blur: a sufficient accommodative stimulus

Documenta Ophthahnologica 43,1 : 65-89, 1977

BLUR: A SUFFICIENT ACCOMMODATIVE STIMULUS*

STEPHEN PHILLIPS & LAWRENCE STARK (Berkeley, CoL, USA)

ABSTRACT

Experiments under a variety of open and closed loop feedback configurations demonstrate that accommodative responses to target blur are equivalent to those to defocus blur; this supports blur as the 'sufficient' neurological stimulus to accommo- dations. The hunting action of accommodation compensates for the even error aspect of blur and also adaptively minimizes any close loop error components while finally accepting open loop components.

INTRODUCTION

Blur is usually not presumed to be the sole stimulus to the human eye focusing sytem since retinal blur alone presents several interesting intrinsic problems which, at first glance, make it less than an ideal accommodative stimulus. Its first basic deficiency is that the direction of the correct focusing response direction cannot be instantly asserted from the blurriness of the retinal image since nonabberrant blur is an even-error signal containing only amplitude information. Its second deficiency is that 'target blur' produced by blurring an object by projecting its out-of-focus image on to a screen apparently does not evoke an accommodative response although its retinal image is equivalent to the 'defocus blur' caused by direct light- vergence defocus. The accommodative response should thus also have these two defects if blur is the accommodative stimulus, but experimental evidence did not at first provide this support and as a result blur alone has traditionally been thought to be insufficient as a focus stimulus; other focus stimuli clues have consequently been suggested as substitues for, or necessary accompaniments of blur in order to drive and control the state of accommodation (Fincham, 1937, 1951; Allen, 1954; Campbell, 1954; Campbell & Westheimer, 1960; Crane, 1966; Morgan, 1968; Davson, 1972; Toates, 1972). The even-error deficit, however, has been found to be

reflected in the human accommodative response (Stark & Takahashi, 1965; Troelstra et al., 1964a; and Shirachi, 1974) although some controversy still exists (Cornsweet & Crane, 1973).

* We acknowledge partial support from NIH Training Grants in Bioengineering and in Physiological Optics, and the helpful discussion with our colleagues, Prof. V.V. Igxishnan and Dr. Douglas Shixachi.

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This paper now introduces direct experimental evidence that the accommodat ion system resl:onds to either defocus blur, target blur or to both stimuli together. By implementing a variety of experimental techniques in- volving the feedback configuration of the accommodat ion sytem, the specific target condition can be controlled by the direct measurement of the accommodative response. As a consequence, accommodation can be stimulated with either open or closed loop stimuli. It will be shown that given the appropriate feedback conditions

The experiments to be described below, which include repeating and ex- panding Fincham's (1951) target blur experiments, are not designed to show that blur is the sole stimulus to accommodation making it a necessary stimulus condition, for i t is well documented that many other sorts of sensory information such as binocular disparity, perceived proximity, angular size, chromatic and spherical aberrations in addition to purely volitional effects can influence the state of accommodation (Fincham, 1951; Allen, 1954; Heath, 1956; Marg, 1957; Alpern, 1958; Campbell & Westheimer, 1959; Troelstra et al., 1964b; Stark & Takahashi, 1965; Randle, 1970; Cornsweet & Crane, 1973). Tangentially, additional observa- tions made here on response to target blur support studies producing evidence that the accommodation response has even error characteristics.

A further aim of this investigation is to at tempt to understand better the mechanism by which a retinal blur is transformed into a meaningful error signal with which the accommodative neural controller can operate to produce both a response movement and a sustained refractive state. It should be noted that the term, blur, is meant to include the various derivatives of blur (Fujli, Kondo & Kasai, 1969), as well as blur amplitude itself.

METHOD

In order to investigate the sufficiency of blur, it must be considered whether or not it is possible to drive the accommodative system with blur and be totally assured that all other visual information has been eliminated that might otherwise act as a focusing stimulus. There exist various optical configurations that can produce upon the retina relatively clean non-aberrant defocus blurs; unfortunately, it is generally difficult to prove that the blurred retinal image thus produced does not contain second order aberrant effects. This problem is compounded by the fact that the optical reference points of the eye are arduous to locate exactly and also move as a function of the state of focus.

On the other hand, creating a blurred retinal image by simply viewing a blurred picture, one devoid of sharp contours, eliminates the above dilemma

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since it is created without changing the light-vergence received by the eye. The retinal image thus contains no distance information or other focusing clues besides blur itself.

A convenient way of producing a blurred picture is by projecting an out-of-focus image on to a screen as was done by Fincham (1951) and Smithline (1974); in this way the amount of target blur can be readily controlled by driving the focusing motor of the projector lens or alternately modulating the target to projector lens distance. Also possible is modulat ion of the focus control of an oscilloscope which although simple to implement limits one to the characteristics of the scope screen and further limits one to pictures that are easily generated.

