Comparison of three-dimensional retinal imagingmethods: the method of scanning lasertriangulation

M. T. Milbocker and Y. M. Reznichenko

Three methods of three-dimensional imaging of the vitreous and the fundus of the human eye arecompared. Equations are derived for the theoretical depth resolution of stereophotogrammetry, scanninglaser tomography, and scanning laser triangulation. Scanning laser triangulation provides superior depthresolution without requiring axial scanning. A description of a prototype scanning laser triangulator isgiven.

Key words: Three-dimensional imaging, scanning laser triangulation, scanning laser tomography,stereophotogrammetry.

Introduction

Three-dimensional imaging of the vitreous and thefundus of the human eye provides important informa-tion for the diagnosis and treatment of eye disease. Ofinterest are fundus changes such as tumor growthand displacement of vessels. Detailed study of thetopology of the optic nerve head is useful in glaucomaresearch.' Topological abnormalities of the retinamay reveal the beginnings of retinal tears, and three-dimensional imaging of a detached retina is essentialin assessing proper curative measures. A review ofelectro-optical methods for fundus imaging has beengiven by Peli.2 For clinical applications, topographicrepresentation of the fundus is accomplished prima-rily by the stereophotogrammetry method, in which acomputer correlates local structures in a pair ofstereo images. Position disparity between the twoimages allows the system to calculate a relative depthat each point. A network of such points produces acontour map of the area.3 The accuracy of the depthmeasurement depends on the degree to which twoimages are correlated in space and time. Two meth-ods, scanning laser tomography and scanning lasertriangulation, eliminate the need for two images.Scanning laser tomography operates on the principleof confocal imaging.4 Confocal instruments image a

The authors are with the Eye Research Institute of the RetinaFoundation, 20 Staniford Street, Boston, Massachusetts 02114.

Received 30 August 1990. 0003-6935/91/284148-06$05.00/0. a

a 1991 Optical Society of America.

plane in a three-dimensional volume. By continu-ously adjusting the axial position of the focal plane,one can sample the volume in a series of slices, whichcan then be reconstructed as a three-dimensionalimage. Scanning laser triangulation also operates onthe principle of confocal imaging; however, the needfor axial scanning is eliminated by applying theprinciple of triangulation. In this paper we evaluatethe axial depth resolution on theoretical grounds,using stereophotogrammetry, scanning laser tomog-raphy, and a new method of scanning laser triangula-tion.

Method of Stereophotogrammetry

Stereo imaging is the standard for measuring axialdistance within the eye and evaluating topologicalfeatures of the fundus such as the optic nerve head.Stereophotogrammetry can be divided into active(structured-light) and passive (stereo-disparity) sys-tems. Structured-light methods involve projectingparallel stripes of light onto the fundus, so thatvariations in the topology of the fundus distort thestripes from a straight line. Structured-light systemsare usually fast, accurate, and inexpensive high-resolution systems. In passive stereophotogramme-try, simultaneous or sequential stereo image pairs areobtained through two separate regions of the ocularpupil. Simultaneous stereo image pairs avoid uncer-tainty in the measure of the stereo base as a result ofeye movement. Refer to Fig. 1: depth resolution Atdepends on the stereo base , the distance betweenstereo pupils; the stereo angle ; and the angularresolution of the system A. For small ai, the relation-

4148 APPLIED OPTICS / Vol. 30, No. 28 / 1 October 1991

DETECTION

(a)

Fig. 1. Schematic of the imaging paths used in the method ofstereophotogrammetry. At is a measure of the depth resolution ofthis method. (a) Axial slice of beam paths within the eye, (b) pupildiagram in the plane of the ocular pupil.

bundles are deflected by synchronized mirrors, largelycompensating for the motion of the scanning spotwith respect to the confocal diaphragm. The time-varying signal of the photomultiplier tube is anencoded image of the fundus of high spatial resolu-tion in a well-defined plane. The focal plane of thescanning beam in the eye is changed by an activeoptical focusing unit. The returned scanning beam isfocused upon a diaphragm located at a plane conju-gate to the chosen focal plane of the scanning laserbeam. The confocal configuration allows only lightoriginating from the illuminated focal plane on thefundus to pass through the diaphragm to a photomul-tiplier tube. Refer to Fig. 2: the depth resolution ACdepends on the diameter of the aperture of thetomographic scanner and the radius of the image ofthe confocal diaphragm p, in the image plane. Refer tothe shaded triangle in Fig. 2: it follows from simplegeometry that

At = + P /as

a = 812b,,.

ship is expressed as

At = + PAa/2a'. (1)

In the case of the eye, the depth resolution A isdiffraction limited according to the Rayleigh princi-ple5

Aa I X/8. (2)

Substitution into Eq. (1) yields

At + 2nXc',/I8, (3)

(4)

(5)

The minimum confocal diaphragm size is the diffrac-tion-limited focal spot given by the Rayleigh principle,yielding for p,

pmi. = nX4, /. (6)

Substituting Eqs. (5) and (6) into Eq. (4) yields theaxial resolution of a point object above the focal planein the eye:

At = ± 2nXe,'/S'. / (7)

where IP is the stereo base, is the entrance pupil forthe fundus imaging device, id is the focal length of theeye filled with air, and n is the refractive index of thevitreous.

