Piñero, David P.*; Ortiz, Dolores*; Alio, Jorge L.†
Scattering is a physical phenomenon inherent to light propagation through media with optical inhomogeneities, characterized by spatial variations in the refractive index.1,2 It is also an important phenomenon in the human eye, resulting in glare and hazy vision1,3–5 (Fig. 1). This phenomenon causes light deviation from the theoretical straight trajectory as a consequence of these inhomogeneities or non-uniformities in the medium through which it passes. It is due to a combination of diffraction, refraction, and reflection. An example of a scattering situation would be a light beam incident on a transparent object embedded in a medium of a different refractive index. In this specific case, part of the light would be reflected by the object surface, some would be refracted by the surface and would pass through the surface in a forward direction and some would be reflected inside the object a number of times and would be refracted afterward, either backward or forward. In addition, light outside the object but near its edge would be diffracted in a forward direction. All this results in degradation of the final quality of the image. Such local disturbance to the wavefront must be discriminated from general shape errors of the wavefront, as can be described with lower and higher order aberrations. These lead to blur and defocus for any imaging optical system. However, the term “scattering” is normally used only to describe these optical effects generated by refractive index variations or inhomogeneities on a microscopic scale, specifically on the scale of the order of the wavelength of light.2 This kind of inhomogeneity causes the light rays to spread over much larger angles compared to wavefront aberrations and cannot be detected with the currently available wavefront sensors. To understand visual function, this type of scatter must be differentiated from the effects of classical low and higher order wavefront aberrations.5,6
According to physical theory, the scatter component due to microscopic inhomogeneities is dependent on a number of factors.2 Intensity and direction of scattered light are a function of the scattering properties of the media and the wavelength of the incident light.2 According to the Mie theory, the intensity and direction of scattered light by an isotropic, homogeneous and spherical particle can be calculated using the following mathematical relationship, assuming a flat monochromatic incident wavefront and a homogeneous surrounding medium2,7:
where Is is the intensity of scattered light, s, the scattering coefficient of the particle for which Mie derived exact formulas, I0, the intensity of incident light, λ, the wavelength of light, and d, the position where the scattering is measured.
Equation (Uncited)Image Tools
Is and s parameters are a function of three parameters, the angle of incident light (θ), x, and m. x and m are calculated with the following expressions:
where D is the diameter of the spherical particle, n1, the index of refraction of the particle, and n2, the index of refraction of the surrounding media.
Equation (Uncited)Image Tools
It should be considered that Mie theory is rigorous for spheres and correct for any size, but there are simpler solutions for specific or particular situations, which are common. This is the case of Rayleigh scattering theory, which is only correct for small particles, with a diameter of less than one tenth the wavelength of the incident light.2 It can be deduced from the Mie theory assuming such condition for the scattering particle. This and other approximate theories have successfully explained light scattering results from the human eye lens but after exact solutions have been applied.8–10 However, other inhomogeneities with non-spherical shape are possible, and the angular distribution of scattered light may not be well predicted by the Mie theory. In addition, the complexity increases if the light is scattered more than once.2
In the human eye, scattering and optical aberrations are important phenomena responsible for the degradation of optical quality.6–8 A vast literature on this subject exists. Some selected references are given here.11–20 Small particles, foreign bodies, density fluctuations, surface roughness of the different ocular optical elements can be considered as non-uniformities that can act as potential microscopic scatterers. It should be considered that the cornea and lens consist of cells and connective tissue, which can contain inhomogeneities on the scale of the order of the wavelength of light. These microscopic inhomogeneities are able to reduce the retinal image quality, inducing a veil of straylight over the retina. In the eye, it has been found that 1.4 μm diameter particles in the lens,9,10 later suggested to be multilamellar bodies,8 could account for a great part of the observed forward scattering.3 However, wavefront aberrations are also a source of optical degradation. Therefore, the light distribution in the retinal image [point spread function (PSF)] is the consequence of the conjugated effect of light scatter induced by microscopic inhomogeneities and classical wavefront aberrations together. In ophthalmology and optometry, the most important scattering component to analyze is the forward scattering, which represents the scattered light that reaches the retina with the potential of inducing a veiling illuminance superimposed on the retinal image reducing retinal contrast.17 The backscattered light is typically used only to assess the quality of ocular tissues (e.g., slit-lamp examination).21,22
No back and forward scattering would be found in an ideal eye with totally clear and perfect optical surfaces. However, the human eye is an imperfect optical system and it is affected by diffraction, aberration, and scatter. Therefore, the scattering phenomenon is an additional limiting factor for the resolution of the ocular optical system and its evaluation should be also considered in the clinical practice. The cornea21,23–26 and crystalline lens9,10,16,27–38 are sources of back and forward scattering, especially when their transparency has been significantly affected.8,14,19,22,35,39–51 The increase in the magnitude of forward scattering, when a corneal or lenticular opacity is present, can induce a significant reduction in the retinal contrast and a limitation of visual performance. Indeed, visual function limitations in relation to the increase in ocular scattering have been detected in patients with cataract17,52–54 and corneal haze55–57 (Fig. 2). However, cornea and crystalline lens are not the only causes of ocular scattering. There are other ocular elements and factors contributing to the global level of scattering (Fig. 3).
The iris and sclera are also two potential sources of forward scattering. Although their function is to prevent light entering the eye, they are not totally opaque. Light can partly pass through the iris and sclera depending on the level of pigmentation and density of these structures, generating intraocularly scattered light.4,58,59 In subjects with high pigmentation (brown eyes), the contribution of the iris and sclera to the global level of ocular scattering will be minimal whereas it will become more significant for subjects with less pigmentation.
The retina can also be a source of scattering. Light is not only absorbed when reaching this structure but also part of this light is reflected to different retinal areas that contributes to intraocular scattering.4,58 This type of scattering is especially dependent on the level of pigmentation of the subject. Finally, the vitreous humor scatters light, but studies on its scattering effects in patients are lacking. In normal conditions, this element is a transparent gel because of the regular structure of its fibrils. However, in pathological conditions, the transparency of this element could be severely affected, becoming an important source of scattering. If blood, cells, or other byproducts of inflammation get into the vitreous, they could act as non-uniformities inducing scattering. Posterior uveitis or retinal hemorrhages are examples of pathologies that could induce vitreous cloud and then significant scattering.
