Plasticity in the growth of the chick eye: Emmetropization achieved by alternate morphologies

Abstract

Both refractive properties of the eyes and ambient light conditions affect emmetropization during growth. Exposure to constant light flattens the cornea making chicks hyperopic. To discover whether and how growing chick eyes restore emmetropia after exposure to constant light (CL) for 3, 7, or 11 weeks, we returned chicks to normal (N) conditions with 12 hrs. of light alternating with 12 hrs. of darkness (designated the “R”, or recovery, condition) for total periods of 4, 7, 11, or 17 weeks. The two control groups were raised in CL conditions or raised in N conditions for the same length of time. We measured anterior chamber depths and lens thicknesses with an A-scan ultrasound machine. We measured corneal curvatures with an eight-axis keratometer, and refractions with conventional retinoscopy. We estimated differences in optical powers of CL, R and N chicks of identical age by constructing ray-tracing models using the above measurements and age-adjusted normal lens curvatures. We also computed the sensitivity of focus for small perturbations of the above optical parameters. Full refractive recovery from CL effects always occurred. Hyperopic refractive errors were absent when R chicks were returned to N for as little as one week after 3 weeks CL treatment. In R chicks exposed to CL for 11 weeks and returned to N, axial lengths, vitreous chamber depths and radii of corneal curvatures did not return to normal, although their refractions did. While R chicks can usually recover emmetropia, after long periods of exposure to CL, they cannot recover normal ocular morphology. Emmetropization following CL exposure is achieved primarily by adjusting the relationship between corneal curvature and axial length, resulting in normal refractions.

1. Introduction

It is well known that the growth of the eye is influenced by the state of focus on the retina, as well as by the magnitude and timing of illumination. In the early stages of growth, the eyes of chicks appear to be very malleable, responding with reversible changes in rate of vitreous chamber growth due to defocus (Wallman & Adams, 1987) and flattening of the cornea in constant light (Padmanabhan, Shih & Wildsoet, 2007). It is the length of the malleability period following exposure to constant light (CL) that this paper addresses. The eye's response to CL and recovery from it is particularly interesting in that it involves simultaneous alterations of almost all the important optical parameters of the eye: the shape of the cornea, the depth of the anterior chamber, the shape of the lens, as well as the depth of the vitreous chamber (Li, Troilo, Glasser & Howland, 1995a). It is generally assumed that only the refractive indices of the various media are unaffected. In this study we measured directly and estimated the changes in the optical parameters of the eye in response to CL and removal to normal (N) conditions with 12hrs of light alternating with 12 hours of darkness.

Raising chicks (Gallus domesticus) in CL alters proportional growth of the eye, producing the physiological change known as hyperopia, or “far-sightedness” (Harrison & McGinnis, 1967; Lauber, Schutze & McGinnis, 1961; Li, Troilo, Glasser & Howland, 1992). CL chicks have small, flat, thick corneas with high stromal cell densities, shallow anterior chambers, and deeper vitreous chambers compared to N chicks (Li, Troilo, Glasser & Howland, 1995b; Wahl, Li, Choden & Howland, 2009).

Disproportionate growth resulting in CL-induced hyperopia is due to a damping effect of CL on the melatonin rhythm (Li & Howland, 2000). A reduction in average melatonin concentration occurs in the retina, pineal gland and blood circulation of CL chicks. When CL chicks are treated with melatonin eye drops during the subjective night, the eye is protected and grows normally. Conversely, when chicks in normal day/night cycles are treated with the melatonin receptor antagonist luzindole, they develop hyperopia (Li & Howland, 2002; Wahl, Li, Takagi & Howland, 2011).

It is likely that shape changes of the eye are effected by connective tissues, because the higher stromal cell densities observed in CL chicks occur in corneas that are smaller than normal (Wahl, Lee, Choden, and Howland, 2009), suggesting that the production of matrix is affected. There is a circadian rhythm in proteoglycan synthesis associated with the rhythm in ocular elongation (Nickla, Rada & Wallman, 1999). The normal process of extracellular matrix accumulation may be slower in the mammalian CL sclera because collagen (hydroxyproline) and glycosaminoglycan production is decreased in CL (Norton & Rada, 1995). The intraocular pressure (IOP) of normal chick eyes is high during the day and low in the night (Li, Wahl & Howland, 2002; Nickla, Wildsoet & Wallman, 1998). The growth rhythm of the eye, as well as the IOP rhythm, are absent in CL conditions (Papastergiou, Schmid, Riva, Mendel, Stone & Laties, 1998). While these rhythms have not been established as important factors in normal ocular growth, their absence, correlated with abnormalities in ocular growth, is suggestive. Moreover, when melatonin rhythms are blocked in chicks raised in N conditions, they develop hyperopia (Li & Howland, 2002; Wahl, Li, Takagi & Howland, 2011).