Despite the widespread use of stereophotogramme-try, several problems are associated with it. The pupilof the eye is often crowded, two pupils are needed forthe stereo image pairs, and one pupil is needed forillumination. When the entire pupil is used, distor-tion results from the shape of the lens and the cornea.Baumbach et al.6 incorporate an interferometric cali-bration of their system, but its accuracy depends onthe precise placement of illumination and detectionpupils relative to the ocular pupil.

Method of Scanning Laser Tomography

These instruments use the principles of scanningconfocal microscopy to image a well-defined planewithin a volume. A collimated laser beam scans thesurface of the fundus, and the returned light imagesthe fundus in a plane conjugate to the focal plane.' Apinhole (confocal diaphragm) located in this planepermits a flying spot of light formed upon the fundusto pass through and be detected by a photomultipliertube. Both the illuminating and the observing light

Equation (7) shows that increasing the numericalaperture n, while holding constant the radius of theconfocal diaphragm p, improves axial resolution. Thisassumes that a diffraction-limited condition exists for

(b)ILLUMINATION

Fig. 2. Schematic of the imaging paths used in the method ofscanning laser tomography. At is a measure of the depth resolutionof this method. (a) Axial slice of beam paths within the eye, (b)pupil diagram in the plane of the ocular pupil.

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the eye. However, the asphericity of the cornea andlens introduce phase errors in the returned lightbeam. The human eye is known to be a diffraction-limited system up to a pupil diameter of 2.4 mm.8

In scanning tomography the image quality is highlydependent on the synchronization of three indepen-dent scanning elements: two angular movements andone axial movement. A dedicated computer equippedwith specialized software is common. Image qualitycan also be impaired by eye movements. A scanningfrequency of 30 fundus scans/s is a relatively longexposure time during which high-frequency (>20Hz), low-amplitude (<120 m) eye movements de-grade resolution.9 A tracking device must be used tocompensate for eye movement and consequently im-prove image resolution. In addition, scanning devicestypically employ optics that need to be corrected foroptical distortion over the full range of a scan. Opticalschemes that correct optical distortion also decreasethe axial resolution. A difficult-to-eliminate sensitiv-ity to cornea and lens reflection is peculiar to suchsystems.

Method of Scanning Laser Triangulation

Triangulation is a common procedure for measuringdistances. It is conceptually similar to stereophoto-grammetry. In triangulation the illumination anddetection pupils in the ocular pupil are separated by adistance called the triangular base 1P. In scanninglaser triangulation the confocal aspects of scanninglaser tomography are combined with the method oftriangulation. In the triangular system axial longitu-dinal scanning movement is unnecessary since varia-tions in axial distance amount to x-y image displace-ment in the confocal plane.

Refer to Fig. 3: the axial resolution At depends onthe length of the triangular base f3, the focal length ofthe eye + = Pn, and the radius of the confocaldiaphragm p. We obtain the analogs to Eqs. (4), (5),

Fig. 3. Schematic of illumination and imagingbeam baths used inthe method of scanning laser triangulation. AC is a measure of thedepth resolution of this method. (a) Axial slice of beam pathswithin the eye, (b) pupil diagram in the plane of the ocular pupil.

and (6), respectively:

(8)

(9)

Am = P, /a,

ima = ( + C/<

P = 4,/8. (10)

Substituting Eqs. (9) and (10) into Eq. (8) yields

A = 2nA., 2 /(p + 8)8. (11)

The diameter of the confocal diaphragm is limited bydiffraction as in the method of scanning laser tomog-raphy.