In general terms, any ocular condition affecting the transparency of any optical element of the eye is accompanied by an increase in ocular scattering. Indeed, higher levels of ocular scattering have been observed in elder patients,53,59–61 after corneal surgery22,23,39–40,42,43,44,55–57,62 and also in some pathological processes.63–65
Considering the potential sources of forward scattering existing in the human eye, the intraocular forward scattering can be defined as the sum of the scattering components induced by each of these sources. From a theoretical point of view, an additive model for the calculation of the total ocular forward scattering can be defined4:
where sc, scr, sop, sv, and sr are the scattering components associated with the cornea, crystalline lens, theoretically opaque structures (iris, sclera), vitreous and retina, respectively, and θ is the scatter angle, which is the difference between the angle of light incidence into the eye and the angle of observation.
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As can be seen in the previous expression, the scattering is highly dependent on the scatter angle.17,60,61 All the scattering components associated with each ocular element are clearly dependent on this angle.4,17,26,58,61,66–68 Indeed, the percentage of back or forward scattered light varies as a function of the angle of light incidence. Backward scatter would be clinically more meaningful, if it were predictive of forward scattering. Several studies have looked into this. However, results show that backward scatter does not predict forward scattering to a large extent47 and that in the lens essentially different light scattering processes govern backscatter when compared with forward scatter.38
There are several instruments providing coefficients that attempt to characterize ocular scattering, but most of them are indirect measurements or do not have clinical validation. There is a lack of standardization for the measurement procedure of scattering and there are no standard criteria for defining those parameters that should be used for the characterization of ocular scattering. In the current review, we attempt to summarize the contribution to ocular scattering provided by different authors as well as the different devices developed to characterize ocular forward scattering.
IMPACT OF OCULAR SCATTERING ON QUALITY OF VISION
The negative effect of scattering on vision quality is widely recognized. Indeed, it has long been accepted61,62,69,70 that an increase in intraocular scattering may be one of the most important causes of glare complaints because it causes a considerable degradation of visual function (Fig. 1). Specifically, the intraocular scattering phenomena can produce visual problems, such as difficulties in night driving and extreme photophobia. Even in low light conditions, there can be problems with recognizing faces or objects, or with hazy vision. Additionally, contrast sensitivity could be clearly compromised, even in photopic conditions.70,71
Relation Between Scattering and the PSF
Scattering can be mathematically connected with some ocular optical quality parameters, as the PSF.5 The PSF is the light distribution on the retinal image that corresponds to a point object. Fig. 4 gives the central portion (note the arcminute scale) of the PSF obtained with a commercially available double-pass (DP) device. As can be seen, such presentation of the PSF is extremely limited, especially for the illustration of the effect of the scattering on the retinal image. It should be considered that the present article concerns the areas at large distances around it, clearly not visible using this technique. It is well accepted that the external contour (covering the area within 1 and 90°) of the PSF distribution corresponds to the scattering effect.60,61,68 This external contour receives ∼10% of light reaching the retina.4 It should be considered that the PSF at ∼10° drops off in proportion to the inverse square of the angle (Stiles-Holladay's approximation).5,60,61 On the contrary, ocular wavefront aberrations have their main effect on the central area of the PSF.
Between 1 and 90°, the relationship between PSF and intraocular scattering could be characterized by the equation4:
where s is the scattering coefficient (in degree2/sr), and θ, the visual angle in degrees.
Equation (Uncited)Image Tools
This formula has general use. By using this definition, the scattering coefficient changes weakly with angle and also for corneal and lenticular turbidities.17,72
The s parameter does not depend much on pupil size if cornea and lens are not pathological and they maintain their normal transparency (homogeneous scattering coefficient on all optical media and no other elements inducing scattering in the eye). However, the scattering phenomenon is not uniform over the pupil area because of the presence of different factors modifying its contribution to the PSF as a function of pupil size.68 One of these factors is the level of scatter induced by light passing through theoretically opaque structures as sclera or iris. This kind of scatter adds a more or less isotropic veil of light on the retina, which is dependent on the material properties of iris and sclera. This component contributing to the ocular scattering becomes increasingly important with smaller pupils.68 Other factors contributing to the scattering variability in terms of pupil size could be, for example, the zonule area that holds the crystalline lens or the vitreous inhomogeneities.68
In a more refined model, based on healthy eyes and not considering the cornea and the crystalline lens as the unique sources of scattering, the relation between pupil size and scattering has been defined as follows68:
This expression characterizes ocular light scatter considering the effect of sclera and iris, where a and b are experimental parameters that characterize the intraocular scattering, p, the pupil size, EHA, equivalent hole area, PA, pupillary area, and θ, the incident angle.
Equation (Uncited)Image Tools
This mathematical model is not valid to characterize the impact of intraocular scattering on the PSF in those eyes with variable light dispersion in each of their ocular scatterers (presence of localized inhomogeneities with different geometry and refractive index). In those cases, the relationship between scattering and pupil size will become more complex, necessitating new models to characterize such relationship.
Relation Between Scattering and Subjective Complaints
Forward-scattered light in the eye produces a veiling light over the retina and a reduction of the retinal contrast, whereas back-scattered light theoretically only reduces the amount of light reaching the retina.1 The effect of forward scattering may be partly mitigated by the directional sensitivity of the photoreceptors, known as the Stiles-Crawford effect (light entering the eye via the center of the pupil is about five times more effective than light entering via the border of the pupil).73,74 This physiological effect relates mainly to the cones and then it is mainly a photopic phenomenon. It does not greatly reduce the effects of scattered light under low light level conditions.1
The forward scattering induces disability glare which is the perception of a veil of light when a strong light source is presented in the field of view.3,69,70 Disability glare induces an almost complete blindness close to the light source and a hampered visual performance further away.4,60,61 This kind of visual complaint is in direct relation with the angle between the line of sight and the glare source (the angle of light incidence), and also with age,50 as happens with the optical magnitude of ocular scattering. A specific expression was developed by the Commission Internationale de l'Eclairage for defining the relationship between disability glare on the one hand, and age, pigmentation, and angle on the other, also considering the Stiles-Crawford effect, for normal eyes.60 A simplified version is3,60:
where Lveil is the luminance of the veiling background in cd/m2, Eglare, the illuminance at the eye by the glare source in lux, and θ, the angular distance in degrees between the line of sight and the glare source. This expression is valid in the conventional angle domain between 1 and 30°. It gives a population-average value, and it must be noted that interindividual differences are significant, also within the normal population.
