The Ciliary Corona: Physical Model and Simulation of the Fine Needles Radiating from Point Light Sources

Abstract

purpose. Most people see, around bright lights against dark backgrounds, a radiating pattern of numerous fine, slightly colored needles of light—the so called ciliary corona. The purpose of this study was to try to explain this phenomenon.

methods. Recently, it has been shown that light-scattering in the eye, measured psychophysically and on human donor lenses, can be explained assuming the presence of specific distributions of small particles in the eye. Light entering the eye is diffracted by these particles. Each such particle causes a circular diffraction pattern on the retina of tens of degrees, much like the well-known Airy pattern. The optics of combining many such diffraction patterns was modeled and the resultant pattern simulated graphically. The simulations were compared with observations on the ciliary corona, as seen by the natural eye.

results. The diffraction discs originating from all the particles coherently superimposed on the retina. Because of phase differences this resulted in breaking the Airy-like discs into a fine spotted pattern when monochromatic light was used. For white (polychromatic) light, the spots line up to form the very fine-line pattern seen in the ciliary corona. Details such as the width and color of the needles follow from the theoretical treatment and were demonstrated by simulations.

conclusions. The details of the ciliary corona can be understood on the basis of polychromatic light-scattering by the particles predicted to be present in human eye lenses on the basis of light-scattering studies of donor lenses.

Light scattering in the eye’s optical media causes a veil of stray light over the retina. ^{1 2 3} This stray light leads to deleterious visual effects, such as glare while driving at night or haziness of vision, which increases with age. ^{1 3 4} The proteins in the eye lens have long been considered an important source of light-scattering, especially when aggregates form. ^{5 6 7 8} Examination of optical scattering from donor lenses has been used to estimate the proportion of light-scattering sources within the lens (0.000006) and the size of these sources (∼0.7-μm radius). ^{9 10 11 12} The forward scatter seen from donor lenses was also consistent with the perceived scatter in vivo (i.e., retinal stray light). ^{10 12} Backward directions of scattering are dominated by particles of much smaller size. ¹² For backward directions, irregular reflections by the “zones of discontinuity” in the lens, also play a role. ¹² Bettelheim ⁷ has noted that the density of larger particles need not be high to explain the intensity of forward light-scattering. In fact, the experimentally determined levels of light-scattering and stray light are consistent with particles that occupy only 0.000006 of the volume of the human eye lens. ¹² A morphologic search by Gilliland et al. ^{13 14} led to the identification of candidate particles for forward light-scattering in human lenses. 

However, with these positive results, a new question emerged. The scattering pattern of such particles consists of a dominating central disc of more or less uniform light, extending over more than 10°. It resembles the well known Airy pattern that describes diffraction of light around a circular object. However, what we subjectively see around a point source of light does not resemble a smooth disc at all. Instead, we perceive a very fine pattern of innumerable needles of light, fanning out from the point object over several degrees. It must be noted that the pattern at some angular distance from the source is considered here. At the site of the source itself, a white stellar shape with a small number of spokes is often observed, but this depends on the subject. With squeezing or cataract, the spokes can extend considerably. These effects were not considered in this study. The pattern of innumerable needles is familiar to most people. Typically, it is seen around a (distant) white lamp against a dark sky at night or a halogen spot at home. The phenomenon is called ciliary corona, ¹⁵ “cilia” being Latin for eyelashes (but also for eyelids). It was the purpose of the present study to try to understand this seeming discrepancy and to explain the origin of the ciliary corona. 

