Three-dimensional optometer III

Three-dimensional optometer Il

Tsunehiro Takeda, Yukio Fukui, Kazushi Ikeda, and Takeo lida

We describe a newly developed three-dimensional optometer III (TDO III) that can measure simulta-neously three major ocular functions-accommodation, eye movement, and pupil diameter-and headmovement in an actual working environment. The TDO III permits free head movement as well as freeeye movement because the measurement component is mounted on the head. Its size has been reducedsubstantially compared with the original model. The remaining weight of TDO III is counterbalanced tominimize head loading weight. Normal lighting is permitted, and it is unnecessary to dilate the pupilwithadrugfor measurement. TDO III can measure accommodation from -12.7 to +26.6 D and 100% of

the pupil diameter change when the eye moves within a 40° horizontal and 30° vertical area. Headmovement is permitted within a sphere 200 mm in diameter. The accuracy when measuring both theaccommodation and pupil diameter with TDO III is ±0.25 D and ±0.3 mm, respectively. The error whenmeasuring the angles of the eyes is less than ± 0.50. The eye position accuracy is ± 10 mm, and the threeCartesian angles are ± 10. The accuracy of TDO III has been intensively investigated in both artificialand human eyes.

Key words: Accommodation, eye movement, pupil diameter, head movement, objective measurement.

1. Introduction

The importance of visual information has been receiv-ing wide recognition. Hence many fields demand thesimultaneous measurement of three major ocularfunctions-accommodation, eye movement, and pu-pil diameter-in a real working environment. Theevaluation of visual fatigue induced by prolongedwork at a visual display terminal (VDT) is one suchexample. Although a number of researchers havetried to achieve this goal, so far we believe that nonehas succeeded completely. ' 2

Takeda et al. 3 developed an apparatus (a DynamicRefractometer) that can measure dynamic accommo-dation easily by modifying a commercial autorefrac-tometer. However, it requires subjects to fix theireye direction to coincide with the optical axis.Takeda et al. 4 then developed a three-dimensionaloptometer (TDO) that can measure the three majorocular functions while the subjects are shifting theireye positions freely while carrying out actual work.

T. Takeda, Y. Fukui, and T. Iida are with the Human InformaticsDepartment, National Institute of Bioscience and Human Technol-ogy, Ministry of International Trade and Industry, 1-1 Higashi,Tsukuba Science City, Ibaraki, Japan. K. Ikeda is with theFaculty of Engineering, University of Tokyo, Tokyo, Japan.

Received 24 November 1992.0003-6935/93/224155-14$06.00/0.© 1993 Optical Society of America.

It has proved its usefulness in measuring the accom-modation induced by apparent depth sensation whilethe subject is looking at pictures. The TDO still hasone major restriction in that it requires the subjectsto hold their heads still on a chin rest. Hence it hasbeen pointed out that this posture restriction mightinfluence visual fatigue during TDO measurement.

We have now developed an apparatus, called athree-dimensional optometer III (TDO III), that per-mits free head movement as well as free eye move-ment. The TDO III is designed to combine thelight-relay system of the TDO and the optical compo-nent of an autorefractometer into a single compactsystem. The optical system is mounted on the sub-ject's head with its weight counterbalanced. Sub-jects feel no weight and can move their headssmoothly, any movement being measured by a mag-netic measurement device.

In this paper we analyze the optical principles usedin developing the TDO III and formulate them to beapplicable for future development or other opticalsystems. The main purpose of this paper is todescribe optical principles, which were not mentionedin Ref. 4, the basic design procedure, improvementsin TDO III compared with the former model, andhead-movement measurement. The accuracy of TDOIII is intensively investigated not only with artificialeyes but also with human eyes. Finally its character-istics are summarized.

1 August 1993 / Vol. 32, No. 22 / APPLIED OPTICS 4155

2. Optical Principles of TDO III

Three basic optical principles of TDO III are ex-plained in this section.

A. Relay Lens System

Consider a lens system with a spherical lens of focallength f. Assume that a and b are the distances froman object to the lens and from the lens to an image ofthe object, respectively. Then the lateral magnifica-tion m becomes a hyperbolic function of f, since m =-b/a = -f/(a - f) with the well-known Gaussianlens formula. On the other hand, an afocal relaylens system, consisting of two identical convex lenses,has been widely used to relay images with constantlateral magnification independent of distance. Craneand Clark6 analyzed a general afocal system consist-ing of two convex lenses of different focal lengths fiand f2. They found that such systems have a con-stant lateral magnification of f2/ fi and longitudinalmagnification of b' = (fi + f2)f 2/fl - (f2 /f1)2 a (whereb' is the distance from the second lens to the image).Hence the object is magnified laterally (2/f) andaxially (f2/fl)2. They called such a system a relaylens pair.

We have generalized the results of Crane and Clarkas shown in the following. Constant lateral magnifi-cation is essential to transfer object space into imagespace without distortion. Let us suppose that twoobjects A and B have the same height and are imagedby our general relay lens system [Fig. 1(a)]. The rayr1 that is parallel to the optical axis and passesthrough the top of the objects A and B becomesanother ray r2 parallel to the optical axis, because theray r2 has to pass the top of images A' and B', whichare equally magnified. Therefore we can determinewhether a lens system is a relay lens system byexamining whether a ray parallel to the optical axisbecomes another parallel ray in the image space.Using this principle, we can classify the general lenssystems as follows:

(1) One convex lens: A relay lens system cannotbe realized with only one convex lens, because a rayparallel to the optical axis cannot emerge as a parallelray in this case.

(2) Two convex lenses: A ray parallel to theoptical axis converges at a focal point. Hence an-other lens should be placed so as to produce an afocalcombination, as shown by Crane and Clark. Noother two-lens system can produce a relay lens pair.

(3) Three convex lenses: The principal configura-tion is shown in Fig. 1(b). The first lens causes theparallel ray to converge at the focal point F1, and thethird lens produces a parallel ray from the focusedray. Hence the second lens should be located so as tosatisfy the Gaussian lens formula as shown in thefigure. Two free parameters exist in this case; theyare the focal length of the second lens and its location.The lateral magnification becomes (f3 /f1 )(b/a).Figure 1(c) shows another possible configurationreducible to the two-lens-system case; that is, the first

t A

(a)

Re I ay.Len SYat em

Optica Ais

A' 13'

1 q -- 13

(b) 1 {3

(c)

(d)

(e)

f3 /

A3/ Il

-f3l /f,

Fig. 1. (a) Schematic diagram of the general relay lens systems.(b) Principal configuration of the relay lens systems with threelenses; the second lens satisfies the Gaussian lens formula concern-ing F1 and F3. (c), (d) Configurations reducible to the two-lenscase. (e) An extreme case of (c) and (d). The lateral magnifica-tions are (b) f 3 q/fi p, (c) f3/fi*, (d) f3*/f1 , and (e) f 3/f1, where fi* andf3* are compound focal lengths.

lens pair of the lenses becomes a lens combinationthat focuses the parallel ray to a focal point of thethird lens, as in Fig. 1(c). In Fig. (d), the mirrorimage of Fig. 1(c) is self-explanatory. An extremecase is shown in Fig. 1(e). The second lens is locatedat the focal point of the first and third lenses. Thesecond lens, L2, shifts only the image position andmaintains the lateral magnification in this case.The lateral magnification becomes (3/fl) for Figs.1(c)-1(e), although a compound focal length should beused in Figs. 1(c) and 1(d).

