measurement of corneal thickness by laser doppler...

Investigative Ophthalmology & Visual Science, Vol. 33, No. 1, January 1992Copyright © Association for Research in Vision and Ophthalmology

Measurement of Corneal Thicknessby Loser Doppler Interferometry

C. K. Hitzenberger, W. Drexler, and A. F. Fercher

The laser Doppler interferometry (LDI) technique, which was recently developed for axial eye lengthmeasurement, has been modified to measure the corneal thickness of the human eye in vivo. Highaccuracy is achieved. The standard deviation of the technique is about 7 nm, and improvement by afactor of 5 is possible. First comparisons with a usual slit lamp pachometer show a general agreementbut a systematic difference of about 20 jum. Possible reasons for this discrepancy are discussed. Finally,the new method is compared to standard optical and ultrasound pachometry from a theoretical point ofview, and advantages and drawbacks of the various techniques are discussed. Invest Ophthalmol VisSci 33:98-103,1992.

Measurements of corneal thickness (CT) are per-formed in many physiological and clinical studies.Most of these measurements are performed by usingpachometers of the Haag-Streit type, whose principlesand error sources are discussed in the literature.1"6

During the past few years, new optical methods formeasuring intraocular distances have been reported.The femtosecond optical ranging technique was usedto determine the CT of anesthetized rabbit eyes invivo.7 A modification of the slit lamp technology wasproposed to measure the thickness of the human ret-ina.8 The axial length of the human eye was measuredby interferometry with partially coherent light.9 Animproved version of this technique, laser Doppler in-terferometry (LDI), reduced the measuring time to 3seconds.l0" In this work, the LDI technique was mod-ified to enable the measurement of CT.

The main purposes of this report are:

1. to present the modified instrument;2. to demonstrate the feasibility of CT measurements

in human eyes in vivo;3. to show first comparisons with measurements

carried out by a pachometer of the Haag-Streittype and to discuss the results; and

4. to compare the new method to standard opticaland ultrasound pachometry from a theoreticalpoint of view.

From the Institut fur Medizinische Physik, Universitat Wien,wahringer StraRe 13, A-1090 Wien.

Submitted for publication: February 15, 1991; accepted August23, 1991.

Supported by grant P 7300-MED from the Austrian Fonds zurForderung der wissenschaftlichen Forschung (FWF).

Reprint requests: Christoph K. Hitzenberger, PhD, Institut furMedizinische Physik, Wahringer StraCe 13, A-1090 Vienna, Aus-tria.

Materials and MethodsDescription of the Method

The method of measuring intraocular distances byLDI is described in detail in a previous paper.l0 Only ashort summary is presented here with the main alter-ation that allows the measurement of CT.

Figure 1 shows a sketch of the instrument used inthis work. A multimode laser diode emits a light beam(wavelength = 780 nm, power = 250 /*W) with highspatial coherence but short coherence length (CL).(The HeNe laser and the single mode laser diode, aswell as the infrared scope, are used only for alignmentpurposes.)

This beam passes a Michelson interferometer,which splits the beam in two parallel, coaxial beams: areference beam 1, and a measuring beam 2, which isretarded with respect to beam 1 by twice the differ-ence, d, of the interferometer arm lengths. In addi-tion, the interferometer mirror of the measuringbeam is shifted with constant speed, causing aDoppler shift of beam 2.

The Michelson interferometer replaces the origi-nally used Fabry Perot interferometer. Because thereference arm and the measurement arm of the Mi-chelson interferometer are separated spatially, themeasurement arm can now be shorter, equal to, orlonger than the reference arm. This enables an exactbalance of the two interferometer arm lengths withthe possibility of performing measurements in the vi-cinity of this balance, which is necessary for measur-ing short distances such as the CT. This was not possi-ble with the Fabry Perot interferometer, because theframe of the interferometer plates prevented their clo-sure to zero distance.

Both beams, 1 and 2, illuminate the eye via a beamsplitter cube and are reflected at the anterior and the

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No. 1 INTERFEROMETRIC MEASUREMENT OF CORNEAL THICKNESS / Hirzenberger er ol 99

Fig. 1. Block diagram ofthe laser Doppler interfer-ometer modified for mea-suring the corneal thickness.HeNe = helium neon laser;SMLD = single-mode laserdiode; MMLD = multi-mode laser diode; BSC= beam splitter cube; MI= Michelson interfero-meter; PD = photodetector;AMP = amplifier; PC = per-sonal computer; SM = step-per motor; IR = IR-scope;A,P = anterior and posteriorcorneal surface.