Methods

Theory

The basis for the explanation was sought in the fact that retinal stray light is the summation of scattered light from many particles. Figure 1gives a schematic representation of light-scattering by three particles in the lens, illuminated by an infinite point source of monochromatic light. Simpson ¹⁵ has pointed out that the phenomenon of the ciliary corona bears subjective resemblance to what is perceived when looking through a glass powdered with very fine lycopodium powder. The data on human donor lenses predict a median value for the particle size of 0.724 μm radius and a median volume fraction of 0.000006 for these particles. ¹² If the particles are assumed to be spherical, each would occupy a volume of 4/3πr³ = 1.6 μm³, and many thousands of particles would occupy a 4-mm diameter pupil. Each of these particles diffracts light so as to project an Airy-like disc on the retina when the eye looks at a distant point source (Fig. 2A) . Please refer to textbooks, such as that by van de Hulst, ¹¹ for background about light-scattering by small particles. The diffraction disc is centered around the direct retinal projection of the point source. Because this is true for all the particles, many diffraction discs overlap. Particles with larger sizes project smaller discs compared with particles with smaller sizes. The radius (the first 0) of an Airy disc is 1.22 λ/2r radian, with λ the wavelength of the incident light, and r the radius of the particle. One radian corresponds to 180/π°. The Airy pattern describes diffraction around a more or less opaque circular disc. The particles in the human eye lens can be assumed to be more or less transparent. Only the index of refraction is assumed to be different from its surroundings. The true scattering characteristic of such particles (the Rayleigh-Gans-Debeye approximation ¹¹ ) is somewhat different from the Airy type, with a radius of 1.43 λ/2r. For a wavelength of 0.56 μm in air, λ = 0.56 μm/1.336 (1.336 is the index of refraction of the vitreous), and the radius of the diffraction disc on the retina using this formula would be 24° for r = 0.724 μm. The Rayleigh-Gans-Debeye approximation was actually used in the present and previous studies. This bears virtually no connection, however, to the present discussion on the ciliary corona, because the difference between the two approximations affects only the intensity distribution, not the phase differences between the scattered waves. 

When the eye is looking at an ideally small point of light, different positions in the pupil of the eye are illuminated coherently (complete spatial coherence). True sources, of course, are never ideally small, but if the size is limited to the visual resolution limit of the eye, a high degree of coherence is obtained all over the pupil plane. In this way, all particles in the eye lens are illuminated with coherent light, and, as a consequence, all their retinal diffraction discs are coherent as well. Differences in depth of the particles are of little consequence with respect to coherence, because it is the total optical distance to the retina that counts. However, because all particles are at different locations, phase differences between the diffraction discs occur. This difference is illustrated in Figure 1by the scattered wavefronts emitted from the particles. Only at the center of the retinal projection do the wavefronts coincide. Away from the center, they do not coincide, and phase differences occur. 

Let us consider the case of two particles. The situation is then more or less comparable to the situation when using a retinometer. Two points in the pupil plane project a coherent light disc on the retina. Because of the phase differences on the retinal plane, interference fringes arise (Fig. 2B) . For a larger distance between the points in the pupillary plane, the fringes are narrower and vice versa. Two particles at distance (D) project two overlapping discs with a phase difference equal to 2πθ D/λ, with θ the visual angle in radians and λ the wavelength of the incident light. For two particles at a distance of 2 mm in the pupillary plane and a wavelength of 0.56 μm in air, the fringes of the resultant interference pattern would have a period of approximately 0.0002 radians (0.7 minutes of arc). This compares with the finest detail the human eye can resolve. In Figure 2B , the situation is exemplified for two particles with a distance (D) of 3.5 times their radius (r). When three particles combine, interference would result in three overlapping sets of such fringes (Fig. 2C) , corresponding to the three possible pairs of particles, and so forth. With many particles distributed over a 4-mm diameter pupil, the result would be a more or less random pattern of very fine dark and light spots, with spot sizes at the limit of visual resolution (Fig. 2D) . Thus, because of interference, the smooth Airy-like disc breaks up in spots. This is the case with monochromatic light. It can be argued that at a different wavelength, the whole spot pattern would be identical, apart from a scale factor corresponding to the ratio between the two wavelengths. The details of the spot pattern are dictated by the precise distribution of all scattering centers. To go further, with white light, the spots for the different colors that constitute white light would line up and form line segments. Many line segments would overlap, and it is no longer easy to argue what the resultant pattern would look like. 

