss in aged and cataractous nuclei [7]. The scattering centres have been identified as protein aggregates (having a size comparable with the wavelength of visible light) found in the nuclei of young and aged normal lenses [8] as well as in the nuclei of cataractous lenses [ 9, lo]. On aging, these protein aggregates collapse into denser agglomerates [8] ; as a consequence the random spatial fluctuations in refractive index between these aggregates and the surrounding medium increase, thus producing increased light scattering [ll]. The processes of Elsevier Sequoia/Printed
in The Netherlands
408
nucleus colouration and light scattering coexist, but do not appear to be correlated [ 121. In this work photoacoustic (PA) spectroscopy was used to characterize quantitatively the contribution of the absorption in the nucleus to the light loss in cataractous human lenses (in Appendix A the PA effect in solids and its use in spectroscopy are briefly outlined). The PA technique was used since it allows the spectroscopic analysis of opaque and light-scattering samples. The quantitative measurements yield directly the light loss per unit path length in the lens nucleus. Moreover, another point is of concern here. The cataract, i.e. any opacity of the lens sufficient to degrade the retinal image, is now commonly treated by surgical replacement of the lens with a plastic one, after either intracapsular (complete lens removal) or extracapsular (posterior capsule left in situ) extraction. On replacement of the natural UVA- and blue-absorbing lens, the artificial lens (commonly made of polymethylmethacrylate (PMMA) with added UV-absorbing molecules) offers UVA filtering, but with a wide disparity in UV protection among intraocular lenses (IOLs) from different manufacturers [ 131. More critically, if the implanted lens is made of clear PMMA any blue filtering is absent and the UV filter is effective only in the UVB region. Thus, if the implanted IOL transmits UV light more than the extracted natural lens, a natural filter is lost and the retina is exposed to hazardous radiant energy of short wavelength [14,15]. Hence, it would be useful to quantify the amount of UV and blue light absorption of the cataractous lens; in principle, once the absorption spectrum of the extracted lens is determined it is possible to approximate its absorption characteristics even after IOL implantation, e.g. by suitable filtering spectacles, which also avoids the sudden change in colour vision sensitivity after lens replacement. In addition, this information could be useful in manufacturing UV-filtering IOLS.
2. Materials and methods 2.1. Samples Twenty patients were considered in this study (Table l), aged from 51 to 83 years. They showed (cortical and/or nuclear) lens opacities which were clinically classified as cataractous (senile cataract). After planned extracapsular extraction the removed nucleus was cleaned of any cortical material and kept frozen for successive spectroscopic evaluation. Only one nucleus was used for each patient, except for patient 7. The photoacoustic spectrum of the cataractous lens nucleus was measured in the range 250 - 600 nm. Each extracted lens was dissected in half with a sterile steel blade along a transverse plane, so that the two hemispheres obtained were two planeconvex half lenses; one of them was placed into the PA cell with the flat inner nuclear part face up.
409
TABLE 1 Data on patients Case number
Age (years)
Clinical cataract classification (by slit lamp observation)
1 2 3 4 5 6 7s 7d 8 9 10 11 12 13 14 15 16 17 18 19 20
82 68 74 70 70 60 83 83 68 70 53 65 71 72 73 71 77 51 71 64 68
Nuclear Cortico-nuclear Cortico-nuclear Nuclear Nuclear Cortico-nuclear Nuclear Nuclear Posterior subcapsular Cortico-nuclear Cortico-nuclear Nuclear and posterior Nuclear and posterior Cortico-nuclear Cortico-nuclear Nuclear and posterior Nuclear Cortico-nuclear Cortico-nuclear Nuclear and posterior Nuclear and posterior
subcapsular subcapsular
subcapsular
subcapsular subcapsular
2.2. Equipment
The spectrometer used was a custom-assembled PA apparatus for solid and liquid samples. The light source was a 1000 W xenon arc lamp (CanradHanovia) in a Kratos housing; the grating monochromator was a 0.3 m GCA-McPherson model 218; the light modulator was an electromechanical chopper by EG&G (model 196), working at a frequency of 40 Hz. The PA cell and preamplifier were EG&G models 6003 and 6005 respectively; the cell was filled with air at room temperature and atmospheric pressure. The signal from the microphone contained in the cell was fed to an EG&G model 5206 dual-phase lock-in amplifier which detected the components of the signal in phase and in quadrature with the incident light. The scanning speed of the monochromator was 50 nm mm’. The PA signals were digitally acquired by a personal computer (IBM model XT 286) through analogue-todigital conversion at a rate of two samples per nanometre. The raw spectra were digitally low-pass filtered; since the absorption bands of interest have quite large central widths, the smoothing applied (moving average filtering) was such that the final spectral resolution was about 5 nm. 2.3. Methods In the first series of measurements, we recorded the amplitude S of the PA signal. In order to correct the spectra for the output spectrum of the
410
xenon lamp in the measured spectral range, a part of the light beam was sent to a pyroelectric detector; an analogue ratiometer (Princeton Applied Research model 193) provided the ratio between the amplitude of the PA signal and the signal from the lock-in amplifier (Ithaca model 353) connected to the pyroelectric detector. This ratiometer also gave the ratio of the component in quadrature to the component in phase of the PA signal, i.e. tan @. The signal amplitude was not directly proportional to the optical absorption coefficient; however, it has been proved that for thermally-thick samples the tangent of the phase of the photoacoustic signal varies linearly with the optical absorption coefficient (a brief resume of this theoretical description is given in Appendix A). This being the case for the material of the lens nucleus, we also measured the tan 4 signal: the measurements of the amplitude S and tan rj provided the absolute value of the optical absorption coefficient /3, (in reciprocal centimetres) in the UV and visible spectra of the analysed lens nuclei (for details on PA phase measurements see ref. 16). 3. Results In order to illustrate how the PA spectra were processed, Fig. 1 shows the PA spectrum of a cataractous nucleus (case 16) in the range 250 - 500 nm. Curve a is the absorption spectrum computed by the tangent of the phase PA signal, i.e. the plot of the quantity (tan $J - 1)/p us. wavelength (see Appendix A, eqn. (A2)). This curve represents the optical absorption spectrum only for moderately high absorption (below approximately 400 nm) and shows an anomalous increase for longer wavelengths (due to the
-
Wavelength,nm
Fig. 1. Curve a, the absorption spectrum of the nucleus of a cataractous lens (case 16) derived from the tangent of the phase PA spectrum (eqn. (A2) in Appendix A). Curve b, the absorption spectrum of the same nucleus derived from the amplitude PA spectrum (eqn. (Al) in Appendix A).