The axial depth measured by triangulation com-bines some of the advantages of stereophotogramme-try and scanning tomography. Scanning triangula-tion eliminates one of the detection pupils at the eyebecause it requires only a single pupil for illuminationand one for detection. The axial distance is deter-mined by measuring a displacement of the illumi-nated fundus image in a confocal plane and notbetween two images received through two separatepupils. By measuring the centroid position of the spotimage in the confocal plane one effectively measuresthe position of light passing through a confocaldiaphragm that is the size of the smallest spatialresolution element of the detector. The result isenhanced axial spatial resolution. Axial scanning iseliminated, simplifying scanning schemes and theiralignment. This has the additional advantage ofreducing the time required to scan the fundus, whichconsequently reduces the deleterious effect of eyemovement. With a confocal diaphragm the light-passing aperture is fixed; therefore distortions in theeye-instrument system directly affect the quantity oflight reaching the detector. The scanning triangula-tion method uses a two-dimensional charge-coupleddevice detector to collect the returned light. Theconfocal diaphragm in this system is the mathemati-cal treatment of the spatial character of the signal.The presence of out-of-plane or distorted light can becompensated for by an algorithm.

The disadvantages of triangular scanning methodscompared with concentric scanning methods are thatin the latter system we can use a larger pupil andnumerical aperture, which provide an improved dif-fraction-limited depth resolution.

Description of a Scanning Laser Triangulator

The principle of scanning laser triangulation involvessynchronized deflection of a pixel of light across thefundus, as shown in Fig. 4. The galvanometer-drivenmirrors, 1 and 2, direct the light bundle onto anophthalmoscopic lens, 3. The distance between theophthalmoscopic lens and the eye is adjusted suchthat the light bundle focuses on the fundus.

The illumination and detection pupils are arrangedsymmetrically and defined by mirrors 1 and 2, respec-tively. The plane that contains both mirrors and isoriented orthogonal to the optical axis is conjugated

4150 APPLIED OPTICS / Vol. 30, No. 28 / 1 October 1991

confocal plane by Az:

AZ = A(X'fonmd, = AcM0mdt cos a Ak,.

CCDDetector

r

5 3 p Eye

Fig. 4. Schematic of a prototype laser scanning triangulator.Planes labeled p are ocular pupillary image planes, and planeslabeled r indicate a retinal image plane. Labels 1 and 2 indicategalvanometer-controlled mirrors for scanning the retina in twodimensions.

to the plane cutting the ocular pupil. This symmetrymakes the path lengths of the illuminating and theobserving light bundles equal. The observing lightbundle is descanned on the opposite sides of mirrors 1and 2. An image of the fundus is formed by lens 4 on aconfocal diaphragm. The diaphragm locates a spot oflight in three dimensions. This plane is again focusedby lens 5 on a segmented detector.

All spots in an ideally smooth hemisphere corre-sponding to the mean position of the fundus have anassociated observing light bundle centered on thedetector. This is indicated by principal rays. Forpoints above and below this ideal hemisphere adifferent path is described. One such path is indicatedby the dashed line. As a result, the spot image isdecentered on the detector. The displacement of thespot at the detector varies linearly with the out-of-plane distance at the fundus. The axial resolution isthus made spatially invariant by decoupling the x-ybeam position in the ideal fundus plane with the zposition out of plane. Refer to Fig. 5: the retina islocated out of the focal surface of the eye. Lightreturned from the retinal surface is displaced in the

Fig. 5. Depiction of light paths when the retina is located out ofthe focal surface of the eye.

A4 is defined as the distance between the retina andthe focal surface of the eye. We indicate the triangula-tion base as 13 and the focal length of the eye as (g. Thepupil magnification in the detection path is mdet, andthe focal length of the confocal lens is jc.

Distortion-Limited SystemsEquation (6) is valid for a confocal system with theillumination and the detection pupils aligned. Mis-alignment of the illumination and the detection pu-pils results in the displacement of the illuminationspot in the object plane relative to the position of theconfocal image in the image plane. As a result, theconfocal image is decentered on the confocal dia-phragm. The confocal error results from differencesin pupil magnification along the illumination and thedetection paths of the scanning system. The confocalerror can be written explicitly as

Ecn = (Pih1Pdeti1, -1)OL (13)

where the magnification between entrance and exitillumination pupils in the illumination pathway is pil,

the magnification between entrance and exit pupils inthe detection pathway is I'det, the magnification be-tween the illumination pupil and the eye is ,, thescanning angle is a, and the focal length of the lensbetween the detection pupil and the confocal dia-phragm is 4.

Confocal error depends on geometrical distortion.It may be negligible for small scanning amplitudesbut becomes important for scanning amplitudesgreater than 1 deg. We call a scanning laser systemdominated by confocal error a distortion-limited sys-tem. It is advantageous to examine some of thesources of geometrical distortion in a generalizedscanner. The five principal sources are (1) opticaldistortion, (2) pupil aberration, (3) mechanical distor-tion of the scanning mechanism, (4) pupil positioninside the eye, and (5) distortion in the ocular optics.