CD

zCD

BSC

BSC

Ml

PC

SMLD

IR

AMP

MMLD

BSC

BSC

posterior corneal surface. This introduces an addi-tional path difference that is twice the optical thick-ness of the cornea.

The intensity of the superimposed reflected beamsis detected by the photodetector and amplified andrecorded as a function of the stepping motor positionwith a personal computer. If the total path differencebetween beam 2, reflected at the anterior, and beam 1,reflected at the posterior corneal surface, is less thanCL, these beams will interfere and the intensity will bemodulated by the Doppler frequency fD.

From the stepping motor position, where a signalwith fD is registered, the difference of the interferom-eter arm lengths, d, can be determined and the opticalthickness = d ± CL/2 is obtained. The accuracy of thistechnique depends on CL. The multimode laser diodehas a CL of about 110 /im. By determining the centerof the signal peak, the accuracy can be even betterthan CL/2. The position of the center of the peak isdetermined by a "mouse" controlled cursor readouton the personal computer. The accuracy of this dis-tance readout is 0.5 jim, but because of the signalnoise, the overall precision of CT measurement isabout 10 ixm.

To convert the optical thickness to the geometricalthickness, it must be divided by the group refractiveindex ng of the cornea.1012 The value ng = 1.3856,10

which is based on the phase refractive index n at awavelength of 550 nm13 and on the dispersion ofwater,14 was used.

In Vivo Measurements

In performing in vivo measurements, laser safetyregulations must be met. The power of alignment and

measurement lasers are the same as in the case of theaxial eye length measurement,10 which was shown tobe well within the safety limits.15

Another important point with in vivo measure-ments is the alignment of the subject's eye with thelaser beam. In this work, the central CT is measuredalong the vision axis. This is achieved by asking thesubject to look at the beam (the wavelength 780 nm isjust visible; the beam appears to the subject as weakred spot). The diameter of the beam is about 2 mm.Therefore, the vision axis of the eye must be alignedwith the center of the beam with an accuracy of ± 1mm. (In the case of larger deviation, no part of thereflected beam is reflected back parallel to the illumi-nating beam; therefore neither the IR scope nor thephotodetector receives any light). This can be easilyachieved by adjusting the subject's head using a headrest that is commonly used with slit lamps, which ismounted on a x-y translation stage.

The geometry of the detection unit (a small aper-ture transmits light only within a narrow angle to theincident beam back to the detector) ensures that evenwith maximum misalignment of ± 1 mm the positionof the cornea, from which light is reflected into thephotodetector (the position at which the CT is mea-sured) does not deviate more than 0.3 mm from thepoint where the corneal surface is perpendicular tothe vision axis. This deviation can be further reducedto about 0.1 mm by visually aligning the photodetec-tor with the center of the interference fringes, whichare produced by the overlapping beams of cornealand retinal reflection.10

In vivo measurements were carried out on botheyes of 9 volunteer subjects, who provided full in-


100 INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / January 1992 Vol. 33

GO

!5D

-1.50 -1.00 -O.M It

Interferometer arm length

Fig. 2. Calibration mea-surement. The cornea is re-placed by a single interface(mirror). The intensity, I, isplotted versus the interfero-meter arm length difference,d. The main peak is at d= 0.0 ± 0.002 mm. The twosmaller peaks at distances ofabout ±1.1 mm from themain peak are subsidiarypeaks of the coherence func-tion of the MMLD.

formed consent. They suffered from no eye diseases,according to their knowledge. They were emmetropicor myopic, up to 10 diopters. In the case of CT mea-surements, none of them had to wear spectacles to geta signal of good quality.

Pachometer Measurements

A first comparison with a modified version of thewidely used Haag-Streit type pachometer was per-formed. It was manufactured by Nikon company(Tokyo, Japan) and has two small light-emittingdiode (LED) lights to assist in alignment. It was usedwith a Nikon zoom-photo slit lamp microscope FS-2with a slit width of 50 ixm. The pachometer readingwas converted to corneal thickness using a table sup-plied by the manufacturer.