411
effect of the pressure term on the PA signal). Curve b is the absorption spectrum of the same sample, that is the plot of Pa us. wavelength obtained using both the amplitude S and the tan rj spectra as explained in Appendix A. Figure 1 shows that these spectra agree closely below approximately 400 nm and diverge in the visible. All PA spectra were processed as for curve b in order to yield /3, us. wavelength X. Figure 2 shows the UV-visible absorption spectra of the nuclei of seven cataractous human lenses. Only seven spectra are shown here for clarity; they were chosen so as to include a brunescent (brown) nucleus (case 4), a non-coloured nucleus (case 17) and nuclei with intermediate colouration (pale yellow nuclei, cases 1 and 7d; yellow nuclei, cases 20 and 7s; deep yellow nucleus, case 5). All spectra show a peak (as about 280 nm) and a shoulder (at about 350 nm). This shoulder is due to increased pigment deposition inside the lens nucleus and correlates with the degree of lens colouration.
600-
Oh 600
'0
-
Wavelength, nw
Fig. 2. Absorption spectra of nuclei from cataractous human lenses. Case numbers as in Table 1. Inset: the long-wavelength portion only of the spectra is shown for clarity.
In general, the nuclei from cortico-nuclear cataractous lenses have lower absorption than those with nuclear cataract. They appear to have various degrees of pigmentation, possibly depending on the time of onset of the cortical opacity which, once developed, should filter out UV radiation and prevent any further nuclear pigmentation by tryptophan photodegradation. For example, this seems to occur for case 17 (a lens (51 years) with corticonuclear opacity). In fact this nucleus has a p, value at 350 nm even lower than that reported for a non-cataractous nucleus of the same age [ 171. For cases 1 and 7d the relatively low value of & at 350 nm seems to be in disagreement with the clinical classification (nuclear cataract). However,
412
the turbidity of this nucleus may indicate that in this case the opacification is due to light scattering, to which our measurements are insensitive (see Appendix A).
4. Discussion The first study on the PA spectroscopy of cataractous lenses (brown nuclear, cortical and cortico-nuclear cataract) was carried out by Lerman et al. [X3]; qualitative PA spectra of the lens nuclei were obtained in the range 250 - 830 nm. A few remarks should be made on the different materials and methodology used in this study compared with ref. 18. Firstly, in this study cortical cataracts were not analysed. Moreover, we analysed only the lens nuclei, whereas Lerman et al. kept the lens in toto (possibly after intracapsular extraction of some of their lenses). However, the experimental conditions in the PA cell were actually the same, since Lerman et al. scraped the capsular and cortical material aside to expose the nucleus to the incident light. Lerman et al. [ 181 ascribed the 280-nm band to the absorption of protein-bound tryptophan and the shoulder occurring at about 350 nm to photochemically-induced fluorescent chromophores in the lens nucleus. In order to quantify the absorption maximum in the latter band, they computed the ratio of the PA signals (amplitude in relative units) at 340, 350, 355 and 360 nm (,!&, SssO, &, Ss6,,) to the value S2s0 at 280 nm. This PA intensity ratio was used in order to specify the relation of the development of the 340 - 360 nm shoulder to the extent of nuclear cataract formation. However, S is not proportional to /3, (see Appendix A, eqn. (Al)) but flattens (saturation effect) for high values of 0,. The presence of a partial saturation of the major peak at 280 nm produces a reduction in this peak in the spectra of Lerman et al., so that the above ratios are systematically overestimated. Moreover, Fig. 2 seems to indicate that the higher the shoulder, the higher the peak at 280 nm (as found in ref. 18); this could be due to the presence of a band at about 280 nm in the UV spectrum of a purified fluorogen found in the insoluble protein fraction of the lens nucleus [ 21. However, we would expect this effect to combine with a reduction in the 280~nm absorption contributed by protein-bound tryptophan, since increased pigmentation accompanies tryptophan depletion in the lens proteins [l, 31. Finally, in order to relate the increased absorption at the shoulder to the increased deposition of nuclear pigments it is not advisable to take the ratio of the 350-nm absorption to the 280-nm absorption. Our values of S3JS2s0 are also in the range 0.1 - 0.5 as in ref. 18; the correct values for comparison P3501P280are in the smaller range 0.1 - 0.2. If we want to correlate the development of nuclear cataract to the 350 nm absorption [18], we can compare directly the values of &, at 350 nm for nuclei of different pigmentation, since p, at 350 nm is proportional to the concentration of the 350 nm chromophore.
413
The same comparison is appropriate when relating the increasing pigment concentration with increasing age of the subject. For example, the /3s5,, values for cases 1 and 17 (Fig. 2) are in the ratio 2:1, which provides an indication of the twofold increase in 350 nm chromophore concentration between a non-coloured nucleus (51 years) and a pale yellow nucleus (82 years). 4.1, Influence of pigment fluorescence The absorbing pigments in the insoluble protein fraction of the cataractous lens are reported to be fluorescent compounds, with at least two fluorogens [ 11.The PA signal is related to the non-radiative de-excitations in the sample; we obtained a PA signal at the activation wavelengths of the chromophores (at 350 nm) because the fluorescence yield is low for this fluorogen [ 191 and because of the process of quenching. 4.2. Influence of light scattering It is well known that optical measurements, e.g. transmission spectroscopy, are very sensitive to light scattering. PA spectroscopy is also influenced by scattering [ 20 - 221; however, in refs. 20 - 22 only the isotropic case is discussed in great detail. From the general formulation of the light-scattering effect in PA measurements [22] we can derive useful indications for nonisotropic scattering. In order to derive quantitative predictions, we need a preliminary estimate of the scattering coefficient 0,. From measurements of the transmission of visible light in age-matched normal and cataractous lenses in toto [ 1, 17, 191 (assuming that the light loss in the visible is entirely due to the scattering of light inside the lens) we have estimated that p, is of the order of 2 - 3 cm-’ at 500 nm. The scattering process cannot be entirely responsible for the light loss, since nuclei of cataractous lenses can be limpid to visual inspection, but absorb in the visible. In these cases the absence of turbidity does not seem to agree with previous indications [8] that the scattering originates from pre-existent protein structures in the nucleus which collapse and produce denser agglomerates. This process implies that water leaves the aggregates [9] and can be found in the surrounding medium [23], thus producing the spatial inhomogeneities in the refractive index and the increased light scattering inside the nucleus. In order to explain the condition of an absorbing but limpid nucleus, we can introduce the hypothesis of a loss of interstitial water from the lens core which causes a reduction in the inhomogeneities in the refractive index in the nucleus and an increase in the surrounding medium. Indeed, it is known from clinical experience that the process of nuclear sclerosis is paralleled by a loss of liquid from the lens nucleus into the surrounding region. However, this condition will not improve visual acuity, because on going through the lens, light will propagate inside regions of different densities and will be internally reflected. In conclusion, it appears reasonable to suppose that the process of light scattering in the nucleus by large protein aggregates [8] has a limited evolution, the final stage being a condition in which the light loss
