Mêasurement of corneal thickness by low-coherence interferometry

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  • Measurement of corneal thickness bylow-coherence interferometry

    Christoph K. Hitzenberger

    A special interferometric technique, which uses light of low-coherence length and the Doppler principle, isapplied to measurement of the thickness of the human cornea in vivo. The special construction of theinstrument eliminates any influence from eye motions on the thickness results. With a superlumines-cent diode as a light source, a precision of 1.5 pLm is obtained. This is 3-8 times better than theprecision of existing instruments. Since interobserver and interinstrument variability are avoided bythe measurement principle, the improvement in total accuracy, compared with that when existinginstruments are used, should be even better.

    Key words: Corneal thickness, pachometry, interferometry, low-coherence interferometry, laserDoppler interferometry.

    IntroductionPrecise measurements of corneal thickness (CT) arenecessary in several cases of modern ophthalmology.They are currently performed mainly with the classi-cal optical slit lamp pachometers of the Haag-Streittype or with ultrasound pachometers. The princi-ples and error sources of these instruments have beendiscussed in the literature.1-5 Typical applicationsof these measurements are, e.g., the examination ofcorneal tolerance to new contact-lens materials andto corneal refractive surgery. Furthermore, it hasbeen suggested that they are helpful in the diagnosisof several corneal disorders.6

    In the past few years two new closely related opticalranging methods have been applied to the measure-ment of intraocular distances. Fujimoto et al,7 usedthe femtosecond optical-ranging technique to deter-mine the corneal thickness of anesthetized rabbiteyes in vivo. Fercher et al.8 used interferometrywith partially coherent laser light to demonstrate themeasurement of the axial length of the human eye invivo. Hitzenberger9 and Fercher et al.10 used animproved version of this technique, laser Dopplerinterferometry (LDI), to reduce the measuring timeto 3 s and to measure the thickness of the humanretina in vivo.9 1 Furthermore they demonstratedthe recording of fundus profiles in vivo.9,10 A similar

    The author is with the Institut fMr Medizinische Physik, Univer-sitat Wieii, Wahringer Strasse 13, A-1090 Vienna, Austria.

    Received 28 February 1992.0003-6935/92/316637-06$05.00/0. 1992 Optical Society of America.

    technique was used by Clivaz et al. 12 to determine thethickness of arterial walls in vitro and by Swanson etal.13 for measuring the distances of anterior eyestructures in an anesthetized rabbit eye in vivo. Anadvanced version of this technique, optical coherencetomography, was used by Huang et al.14 to obtaincross-sectional images of the human retina in vitro.

    A modified version of the LDI technique was usedby Hitzenberger et al. 15 to demonstrate the feasibilityof CT measurements. In this paper further improve-ments in this technique are reported. The precisionis increased by the use of a light source with a shortercoherence length. The principle for eliminating theinfluence of eye motions on the measurement preci-sion is described, and the results from in vivo measure-ments are reported. Finally the new technique iscompared with other methods from a theoreticalpoint of view.

    Description of the Instrument

    Principle of MeasurementThe theory of measuring intraocular distances byinterferometry with partially coherent light has beendescribed in previous papers.8"10 Experimental de-tails on the application of the LDI technique in thecase of axial eye-length measurement have beenreported also.9 Therefore only a short summary ispresented here with the main alterations enabling themeasurement of CT, improving the precision, andeliminating the effect of eye motions on the precision.

    Figure 1 shows a sketch of the instrument used inthis work. It consists of four main units: the light

    1 November 1992 / Vol. 31, No. 31 / APPLIED OPTICS 6637

  • Measurement .. c /Mirror . _ _ _

    MichelsonInterferometer

    ReferenceMirror

    Fig. 1. Block diagram of the laser Doppler interferometer.

    source, the Michelson interferometer, the illumina-tion and detection unit, and the signal-recording andcontrol unit. The light source contains a He-Nelaser (used for alignment purposes) and a superlumi-nescent diode (SLD) (General Optronics Model GOLS3000 TO8), which is used for the measurement.This SLD emits a light beam (wavelength _ 830nm) with a high spatial coherence but a short coher-ence length .

    This beam passes the Michelson interferometer,which splits the beam into two parallel, coaxialbeams: a reference beam 1 and a measuring beam 2,which is delayed with respect to beam 1 by twice thedifference d in the interferometer arm lengths. Inaddition the interferometer mirror of the measuringbeam is shifted by the stepper motor with constantspeed v, causing a Doppler shift of beam 2..