Study Protocol

In the present study this summation of coherent Airy-like discs on the retina was studied by computer simulation MatLab software (The MathWorks, Natick, MA). The study adhered to the guidelines of the Declaration of Helsinki for research in human subjects. The outcome was compared to the subjective appearance of actual ciliary coronas. Subjects were asked to tell us about the details that were observed in the ciliary corona of their own eyes. For this, a bare 100-W halogen lamp was used, viewed on its smallest side (1.8 × 1.0-mm filament size), located 4 meters from the subject against a black background. The viewing condition was otherwise unrestricted. The intensity of this light was relatively easily to bear, with no adverse effects such as frequent blinking or excessive tearing. Approximately 20 individuals were asked for more global descriptions (appearance of “very fine needles,” presence of “weak colorations,” global extent) while wearing their habitual correction. Four ophthalmically normal subjects participated in a more elaborate process and systematic comparison. In these four subjects habitual correction was used, and also best correction with trial lenses, but this made no difference. Natural as well as dilated pupils were used. We tried to make the observations on the subjective appearance as quantitative as possible. This was possible with respect to the estimation of maximum extent of the corona (∼8°, see the Results section) and the ratio between inner and outer end of the line segments seen in the corona (∼0.7, see the Results section). The other observations remained qualitative (e.g., “bluish” end “reddish” end regions, needles being “very fine,” but “coarser” for smaller pupils. See the Results section). Their retinal stray-light values were measured quantitatively using a psychophysical approach, “the direct compensation method” described in the literature. ^{2 16} Their measured stray-light values are in the normal range for the respective ages. ⁴ In short, this method involves presenting a flickering ring to the subject. Because of light-scattering in the eye, part of the flickering light from this ring also reaches the center of the retinal projection of this ring. Because of that, the subject perceives a (faint) flicker in the center of the ring. With counterphase modulating light added to the center, this stray-light flicker can be silenced. The amount of counterphase-modulating light needed for silencing directly corresponds to the strength of retinal stray light in the respective individual. This approach was implemented in a noncommercial instrument, ¹⁶ as used in the present study, but recently a market instrument was manufactured by Oculus GmbH (Wetzlar, Germany). Main subjects were the three authors and one other member of the group. The stray-light values are given as the log stray-light parameter (log(s)) for 10° of visual angle ⁴ : subject MH, age 25, glasses OD sphere (S): −7.0, cylinder (C): −0.75, OS S: −6.75, C: −2.25, log(s) = 0.8; subject AR, age 31, glasses OD S: −1.75, OS S: −1.5, log(s) = 0.9; subject JC, age 31, glasses OD S: −4.25, OS S: −4.25, log(s) =1.0; subject TB, age 54, no correction (OD S: −0.75, OS S: −0.37), log(s) = 1.1. 

Results

Figure 2shows the patterns simulated for 1, 2, 3, and 30 particles. The 30-particle simulation is exemplified in Figure 2Dfor the (unrealistic) situation that the 30 particles are homogeneously distributed over an area with a diameter of 17 times their radius. This is unrealistic because, in fact, the particles are very tiny compared with the pupillary diameter, and, as a consequence, their diffraction discs are very large (24° for a particle of 0.724 μm) compared with the fine grain caused by interference. The size of the grain is as fine as the central part of the retinal point-spread function (for the pupil size used). Recall that in the Methods section the interference fringes for two particles at a 2-mm distance were shown to be 0.7 minutes apart. This grain size does not depend on the number or size of the particles. The grain in Figure 2Dwould have been virtually the same for different particle sizes or numbers, as long as the sizes were small compared with the pupillary diameter, and the particles were distributed more or less homogeneously over the pupil. We must note that, in fact, diffraction discs of very different sizes are combined because the particles in the eye vary considerably in size. ¹² Because of this, the typical Airy-like structure consisting of a central disc surrounded by rings gets lost. The combined effect is a monotonic decrease of the scattered light intensity with angular distance. The same decrease with angular distance was found with psychophysical stray-light measurement. ⁹ Because of the low intensities involved, subjectively we perceive the ciliary corona only over a few degrees, depending on the strength of the light source. Simpson ¹⁵ concluded from the limited size of the ciliary corona that the (in his time, hypothetical) particles should be smaller than 10 μm in diameter. Subjectively, the maximum extent of the ciliary corona in our laboratory was approximately 8° for the four subjects (MH 6.4, AR 8.6, JC 9.0, TB 10), whereas with psychophysical measurement techniques stray light can be assessed far beyond that. ^{1 2 16} Note that these values for the subjective extent of the ciliary corona increase with increasing stray light of the subjects (and age), as might be expected. 