414
by scattering in the nucleus is not high. As for the relative role of scattering and absorption loss of visible light in the nucleus, it will depend on the degree of nuclear brunescence and on the evolution of the syneresis process [8,9, 23, 241. The spectral region of interest can be divided into two: (i) the visible, where the scattering coefficient p, is possibly greater than the absorption coefficient &, (turbid but non-pigmented nuclei), but where both have quite limited values and (ii) the UV region, where both 0, and &, have much higher values, but ~3,< 0,. In fact, even assuming a X4 dependence of the scattering coefficient, we estimate 0, = 8 - 12 cm-’ at 350 nm. This will imply /3, < p,, since even for normal lenses the total light absorption coefficient in the nucleus is about 40 cm- ’ at 350 nm and 50 years [1’7]. In the visible region, the incident light beam and the distribution of scattered photons have penetration lengths inside the sample which are greater than the thermal diffusion length of the sample (approximately 35 pm, see Appendix A): in this case the PA signal is not affected by the internal scattering. In the UV region, the PA signal is scarcely affected by isotropic scattering and virtually unaffected by non-isotropic scattering. From the above considerations we argue that our PA measurements yield the optical absorption coefficient; the contribution of light scattering is estimated to be of the order of 10% in the UV region (i.e. within the limits of optical density measurements for these optical systems [19]). This is confirmed by the comparison of our values for p, for non-brunescent but turbid nuclei (0, = 18 cm-’ at 400 nm) with the values reported for agematched normal nuclei [17] (0, = 25 cm-’ at 400 nm), as shown in Fig. 2 (cases 1 and 7d). Although literature data [ 1,191 on the absorption of the lens in toto suggest that the data recently reported [17] on the absorption of the lens nucleus are overestimated, it is evident that our measurements are not affected by scattering, which does not occur in the normal lenses analysed in ref. 17.
References 1 S. Lerman and R. Borkman, Spectroscopic evaluation and classification of the normal, aging and cataractous lens, Ophthalmic Res., 8 (1976) 335 - 353. 2 S. Lerman, A. Ti Tam, D. Louis and M. Hollander, Anomalous absorptivity of lens proteins due to a fluorogen, Ophthalmic Res., 1 (1970) 338 - 343. 3 R. B. Kurzel, M. L. Wolbarsht and B. S. Yamanashi, Spectral studies on normal and cataractous intact human lenses, Exp. Eye Res., 17 (1973) 65 - 71. 4 J. A. Jedziniak, J. H. Kinoshita, E. M. Yates, L. 0. Hacker and G. B. Benedek, On the presence and mechanism of formation of heavy molecular weight aggregates in human normal and cataractous lenses, Exp. Eye Res., 15 (1973) 185 - 192. 5 J. A. Jedziniak, J. H. Kinoshita, E. M. Yates and G. B. Benedek, The concentration and localization of heavy molecular weight aggregates in aging normal and cataractous human lenses, Exp. Eye Res., 20 (1975) 367 - 369. 6 S. Lerman, J. F. Kuck, R. F. Borkman and E. Saker, Induction, acceleration and prevention (in vitro) of an aging parameter in the ocular lens, Ophthalmic Res., 8 (1976) 213 - 226.
415 7 R. C. Zeimer tance,
and J. M. Noth,
and study
of lens scatter,
A new method fluorescence
of measuring in uiuo the lens transmitand transmittance, Ophthalmic Res., 16
(1984) 246 - 255. 8 E. L. Siew, D. Opalecky and F. A. Bettelheim, Light scattering of normal human lens. II. Age dependence of the light scattering parameters, Exp. Eye Res., 33 (1981) 603 614. 9 F. A. Bettelheim, E. L. Siew and L. T. Chylack Jr., Studies on human cataract III. Structural elements in nuclear cataracts and their contribution to turbidity, Invest. Ophthalmol. Vis. Sci., 20 (1981) 348 - 354. 10 K. D. Caldwell, B. J. Compton, J. C. Giddingo and R. J. Olson, Sedimentation fieldflow fractionation: a method for studying particulates in cataractous lens, Invest. Ophthalmol. Vis. Sci., 25 (1984) 153 - 159. 11 G. B. Benedek, Theory of transparency of the eye, Appl. Opt., 10 (3) (1971) 459 473. 12 L. T. Chylack, Jr., B. J. Ransil and 0. White, Classification of human senile catatactous change by the American Cooperative Cataract Research Group (CCRG) method: III. The association of nuclear color (sclerosis) with extent of cataract formation, age and visual acuity, Invest. Ophthalmol. Vis. Sci., 25 (1984) 174 - 180. 13 M. A. Mainster, The spectra, classification, and rationale of ultraviolet protective intraocular lenses, Am. J. Ophthalmol., 102 (1986) 727 - 732. 14 D. H. Sliney, Ultraviolet radiation and the cataract patient, Cataract, 6 (1985) 20 - 24. 15 J. Marshall, Radiation of the ageing eye, Ophthalmol. Physiol. Opt., 4 (1984) 1 - 23. 16 P, Poulet, J. Chambron and R. Unterreiner, Quantitative photoacoustic spectroscopy of thermally thick samples, J. AppZ. Phys., 51 (1980) 1738 - 1742. 17 J. Mellerio, Yellowing of the human lens: nuclear and cortical contributions, Vision Res., 27 (1987) 1581- 1587. 18
S. Lerman, B. S. Yamanashi, R. A. Palmer, J. C. Roark and R. Borkman, Photoacoustic, fluorescence and light transmission spectra of normal, aging and cataractous lenses, Ophthalmic Res., 10 (1978) 168 - 176. 19 R. A. Weale, Human lenticular fluorescence and transmissivity, and their effects on vision, Exp. Eye Res., 41 (1985) 457 - 473. 20 P. Helander, Theoretical aspects of photoacoustic spectroscopy with light scattering samples, J. Appl. Phys., 54 (1983) 3410 - 3414. 21 P. Helander, I. Lundstrom and D. McQueen, Light scattering effects in photoacoustic spectroscopy, J. Appl. Phys., 51 (7) (1980) 3841 - 3847. 22 Z. A. Yasa, W. B. Jackson and N. M. Amer, Photothermal spectroscopy of scattering media, Appl. Opt., 21 (1982) 21 - 31. 23 F. A. Bettelheim, S. Ali, 0. White and L. T. Chilack, Jr., Freezable and non-freezable water content of cataractous human lenses, Invest. Ophthalmol. Vis. Sci., 27 (1986)
122 - 125. 24 F. A. Bettelheim, (1979)
189
Syneresis
and its possible
role in cataractogenesis,
Exp. Eye Res., 28
- 197.