    The Michelson interferometer replaces the FabryLPerot interferometer, which was used in the firstversion, of the instrument. Because the referencearm and the measurement arm of the Michelsoninterferometer are separated spatially, the determina-tion of the point of zero path-length difference andthe measurements in its vicinity are possible. Thisis necessary for precise measurements of short dis-tances such as the CT; it was not possible with theFabry-Perot interferometer, because the frame ofthe interferometer plates prevented their closure tozero distance.

    Both beams, 1 and 2, illuminate the eye through

    Optical CornealThickness

    A and P are the anterior and posterior corneal surfaces.

    the beam-splitter cube of the illumination and detec-tion unit. They are reflected at the anterior and theposterior corneal surface, which introduces an addi-tional path difference of twice the optical CT (OCT).The reflected beams are superimposed on the photode-tector (silicon avalanche diode, RCA ModelC30902EQC-02) and on the video camera (PhilipsModel LDH 0702/20), which is used for alignmentmonitoring during the measurement procedure. Ifthe total path difference between beam 2, reflected atthe anterior, and beam 1, reflected at the posteriorcorneal surface, is less than l,, these beams willinterfere, and the intensity of the correspondinginterference pattern will be modulated by the DopplerfrequencyfD = 2v/X.

    The intensity of the superimposed reflected beamsis detected by the photodetector, amplified, and fil-tered by a bandpass filter that transmits only signalswith D. The envelope of this signal is recorded as afunction of the stepping-motor position with thepersonal cmputer. From the stepping-motor posi-tion, where a signal with fD is registered, d can bedetermined and OCT = d 4/2 is obtained.Therefore thb accuracy of this technique depends on1,. In the case of the SLD used in this work, 1 - 40am full width at half-maximum. By determiningthe signal peak position, one can obtain an accuracyof better than 14/2. The position of the peak isdetermined by a cursor readout on the personal

    6638 APPLIED OPTICS / Vol. 31, No. 31 / 1 November 1992

  • computer. The resolution of this cursor readout is0.5 pm.

    For the OCT to be converted to the geometrical CT,it must be divided by the group refractive index ng ofthe cornea.9"16 Since this value is not available in theliterature, as a first approximation the value ng =1.38569, which is based on the phase refractive indexof the cornea at = 550 nm (Ref. 17) and on thedispersion of water,18 was used.

    The measurement is performed by scanning adistance of 3 mm from -1.5 to +1.5 mm by themirror of the measurement arm. This takes 2 sand yields two corneal thickness results (because ofthe symmetry of the coherence function about thepoint d = 0). During this time the eye is illuminatedby 200 pW or 520 pLW/cm2 (averaged over a 7-mmaperture). Since this is permitted for 25 min for X =830 nm,19 the laser safety limit is met.

    The dynamic range of the instrument is 45 dB.Here the dynamic range is defined as the reflectivityratio of the anterior and posterior reflecting surfaces,which produces a signal just discernible from noise.This definition is more realistic for the purpose ofmeasuring the distance between a strong and a weakreflecting surface (as in the case of corneal thicknessmeasurements) than the usual definition used inother papers, which report dynamic ranges of 90-110dB when conventional interferometric setups areused.12"13 In this case the dynamic range is definedas the ratio of reflectivity equal to 1 and the reflectiv-ity of an interface producing a signal that is equal tonoise in the absence of an additional strong reflectinginterface in the light path. (This strong additionalreflection at the anterior corneal surface increasesthe noise because it produces a bright incoherentbackground.)

    Elimination of the Influence of Eye MotionsWhen an interferometric technique is used for in vivomeasurements, care has to be taken to eliminate anyadverse influence from object motions. Longitudi-nal motions (those parallel to the illuminating beam)and lateral motions (those perpendicular to the illumi-nating beam) must be considered separately.

    As a background to a discussion of how the influ-ence of longitudinal motions is avoided, the usualinterferometric setup is shown in Fig. 2. In this casethe object (the cornea) is placed in one arm of theinterferometer. The path difference within the cor-nea is determined by shifting the mirror of thereference arm. The two mirror positions at whichinterference occurs indicate equal interferometer armlengths excluding and including the OCT, respectively.These two positions are determined subsequently,and their difference equals the OCT. Thereforelongitudinal motions are critical. Any object motionduring the measurement time would alter the resultby the full amount of the motion; this would inhibit aprecise measurement on a living, unanesthetized eye.