(4) Four lenses or more: By combining groups oflenses to be equivalent to a lens, this case falls intoeither (2) or (3).

Hence an enormous number of lens combinationscan produce a relay lens system. With the aid of theclassifications above, we can design rather freely anyrelay lens system of specified magnification and speci-fied optical length. Although for simplicity onlyconvex lenses are considered in the above discussion,it is not difficult to generalize the results to the relaylens systems that include concave lenses. Anotherexplanation of the relay lens systems can be found inFukui et al.,7 who developed an automatic generationprogram for the relay lens systems.

4156 APPLIED OPTICS / Vol. 32, No. 22 / 1 August 1993

. .

J- -1f , - A

__'J" -

B. Ray-Direction Conversion System

Ellipsoidal and spherical mirrors are two candidatesthat seem to be capable of converting the ray direc-tion to inject measurement light into an eye accordingto the eye position.

All rays that pass through one focal point of anellipsoidal mirror pass through the other point afterreflection. Therefore, if a movable plane mirror islocated at one focal point and an eye is located at theother focal point, the measurement light could alwaysbe injected into the eye by tilting the mirror accordingto the eye direction. However, the magnification ofthe image varies according to the light direction, as iswell known. This means that a stationary image ofthe eye is located at the position of the plane mirror,and the size of the image varies according to the eyeposition. This property probably has an influenceon the measured accommodation. Moreover, if thepupil diameter is reduced to less than the minimumdiameter required, which is 3 mm for almost allautorefractometers at present, the measurement can-not be performed. Although there might be sometechniques for overcoming these problems, it is diffi-cult to obtain a high-quality ellipsoidal mirror ofseveral hundred millimeters, because ellipsoidal mir-rors cannot be polished mechanically. Therefore wehave given up the possibility of using an ellipsoidalmirror.

Figure 2 shows a ray-direction conversion systemwith a spherical mirror SM. A plane galvanomirrorGM is placed at the center O' of the spherical mirror,and an eye is located at the conjugate point O'through the half-mirror HM. If the mirror GM isrotated by Om in the proper direction when the eyerotates 20m, the measurement light will always beinjected into the eye. Effectively a stationary imageof the eye is formed at the mirror GM, and the size isthe same as the eye. However, this configurationhas two inherent problems: (1) The intensity of themeasurement light decreases to <1/16, because thelight passes the half-mirror four times; (2) the re-flected light from the mirror SM is much stronger

SM .02 01 03 M' L

_~~ E i)H GMHM

Fig. 2. All the rays that pass through the center of curvature of aspherical mirror pass through the same point after reflection. Aplane galvanomirror, GM, is located at the center of a sphericalmirror, SM, and an eye, E, is located at the conjugate point withrespect to a half-mirror, HM. Then, if mirror GM is tiltedaccording to the eye direction, measurement light ML can beintroduced into the eye irrespective of the eye direction. 01, 02,

03, eye directions; 0e,

0m, rotation angles.

than the signal light reflected from a retina andhampers the measurement. Therefore the galva-nomirror GM and the eye are shifted slightly in thedirection perpendicular to the paper in Fig. 2. Sincethe shift produces considerable distortion, two spher-ical mirrors, which are placed to make the shiftdirection orthogonal, are used to minimize the distor-tion.4 The use of two spherical mirrors also providesa much easier way to use two galvanomirrors tocompensate for eye movements instead of a singlemirror that needs to be tilted about two axes. Weadopted this system to TDO III.

C. Optical-Axis Conversion System

A movable mirror MM is located at the focal point oflenses L and L2 in Fig. 3. Then, if it is tiltedthrough 0, a beam that is parallel to the optical axis(solid lines) is displaced as shown by the dotted lines.Next the light emerges from lens L2 and is parallelwith the optical axis again. This means that theoptical axis is shifted by f2 tan 0, and the new opticalaxis is parallel to the original one. We can easilygeneralize as follows: If and only if a mirror islocated at the focused points of inputted parallelbeams in a general relay lens system, does it becomethe optical-axis conversion mirror.

If a mirror rotatable about two orthogonal axes isused, the optical axis can be moved two dimensionally.This mechanism is simple and permits the design of aflexible optical system. We expect that this mecha-nism will pave the way for development of a next-generation TDO.

3. TDO III System

The design principle and the system realized by TDOIII are described here and compared with those of theformer model.4 Hereafter TDO III is the newlydeveloped optometer, and TDO I is the former optom-eter.4 TDO is used when discussing the commoncharacteristics of the TDQ III and the TDO I. Sincethe optical system of the autorefractometer and the

A

Fig. 3. Schematic configuration of an optical-axis conversionsystem. A movable mirror, MM, is located at the afocal point oflenses L and L2. The incident parallel beams are swung by f2tan 0 and become parallel beams again. The relay lens system, L1and L2, can be generalized according to the principle explained inSubsection 2.A. fi, f2, focal lengths.


control system of the TDO III are the same as those inTDO I, an explanation of them has been omitted forthe most part in the following.

A. Principal Design

To allow for the subject's head movement whilemeasuring the three major ocular functions with theTDO III, we tried to mount the optical relay lenssystem on the subject's head and to connect it withthe optical part of the autorefractometer. Two possi-ble methods were assessed first, i.e., (1) the optical-fiber method and (2) the optical-link method.

Since optical fibers are flexible, they allow free headmovement. Image relay with optical-fiber bundleshas improved remarkably in quality, and its price hasalso dropped. Thus an optical-fiber link was the firstcandidate. However, the principle of the autorefrac-tometer that is used in TDO I requires that themeasurement light be introduced into the eye pre-cisely as in the original apparatus. This means thatthe optical fiber must preserve light direction.Although the coherent optical-fiber bundle preserveslight intensity, it cannot preserve light direction.Another type of autorefractometer that uses theretinoscopic principles does not require that raydirection be preserved but only light intensity. Inthis case the optical-fiber method would be usable.Since the principal of the retinoscopic optometer issimple, the measurement apparatus can be fairlysmall. Although it seems to be suitable for TDO III,the precision of the retinoscopic autorefractometerthat is now available commercially is not adequate forour purpose. Therefore we judged the optical-fibermethod to be inapplicable to TDO III.