Statistics

Six measurements or more were performed on eacheye by LDI and the pachometer. Mean values andstandard deviations were calculated for each eye andmethod separately. The results of the two methodswere compared by a paired Student's t-test after nor-mal distribution evaluated by the Kolmogorov-Smir-nov test.

Results

Figure 2 shows an example of a calibration measure-ment. The point of equal interferometer arm lengthsis determined by replacing the cornea with a singleinterface (mirror). A distance of 3 mm is scanned bythe measuring arm of the interferometer, from -1.5mm to +1.5 mm. The signal intensity I (ordinate) isplotted as a function of the interferometer arm lengthdifference d (abscissa). Because of the high intensity ofthe signal at d values close to zero, the graph is dis-torted in this region because of nonlinearities of the

amplifier and the AC-DC converter, which makes anexact location of the signal maximum difficult. There-fore, the smaller, subsidiary peaks in distances of mul-tiples of 1.1 mm from the main peak—they are a re-sult of periodic repetition of the coherence function ofthe laser—are used for calibration of the balance ofthe interferometer arm lengths. This can be done toan accuracy of about 2 nm SD.

Figure 3 shows the result of a typical measurementof the optical thickness of a cornea (subject LS. R.). Adistance of -1.5 mm to +1.5 mm is scanned. Besidesthe broad, distorted main peak and the subsidiarypeaks of the periodic coherence function, two addi-tional signal peaks are observed in equal distancesfrom the main peak. (Because of the symmetry of thecoherence function, the signal is symmetric at aboutthe point d = 0.) Their distance to the main peakequals the optical thickness of the cornea. In this case,the optical thickness = 712 ± 10 /xm (mean value of 6measurements ± SD). The time required for one scanis about two seconds. Because two signals from thecornea are obtained during one scan, the measuringtime for one signal is only one second.

The optical thickness of the other 17 corneas wasmeasured in a similar way. The values are shown inTable 1, with the calculated geometrical thickness.The values of the pachometer readings also are in-cluded in Table 1 (mean values of 6 measurements).In 2 cases, only the right eye was investigated becauseof geometrical limitations of the pachometer (the sub-jects' noses were too large).

The mean SD values of the single measurement are:optical thickness (LDI), 10 /i.m; geometrical thickness(LDI), 7 ixm; geometrical thickness (pachometer),15 /im.

DiscussionWe have shown that the LDI technique, which was

recently developed for the measurement of the axial


No. 1 INTERFEROMETPJC MEASUREMENT OF CORNEAL THICKNESS / Hirzenberger er ol 101

Fig. 3. Measurement ofthe optical thickness, OT, ofthe cornea. I is plotted ver-sus d. In addition to themain and the two subsidiarypeaks, two peaks can be ob-served at a distance OT= 712 ± 10 Mm from themain peak.

J5o

iu.00 m +1.00 +1.50

Interferometer arm length difference d

eye length, also can be used for measuring the cornealthickness. Eye length and CT now can be measuredwith the same instrument.

The CT measurement is performed along the visionaxis perpendicular to the corneal surface. In the sec-tion on materials and methods, it was shown that de-viations of measuring position from vision axis can berestricted to values of less than 0.3 mm without diffi-culty. These deviations can occur because of lateraleye motions of ± 1 mm during a single measurementor alignment differences between the individual mea-surements of a measurement series. Note that longitu-dinal eye motions along the optical axis during themeasurement procedure cannot affect the result inany way. The reason is the simultaneous use of thetwo waves reflected at the two corneal interfaces. The

Table 1. Corneal thickness (in micrometers)determined by LDI and OP

SubjectOT

(LDI)GT

(LDI)GT

(OP) Difference

AF.L.AF.R.CH.L.CH.R.WD.R.LI.L.LI.R.KL.L.KL.R.HS.R.LS.L.LS.R.GG.L.GG.R.PH.L.PH.R.

754750749748717676679746733759726712748754812814

544542540540518488490539529548524514540544586587

527513506508514487458535522522490508520518570572

172934324132472634620261615

OT = optical thickness; GT = geometrical thickness; LDI = determined bylaser Doppler interferometry; OP = determined by optical pachometry.