Appendix A In gas-microphone photoacoustic (PA) spectroscopy [Al, A21 a beam of monochromatic modulated light is incident on the surface of the sample placed in a sealed cell. A fraction of the light energy absorbed by the sample is converted into a modulated heat flow; acoustic pressure waves arise in the gas contained in the cell adajacent to the sample surface, and it is possible to measure their intensitives with a sensitive microphone. This PA signal depends on the optical absorption coefficient of the sample, and by varying
416
the wavelength of the incident light it is possible to measure the light absorption spectrum of the sample. Our samples (lens nuclei) are macroscopically homogeneous, light scattering and thermally thick, i.e. the thermal diffusion length I-( inside the sample is much smaller than the sample thickness; its value (at the working frequency of 40 Hz) is about 35 pm. Assuming spherical scatterers and a light-scattering process of the Rayleigh-Debye type [A3, A41 (small nuclear inhomogeneities in refractive index [A5, A6]), we have an asymmetry between forward and back scattering. This asymmetry depends on the parameter Zna/h, where a is the radius of the scattering centres and h is the wavelength of the incident light. In our case a has values comparable with the wavelength of the incident light [A5 - A7]; therefore, the scattering is forward scattering in the direction of the propagating collimated beam, which hardly changes the energy distribution inside the sample compared with propagation in non-diffusing media. If the scattering is assured to be isotropic, its influence on PA measurements will be overestimated. The scattering produces a significant enhancement of the PA effect for absorbing samples only if the scattering length is comparable with the thermal diffusion length (l/p, d p, i.e. 0, > 300 cm-i) and /3, % 0,. However, in this case the PA signal is a real quantity, i.e. its phase $ does not provide any information about the absorption spectrum of the sample [A8]. This does not occur in our case, since tan 4 does provide the absorption spectrum. When l/p, % p, i.e. & 6 300 cm-‘, the PA signal is insensitive to scattering if & > 0, and it is slightly affected by isotropic scattering if 0, < 0,. This influence is reduced as the scattering is forward peaked. Taking into account our preliminary estimates for the scattering coefficient /3,, we conclude that to a good approximation our samples can be treated as non-scattering for the purpose of PA measurements. For thermally-thick samples, the amplitude S and the phase $I of the PA signal are given by [A91
s=
AP,P
w{@,p+ 1)2
tan@=&&+1
+ 1}“2
(Al) (AZ)
where A is a constant independent of wavelength and /3, but dependent on the thermal properties of the sample and the experimental conditions, and o is the modulation frequency of the incident light. Since the constant A is usually unknown, the measurement of the PA amplitude S alone provides the qualitative absorption spectrum (S Q:A&p) for low optical absorption (&J & l), whereas in all other cases the spectrum is flattened (saturation). By measuring both S and tan C$we can eliminate the saturation phenomenon. The above relationships do not account for the contribution to the PA amplitude S from the thermal expansion of the sample (the so-called pressure term). Usually (and also in our experimental conditions) this
417
contribution is very small and its influence does not alter the trend of the PA amplitude S vs. wavelength; however, even a small pressure term does contribute to the phase 4 of the PA signal so as to alter the trend of tan 4 for low values of Pa. For these reasons, relationships for both S and tan 4 were taken into account in order to compute 0,. For a moderately high value of 0, the latter relationship yields 0,~ with sufficient precision [A9]. We determined 0,~ from the values of tan 4 (eqn. (A2)) and S at many wavelengths where /3& is high (around the peak value at 280 nm); we deduced many values of A from enq. (Al) and obtained the mean value. This value was then used to obtain 0, from the measurement of S using eqn. (Al). References for Appendix A AI A2 A3 A4 A5
A6
A7
A8 A9
A. C. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy, Wiley, New York, 1980. A. C. Tam, Applications of photoacoustic sensing techniques, Rev. Mod. Phys., 58 (1986) 381 - 431. H. C. van De Hulst, Light Scattering by Small particles, Wiley, New York, 1957. M. Kerker, The Scattering of Light, Academic Press, New York, 1969. E. L. Siew, D. Opalecky and F. A. Bettelheim, Light scattering of normal human lens. II. Age dependence of the light scattering parameters, Exp. Eye Res., 33 (1981) 603 - 614. F. A. Bettelheim, E. L. Siew and L. T. Chylack, Jr., Studies on human cataract III. Structural elements in nuclear cataracts and their contribution to turbidity, Invest. Ophthalmol. Vis. Sci., 20 (1981) 348 - 354. F. A. Bettelheim, S. Ali, 0. White and L. T. Chylack, Jr., Freezable and nonfreezable water content of cataractous human lenses, Invest. Ophthalmol. Vis. Sci., 27 (1986) 122 - 125. P. Helander, Theoretical aspects of photoacoustic spectroscopy with light scattering samples, J. Appl. Phys., 54 (1983) 3410 - 3414. P. Poulet, J. Cambron and R. Unterreiner, Quantitative photoacoustic spectroscopy of thermally thick samples, J. Appl. Phys., 51 (1980) 1738 - 1742.
QUANTITATIVE CATARACTOUS UMBERTO ALFONSO
BERNINIa, SCALAb
and Photobiology,
B: Biology,
PHOTOACOUSTIC HUMAN LENSES RAFFAELE
RECCIAb,
4 (1990)
407 - 417
407
SPECTROSCOPY OF
PAOLO
RUSSOa
and
aDipartimento di Scienze Fisiche, Universito’ di Napoli (Italy) bClinica Oculistica, II Facoltci di Medicina e Chirurgia, Universita’ di Napoli (Italy) (Received
January
21, 1989;
accepted
June 17,1989)
Cataract, lens nucleus, photoacoustic spectroscopy, extracapsular cataract extraction, UV absorption.
Keywords.