Optical distortion is generally minimized in symmet-rical systems. The illumination and the detectionoptical paths should be as similar as possible. Confo-cal systems often satisfy this condition through theuse of the same optical components for illuminationand detection. In addition, distortion can be furtherreduced by positioning the illumination and detectionpupils symmetrically around the optical axis.

Another source of confocal error is pupil aberra-tion. Pupil aberration degrades the spot image insidethe eye as well as shifting the position of the spotimage depending on the orientation of the chief ray.Pupil aberration is corrected by minimizing sphericalaberration and coma in the pupils. Even when pupilaberrations are fully corrected, the position of thespot image moves inside the eye if the pupils are notconjugated to the plane of the scanning axes of the

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(12)

scanning elements. We call this source of confocalerror mechanical distortion. The magnitude of themechanical distortion is proportional to the separa-tion distance of the illumination or the detectionpupil from the axis of scan in the plane of thescanning mirror. For scanning systems that employprisms, polygons, and cubes, it is generally too dif-ficult to compensate completely for the distortioncaused by the axis of rotation of these scanningelements.

The first three sources of confocal error mentionedabove are specific to the instrument design, but it isalso important to correct distortion that is due to theeye. The effect that the eye has on distorting theincident beam and the returned image depends on theposition of the light bundles in the plane of the ocularpupil. The optical system of the eye approximates aconcentric optical system, i.e., the spherical surfacesof curvature within the eye share a common center.In a concentric system distortion is minimized whenthe light bundles are placed at the center of curva-ture. Although there are many surfaces of curvaturewithin the eye, each slightly decentered from theothers, the small differences in index of refraction atthese surfaces renders most distortions caused by thesurfaces unimportant. Two of the most importantsurfaces are the cornea and the retina. The center ofcurvature of the cornea lies approximately in thesecond surface of the lens. The center of curvature ofthe retina lies approximately 5 mm posterior to thatof the cornea. Distortion that is due to the optics ofthe eye is minimized when the pupils are placedbetween these two points.

Discussion

Stereophotogrammetry, scanning laser tomography,and scanning laser triangulation are capable of imag-ing the retina in two dimensions. The last-namedtwo, because they are confocal, generally achievehigher image contrast. However, our emphasis herehas been on measuring the third dimension. Equa-tions (3), (7), and (11) provide a direct comparison ofdepth resolution achievable in the three methods.Their differences lie with the terms in the denomina-tor. Since the stereo base of the methods of stereopho-togrammetry satisfies 1 < 8, the axial resolution ofscanning laser tomography can often exceed that ofstereophotogrammetry. The real advantage of thescanning laser triangulation method is seen when onenotes that + 8 > 8 13, thus providing for a distinctadvantage in axial resolution. It should be noted thatthe constraints on the diameter of to. are somewhatrelaxed over those of ti.p However, because of theasphericity of the cornea, practical considerationsrequire that atom = 8

tri.

Summary Conclusion of Methods of Three-DimensionalImaging Inside the Eye

An absolute comparison of stereophotogrammetry,laser scanning tomography, and laser scanning trian-

gulation is difficult, in part because these methods arenot often applied at their theoretical resolution lim-its. Therefore it is useful to list those advantages thatare inherent in each system. Perhaps these can serveas a guide to selecting the best method for a givenapplication.

Stereophotogrammetry

The instrument for performing stereophotogramme-try is commercially available.

In eyes with clear ocular media, the two-dimen-sional spatial resolution can be better than thatachieved with the other two methods.

Laser Scanning TomographyThe instrument is commercially available.

In eyes with clear ocular media, the axial depthresolution is better than that achieved with stereopho-togrammetry. The two-dimensional spatial resolu-tion is comparable.

The confocal feature of the device reduces lightfrom scatterers in the vitreous.

In practice, opacities in the lens and the vitreouscan be partially overcome.

The instrument is well suited to operation in acontinuous-scanning mode.

Patient discomfort is reduced since the laser poweris 2 orders of magnitude below that required forstereophotogrammetry.

Laser Scanning Triangulation

The method shares the advantages of scanning lasertomography except that a commercial instrument isnot available. However, the following are additionaladvantages:

The method is well suited to observing dynamicchanges in retinal topology during examination. Theinstrument operates in a continuous-scanning modeand eliminates the need for axial depth scanning. Therefresh time between topological maps is substan-tially reduced.

The method provides the potential for better axialdepth resolution than the other two methods.

The method offers direct axial depth measurementfor scanning thin volumes. No optical sectioning isrequired.

Image contrast is generally improved since theillumination and imaging light beams are separatedin the anterior region of the eye.

We thank Francois Delori, Robert Webb, GilbertFeke, and Douglas Goger for useful comments con-cerning three-dimensional imaging within the eye.This research was supported by National Institute ofHealth grant EY01303.

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