In principle, one of the many relay lens systemsexplained in Subsection 2.A could be used to transfermeasurement light from the autorefractometer andthe optical components mounted on a head. Severalmechanisms seem to be applicable that allow freehead movement, while the measurement light istransferred into the eye and the image at the retina isreturned to the measurement apparatus. However,in practice the light for the measurement beam that isreflected from the surfaces of the relay lenses tends toveil the real signal of the image at the retina.Several methods to eliminate the influence of re-flected light from the lens surfaces on the photocell inthe autorefractometer were tried, but this was diffi-cult to accomplish. Hence we gave up on the applica-tion of this method also.

Finally we decided to mount on the subject's head asingle optical system that combined as a unit thereduced-size relay lens system of TDO I and theoptical component of the autorefractometer in TDO I.

B. Realized System

Figure 4 shows the TDO III system. The weight ofthe optical component of TDO III is counterbalancedby another weight as shown in the figure. Thus thesubjects feel virtually no weight. The optical compo-nents are suspended from a three-axis movable sup-

Fig. 4. The TDO III system. The optical components are con-tained in a box on the subject's head. Controllers are located atthe left.

port. Therefore the subjects can move their headand eyes freely, while head movement and the re-sponse of three major ocular functions are beingmeasured simultaneously.

The weight of the optical components is 35 kg.The dynamic frictional torques are 1.3 N m aroundthe second horizontal axis Z (from front to rear), 0.83N m around the first horizontal axis X (from left toright), and 1.2 N m around vertical axis Y. The XYZaxes can be confirmed in Fig. 7. The inertia is 0.24kg m2 around the Z axis, 0.19 kg m2 around theX axis,and 0.18 kg m2 around the Y axis, if the weight isdistributed homogeneously. Therefore the influ-ence on the subjects is rather small, although it seemsgreat. The subjects actually report that they do notfeel any great restriction when moving their heads.

The subjects are required to hold their heads on achin rest with two cloth bands. Alignment is easilyperformed with a three-axis movable chin rest that isdriven by small motors. The alignment can be donein several minutes with the aid of a CCD cameralocated on the optical axis and a CCD camera locatedjust below the eye. It can be performed within 10 sfor an immediate repetition on the same subjects.The second camera is used to determine the distancebetween the apparatus and the eye and to monitor thereal eye movement by monitoring the first Purkinjeimage.

The control system of the galvanomirrors, theeye-movement-measurement apparatus, and the pu-pil diameter are shown in the left half of Fig. 4.Since these are virtually the same as the ones used inTDO I, they are not described in this paper. Thesettling time of the galvanomirrors is 110 ms, andthe cutoff frequency is 6.4 Hz as described in Ref. 4.

The magnetic sensor, from McDonnell DouglasCorporation (ISOTRAK), is used to measure headmovement as shown at the top right of Fig. 4. Theweight of the sensor is only 23 g. The resolution is


ISOTRAK

(McDonnell

Douglas)

.-, A x drivea Y drive

,tical Measurementpi ght

ystem

(NAC) Eye Image

I II Hi

X-Y Tracker

Area Analyzer

(Hamamatsu C3160)

Fig. 5. System configuration of TDO III. The C3160 has the functions of theX-Ytracker and area analyzer.

+ 1 mm for position and ± 10 for orientation. Themaximum measurement speed is 53.3 Hz.

Figure 5 depicts the system configuration of TDOIII. The measurement of accommodation is per-formed by the optical system of the autorefractome-ter (modified from the NIDEC AR-1100). Althoughthe subjects are required to gaze into the apparatusand fix their eye position with the original AR-1100,they are permitted to move their eye freely to watchobjects with the aid of the relay lens system.

The X-Y tracker in the percept scope (the firstfunction of C3160, Hamamatsu Photonics) measureseye movement, and the galvanomirrors are driven sothat they maintain the monitored eye in the center ofthe cathode ray tube (CRT) by using the measureddata by the servo controller of TDO III. The servocontrol mechanism ensures that measurement lightis injected into the eye irrespective of eye movement.The pupil diameter is measured by the second func-tion of the percept scope (the area analyzer). It slicesthe monitored image of the eye by a given thresholdlevel on the CRT and counts pixels brighter than thethreshold level. Then the pupil diameter is calcu-lated, assuming that the pupil is a circle.

The microcomputer controls the measurement tim-ing, taking in the data of the three ocular functionsand head movement. The program that does that iswritten in C language, except for the portion that iswritten by an assembler language for acquiring thedata as fast as possible.

A unit magnification relay lens system was re-quired for the TDO III. A set of three lenses withunit magnification can be chosen to form a relay lenssystem (Subsection 2.A). However, for the magnifi-cation requirement to be fulfilled, the third lens withf/2 focal length needs to be located where the secondgalvanomirror is located. Therefore a relay lenssystem with four lenses is adopted, as shown in Fig. 6.The focal lengths of lenses L3 and L4, which can beselected according to the principal explained in 2.A,are chosen to be f/2 for convenient construction.

Figure 7 depicts the top view of the realized relaylens system of the TDO III. Lenses L, and L2 in Fig.6 are replaced by spherical mirrors B and E. The

optical length modulators L-O and mirrors D, H, andJ are inserted. The focal lengths of B and E weredetermined to be the same and were chosen to be thesmallest in conditions where a 400 horizontal and 30°vertical visual field is allowed. The eye being mea-sured is always the right eye, although both eyes aremeasurable with TDO I. The dichroic mirror wasplaced as close to the eye as possible to reduce its size.The focal length f of the relay lens system wasdetermined to be 89.33 mm. Then the size of therelay lens system of TDO III became 0.672x that ofTDOI.

A glass, located between B and C in Fig. 7 toincrease the stability of the dichroic mirror in TDO I,is removed to eliminate any distortion effect from theglass in TDO III. The optical design was performedintensively once again, by using the improved com-puter aided design program, which permits precisethree-dimensional ray tracing. The length betweenC and D is modified slightly to minimize distortion.

