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Clinical use of the ocular point spread function for retinal image quality assessment Expert Rev. Opthalmol. 3(5), 523–527 (2008)
Robert Montés-Micó†, Teresa Ferrer-Blasco, Alejandro Cerviño, Jose Manuel González-Méijome and Cristina Puchades Author for correspondence Optometry Research Group, Optics Department, University of Valencia, Dr. Moliner 50, 46100 – Burjassot, Valencia, Spain Tel.: +34 963 544 764 Fax: +34 963 544 715
[email protected] †
The purpose of this study is to demonstrate the clinical use of the point spread function (PSF) as metric for the assessment of retinal image quality in eyes with different ocular conditions. The PSF was computed from the wavefront aberrations obtained in seven eyes with different ocular conditions: emmetropia, myopia, hyperopia, post-myopic laser in situ keratomileusis (LASIK), post-hyperopic LASIK, keratoconus, Intacs® in keratoconus, radial keratotomy (RK), LASIK after RK, cataract, phacoemulsification after cataract surgery, and LASIK after astigmatic keratotomy. The Strehl intensity ratio was calculated for all the PSFs computed. The PSF was correlated with the change in the optical elements of the eye: cornea and lens. Corneal refractive surgery, keratoconus, Intacs insertion and cataract surgery induce different changes in the optics of the eye which were well reflected by the PSF and the Strehl intensity ratio. Spread of the PSF in each case was caused by optical aberrations and/or scatter. The PSF measurement and the Strehl intensity ratio calculation is useful for the qualitative assessment of the retinal image and for quantifying optical degradation imposed by different optical conditions. Keywords : point spread function • retinal image quality • Strehl ratio
The eye is not a perfect optical system. As a result, when visual stimuli are imaged through the cornea and lens, they undergo a certain degree of degradation. This degradation affecting the final retinal image depends on the optical quality of the whole eye. One of the most useful ways to approach the assessment of retinal image change is by means of the point spread function (PSF). The PSF represents the distribution of light intensity in the image plane of a light point source [1] . The shape of the PSF depends on diffraction, defocus, aberrations and scattering phenomena affecting the light travelling through the ocular media. Defocus, aberrations and scattered light broaden the PSF and in the absence of these the PSF is only affected by diffraction and is therefore called ‘diffraction-limited PSF’. The shape of the PSF also depends on the shape and diameter of the aperture stop, which in the case of the human eye corresponds with the pupil and is generally considered to be circular in shape. Should the eye have perfect optics, then the image of a small point source on the retina would be identical to the point itself. However, ocular optics are far from perfect so the relative www.expert-reviews.com
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intensity of the light point source is distributed across the retina. The PSF for a perfect optical system with a circular aperture would be the Airy disc, which is the Fraunhofer diffraction pattern for a circular pupil. It is often difficult to compare the PSF of the eye under different conditions. Comparisons are much easier if the PSF can be characterized by a single metric that specifies the image quality into some meaningful scale. The Strehl intensity ratio (S) is a measure of the effect of aberrations on reducing the maximum value or peak of the PSF, and it is defined as follows: S=
maximum light level value of aberrated PSF maximum light level value of unaberrated PSF
Since the effect of aberrations is to spread out the PSF and decrease the maximum peak height, the Strehl intensity ratio is always less than or equal to one. The greater the aberrations, the lower the Strehl intensity ratio value and therefore the poorer the image quality. A criterion for a good, near to diffraction-limited system is that the Strehl intensity ratio has a value higher than or equal to 0.8.