The morphology and physiological optics of the chick eye are particularly sensitive to fluctuations in melatonin levels during the developmental period (Wahl, Li, Takagi & Howland, 2011). Since melatonin rhythms affect ocular growth (Wiechmann & Summers, 2008), and melatonin rhythms are damped by CL (Li & Howland, 2000, 2002) one can conclude that it is through this damping during development in CL that abnormal ocular growth occurs. We wished to determine whether, and for how long, these effects of CL-induced damping of the melatonin rhythm are reversible during the growth period of the chick. This has already been investigated in a study of lens-induced ametropia for recovery from a single age (Padmanabhan, Shih & Wildsoet, 2007) which found that effects were reversible after hatchlings had been exposed to CL for 2 weeks.

Here we report on the extent of morphological and optical recovery possible in chicks following various durations of CL exposure. Because we found that refraction always returned to normal while morphology did not, we used a model eye to explain this outcome.

2. Methods

2.1 Animal husbandry and lighting regimes

Hatchling Cornell-K strain chicks (average weight 35.8 +/− 2 gm.) were used in this study, and they were one day old at the start of the experiment. The illumination level in the aviary was 700 lux during the light-on period. Illumination was supplied by fluorescent lamps (Sylvania 40 W, Cool White). Hatchling chicks were raised in temperature controlled brooders (30°C). Food (Agway), crop gravel, and water were provided ad libitum. Two different control groups of chicks were raised either under N or CL for up to 17 weeks. The experimental group, R (“recovery”) was raised under CL for 3, 7, or 11 weeks (Table 1) and then placed in N for the remainder of the experiment. The number of chicks in each experimental group is given in Table 1.

Table 1.

Designations and Numbers of Control and Experimental Chicks in Groups

	Group	Number of Chicks
Normal (Control)	N4	6
“	N7	6
“	N11	8
“	N17	3
Constant Light (Control)	CL4	7
“	CL7	5
“	CL11	6
“	CL17	3
Recovery (Experimental)	CL3/N1	6
“	CL3/N4	6
“	CL7/N4	2
“	CL11/N6	3

All animals were handled in strict accordance with good animal practice as defined by the N.I.H. and the Cornell Institutional Animal Care and Use Committee (IACUC), and all animal work was approved by the Cornell IACUC under protocol number 89-101-01.

2.2 Corneal curvature and refraction measurements

All measurements were made on the right eyes of the chicks using techniques described in Li, et al 1995(a). We used an infrared keratometer and a conventional streak retinoscope to measure the corneal curvatures and refractions of the chicks. An “A” scan ultrasound (3M Biosound, Esoate, Indianapolis, IN) was used to measure axial length, fitted with a 10 MHz ultrasound probe extended with a 10 mm length of soft rubber tubing filled with ultrasound transmission gel (Aquasonic; Parker Laboratories, Fairfield NJ). Proparacaine HCl, (0.5%) was used as a corneal anesthetic. No other anesthetic agents were used in this study. The chick was hand-held and the open end of the tube was placed on the corneal surface near the optic axis. Prior work has shown that when both eyes of the chick receive the same treatment, the results in both eyes are virtually identical (Li and Howland, 2006) so only measurements from right eyes are reported. All measurements were made during the day between 10:00 am and 2:00 pm. We monitored those aspects of the eye known to be affected or possibly affected by CL. These included corneal radius of curvature, anterior chamber depth, refraction, lens thickness and vitreous chamber depth. Measurements were made at the end of the study for the two control groups of chicks (N or CL) exposed to 12/12 or constant light cycles. For the experimental chicks (R) measurements were made at the end of the experiment and at the times when chicks were changed from CL to a 12/12 cycle. Corneal curvature measurements were made by taking video images of reflections from an array of eight infra-red light emitting diodes arranged in a 30-cm circle around a video camera at a distance of 137 mm from the animal. Measurements were made in four orthogonal meridians and averaged. The distance between opposed LEDs is inversely proportional to the dioptric power of the cornea, and the apparatus was calibrated using ball bearings of known diameter (Glasser, Troilo & Howland, 1994).