Since the subject's state of accommodation can be measured continuously with a slit-lamp optometer (O'Neill & Stark, 1968; Philips, Shirachi & Stark, 1972), this signal can be used to drive the projector focus and hence the amount of target blur seen by the subject. In this way it is possible to create a closed-loop feedback condition of accommodative control with respect to target blur which in normal vision is 'open looped. ' Furthermore, this new target blur feedback loop can replace the normal defocus blur closed-loop feedback signal, if desired, by opening this latter feedback loop. The following description of the experimental equipment will help to clarify these various feedback configurations.

A schematic drawing of the apparatus used in these experiments is shown in Figure 1. The apparatus consists of basically two parts, the ocular stimulator and the slit-lamp optometer with its associated electronics by which the accommodative response was measured. The ocular st imulator can produce two types of blur stimuli; moving servo-cart one changes the optical distance from the eye to the target seen on the projection screen and thus provides a light vergence or defocus blur stimulus. Alternatively moving the servo-cart two changes the optical distance from the projector to the target screen and thus controls target blur.

In normal vision target blur is open looped, as already noted, since it cannot be affected by accommodating; providing a negative feedback loop from the slit-lamp optometer output to the projector focus servo-cart two so that by accommodating in a particular specified direction the target blur can be reduced closes this loop. Of course, there could be conflict if by accommodating to clear the target blur, defocus blur were then increased, it being still in a closed loop condition. To avoid this situation, defocus blur can be open looped so that the target on the projection screen will always be optically focused upon the retina independent of the level of accommodation. There were two ways in which this defocus open loop was implemented in these experiments.

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PROJE~TOR SERVO - - -

V AP! v ~ . . . . . . . . ~' ~ = ' . ~ f ~ ' I

AMP2 SWI CL PM

A . OL GENERATOR RESPONSE

' -- t t STRIP A M R a 0 OR

Fig. 1. Schematic of equipment used to stimulate and measure the accommodative response. The response is monitored dynamically with an infrared slit lamp optometer while the stimulator can introduce either defocus blu.r created by changing the optical distance to the projection screen or target blur produced by imaging varying out of focus targets onto the screen.

The target is projected onto the screen via lens L4 and mirror M5 with its state of focus controlled by the position of servo cart two. Lens L2 produces an image of the screen at a position somewhere between mixrors M4 and M1; its location controlled by the servo cart one. The subject Wiews: this latter image through the badal lens L1.

LI: +10 diopter badal lens; L2:+10 diopter imaging lens; L3: spherical and cylin- drical co~ective lens as required by subject; L4: projector focus lens; M1, M2, M3, M4, M5: front surfaced mirrors; DI: diffusing screens; F1 and F2: infrared filters; F3: monochromatic filters, as required; AP: artificial pupil; SL: slit lamp; SM: slit lamp microscope optometer; PM: photomultiplier tube of optometeL

The simplest method consisted of inserting a very small artificial pupil (AP in Figure 1) positioned in an optical congruent plane to the natural pupil of the eye. This small aperture provided a depth of focus of at least 10 diopters which was always greater than the accommodative range of the subjects used (Kasai et al., 1970; Oshirna, 1958; Ogle & Schwartz, 1959; Westheimer, 1953). This depth of focus effectively eliminated the normal negative feedback caused by defocus. Very small apertures were avoided to minimize

diffraction aberration. The second method of opening the negative feedback of defocus blur

consisted of providing positive position feedback to servo-cart one which would effectively cancel the normal negative optical feedback of the eye's refractive error. Physically this meant continuously measuring the state of accommodation by the automatic optometer and feeding its output to the

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motor of servo-cart one which would then adjust the optical distance of the real image of the target by exactly the same amount as the subject accommodated; thus a subject accommodating from 2 to 4 diopters would result in the servo simultaneously changing the target image distance from 2 to 4 diopters and consequently maintaining a focused target (or for that matter any constant amplitude of defocus blur desired) on the retina independent of the level of accommodation.

The third more conventional way of opening this negative feedback loop of accommodative defocus is by a cycloplegic. This procedure has the dis- advantage that it makes the accommodative response unobservable except by recourse to surgical implantment of micro-electrodes into the ciliary ganglion; this third method was not used in these human experiments.

OCULAR STIMULATOR DETAILS

The defocus part of the stimulator is a modified Badal optometer similar to one described by Crane et al. (1970). The entrance pupil of the observer's eye is placed at the focal point of the +10 diopter badal lens (L1 in Fig. 1) (Badal, 1876; Ogle, 1961). The image of the target as seen through this lens does not change angular size (neglecting second order effects) as a function of the optical distance between the eye and target image. In addition the target illuminance as it enters the eye does not change with target distance; a true Maxwellian view also provides constant retinal illuminance of the target whenever the artificial pupil is made smaller than the natural pupil. The contralateral eye was always occluded.