    Therefore the usual arrangement has been changed,as has already been mentioned (Fig. 1). The object

    ReferenceMirror

    ReferenceArm

    Super-luminescentDiode

    Beam splitter

    Cornea

    /

    MeasurementArm P

    - OCT -Optical Corneal

    Thickness

    Idtorl

    Fig. 2. Block diagram of the usual interferometric setup. A andP are the anterior and posterior corneal surfaces.

    (the cornea) is not part of one of the interferometerarms but located outside of the interferometer. Themeasurement is performed by matching the un-known path difference within the cornea with theknown path difference in the interferometer. Thispath-length matching uses reflections from both cor-neal surfaces simultaneously and is independent ofthe distance between the cornea and interferometer.Only one mirror position has to be determined tocarry out the measurement, and therefore longitudi-nal eye motions do not influence the result at all.(This does not contradict the fact that a path differ-ence scan for CT measurement usually includes thepoint of zero path difference. At this point a strongsignal peak occurs by the interference of the lightbeams traveling in the two interferometer arms.This signal, which is independent from the path-length matching signal, is used only as a convenientcalibration point.)

    Lateral eye motions can influence the result of CTmeasurements, because the CT depends on the mea-suring position. It is smallest in the center of thecornea and increases at its periphery. In this studythe central CT is measured along the vision axis.This is achieved by asking the subject to look at thebeam. (Because of the broad emission spectrum ofthe SLD, it contains wavelengths that are barelyvisible; the beam appears to the subject as a weak redspot.) If a precision of 1-2 ,um is to be achieved,the CT variation in the area at which the measure-ment is performed (i.e., the area to which the eye canbe aligned repeatedly) should be well below 1 Lm.This is achieved by the geometry of the illuminationand detection unit.

    Figure 3 shows the eye in the case of the maximumpossible decentered position that permits reflected

    1 November 1992 / Vol. 31, No. 31 / APPLIED OPTICS 6639

    ) b

  • . 2'

    Anterior CornealSurface

    Center

    Axis

    OC I iI 4rI II I1- A -Oj

    Object CornealPlane Plane

    1 2Fig. 3. Schematic of the illumination and detection unit: 1, 2, edges of the illuminating beam; 1', 2', edges of the reflection cone; the areabetween 1' and 3', part of the reflection cone transmitted through the aperture; MP, measurement position; PI, Purkinje image; OC, centerof the object plane.

    light to illuminate the photodetector. In this casethe deviation x between the measurement positionMP and the vision axis is at a maximum. The eye isilluminated by a beam with 2-mm diameter (itsedges are labeled 1 and 2 in Fig. 3) through the beamsplitter. It is reflected at the cornea in a cone (theedges of the reflection cone are labeled 1' and 2')whose origin is known as the first Purkinje image PI,which is located 3.8 mm (the half of the cornealradius r) behind the anterior corneal surface.20(For clarity reasons only the anterior corneal surfaceis shown in Fig. 3; the geometry in the case of theposterior surface is almost identical.) The aperturetransmits only part of this cone (1'-3') to the lens ofthe detection unit.

    The object plane, which is imaged on the imageplane by the lens, is located at a distance A 15 mmin front of the corneal plane (the tangent plane to thecornea at the vision axis). The center of the objectplane, the point OC (which is aligned with the beamcenter of the illuminating beam), is imaged onto thephotodetector. The only light beam, which hits thephotodetector (through point OC), is reflected atpoint MP at the cornea, the position at which the CTis measured. In the case of the maximum possibledecentration, MP lies at the edge of the illuminatingbeam. From simple triangle geometry the distance xcan be determined: x = r x r/2A (where r is theradius of the illuminating beam). With r = 1 mm,r = 7.6 mm, and with A 15 mm, x 0.25 mm.

    This means that, if the eye is decentered by < 1.25mm (r + x), the CT is measured within a circle with a0.25-mm radius around the vision axis. (At largerdecentrations no light will fall into the photodetectorand no signal will be observed.) The variation of CTin an area of this size at the center of the corneais

  • 1.00

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    0.00 I'- Y ' V"' I "lNV pf 'Y. I' , rll ' IVIR1 I ' - 'a I ' 1 ' 11 V ' 'I I VIf IW 1I -It T I I-1.50 -0.75 +0.00 +0.75 +1.50

    mm

    Interferometer arm length difference dFig. 4. Measurement of the OCT. The intensity of the Doppler signal is plotted versus the interferometer arm length difference d.The three strong peaks at positions d = -1.3, 0, + 1.3 mm are caused by the coherence function of the SLD. The two smaller peaks at adistance OCT _ 750 ,um from the central peak are caused by the posterior corneal surface.