2.3 Bootstrap and Monte Carlo tests of significant differences between optical parameters of N, CL and R birds

Because some of our sample sizes were very small, we were reluctant to use conventional parametric statistics to compute significance differences between mean optical parameters of different treatments. Accordingly, we wrote a bootstrap computer program to compute the probabilities that the average numerical results of different treatments differ significantly from each other. We first entered the data for each treatment beginning with the number of data points, followed by the data. The number of data points in each treatment need not have been, and often were not, equal. The program then computed and stored the means of each treatment and their differences. For each comparison it gathered all of the data of the two treatments into one distribution. It then drew two samples (with replacement) from this distribution, each sample of the pair having the same size as one or the other of the treatments. This procedure was repeated 500,000 times. The ratio of the number of times the difference in means of data from the two treatments exceeded the actual differences was computed. This ratio was taken to be an approximation of the chance probability of obtaining those differences. We found that this program gives much more conservative results than Fischer's PLSD test and almost as conservative results as Scheffe's post hoc test (Statview, Abacus Concepts, Berkeley CA). Its precision in estimating the probabilities was on the order of 0.0004 (standard deviation of five repeated tests of 500,000 trials at 0.05 level).

Because these tests of significant differences between treatments examined one pair of treatments at a time, we needed to find a correction factor that would account for the fact that we had made repeated tests at one time. The employment of multiple, simultaneous tests increases the probability that we would score as significant results that were actually much more probable than our 5% significance level (i.e., p< 0.05). Assuming that the probabilities of those tests where significance was found were independent of each other, we computed the joint probabilities of combinations of the most significant results. At the 5% level of joint significance, all tests with significance levels less than or equal to 0.005 were found to be jointly significantly different from each other.

2.4 Computer modeling to check for alterations in the refractive power of the lens or its index of refraction in N, CL, and R chicks

In order to determine if the CL treatment resulted in a change in lens power, (or less likely, the refractive indices of the lenses) we employed a paraxial schematic eye for the Cornell K strain chicken (Schaeffel & Howland, 1988). Modifications of this model consisted of adjusting the radii of curvature of the lenses of each age group so that the difference between the measured and predicted refractive errors of the group was within +/− 0.25 diopters (D) of zero.

We did not measure the radii of curvature of the lenses of our experimental birds, but we could calculate alterations in the power of the lens or their refractive indices by modeling the eyes. For this purpose we used the measured refraction, corneal curvature, anterior chamber depth, lens thickness, and axial length, along with the above described lens curvatures. If the lenses of CL birds had flattened, or had their refractive indices decreased, without emmetropizing compensation increasing the axial length, then optical models of these birds when fully corrected should require an additional negative refractive correction. Conversely, had the power of the lenses or their refractive indices increased, the additional refractive correction would be positive. We constructed a computer program in BASIC that computed the vergence of paraxial rays passing through the surfaces of the eye. We also used this program to estimate the sensitivity of refraction to small alterations in the optical parameters: corneal curvature, anterior chamber depth, anterior lens curvature, lens thickness, vitreous lens curvature and vitreous chamber depth. We used the bootstrap method to see if there were significant differences in additional lens corrections between the treatment and control groups. The model eye program is given in the Appendix.

3. Results

We measured these anatomical parameters: radius of corneal curvature (Fig1), anterior chamber depth (Fig2), lens thickness (Fig3), axial length (Fig 4), and vitreous chamber depth (Fig5). We compared these variables with the refraction of the eye in each experiment (Fig 6) to determine how anatomical changes were correlated with refractive recovery.

Figure 1.

Ordinate: Radius of corneal curvature in mm. measured with keratometry. Larger numbers indicate flatter corneas. Error bars indicate +/− one standard error of the mean.

