ViewMedia.pdf

JOSA COMMUNICATIONS

White-light speckle optometer

R. D. Bahuguna and D. Malacara

Centro de Investigaciones en Optica, A.C., Apartado Postal 948, Leon Gto., 37000 Mexico

K. Singh

Department of Physics, Indian Institute of Technology, Delhi, New Delhi-110016,India

Received January 29, 1983; accepted August 12, 1983

A white-light speckle optometer is proposed for accommodation studies. It consists essentially of a coarse reflect-

ing diffuser illuminated by a white-light point source. The source rotates on a disk, thus producing a rotating scat-

tered field from the diffuser. This in turn produces speckle motion for the defocused eye and zero motion for the

focused eye. The optometer competes quite well with the laser speckle optometer.

SYNOPSIS OF LASER OPTOMETRY

When a diffuse object is illuminated by a laser, it appears to

be covered with a fine granular structure, the so-called speckle

pattern.' If the eye is kept stationary, the specklepattern also

remains fixed. Movement of the head, however, results in

parallax movements between the conjugate speckle pattern

and the illuminated patch on the surface. The speckle pat-

tern thus appears to move with respect to the surface. The

direction and the speed ofthe parallax movements depend on

the ametropia of the observer. Following the theoretical

explanations of the origin of speckles by Rigden and Gordon 2

and Oliver, 3 Knoll was the first to explore the possibility of

devising a new method for subjective refraction. 4

In this technique a diffusely reflecting cylinder rotates with

a slow speed about its axis. This is illuminated by a diverging

laser spot. With such an arrangement, speckle movement

depends on the refractive power of the meridian of the eye that

is perpendicular to the drum axis. Knoll devised a gimbal

mount to explore different refractive meridians. The diam-

eter of the drum was 18 cm and the speed of rotation was 1

revolution per hour (rev/h). The moving speckle pattern can

be made stationary by the use of appropriate correcting lenses.

The retina is then conjugate with the plane of stationarity,

whose position is a function of the drum radius and of the

curvature and obliquity of the incident illuminating wave

front. 5 ' 6

The laser refractive technique has attracted many workers

who have used and studied it in detail. 7 - 18 Many ingenious

features have since been incorporated' 9 to aid in the precise

determination of the zero-movement condition.

When the laser source is replaced by a white-light point

source, instead of speckle, one sees a uniformly illuminated

spot on the surface of the drum of the optometer. This is

primarily because of incoherent summation of the scattered

light from the different scattering centers within the point-

spread function of the eye. Here one speculates that in-

creasing the separation between the scattering centers, such

that on the average one scatterer 2 ' falls within the spread

function of the eye,could perhaps show up a grainy appear-

ance somewhat similar to the speckles. This has indeed been

found to be experimentally true, as we see below.

PREPARATION OF THE DIFFUSER:

STRUCTURE OF SPECKLE

Not only must there be a large separation between two scat-

terers that are close to one another; in addition, the diffuse

surface must be highly reflecting. This is because white-light

point sources are relatively weak compared with the laser. By

working along these lines, we have made an optometer that

works with a small-filament flashlight bulb.

The required surface could be prepared in one of several

ways. One of the simpler ways is to press a thin reflecting

aluminum foil on a coarse emery paper (size #36). In this

way the foil is made to follow the contours of the emery surface

closely. The foil is then slowly peeled off, thus giving the

required diffuse surface.

A close examination of the speckle structure is in order here.

Figure 1 illustrates the mechanism of its formation. A specific

scatterer P located on the diffuser is viewed by a defocused

eye. S is a white-light point source illuminating the diffuser.

W is the distorted (aberrated) wave front, scattered by P, at

the pupil plane of the eye. This wave front, besides having

phase fluctuations, has strong intensity fluctuationsconsisting

of a distorted cobweb structure with sharp bright lines to-

gether with fringes. If the eye is hypermetropic,this structure

projects itself straight on to the retina. On the other hand,

if the eye is myopic, it gets inverted. The extent of this

structure is limited by a circular boundary that is the projec-

tion of the eye pupil on the retina.

REPLACING LASER LIGHT WITH WHITE

LIGHT

De Palmer 2 0 suggested that white light could be used for

measuring ocular refraction if a finely ground glass is used.

He further suggested that a specially made surface could

possibly improve the performance. We have carried out some

experiments from which we conclude that a finely ground glass

is not particularly suitable; however, the idea of using white

light is fascinating.

0740-3232/84/010132-00$01.00

JOSA Communications

Vol. 1, No. 1/January 1984/J. Opt. Soc. Am. A

133

W DL R

Fig. 1. Schematic diagram showing the mechanism of formation of

speckles. S, source; P, scattering center; W, distorted wave front; D,

pupil of the eye; L, lens of the eye; R, retina.

spaced flashlight bulbs (with small filaments) fixed on its rim.