© 2008 Expert Reviews Ltd
ISSN 1746-9899
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The use of the PSF as an optical quality metric is an important tool to evaluate the optical quality of the eye. Normal and pathological eyes, as well as those submitted to refractive surgery procedures, will show different PSF. The study of the PSF in each case will then give us valuable information about the visual quality of our patients’ eyes. In this special report, the PSF of several eyes with different optical conditions will be evaluated in order to show the clinical use of PSF analysis. Patients & methods
Patients with different optical conditions were evaluated. Table 1 shows the optical and pathological characteristics of each eye. To evaluate the retinal image quality we have used 2D Fourier transform to compute the PSF from the wavefront error [2] . For theoretical calculations and maps illustrations we have used the CT-View 6.8 software (Sarver & Associates, Inc, Carbondale, IL, USA). Wavefront error was measured by means of a COASTM aberrometer (Wavefront Sciences, USA), which is based on the Hartmann–Shack aberrometer [3] . The measurements were carried out in a darkened room to avoid the need to dilate the pupil pharmacologically: aberrations could then be measured over the full extent of a physiologically natural pupil. PSF was computed for one pupil diameter: 6 mm (mesopic level). To make a comparison between images PSFs of different conditions, they were computed considering only higher-order aberrations, being defocus and astigmatism cancelled. The reason for this was because sphero-cylindrical aberrations in the human eye cause the defocused PSF on the retina to appear different depending on whether it is focused in front of or behind the retina [4] . Then, to make possible a direct comparison between eyes with different optical conditions only higher-order aberrations were considered. The patient was instructed to blink three or four times and fixate on a distant image created by the aberrometer while keeping their eyes wide open for as long as possible. During this period of nonblinking one image was captured with the aberrometer. In all cases, measurements were done at 6 s after the blink in order to avoid changes in ocular aberrations due to tear film break-up [5,6] . The tenets of the Declaration of Helsinki were followed in this study. Informed consent was obtained from all patients after the nature and possible consequences of the study had been explained. Institutional Review Board approval was obtained. Results Figure 1 shows the PSFs computed from the wavefront aberrations for all cases evaluated. To facilitate the comparison between PSF of different eyes the Strehl intensity ratio for all cases was calculated. Since PSF was computed from higher-order aberrations, the Strehl intensity ratio has been defined under the maximum light level value of higher-order aberrated PSF.
Discussion
Eye 1 from figure 1 shows a good PSF with a high Strehl ratio value. This PSF has been computed from the wavefront aberration of a young emmetropic eye. The effect of diffraction and 524
scatter can be neglected, and only higher-order aberrations affect the final retinal image. In this case, low levels of higher-order optical aberrations spread the final image slightly, reflecting an extraordinarily good optical quality. Despite eyes 2a and 3a representing, respectively, a myopic and a hyperopic eye previously corrected (cancelled their defocus in PSF reconstruction), their PSFs are not perfectly symmetric and different to that found in eye 1. Paquin et al. found that moderate and high myopic eyes show large values of higher-order aberrations compared with emmetropic eyes, increasing their value as the baseline level of myopia increased [7] . Emmetropic eyes yielded similar results to those found for low myopic eyes (up to -3.00 D). Similar conclusions have been reported by other authors [8–10] . Llorente et al. concluded that similar or even larger amounts of higher-order optical aberrations are found in hyperopic compared with myopic eyes [11] . This study showed that spherical aberration and third-order aberrations were slightly higher in hyperopes than in myopes of similar absolute refractive errors. Large higher-order aberrations values imply poorer PSFs, which agrees with the Strehl ratios found in each case. After laser in situ keratomileusis (LASIK) surgery, the PSF for the myopic and hyperopic eyes (images 2b and 3b, respectively) is worse when compared with images obtained prior to surgery. The PSF spread comes from the increase in higher-order aberrations after LASIK surgery. This is supported by the results found in previous reports on higher-order optical aberrations after corneal laser surgery in both myopic [12–14] and hyperopic eyes [15,16] . The Strehl ratio is consequently worse than that found prior to surgery. The PSF of the keratoconic eye (image 4a) is quite different compared with the previous PSFs. The spread of the PSF is due to the high degree of corneal irregularity [17] . Maeda et al. found that higher-order aberrations in keratoconic eyes were significantly higher than those in normal eyes (increase factor of ×6.05 for a 6-mm pupil) [18] . Large values of coma- and spherical-like aberrations spread the PSF. The PSF in this case is not centralsymmetric possibly due to odd-symmetric (coma) or irregular aberrations associated with this ocular condition. After Intacs® insertion (image 4b) the PSF is reduced (in terms of spread), therefore increasing the Strehl ratio. This reflects an improvement with