Figures 1 through 6. Abcissa: constant light (light grey bars, CL time in weeks), constant light followed by normal conditions (medium grey bars, CL time in weeks/N time in weeks), and normal conditions (black bars N time in weeks). For numbers of birds in each group see Table 1. P values in each figure refer to significance of differences between recovery animals and controls (N or CL).

Figure 2.

Ordinate: Anterior chamber depth in mm. measured from the anterior surface of the cornea to the anterior surface of the lens measured with ultrasound. Error bars as in Fig. 1.

Figure 3.

Ordinate: Lens thickness in mm. measured with ultrasound. Error bars as in Fig. 1.

Figure 4.

Ordinate: Axial length in mm. measured with ultrasound from the surface of the cornea to the vitreal surface of the retina. Error bars as in Fig. 1.

Figure 5.

Ordinate: Vitreous chamber depth in mm. measured with ultrasound as the difference between axial length minus the anterior chamber depth plus the lens thickness. Error bars as in Fig. 1.

Figure 6.

Ordinate: Refraction in diopters measured with streak retinoscopy. Error bars as in Fig. 1.

The control groups of CL chicks and N chicks exhibited the expected differences in growth and refraction (Figs 1-6 lightest and darkest bars). We wished to see whether the recovery chicks (CL/N medium gray bars, Figs. 1-6) recovered normal parameters and how that depended upon age and lengths of exposure to CL and N conditions.

In Fig. 1, it may be seen that four weeks of N following either 3 or 7 weeks of CL restores normal corneal curvature. Continuing to Fig. 2, one week in N was insufficient to restore anterior chamber depth (ACD, p=0.03), however 4 weeks in N after 3 weeks in CL restored ACD. After 11 weeks in CL, ACD did not recover (p=0.016). In Fig. 3, it may be seen that no differences in lens thickness were observed between any of the groups at 4 wks. After 3 weeks in CL and 4 weeks in N the lens exhibited normal thickness. Only partial recovery was observed at longer CL exposures, as recovery groups did not significantly differ from either of the control groups. In Fig. 4, chicks recovering from 3 weeks exposure to CL have significantly longer axial lengths than CL controls (p = 0.044, CL3/N1; p=0.012, CL3/N4). After 11 weeks of CL, R chicks have axial lengths that are longer than N controls (p = 0.003). In figure 5, one week in N conditions following 3 weeks in CL was insufficient to restore vitreous chamber depth (VCD) (p = 0.019). Four weeks in N conditions following three weeks CL did restore VCD (p = 0.003), but after 11 weeks in CL, six weeks of N conditions did not restore VCD (p = 0.005). Lastly, in Fig 6, refraction represents the functional result following growth recovery after 3, 7, or 11 weeks of CL exposure. In every instance R animals exhibited normal refractions.

Our results for CL and N control chicks duplicated what has been found in previous studies (Harrison & McGinnis, 1967; Lauber, Schutze, & McGinnis, 1961; Li, Troilo, Glasser & Howland, 1992). As may be seen in Table 2 the cornea is always flatter in CL, the anterior chamber is shallower, the lens is thinner, and the refraction is hyperopic, while the axial length generally does not differ from normal birds (all p <0.05). When recovery is possible, ACD and lens thickness return toward normal values; however the axial lengths of R birds from 7 weeks onward are longer than those of N birds (p < 0.03).

Table 2.

Optical Measurements and Assumed Lens Radii for N, CL and R Chick Schematic Eyes

Condition		Number of chicks	Corneal Radius of Curvature (mm)	Anterior Chamber Depth (mm)	Front of Lens Radius of Curvature (mm)	Lens Thickness (mm)	Rear of Lens Radius of Curvature (mm)	Axial Length (mm)	Refractive Error of Eye (D)	Additional Lens needed to match Model's Axial Length (D)
N4	N	6	3.745	1.625	4.873	2.639	−3.546	10.642	4.083	0.25
CL4	CL	7	4.255	0.897	4.873	2.623	−3.546	10.423	12.571	−1.0
CL3/N1	R	6	4.022	1.17	4.873	2.662	−3.546	10.73	4.583	0.875
N7	N	6	4.28	1.77	5.371	2.90	−3.667	11.90	2.42	0.25
CL 7	CL	5	4.94	0.91	5.371	2.76	−3.667	11.46	12.30	−0.875
CL3/N4	R	6	4.287	1.93	5.371	2.97	−3.667	12.053	3.083	0.25
N11	N	8	4.565	2.011	6.246	3.389	−3.739	12.754	3.375	2.0
CL 11	CL	6	6.515	0.97	6.246	3.095	−3.739	13.218	14.50	0.625
CL7/N4	R	2	4.90	1.61	6.246	3.245	−3.739	13.325	4.50	−2.25
N17	N	3	4.708	2.124	6.352	3.598	−4.061	13.21	3.667	2.125
CL17	CL	3	6.38	0.79	6.352	3.253	−4.061	13.967	11.667	−2.625
CL11/N6	R	3	5.832	1.079	6.352	3.487	−4.061	14.547	2.333	−0.5