The mirror F is the optical-axis conversion mirrorexplained in Subsection 2.C. The mirror can berotated about two axes by electric motors. The L-Omirrors serve as an optical length modulator (opticaltrombone) when the M and N mirrors are movedtogether. Hence the optical center of the systemindicated by Eye can be moved three dimensionallywith these two mechanisms. We have confirmed

L2 (f) Ll(f)Fig. 6. Simplified configuration of the relay lens system of TDOIII. L and L2 replace the function of two spherical mirrors. Thefocal lengths are shown in parentheses. GM1, GM2, galvanomir-rors; F, optical-axis conversion mirror.


'0

+.' IrV .0),':

Galvonomirror

Driver

(General Scanning

GFZZOD)

Controller of

3-D Optomer

(NAC)

X pos. cont.

Y os. cont.

X pos.

I Y pos.!ad Movement

Accommodation

Iris Area

.

. . S

Subject

L I >co >- L

Microcomputer

(NEC PC-9801)

I I

n

zFig. 7. Relay lens system of TDO III (top view): AA', dichroic mirror; B, E, spherical mirrors; C, G, galvanomirrors; I, K, convex lenses; F,optical-axis conversion mirror; L-O, optical-length modulator mirrors; D, H, J, relay mirrors; AR, autorefractometer; Z, z axis.

that these mechanisms perform as expected when theTDO III optical system is used. There is a possibilitythat, by using these mechanisms, we can develop thenext generation of the TDO, which will not requireoptical components to be mounted on the subject'shead.

4. Data Calibration

A. Eye Function Data

The TDO's use a system where all the input rays thatpass through the center of curvature of the sphericalmirror are reflected and pass the same point.However, the galvanomirrors are not located at thecenter of the spherical mirrors but near the centerpoints to prevent reflected measurement light fromthe concave mirror from veiling the signal lightreflected from the retina. This location causes pri-mary image distortion. Relay lenses I and K in Fig. 7are tilted 15 deg to keep the reflected measurementlight from the surfaces of the lenses from influencingthe measurement. This causes secondary image dis-tortion.

As the X-Y tracker uses the distorted image toextract the center of the Purkinje image, the mea-sured angles of the rotated galvanomirrors became asplotted in Fig. 8 for the earlier TDO I. The artificialeyes were mounted on a two-axis rotatable stage.They were rotated 5 deg each for 30 deg horizontallyand 20 deg vertically as shown by the grid in thefigure. They were measured 3 times and averaged.The three artificial eyes measured were -0.31 D (0),-5.14 D (A), and -9.44 D (E). There was a consid-erable amount of cross talk between the two galva-nomirrors.

Figure 9 shows the data measured by TDO III inthe same conditions. Since the optical system wascarefully redesigned, the cross talk has been reducedconsiderably. Figure 10 shows the angles correctedwith a multivariable polynomial correction matrixthat is explained in the appendices of Ref. 4. Theresults were satisfactory for measuring eye position.

Figure 11 shows the difference between the mea-sured accommodation levels by TDO III and thedioptric settings of the three artificial eyes for 35different directions. The diopters are shown fromeach direction, that is, from each crossing point of thegrid. The grid is equal to 5 diopters for accommoda-tion presentation. The ideal data should be locatedon the grid. The measured diopters were all biggerin absolute value and had only a small influence onthe eye direction. So, the correction is much easierthan the one for the angles. The correction wasperformed by the same technique, and the result isshown in Fig. 12.

B. Head-Movement Data

The TDO III system adopts the ISOTRAK for measur-ing head movement. The ISOTRAK utilizes low-

0 0

-a (:

oo

00

U 01Z~~

0

0

0O0

Fig. 8. Uncorrected eye angles of three artificial eyes for 35different eye directions (5Y/division) with TDO I.


AQ A A AO All 0A

a A 'RI A

Q A i ___ i _ _

Fig. 9. Uncorrected eyecondition as in Fig. 8.

angles with TDO III for the same

Fig. 11. Difference between the measured diopters and the diop-ters of three artificial eyes for 35 different eye directions (50/divi-sion for eye direction and 5 D/division on the accommodationdifference on the ordinate).

frequency magnetic technology to determine the posi-tion and the orientation of the head. It requires thatmetals be at least 4 ft (1.2 m) away. However, theaim is to measure the head position and the orienta-tion with which the optical system is mounted.Hence it would be difficult to keep all metals 1.2 maway from the sensor of the ISOTRAK.

Figure 13 shows the measured data of sensorpositions when the sensor is place 20 cm (), 30 cm(A), and 40 cm (0) away from the edge of the TDO IIIcase by maintaining the height of the sensor constant.Each datum was measured when the sensor wasmoved by 5 cm with a 20-cm width and 15-cm depthon a level plane some 15 cm below the source of themagnetic field of the ISOTRAK. The figure showshow the measured data are influenced by the metal inTDO III. It shows that the farther away the sensoris placed from the case, the smaller the influencebecomes. The complicated influence of the metalwas found when the height of the sensor (the levelplane) was altered.

Since the sensor of the ISOTRAK is mounted onthe case that contains the optical parts of TDO III,the orientation of the head is the same as theorientation of the sensor. Therefore the precision of

Fig. 10. Corrected eye angles of three artificial eyes for 35different eye directions with TDO III (50/div).

the orientation of the head and the eye (provided thatthe eye position is fixed) is the same as the ISOTRAKprecision.

On the other hand, the position of sensor s and theposition of the center of the eye position e is ex-pressed as

e = s + T(O)r;

where T(O) is the rotation matrix that depends onorientation 0 and r is the vector from the sensor tothe rotational center of the eye. Then, if no headrotation exists as T(O) = constant, the error in sensorposition (s) is equal to the error in eye position (e).However, if an error exists in the orientation measure-ment (0), the error in the eye position becomes T(80)r.Hence, if the distance between the sensor and the eyebecomes smaller, the error caused by the orientationerror becomes smaller and vice versa. When thisrelation and the influence of metal shown in Fig. 13were taken into account, it was determined that thesensor should be located 30 cm from the TDO III case.

The sensor position was designed to suppress theerror originating from the orientation error andcorrect the remaining error by using the multivari-

Fig. 12. Corrected diopters of three artificial eyes for 35 differentdirections (5 diopters and 5W/division).


(I& J§

i� 13 ill 8

1)I Al

8 13 I! I 0 �

I1)t & 8 f � i f Q

I T 2 I

II

I

I

I

II

Fig. 13. Measured sensor positions when the sensor is located at20 cm (D), 30 cm (A), and 40 cm (0) from TDO III (5 0/div).

able polynomial correction matrix.4 Vector r be-came -658, 275, 167 expressed in millimeters in thiscase. This means that the 1 error of orientationbecomes roughly the same as the 10-mm error in theposition. Although the error seems great at firstimpression, the error becomes < 0.17 D if the accom-modation does not exceed -4 D (not closer than 25 cmto the subject's eye). Therefore it can be judged to beadmissible. The sensor was located on a woodenarm as shown in Fig. 4.