Standard deviations: OT (LDI) 10 ^m; GT (LDI) <; 7 ^m; GT (OP) ^ 15

Difference: 19 /xm ± 12 nm (mean value and standard deviation).

errors in CT values caused by these small deviationsare negligible because the variation of CT within 0.3mm off the vision axis is only about 0.1%,16 or 0.5 nmfor a cornea with CT = 500 ixm. Therefore, the repeat-ability of measurement is very high if the patient isable to cooperate and has no problems with fixationof the beam. Microsaccades usually do not exceed anangle of xh°.xl The resulting deviation of the measur-ing position from the vision axis should therefore beless than 50 nm. Large eye motions can be observedvia the IR scope during measurement, and the corre-sponding CT value will be excluded from the finalresult.

The standard deviation of the geometrical thick-ness was 10 /im or less (mean value, 7 /im), which is afactor of about 3 smaller than in the case of the axialeye length measurement.10 There are two reasons forthe higher precision in the case of CT. First, the pulsa-tion of the eye length with the heart beat, which is inthe order of a few micrometers,18 does not influencethe measurement of CT. Second, small deviationsof vision axis and measurement axis due to saccadiceye movements between individual measurementsshould have a greater influence on eye length resultsthan on CT results.

Comparison with Pachometer Measurements

The LDI and pachometer methods show a generalagreement of the results, but there is a systematic dif-ference with high significance (P < 0.0001). The val-ues obtained by LDI are about 19 nm longer than thepachometer results. There are three possible reasonsfor this discrepancy:

1. The precise ng value of the cornea for a wavelengthof 780 nm is not known. It was calculated assum-ing water dispersion. Although this approximationseems to be correct for aqueous and vitreous,10 it is


102 INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / January 1992 Vol. 33

probably wrong in the case of the cornea. A valueof ng = 1.4365 would yield an agreement betweenLDI and pachometer, but this value seems toohigh.

2. The discrepancy could be caused by a too low pa-chometer reading resulting from a smaller effectivewidth of the illuminating slit on the posterior sur-face of the cornea than the true slit width. Thiseffect could yield readings that are 30 fim too low.3

3. The thickness of the tear film, about a few microm-eters, is included in the LDI results.

The dominant error source is not yet clear. A carefulmeasurement of the ng value of the cornea for thewavelength in use (780 nm) will help clarify this point.If only relative values of CT are required, this differ-ence is only of minor interest.

In the following section, the advantages and draw-backs of LDI and conventional optical and ultra-sound pachometers will be discussed. The first pointregards the precision of the different techniques. Ourstandard deviation of the reading of the optical pa-chometer was about 15 nm, which is of the same mag-nitude as reported in the literature, where the valuesrange from 12 to 14 m.4'5-19 According to the litera-ture,16 this value can be reduced to about 5 to 8 nm byvery experienced operators.

However, different studies on large numbers ofeyes, carried out with this technique, reported meanCT values that differ by up to 60 jim.5 The reasons forthese discrepancies are probably different alignmentmethods of the two half-images formed by the beam-splitter of the pachometer56 and different slit widthsettings of the slit lamp during measurement.6 Buteven with the same alignment method and slit width,considerable inter-observer discrepancies occur. TheCT values of the same eye, measured by different ob-servers, differed by up to 20 nm.6 The reasons forthese discrepancies are probably differences in theperceptive properties of the observer and difficultiesin denning exactly the "edges" of the bright bands ofthe optical section that need to be aligned in the twohalf images.6

Problems with inter-observer discrepancies werenot encountered using ultrasound pachometers.20

The standard deviations of measurements carried outwith these instruments is reported to be of the order of5 /urn.20'21 However, large differences in the readingsof different instruments when measuring the identicalpoint in the same eye were encountered. In measuringthe central CT, the maximum differences were about50 im. Measuring peripherally, deviations of up to150 fim were encountered.21 Because all of the instru-ments were set at the same sound speed (1640 m/s)the reasons for these discrepancies are not clear. An-other disadvantage of ultrasound pachometry, com-

pared to conventional optical pachometry and LDI, isits need for mechanical contact between instrumentand eye. Therefore, anesthesia is needed and the pa-tient's comfort is reduced.