Mean values of measured optical parameters for experimental groups at ages 4, 7, 11, and 17 weeks used to fit ray trace to axial length of the eye, except lens curvatures which were taken from the literature (Light grey columns). Values in the last column indicate computed values of refractive errors for the model eyes using TurboBasic as described in Methods (see Appendix). Negative values indicate that the axial length of the actual eye is longer than that of an emmetropic model eye. All distances are in mm. Refractive error and lens powers are in diopters (D).

The two most important results of these experiments are: 1) Some anatomical measurements did not return to normal in R chicks, as summarized above, and 2) The refraction of R chicks always returned to normal.

To understand how a changed morphology could still result in normal refractions we constructed a series of model eyes with the measured dimensions of our experimental animals. The only parameters that were not measured in our studies were the anterior and posterior radii of curvature of the lenses and the refractive indices of the media. We used reported values for the refractive indices of the media and used lens curvatures of appropriately aged N chicks (Schaeffel & Howland, 1988). The measured parameters from chicks in experimental and control groups that were used in the model eyes together with assumed values of lens curvatures (light grey columns) are in Table 2. Also included are the additional lens corrections needed to match the measured refractive errors of the eyes (last column, Table 2).

The results of our optical modeling of chick eyes allowed us to predict the refractive errors using mean anterior and posterior lens curvatures of same aged chicks, and to compare these to their actual refractions (measured values in Table 2). By using the method of bisection to solve the implicit equations, we converted the model's focal point distances into diopters by finding the power of a corrective lens that would make the two focal points of the model and the actual refraction coincident, and hence refractions equivalent (last column of Table 2). It will be seen that the total additional errors never exceeded +/− 3D in these eyes of powers > 160D.

To understand how different morphologies in the model can result in essentially the same refraction we used the models to predict the effect of a 0.2 mm increase in each morphological parameter (Columns, Table 3), holding the other variables constant for each one.

Table 3.

Dioptric change for a 0.2mm increase in parameter in normal chick eyes

Age	Change in Corneal Radius of Curvature	Change in Anterior Chamber Depth	Change in Anterior Lens Radius	Change in Lens Thickness+	Change in Posterior Lens Radius	Change in Vitreous Chamber Depth+
N 4wk	4.5	1.65	1.00	0.25	0.50	−3.0
N 7 wk	1.5	0.25	0.375	.125	0.375	−1.25
N 11 wk	1.5	0.25	0.375	.125	0.375	−1.125
N 17 wk	1.375	0.25	0.25	.125	0.25	−1.00

Table 3 values are calculated from Table 2.

⁺When the lens thickness was increased the anterior and vitreous chamber depths were each decreased by half this amount. Thus this dioptric change reflects the lens center remaining in position while the lens displaces both aqueous and vitreous.

It may be seen from the computations in Table 3 that changes in the corneal radius have the most effect on the refraction, followed closely by alterations of the vitreous chamber depth. The next most important factors are the anterior chamber depth and the lens radii. Lastly changing the lens thickness has the least effect on refraction of all the parameters studied.

4. Discussion

Our results provide evidence that CL chickens can recover emmetropia from abnormal ocular development after switching back to N. However, they are unable to restore normal ocular proportions if exposed to 11 or more weeks of CL (e.g. Fig 2). Vitreous chamber elongation occurring under CL shown in this study (Fig 5) may result from the emmetropization of the hyperopia caused by the flattening of the corneas. These results are supported by the findings of an earlier work (Troilo and Wallman, 1991, VR, 31:1237) reporting a similar effect in a longitudinal study of eyes recovering from dark induced hyperopia, which produces large eyes with flat corneas. In that study, it was shown that emmetropia was restored by increasing the size of an already enlarged eye. These findings argue for regulation of refraction over eye morphology.

