Articles

Measurement of the Axial Length of Cataract Eyes by LaserDoppler InterferometryC. K. Hitzenberger,* W. Drexler* C. Dolezal* F. Skorpik,\ M. Juchem,f A. F. Fercher*and H. D. Gnadf

Purpose. To examine the applicability of the recently developed laser Doppler interferometrytechnique for measuring the axial length of cataract eyes in a realistic clinical situation. Todetermine the performance of the instrument as a function of cataract grade. To compare theresults to those of ultrasound methods.Methods. A total of 196 cataract eyes of 100 patients were examined. The axial eye length wasdetermined by laser Doppler interferometry and by two different ultrasound techniques, theapplanation technique and the immersion technique. The cataract grade was determined by acommercial instrument that measures backscattered light.Results. Laser Doppler interferometry worked very well except in the cases of the highestcataract grades (4% of the eyes of this study were not measurable because of a too-high lensdensity). Only 3.5% of the other eyes were not measurable because of fixation problems of thepatients. The precision of laser Doppler interferometry is not influenced by the cataract grade(except the highest grade). The standard deviation of the geometric eye length is approxi-mately 20 fim. Linear regression analysis revealed a very good correlation of laser Dopplerinterferometry and ultrasonic measurements, but a systematic difference was found. The eyelengths measured by laser Doppler interferometry were about 0.18 mm longer than thosemeasured by the immersion technique and about 0.47 mm longer than those measured by theapplanation technique.

Conclusion. These differences are attributed to the laser Doppler interferometry results in-cluding the retinal thickness and indentation of the cornea by the applanation technique. Themain advantages of the laser Doppler interferometry technique are high precision, high accu-racy, and more comfort for the patient because it is a noncontact method, anesthesia is unnec-essary, and the risk of corneal infection is avoided. Invest Ophthalmol Vis Sci 1993;34:1886-1893.

An modern ophthalmology the precise knowledge ofintraocular distances is very important. The axiallength of the eye is one of the main parameters for all

From the *inslitut fur Medizhiische Phy.silt, Universittit Wien, Vienna, and the^Department of Ophthalmology, Lahiz Hospital, Vienna, Austria.Supported by grant P 7300 MED from the Austrian Fonds zur Fordennig derluissenschaft lichen Forschuiig (FWF).Submitted for publication,: February 10, 1992; accepted June 29, 1992.Proprietary Interest Category: P.Reprint requests: Christoph K. Hitzenberger, Institut fur Medizhiische Physik,Wa'hringer Strafie 13, A-1090 Vienna, Austria.

intraocular lens power calculation formulae. Todaythe common method for measuring intraocular dis-tances is the ultrasonic echo-impulse technique (UStechnique). Since the first measurements in 1956,1 thistechnique has been steadily improved and is now ofclinical standard. The US technique enables the mea-surement of the axial eye length as well as any otherintraocular distance, independent of the clarity of thecrystalline lens, but because of the necessary mechani-cal contact between instrument and eye topical anes-thesia is needed and the risk of local infections exists.

1886Investigative Ophthalmology & Visual Science, May 1993, Vol. 34, No. 6

Copyright © Association for Research in Vision and Ophthalmology

Interferometric Measurement of Cataract Eye Length 1887

Another drawback is the limited resolution attained bythe US technique.

During the past few years, new optical methodsfor measuring intraocular distances were reported.The femtosecond optical ranging technique was usedto determine the corneal thickness of anesthetizedrabbit eyes in vivo.2 A modification of the slit lamptechnology was proposed to measure the thickness ofthe human retina.3 The axial length of the human eyewas measured by interferometry with partially coher-ent light.4 An improved version of this technique, laserDoppler interferometry (LDI), reduced the measuringtime to 3 seconds,56 and, with a modified instrument,enabled the measurement of the corneal thickness.7

First measurements of the axial eye length, carriedout by the LDI technique on healthy eyes of volunteersubjects, were in good agreement with US results, withthe added advantage of much greater precision.5 Themain remaining question, from a clinical point of view,is whether the LDI technique can be applied also tocataract eyes, since light scattering by cataract lensesmight limit the use of an interferometric technique.