Summary Quantitative photoacoustic spectra of the nuclei of cataractous human lenses with various degrees of colouration and opacification were measured in the spectral range 250 - 600 nm. The lens nuclei were obtained from 20 cataractous patients through extracapsular cataract extraction. These measurements yield the light loss per unit path length in the nucleus of cataractous lenses.
1. Introduction The increased light absorption in the nuclei of human lenses which occurs during the process of aging has been associated with the development of pigments in the lens nucleus whereby it develops a yellow colouration [l]. These pigments are fluorogen compounds which accumulate in the water-insoluble fraction of lens proteins [2 - 51, and are thought to be photodegradation products of UV-absorbing molecules [ 1,2,6]. The light absorption due to pigment deposition in the nucleus is not large at wavelengths greater than 400 nm except for extreme pigmentation (brown or black nuclei). However, this is not the only cause of light loss in the nucleus. Light scattering also contributes to light loss in aged and cataractous nuclei [7]. The scattering centres have been identified as protein aggregates (having a size comparable with the wavelength of visible light) found in the nuclei of young and aged normal lenses [8] as well as in the nuclei of cataractous lenses [ 9, lo]. On aging, these protein aggregates collapse into denser agglomerates [8] ; as a consequence the random spatial fluctuations in refractive index between these aggregates and the surrounding medium increase, thus producing increased light scattering [ll]. The processes of Elsevier Sequoia/Printed
in The Netherlands
408
nucleus colouration and light scattering coexist, but do not appear to be correlated [ 121. In this work photoacoustic (PA) spectroscopy was used to characterize quantitatively the contribution of the absorption in the nucleus to the light loss in cataractous human lenses (in Appendix A the PA effect in solids and its use in spectroscopy are briefly outlined). The PA technique was used since it allows the spectroscopic analysis of opaque and light-scattering samples. The quantitative measurements yield directly the light loss per unit path length in the lens nucleus. Moreover, another point is of concern here. The cataract, i.e. any opacity of the lens sufficient to degrade the retinal image, is now commonly treated by surgical replacement of the lens with a plastic one, after either intracapsular (complete lens removal) or extracapsular (posterior capsule left in situ) extraction. On replacement of the natural UVA- and blue-absorbing lens, the artificial lens (commonly made of polymethylmethacrylate (PMMA) with added UV-absorbing molecules) offers UVA filtering, but with a wide disparity in UV protection among intraocular lenses (IOLs) from different manufacturers [ 131. More critically, if the implanted lens is made of clear PMMA any blue filtering is absent and the UV filter is effective only in the UVB region. Thus, if the implanted IOL transmits UV light more than the extracted natural lens, a natural filter is lost and the retina is exposed to hazardous radiant energy of short wavelength [14,15]. Hence, it would be useful to quantify the amount of UV and blue light absorption of the cataractous lens; in principle, once the absorption spectrum of the extracted lens is determined it is possible to approximate its absorption characteristics even after IOL implantation, e.g. by suitable filtering spectacles, which also avoids the sudden change in colour vision sensitivity after lens replacement. In addition, this information could be useful in manufacturing UV-filtering IOLS.
2. Materials and methods 2.1. Samples Twenty patients were considered in this study (Table l), aged from 51 to 83 years. They showed (cortical and/or nuclear) lens opacities which were clinically classified as cataractous (senile cataract). After planned extracapsular extraction the removed nucleus was cleaned of any cortical material and kept frozen for successive spectroscopic evaluation. Only one nucleus was used for each patient, except for patient 7. The photoacoustic spectrum of the cataractous lens nucleus was measured in the range 250 - 600 nm. Each extracted lens was dissected in half with a sterile steel blade along a transverse plane, so that the two hemispheres obtained were two planeconvex half lenses; one of them was placed into the PA cell with the flat inner nuclear part face up.
409
TABLE 1 Data on patients Case number
Age (years)
Clinical cataract classification (by slit lamp observation)
1 2 3 4 5 6 7s 7d 8 9 10 11 12 13 14 15 16 17 18 19 20
82 68 74 70 70 60 83 83 68 70 53 65 71 72 73 71 77 51 71 64 68
Nuclear Cortico-nuclear Cortico-nuclear Nuclear Nuclear Cortico-nuclear Nuclear Nuclear Posterior subcapsular Cortico-nuclear Cortico-nuclear Nuclear and posterior Nuclear and posterior Cortico-nuclear Cortico-nuclear Nuclear and posterior Nuclear Cortico-nuclear Cortico-nuclear Nuclear and posterior Nuclear and posterior
subcapsular subcapsular
subcapsular
subcapsular subcapsular
2.2. Equipment
The spectrometer used was a custom-assembled PA apparatus for solid and liquid samples. The light source was a 1000 W xenon arc lamp (CanradHanovia) in a Kratos housing; the grating monochromator was a 0.3 m GCA-McPherson model 218; the light modulator was an electromechanical chopper by EG&G (model 196), working at a frequency of 40 Hz. The PA cell and preamplifier were EG&G models 6003 and 6005 respectively; the cell was filled with air at room temperature and atmospheric pressure. The signal from the microphone contained in the cell was fed to an EG&G model 5206 dual-phase lock-in amplifier which detected the components of the signal in phase and in quadrature with the incident light. The scanning speed of the monochromator was 50 nm mm’. The PA signals were digitally acquired by a personal computer (IBM model XT 286) through analogue-todigital conversion at a rate of two samples per nanometre. The raw spectra were digitally low-pass filtered; since the absorption bands of interest have quite large central widths, the smoothing applied (moving average filtering) was such that the final spectral resolution was about 5 nm. 2.3. Methods In the first series of measurements, we recorded the amplitude S of the PA signal. In order to correct the spectra for the output spectrum of the
410
xenon lamp in the measured spectral range, a part of the light beam was sent to a pyroelectric detector; an analogue ratiometer (Princeton Applied Research model 193) provided the ratio between the amplitude of the PA signal and the signal from the lock-in amplifier (Ithaca model 353) connected to the pyroelectric detector. This ratiometer also gave the ratio of the component in quadrature to the component in phase of the PA signal, i.e. tan @. The signal amplitude was not directly proportional to the optical absorption coefficient; however, it has been proved that for thermally-thick samples the tangent of the phase of the photoacoustic signal varies linearly with the optical absorption coefficient (a brief resume of this theoretical description is given in Appendix A). This being the case for the material of the lens nucleus, we also measured the tan 4 signal: the measurements of the amplitude S and tan rj provided the absolute value of the optical absorption coefficient /3, (in reciprocal centimetres) in the UV and visible spectra of the analysed lens nuclei (for details on PA phase measurements see ref. 16). 3. Results In order to illustrate how the PA spectra were processed, Fig. 1 shows the PA spectrum of a cataractous nucleus (case 16) in the range 250 - 500 nm. Curve a is the absorption spectrum computed by the tangent of the phase PA signal, i.e. the plot of the quantity (tan $J - 1)/p us. wavelength (see Appendix A, eqn. (A2)). This curve represents the optical absorption spectrum only for moderately high absorption (below approximately 400 nm) and shows an anomalous increase for longer wavelengths (due to the
-
Wavelength,nm
Fig. 1. Curve a, the absorption spectrum of the nucleus of a cataractous lens (case 16) derived from the tangent of the phase PA spectrum (eqn. (A2) in Appendix A). Curve b, the absorption spectrum of the same nucleus derived from the amplitude PA spectrum (eqn. (Al) in Appendix A).