Equation (Uncited)Image Tools
METHODS FOR MEASURING THE OCULAR SCATTERING
The definition of a standard procedure for measuring and describing ocular scattering is still an ongoing issue. The Zernike polynomial expansion is used as the mathematical standard for describing ocular aberrations and some devices were developed for this purpose. In addition, several methodologies have been described and used to measure or quantify back and forward intraocular scattering,51–58 using different coefficients and calculations, which cannot be compared. For example, some of these devices provide an estimation of the ocular scattering for different angle domains. Therefore, there is no general agreement about the parameters and conditions that should be used for evaluating the scattering phenomenon in the human eye in a standardized way. In addition, several devices described for measuring ocular scattering have not been validated in clinical practice or they have demonstrated a limited accuracy.
The first criterion for classifying the methods of measuring the ocular scattering is the type of scattered light analyzed: back or forward scattering. As noted, the most important component is forward scattering, and the main focus here is to review procedures for measuring intraocular forward scattering. However, the analysis of backscattered light in the eye should be mentioned because it has been shown to be useful in providing information about the transparency and quality of ocular tissues. Several procedures have been developed for analyzing in vivo backscattered light by the cornea or the crystalline lens by means of a digital analysis of the images obtained with a slit lamp or a Scheimpflug camera.21–25,28,31,34,36,37,39,40,43,49,50,54,55,57 In addition, Bueno et al.12 developed a system for quantifying backscattered light by the anterior segment (including cornea and lens) by means of the digital analysis of the fourth Purkinje image. This specific procedure was successfully first tested in an artificial eye and later in normal eyes wearing customized contact lenses inducing different amounts of scatter.12
Both psychophysical and optical methodologies have been developed to measure intraocular forward scattering. In psychophysical procedures, the assessment is dependent on the patient's performance but is more meaningful in that it relates to actual vision function. In contrast, the optical procedure is less dependent on patient response and has a limitation in the angular domain, providing a less functional measure.
Psychophysical or Functional Measurements
The Compensation Comparison Method
The most relevant psychophysical procedure described for measuring intraocular forward scattering is the compensation comparison method. This procedure75 is the basis for the development of a commercially available device, the C-Quant, manufactured by Oculus (Oculus Optikgeräte GmbH, Wetzlar-Dutenhofen, Germany). This method was developed to overcome the limitations of a previous method (direct compensation method), which was an initial psychophysical procedure developed for measuring ocular scattering.76 A stimulus similar to the one used in the direct compensation procedure (central and peripheral light) is presented to the subject, but the central field of the test is divided into two halves in the compensation comparison method (Fig. 5). The task of the subject in the direct compensation method is to compare different stimuli sequentially whereas in the compensation comparison method, the two central stimuli are presented simultaneously to be compared by the subject.
The stimulus light is presented in the peripheral ring (flickering light presented in the peripheral ring of the stimuli), which is scattered by the ocular components into the central area, modulating the brightness of the two central half-disks. The compensation light is presented in one of the two central halves (randomly chosen) (field B), and it is modulated at the same frequency in counter-phase with the peripheral stimulus, whereas no compensation light is presented in the other half (field A) (Fig. 5). As a result, the two halves flicker, and in general will differed in perceived modulation depth: one resulting from the scattered light (field A) and the other resulting from the combination of the scattered and the compensation light (field B) that flickers in counterphase with the scattered light.75 The variable modulation of the compensation light makes its half appear to flicker more or less than the unmodulated half, depending on the brightness of modulation. During testing procedure with this method, a series of limited-duration stimuli are presented differing in the amount of compensation light presented in the field B. The task for the subject is to decide for each stimulus which half of the test field flickers more strongly.75 The subject's responses are recorded by means of two push buttons, representing the left and right test fields.
A psychometric curve (Fig. 6) is fitted to the subject's responses, using a psychophysical model for this flicker comparison task. The straylight parameter s (an estimation of the intraocular scattering, defined above in Eq. 4 as “scattering coefficient”) and a measure for the measurement quality is derived from this curve.75 A 2- alternative forced-choice psychophysical method (2AFC) is used for recording subject responses. With this method, the subject indicates a choice even when there is no perceived difference between the two halves, and as the number of trials increases each half will be chosen ∼50% of the time. Presented stimuli depend on previous responses and after finishing the procedure, all responses are used to calculate the horizontal position of the psychometric curve (Fig. 6). The fitting process of this curve makes use of a maximum-likelihood procedure (the best-fitting psychometric function is the one that gives the highest total-likelihood value of a certain answer against the magnitude of the stimulus).77 An individual-specific measurement quality criterion can be used to check and reinstruct or to exclude measurements. This is the main advantage of the compensation comparison technique with respect to the previous direct compensation technique. Recently, it has been shown that this psychophysical technique provides a measure of straylight that is compatible with those made by laboratory optical methods (not those described below).5
Using the C-Quant device and then the compensation comparison method, the scattering can be quantified by means of the parameter “s,” called the straylight parameter. The straylight value s lies at half the value of the 50% point of the psychometric curve and then is located 0.3 log units below this 50% point5,75 (Fig. 6). This value is obtained by the ratio between the scattered light and the intensity of the luminous stimulus that plays the role of scattering source. The parameter “s” is usually expressed in log units. The higher the log(s) value, the higher the intraocular magnitude of forward scattering. Previous published studies41,53 using this method found that the mean value for this parameter in healthy eyes and young patients is around 0.9. This value will start to increase from 40 years old until mean values of 1.2 at 70 years old and 1.4 at 80 years old.41 With cataract, this value can reach values around 2 or higher.
This psychophysical procedure allows measuring the scattering at large eccentricities, when the scattering has a significantly higher potential for degrading the retinal image. This is an additional advantage of this kind of procedure.
Other psychophysical procedures have been described for the measurement of ocular scattering, as the indirect measurement by analyzing the reaction time or the use of the halometer.
The reaction time, which is defined as the time interval between the presentation of a stimulus and the subject's response, is one specific concept proposed for the evaluation of intraocular forward scattering.78 It is assumed that this time is significantly affected when a high magnitude of intraocular scattering is present. The patient should indicate when is able to discriminate different sinusoidal gratings in a specific glare condition. A numeric parameter is estimated for quantifying the intraocular scattering, known as the diffusion factor, which is calculated with the following expression78:
where GE is the glare effect and Eg, the illuminance on the eye used for inducing the glare effect. GE is calculated according to the following expression:
Equation (Uncited)Image Tools
where Yg is the reaction time with glare and Ywg without glare.
Equation (Uncited)Image Tools
This specific psychophysical procedure for evaluating the intraocular scattering has not been validated clinically. It should be tested in a large sample of patients, including eyes with large amounts of scattering (cataracts, corneal haze …).