Figure 3gives the simulation for an area of 4.6° × 4.6°, a pupil size of 0.2-mm diameter and particles with a wide size distribution around 0.724 μm. In fact, the precise size distribution is of little consequence for the characteristics shown in this figure. Figure 3Agives the simulation for 450-nm wavelength light, and Figure 3Bgives the same for 650 nm. As can be seen, wavelength has only a scaling effect. Precisely the same pattern is observed in Figures 3A and 3B , only sized differently. The scaling is in exact proportion to the wavelength size—in this case, in a ratio of 450:650. This scaling effect forms the basis for the line pattern perceived in the ciliary corona. Realize that the ciliary corona is observed when using white (broad-band) light. Each wavelength contained in that light projects a pattern like that in Figures 3Aor 3Bon the retina. All the spots in this pattern line up for the different wavelengths, and an abundance of radiating lines can be expected. Each line would be colored according to the wavelength spectrum, blue on the inside to red on the outside. However, many lines would overlap, since the spots from which they originate are very close together. Because overlapping lines all point in precisely the same direction (the center), the overlap does not disturb the expected fine line appearance. It is expected to changes the coloration, since differently colored portions are summed together. In fact it is expected that the coloration is very much desaturated compared with a true wavelength spectrum. To view the exact nature of these lines, and of the whole pattern of lines, computer simulation is helpful. The simulation is shown in Figure 4for equal-energy white light. The similarity to the subjectively perceived ciliary corona is striking. The simulation presented in the figure may differ from the actual corona, in saturation and contrast, because of printing and observation differences. 

The details in the simulated patterns were visually compared by many observers to what they observed around an actual point source of light (a halogen lamp at 4 m) on the basis of several criteria. All observers agreed that the simulation was, in a general manner, similar to the actual ciliary corona. Such aspects include the fineness and abundance of the needles, the fact that they are made up of line segments, the weak coloration, and the extent as mentioned earlier. Differences could include the level of saturation and contrast and the fact that true cilia seem to move all the time. It must be noted here that a comparison between entoptic phenomena and simulation can never really succeed. An important problem is that the dynamic span of our visual system (i.e., the differences in luminance that the visual system can cope with more or less reliably) is much greater than that of simulation devices (CRTs). In case the effect of some form of stimulation is to be simulated, the stimulus itself must be left out of the simulation. In our case, the actual light source could not be present in the simulation. Also, as explained earlier, the details of the corona depend on the precise particle distribution (their location), which is different for each individual. Moreover, with the pupil being in (slight) motion all the time for each individual, changing populations of particles contribute to the corona. This is the presumed explanation for the continuous movements observed by many subjects in the actual corona. At most, our model for the particle distribution is a statistical one, not one that describes actual location details. Moreover, the (statistical) particle size distribution varies somewhat between individuals as well. To gain more certainty about the true nature of the corona, the four main observers aged between 25 and 54 years had to make some observations of a more physical nature on sizes and coloration. But the results were remarkably similar between the different observers as well as between the observers on the one hand and the simulation (Fig. 4) . 

Each of the four observers had to judge explicitly the following (in addition to the extent mentioned earlier), also using artificial pupils and dilation: coloration, width, and length of the line segments (cilia). They all agreed on the following points: (1) The cilia seem to consist of separate line segments with weakly colored end regions. (2) The end regions closer to the center are bluish; the outer end regions are reddish. (3) The bluish end regions are closer to the center by about a factor of 0.7, compared with the reddish end regions. This is more or less proportional to the corresponding wavelengths (i.e., 450:650 nm). (4) Correspondingly, the line segments are proportionally longer if they are farther away from the center. (5) The cilia are very thin, close to the finest detail the eye can resolve. (6) Pupil size had the effect of the cilia being coarser for smaller pupil sizes (not shown in a figure). All this can be recognized by most normal observers in the subjectively experienced ciliary corona. Each of these six points was seen also in the simulations, suggesting correspondence to exist between subjective observation and the proposed explanation of the phenomenon. The readers are invited to judge for themselves points 1 to 5 in Figure 4 . 

One more observation was added. With monochromatic light, a spot pattern, instead of a line pattern, is to be expected. Looking through interference filters at the halogen lamp, indeed a spot pattern is seen, more coarse for long-wave light, in correspondence with Figure 3 . This observation is easily confirmed, by looking at a sodium lamppost at night. 

Discussion

Forward light-scattering is important in the human eye and has several sources. This study addressed the entoptic phenomenon of the ciliary corona as originating from light scattering by small particles. Another entoptic phenomenon, of direct relevance to the present study, is that of the “lenticular halo.” ¹⁵ The lenticular halo is a colored band, much like the rainbow, perceived surrounding a bright spot of light at a mean distance of 3° radius. The inference in this case is that it originates from the fibrous structure of the eye lens. ¹⁵ The model is that the lens fibers form a diffraction grating, arranged in a circular fashion, much like the spokes of a wagon wheel. ¹⁵ The grating constant derived from the angular distance of the lenticular halo corresponds neatly to the width (periodicity) of the lens fibers—hence, the inference. ¹⁵ In our study, the lenticular halo was a bit of a nuisance, because it can be quite bright compared with the ciliary corona. However the lenticular halo appears only with larger pupil sizes, depending on the subject. 