To answer this question, an extensive study on theapplicability of the LDI technique for measuring theaxial length of cataract eyes was conducted. The pur-pose of this study was to clarify the following ques-tions: Is the technique feasible for measurements onelderly patients? To which quantitative degree of cata-ract is the technique applicable? How do the results ofLDI compare to those of the US technique? The re-sults are reported here.

MATERIALS AND METHODS

Laser Doppler InterferometryThe method of measuring the axial eye length by LDIhas been described elsewhere.56 The measurementsreported here were made with an improved instru-ment initially used for measuring the corneal thick-ness.7 The laser power was shown to be well within thesafety limits.5'7'8

An important point with in vivo measurements isthe alignment of the subject's eye with the laser beam.In this work, the axial eye length is measured parallelto the vision axis. This is achieved by asking the patientto look at the beam (the wavelength X = 780 nm is justvisible and the beam appears to the patient as a weakred spot). The alignment of the eye with the center ofthe beam is achieved by a head rest of the type that iscommonly used with slit lamps, which is mounted onan x-y translation stage. In case of patients experienc-ing strong tremors, the fixation of the head can beassisted by adjustable temple supports; a head fixationby a bite board is no longer necessary. With this sys-tem, the alignment of vision axis and beam center can

be maintained within approximately ±0.5 mm duringthe measurement time of roughly 3 sec. This accuracyensures that the width of the interference fringes,which cause the LDI signal, is not less than the widthof the photodetector, so the measurement can bemade.

Longitudinal eye motions (ie, parallel to the opti-cal axis) occurring during the measurement time donot affect the results in any way. This is achieved by thespecial interferometric setup, which uses reflectionsfrom both the cornea and the retina simultaneouslyfor the path length matching and therefore does notdepend on the distance between eye and interfer-ometer.

The precision of LDI was shown to be approxi-mately 30 /urn standard deviation (SD) for the opticallength (OL) of the eye. This value includes eye lengthchanges due to blood pulsations, which are of theorder of a few /um.9 OL is converted to the geometriclength (GL) by a method that is based on Gullstrand'sschematic eye10 and uses the group refractive indicesof the eye media:5

GL; = GLS + (OL; - OLs) / iV

(GLJ: individual GL, GLS: schematic GL, OL;: individ-ual OL, OLS: schematic OL, n^,: group refractive in-dex of the vitreous). The following constants wereused:5 GLS = 24 mm, OLS = 32.518 mm, n^ = 1.3445.The precision of the GL values was shown to be betterthan 25 /um.5

Usually 8-12 measurements were carried out oneach eye by LDI to ensure that at least five evaluableresults were obtained. A measurement is called evalu-able if a visual check of the measurement curve on thecomputer monitor showed a sufficient separation ofsignal and noise. In some cases with excellent signal-to-noise ratio, fewer measurements were carried out.

Ultrasound MeasurementsUS measurements were performed using two differenttechniques: Each eye was measured once with a DBR310 (Sonometrics, NY), employing the easy to use ap-planation technique (A-US technique). The instru-ment uses a mean sound velocity of 1550 m/s for axialeye length measurements; a separate measurement ofindividual intraocular distances was not performed.These measurements were carried out routinely byhospital staff members on all patients undergoing cata-ract surgery.

During the study a systematic difference betweenLDI and A-US results was observed, so we decided tomeasure 50 eyes additionally by the more accurate butalso more complicated water-immersion technique (I-US technique). A Kretztechnik 7200 MA Hochfre-quenz Echograph (Kretztechnik, A-4871, Zipf, Aus-

1888 Investigative Ophthalmology & Visual Science, May 1993, Vol. 34, No. 6

tria) was used, employing a transducer with 5 mm di-ameter and a frequency of 10 MHz. The soundvelocities were taken 1532 m/s for the aqueous andvitreous humor and 1641 m/s for the lens, respec-tively." The calibration of the instrument was checkedby measuring a phantom (a trough consisting of planeparallel plates of acryl glass, filled with distilled water)of known dimensions and sound velocity. The resultswere equal (within the accuracy limits of this tech-nique) to those of the LDI technique.

