Wavelength-tuninginterferometry of intraocular distancesF. Lexer, C. K. Hitzenberger, A. F. Fercher, and M. KulhavyWe describe basic principles of wavelength-tuning interferometry and demonstrate its application inophthalmology. The advantage of this technique compared with conventional low-coherence interferom-etry ranging is the simultaneous measurement of the object structure without the need for a movingreference mirror. Shifting the wavelength of an external-cavity tunable laser diode causes intensityoscillations in the interference pattern of light beams remitted from the intraocular structure. A Fouriertransform of the corresponding wave-number-dependent photodetector signal yields the distribution ofthe scattering potential along the light beam illuminating the eye. We use an external interferometerto linearize the wave-number axis. We obtain high resolution in a model eye by slow tuning over a widewavelength range. With lower resolution we demonstrate the simultaneous measurement of anteriorsegment length, vitreous chamber depth, and axial eye length in human eyes in vivo with data-acquisitiontimes in the millisecond range. © 1997 Optical Society of AmericaKey words: Wavelength tuning, interferometry, wavelength-tuning interferometry, intraocular dis-tances.1. IntroductionThe precise knowledge of intraocular distances is inincreasing demand in modern ophthalmology. Oneneeds the axial eye length and the anterior chamberdepth to calculate the refractive power of artificialintraocular lenses for cataract surgery. Precisemeasurement of the corneal thickness is essential forcorneal refractive surgery, and the determination ofthe thickness of retinal layers might improve the di-agnosis of several diseases and be helpful in monitor-ing therapeutic effects. In recent years a newnoncontact technique, partial coherence interferom-etry ~PCI!, has been developed. PCI enables themeasurement of intraocular distances with unprece-dented precision and resolution.1–3This techniquewas extended to optical coherence tomography~OCT!, a new imaging modality capable of obtainingtwo-dimensional optical cross sections of ocularstructures.4–6Both techniques work in the time do-main. A broadband light source such as a superlu-minescent diode is coupled with a Michelsoninterferometer. The sample to be measured isplaced in one arm of the interferometer; the otherarm contains the reference mirror. The referencepath length is changed in order to match the lighttransit times in the reference beam to the light tran-sit time in the object.An alternative approach for measuring optical dis-tances is to use frequency- or Fourier-domain tech-niques. In these techniques a fixed-reference pathlength is used. The object is illuminated by a broad-band light source, and the frequency- or wave-number-dependent response of the object on theremitted light is detected with a photodetector-arrayspectrometer or by tuning the wavelength.7Spec-trometric techniques have already been used to mea-sure the anomalous dispersion of gases and metalvapors,8,9the thickness and refractive index of lami-nae,10,11the film thickness of semiconductor layers,12the absolute displacements,13and recently the groupdelay on laser mirrors.14The distance informationis contained in the width of channels in the spectrum.In addition, the application of spectrometric tech-niques used to measure single7,15and multiple in-traocular distances16–18have been described.In wavelength-tuning interferometry ~WTI! the ob-ject is illuminated by a tunable laser at differentwavelengths. In this case one can record the spec-trum with a single photodetector. A simplified ver-sion of this technique has already been used tomeasure the axial length of human eyes. The dis-tance information was obtained by counting the in-The authors are with the Institute of Medical Physics, Univer-sity of Vienna, Wa¨hringer Strasse 13, A-1090 Wien, Austria.Received 2 December 1996; revised manuscript received 26 Feb-ruary 1997.0003-6935y97y256548-06$10.00y0© 1997 Optical Society of America6548 APPLIED OPTICS y Vol. 36, No. 25 y 1 September 1997terference fringes that pass a fixed point in aninterferogram while the wavelength of a pulse-mode-operated laser diode was changed.19However, thisfringe-counting method does not exploit the full in-formation content of the time-domain signal and cantherefore only be used if a single distance is to bemeasured. To obtain access to more complex objectstructures, one can use backscattering techniques.18WTI has some previous history: In 1960, Hymans etal.20described a radar system with a sawtooth fre-quency sweep. Later fiber-optic frequency-domainreflectometry techniques were described by Mac-Donald21by using a rf-modulated laser beam andEickhoff and Ulrich22by using frequency tuning of aHe–Ne laser. Currently, the most promising coher-ent tunable light sources are semiconductor lasersand solid-state lasers. To achieve laser tuning, thegain margins of the cavity modes have to be rear-ranged or the frequency of the cavity modes must beshifted. Several techniques such as distributedBragg reflector lasers, multisection distributed feed-back lasers, multiple-cavity lasers, external-cavity la-sers, and filter techniques23have been developed.24To exploit the full potential of WTI, it is importantthat wavelength tuning is performed continuouslywithout nonlinearities and jumps as caused by modehops.We present an improvement of WTI that can mea-sure several intraocular distances simultaneously.We use an external-cavity laser. However, othercontinuously tunable transversal single-mode lasersmight be used within their mode-hop-free spectralrange. We demonstrate the WTI technique in amodel eye with high resolution and in human eyes invivo with low resolution but an acquisition time in themillisecond range.2. Fourier-Domain Backscattering Optical CoherenceTomographyIf an object is illuminated by a monochromatic wavewith wavelength l and wave vector ki, the Fouriertransform of the diffracted homogeneous wave imme-diately outside the object is related to the Fouriertransform of the object scattering potential along asemicircular arc in Fourier ~K2! space.25kSis thewave vector of the scattered wave; ukiu 5 uksu 5 2pyl.K 5 ks2 kiis the scattering vector. This forms thebasis of the Fourier diffraction theorem.26Further-more, the scattered wave detected in the far fieldE~s!~ks! is directly related to the Fourier transform ofthe