411
effect of the pressure term on the PA signal). Curve b is the absorption spectrum of the same sample, that is the plot of Pa us. wavelength obtained using both the amplitude S and the tan rj spectra as explained in Appendix A. Figure 1 shows that these spectra agree closely below approximately 400 nm and diverge in the visible. All PA spectra were processed as for curve b in order to yield /3, us. wavelength X. Figure 2 shows the UV-visible absorption spectra of the nuclei of seven cataractous human lenses. Only seven spectra are shown here for clarity; they were chosen so as to include a brunescent (brown) nucleus (case 4), a non-coloured nucleus (case 17) and nuclei with intermediate colouration (pale yellow nuclei, cases 1 and 7d; yellow nuclei, cases 20 and 7s; deep yellow nucleus, case 5). All spectra show a peak (as about 280 nm) and a shoulder (at about 350 nm). This shoulder is due to increased pigment deposition inside the lens nucleus and correlates with the degree of lens colouration.
600-
Oh 600
'0
-
Wavelength, nw
Fig. 2. Absorption spectra of nuclei from cataractous human lenses. Case numbers as in Table 1. Inset: the long-wavelength portion only of the spectra is shown for clarity.
In general, the nuclei from cortico-nuclear cataractous lenses have lower absorption than those with nuclear cataract. They appear to have various degrees of pigmentation, possibly depending on the time of onset of the cortical opacity which, once developed, should filter out UV radiation and prevent any further nuclear pigmentation by tryptophan photodegradation. For example, this seems to occur for case 17 (a lens (51 years) with corticonuclear opacity). In fact this nucleus has a p, value at 350 nm even lower than that reported for a non-cataractous nucleus of the same age [ 171. For cases 1 and 7d the relatively low value of & at 350 nm seems to be in disagreement with the clinical classification (nuclear cataract). However,
412
the turbidity of this nucleus may indicate that in this case the opacification is due to light scattering, to which our measurements are insensitive (see Appendix A).
4. Discussion The first study on the PA spectroscopy of cataractous lenses (brown nuclear, cortical and cortico-nuclear cataract) was carried out by Lerman et al. [X3]; qualitative PA spectra of the lens nuclei were obtained in the range 250 - 830 nm. A few remarks should be made on the different materials and methodology used in this study compared with ref. 18. Firstly, in this study cortical cataracts were not analysed. Moreover, we analysed only the lens nuclei, whereas Lerman et al. kept the lens in toto (possibly after intracapsular extraction of some of their lenses). However, the experimental conditions in the PA cell were actually the same, since Lerman et al. scraped the capsular and cortical material aside to expose the nucleus to the incident light. Lerman et al. [ 181 ascribed the 280-nm band to the absorption of protein-bound tryptophan and the shoulder occurring at about 350 nm to photochemically-induced fluorescent chromophores in the lens nucleus. In order to quantify the absorption maximum in the latter band, they computed the ratio of the PA signals (amplitude in relative units) at 340, 350, 355 and 360 nm (,!&, SssO, &, Ss6,,) to the value S2s0 at 280 nm. This PA intensity ratio was used in order to specify the relation of the development of the 340 - 360 nm shoulder to the extent of nuclear cataract formation. However, S is not proportional to /3, (see Appendix A, eqn. (Al)) but flattens (saturation effect) for high values of 0,. The presence of a partial saturation of the major peak at 280 nm produces a reduction in this peak in the spectra of Lerman et al., so that the above ratios are systematically overestimated. Moreover, Fig. 2 seems to indicate that the higher the shoulder, the higher the peak at 280 nm (as found in ref. 18); this could be due to the presence of a band at about 280 nm in the UV spectrum of a purified fluorogen found in the insoluble protein fraction of the lens nucleus [ 21. However, we would expect this effect to combine with a reduction in the 280~nm absorption contributed by protein-bound tryptophan, since increased pigmentation accompanies tryptophan depletion in the lens proteins [l, 31. Finally, in order to relate the increased absorption at the shoulder to the increased deposition of nuclear pigments it is not advisable to take the ratio of the 350-nm absorption to the 280-nm absorption. Our values of S3JS2s0 are also in the range 0.1 - 0.5 as in ref. 18; the correct values for comparison P3501P280are in the smaller range 0.1 - 0.2. If we want to correlate the development of nuclear cataract to the 350 nm absorption [18], we can compare directly the values of &, at 350 nm for nuclei of different pigmentation, since p, at 350 nm is proportional to the concentration of the 350 nm chromophore.