The lengths of the individual intraocular distances(aqueous, lens, vitreous) were determined from Polar-oid photographs of the screen of the I-US instrumentand added to obtain the total GL of the eye. Two mea-surements were performed on each of the 50 eyes bythis technique and the mean value of both measure-ments was taken as final result.

Cataract GradingCataract grading was performed by use of the OpacityLensmeter 701 from Interzeag company (CH-8952,Schlieren-Ziirich, Switzerland). This instrument mea-sures backscattered light from the eye lens, which isilluminated by a light beam of 1.5 mm diameter.12 Themeasurement is thus restricted to the central area ofthe lens. The result of the measurement is a dimen-sionless number between 0 and 99, which we will referto as lens meter unit (LMU). Higher LMU values indi-cate higher lens densities. According to the manufac-turer, normal lenses give values between 0 and 20LMU, while higher values indicate cataract lenses.

The instrument was used strictly according to theuser's manual. Five measurements were performed oneach eye after checking that the pupil diameter was atleast 4 mm; mean values and SD were calculated by theinstrument automatically. The reproducibility of themeasurements was usually very good (SD about1 LMU).

For the purposes of this study, the eyes were clas-sified according to their LMU values into groups ofwidth 5 LMU, ranging from 15 to 20 LMU, 20 to 25LMU, and so on. Values above 90 LMU were com-bined into one group.

PatientsThe study group consisted of patients undergoing cata-ract surgery at the Department of Ophthalmology ofthe Lainz Hospital, Vienna, Austria, during the first 6months of the year 1991. No special selection of pa-tients was made, so they resemble a typical collective ofcataract grades. One hundred patients participated inthe study; ages ranged 43-97 yr, mean value ± SDwere 74 ± 10 yr. Thirty-six patients were men and 64were women. One hundred ninety-six cataract eyeswere investigated by LDI, A-US, and Lensmeter, fiftyof these eyes were measured additionally by I-US.

The study followed the tenets of the Declarationof Helsinki. Informed consent was obtained from allpatients after the nature and possible consequences ofthe study were explained. Approval by the institutionalhuman experimentation committee was obtained.

StatisticsIn a summary statistics, the distribution of cataractgrades was determined. The total percentage of eyesmeasurable by LDI, the percentage of evaluable singleLDI scans, and the repeatability (the SD) of the LDIresults were determined as a function of cataractgrade.

Linear regression analysis was used to test forcorrelations between the following parameters:GL(LDI) vs GL(A-US); GL(LDI) vs GL(I-US);GL(LDI) vs DA; GL(LDI) vs DI; LMU vs DA; LMU vsDI(GL(LDI; A-US; I-US): geometrical length deter-mined by LDI, A-US, and I-US, respectively; DA: dif-ference between GL(LDI) and GL(A-US); DI: differ-ence between GL(LDI) and GL(I-US); LMU: lensmeter units (cataract grade)).

Finally, the eye length results obtained by the dif-ferent measurement techniques were compared by apaired Student's t test after checking for normal distri-bution of the differences by the x2 test.

RESULTS

Influence of Cataract Grade on LDI ResultsFigure 1 shows the frequency distribution of cataractgrades of the eyes of this study. The number of eyes ineach class is shown at each histobar. The number inparentheses indicates the number of eyes that weremeasurable by LDI. Most of the eyes are graded in lowto intermediate classes. Only a relative small amountof eyes is graded in classes higher than 60 LMU. Nineeyes had values higher than 90 LMU. Seven of themwere out of the measuring range of the instrument (ie,> 100 LMU). These eyes were judged as completelyopaque by an ophthalmologist.

LDI was able to measure 90.5% of the eyes. Only12 eyes in classes below 90 LMU were not measurable:computer problems prevented the measurements infour cases, fixation problems of the patients in sevencases, and high lens opacity in one case. Only two ofthe nine eyes in the class > 90 LMU could be measuredby LDI.