Emmetropization is the driving force behind anatomical growth of the eye. Not only does the eye change shape and achieve emmetropia after corneal and lens flattening due to CL, but also after lens-induced hyperopia during growth in the chick (Padmanabhan, Shih & Wildsoet, 2007). These authors found that one week of exposure to N was sufficient to reverse the effects of two weeks of CL on anterior and vitreous chamber dimensions, although we show here that one week of N is insufficient to cause anatomical recovery after three weeks of CL (Figs. 2 & 5).

Since some of our individual recovery experiments had small numbers of birds, we look at the overall results to see a consistent pattern, namely, emmetropization occurs following return to N conditions in all cases even though not all of the anatomical parameters return to normal (see figures 1-6 and Table 2). We cannot extrapolate from these results whether extended time (>7 weeks) in N conditions after CL exposure could correct the residual anatomical differences shown in our CL11/N6 birds. It is possible that full recovery might occur over an extended time.

4.1 A model of the action of constant light on refraction and recovery

The effects of CL on the increase of the radius of curvature is most likely mediated by the obliteration of the daily melatonin rhythm (Li and Howland 2000; Li and Howland 2002; Rada & Weichman 2006). One possible explanation of the results of our experiments can be formulated as follows: The primary cause of the action of CL on refraction stems from the fact that exposure to CL increases the radius of curvature of the cornea (Li , Troilo, Glasser and Howland,1995a). This flattening of the cornea has the same effect as placing a negative lens in front of the eye, which is known to cause the compensatory growth of the vitreous segment until the image is focused on the retina (the emmetropization process). Unfortunately, in CL, total compensation is never attained as the effect on refraction of corneal flattening outpaces compensatory axial elongation. In growing chicks when the CL condition is replaced by a sufficient interval of N, the cornea regains its normal curvature (Fig 1), and emmetropization is restored, in part, by this and by the growth in length of the vitreous chamber.

This model also accounts for the results of Padmanabhan et al. (2007), who found that CL chicks could not compensate for a 10 D negative lens, but could compensate for positive lenses of similar power while in CL. In constant light the growth of the vitreous segment fails to keep pace with the flattening of the cornea, resulting in hyperopia. Thus it is impossible to compensate for the addition of a negative lens since the rate of growth in the vitreous chamber cannot increase further. However the addition of a positive lens has the same effect as increasing the curvature of the cornea, and will necessarily slow the rate of growth of the vitreous segment, allowing compensation to take place.

5. Conclusions

Despite the resultant differing morphologies, refraction always returned to normal under the conditions we imposed. Our results suggest that in CL the ocular development and hence eye shape is altered. The final ocular morphology in recovery depends upon both the time spent in CL and the time spent thereafter in N. This can be explained by a differential reduction of plasticity in the cornea vs. the emmetropizing growth of the sclera.

• Ocular recovery from constant light effects is possible in chicks.

• Chicks restore emmetropia by adjusting corneal curvature and axial length.

• After 11 weeks of constant light, chicks cannot recover normal ocular morphology.

Appendix

The following TurboBasic program was used to compute optical parameters of the model eye as described in Section 2.4 of the Methods.