413
The same comparison is appropriate when relating the increasing pigment concentration with increasing age of the subject. For example, the /3s5,, values for cases 1 and 17 (Fig. 2) are in the ratio 2:1, which provides an indication of the twofold increase in 350 nm chromophore concentration between a non-coloured nucleus (51 years) and a pale yellow nucleus (82 years). 4.1, Influence of pigment fluorescence The absorbing pigments in the insoluble protein fraction of the cataractous lens are reported to be fluorescent compounds, with at least two fluorogens [ 11.The PA signal is related to the non-radiative de-excitations in the sample; we obtained a PA signal at the activation wavelengths of the chromophores (at 350 nm) because the fluorescence yield is low for this fluorogen [ 191 and because of the process of quenching. 4.2. Influence of light scattering It is well known that optical measurements, e.g. transmission spectroscopy, are very sensitive to light scattering. PA spectroscopy is also influenced by scattering [ 20 - 221; however, in refs. 20 - 22 only the isotropic case is discussed in great detail. From the general formulation of the light-scattering effect in PA measurements [22] we can derive useful indications for nonisotropic scattering. In order to derive quantitative predictions, we need a preliminary estimate of the scattering coefficient 0,. From measurements of the transmission of visible light in age-matched normal and cataractous lenses in toto [ 1, 17, 191 (assuming that the light loss in the visible is entirely due to the scattering of light inside the lens) we have estimated that p, is of the order of 2 - 3 cm-’ at 500 nm. The scattering process cannot be entirely responsible for the light loss, since nuclei of cataractous lenses can be limpid to visual inspection, but absorb in the visible. In these cases the absence of turbidity does not seem to agree with previous indications [8] that the scattering originates from pre-existent protein structures in the nucleus which collapse and produce denser agglomerates. This process implies that water leaves the aggregates [9] and can be found in the surrounding medium [23], thus producing the spatial inhomogeneities in the refractive index and the increased light scattering inside the nucleus. In order to explain the condition of an absorbing but limpid nucleus, we can introduce the hypothesis of a loss of interstitial water from the lens core which causes a reduction in the inhomogeneities in the refractive index in the nucleus and an increase in the surrounding medium. Indeed, it is known from clinical experience that the process of nuclear sclerosis is paralleled by a loss of liquid from the lens nucleus into the surrounding region. However, this condition will not improve visual acuity, because on going through the lens, light will propagate inside regions of different densities and will be internally reflected. In conclusion, it appears reasonable to suppose that the process of light scattering in the nucleus by large protein aggregates [8] has a limited evolution, the final stage being a condition in which the light loss
414
by scattering in the nucleus is not high. As for the relative role of scattering and absorption loss of visible light in the nucleus, it will depend on the degree of nuclear brunescence and on the evolution of the syneresis process [8,9, 23, 241. The spectral region of interest can be divided into two: (i) the visible, where the scattering coefficient p, is possibly greater than the absorption coefficient &, (turbid but non-pigmented nuclei), but where both have quite limited values and (ii) the UV region, where both 0, and &, have much higher values, but ~3,< 0,. In fact, even assuming a X4 dependence of the scattering coefficient, we estimate 0, = 8 - 12 cm-’ at 350 nm. This will imply /3, < p,, since even for normal lenses the total light absorption coefficient in the nucleus is about 40 cm- ’ at 350 nm and 50 years [1’7]. In the visible region, the incident light beam and the distribution of scattered photons have penetration lengths inside the sample which are greater than the thermal diffusion length of the sample (approximately 35 pm, see Appendix A): in this case the PA signal is not affected by the internal scattering. In the UV region, the PA signal is scarcely affected by isotropic scattering and virtually unaffected by non-isotropic scattering. From the above considerations we argue that our PA measurements yield the optical absorption coefficient; the contribution of light scattering is estimated to be of the order of 10% in the UV region (i.e. within the limits of optical density measurements for these optical systems [19]). This is confirmed by the comparison of our values for p, for non-brunescent but turbid nuclei (0, = 18 cm-’ at 400 nm) with the values reported for agematched normal nuclei [17] (0, = 25 cm-’ at 400 nm), as shown in Fig. 2 (cases 1 and 7d). Although literature data [ 1,191 on the absorption of the lens in toto suggest that the data recently reported [17] on the absorption of the lens nucleus are overestimated, it is evident that our measurements are not affected by scattering, which does not occur in the normal lenses analysed in ref. 17.
References 1 S. Lerman and R. Borkman, Spectroscopic evaluation and classification of the normal, aging and cataractous lens, Ophthalmic Res., 8 (1976) 335 - 353. 2 S. Lerman, A. Ti Tam, D. Louis and M. Hollander, Anomalous absorptivity of lens proteins due to a fluorogen, Ophthalmic Res., 1 (1970) 338 - 343. 3 R. B. Kurzel, M. L. Wolbarsht and B. S. Yamanashi, Spectral studies on normal and cataractous intact human lenses, Exp. Eye Res., 17 (1973) 65 - 71. 4 J. A. Jedziniak, J. H. Kinoshita, E. M. Yates, L. 0. Hacker and G. B. Benedek, On the presence and mechanism of formation of heavy molecular weight aggregates in human normal and cataractous lenses, Exp. Eye Res., 15 (1973) 185 - 192. 5 J. A. Jedziniak, J. H. Kinoshita, E. M. Yates and G. B. Benedek, The concentration and localization of heavy molecular weight aggregates in aging normal and cataractous human lenses, Exp. Eye Res., 20 (1975) 367 - 369. 6 S. Lerman, J. F. Kuck, R. F. Borkman and E. Saker, Induction, acceleration and prevention (in vitro) of an aging parameter in the ocular lens, Ophthalmic Res., 8 (1976) 213 - 226.
415 7 R. C. Zeimer tance,
and J. M. Noth,
and study
of lens scatter,
A new method fluorescence
of measuring in uiuo the lens transmitand transmittance, Ophthalmic Res., 16
(1984) 246 - 255. 8 E. L. Siew, D. Opalecky and F. A. Bettelheim, Light scattering of normal human lens. II. Age dependence of the light scattering parameters, Exp. Eye Res., 33 (1981) 603 614. 9 F. A. Bettelheim, E. L. Siew and L. T. Chylack Jr., Studies on human cataract III. Structural elements in nuclear cataracts and their contribution to turbidity, Invest. Ophthalmol. Vis. Sci., 20 (1981) 348 - 354. 10 K. D. Caldwell, B. J. Compton, J. C. Giddingo and R. J. Olson, Sedimentation fieldflow fractionation: a method for studying particulates in cataractous lens, Invest. Ophthalmol. Vis. Sci., 25 (1984) 153 - 159. 11 G. B. Benedek, Theory of transparency of the eye, Appl. Opt., 10 (3) (1971) 459 473. 12 L. T. Chylack, Jr., B. J. Ransil and 0. White, Classification of human senile catatactous change by the American Cooperative Cataract Research Group (CCRG) method: III. The association of nuclear color (sclerosis) with extent of cataract formation, age and visual acuity, Invest. Ophthalmol. Vis. Sci., 25 (1984) 174 - 180. 13 M. A. Mainster, The spectra, classification, and rationale of ultraviolet protective intraocular lenses, Am. J. Ophthalmol., 102 (1986) 727 - 732. 14 D. H. Sliney, Ultraviolet radiation and the cataract patient, Cataract, 6 (1985) 20 - 24. 15 J. Marshall, Radiation of the ageing eye, Ophthalmol. Physiol. Opt., 4 (1984) 1 - 23. 16 P, Poulet, J. Chambron and R. Unterreiner, Quantitative photoacoustic spectroscopy of thermally thick samples, J. AppZ. Phys., 51 (1980) 1738 - 1742. 17 J. Mellerio, Yellowing of the human lens: nuclear and cortical contributions, Vision Res., 27 (1987) 1581- 1587. 18
S. Lerman, B. S. Yamanashi, R. A. Palmer, J. C. Roark and R. Borkman, Photoacoustic, fluorescence and light transmission spectra of normal, aging and cataractous lenses, Ophthalmic Res., 10 (1978) 168 - 176. 19 R. A. Weale, Human lenticular fluorescence and transmissivity, and their effects on vision, Exp. Eye Res., 41 (1985) 457 - 473. 20 P. Helander, Theoretical aspects of photoacoustic spectroscopy with light scattering samples, J. Appl. Phys., 54 (1983) 3410 - 3414. 21 P. Helander, I. Lundstrom and D. McQueen, Light scattering effects in photoacoustic spectroscopy, J. Appl. Phys., 51 (7) (1980) 3841 - 3847. 22 Z. A. Yasa, W. B. Jackson and N. M. Amer, Photothermal spectroscopy of scattering media, Appl. Opt., 21 (1982) 21 - 31. 23 F. A. Bettelheim, S. Ali, 0. White and L. T. Chilack, Jr., Freezable and non-freezable water content of cataractous human lenses, Invest. Ophthalmol. Vis. Sci., 27 (1986)
122 - 125. 24 F. A. Bettelheim, (1979)
189
Syneresis
and its possible
role in cataractogenesis,
Exp. Eye Res., 28
- 197.