Figure 14 shows the corrected head position whenthe multivariable polynomial correction matrix withsecond degree is used. The precision of the positionfalls to ± 1 mm with the correction if the orientationhas no error.

There are many detailed improvements in TDO IIIcompared with TDO I. They can be summarized asfollows, although some are not discussed in thispaper:

(1) Head movement is allowed.(2) The position and direction angle of the rota-

tion center of the subject's eye are measured by amagnetic sensor.

(3) Measurement accuracy is improved.(4) Noise is reduced.(5) Measurement is stabilized.(6) An efficient alignment method is provided by

an electrically driven chin rest.(7) Improvement in usability is provided by a

systematic design of the system.(8) There is software improvement for carrying

out the analyses.(9) There is an equivalent shift system for the

optical center.

5. Performance Examination with Artificial Eyes

Figure 15 shows the noise levels of TDO III with anartificial eye. Accommodation (Acc.), horizontal(R.X), and vertical (R.Y) eye positions and pupildiameter (Pup.) are shown from top to bottom withappropriate ordinates. The abscissa shows time,

Fig. 14. Corrected sensor positions with a multivariable polyno-mial matrix when the sensor is located 30 cm from TDO III (5cm/div).

and 14.7-s data are shown. In TDO III the firstPurkinje image position was measured by the C3160instead of the C1055 from Hamamatsu PhotonicsSystems Corporation. The C3160 uses digital tech-niques and has better resolution. The galvanomir-rors were changed from G325 to GF220D fromGeneral Scanning Inc. The latter has a smallerjitter. Therefore the noise levels became less thanhalf of that in TDO I, namely, ±0.02 D for accommo-dation, ±0.18° for horizontal eye movement, +0.25°for vertical eye movement, and ±0.11 mm for thepupil diameter.

Figure 16 shows the measured data when theartificial eye was tilted ±20° horizontally and ±150vertically in 5° steps. It shows that the eye positionswere measured precisely, except for a 150 upwardmeasurement in the last. The artificial eye could notbe tilted fully 15° upward, because it collided withpart of the TDO III case. The figure clearly showsthat the accommodation measurement is virtuallyuninfluenced by the eye movement except for the lastpart where the model eye is not moved properly.

-5. 1 No e ei fT D II

01

R.c at--our--l---1--- .. ---- 1....

leg. t-liel l rI 30.

Y .-- _-.-....-- ...........................

mm - i

[ 0 _ _ ITime(sec) - 4.9 -4

Fig. 15. Noise levels of TDO III, which are approximately half ofthose of TDO I: Acc., accommodation; R.X, horizontal eye posi-tion; R.Y, vertical eye position; Pup., pupil diameter.


a-I .1 I P F Ic

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mm1 1. ....... .... ... ..

(-54 14D)

Time(sec) - 31.8 -*Fig. 16. Measured data when an artificial eye (-5.14 D) was tilted±20° horizontally and ± 15° vertically in 50 steps: Acc., accommo-dation; R.X, horizontal eye position; R.Y, vertical eye position;Pup., pupil diameter.

Also, horizontal and vertical eye position measure-ments are satisfactorily decoupled.

The estimated pupil diameter is considerably inerror at near 200 to the right (20° in R.X; the plusangle indicates the right direction from a subject inthe horizontal eye position measurement) and 150downward. Since TDO III is always monitoring theeye from the optical axis, which is always maintainedperpendicular to the cornea, the accuracy of thepupil-diameter measurement depends fully on theaccuracy of the percept scope in principle. However,the monitored image of the eye is somewhat degradedat the edges of the allowed visual field, because themirrors cannot be tilted properly at the extremes ofthe field. Except for the measurement boundariesthe pupil-diameter measurement is judged to besatisfactory with the artificial eyes.

TDO III uses a pure integral controller on the errorbetween the angle of the eye and a galvanomirror.The integrator nullifies the error whenever it exists,thus ensuring that the measurement light is injectedinto the eye perpendicularly and there is no need for acorrection on the pupil diameter in terms of gazedirection.

TDO III also uses another servo control mecha-nism to match the two IR measurement beams on theretina when accommodation is measured. Since theposition measurement of the first Purkinje imagewith the X-Y tracker and the beam position detectorwith the AR-1100 use the center of gravity of opticalimages, the influence of the reflection differencebetween artificial and human eyes is minor. Al-though the human fundus reflects the measurementlight from a distribution at deeper levels of the retina,the nature of this reflection should not change sub-stantially during accommodation. Therefore modeleyes with a two-dimensional diffuse reflector as afundus can be safely used for calibration for real eyes,and the measurement accuracies of the accommoda-tion and the eye movement with the artificial eyes canbe expected to be preserved with the real eyes.

6. Performance Examination with Human Eyes

Data for assessing the TDO III performance withhuman eyes are presented from the following.Three males served as subjects for most experiments.They had a visual acuity of 1.0 or better with correc-tion. Subject GR was 26 years old, emmetropic, andhad an accommodative amplitude of 4.0 D. SubjectLC was 30 years old, slightly hyperopic, and had anamplitude of 4.5 D. Subject CM was 32 years old and-5.5 D myopic, with a 3.25-D amplitude. SubjectCM wore a contact lens that corrected his visualacuity to 1.0. The subjects were trained as observersfor visual experiments generally, but they had noprior experience of the experiment with TDO III.

Two other males who also had visual acuity of 1.0and more with correction served as subjects for thecycloplegic experiment. HN was 32 years old, emme-tropic, and had an accommodative amplitude of 5.0 D.HK was 34 years old, -4.5 D myopic, and with 4.5 Dof accommodative amplitude. They had ample expe-rience of visual experiments with TDO III.

The accommodative amplitudes of the subjectswere calculated from the dynamic accommodativeramp responses by averaging the uppermost andlowermost steady-state portion of the responses andthen subtracting the values (see Fig. 21). Objective-ly measured accommodative amplitude is generallyover 1 D less than the subjectively measured one.Thus the accommodative amplitude of these subjectsare normal, although it might be interpreted to be afew diopters smaller from common knowledge ofsubjective measurements.