Each bulb is covered from behind by a baffle B to prevent light

from reaching the aluminum diffuser D when the bulb goes

to the rear side. B is blackened from inside so as not to reflect

the light from the source, thus avoiding any degradation of

spatial coherence. S is a screen with an aperture that allows

only one bulb to illuminate the diffuser at a time. The ob-

server at 0 sees the speckle moving in case he is unable to

accommodate on the surface. It should be noted that, unlike

the laser speckle optometer, the plane of stationarity is the

surface ofthe diffuser and is independent ofthe illumination

geometry.

The suitable speed of rotation has been found to lie between

1 and 4 rev/min. It should be noted, however, that the speckle

speed, although dependent on the angle of illumination that

changes with the position of the source through relation (1),

is found experimentally to be almost constant. This is be-

cause the individual scatterers scatter mainly in the i = r re-

gime because of small-angle scattering. They appear and

disappear as the source angle changes because of their dif-

ferent orientations.

In a practical system the stimulus target is viewedthrough

a beam splitter according to standard practice. A slightly

concave diffuser is more suitable than a plane diffuser as it

concentrates more light toward the observer. For cylindrical

power measurements the axis ofthe disk is rotated to explore

the different refractive meridians. The accuracy of accom-

modation measurements is found to be ±0.25 D.

ANGULAR ROTATION OF THE SOURCE

If we refer to Fig. 1 we see that, if the source S is given an an-

gular motion clockwise,W rotates clockwiseabout P and the

projected pattern on the retina moves down. Hence the ob-

server sees the pattern moving up. The motion reverses in

the case of myopic eye.

The angular motion br of the scattered wave front in the

direction r is related to the angular motion bi of the source as

follows 2 2 :

br=-bi,(1

cos r

where i is the mean angle of illumination.

By working along the lines of previous work, 2 3 we find that

the speckle motion d on the retina is given by

bu'bi cos i

M'cosr

cos

(2)

CONCLUSIONS

The white-light speckle optometer described above competes

quite well with the laser speckle optometer. It has the ad-

vantage of using an inexpensive white-light source. For larger

viewing distances, the diffuse surface should be relatively more

coarse. The standard deviation of ammetropia is found to be

±0.25 D.

where M' is the optical magnification by the eye and 5ui is the

amount of defocus.

CONTRAST OF SPECKLES: APPROPRIATE

DENSITY OF SCATTERERS

With the focused eye the speckles appear to boil. The boiling

is because the amount of light scattered by the different

scatterers changes with the angle of illumination. With de-

focusing, the contrast is reasonably good, provided that the

scatterers are still resolved by the defocused eye. It is

worthwhile to estimate the minimum required spacing be-

tween the scatterers for an amount of defocus AD (in diop-

ters). The diameter of the defocused spread function is easily

seen to be given by

REMARKS

In the laser speckle method using the He-Ne wavelength, a

correction of about +0.32 D has to be made to conform with

the daylight conditions. 24 This effect is due mainly to chro-

matic aberration of the eye. In the white-light speckle

method, such a correction is, however, not needed. Moreover,

the target can be fixed onto the diffuse surface since the plane

of stationarity is the surface. 2 5

xdAD,

where d is the distance of the observer from the diffuser in

meters and x is the diameter of the pupil of the eye in meters.

Some typical values of d, x, and AD are 1 m, 4 mm, and 1

diopter, which gives xdAD = 4 mm. This is the estimate of

the spacing between two nearby scatterers showing that, for

good contrast, the scatterers have to be widely spaced.

DESIGN OF THE OPTOMETER

The design of the apparatus is illustrated in Fig. 2. A is a

slowly rotating disk of diameter 40 cm and has seven equi-

A 0

Fig. 2. Basic design of the white-light speckle optometer. A, ro-

tating disk; B, baffle; b, flashlight bulb; S, screen; D, diffuser; 0, ob-

server.

i,(1

A laser speckle optometer can

134

J. Opt. Soc. Am. A/Vol. 1, No. 1/January 1984

JOSA Communications

also be made following the above design. The point sources

could be generated by small spherical mirrors, which reflect

light from an expanded laser beam, mounted on the disk. The

plane of stationarity would then be the surface, as is the case

with white light. The choice of the diffuse surface could be

the same as that used in the existing laser optometer or could

be the one used in the above study. A large collection of ex-

perimental data from different subjects is, however, needed

to establish the superiority of one surface over the other in this

case.

The white-light grainy structure obtained in our study is

not the Gaussian speckle. Actually there is no interference

among different scatterers. The pattern that appears like a

distorted cobweb when viewed with the defocused eye is ba-

sically formed by the distorted wave fronts from individual

scatterers. Thus the structure is characteristic of individual

scatterers. In the literature this is called non-Gaussian

fluctuations.

2 6

A familiar example is the swimming-pool

aid of speckle pattern produced by coherent light," Vision Res.

12, 411-420 (1972).

6. W. N. Charman, "On the position of the plane of stationarity in

laser refraction," Am. J. Optom. Physiol. Opt. 51, 832-837

(1974).