Appendix A In gas-microphone photoacoustic (PA) spectroscopy [Al, A21 a beam of monochromatic modulated light is incident on the surface of the sample placed in a sealed cell. A fraction of the light energy absorbed by the sample is converted into a modulated heat flow; acoustic pressure waves arise in the gas contained in the cell adajacent to the sample surface, and it is possible to measure their intensitives with a sensitive microphone. This PA signal depends on the optical absorption coefficient of the sample, and by varying
416
the wavelength of the incident light it is possible to measure the light absorption spectrum of the sample. Our samples (lens nuclei) are macroscopically homogeneous, light scattering and thermally thick, i.e. the thermal diffusion length I-( inside the sample is much smaller than the sample thickness; its value (at the working frequency of 40 Hz) is about 35 pm. Assuming spherical scatterers and a light-scattering process of the Rayleigh-Debye type [A3, A41 (small nuclear inhomogeneities in refractive index [A5, A6]), we have an asymmetry between forward and back scattering. This asymmetry depends on the parameter Zna/h, where a is the radius of the scattering centres and h is the wavelength of the incident light. In our case a has values comparable with the wavelength of the incident light [A5 - A7]; therefore, the scattering is forward scattering in the direction of the propagating collimated beam, which hardly changes the energy distribution inside the sample compared with propagation in non-diffusing media. If the scattering is assured to be isotropic, its influence on PA measurements will be overestimated. The scattering produces a significant enhancement of the PA effect for absorbing samples only if the scattering length is comparable with the thermal diffusion length (l/p, d p, i.e. 0, > 300 cm-i) and /3, % 0,. However, in this case the PA signal is a real quantity, i.e. its phase $ does not provide any information about the absorption spectrum of the sample [A8]. This does not occur in our case, since tan 4 does provide the absorption spectrum. When l/p, % p, i.e. & 6 300 cm-‘, the PA signal is insensitive to scattering if & > 0, and it is slightly affected by isotropic scattering if 0, < 0,. This influence is reduced as the scattering is forward peaked. Taking into account our preliminary estimates for the scattering coefficient /3,, we conclude that to a good approximation our samples can be treated as non-scattering for the purpose of PA measurements. For thermally-thick samples, the amplitude S and the phase $I of the PA signal are given by [A91
s=
AP,P
w{@,p+ 1)2
tan@=&&+1
+ 1}“2
(Al) (AZ)
where A is a constant independent of wavelength and /3, but dependent on the thermal properties of the sample and the experimental conditions, and o is the modulation frequency of the incident light. Since the constant A is usually unknown, the measurement of the PA amplitude S alone provides the qualitative absorption spectrum (S Q:A&p) for low optical absorption (&J & l), whereas in all other cases the spectrum is flattened (saturation). By measuring both S and tan C$we can eliminate the saturation phenomenon. The above relationships do not account for the contribution to the PA amplitude S from the thermal expansion of the sample (the so-called pressure term). Usually (and also in our experimental conditions) this
417
contribution is very small and its influence does not alter the trend of the PA amplitude S vs. wavelength; however, even a small pressure term does contribute to the phase 4 of the PA signal so as to alter the trend of tan 4 for low values of Pa. For these reasons, relationships for both S and tan 4 were taken into account in order to compute 0,. For a moderately high value of 0, the latter relationship yields 0,~ with sufficient precision [A9]. We determined 0,~ from the values of tan 4 (eqn. (A2)) and S at many wavelengths where /3& is high (around the peak value at 280 nm); we deduced many values of A from enq. (Al) and obtained the mean value. This value was then used to obtain 0, from the measurement of S using eqn. (Al). References for Appendix A AI A2 A3 A4 A5
A6
A7
A8 A9
A. C. Rosencwaig, Photoacoustics and Photoacoustic Spectroscopy, Wiley, New York, 1980. A. C. Tam, Applications of photoacoustic sensing techniques, Rev. Mod. Phys., 58 (1986) 381 - 431. H. C. van De Hulst, Light Scattering by Small particles, Wiley, New York, 1957. M. Kerker, The Scattering of Light, Academic Press, New York, 1969. E. L. Siew, D. Opalecky and F. A. Bettelheim, Light scattering of normal human lens. II. Age dependence of the light scattering parameters, Exp. Eye Res., 33 (1981) 603 - 614. F. A. Bettelheim, E. L. Siew and L. T. Chylack, Jr., Studies on human cataract III. Structural elements in nuclear cataracts and their contribution to turbidity, Invest. Ophthalmol. Vis. Sci., 20 (1981) 348 - 354. F. A. Bettelheim, S. Ali, 0. White and L. T. Chylack, Jr., Freezable and nonfreezable water content of cataractous human lenses, Invest. Ophthalmol. Vis. Sci., 27 (1986) 122 - 125. P. Helander, Theoretical aspects of photoacoustic spectroscopy with light scattering samples, J. Appl. Phys., 54 (1983) 3410 - 3414. P. Poulet, J. Cambron and R. Unterreiner, Quantitative photoacoustic spectroscopy of thermally thick samples, J. Appl. Phys., 51 (1980) 1738 - 1742.