Another psychophysical device that could be useful for evaluating the effect of intraocular scattering is the halometer. This instrument was designed specifically to measure the halo effect.79,80 However, a halo is not only the consequence of ocular forward scattering but also of ocular wavefront aberrations. Therefore, it is difficult to differentiate with accuracy the isolated effect of ocular scattering. It is useful for obtaining an idea of the quality of vision for a specific case.
Comparative Analysis of Hartmann-Shack Wavefront Sensor and DP System Evaluation
The DP technique (Fig. 7) was proposed as a method to estimate retinal image quality half a century ago. The technique is based on the recording of the retinal image after DP through the ocular media and retinal reflection.81–88 This methodology demonstrated the ability to provide accurate estimates of the eye's image quality.81–88 From the images obtained with this system, the ocular modulation transfer function (MTF) can be calculated. This function represents the loss of contrast produced by the eye's optics on a sinusoidal grating as a function of its spatial frequency (Fig. 8). This function (MTF) provides information about the small-angle global optical quality of the eye, including all aberrations and diffraction.85,89
The Hartmann-Shack (HS) sensor is the most commonly wavefront sensor used today, and it is the basis for most of the clinical devices for measuring ocular aberrations currently.90,91 This system consists of an equifocal microlens array, conjugated with the eye's pupil, and a camera placed at the focal plane of the microlenses (Fig. 9). If a distorted (i.e., aberrated) wavefront reaches the sensor, the pattern of spots or centroids is irregular. The displacement of each spot with respect to the ideal position is proportional to the derivative of the wavefront over each microlens area. Although these wavefront sensors are extremely useful, their main drawback is the poor precision in cases of significant higher-order aberrations and scattering because of limitation imposed by the microlens sampling (typically more than 100 μm apart).
The comparison of the MTF derived from a wavefront sensor and the MTF derived from a DP system is interesting. Shahidi and Yang92 described a complete system to do so, and referenced older sources about the same idea. The MTF obtained with a DP system provides information surpassing HS systems. It includes optical errors involved in retinal image degradation, aberrations of the highest orders, missed by HS systems. Often this difference is called “scattering,” but it must be realized that this is different from the scattering discussed above, because it is limited to small angles. We will call this difference “DIPminHS” (Fig. 10). It is assumed that the contribution of diffraction is minimal, considering the magnitude of the normal pupil size at different ages.
A numerical index for quantifying the magnitude of DPminHS was defined using this comparative methodology. For calculating this index, the Strehl Ratio (SR) is used as a single metric to compare the estimates of image quality provided by both methods. The SR is a parameter commonly used for estimating the overall optical quality, defined as the ratio of the intensity at the peak of the image formed by an aberrated optical system to the intensity of the aberration-free system. The relative difference of the SRs provided by the two methods (SRHS−DP) accounts for the difference between both DP and HS methods, which is assumed to be in direct relation with the magnitude of intraocular scattering,89 but, as commented before, it must be realized that this concept of scattering is different from that discussed above, because only small angles are considered:
where SRHS and SRDP are the SRs obtained with the HS and DP systems, respectively.
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The SRHS−DP coefficient ranges from 0 to 1. The value 0 would be associated with identical HS and DP contributions and, an eye only affected by low and mid-order aberrations. In contrast, the value of 1 will be associated theoretically with a complete lack of transparency, with the scattering as the predominant factor.89
Statistically significant differences were found in this coefficient of SRs between normal subjects and patients normally affected by abnormal increases of intraocular scattering (post-LASIK, cataract).93 Furthermore, Díaz-Doutón et al.89 found a mean value of the SRHS−DP coefficient of 0.188 for a 2-mm pupil in a sample of normal young subjects. In this study, the data dispersion was small, providing both HS and DP systems similar estimates of the image quality in normal young eyes. A different situation was observed in a sample of elderly patients with early signs of cataract (mean SRHS−DP: 0.512 ± 0.094 for a 2-mm pupil). The HS system provided an estimate of the retinal image significantly better than the measurement obtained with the DP system. Therefore, in eyes significantly affected by scattering the wavefront analysis may produce an overestimation of the image quality. Other types of eyes also showed differences between the HS and DP image quality estimations in this study: post-LASIK (mean SRHS−DP: 0.36 ± 0.14 for a 2-mm pupil) and intraocular lens-implanted eyes (mean SRHS−DP: 0.38 ± 0.15 for a 2-mm pupil). In all these cases, a high variability in the value of the SRHS−DP coefficient was reported. This variability could be explained by several factors as differences in the degree of corneal haze or differences in the severity of posterior capsule opacification.89
Regarding this methodology, it should also be considered that in conditions of high intraocular scattering and also in aberrated eyes, the spots of lights could appear much distorted as a consequence of scatter and aberrations, being difficult to determine their exact position. This could be a source of bias in the final determination of wavefront aberrations and scattering and therefore a limitation of this optical method.
Other approach to the measurement of ocular scattering is the analysis of the PSF obtained with a simple DP system. Quantitative indices can be derived considering that the theoretical effect of scattering is limited to the peripheral area of the PSF obtained with a DP system. However, it should be considered that the PSF obtained with this methodology is limited to small angles (within minutes of arc range). This is the basis of a commercially available device, the OQAS system (Visiometrics SL, Terrassa, Spain),94 which has adopted the DP procedure for this kind of measurements. The manufacturer proposes a parameter called Ocular Scattering Index for quantifying theoretically the effect of ocular scattering. This parameter is obtained using a proprietary algorithm based on the analysis of the external contour of the PSF distribution. However, to our knowledge, this Ocular Scattering Index has not been clinically validated.
This DP-based procedure is only valid for angles in the range of arcminutes81,82,95,96 and is only able to measure the magnitude of scattering in the most favorable optical conditions, i.e., a small angular distance between the line of sight and the light source (near angle scatter). In these conditions, the effect of scattering is almost 0. This is one of the limitations for this kind of procedures and also for the comparative analysis between DP and HS systems.
Other limitation of these procedures is the interpretation of the PSF for obtaining an estimation of intraocular scattering. It is assumed that the peripheral contour (covering the area within 1 and 90°) of the PSF is mainly because of intraocular forward scattering. The normal PSF drops four orders of magnitude (a factor 10,000) over 12 min of arc, 6 orders down at 1° and almost 10 orders at 90°.5 Therefore, a small part of the effect of aberrations on PSF could be considered as scatter, especially when significant amount of lower and higher order aberrations are present. Depending on the analysis performed, the lower order aberrations could contribute to the value of the scattering index, producing a potentially misleading interpretation of the optical performance of the analyzed eye.
In addition, it should be considered that the use of middle wavelength (green-yellow) is mandatory for proper assessment of DP images.81,82,95,96
Analysis of Light Spot Images Obtained with a Hartmann-Shack Sensor
This method was initially designed for quantifying and localizing the lenticular forward scattering. Because the microlens array of an HS system is optically conjugate to the anterior lens surface (pupil plane), a localized lenticular source of scattering will affect a limited number of spots or centroids in the final image (Fig. 11). The analysis of these light spots affected by the scattering source will provide information about the localization of such source and the level of forward scattering induced by it (Fig. 11).
Donnelly et al.47 defined five different forward scatter metrics that could be obtained by analyzing the light spot pattern obtained with the HS system: maximum mean for all PSFs in the HS image (Max_Mean), maximum standard deviation for all PSFs in the HS image (Max_SD), maximum pixel value in the HS image (Max_Max), mean of means for all PSFs in the HS image (Mean_Mean), and mean standard deviation for all PSFs in the HS image (Mean_SD). All these metrics could be calculated from the brightness of pixels within an area containing each lenslet's PSF tail, which is called the pixel neighborhood.47 A pixel neighborhood was defined as the square perimeter surrounding the central location (centroids) of each PSF of total pixels M determined by average centroids spacing. To emphasize pixel information within the tails of the lenslet PSFs (corresponding to each microlens), a pedestal threshold (large gray disc filling the pupil area) is calculated to minimize the effect of non-lenticular scattering that affects all lenslets. Considering all these issues, the following calculations were described for the obtaining of these five metrics of forward scattering47:
* first step—calculation of these intermediate parameters considering that each pixel in the neighborhood has a value p based on the number of photons captured at pixel location (i,j) and that N is the number of PSFs in the HS spot pattern.
* Sum of all pixel values within a lenslet PSF neighborhood excluding the center,
* The sum of the squares of sum_n,
Equation (Uncited)Image Tools
* The mean pixel value within a lenslet PSF neighborhood,
Equation (Uncited)Image Tools
* Standard deviation of the pixel values within a lenslet PSF neighborhood,
Equation (Uncited)Image Tools
* Maximum pixel value within a lenslet PSF neighborhood,
Equation (Uncited)Image Tools
* second step—calculation of the following five scattering metrics:
Equation (Uncited)Image Tools
Cerviño et al.97 demonstrated that Max_SD was a repeatable parameter in model and human eyes. This methodology was demonstrated to be strong against realignment and misalignment as well as sensitive. In addition, these same authors also found a correlation of 69% between functional (C-Quant) and this objective measurement of scattering (Max_SD).97
As a limitation of this kind of procedure for quantifying the forward scattering, it should be mentioned that it is only able to detect lenticular scattering sources,98 not analyzing all ocular sources of scattering.
Analysis of the Degree of Polarization of Light Emergent from the Eye
This procedure was described by Bueno et al.99 as an additional procedure for the estimation of intraocular scattering. This procedure is based on measuring the degree of polarization of the light in images formed after a double pass through the system by means of a dual apparatus composed of a modified DP imaging polarimeter and a wavefront sensor. It should be considered that the light depolarization in an optical system is related to the scattering.100 Indeed, the degree of polarization was found to be well correlated with the level of scattering in theoretical simulations but this method has never been used for clinical purposes. As this method relies on the reflected PSF from the fundus, it should be considered that the DP artifact of light spreading in the deeper layers, especially for red light, can be a source of error.
SUMMARY AND CONCLUSIONS
Intraocular forward scattering is an optical phenomenon generating a degradation of the retinal image, as do ocular aberrations or diffraction. A distinction must be made between classical light scattering, which is scattering over large angular distances, typically 1 to 90°, and light spreading over minutes of arc, which is dominated by aberrations. Several ocular elements, e.g., the cornea or the crystalline lens, act as sources of scatter and contribute to the global magnitude of ocular scattering. This phenomenon is especially relevant in specific situations, such as pathologies or after several types of surgeries, because the ocular media transparency and/or the regularity of the optical surfaces of the ocular system could be affected. In such cases, the determination of the level of ocular scattering is important for a better understanding of the visual performance of the patient. For example, the measurement of ocular scattering can be quite useful for detecting some prepathological situations as well as for understanding some photic phenomena or night vision disturbances reported by several patients with specific ocular conditions. Table 1 summarizes the main clinical applications for the measurement of ocular scattering.
Different methodologies have been described and proposed for quantifying the magnitude of ocular scattering. However, few clinical reports have been published validating these kinds of systems for clinical practice. The compensation comparison method is the only method that has been validated in different kinds of subjects using large samples sizes. This method has been comprehensively studied and a range of normality for the scattering parameter estimated with this methodology has been obtained. This is advantageous because it allows the clinician to detect those cases with scattering levels outside of the normal ranges, which is extremely useful for clinical practice. Another advantage is the possibility of measuring the level of intraocular scattering for large eccentricities (wide-angle scatter), which can be particularly relevant for visual performance. In contrast, the main disadvantage of this methodology is its dependence on patient's response, as in any psychophysical procedure. This makes the measures dependent on the cooperation and ability of subjects to provide reliable responses. In such cases, the procedure can be time consuming.
However, optical approaches provide a more independent measurement of ocular scattering, not dependent on subject responses. All are based on a DP system or an HS wavefront sensor, or both together. These kinds of methods for measuring scattering have the limitation of providing estimations of scattering for a small angle domain, where the level of scattering is minimal. In addition, some devices, especially those based only on the double pass system, provide estimations of scattering based on the analysis of the PSF and assuming that its external contour is only because of the scatter. These assumptions are not accurate in all cases, especially in highly aberrated eyes. No studies with large samples have been performed with these optical methodologies for measuring ocular scattering. Therefore, normal ranges have not been defined, limiting their utility as screening methods. In the future, studies in different kind of populations should be performed and reported to implement the clinical application of this methodology.
In general terms, there is an additional disadvantage for all these procedures, both psychophysical and optical: there is a lack of standardization in the conditions and parameters that should be used for providing a general description of the ocular scattering. Each measuring device provides its own mathematical parameter defining the level of scattering. Standard criteria for characterizing scattering should be defined, as has occurred with the description of optical aberrations using Zernike polynomials. This standardization is crucial for the introduction of scattering measurements in clinical practice as a common and useful tool in different diagnostic procedures.
Ocular scattering is an important factor that should be considered when evaluating ocular optical quality. With the study of this parameter and aberrations, clinicians will be able to provide explanations for visual disturbances by providing a more complete description of ocular optical performance. More studies on the application of measurement methodologies and a standardization of the description of scattering are needed.
We thank the contribution of the reviewers and the editorial board of the Optometry and Vision Science to the content of this article. Their help has been crucial for the development of this review.