    The signals from the posterior corneal surface arelocated at equal distances from the central peak,between the central peak and sidelobes. Their dis-tance to the central peak equals the OCT of thecornea. In this case OCT = 748 + 2.2 Atm [a meanvalue of 10 measurements standard deviation (SD)].The geometrical CT = 540 1.6 [um in this case.(The value 1.6 pum is the repeatability in this case;errors caused by a possible inaccuracy of the ng valueof the cornea are neglected here.) The CT of theother 13 eyes was measured in a similar way. Theresults ranged from 489 to 547 [Lm. The SD valuesof the geometrical CT ranged from 0.7 to 2.8 lm, theaverage being 1.53 pm.DiscussionIt was shown that the LDI technique is capable ofmeasuring the central corneal thickness with a preci-sion of 1.5 [um if a SLD with l = 40 [um is used.By a factor of 5 this is better than in the case of arecent report on preliminary results with this tech-nique.'5 In this case we achieved a precision of 7 jmby using a multimode laser diode where 4, 220 [im.(This laser diode was the reason for the acronym LDI;although it might be somewhat misleading, becausethe principle of low-coherence length is usually notassociated with lasers, this acronym is adopted forconsistency with previously published work.) Sincethe precision is improved by about the same factor asthat expected from the l values, it can be concludedthat the method of transversal stabilization of themeasuring point on the corneal surface is sufficient.

    Compared with the classical pachometric tech-niques, the precision obtained by LDI is much better.With the optical pachometer of the Haag-Streit type,a precision of the order of 13 jim (SD) is usually

    obtained.3 Additionally considerable interobserverdiscrepancies of up to 20 pum occur.2 The reason forthese discrepancies is probably that this techniquedepends on the perceptive properties of the operator.2The LDI technique should not suffer from this prob-lem.

    The SD of measurements carried out with ultra-sound pachometers is reported to be 5 m.4 ,5However, large differences in the readings of differentinstruments were found. The maximum differenceswere 50 [um in the case of central CT measure-ments and up to 150 ,um in the case of peripheral CTmeasurements.4 These discrepancies are trouble-some, especially for the purposes of refractive surgery.Undercorrections, overcorrections, and even perfora-tions can occur if data from different instruments areused. The reasons for these discrepancies are notclear. This problem should not occur with LDI,because the CT is directly read from another lineardistance, which avoids calibration problems. Theonly remaining error source is the value of ng, whichis used for the optical-to-geometrical CT conversion.This problem exists also with the ultrasound tech-nique, because the true value of sound speed in theliving human corneal tissue is not known with greataccuracy. 4

    Another disadvantage of ultrasound pachometry,compared with both conventional optical pachometryand LDI, is its need for mechanical contact betweeninstrument and eye. This implies a risk of infectionand the need for anesthesia, which reduces thepatient's comfort.

    The 4, of our SLD is of the same order as the lengthof the femtosecond light pulses used to measure thethickness of anesthetized rabbit corneas.7 Thismeans equal accuracy in principle but with the great

    1 November 1992 / Vol. 31, No. 31 / APPLIED OPTICS 6641

  • advantage of lower cost with the LDI technique.The SLD used in measurements employing the classi-cal interferometric setup 3 and in the optical coher-ence tomography techniques has about the same l asthe one used in this work. Consequently the preci-sion of longitudinal measurements is the same.

    The advantage of the optical coherence tomographytechnique is its ability to obtain cross-sectional im-ages with a lateral resolution of 9 jim. LDI has beenused to measure fundus profiles too but only with lowlateral resolution.9,'0 In the case of the cornea onlythe central CT has been measured. This is sufficientfor examining the corneal tolerance to new contactlens materials. (In this case the corneal swellingcaused by hypoxia-induced edema is measured.) Forpurposes of refractive surgery, peripheral measure-ments are required in addition. These measure-ments can also be performed by LDI without difficulty.A first approach will be the use of a separate fixationlight that makes an adjustable angle with the measure-ment beam. (This method has been used success-fully in the fundus profile measurements.)