Figure 2 shows the evaluability of single measure-ments as a function of cataract grade. The cataractsclassified higher than 55 LMU were combined in threegroups: 55-65 LMU, 65-90 LMU, and > 90 LMU,respectively, for statistical purposes (each class con-tains at least 5 eyes). The abscissa shows the cataractclasses and the ordinate the percentage of evaluable

Interferometric Measurement of Cataract Eye Length 1889

S IS S !8V S IS S

CATARACT GRADE (LMU)

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FIGURE l. Frequency distribution of cataract grades. The number of eyes graded in eachcataract class is plotted vs the cataract grade (in lens meter units: LMU). The number printedin each histobar equals the number of eyes graded in this class. Where the number of eyesthat were measurable by LDI differs from the total number of eyes, the number of evaluableeyes is shown in parentheses.

single measurements in each class. This is the meanvalue (in percent) of the ratio evaluable/total numberof measurements carried out on each eye and is a mea-sure of the number of times an eye has to be scannedto get a certain number of evaluable results. This eva-luability must not be confused with the percentage ofeyes measurable in each class (this was nearly 100% inall of the classes below 80 LMU). The evaluability de-creases gradually from approximately 75% in the caseof the lowest cataract class to approximately 40% inthe classes ranging 55-90 LMU. The sudden drop to

below 15% in the class above 90 LMU reflects the largenumber of eyes in this class that were not measurable.These evaluability percentages, however, are onlycrude figures. A strong variability between the individ-ual eyes within the cataract classes is observed. Espe-cially in the cases of the higher cataract classes, theevaluability can vary from about 20 to 90% (the im-measurable eyes excluded), strongly depending on theindividual patient's fixation capability.

The mean SD of GL of all 177 eyes is 19 /tun. Thevalue of the SD is roughly constant for the cataract

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CATARACT GRADE (LMU)

FIGURE 2. Evaluability of single LDI scans. The percentage of single LDI scans that wereevaluable is plotted vs the cataract grade. This is a measure of the number of times (ataverage) a single eye has to be scanned to get a certain number of evaluable results and iscorrelated with the mean signal-to-noise ratio. It must not be mixed up with the total percent-age of evaluable eyes in each class.

1890 Investigative Ophthalmology & Visual Science, May 1993, Vol. 34, No. 6

grades between 15 and 90 LMU. It is approximately30 /im above 90 LMU, but in this class only two eyeswere measurable.

Comparison of LDI and US MeasurementsFigure 3 shows a plot of GL values measured by LDIand by US, respectively. The values obtained by US areplotted as a function of the LDI results. In Figures 3aand 3b, the A-US values and the I-US values, respec-tively, are shown. A linear regression analysis was per-formed in each case. The solid line in each figure is thecorresponding regression line, the dotted lines at eachside of the regression line show the 95% predictionlimits (ie, 95% of the data are located between these

lines). The correlation is excellent in both cases withcorrelation coefficient r = 0.97 and 0.99 in Figures 3aand 3b, respectively. The slopes of the regression linesand their standard errors are 0.99 ± 0.02 (Fig. 3a) and1.02 ± 0.02 (Fig. 3b). The vertical width of the 95%prediction interval is approximately 1 mm (Fig. 3a)and 0.5 mm (Fig. 3b) for the range of GL values cov-ered by these figures.

A systematic difference between LDI and US val-ues was observed. The mean value of DA (GL(A-US)- GL(LDI)) ± SD is -0.47 ± 0.25 mm (n = 179), themean value of DI (GL(I-US) - GL(LDI)) ± SD is— 0.18 ± 0.12 mm (n = 50). These values are highlysignificant. A paired Student's t test showed signifi-

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FIGURE 3. Comparison of LDI and US results. The geometric eye length (GL) obtained by US,is plotted vs the GL obtained by LDI. Solid line: regression line. Dashed lines: 95% predictionlimits. (A) US values measured by applanation technique (A-US). (B) US values measured byimmersion technique (I-US). Very good correlations are observed.