A. Accommodation

First we compare the accommodation responses mea-sured with TDO III with those measured with astigmatoscope9 (Fig. 17). In the TDO III measure-ment (solid line) a target was presented by a Badallens system that was attached to TDO III and movedfrom +2 to -10 D at a speed of -0.5 D/s. Wechecked the speed of the target beforehand to be sureit was slow enough to permit the static accommoda-tion to be measured continuously. The responsecurve is the average of five measurements. The datafrom the stigmatoscope were measured 10 times andaveraged. They are plotted when the correspondingtargets are shown for for the TDO III measurement.The abscissa shows the target's diopter for stigmato-scope measurement. Circles represent the averagevalue, and bars represent standard deviations. Sub-ject CM wore a soft contact lens for both experiments.(TDO I could not measure a subject wearing a contactlens, but TDO III can because it has been improvedremarkably in many aspects.)

The response as measured by TDO III is smaller inabsolute value than that found with the stigmato-scope by 0.5 D over the full range. The subject hada greater objective amplitude of accommodation inthe TDO III measurement than in the stigmatoscopicmeasurement. This was probably caused by thedifference in the targets. The target used in the


r r T: ~~~~~~~~~~~~~~~~. ... . :.= :r

Aoce.@ | , , / " SubC11

-4: ------------- - -- ----

,Ta en

-2'--------------_-__F_.___

-0 - f o- ----- --- -- -- -- ---

T ime (sec) 4- 8.0 -

Fig. 17. Solid line, accommodative response when the subject isgazing at a Badal stimulator, as recorded with TDO III. Thestimulus was moved from 2 to -1I0 D with a speed of - 0. 5 D/s; 0represents the accommodation measured with the stigmatoscope,and the bar represents standard deviation. The horizontal axisshows time and the stimuli diopter. The vertical axis shows theresponse diopter. Agreement is excellent.

TDO III measurement was a Maltese cross.'10 It hada wide spatial-frequency spectrum and hence re-mained an accommodative cue even when the subjecthad a blurred image. On the other hand, the targetused in the stigmatoscope had a narrower frequencyspectrum. Although there was a small offset anddifference at both ends of the measurement, it can beseen that the agreement in both measurements waspretty good.

The second study involved checking the accommo-dation in two different ways without moving the eyeexcessively. A target, printed on film and backlitwith a flashlight, was moved by a plotter (HP Color-Pro 7440A) with a precision of 1/300 diopter in theBadal lens stimulator. The target was presented ina totally dark room to eliminate visual cues except formovement of the backlit target. The same targetwas also moved on an optical bench under normallighting. Figure 18 shows an example of responsesrecorded with subject GR when monocularly lookingat two targets. Both sets of targets were sequen-

-5, Rl , S. ...... ........t. bGF

A ..

D ---- - - ---

. .-----.-rzc.- , .

Time(sec) - 12.3 -

Fig. 18. Response of subject GR with monocular vision while he islooking at a real target and Badal stimulator. The vertical scale isin diopters, and the horizontal scale is in seconds. Both responsesshow good agreement.

tially positioned at -5.0, -4.0, -3.0, -2.0, and -1.0D stepwise, and both sets of responses were recorded.All subjects had considerable lags in accommodation,which tended to become less when the targets werepositioned farther from the subjects. The responsewas slightly greater with the real target than with theBadal stimulator. The nearer the target was posi-tioned to the subjects, the greater the differencebecame. Because the real target changes its visualangel as it moves, it presents size as well as vergencecues, and it is natural that the real target inducesmore accommodation. Except for the difference allthe responses were consistent with one another.

B. Eye Movement

Figure 19 shows the eye-movement trace with a10-ms interval for 20 s in which subject HN gazedsequentially at five targets on a cross separated by 10°with a bite board. The targets were located at -3 D(33 cm). Although Maltese cross fixation targetsaided in steady fixation, considerable fixation eyemovement was recorded. A videotaped TV monitorimage of the eye taken by the second CCD camera inTDO III was used to check the fixation eye move-ment, and it was found that movement did exist.Therefore it was difficult to assess the accuracy of theamplitude of the eye movement by TDO III withhuman eyes. On the other hand, the movement ofthe first Purkinje image in the TV recording was toosmall and influenced by eye positions for the ampli-tude accuracy to be confirmed. Although it is almostimpossible to determine real accuracy with livingeyes, the accuracy of the eye movement with TDO IIIcan be said to be at least better than ± 0.50 from thistracing. Also, the figure shows that the smoothpursuit between targets is not straight, as its behav-ior is well known from preceding research."

10.1

0.0

R. Ydeg.

R.X deg1-20 1-10 10 110

Fig. 19. Trace of eye positions while subject NH gazedtargets on a cross separated by 100 with a bite board.

.20

at five


..... ......... .... .... . ....... . .............. . .. .............. . ............... ...............

.. ........... ...

Su b. HN

....... . .. ............

... ........... . .... ......... ...... .. ...... ................ ...-10.0

C. Pupil Diameter

Figure 20 shows the linearity of the pupil-diametermeasurement with the area analyzer. The pupildiameter was changed by a flashlight stimulus. Theeye images, magnified 4x optically, were videotaped,and the pupil diameters were measured with a scaleon a hard copy. Time was superimposed by a micro-computer on the videotape, and the data of the areaanalyzer were compared at the same time. Variouspupil diameters are plotted on the figure, and thelinearity is found to be within ± 0.3 mm.

Figure 21 shows the relationship between theaccommodation and the pupil-diameter responseswhile subject GR is gazing at the target in the Badalstimulator. The target approached the subject from+2 to - 10 D at a speed of - 0.5 D/s in three differentvertical directions (0°, -8°, - 16°). The figure showsthat a slight accommodation was evoked by depress-ing the line of sight, but the near point was notchanged.9 The pupil constricted as the target ap-proached the subject and continued to constrict fur-ther after the accommodation was saturated. Thedecrease in the pupil diameter extended the depth offocus and changed the subjective near points. Thiscould be the origin of Ripple's measurement of theapproach of subjective near points as the gaze direc-tion was lowered.1 2

D. Responses under Cycloplegia

Visual responses were recorded when several drops ofa mydriatic drug (0.50% tropicamide and 0.50% phen-ylephrine hydrochloride) were used on two subjects.The paralysis of the normal accommodation and pupilresponses should make the associated measurementscomparable with those obtained with artificial eyes.Figure 22 shows the accommodative responses ofsubject HN measured with the Dynamic Refractome-ter3 at 5-min intervals for more than 20 min. Thestimulus was moved from 1 to -7 D at -0.1 D/s toascertain the full accommodative amplitude. It wasconfirmed that the accommodative amplitude re-duced to < 0.25 D after 20 min and remained at thislow level for 40 min for the two subjects. Although

5.5

20 /

5 4.5

3.5 a AU.- 3 /R

Pupil Diameter by Videotape Measurement(mm)

Fig. 20. Linearity of the pupil-diameter measurement.

-5. ~~~~~~~I I

D t1.0 Su7.0 00 . - -t

Pup. I -

mm5.0 I-7.0 ' I -80j

Pup.

7.0_ _ __ _ _ 1

Time(sec) 4 7.0 e

Fig. 21. Accommodation and pupil-diameter responses of subjectGR while watching the target in the Badal stimulator that movedfrom 2 to -10 D with a speed of -0.5 D/s. The target moved onthe line of gaze of , -8°, and -16°.

the far point for HN was 0.3 D in natural condi-tions, it approached 0.75 D after the use of the drug.The pupil diameter became 7.6 mm after 15 minand demonstrated a < 0.2-mm change against a flash-light stimulus.

Figure 23 shows the typical dynamic visual re-sponse of subject HN under cycloplegia as he fixatedsuccessively on the same five targets described in Fig.19 without a bite board. The mean accommodationwas 0.72 D, and its standard deviation was 0.10 D.Therefore the maximum accommodative fluctuationwas less than 0.25 D. Although the subject wasinstructed to gaze at the center of the Malteseliketargets, the fixational eye movement remained andwas found to be less than 0.60 for the stationaryparts in this record. The mean pupil diameter was

20s

Fig. 22. Accommodative responses of HN to ramp stimuli from+1 to -7 D with a speed of -0.1 D/s after a mydriatic cycloplegiaat intervals of 5 min for up to 20 min.


-0. CPcc.

D1.0

20. QR. Xdeg.-20.120. R. Y

deg.-20.110. Pup.

mm6.0

V -. A Sub.H1

I -

K~~~~~~~~~fl~~~~~~~I-- lv-xri L J_._. __-, __ _ _' _

________ _ _ L _ ___T i me (sec) -- 30. 0

Fig. 23. Visual responses of HN under cycloplegia while hewatched five targets on a cross located -3 D (33 cm) from him. Hedirected his eyesight at C (center) - down -> C -> up -> C -> left --

C - right ->C.

Fig. 24. Example of the measured data of head movement. Thelengths of the axes are 10 cm.

7.6 mm, and its standard deviation was 0.10 mm.The fluctuation in the pupil diameter was also con-firmed to be less than ± 0.3 mm. The change in pupiland accommodative responses at 60 s from thebeginning seems to be rather large. However, it wasprobably influenced by a slow blink indicated in thepupil response. Although the accommodation andeye movement appear to be synchronized in severalparts of the record, the correlations between accom-modation and horizontal or vertical eye movementswere found to be -0.14 and 0.39, respectively.Therefeore such synchronization is not confirmed,and microfluctuations of accommodation, eye move-ment, and pupil diameter can be judged to be notmere noise but mainly intrinsic responses of humaneyes. Although the accuracies of the respective re-sponses might in fact be better, they were assumed toequal the values derived from Figs. 19 and 23 (±0.25D, 0.5, +0.3 mm; the slight influence of the biteboard is shown in the figures) to be on the safe side.

Besides the above data, several other related datawere reported in Refs. 5 and 9 with the TDO; i.e., (1)small but definite accommodation was induced bydownward gaze, but no accommodation change wasfound with a horizontal gaze shift, (2) the subjectsshowed 0.7-D accommodation on average with theapparent distant stimulus in paintings, (3) they accom-modated in a similar way to the apparent depthsensation induced by moving random dots on a CRT,and (4) they showed accommodation even when theyperceived different depth sensations without movingtheir eyes. All these data lead us to conclude thatTDO III measures accommodation properly, at leastin its relative volume, while the eye is moving towatch real objects; eye-movement and pupil-diametermeasurements are also reliable, at least within thespecified values listed above.

E. Head Movement

Figure 24 depicts head movement measured by theISOTRAK in a three-dimensional representation.

Subject HK moved his head freely while performingVDT work. His head was monitored with a TVcamera suspended from the ceiling. Two-dimension-al data were compared with the X, Y data of theISOTRAK and were confirmed to be in good agree-ment. The accuracy in eye-location measurementwas confirmed to be within ± 10 mm. Hence therelationship between the eye responses and headmovements can be analyzed with the TDO III system.One immediate application would be to analyze re-sponses while a person drives a car simulator.

7. Discussions and Conclusions

The absolute measurement of accommodation is ex-tremely difficult and seems to be impossible in princi-ple from current knowledge, although there has beenlittle discussion on this issue. The existence ofaccommodation lag has been admitted widely,13 butits characteristics and real causes are not well known.Objective measurements with refractometersl 4 5 orretinoscopes8 have shown that the accommodationlag is at a minimum in the vicinity of the far point andincreases as the target approaches the subject. Onthe other hand, subjective measurements with laseroptometers or the stigmatoscope have shown that it isat a minimum in the vicinity of the dark focus orintermediate resting point. 6"17 Figure 17 clearlyshows the general trend of the two different methods.The accommodation response started at 5 s with anaccommodation lag of 0.5 D and increased its lagwith the TDO III measurement, while the accommo-dation response with the stigmatoscope measure-ment seemed to appear a bit earlier. The intermedi-ate resting position is -0.4 D from this recording.This trend coincides well with those reported inearlier studies. Since there is no established methodfor assessing the absolute value of accommodation,we cannot say which data are more reliable. Howev-er, the agreement in relative value in both measure-ments demonstrates the reliability of the dynamicmeasurement of accommodation with TDO III.


A._,_.__. __,,, A_

The model eyes have a two-dimensional diffusereflector as a fundus, while the human fundus reflectsspecularly at one depth and diffusely in a distributionof deeper levels. But the state of reflection shouldnot be changed substantially by accommodation.The possible minor influence should appear symmet-rically even if the reflected measurement light mightbe changed in size, brightness, and/or scatter by theaccommodation, because the measurement light isalways injected into the eyes perpendicularly. If thisassumption holds, the difference in the measuredaccommodation responses between artificial eyes andhuman eyes should be constant. Judging from thesetheoretical considerations, the relative value of theaccommodative measurement with TDO III can besaid to be fairly reliable.

The main problem in accommodation measure-ment is obtaining an absolute value or an originsetting. That is, the gain in the accommodativemeasurement can be predicted by optical calculationand calibrated with artificial eyes, but the originneeds to be determined by subjective judgment, evenwith the AR-1100 measurement. NIDEC gathereddata on over 1000 eyes with different refractivepowers to determine the origin, and for years thismachine has been used in selecting corrective lenses.We have also checked the accuracy with many hun-dreds of eyes and have found the function to besatisfactory. Therefore we think that the origin ofthe AR-1100 is currently set properly. Except forthis origin uncertainty the relative accommodativevalue of TDO III is excellent, as shown in theexamples in Figs. 16-18, 21, and 22.