The optical distance between the projector screen and the eye is changed by moving the mirrors M2 and M3 with respect to mirrors M1 and M4 by a fast servo system. This procedure turns out to be simpler than trying to physicaUy move the projection screen which would also involve moving the whole projection system, a relatively large mass of equipment. The target is projected onto the front surface screen by mirrors M5 and lens L4. The distance between lens L4 and the target mount on the servo-cart determines the amount of target blur imaged onto the screen and subsequently seen by the subject. A front surfaced projection screen was chosen after it was found that rear projection screens have the undesirable feature of passing some of the fight vergence of the projector 's optics in addition to creating fight vergence originating from the screen surface.

The target, as observed by the subject, could be maintained at a constant level of il lumination if the diameter of the artificial pupil was changed by appropriate compensating adjustment of the fight intensity output of the projector lamp. Music through stereo headphones effectively masked ex-

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ternal sounds that might otherwise act as a focus clue and in addition tended to reduce the effects of boredom and fatigue during the experiments.

RESULTS

The following sections present the monocular accommodative response behavior to all four of the various open and closed loop target blur and defocus blur combinations.

Closed loop defocus blur and open loop target blur

In normal vision a person has no control over target blur (target quality) but can control defocus blur or refractive error by accommodating, assuming he is still young enough to enjoy this capacity. Thus target blur is open looped while defocus blur is closed looped.

Figure 2 shows the normal accommodative response to four diopter step

changes of target distance - a defocus blur stimulus; it is this type of response typically reported in the literature on accommodation when viewing a sharply defined target. The best responses occur following a stimulus containing no target blur. Reducing the target quality either by

introducing a constant amount of target blur or by reducing the visual acuity of the subject results in a diminished focus response (Heath, 1956). In the extreme case of an empty visual field no accommodative movement occurs to changes in light vergence (Heath, 1962; Whiteside, 1953, 1959; Mellerio, 1965).

Alternately maintaining the target at the same distance and introducing step changes in target blur with the projector apparatus results in the behavior depicted in Figure 3. The introduction of four diopters of target blur is indicated by the wide bands. This recording definitely demonstrates that rapid changes of target blur alone effects the monocular accommodative system; as changes in focus produces defocus blur, the accommodative response generally quickly settles back to its original level determined by the actual target distance. This occurs after initial responses in either direction and lasting up to several seconds in many cases.

The modified Badal stimulator was carefully aligned with respect to the subject's eye so that the defocus blur stimuli was relatively clear of additional visual clues or aberrations. The subjective appearance of defocus blur was consequently quite similar to that of target blur; it was for this reason that the subjects were not able to instantly distinguish that the target blur changes were not in fact defocus blur errors and so accommodated to attempt to refocus the target. If the target blur were maintained for a period

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.

ACCR 3 - (diopter) -

I - O -

A C CST 5 -

DEFOCUS I - BLUR

(diopter)

. r "~ r , " - v" ~, f "/ i

i

; : i

I i = l _ ~ m ~i, ' - ,e 'n./ . . . . .

[ i I t I j I I I f I I 1 . 4 ~ ' I! ! ! ! t i I I I I j t ~

I 0 I0 2 0

T I M E (se c.) Fig. 2. Normal accommodative responses to closed loop defocus blur stimuli. The target was randomly moved between 1 and 5 diopters while the target itsetf was maintained sharp.

, : i z �84 : ~ ; ! i . . . . I �84 A C C R 4 - - . , , i , i ; ; i , i ~

T A R G E T

B L U R

( 4 d i o p t e r s

0 I0 2 0 3 0 4 0 ( - ~ - = T A R G E T B L U R R E D ) T I M E ( s e c , )

Fig. 3. Effect of repeated open loop target blur changes on the accommodative response. Defocus blur was closed looped. The target was kept at 1.5 diopters refractive distance while it was periodically blurred the equivalent of 4 diopters.

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of time or if steps of target blur were periodically repeated, the subject would learn or adapt using the normal defocus blur feedback that he was unable to reduce the blur caused by the changes of open loop target blur and subsequently reduced his response to these blur changes. Being able to see additional visual clues such as the edges of the projection screen, knowl- iedge of the actual screen distance by removal of the intervening lens and mirrors along with corresponding size and illuminance changes resulted in substantially reducing the accommodative response to target blur almost from the start of the experiment.