regards to the optical quality of the eye. The aim of Intacs insertion is to reshape the abnormal cornea in order to reduce the asymmetric irregular astigmatism [19,20] . Boxer Wachler et al. found a reduction in the I-S index value from 25.62 to 6.60 after Intacs insertion [19] , which reflects the regularization effect of Intacs implantation. This effect is correlated with the improvement in corneal optical quality and, consequently, a reduction of the PSF spread (large Strehl ratio value). Image 5a shows the PSF of an eye submitted to radial keratotomy (RK) 9 years before examination. The spread of the point source along the vertical axis may be observed. Although the radial incisions were performed symmetrically to remove previous myopia (-4.75 D), the effect was more pronounced in a specific axis. Applegate et al. found an increase of corneal aberrations after RK compared with those before the surgery [21,22] . This would Expert Rev. Ophthalmol. 3(5), (2008)
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Figure 1. Point spread function (PSF) for different eyes computed from higher-order aberrations. Each image subtends 50 arc min. Strehl ratio value appears in the bottom of each image. 1: emmetropic eye; 2a: myopic eye; 2b: post-myopic laser in situ keratomileusis (LASIK); 3a: hyperopic eye; 3b: post-hyperopic LASIK; 4a: keratoconus; 4b: Intacs® insertion in keratonocus; 5a: eye with radial keratotomy; 5b: LASIK performed after radial keratotomy; 6a: cataract; 6b: post-phacoemulsification; 7a: high-astigmatic eye; 7b: high-astigmatic eye after astigmatic keratotomy; 7c: LASIK after astigmatic keratotomy in a high-astigmatic eye.
explain the degraded PSF found in the case shown here. The effect of LASIK surgery on the PSF of this eye is shown in image 5b. It is obvious that there is a worsening in the PSF computed. Corneal irregularities created by the LASIK surgery spread the point source along different axis, reducing the optical quality of the eye (low Strehl ratio value). It may be argued that in the case of an eye with previous RK surgery (i.e., with radial incisions on the cornea) LASIK ablation does not induce the same effect on an area with an incision scar in relation to a incision-free area. This effect would be expected to produce asymmetry as a function of the incision-meridian of the cornea and, consequently, changes www.expert-reviews.com
in the coma-like aberrations. This would indicate the difficulty for obtaining a regular surface by means of conventional LASIK ablation on previously irregular corneas. Image 6a shows the PSF of patient with a cortical cataract. It is interesting to find out how this image was created. The Hartmann–Shack aberrometer places a near diffraction-limited point source on the retina by passing a narrow beam through the eye’s pupil. The light from the retinal point propagates forward from the retina to the lens. When this light hits a local cataract within the lens, scattering occurs. The PSF of the lenslets are then affected depending on the severity of the cataract (and also 525
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on the location). The PSF image obtained in this eye contains spreading all over the central area due to central light scatter. Kuroda et al. [23] and Donnelly et al. [24] have quantified scatter from Hartmann–Shack measurements to evaluate cataracts. They found that retinal scattering also affects the lenslets of the aberrometer creating a luminance pedestal across the pupil. The PSF computed in the present study is also affected by this retinal scattering. In fact, once the cataract was removed, the PSF obtained (image 6b) still exhibited considerable amounts of spread, although minimal compared with that prior to surgery. This spread comes from retinal scatter and possibly other sources of intraocular scatter. The improvement in the PSF after cataract removal and intraocular lens insertion is obvious, however (×1.45 increase factor of the Strehl ratio). The last series of images represent the change in the PSF after astigmatic keratotomy (AK) combined with LASIK surgery (see Montés-Micó et al. [25] for a description). After AK incisions the PSF reflects a spread of light along a specified axis (image 7b). This reveals a more pronounced change in a corneal meridian which correlates with a reduction of the astigmatism. Corneal spot diagrams, directly related to the spread of the retinal image, computed by Montés-Micó et al. [25] after AK incisions corroborates this change. After LASIK surgery (image 7c) there is a reduction of the spread improving the Strehl ratio value. Montés-Micó et al. found a reduction in coma-like aberrations after LASIK in this type of surgery (×0.62 factor; p = 0.008) [25] . They suggested that LASIK ablation regularizes the central corneal surface, reducing the changes caused by the AK incisions. Despite the reduction of coma-like aberrations and the spread of the image, some asymmetries can still be seen. The effect of spherical aberration after myopic ablation and residual coma-like aberrations modify the final PSF. Expert commentary
Through different clinical cases it has been shown that the PSF is an interesting optical quality metric with remarkable clinical relevance. The benefit of an ocular surgical procedure could References
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Papers of special note have been highlighted as: • of interest •• of considerable interest 1
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Charman WN. Optics of the eye. In: Handbook of Optics I. (2nd Edition). McGraw–Hill, NY, USA (1995).
be easily assessed by PSF evaluation. Visual symptoms referred to by many patients are related to the PSF, therefore the use of PSF assessment in ophthalmology would be useful for clinicians to objectively estimate the change in visual quality of clinically evaluated patients. Further studies should combine wavefront aberrations measurement with the PSF analysis to simulate the patient visual performance. Five-year view
Over the next 5 years, the application of new optical metrics will increase in different refractive and ocular surgery procedures, since the optical information provided is extremely helpful for clinicians and ocular surgeons. Considerable improvement of current refractive surgery techniques can be expected, and new metrics for optical quality estimation will expand the knowledge and applications of refractive procedures. Financial & competing interests disclosure
This research conducted by Robert Montés-Micó (#UV-AE-20070225#), Jose Manuel González-Méijome (#UV-ESTPC-08-2054#), Alejandro Cerviño (#UV-AE-08-2291#) and Red Temática de Optometría (Ministerio de Ciencia e Innovación SAF2008-01114-E) was supported in part by Universitat de Valencia Research Grants. The authors have no other relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript apart from those disclosed. No writing assistance was utilized in the production of this manuscript.
Key issues • The use of the point spread function (PSF) as an optical quality metric is an important tool to evaluate the optical quality of the eye. • Normal, pathological and those eyes submitted to refractive surgery procedures exhibit different PSF. • The study of the PSF in each case gives highly valuable information regarding to the visual quality of our patients.
Montés-Micó R, Alió JL, Muñoz G, Charman WN. Temporal changes in optical quality of air-tear film interface at anterior cornea after blink. Invest. Ophthalmol. Vis. Sci. 45, 1752–1757 (2004).
6
Atchison DA, Smith G. Appendix 4. In: Optics of the Human Eye. Butterworth– Heinemann, London, UK (2000).
Montés-Micó R, Alió JL, Muñoz G et al. Postblink changes in total and corneal ocular aberrations. Ophthalmology 111, 758–767 (2004).
7
Cerviño A, Hosking SL, Montés-Micó R, Bates K. Clinical wavefront analyzers. J. Refract. Surg. 23, 603–616 (2007).
Paquin MP, Hamam H, Simonet P. Objective measurement of optical aberrations in myopic eyes. Optom. Vis. Sci. 79, 285–291 (2002).
8
Collins MJ, Wildsoet CF, Atchinson DA. Monochromatic aberrations and myopia. Vision Res. 35, 1157–1163 (1995).
9
He JC, Sun P, Held R et al. Wavefront aberrations in eyes of emmetropic and moderately myopic school children and young adults. Vision Res. 42, 1063–1070 (2002).
•
Latest review on clinical wavefront analyzers.
4
Wilson BJ, Decker KE, Roorda A. Monochromatic aberrations provide and odd-error cue to focus direction. J. Opt. Soc. Am. 19, 833–839 (2002).
526
10
Marcos S, Barbero S, Llorente L. The sources of optical aberrations in myopic eyes. Invest. Ophthalmol. Vis. Sci. 43, 1510 (2002).
•
The Association for Research in Vision and Opthamology presentation on the characteristics of aberrations in myopic eyes concluding that the increase of aberrations in myopia can be explained by physical properties of the ocular components and that some compensatory interactions of ocular components are lost in high myopia.
11
Llorente L, Barbero S, Cano D et al. Myopic versus hyperopic eyes: axial length, corneal shape and optical aberrations. J. Vis. 4, 288–298 (2004).
12
Moreno-Barriuso E, Lloves JM, Marcos S et al. Ocular aberrations before and after myopic corneal refractive surgery:
Expert Rev. Ophthalmol. 3(5), (2008)
Retinal image quality & point spread function
13
14
•
15
16
17
18
•
Boxer Wachler BS, Chandra NS, Chou B et al. Intacs for keratoconus. Ophthalmology 110, 1031–1040 (2003).
LASIK-induced changes measured with laser ray tracing. Invest. Ophthalmol. Vis. Sci. 42, 1396–1403 (2001).