David P. Piñero Llorens
Avda de Denia s/n, Edificio Vissum
03016 Alicante, Spain
1.Atchinson DA, Smith G. Optics of the Human Eye. Oxford, UK: Butterworth-Heinemann; 2000.
2.Van de Huslt HC. Light Scattering by Small Particles. Mineola, NY: Dover Publications; 1981.
3.Vos JJ. On the cause of disability glare and its dependence on glare angle, age and ocular pigmentation. Clin Exp Optom 2003;86:363–70.
4.van den Berg TJ. Analysis of intraocular straylight, especially in relation to age. Optom Vis Sci 1995;72:52–9.
5.van den Berg TJ, Franssen L, Coppens JE. Straylight in the human eye: testing objectivity and optical character of the psychophysical measurement. Ophthalmic Physiol Opt 2009;29:345–50.
6.Mrochen M, Semchishen V. From scattering to wavefronts—what's in between? J Refract Surg 2003;19:S597–601.
7.Mie G. Beitrage zur optik truber medien, speziell kolloidalen metalosungen. Ann Phys 1908;25:377–45.
8.Costello MJ, Johnsen S, Gilliland KO, Freel CD, Fowler WC. Predicted light scattering from particles observed in human age-related nuclear cataracts using Mie scattering theory. Invest Ophthalmol Vis Sci 2007;48:303–12.
9.van den Berg TJ, Spekreijse H. Light scattering model for donor lenses as a function of depth. Vision Res 1999;39:1437–45.
10.van den Berg TJ. Light scattering by donor lenses as a function of depth and wavelength. Invest Ophthalmol Vis Sci 1997;38:1321–32.
11.Pérez GM, Manzanera S, Artal P. Impact of scattering and spherical aberration in contrast sensitivity. J Vis 2009;9:19.1–10.
12.Bueno JM, De Brouwere D, Ginis H, Sgouros I, Artal P. Purkinje imaging system to measure anterior segment scattering in the human eye. Opt Lett 2007;32:3447–9.
13.Westheimer G, Liang J. Influence of ocular light scatter on the eye's optical performance. J Opt Soc Am (A) 1995;12:1417–24.
14.De Brouwere D, Ginis H, Kymionis G, Naoumidi I, Pallikaris I. Forward scattering properties of corneal haze. Optom Vis Sci 2008;85:843–8.
15.Kim KB, Shanyfelt LM, Hahn DW. Analysis of dense-medium light scattering with applications to corneal tissue: experiments and Monte Carlo simulations. J Opt Soc Am (A) 2006;23:9–21.
16.Tang D, Borchman D, Schwarz AK, Yappert MC, Vrensen GF, van Marle J, DuPre DB. Light scattering of human lens vesicles in vitro. Exp Eye Res 2003;76:605–12.
17.de Waard PW, Ijspeert JK, van den Berg TJ, de Jong PT. Intraocular light scattering in age-related cataracts. Invest Ophthalmol Vis Sci 1992;33:618–25.
18.Fukaya Y, Hara T, Iwata S. Light scattering caused by cells on the intraocular lens. J Cataract Refract Surg 1988;14:396–9.
19.Delaye M, Clark JI, Benedek GB. Identification of the scattering elements responsible for lens opacification in cold cataracts. Biophys J 1982;37:647–56.
20. Andreo RH, Farrell RA. Corneal small-angle light-scattering theory: wavy fibril models. J Opt Soc Am 1982;72:1479–92.
21. Patel SV, Winter EJ, McLaren JW, Bourne WM. Objective measurement of backscattered light from the anterior and posterior cornea in vivo. Invest Ophthalmol Vis Sci 2007;48:166–72.
22. McCally RL, Freund DE, Zorn A, Bonney-Ray J, Grebe R, de la Cruz Z, Green WR. Light-scattering and ultrastructure of healed penetrating corneal wounds. Invest Ophthalmol Vis Sci 2007;48:157–65.
23. Lohmann CP, Fitzke F, O'Brart D, Muir MK, Timberlake G, Marshall J. Corneal light scattering and visual performance in myopic individuals with spectacles, contact lenses, or excimer laser photorefractive keratectomy. Am J Ophthalmol 1993;115:444–53.
24. Smith GT, Brown NA, Shun-Shin GA. Light scatter from the central human cornea. Eye (Lond) 1990;4(Pt 4):584–8.
25. Olsen T. Light scattering from the human cornea. Invest Ophthalmol Vis Sci 1982;23:81–6.
26. McCally RL, Farrell RA. Structural implications of small-angle light scattering from cornea. Exp Eye Res 1982;34:99–113.
27. Thaung J, Sjöstrand J. Integrated light scattering as a function of wavelength in donor lenses. J Opt Soc Am (A) 2002;19:152–7.
28. Wegener A, Müller-Breitenkamp U, Dragomirescu V, Hockwin O. Light scattering in the human lens in childhood and adolescence. Ophthalmic Res 1999;31:104–9.
29. Hemenger RP. Dependence on angle and wavelength of light scattered by the ocular lens. Ophthalmic Physiol Opt 1996;16:237–8.
30. van den Berg TJ. Depth-dependent forward light scattering by donor lenses. Invest Ophthalmol Vis Sci 1996;37:1157–66.
31. Fujisawa K, Sasaki K. Changes in light scattering intensity of the transparent lenses of subjects selected from population-based surveys depending on age: analysis through Scheimpflug images. Ophthalmic Res 1995;27:89–101.
32. van den Berg TJ, Ijspeert JK. Light scattering in donor lenses. Vision Res 1995;35:169–77.
33. Yaroslavsky IV, Yaroslavsky AN, Otto C, Puppels GJ, Vrensen GF, Duindam H, Greve J. Combined elastic and Raman light scattering of human eye lenses. Exp Eye Res 1994;59:393–9.
34. Qian W, Soderberg P, Lindstrom B, Chen E, Magnius K, Philipson B. Spatial distribution of back scattering in the nuclear area of the non-cataractous human lens. Eye (Lond) 1994;8(Pt 5):524–9.
35. Whitaker D, Steen R, Elliott DB. Light scatter in the normal young, elderly, and cataractous eye demonstrates little wavelength dependency. Optom Vis Sci 1993;70:963–8.
36. Smith GT, Smith RC, Brown NA, Bron AJ, Harris ML. Changes in light scatter and width measurements from the human lens cortex with age. Eye (Lond) 1992;6(Pt 1):55–9.