A sample recording of this lat ter condition is given in Figure 4. For this recording the target blur stimulus was produced by projecting a picture onto a large projection screen (one meter by one meter size) placed two meters from the subject. The picture was blurred by rapidly moving the projector lens focus. It is felt that this situation closely represents Fincham's 1951 target blur experiment where there existed readily available distance sensory

DE FOCUS 0.5 .. . . . [ BLUR 3 -- - - !

(diopter)-

TARGET 4 - ~ - - BLUR [

(d iopter ) 0 - ~

0

(d iopter ) 2 3

I " I ' I ........ I I

0 I0 20 30 40

TIME (sec.)

Fig. 4. The response of accommodation to blurring of a projected picture. The subject directly viewed the large projection screen placed 2 meters away with no intervening optics; a host of monocular perceptual distance clues relating to the projection screen position were available to the subject. A reference 2.5 diopter closed loop defocus stimulus was initially given by inserting a +2.5 diopter lens followed by presentations of 2.5 diopters of open loop target blur produced by defocusing the projector lens.

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ACC R

(diopter)

BI S'

(dlo

0 I0 20 30 40 50 6 0 (-,m.. TARGET BLURRED) T I M E ($ec.) ( p=TARGET POSITION)

Fig. 5. Behavior of accommodation to open loop target blur randomly mixed with closed loop defocus blur stimuli. Four diopters of target blur was used. The subject's accommodation system was easily fooled by target blur since its appearance was essen- tiaUy identical to the defocus blur stimulus. Responses can be observed to occur to both the introduction as well as the removal of the target blur.

clues, not including disparity, however, (since all experiments reported in that paper were monocular) with which target blur could be distinguished from defocus blur.

Figure 4 demonstrates that rapid exertions up to one diopter of accommodation still do occur occasionally in response to blurring of the target; Fincham's conclusions in not reporting any accommodative movement are understandable since these rapid movements would not be detect- able using his static monitoring technique. These responses would un- doubtedly be reduced further if both eyes viewed the target by providing the stabilizing influence of the synkinestic signal from (disparity) vergence- accommodation~ On the other hand, Figure 5 graphically shows that large

and substantial accommodative responses continue to occur to rapid changes in the magnitude of target blur in apparent attempt to refocus the target if other visual distance clues are first eliminated from defocus blur and if in addition target blur is randomly mixed with presentations of

defocus blur. As before, the negative feedback of the closed looped defocus blur normally bring the response back, particularly whenever the target blur is reduced to zero. A very interesting aspect of these recordings is that a focusing effect can be seen to occur to both the introduction as well as the removal of target blur. This observation signifies that the accommodation system is particularly sensitive to any temporal changes of retinal blur in addition to its magnitude.

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Open loop defocus blur and open loop target blur

The above experiments can be repeated, this time eliminating the normal closed loop feedback to defocus blur creating the condition of open loop defocus blur and open loop target blur. In this configuration the subject receives a clear, sharp image of the target on his retina independent of his level of accommodation, if initially target blur and defocus blur are set to zero; in addition any arbitrary constant amounts of defocus blur and target blur may be introduced over which the subject's accommodation has no

control. Figure 6 shows a typical response of accommodation to the introduction

of target blur when both it and defocus blur are open looped. The responses are larger than in Figure 3 where the restraint of negative feedback of defocus blur prevented these larger excursions. Similar recordings can be obtained if changes of defocus blur are introduced instead of target blur. It

appears that any time blur is rapidly increased or decreased it evokes an accommodative response; this response may fluctuate in either or both refractive directions. If the amount of blur (including no blur) is maintained for a period of time, the state of accommodation drifts to about one diopter, ignoring noise and small fluctuations. This phenomenon is described as open loop myopia and is discussed by Phillips (1974).

4

A C C R 3 - (diopter) 2 -

I - O -

TARGET BLUR

(4 d i o p t e r s )

0 I0 EO 3 0

T I M E (sec . )

Fig. 6. Accommodation responding to changes of open loop target blur while defocus blur was also open looped using a small artificial pupil. Accommodation stayed at approximately the open loop myopic position (in this recording about 1-1/2 diopters) but as can be seen does respond considerably to the rapid target blur changes.

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Open loop defocus blur and closed loop target blur

It has not been shown, so far however, that target blur (without, of course, any of the variety of distance clues often associated with defocus blur) can in fact control the level of accommodation in a similar manner as does normal closed looped defocus blur. To demonstrate this capability, target blur must be in a closed loop configuration; a negative feedback to the target blur must be provided. This is accomplished by having the electrical output of the slit-lamp optometer driving the projector focusing servo cart two such that the subject's crystalline lens movement controls the amount of target blur in exactly the same sort of way defocus blur is modified by lens movement or accommodation in normal vision. An alternate way of describing this feedback configuration is to say that by accommodating in one direction the subject is rewarded by seeing less target blur but sees more blur if he starts accommodating in the other direction.