7. W. N. Charman, "Speckle movement in laser refraction. I.

Theory," Am. J. Optom. Physiol. Opt. 56, 219-227 (1979).

8. W. R. Baldwin and W. B. Strover, "Observations of laser standing

wave patterns to determine refractive status," Am. J. Optom.

Arch. Am. Acad. Optom. 45, 143-151 (1968).

9. W. 0. Dwyer, P. Kent, J. Powell, R. McElvaih, and J. Redmond,

"Reliability of laser refraction technique for different refractive

groups," Am. J. Optom. Arch. Am. Acad. Optom. 49, 929-931

(1972).

10. J. A. M. Jennings and W. N. Charman, "A comparison of error

in some subjective methods of refraction," Ophthalmic Opt. 13,

8-18 (1973).

11. D. Malacara, "Measurement of visual refractive defects with a

gas laser," Am. J. Optom. Physiol. Opt. 51, 15-23 (1974).

12. W. N. Charman and J. A. M. Jennings, "Evaluation of laser re-

fraction using naive subjects," Ophthalmic Opt. 14, 1041-1051

(1974).

13. D. E. Phillips, W. Sterling, and W. 0. Dwyer, "Validity of the laser

refractive technique for determining cylindrical error," Am. J.

Optom. Physiol. Opt. 52, 328-331 (1975).

14. D. E. Phillips, G. S. McCarter, and W. 0. Dwyer, "Validity of laser

refractive technique for meridional measurement," Am. J. Optom.

Physiol. Opt. 53, 447-450 (1976).

15. C. Haine, W. Long, and R. Reading, "Laser meridional refrac-

tometry," Am. J. Optom. Physiol. Opt. 53, 194-204 (1976).

16. R. T. Hennessy and H. W. Leibowitz, "Laser optometer incor-

porating Badal principle," Behav. Res. Meth. Instrum. 4, 237-239

(1972).

17. W. N. Charman and J. Tucker, "Accommodation and color," J.

Opt. Soc. Am. 68, 459-471 (1978).

18. D. A. Owens, "The Mandelbaum effect: evidence for an ac-

commodative bias toward intermediate viewing distances," J. Opt.

Soc. Am. 69, 646-652 (1979).

19. K. Ukai, H. Ohzu, and T. Takata, "Refractometer and optometer

by aid of laser speckle pattern," in Proceedings of the Interna-

tional Symposium on Ophthalmological Optics (University of

Tsukuba, Tsukuba, Japan, 1978),pp. 95-98.

20. D. A. Palmer, "Speckle patterns in incoherent light and ocular

refraction," Vision Res. 16, 436 (1976).

21. By a scatterer we mean a small scattering region that, although

extended, is coherent, thus producing a single distorted wave

front.

22. M. Frangon, Laser Speckle and Applications in Optics (Aca-

demic, New York, 1979), p. 125.

23. D. A. Gregory, "Basic physical principles of defocused speckle

photography: a tilt topology inspection technique," Opt. Laser

Technol. 8, 201-213 (1976).

24. Y. Le Grand, Optique Physiologique III (Editions de la Revue

d'Optique, Paris, 1956), p. 18.

25. For studies that involve something other than testing the eye, a

beam-splitter system is advantageous in bringing the desired

targets in the field of view.

26. E. Jakeman, J. G. McWhirter, and P. N. Pusey, "Enhanced

fluctuations in radiation scattered by a moving random phase

screen," J. Opt. Soc. Am. 66, 1175-1182 (1976).

effect.

Another fine structure superposed upon the above-men-

tioned structure is due to the scatterers present on the cornea

that project a shadow on to the retina. This projection occurs

because the scattering centers on the aluminum surface act

like small sources. This structure is not too noticeable and

thus does not significantly interfere with accommodation

studies.

It is worth noting that any rotating optical field with strong

spatial-intensity modulation on its wave front can, in princi-

ple, be used as an optometer. For example, a rotating Young

fringe pattern could also be used.

ACKNOWLEDGMENTS

The authors are grateful to M. S. Sodha, A. K. Ghatak, and

M. V. R. K. Murty for their interest in the work, to G. Ro-

drigues and S. Bhattacharya for useful discussions and ex-

perimental help, and to J. Castro and H. Sotelo for technical

assistance.

REFERENCES

1. J. C. Dainty, ed., Laser Speckle and Related Phenomena

(Springer-Verlag, Berlin, 1975).

2. J. D. Rigden and E. I. Gordon, "The granularity of scattered op-

tical maser light," Proc. IRE 50, 2367-2368 (1962).

3. B. M. Oliver, "Sparkling spots and random diffraction," Proc.

IEEE 51, 220-221 (1963).

4. H. A. Knoll, "Measuring ametropia with a gas laser," Am. J.

Optom. Arch. Am. Acad. Optom. 43, 415-418 (1966).

5. E. Ingelstam and S. I. Ragnarson, "Eye refraction examined by

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika: