網膜鏡檢和光屈光法之結合及改進

Full title: HAND-HELD PHOTOREFRACTOR – READING

REFRACTION FROM THE DISTANCE BETWEEN THE EYE AND THE LIGHT SOURCE

Short Title: Hand-held Photorefractor

Number of words: ~2500

Number of figures: 7

Section codes: EY, VI.

Ai-Hou Wang, MD, PhD. Department of Ophthalmology

National Taiwan University Hospital 7 Chung-shan S. Rd. Taipei, Taiwan 100 Phone: 886-2-23970800 x5187

FAX: 886-2-23412875

E-mail: [email protected]

Keywords: refractive error, optics, amblyopia, photorefraction, photorefractor.

Grant support: National Science Council of the Republic of China, NSC 88-2314-B-002-374.

Proprietary interest category: None.

Abstr act

Pur pose.

Conventional photorefractors applying either camera or video have fixed distance between the viewing line and the light source and read the refraction from the size of the crescent. Since the

relationship between the crescent size and the refraction is not linear and the resolution at higher refractive error is poor, a hand-held

photorefractor was introduced which employed fixed crescent:pupil ratio as endpoint and read the refraction from the varying distance between the eye and the light source. The relationship between the distance and the refraction is linear.

Methods.

For ‘axial’ myopia and hyperopia, a simple formula holds that do = Ratio•Pu•lo•R where do is the distance between the eye and the

light source; Ratio is the non-crescent:pupil ratio; Pu is the pupil diameter; lo is the test distance and R is the refraction relative to the vergence of the

test distance. A design of hand-held photorefractor, similar in shape with direct ophthalmoscope and retinoscope, was proposed that by sliding the

light source up and down and looked through a fixed viewing hole for a fixed crescent:pupil ratio, the refraction could be read from a linear scale with good resolution. Oblique astigmatism could be read simply by

aligning the instrument with the oblique crescent, no need to rely upon complicated calculation.

Results.

With random combination of spherical and cylindrical lenses in front of a model eye I read the refraction blindly with a prototype of this hand-held photorefractor. The result was satisfactorily accurate.

Conclusions.

A practical hand-held photorefractor was designed, with which the refraction could be read on a linear scale with good resolution, and the axis of oblique astigmatism could be determined by simply aligning the instrument with the tilted crescent.

Intr oduction

Pediatric refraction, despite technology advancement, is still a crucial clinical challenge. Autorefractor is accurate, but it is only applicable to children older than 2 year-old. Refracting children under 2 year-old depends mainly upon retinoscopy. Putting neutralizing lens or the retinoscopic rack near the children’s eye is a major practical barrier of this technique. Photorefraction can refract at a distance from the

children1-3. It is nevertheless not accurate enough. How to increase its accuracy and convenience is an ongoing hot topic nowadays.

Photorefractor is mostly operated by paramedical personnel to screen amblyogenic factors before referring to ophthalmologists/

optometrists for further evaluation. Retinoscopy remains the most accurate measure which most ophthalmologists/optometrists rely on.

Conventional eccentric photorefractors applying either camera or video have fixed distance between the viewing line and the light source and read the refraction from the size of the crescent1,2,4-7. The relationship

between the crescent size and the refraction is not linear and the resolution at higher refractive error is poor. I introduced a hand-held photorefractor employing fixed crescent:pupil ratio as endpoint and reading the refraction from the varying distance between the eye and the light source. The relationship between the distance and the refraction is linear.

In this study, a novel refractor was designed employing the optical principle of photorefractor, with its appearance simulating that of direct ophthalmoscope and its operation mimicking that of retinoscope. Since it is operated on a clinical basis, at a distance from the children and without the need of neutralizing lens, I think it will help

Mater ials and Methods

For ‘axial’ myopia and hyperopia, a simple mathematical formula holds:

do = Ratio•Pu•lo•R

I derive it with the notations illustrated as following (Fig.1,2,5,6), do : distance between the eye and the light source. do stands for

‘distance at object space’. (do≧0)

di : distance between the images of the eye and the light source at the

conjugate plane. di stands for ‘distance at image space’. (di≧0)

lo : distance between examiner and examinee. lo stands for ‘length at

object space’. (lo＞0)

li : distance between the conjugate plane and principle plane of the

eye. li stands for ‘length at image space’. (li＞0)

Pu : pupillary diameter. (Pu＞0)

P : power of the refractive components of the eye. (P＞0)

R : refraction ‘relative to the vergence at test distance’. For example: The vergence is -2D at 50 cm test distance. Then R = -1 for -3D

2 ).etc..

x : the distance between retina and conjugate plane. (x＞0 for P＜0 and x＜0 for P＞0)

a+b : the retinal area representing the whole pupil the examiner sees. a : represents non-crescent part of the pupil. (a＞0)

b : represents the crescent part of the pupil. (b≧0)

b+c : the image (blurred) of the light source on the retina. a

Ratio = : proportion of non-crescent part of the pupil.

a + b

From Newton’s geometric optics, variables at image side, li, di and x,

were represented by variables at object side (Fig. 1,2,5,6):

Fig 1,2 about here

1 1 lo

+ = P → li = eq.(1)

do di li•do do = → di = = eq.(2) lo li lo P•lo - 1 1 1 ( - R ) + = P lo li+ x lo lo → x = - eq.(3) lo•P +lo•R - 1 P•lo - 1

For myopic eye, i.e. relatively more myopic than the vergence of the test distance, R<0 (x>0), from Fig.1

a li + x = di li a di•( li + x) → Ratio = = a + b Pu•x a + b x = Pu li

a do

Ratio = =

a + b - Pu•lo•R

→ do = - Ratio•Pu•lo•R eq.(4)

For hyperopic eye, i.e. relatively more hyperopic than the vergence of the test distance, R>0 (x<0), from Fig.2

a li + x = di li a + b - x = Pu li

Similar to the derivation of eq.(4) we get

do = Ratio•Pu•lo•R eq.(5)

Eq.(4) and (5) show that, for axial myopia and hyperopia

R is directly proportional to do

R is inversely proportional to Pupil diameter

R is inversely proportional to Test distance

R is irrelevant to Refractive components of the eye

For example:

If pupil is dilated to have 8mm diameter, test distance is 50cm and ¼ crescent:pupil is used as endpoint of reading,

Pu = 8 mm = 0.008 m lo = 50 cm = 0.5 m

Ratio = ¾ = 0.75 ( ¾ non-crescent and ¼ crescent)

then do = 0.75•0.008•0.5•R = 0.003 R

i.e. Every 3 mm of do corresponds to 1D of refraction. And with 4.8 cm

range of do it measures -18D (R=-16) to 14D (R=16)

Alternatively, if disappearance of crescent is used as endpoint of reading, Pu = 8 mm = 0.008 m

lo = 50 cm = 0.5 m

(limiting condition whereby crescent disappears)

then do = 1•0.008•0.5•R = 0.004 R

i.e. Every 4 mm of do corresponds to 1D of refraction. And with 4.8 cm

range of do it measures -14D (R=-12) to 10D (R=12)

Practically, Ratio = ¾ ( ¾ non-crescent and ¼ crescent ) may be easier to detect than Ratio = 1 (no crescent, disappearance of crescent) as the endpoint of reading, despite that the latter has better resolution than the former, i.e. 4mm for 1D vs. 3mm for 1D.

From the fact that R is directly proportional to do, a hand-held

photorefractor (Fig. 3) similar in shape to direct ophthalmoscope and retinoscope was designed. By sliding the light source and prism up and down, the distance between examiner’s eye and the light source varied within a range of 5cm. With a fixed crescent:pupil ratio as the endpoint, the refraction could be read on a linear scale up to 10+D on either myopia or hyperopia side. The resolution was also practically adequate, i.e. 3-4mm for 1 diopter.

Fig. 3 about here

Oblique astigmatism gives tilted crescent. Conventional photorefractors measure the refraction along two or three fixed meridians and calculate the power and axis of oblique astigmatism through complicated

formulas8,9. This results in even more inaccuracy upon a basis of

pre-existed inaccuracy of the technique of photorefraction10. Hand-held

photorefractor reads oblique astigmatism by simply aligning the instrument with the oblique crescent and gets the power at two major axes.

Results

A prototype of this hand-held photorefractor was made and tested on model eye. The model eye was set at emmetropia and in front of it I blindly put two lenses which were selected from a pool of -6D to +6D spherical and -6D to +6D cylindrical lenses. Since the resultant spherical power and the power and axis of cylinder could not be straightforwardly figured out. I read the refraction with hand-held photorefractor first and later on calculated the resultant refraction with computer to see the goodness of fit. The result was satisfactorily accurate.

Discussion

Despite an ophthalmoscope is not a retinoscope11, it is optically a photorefractor. Ophthalmoscope makers tried to make light path and viewing line coaxial for small pupil examination. But most

ophthalmoscopes actually have small distance in between, which mimics the optics of photorefractor (Fig. 6). This is obvious if we observe model eye at a distance with ophthalmoscope and continuously change the refraction of the model eye from minus to plus. We will see the whole spectrum of the photorefraction, including the dark zone.

Fig. 4 about here

Calculation of dar k zone:

The limiting condition of photorefraction, i.e. at the margin of dark zone, is when Ratio = 1 or b = 0 (Fig. 5,6), then

do

or R = eq.(6)

Pu•lo

Fig.5,6 about here

-1 -1

The dark zone is from ( - R ) D to ( + R ) D

do do

with a range of 2•R (at limiting condition),

which is directly proportional to do,

inversely proportional to Pu,

inversely proportional to lo. For example: If do = 1 mm = 0.001 m, Pu = 8 mm = 0.008 m and lo = 50 cm = 0.5 m, 0.001 then R = = 0.25 D 0.008•0.5

The dark zone is from -2.25 D ( -1 / 0.5 - 0.25 ) to -1.75 D ( -1 / 0.5 + 0.25 ).

Cr escent size vs. r efr action, with do fixed, in conventional

photor efr action:

Conventional photorefractors employ fixed do and read refraction from

crescent size or the crescent:pupil ratio. do

From eq.(5) Ratio•R =

Pu•lo

The relationship between Ratio and R is hyperbolic, and the curve of crescent:pupil ratio (1-Ratio) vs. refraction, which is often depicted in conventional photorefraction, is non-linear (Fig. 7). This curve has good resolution at lower refractive error but poor resolution at the plateau of higher refractive error8.

Eq.(6) and Fig. 7 show that smaller do, larger pupil and longer test

distance lessen the dark zone, increase the resolution at lower refractive error and decrease the resolution at higher refractive error. On the

contrary, larger do, smaller pupil and shorter test distance increase the

dark zone, yet may increase the resolution at higher refractive error8.

One difference between spot and linear edged (such as photoflash) light source is that when the pupillary light reflex is small (non-crescent Ratio > ¾ ), the latter is really crescent-shaped, but the former makes dome-shaped.reflex. When the reflex is large (non-crescent Ratio < ¼ ), either

light source makes dome-shaped reflex12.

In conclusion, in this study I formulated the optics of photorefraction with spot light source; found the linear relationship between do and

refraction and suggested this relationship, along 5 cm range of do, is

suitable for hand-held photorefraction, and must be superior to the non-linear relationship between crescent size vs. refraction, which was used in most conventional photorefractors.. With its hand-heldness, the oblique astigmatism could be simply measured by aligning the instrument with

Refer ences

1. Howland HC, Howland B. Photorefraction: a technique for study of

refractive state at a distance. J Opt Soc Am. 1974;64:240-249.

2. Kaakinen K, Ranta-Kemppainen L. Screening of infants for

strabismus and refractive errors with two-flash photorefraction with and without cycloplegia. Acta Ophthalmol (Copenh). 1986;64578-582.

3. Hsu-Winges C, Hamer RD, Norcia AM, Wesemann H, Chan C.

Polaroid photorefractive screening of infants. J Pediatr Ophthalmol Strabismus. 1989;26:254-260.

4. Howland HC, Braddick O, Atkinson J, Howland B. Optics of

photorefraction: orthogonal and isotropic methods. J Opt Soc Am. 1983;73:1701-1798.

and empirical measures. Am J Optom Physiol Opt. 1985;62:614-620.

6. Norcia AM, Zadnik K, Day SH. Photorefraction with a catadioptric

lens. Improvement on the method of Kaakinen. Acta Ophthalmol (Copenh). 1986;64379-385.

7. Bobier WR. Quantitative photorefraction using an off-center flash

source. Am J Optom Physiol Opt. 1988;65:962-971.

8. Gekeler F, Schaeffel F, Howland HC, Wattam-Bell J. Measurement

of astigmatism by automated infrared photoretinoscopy. Optom Vis Sci. 1997;74:472-482.

9. Wesemann W, Norcia AM, Allen D. Theory of eccentric

photorefraction (photoretinoscopy): astigmatic eyes. J Opt Soc Am A. 1991;8:2038-2047.

B. Light-intensity distribution in eccentric photorefraction crescents. J Opt Soc Am A Opt Image Vis. 1998;15:1500-1511.

11. Roe LD, Guyton DL. An ophthalmoscope is not a retinoscope. The difference is in the red reflex. Surv Ophthalmol. 1984;28:405-408.

12. Roorda A, Campbell MC, Bobier WR. Slope-based eccentric photorefraction: theoretical analysis of different light source

configurations and effects of ocular aberrations. J Opt Soc Am A. 1997;14:2547-2556.

Legends

Fig. 1 Refraction sketch for R<0, i.e. relatively more myopic than the vergence of the test distance (-1 / do ).

Legends

Fig. 2 Refraction sketch for R>0, i.e. relatively more hyperopic than the vergence of the test distance (-1 / do ).

Legends

Fig. 3 Design of hand-held photorefractor. The examiner’s eye and light source are of equal distance to the examinee’s eye. This is

achieved by sliding the prism (or mirror) and light source together to keep constant distance between light source and the examinee.

To adjust do by sliding the prism up and down is a maneuver

similar to retinoscopy where we slide the lens or light source up and down to change the vergence.

Legends

Fig. 4 Direct ophthalmoscope is itself a photorefractor. The light path and the visual line are not completely coaxial. The optics mimics that of photorefractor.

Legends

Fig. 5 Limiting condition for R<0, i.e. a condition at the border of dark zone.

Legends

Fig. 6 Limiting condition for R>0, i.e. a condition at the border of dark zone.

Legends

Fig. 7 The relationship between Ratio (non-crescetn:pupil) and R is hyperbolic, and the relationship between crescent:pupil (1-Ratio) and refraction is non-linear. This curve is often depicted in

Figur es

retina P conjugate plane eye c do Pu di b light a lo li x

Fig. 1 Refraction sketch for R<0, i.e. relatively more myopic than the vergence of the test distance (-1 / do ).

Figur es

retina P conjugate plane eye c do Pu b di a light x lo li

Fig. 2 Refraction sketch for R>0, i.e. relatively more hyperopic than the vergence of the test distance (-1 / do ).

Figur es

varying do (up to 5cm)

viewing line

light paths sliding the prism (or mirror)

and light source together (sliding up and down) (sliding range ~5cm)

spot light source

Fig. 3 Design of hand-held photorefractor. The examiner’s eye and light source are of equal distance to the examinee’s eye. This is

achieved by sliding the prism (or mirror) and light source together to keep constant distance between light source and the examinee.

To adjust do by sliding the prism up and down is a maneuver

similar to retinoscopy where we slide the lens or light source up and down to change the vergence.

Figur es

d

_o

viewing line

light path

prism

spot light source

Fig. 4 Direct ophthalmoscope is itself a photorefractor. The light path and the visual line are not completely coaxial. The optics mimics that of photorefractor.

Figur es

retina P conjugate plane eye c do Pu di a light x lo li

Fig. 5 Limiting condition for R<0, i.e. a condition at the border of dark zone.

Figur es

retina P conjugate plane eye do Pu c di a light x lo li

Fig. 6 Limiting condition for R>0, i.e. a condition at the border of dark zone.

Figur es

Ratio (Non-crescent proportion) hyperbola R 1-Ratio

(Crescent proportion) do (limiting condition)

R = (dark zone border)

Pu•lo

R

Fig. 7 The relationship between Ratio (non-crescetn:pupil) and R is hyperbolic, and the relationship between crescent:pupil (1-Ratio) and refraction is non-linear. This curve is often depicted in