Defocus blur must be open looped so that there would be no defocus

error to also stimulate and control accommodation. In this first set of experiments defocus blur was open looped by increasing the depth of focus using the small artificial pupil as previously described. Various gains and biases in the feedback amplifiers were adjusted dependent upon the initial of precalibration of the optometer at the start of each experimental run and rechecked with a post-calibration.

Figure 7 shows an example of accommodation driven by closed loop target blur. The bottom trace indicates the level of accommodation demanded that would produce zero target blur - the clear image position. This level could be arbitrary set by the experiment and in this particular case was alternately switched back and forth between one and five diopters. The direction of movement of the projector servo-cart two from the point of optimal focus could also be arbitrarily changed during a run and would thus eliminate the possibility of the subject detecting minute asymmetric aberrations of other clues of the projection system producing the target blur and relating these to an accommodative response direction.

In the one diopter position, the subject would see a sharp target if focused for one diopter. The target would become progressively blurred the further the subject accommodated from one diopter. At the times shown in Figure 7 this clear image position was electronically switched so that the subject had to accommodate to 5 diopters to again see a sharp target; remaining at one diopter would result in seeing four diopters of target blur. The middle tracing of Figure 7 shows the accommodative response itself. The upper tracing is the amount of target blur or error seen at any instant

by the subject; it is equal to the difference of the lower (stimulus) and

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TARGET BLUR

(diopter)

2 . L J , I i I I I I :15%', O ~ 1 1 I I . |L,I

,2111 1 1 11 _ LLI II

l i l l t I I ta l l , , , : i i I f i / I ~ f - T " T S . ~

,=, ',= ,,il, :,f I = 1 IL, t[ i I 1 H4(-P ~ - ~ I I t r l t LLt lrl t l / l ~ f I -L~ - - t -4 -~

ACC R

(diopter)

CLEAR IMAGE

P O S I T I O t

(diopter)

0 I0 20 30 40 T I M E (sec.)

Fig. 7. The accommodative mechanism driven by artificially closed loop target blur. Defocus blur has been open looped with small artificial pupil. The accommodative position required to clear up the target blur is given in the lower tracing. The magnitude of the blur, or blur error, seen by the subject is given in the top tracing while the actual accommodative response is in the center,

middle (response) recordings. In this particular experimental situation there were no directional clues contained within the retinal image. The direction of the accommodative response required to clear up the target blur was total ly arbitrary and randomized and, in addition, independent of the quality or minute aberrations of the target blur since the movement direction of the projector servo-cart two away from the point of focus could be externally determined electronically as desired by the experimenter. The even error nature of accommodation in reacting to pure blur is very apparent in records taken during these experiments. The accommodative system had to continuously hunt to find the correct response direction. It was observed that, as expected, incorrect initial response directions were made one-half of the time; this result was not subject dependent as was the case in previously reported experiments (Campbell & Westheimer, 1959; Stark & Takahashi, 1965; Troelstra et al., 1964a; Shirachi, 1974). A higher- speed recording of accommodat ion responding to dosed loop target blur is indicated in Figure 8.

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TAR GET BLUR

(dlopfer)

ACC R (d iopter )

C L E A R IMAGE

POSITION (d iopter )

0 I 2 3 4 5 6 7 T I M E (sec.)

Fig. 8. Accommodation stimulated by closed looped target blur, as in previous figure, but with faster time scale. These sample records show that the accommodation control system can be stimulated by blur and that no additional sensory information is required.

The alternate method of opening the loop on defocus blur was by adding positive feedback so that the target distance was always maintained equal to the clear vision distance of the eye. Figure 9 represents this experimental situation with accommodation driven by closed loop target blur. It can be stated that the behavior of the accommodation mechanism in its desire to minimize the magnitude of retinal blur is independent of the actual method used to open loop on defocus blur. An interesting feature of Figure 9 is the gross even error response at the 16 second mark. Very common in these

closed loop target blur experiments was confusion as to the correct direction of focus. The correct direction of focus often necessitated a series of hunting excursions punctuated with several intervening 'retina refreshing' blinks before establishing the correct focus again.

The recorded results of this section demonstrate that blur alone can, in a

negative feedback condition, be a sufficient stimulus condition for control of accommodation.

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T A R G E T 0 - BLUR 2"

( d i o p t e r ) 4 -~

6 - 6 - -

( d i o p t e r ) 3 - -

2 - - I - - O - -

C L E A R 5 -

I M A G E

P O S I T I O N

( d i o p t e r ) I -

! i i i i i

l ' l k - . § . . . . . . .

i ;

. . . . I . . . . I . . . . ,I . . . . I " ' ' 1 ' ' ' ' 0 5 I 0 15 2 0 2 5

T I M E (se c.) Fig. 9. Accommodation driven by closed loop target blur similar to the two previous figures except in this case defocus blur was open looped using a positive feedback technique. Oscillations (hunting movements) at the end of this recording are due to the even error nature of the target blur. In addition, the system occasionally became marginally stable due to the artifacts in the positive feedback signal caused by blinks similar to the one at the 17 second mark.