Interferometric Measurement of Cataract Eye Length 1891

cance values of P < 2 X 10 15 in both cases (it shouldbe mentioned that only the DI, but not the DA valuespassed the x2 t e s t f ° r normal distribution (DI: P= 0.55, DA: P= 2 X 10"7)).

Linear regression analysis revealed no correlationof GL and the differences DA and DI (the respectivecorrelation coefficients are —0.05 and 0.14). Nocorrelation was found for cataract grade and DA andDI, either (r = -0 .09 and -0 .04, respectively).

DISCUSSION

In this study, the LDI technique, which was recentlydeveloped for the measurement of intraocular dis-tances, was used for the first time to examine a largenumber of cataract eyes. In most cases, no majorproblems associated with the instrument and its mea-surement principle occurred. 196 cataract eyes wereexamined, 177 (ie, 90.5%) were measurable by LDI. Infour cases (2%), the instrument failed because of com-puter problems. This malfunction can be attributed tothe instrument being a prototype; it was not caused bythe measurement principle.

The measurement relies on the fixation ability ofthe patient. In some cases, the patients had fixationproblems. This can be observed by the instrument op-erator during the alignment and measurement pro-cess, because in this case, the reflected beam will moveerratically across (and even beyond) the visual field ofthe infrared scope of the detection unit. In this case, itis difficult or even impossible to align the detector withthe center of the reflected beam (or the center of theinterference fringes, which give rise to the LDI signal),and no signal will occur. However, most of the patientswho had fixation problems were able to fixate thebeam for the 3 sec needed for a single scan. The wholemeasurement session for acquiring approximately fiveevaluable scans took longer (up to 10 min) than in thecases of no fixation problems (about 2-3 min). Inseven cases only (3.5%) the fixation problems were sosevere that no measurement could be carried out suc-cessfully. This percentage can probably be further re-duced by increasing the speed of the stepper motorthat drives the scanning mirror, which decreases mea-surement times to 1 sec or even less.

Cataract Grading

Cataract grading was performed with a commercialinstrument that measures backscattered light from thecentral part of the lens.12 The lens density is given as adimensionless number. No calibration to real physicalunits is available.

Compared to other, more common methods(based on slit lamp photography),1314 the instrument iseasier to use and yields a higher resolution and better

reproducibility. The fact that only lens opacities nearthe vision axis are taken into account is a great advan-tage for the purpose of this study, because only theseopacities are located within the light path of the LDIinstrument and are therefore able to deteriorate theinstrument performance by light scattering. Conse-quently, a useful correlation between instrument per-formance and cataract grade is enabled.

Influence of Cataract Grade on LDIMeasurements

The results of this study show that LDI works very wellwith low to intermediate cataracts (up to 55 LMU).Even with higher cataract grades (up to 90 LMU) LDIworked well. The reason for this good performance isprobably the use of the rather long wavelength of780 nm, which is much less scattered than light ofshorter wavelength. There was only one failure of LDIin this range of cataract grades which could be attrib-uted to lens opacities (the respective lens density was85 LMU). In all other cases, only the signal-to-noiseratio decreases with increasing lens density, which canbe deduced from the gradual decrease of evaluablesingle measurement scans with increasing lens density(Fig. 2). In some cases (about 5% of all measurableeyes), where high lens density and fixation problemsoccurred for the same eye, the evaluation of singlescans became difficult because of the poor signal qual-ity. However, the comparison of several successivescans yielded reliable results even in these cases. (Itshould be mentioned that only six patients (3%) hadcataract grades in the range 65-90 LMU, so the statis-tics of this range are poor.)

No effect of cataract grade on the precision of theLDI results was observed in the range up to 90 LMU.The mean SD of GL of 19 /xm compares well to thevalue of <25 /zm reported for healthy volunteer sub-jects.5

However, 90 LMU seems to be the limit up towhich LDI can be used at present. Seven of the nineeyes (3.5% of the total number of eyes) graded higherthan 90 LMU were not measurable. That most patientsnow apply for cataract surgery in early stages of re-duced visual acuity is very favorable for the LDI tech-nique. If, however, a light source with the requiredcoherence properties emitting at a wavelength X = 1.1nm becomes available, the current limit of 90 LMUmight be extended.