The large discrepancies in the results obtained bydifferent observers or different instruments are themain limitations of existing pachometric techniques.They are cumbersome if the results of different stud-ies are to be compared or if the same patient is exam-ined several times, such as in the case of therapy con-trol, by different observers or instruments. The appli-cation that probably generates the greatest demandfor accurate CT measurements is refractive surgery.In this case, undercorrections, overcorrections, andeven perforations can occur if data from different ul-trasound pachometers are used.

The LDI method should not suffer from the prob-lems mentioned above. The measurement is per-formed by matching two path differences, which ischecked by an electronic system. It does not dependon measurements of absolute light intensities, only onthe determination of the position of a signal peak.Therefore, the perceptive properties of the observerdo not influence the results. Although it was notchecked, an inter-observer variance probably will beavoided. Additional parameters that may influencethe results, such as the slit width of the optical pa-chometer, do not exist with the LDI technique. Be-cause the CT is read directly from another linear dis-tance (the interferometer arm length difference d)there are no calibration problems that might be theerror sources of the ultrasound pachometers. Theonly remaining error source of the LDI technique isthe value of ng, which is used for the optical thicknessto geometrical thickness conversion and which is notknown precisely. But if different LDI instruments usethe same value, the results should be identical. On theother hand, this problem exists with the ultrasoundtechnique, too, because the true value of sound speedin the living human corneal tissue is not known withgreat accuracy.21

The standard deviation of LDI is about 7 ^m for thegeometrical thickness. This is about the same magni-tude as with the ultrasound technique and about halfthe value usually achieved with conventional opticalpachometers. By replacing the multimode laser diodewith a super radiant diode, which has a CL of onlyabout 20 /nm, this value should be reduced by a factorof 5. In this case, the CL has approximately the samelength as the light pulses of the femtosecond pulselaser used to measure the thickness of rabbit corneas.7

This, in principle, would mean equal accuracy butwith the great advantage of lower cost with the LDItechnique.

So far, only measurements of the central CT have


No. 1 INTERFEROMETRIC MEASUREMENT OF CORNEAL THICKNESS / Hirzenberger er ol 103

been discussed. There are several applications inwhich the knowledge of the central CT is sufficient.Measurements of the central CT were suggested to behelpful in the diagnosis of several corneal disorders,22

such as in cases of chronic degenerations and endothe-lial dysfunctions, and for differentiating between dif-ferent types of stromal dystrophy. Numerous studiesindicate the importance of central CT measurementsfor determining the tolerance of the eye to differenttypes of contact lenses.23-24 In this case, the swelling ofthe cornea resulting from edema caused by hypoxia ismeasured in the examination of new types of contactlenses. The application of these measurements alsomight be useful for determining which type of contactlens is tolerated best by a patient. These applicationsrequire several measurements over several hours.Therefore, a noncontact technique that can be per-formed by different observers without inter-observervariability, as with the LDI technique, would be veryuseful in these cases.

In other cases, especially for corneal refractive sur-gery, there is a demand for measuring CT at differentpositions of the cornea—centrally, paracentrally, andperipherally. The main advantage of the ultrasoundpachometers is their ability to carry out these measure-ments. However, as already mentioned, the discrep-ancy between different instruments in performing pe-ripheral CT measurements is even greater than forcentral CT measurements. Peripheral measurementsare difficult using standard optical pachometers, butit has been shown that they are feasible with an elec-tronic pachometer equipped with separate fixationlights that make angles of multiples of 5° with thecentral light.25 So far, LDI only has been used for cen-tral CT measurements, but, in principle, peripheralmeasurements are possible. Separate fixation lights asmentioned above could be attached easily to the in-strument. If the patient has no fixation problems, theCT could be measured at different points of the cor-nea with the same high precision as the central CT. Ifone is not willing to rely on the cooperation of thepatient, an eye tracking system or at least a photo-graphic recording of the measurement position on thecornea (with the HeNe laser switched on as a pointingdevice and the camera triggered with the measure-ment) would need to be used.

Key words: biometry, pachometry, corneal thickness, laserDoppler interferometry, laser interferometry

AcknowledgmentsThe authors thank Mr. H. Sattmann, Mr. R. Baradaran,

and Mr. L. Schachinger for technical assistance.

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