37. Weale RA. Real light scatter in the human crystalline lens. Graefes Arch Clin Exp Ophthalmol 1986;224:463–6.
38. Bettelheim FA, Ali S. Light scattering of normal human lens. III. Relationship between forward and back scatter of whole excised lenses. Exp Eye Res 1985;41:1–9.
39. Patel SV, Baratz KH, Hodge DO, Maguire LJ, McLaren JW. The effect of corneal light scatter on vision after descemet stripping with endothelial keratoplasty. Arch Ophthalmol 2009;127:153–60.
40. Patel SV, McLaren JW, Hodge DO, Bourne WM. The effect of corneal light scatter on vision after penetrating keratoplasty. Am J Ophthalmol 2008;146:913–9.
41. Gilliland KO, Johnsen S, Metlapally S, Costello MJ, Ramamurthy B, Krishna PV, Balasubramanian D. Mie light scattering calculations for an Indian age-related nuclear cataract with a high density of multilamellar bodies. Mol Vis 2008;14:572–82.
42. Kymionis GD, Tsiklis N, Pallikaris AI, Bouzoukis DI, Pallikaris IG. Fifteen-year follow-up after LASIK: case report. J Refract Surg 2007;23:937–40.
43. Hindman HB, McCally RL, Myrowitz E, Terry MA, Stark WJ, Weinberg RS, Jun AS. Evaluation of deep lamellar endothelial keratoplasty surgery using scatterometry and wavefront analyses. Ophthalmology 2007;114:2006–12.
44. Wang J, Thomas J, Cox I. Corneal light backscatter measured by optical coherence tomography after LASIK. J Refract Surg 2006;22:604–10.
45. Fankhauser F II. Postoperative follow up by dynamic light scattering: detection of inflammatory molecular changes in the cornea, the vitreous and the lens. Technol Health Care 2007;15:247–58.
46. Wang J, Simpson TL, Fonn D. Objective measurements of corneal light-backscatter during corneal swelling, by optical coherence tomography. Invest Ophthalmol Vis Sci 2004;45:3493–8.
47. Donnelly WJ III, Pesudovs K, Marsack JD, Sarver EJ, Applegate RA. Quantifying scatter in Shack-Hartmann images to evaluate nuclear cataract. J Refract Surg 2004;20:S515–22.
48. Gilliland KO, Freel CD, Lane CW, Fowler WC, Costello MJ. Multilamellar bodies as potential scattering particles in human age-related nuclear cataracts. Mol Vis 2001;7:120–30.
49. Qian W. Angular change in backscattering of light from the human lens with nuclear cataract. Eye (Lond) 2000;14(Pt 1):56–60.
50. Chang SW, Benson A, Azar DT. Corneal light scattering with stromal reformation after laser in situ keratomileusis and photorefractive keratectomy. J Cataract Refract Surg 1998;24:1064–9.
51. Thurston GM, Hayden DL, Burrows P, Clark JI, Taret VG, Kandel J, Courogen M, Peetermans JA, Bowen MS, Miller D, Sullivan KM, Storb R, Stern H, Benedek GB. Quasielastic light scattering study of the living human lens as a function of age. Curr Eye Res 1997;16:197–207.
52. Michael R, van Rijn LJ, van den Berg TJ, Barraquer RI, Grabner G, Wilhelm H, Coeckelbergh T, Emesz M, Marvan P, Nischler C. Association of lens opacities, intraocular straylight, contrast sensitivity and visual acuity in European drivers. Acta Ophthalmol 2009;87:666–71.
53. van den Berg TJ, Van Rijn LJ, Michael R, Heine C, Coeckelbergh T, Nischler C, Wilhelm H, Grabner G, Emesz M, Barraquer RI, Coppens JE, Franssen L. Straylight effects with aging and lens extraction. Am J Ophthalmol 2007;144:358–63.
54. Siik S, Airaksinen PJ, Tuulonen A. Light scatter in aging and cataractous human lens. Acta Ophthalmol (Copenh) 1992;70:383–8.
55. Corbett MC, Prydal JI, Verma S, Oliver KM, Pande M, Marshall J. An in vivo investigation of the structures responsible for corneal haze after photorefractive keratectomy and their effect on visual function. Ophthalmology 1996;103:1366–80.
56. Braunstein RE, Jain S, McCally RL, Stark WJ, Connolly PJ, Azar DT. Objective measurement of corneal light scattering after excimer laser keratectomy. Ophthalmology 1996;103:439–43.
57. Lohmann CP, Gartry DS, Muir MK, Timberlake GT, Fitzke FW, Marshall J. Corneal haze after excimer laser refractive surgery: objective measurements and functional implications. Eur J Ophthalmol 1991;1:173–80.
58. van den Berg TJ, Ijspeert JK, de Waard PW. Dependence of intraocular straylight on pigmentation and light transmission through the ocular wall. Vision Res 1991;31:1361–7.
59. Ijspeert JK, de Waard PW, van den Berg TJ, de Jong PT. The intraocular straylight function in 129 healthy volunteers; dependence on angle, age and pigmentation. Vision Res 1990;30:699–707.
60. Vos JJ, van den Berg TJ. Report on disability glare. CIE Collection 1999;135:1–9.
61. Vos JJ. Disability glare—a state of the art report. CIE J 1984;3:39–53.
62. Jain S, Khoury JM, Chamon W, Azar DT. Corneal light scattering after laser in situ keratomileusis and photorefractive keratectomy. Am J Ophthalmol 1995;120:532–4.
63. Grover S, Alexander KR, Choi DM, Fishman GA. Intraocular light scatter in patients with choroideremia. Ophthalmology 1998;105:1641–5.
64. Alexander KR, Fishman GA, Derlacki DJ. Intraocular light scatter in patients with retinitis pigmentosa. Vision Res 1996;36:3703–9.
65. van den Berg TJ, Hwan BS, Delleman JW. The intraocular straylight function in some hereditary corneal dystrophies. Doc Ophthalmol 1993;85:13–9.
66. Lovasik JV, Remole A. An instrument for mapping corneal light-scattering characteristics. Ophthalmic Physiol Opt 1983;3:247–54.
67. Bettelheim FA, Kumbar M. An interpretation of small-angle light-scattering patterns of human cornea. Invest Ophthalmol Vis Sci 1977;16:233–6.
68. Franssen L, Tabernero J, Coppens JE, van den Berg TJ. Pupil size and retinal straylight in the normal eye. Invest Ophthalmol Vis Sci 2007;48:2375–82.
69. van den Berg TJ. On the relation between glare and straylight. Doc Ophthalmol 1991;78:177–81.