Comparison of LDI and US Measurements

A very good correlation between LDI measurementsand US measurements was found by linear regressionanalysis. The slopes of the regression lines equal 1within the standard error of the analysis. The half-width of the 95% prediction interval is about 0.5 and

1892 Investigative Ophthalmology & Visual Science, May 1993, Vol. 34, No. 6

0.25 mm in the case of A-US and I-US measurements,respectively.

A systematic deviation with high significance wasobserved for the three measurement techniques. TheLDI technique yields the highest GL values, the A-UStechnique the lowest. No correlation between lengthand differences is observed. Therefore, the systematicdeviations are not caused by errors in the sound veloci-ties or in the refractive indices of the eye media (in thiscase, a linear relationship of length and differenceshould be observed). Also, the lack of correlation be-tween cataract grade and differences indicates that thelens opacities have no influence on sound velocity andrefractive index, at least within the accuracy of mea-surement (or these influences balance each other).

The smaller GL values of the A-US technique canbe attributed to its coupling technique: because of thedirect contact between transducer and eye the corneais indented and the eye shortened.

The larger GL values of the LDI technique can beexplained by a reflection of sound and light at differ-ent layers of the fundus. The LDI signal was shown tooriginate from a reflection at the retinal pigment epi-thelium.5 A weaker LDI signal, which occurs occasion-ally at optical distances of approximately 250 jiim infront of the main signal, was attributed to a reflectionat the internal limiting membrane.5 Using the meangroup refractive index ng = 1.35495 of the schematiceye, this corresponds to a geometric distance of 185ium. This is approximately equal to the mean GL dif-ference between LDI and I-US results. Therefore, weconclude that the US technique measures the distancecornea-internal limiting membrane. This agrees withsome intraocular lens formulae that are based on USmeasurements and take an additional retinal thicknessof 0.2 mm15 into account. (These recent results con-tradict the preliminary results reported earlier,5 whereno systematic difference was observed. However, theearlier US results were based on single measurements.Furthermore, the instrument was not calibrated with aphantom, so they were probably less accurate than theresults reported here.)

The last point to be discussed concerns the accu-racy of the methods. Since the A-US technique is lessaccurate than the I-US technique, it will not be dis-cussed here. The SD of the differences DI (LDI —I-US) is approximately 120 /xm. Because this valuecorresponds to the lower limit of accuracy ranges(120-200 /JIII) reported in literature for the US tech-nique,1615 the deviations of US and LDI techniquesare mainly caused by inaccuracies of the US technique.This is in agreement with theoretical considerations,5

which predicted that the errors caused by the approxi-mations made in the OL to GL conversion of the LDItechnique will be less than approximately 50 urn.

In conclusion, the advantages of the LDI tech-nique are summarized. Its precision of about ±20 pmis unrivalled by the US technique. The total accuracy isbetter (< 50 /xm compared to 120 to 200 nm) even inthe present state, where only the total axial length, butnot the individual intraocular distances are measured(these measurements are possible in principle). TheLDI technique is easy to use and very comfortable forthe patient. It is a noncontact technique that requiresno anesthesia and avoids the risk of corneal infection.There are still many possibilities for further develop-ment of this method. The feasibility of fundus profilemeasurements5 and measurements of the retinal thick-ness517 have already been demonstrated and the possi-bility of further improvement of the resolution by useof a light source of shorter coherence length wasshown.17 By increasing the speed of the stepper motor,the time required for a single scan could be reduced toone second or less. This might reduce the number ofeyes that are not measurable because of fixation prob-lems. Therefore, the LDI technique has a great poten-tial for future applications.

Key Words

biometry, eye length measurement, cataract, laser Dopplerinterferometry, interferometry

AcknowledgmentsThe authors thank Mr. H. Sattmann for the construction ofthe electronics and the software of the LDI instrument.

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