Closed loop de focus and closed loop target blur

The last combination of feedback conditions to be reported is with both

types of blur producing mechanism, target and defocus, in negative feedback loops so that the accommodative response controls the magnitude of

both simultaneously. Coupling target blur and defocus blur so that each

becomes zero at the same level of accommodation gives, of course, the best

focus responses since a sharp image may be obtained. The recordings of

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Figure 10 were produced in this manner. The gain of target blur with respect to an accommodative movement was adjusted to equal that of defocus blur with a pupil diameter of 3 mm; the recordings in Figure 10 were from a subject who maintained this mean pupil diameter during these experiments. The total amount of retinal blur caused by the superposition of both target blur and defocus blur was therefore almost exactly the same as having only defocus blur but with a higher gain equivalent to a 6 mm

pupil; the only difference being caused by the slight difference in depth of focus of the 3 mm pupil versus that of the target blur-projector optical system. Hence, it is reasonable that the responses shown in Figure 10 were found to be quite similar to the normal focus responses of Figure 2.

OPEN LOOP MYOPIC DRIFT

Of particular interest was whether accommodation following a closed loop target blur stimulus would exhibit open loop myopic drift behavior to the one diopter accommodative rest position if its artificial negative feedback were suddenly eliminated as happens whenever normal defocus stimulated

TARGET O - BLUR T 2- (diopterS_ DEFOCUS BLURT2-

O h

ACCR I--~ (d iopter;)~

I[ I--I I

II I

I .... I' ' ''I .... I'' ''I''''I' ' ''I

0 I0 20 50

TIME (see.) Fig. 10. Accommodation driven by both closed loop defocus blur and dosed loop target blur together. In this situation the accommodative response simultaneously reduces both the blur of refractive error and target blur.

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accommodation is 'open looped' (Phillips, 1974). To test this possibility the experiment of Figure 11 was performed in which the subject was accommodating normally between 1 and 5 diopters stimulated by closed loop target blur while defocus blur had been open looped; while focused for the 5 diopter clear image position, the negative feedback of the target blur (or specifically the electrical position signal to the projector servo-cart number two) was externally switched off (i.e. open looped) so that it remained at whatever value it was at the time it was switched. In the recording shown, the target blur was at 0.4 diopters; this blur remained at this amplitude independent of subsequent accommodative movements.

Without this artificial negative feedback signal which forced the change in target blur to depend upon the focus response, the state of accommodation can be seen to drift back and remain at about one diopter until the external target blur feedback loop was reconnected (by turning on the switch and

,41

TAR GET~ "

B L U R 0 -

(diopter) 2 -

ACCR 3 -

(diopter) I - O -

C L E A R 5 -

I M A G E I - POS I TI ON ( d i o p t e r )

'I I ' I

0 I0 2 0 3 0 T I M E (see.)

Fig. 1I. Open loop myopic drift phenomenon is shown caused by turning off the artificial negative feedback loop of target blur; the defocus blur signal was open looped. This recording indicates that it is the information provided by the negative feedback that enables the accommodative control system to maintain focus upon a target at a particular refractive level It is this negative feedback that converts a retina blur into a blur error signal required to activate the accommodation response.

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re-establishing the artificial feedback control) and thus permitting the active accommodative response to again clear the target blur. This experimental phenomenon, open loop myopia and drift, was interesting because, as stated, it could be initiated by simply opening a switch in the artificial electro-mechanical-optical target blur feedback loop. It also proves specifically that it is the information provided by the negative feedback loop that enables accommodation to hold focus upon a particular target and prevents the slow exponential-like drift to the one diopter rest level of the accommodative plant; in addition it further proves that accommodation is indeed a feedback control system.

INDISTINGUISHABILITY OF TARGET BLUR FROM DEFOCUS BLUR

Theoretically target blur and nonaberrant defocus blur should produce exactly the same fight-spread pattern on the retina and consequently be indistinguishable from one another. Psychophysical experiments were run to test this prediction since this test has not been specifically reported in the literature.