From the model simulations presented in this article, it seems clear that the detailed structure of the ciliary corona can be understood on the basis of coherent light-scattering by particles in the eye. The particle distributions may differ considerably between individuals. In particular, age changes in the eye lens may have a significant effect on particle distribution. One might have expected the appearance of the ciliary corona to be different between individuals and to change with age. Also, within one individual, differences can be expected with pupil size. Indeed, for any one individual the ciliary corona is not a very constant pattern. Its details seem to vary continually. In overall appearance though, it is constant according to the six characteristics listed earlier. Between individuals, there may be differences in precise detail, but not in overall appearance. Light-scattering and retinal stray light intensifies with age, due to increases in light-scattering particles, but the coherent summation on the retina is such that the line structure of the ciliary corona remains essentially the same. 

What do we know specifically about these particles and their change with age? The forward light-scattering data on donor lenses ¹² do not allow true identification. These data are consistent with some particle distributions (size and number), assumed to be protein particles. They already occur in young lenses, consistent with young individuals also experiencing the ciliary corona. ¹² The modeling suggested that the number of particles increases with age and the scattering increases per particle, because they grow larger (or maybe more dense), on average. ¹² From the light-scattering data we are not in a position to speculate on other potential changes such as, changes in the protein packing or in the cell surface interdigitations. Of particular interest in this respect is the morphologic search by Gilliland et al. ^{13 14} that led to the identification of candidate particles. They found these particles to be consistent with our theoretical analysis, since the transparent lenses were estimated to have approximately 500 particles per cubic millimeter in the nuclear core, a number that agrees with the analysis and sufficient to produce the phenomenon. 

One might expect that other small-sized disturbances in the eye also would add to the intensity of the corona, without changing its appearance. These disturbances could take the form of cells in the anterior chamber, structures in the anterior vitreous, deposits on the posterior cornea, and deposits on the anterior lens, among others. To take this argument further, one might also expect that these or other small disturbances, on their own, could give the appearance of a ciliary corona. Determining which small irregularities in the eye would be true candidates to add to the ciliary corona is a subject for further study. 

In conclusion, the simulated corona compared very well with what is actually perceived. The predicted patterns show details that are recognized by most normal subjects observing a point source. The ciliary corona can be modeled on the basis of coherent light-scattering by small particles in the eye (lens). This finding strengthens the earlier conclusion ¹⁰ that forward light-scattering by small particles in the eye lens is the dominant source of retinal stray light, especially at older age. 

 Supported by the Dutch Foundation for Technical Sciences (STW).

 Submitted for publication August 3, 2004; revised December 22, 2004, and March 24, 2005; accepted April 2, 2005.

 Disclosure: T.J.T.P. van den Berg, None; M.P.J. Hagenouw, None; J.E. Coppens, None

 The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked “advertisement” in accordance with 18 U.S.C. §1734 solely to indicate this fact.

 

Figure 1.

 

Representation of light-scattering by three particles in the lens, illuminated by an infinite point source of monochromatic light. Each of the three scattered waves is centered around the primary image on the retina. Because the waves arrive on the retina from different directions, phase differences as a function of retina location occur, giving rise to interference.

Figure 2.

 

Illustration of coherent combination of light-scattering by 1 (A), 2 (B), 3 (C), and 30 (D) particles. For clarity, the illustration shows unrealistically small particle distances compared with particle sizes. True particle distances/particle sizes are larger by a factor of 300, meaning that the fringes and grain in (B), (C), and (D) should be smaller by a factor of 300.

Figure 3.

 

Simulations for a 0.2-mm diameter pupil, realistic particle distribution, and monochromatic light. Simulation parameters: coherent combination of light-scattering by 1000 particles uniformly distributed over a 0.2-mm diameter area in the pupillary plane for monochromatic light of 450-nm wavelength (A) and 650 nm wavelength (B). Figuresizes are 4.6° × 4.6° of visual angle.

Figure 4.

 

Simulated ciliary corona for a distant point source emitting equal-energy white light. Simulation parameters: uniform random distribution over a 4-mm diameter pupil of 1000 light-scattering particles of ∼0.724 μm radius. Figure size is 4.6° × 4.6° of visual angle.