70. van den Berg TJ. Importance of pathological intraocular light scatter for visual disability. Doc Ophthalmol 1986;61:327–33.
71. Thaung J, Beckman C, Abrahamsson M, Sjostrand J. The ‘light scattering factor.’ Importance of stimulus geometry, contrast definition, and adaptation. Invest Ophthalmol Vis Sci 1995;36:2313–7.
72. Veraart HG, van den Berg TJ, Hennekes R, Adank AM. Stray light in photorefractive keratectomy for myopia. Doc Ophthalmol 1995;90:35–42.
73. Marcos S, Burns SA. On the symmetry between eyes of wavefront aberration and cone directionality. Vision Res 2000;40:2437–47.
74. Snyder AW, Pask C. The Stiles-Crawford effect—explanation and consequences. Vision Res 1973;13:1115–37.
75. Franssen L, Coppens JE, van den Berg TJ. Compensation comparison method for assessment of retinal straylight. Invest Ophthalmol Vis Sci 2006;47:768–76.
76. van den Berg TJ, Ijspeert JK. Clinical assessment of intraocular straylight. Appl Opt 1992;31:3694–6.
77. Coppens JE, Franssen L, van Rijn LJ, van den Berg TJ. Reliability of the compensation comparison stray-light measurement method. J Biomed Opt 2006;11:34027.
78. Aguirre R, Colombo E, Issolio L, Luque S, Vilaseca M, Pujol J. Tiempo de reacción y contraste umbral en la medida de la difusión intraocular y el deslumbramiento. Opt Pura Apl 2007;40:111–7.
79. Gutiérrez R, Jiménez JR, Villa C, Valverde JA, Anera RG. Simple device for quantifying the influence of halos after lasik surgery. J Biomed Opt 2003;8:663–7.
80. Babizhayev MA, Deyev AI, Yermakova VN, Davydova NG, Kurysheva NI, Doroshenko VS, Zhukotskii AV. Image analysis and glare sensitivity in human age-related cataracts. Clin Exp Optom 2003;86:157–72.
81. Rodríguez P, Navarro R. Double-pass versus aberrometric modulation transfer function in green light. J Biomed Opt 2007;12:044018.
82. Guirao A, González C, Redondo M, Geraghty E, Norrby S, Artal P. Average optical performance of the human eye as a function of age in a normal population. Invest Ophthalmol Vis Sci 1999;40:203–13.
83. Williams DR, Brainard DH, McMahon MJ, Navarro R. Double-pass and interferometric measures of the optical quality of the eye. J Opt Soc Am (A) 1994;11:3123–35.
84. Artal P, Ferro M, Miranda I, Navarro R. Effects of aging in retinal image quality. J Opt Soc Am (A) 1993;10:1656–62.
85. Santamaría J, Artal P, Bescós J. Determination of the point-spread function of human eyes using a hybrid optical-digital method. J Opt Soc Am (A) 1987;4:1109–14.
86. Vos JJ, Walraven J, van Meeteren A. Light profiles of the foveal image of a point source. Vision Res 1976;16:215–9.
87. Campbell FW, Gubisch RW. Optical quality of the human eye. J Physiol (Lond) 1966;186:558–78.
88. Westheimer G. Retinal light distribution for circular apertures in Maxwellian view. J Opt Soc Am 1959;49:41–4.
89. Díaz-Doutón F, Benito A, Pujol J, Arjona M, Güell JL, Artal P. Comparison of the retinal image quality with a Hartmann-Shack wavefront sensor and a double-pass instrument. Invest Ophthalmol Vis Sci 2006;47:1710–6.
90. Prieto PM, Vargas-Martin F, Goelz S, Artal P. Analysis of the performance of the Hartmann-Shack sensor in the human eye. J Opt Soc Am (A) 2000;17:1388–98.
91. Liang J, Grimm B, Goelz S, Bille JF. Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor. J Opt Soc Am (A) 1994;11:1949–57.
92. Shahidi M, Yang Y. Measurements of ocular aberrations and light scatter in healthy subjects. Optom Vis Sci 2004;81:853–7.
93. Luque SO, Díaz-Doutón F, Lapuente V, Pujol J, Arjona M, Artal P. Estimating intraocular scattering from combined Hartmann-Shack and double-pass measurements. Invest Ophthalmol Vis Sci 2006;47:E–abstract 1215.
94. Güell JL, Pujol J, Arjona M, Díaz-Douton F, Artal P. Optical Quality Analysis System; Instrument for objective clinical evaluation of ocular optical quality. J Cataract Refract Surg 2004;30:1598–9.
95. López-Gil N, Artal P. Comparison of double-pass estimates of the retinal-image quality obtained with green and near-infrared light. J Opt Soc Am (A) 1997;14:961–71.
96. Liang J, Westheimer G. Optical performances of human eyes derived from double-pass measurements. J Opt Soc Am (A) 1995;12:1411–6.
97. Cerviño A, Bansal D, Hosking SL, Montés-Micó R. Objective measurement of intraocular forward light scatter using Hartmann-Shack spot patterns from clinical aberrometers. Model-eye and human-eye study. J Cataract Refract Surg 2008;34:1089–95.
98. Donnelly WJ III, Applegate RA. Influence of exposure time and pupil size on a Shack-Hartmann metric of forward scatter. J Refract Surg 2005;21:S547–51.
99. Bueno JM, Berrio E, Ozolinsh M, Artal P. Degree of polarization as an objective method of estimating scattering. J Opt Soc Am (A) 2004;21:1316–21.
100. Bueno JM. Depolarization effects in the human eye. Vision Res 2001;41:2687–96.
101. Goble RR, O'Brart DP, Lohmann CP, Fitzke F, Marshall J. The role of light scatter in the degradation of visual performance before and after Nd:YAG capsulotomy. Eye (Lond) 1994;8(Pt 5):530–4.
102. Beerthuizen JJ, Franssen L, Landesz M, van den Berg TJ. Straylight values 1 month after laser in situ keratomileusis and photorefractive keratectomy. J Cataract Refract Surg 2007;33:779–83.
103. Chang SS, Maurice DM, Ramirez-Florez S. Quantitative measurement of corneal haze after myopic PRK. J Refract Surg 1996;12:412–6.
104. Braunstein RE, Jain S, McCally RL, Stark WJ, Connolly PJ, Azar DT. Objective measurement of corneal light scattering after excimer laser keratectomy. Ophthalmology 1996;103:439–43.
105. Veraart HG, van den Berg TJ, IJspeert JK, Cardozo OL. Stray light in radial keratotomy and the influence of pupil size and straylight angle. Am J Ophthalmol 1992;114:424–8.