In the first experiment nine students of physiological optics at Berkeley were presented two diopters of either type of blur using the stimulator of Figure 1 with the normal condition of defocus blur closed looped. After each presentation they were asked which type of blur they had seen: After perhaps a few initial incorrect answers all of the subjects were consistently able to correctly tell which stimuli were target blur or defocus blur. It was then discovered that these subjects were distinguishing the blurs by actively testing for the existence of the negative feedback loop of defocus blur by accommodating! From records presented previously in this paper, it can be suggested that it is this 'hunting' operating principle that is implemented by the accommodative mechanism to test for the presence of a feedback loop and hence defocus errors whenever additional perceptual clues are not available. Repeating the above experiment but this time limiting the blur presentations to 1/3 second durations to eliminate the usefulness of this active hunting procedure, resulted in the discrimination being almost impossible particularly if the apparatus had been initially carefully aligned. Results of a typical subject were, for example, 54 percent correct and 46 percent incorrect blur discrimination. Interestingly, it was found that the rate of blurring would often falsely affect the decision; the faster changing blur was often associated with target blur and the slower changing blur with defocus blur.

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ADDITIONAL BEHAVIOR EFFECTS OF TARGET BLUR ON ACCOMMODATION

The delay of the accommodative response to nonperiodic target blur was found to be the same as the normal accommodative delay to defocus blur of slightly less than 0.4 seconds (Phillips, Shirachi & Stark, 1972; Randle & Murphy, 1974). However, because of the pure even error nature of target blur, an accommodative response in the correct direction to closed looped

target blur often took more time than this during which time accommodation would be actively hunting for the correct focus direction. These even

error responses could be roughly classified into three groups: the first response class would be those with initial correct direction responses which continued to the final desired focus level indentical to normal odd-error closed loop responses; the second class have a correct initial direction movement but rapidly follow this by short oscillatory exertions before reaching the final focus state; the third group involved an incorrect initial response movement followed by accommodative hunting oscillations before finding and responding in the correct focus direction. The amplitude and time wave-form of this active hunting behavior was different and distinguishable from the ever-present accommodative noise or small amplitude lens vibra- tion by their large amplitude, non-periodic nature, and their correspondence with the stimulus movement.

Opening the loop on defocus blur using positive feedback while closing the loop on target blur occasionally gave some interesting side effects. Figure 12 demonstrates some of these. In general a less stable more oscillatory type behavior was evident; the subject would at times become very confused and not be able to maintain a given accommodative level. This situation was often initiated by a blink; the slit-lamp optometer infra-red light beam momentarily would reflect off the eyelid and saturate the amplifiers of the optometer thus putting in a large transient in the defocus positive feedback loop. This produced a short but confusing impulse blur stimulus to the subject and this psychophysical experience ~of blur change

was very rapid as the apparatus had a bandwidth of 20 Hz., much faster than the 2 Hz. accommodative response bandwidth.

The performance of the accommodation system in following a complexly moving stimulus is poor as indicated in Figure 13. In this figure, accommodation was able to only roughly follow even a slowly moving 0.2 Hz. triangle wave stimulus indicatin that without directional information following a continuously moving stimulus is very difficult. Even-error hand-eye control exhibits similar degraded performance (Smith, 1962).

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'j 2 A C C R 54

(diopter) 5

6 -

C L E A R I - -

I M A G E

P O S I T I O N . ( d i o p t e r ) 5 -

. . . . I . . . . I . . . . I ' ' ' ' I . . . . I ' ' ' ' I ' 0 5 I0 15 2 0 25 3 0

T I M E (see . ) Fig. 12. Accommodation stimulated by closed loop target blur with defocus blur open looped with positive feedback. The non-directional property of target blur along with the noise in the positive feedback signal caused confusion and occasionally resulted in substantial delay in finally reaching the accommodation level demanded by the stimulus image.

DISCUSSION

Figure 14 is a condensed graphical summary of some of the major results of this paper. It is a collection of accommodative responses to the various combinations of feedback and stimuli conditions examined in this study. The blur stimulus is indicated at the top of the figure as a step of amplitude three diopters of either target blur (Bt) or defocus btur (BD) lasting four seconds. The feedback configuration of each type of blur stimulus is given as either open looped (OL) or close looped (CL). As shown in this figure, a closed loop blur stimulus, be it target, defocus or both, will result in a step change in accommodation whereas an open looped blur stimulus will only produce a transient response to the blur magnitude change. The two bot tom pairs of responses in Figure 14 are exact reverse feedback configurations of one another and demonstrate the similarity of target blur and defocus blur.

If retinal blur is not controllable by accommodation in a negative feedback operating mode, then a given constant amount of blur will eventually

83

4 i ~ i , . ~ : - r l ~i~ . . . . . . . : 1

�9 . . , , . . ' = 7 1 i f - ~ i l - l i ~ r ~' ~-~-~ ~ t - - I ~ Ir~l~i.~i-.; D t - u l " l r . . ! [ ~ ITT-T~q 'w- I - - i T - I I 1/'1 IIA,~ I,&.~l.ll#'l II tlf VidlJ

. v l g J r A , ~ . ~ I luf ~1,11' I I ' ~ l U " l ' [ 1 1_1_~_..7t!I_.