The Campbell optometer13 had a relatively narrowlinear range. However, the AR-1100 has a widerange of linearity, because it uses a servo controlmechanism to match the two measurement beams onthe retina. It does not saturate in principle. Therange of movement of the optical parts is the onlylimitation on the measurement range, and this is oneadvantage of the servo control method.

As for eye-movement measurement, TDO III lacksprecision and speed in measuring saccadic eye move-ment, because it uses a TV monitor to detect eyemovement; i.e., the precision is ± 0.50 and the speed is6.4 Hz.4 However, we have developed a specialdevice to overcome this problem by using an imageintensifier and Position Sensitive Detector18 thatattained a precision of ±0.1250 and a speed of 30 Hz.We also expect that high-definition TV cameras willincrease the precision and the speed in the nearfuture.

The principle of TDO III, which always maintainsits optical axis perpendicular to the cornea, elimi-nates influence from the difference in the cornealcurvature of individuals when it measures eye posi-tion, an inevitable problem with other methods.Hence TDO III may be able to measure eye movementmore precisely than other methods. However, cur-rently the accuracy is 0.5°, judging from the TV

resolution and the experimental data in Figs. 15, 16,19, and 23.

The measurement of the pupil diameter is an easytask in principle with TDO III. Because the TVcamera can always acquire a front image of the eyes,no correction is necessary for gaze direction. Howev-er, there are two intrinsic problems with this measure-ment. Since we use an illuminated pupil imagegenerated by the reflection from measuring and/oraligning IR light, the contrast in the image is not asgood as in other common methods that use imagesilluminated by ample IR light from exterior sources.The other reason is that the pupil image is oftencontaminated by an eyelash and/or an eyelid. There-fore the acquired TV image is not so clear, leading tothe rather high noise levels shown in Figs. 16 and 21.Hence the lighting system or sensitivity of the TVcamera should be improved in the near future.

Head movement can be measured satisfactorily in afixed laboratory experiment. However, since thismeasurement uses a magnetic field, it is ratherdifficult to perform in the field, so we are nowdeveloping another optical measurement method withhigher precision.

The measurement speeds were determined fromcutoff frequencies for sinusoidal inputs for accommo-dation and eye movement.4 The final characteristicsof TDO III are summarized in Table 1.

We are now improving TDO III so that (1) it canmeasure vergence, (2) its size will be further reduced,and (3) it can perform measurements without ameasurement unit being mounted on a head. TDOIII can measure the three major ocular functions andhead movement in virtually the same working situa-tions as VDT. It also provides a way of studying the

Table 1. Final Characteristics of TDO lil

Subject of NumericalParameter Measurement Value

Range Accommodation -12.7 to +26.6 DEye movement

Horizontal -20°Vertical -25° to 50

Pupil diameter 0-100%Eye location +200

Speed Accommodation 4.7 HzEye movement 6.4 HzPupil diameter 6.4 HzEye location 50.0 Hz

Resolution Accommodation ±0.02 DEye movement

Horizontal ±0.18°Vertical ±0.25°

Pupil diameter ±0.11 mmEye location ± 1 mm, ± 1 deg

Accuracy Accommodation ±0.25 DEye movement ±0.5°Pupil diameter ±0.3 mmEye location ±10 mm, ±1 deg


cooperative function of ocular and head movement inpsychology. One possible future application is thestudy of human visual characteristics during thecontrol of vehicles such as airplanes and automobiles.TDO III was actually used in a safety study ofHead-Up Display by an automobile company. Anoth-er application would be in the study of humanstereoscopic perception for the development of three-dimensional TV suitable for human viewing.

References1. W. D. O'Neill and L. Stark, "Triple-function ocular monitor,"

J. Opt. Soc. Am. 58, 570-573 (1968).2. H. D. Crane and C. M. Steele, "Generation-V dual-Purkinje-

image eyetracker," Appl. Opt. 24, 527-537 (1985).3. T. Takeda, Y. Fukui, and T. Iida, "An objective measurement

apparatus for accommodation ability change caused by VDTwork," J. Ophthalmol. Opt. Soc. Jpn. 6, 59-66 (1985).

4. T. Takeda, Y. Fukui, and T. Iida, "Three-dimensional optome-ter," Appl. Opt. 27, 2595-2602 (1988).

5. T. Takeda, T. Iida, and Y. Fukui, "Dynamic eye accommoda-tion evoked by apparent distances," Optom. Vision Sci. 67,450-455 (1990).

6. H. D. Crane and M. R. Clark, "Three-dimensional visualstimulus deflector," Appl. Opt. 17, 706-714 (1978).

7. Y. Fukui, T. Takeda, and T. Iida, "Systematic generationmethod of relay optical systems," Appl. Opt. 29, 1947-1951(1990).

8. P. B. Kruger, "Infrared recording retinoscope for monitoringaccommodation," Am. J. Optom. Physiol. Opt. 56, 116-123(1979).

9. T. Takeda, C. Neveu, and L. Stark, "Accommodation ondownward gaze," Optom. Vision Sci. 69, 556-561 (1992).

10. P. B. Kruger and J. Pola, "Stimuli for accommodation:blur, chromatic aberration and size," Vision Res. 26, 957-971(1986).

11. H. Miyai, T. Kasai, and S. Tsuji, "Mechanisms of foveation inasymmetric vergence eye movements," Jpn. J. Med. Electron.Biol. Eng. 18, 413-419 (1980).

12. P. H. Ripple, "Variation of accommodation in vertical directionof gaze," Am. J. Ophthalmol. 35, 1630-1634 (1952).

13. F. W. Campbell and J. G. Robson, "High-speed infraredoptometer," J. Opt. Soc. Am. 49, 268-272 (1959).

14. J. Tucker and W. N. Charman, "Reaction and response timesfor accommodation," Am. J. Optom. Physiol. Opt. 56,490-503(1979).

15. K. Ukai, M. Ishii, and S. Ishikawa, "A quasi-static study ofaccommodation in amblyopia," Ophthalmol. Physiol. Optom.6, 287-295 (1986).

16. H. W. Leibowitz and D. A. Owens, "Night myopia and theintermediate dark focus of accommodation," J. Opt. Soc. Am.65, 1121-1128 (1975).

17. W. N. Charman and J. Tucker, "Accommodation as a functionof object form," Am. J. Optom. Physiol. Opt. 55, 84-92 (1978).

18. K. Hashimoto, T. Takeda, Y. Fukui, and T. ida, "Properties ofhighly sensitive position detector (PSD-II)," J. Ophthalmol.Opt. Jpn. 12, 52-58 (1991) (in Japanese).


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Three-dimensional optometer III