    The main drawback of optical coherence tomogra-phy in its present state (and of any technique usingthe classical interferometric setup) is that the sampleis located in one arm of the interferometer. There-fore the technique is extremely sensitive to longitudi-nal motions of the sample. This makes measure-ments on living, unanesthetized tissue quite difficult.On the other hand the interferometric setup of theinstrument presented here eliminates any influencefrom longitudinal object motions. If therefore theadvantages of both techniques are combined, a power-ful instrument for investigating the living human eyecould be the result.

    The author thanks A. F. Fercher for encouragingthis study and H. Sattmann for the construction ofthe electronics and the software of the laser Dopplerinterferometer. Financial support from the Aus-trian Fonds zur F6rderung der wissenschaftlichenForschung (grant P 7300-MED) is acknowledged.References

    1. N. Ehlers and F. Kruse Hansen, "On the optical measurementof corneal thickness," Acta Ophthalmol. 49, 65-81 (1971).

    2. T. Olsen, C. B. Nielsen, and N. Ehlers, "On the opticalmeasurement of corneal thickness II. The measuring condi-tions and sources of error," Acta Ophthalmol. 58, 975-984(1980).

    3. C. Edmund and M. La Cour, "Some components affecting theprecision of corneal thickness measurement performed byoptical pachometry," Acta Ophthalmol. 64, 499-503 (1986).

    4. A. L. Reader and J. J. Salz, "Differences among ultrasonicpachymeters in measuring corneal thickness," J. Refract.Surg. 3, 7-11 (1987).

    5. A. Gordon, E. A. Boggess, and J. F. Molinari, "Variability ofultrasonic pachometry," Optom. Vis. Sci. 67, 162-165 (1990).

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    8. A. F. Fercher, K. Mengedoht, and W. Werner, "Eye lengthmeasurement by interferometry with partially coherent light,"Opt. Lett. 13, 186-188 (1988).

    9. C. K. Hitzenberger, "Optical measurement of the axial eyelength by laser Doppler interferometry," Invest. Ophthalmol.Vis. Sci. 32, 616-624 (1991).

    10. A. F. Fercher, C. Hitzenberger, and M. Juchem, "Measure-ment of intraocular optical distances using partially coherentlaser light," J. Mod. Opt. 38, 1327-1333 (1991).

    11. C. K. Hitzenberger, A. F. Fercher, and M. Juchem, "Measure-ment of the axial eye length and retinal thickness by laserDoppler interferometry," in Ophthalmic Technologies, C. A.Puliafito, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1423,46-50 (1991).

    12. X. Clivaz, F. Marquis-Weible, R. P. Salath6, R. P. Novak, andH. H. Gilgen, "High-resolution reflectometry in biologicaltissues," Opt. Lett. 17, 4-6 (1992).

    13. E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin,and C. A. Puliafito, "High-speed optical coherence domainreflectometry," Opt. Lett. 17, 151-153 (1992).

    14. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G.Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A.Puliafito, andJ. G. Fujimoto, "Optical coherence tomography,"Science 254, 1178-1181 (1991).

    15. C. K. Hitzenberger, W. Drexler, and A. F. Fercher, "Measure-ment of corneal thickness by laser Doppler interferometry,"Invest. Ophthalmol. Vis. Sci. 33, 98-103 (1992).

    16. S. Pancharatnam, "Partial polarization, partial coherence andtheir spectral description for polychromatic light-part II,"Proc. Ind. Acad. Sci. 57,231-243 (1963).

    17. H. Obstfeld, Optics in Vision (Butterworth, London, 1982), p.31.

    18. H. Naumann and G. Schr6der, Bauelemente der Optik (Hans-er, Munich, 1983), p. 50.

    19. American National Standards Institute, Safe Use of Lasers,ANSI Z 136.1 (American National Standards Institute, NewYork, 1986).

    20. Ref. 17, p. 299.21. C. Edmund, "Determination of the corneal thickness profile by

    optical pachometry," Acta Ophthalmol. 65, 147-152 (1987).22. W. M. Hart, Jr., "The temporal responsiveness of vision," in

    Adler's Physiology of the Eye, R. A. Moses and W. M. Hart, Jr.,eds. (Mosby, St. Louis, Mo., 1987), p. 436.

    23. Y. Ning, K. T. V. Grattan, B. T. Meggitt, and A. W. Palmer,"Characteristics of laser diodes for interferometric use," Appl.Opt. 28, 3657-3661 (1989).

    6642 APPLIED OPTICS / Vol. 31, No. 31 / 1 November 1992

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