4 -

ACCR ( d i o p t e r ) ,

I O -

C L E A R 5 - I M A G E .

P O S I T ION I

( d i o p t e r )

N,] I 1,4 ~ J,'i N i i i 2 " i ~ 2 - t

I I I I I

I I 0 l O T I M E ( s e e . )

Fig. 13. Accommodation attempting to follow a 0.2 Hz triangle-wave dosed loop target blur stimulus. Dioptic blur was open looped. Faster triangle wave stimulus movements could not be tracked.

be ignored; without other stimuli the state of focus will drift to its one diopter rest state. On the other hand, rapid changes of the magnitude of open loop blur will cause significant bidirectional transient accommodative fluctuation unless additional focusing information is available to reduce this transient response.

The accommodative mechanism appears to be sensitive to the changes of blur magnitude, both to increases and decreases, which suggest that the rate of change of blur plays an important role in controlling normal focusing reactions. It is this transient active accommodative fluctuation, or hunting

movement, that apparently operates as a hiU-climbing technique to provide information as to whether the blur error is controUable and thus reducible

84

C O N F I G U R A T I O N

~diopter I s e c .

OL B D ~ ,

CL B D

CL B T

CL OL B T

OL B D

CL B T

Fig. 14. Summary of accommodation response behavior to either a dioptic blur step stimulus (BD) or a target blur step stimulus (BT) as a function of the four possible feedback conditions. A closed loop (CL) blur stimulus will result in a step response while an open loop (OL) stimulus will produce only a transitory response.

85

or not, in addition to providing direction information from an otherwise even-error blur signal. Possibly it is the temporal change of blur when accommodating that specifically enables the system to distinguish a controllable blur from an open loop or uncontrollable blur. Previously, Brodkey & Stark (1967) have also commented on the importance of temporal differentiation in understanding the stimulus to accommodation; Fujii, Kondo & Kasai 969) have discussed the importance of spatial differentiation in accommodative image processing; similarly a generalized auto-correlation function has been conjectured by Engel (1972) as a mechanism involved in blur detection. It appears that blur magnitude (Fry, 1955) and its various derivatives are all important in exciting the focusing mechanism; indeed, the term blur as used in this paper is meant to include all of these characteristics.

Recent technology associated with development of an automatically focusing camera lens has shown that the same sort of sensory error detection problems exist as those involved in the human eye focusing; specifically this involves deciphering defocus blur from other types of non-vergence produced blur or target blur also present in the image and of determining the appropriate direction of lens movement for correct focus; a hill-climbing (peak finding) technique has as a consequence often been implemented in these automated focusing systems. (Baxter et al., 1957; Bliss & Crane, 1964, 1965, 1968; Buchl, 1970; Craig, 1961; Crane & Pressman, 1968; Crawley, 1963; Farbar, 1971; Hand, 1970; Kallman, 1954; Whitney, 1958.)

CONCLUSIONS

A primary statement derivable from these blur experiments is the assertion that blur itself can stimulate the accommodation reflex; that it is a sufficient stimulus condition providing, of course, i t is in an appropriate negative feedback loop.

Using an experimental apparatus providing for variable feedback open and close loop accommodative control of refocus and/or target blur, it has been possible to show the equivalence of defocus blur and target blur as error signals to accommodation. Psychophysical experiments additionally confirm their identical appearance.

The transient nature of accommodative responses to open loop blur errors explains the widespread but false not ion that target blur cannot be a sufficient stimulus to accommodation. On the contrary target blur is effective in closed loop operating condition for evoking accommodation wherein the loop is closed around target blur; and target blur and indeed defocus blur is

86

only transitionally responded to and eventually ignored if not so included

within the closed loopo

Contributors to the literature on accommodation have long hesitated to

accept blur as the stimulus to accommodation because accommodative

responses apparently did not reflect two important features of blur - the

even-error nature of blur and the equivalence of target and defocus blur.

The main results of this paper establishing the equivalence of target and

defocus blur is supplemented by clarification of the adaptive role of accom-

modative hunting in estabhshing the open or closed loop nature of the error

signal and hill-chmbing to minimize any closed loop components only.

Further, using target blur itself, demonstration of the even error nature of

accommodative responses becomes procedurally straightforward.

Thus without minimizing the role of vergence-accommodation, the rich

optical and other clues to target distance, and the higher level 'volitional'

and predictive control of accommodation in normal viewing, we can point

to clear experimental evidence for blur as the sufficient neurological

stimulus to accommodation.

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Authors' address: Departments of Mechanical Engineering, of Physiological Optics, and of Electrical Engineering and Computer Sciences University of California Berkeley, Cal. 94720 USA

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blur: a sufficient accommodative stimulus

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