19
Marcos S, Barbero S, Llorente L, MerayoLloves J. Optical response to LASIK surgery for myopia from total and corneal aberration measurements. Invest. Ophthalmol. Vis. Sci. 42, 3349–3356 (2001).
20
Alió JL, Belda JI. Treating irregular astigmatism and keratoconus. Panama: Highlights of ophthalmology (2004).
21
Applegate RA, Hilmantel G, Howland HC. Corneal aberrations increase with the magnitude of radial keratotomy refractive correction. Optom. Vis. Sci. 73, 585–589 (1996).
Oshika T, Miyata K, Tokunaga T et al. Higher order wavefront aberrations of cornea and magnitude of refractive correction in laser in situ keratomileusis. Ophthalmology 109, 1154–1158 (2002).
22
Study on the relation between magnitude of refractive correction and changes in aberrations post-laser-assisted in situ keratomileusis (LASIK).
Applegate RA, Howland HC, Sharp RP et al. Corneal aberrations and visual performance after radial keratotomy. J. Refract. Surg. 14, 397–407 (1998).
23
Llorente L, Barbero S, Merayo J, Marcos S. Total and corneal optical aberrations induced by laser in situ keratomileusis for hyperopia. J. Refract. Surg. 20, 203–216 (2004).
Kuroda T, Fujikado T, Maeda N et al. Wavefront analysis of higher-order aberrations in patients with cataract. J. Cataract. Refract. Surg. 28, 438–444 (2002).
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Wang L, Koch DD. Anterior corneal optical aberrations induced by laser in situ keratomileusis for hyperopia. J. Cataract. Refract. Surg. 29, 1702–1708 (2003).
Application of wavefront analysis to cortical and nuclear cataract, observing differencial characteristics in the aberrometric patterns.
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Tanabe T, Tomidokoro A, Samejima T et al. Corneal regular and irregular astigmatism assessed by fourier analysis of videokeratography data in normal and pathologic eyes. Opthalmology 111, 752–757 (2004).
Donnelly WJ, Pesudovs K, Marsack JD et al. Quantifying scatter in ShackHartmann images to evaluate nuclear cataract. J. Refract. Surg. 20, S515–S522 (2004).
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Intelligent approach to the objective determination of intraocular scatter by describing new metrics derived from the analysis of the Hartmann–Shack spot patterns.
Maeda N, Fujikado T, Kuroda T et al. Wavefront aberrations measured with Hartmann-Shack sensor in patients with keratoconus. Ophthalmology 109, 1996–2003 (2002). First approach to the characterization of keratoconic eyes versus normal eyes by the analysis of aberrations patterns.
www.expert-reviews.com
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Montés-Micó R, Muñoz G, Albarrán-Diego C et al. Corneal aberrations after astigmatic keratotomy combined with laser in situ keratomileusis. J. Cataract. Refract. Surg. 30, 1418–1424 (2004).
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Affiliations •
Robert Montés-Micó, OD, Mphil, PhD Associate Professor, Optometry Research Group, Optics Department, University of Valencia, Dr. Moliner 50, 46100 – Burjassot, Valencia, Spain Tel.: +34 963 544 764 Fax: +34 963 544 715
[email protected]
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Teresa Ferrer-Blasco, OD, PhD Associate Professor, Optometry Research Group, Optics Department, University of Valencia, Dr. Moliner 50, 46100 – Burjassot, Valencia, Spain Tel.: +34 963 544 764 Fax: +34 963 544 715
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Alejandro Cerviño, OD, PhD Associate Professor, Optometry Research Group, Optics Department, University of Valencia, Dr. Moliner 50, 46100 – Burjassot, Valencia, Spain Tel.: +34 963 544 042 Fax: +34 963 544 715
[email protected]
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Jose Manuel González-Méijome, OD, PhD Assistant Professor, Department of Physics (Optometry), School of Science, University of Minho, 4710-057 Gualtar – Braga, Portugal Tel.: +351 253 604 320 Fax: +351 253 678 981
[email protected]
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Cristina Puchades, OD, MSc Research Assistant, Optometry Research Group, Optics Department, University of Valencia, Dr. Moliner 50, 46100 – Burjassot, Valencia, Spain Tel.: +34 963 544 764 Fax: +34 963 544 715
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