#x2018;program is VERGHH8.txt
#x2018;screen 2
im s(10),r(10),d(10),n(10),h(10),l$(10),rxs(20)
#x2018;open “table.txt” for APPEND as #1
pen “table.txt” for output as #1
ead ns ‘Number of surfaces rxs(0) = −1.9
xs(1) = 6.3
xs(2) = 2.5
xs(3) = −2.5
xs(4) = 10.6
xs(5) = 0.0
xs(6) = −4
xs(7) = 2.5
xs(8) = 3.3
xs(9) = −4
xs(10)= −5.1
 #1,date$,time$
 #1,“Program is VERGHH8.TXT”
nward:
ls
 date$,time$
tot = 0
eadreact,al ‘actual refractive error
$= “#####.###”:c$ =“########” ‘format statement
b$ = “###.##
ead b$:print “Program is VERGHH6 using data for ”; b$?
#x201C;Actual Refractive error is ”;:?using bb$;react
#x2018;Note that correcting lens is simulated by vergence of rays at first surface
x = rxs(nt) ‘correcting lens
 “RX is ”;:?using bb$;rx
frx = 0 then goto fort
erg = 1000/rx
ort: ? “vergence is ”;:? using a$; verg
(1)=1
 “ Surf # radius dist ref indx surface”
#x2018;inputqq
or j = 1 to ns
ead s(j), r(j),d(j),n(j),l$(j)
f j=1 then d(1)=verg
rint using c$;s(j),,:print using a$;r(j),d(j),n(j);:print, l$(j)
ext j print
#x201C; ” ‘leave a blank line
#x2018;now compute vergences and final distance
#x2018;First vergence is a special case
f d(1)=0 then v(1)=0 else v(1) = n(1)/d(1)
#x2018;now compute the rest of the surfaces
or j = 2 to ns
f r(j)= 0 then goto skip ‘skip a surface of no power
(j)=v(j-1)+(n(j)-n(j-1))/r(j) ‘add power of surface to vergence
#x2018;print “verg at start of intv'l after surf of power is”;:print using a$;v(j)
kip:
f d(j)=−1 then goto finish
#x2018;now compute the vergence at the end of the interval before passing
#x2018; through the next surface.
=n(j)/v(j) ‘find the distance to the focus point
#x2018;print “distance to focus = ”;:print using a$;x
h = h(j-1)*d(j)/x ‘find the decrease in ray ht at end of interval
(j)=h(j-1)-dh ‘ray ht at end of interval
#x2018;print “ray height at end of interval = ”;:print using a$;h(j)
p = x-d(j) 'find the distance to the focus point from the end of the interval
(j)=n(j)/xp ‘this is the vergence at the end of the interval
tot = dtot + d(j) ‘add up total distance traversed from 1st surface
#x2018;print “vergence at end of interval is ”;:print using a$;v(j)
#x2018;print “distance to focus = ”;:print using a$;xp
ext j
inish:
(j)=n(j)/v(j)
tot = dtot+d(j)
l = d(j)/h(j-1) ‘ compute focal length
print “Back focus distance ”;:print using a$;d(j)
print “Anterior pole to focus len.”;:print using a$;dtot
? “Actual axial length is ”;:?using a$;al
‘print ”Focal length in last medium”;:print using a$;fl
‘print “Focal length in air ”;:print using a$;fl/n(ns)
del = react-rx
? “Difference in refractive power of lens”;:?using bb$;del
gosub table
input “Enter q to quit ”,q$
‘***** ifnt = 11 then gosub legend
‘****
if q$ = “q” then stop else goto onward
stop
table:
ifnt = 0 then ? #1,“Condition CC ACD FLC LT RLC AL DTOT RE
ARE DEL “ ? #1,b$;:? #1, Using bb$; r(2),d(2),r(3), d(3),r(4),al,dtot,react,rx,del
nt = nt+1 ‘? “nt is ”;nt
return
Legend:
‘gotowaypt
? #1, ‘ ”
? #1,“Legend”
? #1,“ CC is corneal radius of curvature, ACD is anterior chamber depth,
? #1,“ FLC is Front of Lens radius of curvature, LT is lens thicknes
? #1,“ RLC is Rear of lens radius of curvature, AL is axial length of eye
? #1,“ DTOT is axial length of model eye, RE is refractive error of eye
? #1,“ ARE is the corrective lens of model to match model's axial length
? #1,“ with that of eye. DEL is difference in RE and ARE.
? #1,“ Positive values of DEL indicate that the axial length of the
? #1,“ actual eye is shorter than that of the model eye. All distances
? #1,“ are in mm. Refractive error and lens powers are in diopters.
waypt:
inputqq
stop
return
data 4 “Number of surfaces
data 2.42,11.9 REM refraction & al
data “Normal 49 days” REM title axial length correction
data 1,0,0,1, “object surface” REM surface no rad of curvdistnxt surf ref ind
data 2,4.28,1.75,1.336,“cornea”
data 3,4.67,2.9,1.463,“Lens front surface”
data 4, -3.19,-1,1.336, “Lens rear surface”
...