Low_resolution_Thesis_CDD_221009_public - Visual Optics and ...

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CORRELATION BETWEEN RADIUS AND ASPHERICITY simulated corneal topography measurements of pairs of corneal surfaces. One cornea had R=8 mm and Q=0.3 in all cases, while in the other R took values between 8 and 8.1 mm (Fig. A.8(a)), or Q took values between 0.3 and 0.5 (Fig. A.8(b)). To simulate realistic corneal topography measurements, Gaussian noise (with a standard deviation of 10 m) was added to the ellipsoid. Each simulated experimental session consisted on five measurements per cornea. Each pair of series of 5 measurements each was compared, to estimate whether the two corneal surfaces were statistically different. Each experimental session was repeated 1000 times to obtain accurate probability estimates. Two statistical methods were tested: separate t-tests on R and Q (with and without the Bonferroni correction) and the MANOVA test proposed in this study. Figure A.8 shows the probability that the two corneas are identified as significantly different, according to the three statistical methods. The probability was computed for 20 increments of radius in Fig. A.8(a) and 14 increments of asphericity in Fig. A.8(b). We found that MANOVA is capable of detecting changes in R and Q about 4 times smaller than the separate tests. Both the Student’s t-test and MANOVA share most assumptions about the data, including that of normally distributed data. However, MANOVA takes into account the possible correlation between the variables, which we have demonstrated to occur between R and Q of repeated measurements on the same surface. Prop. of significant trials 1 0.8 0.6 0.4 0.2 MANOVA (=0.05) t test for R, Q (=0.05) t test for R, Q (=0.025) 0 0 0.02 0.04 0.06 0.08 R (mm) MANOVA (=0.05) t test for R, Q (=0.05) t test for R, Q (=0.025) 0 0.05 0.1 0.15 0.2 Q Fig. A.8. Proportion of simulated experiments where a significant difference was detected between a reference ellipsoid with R=8 mm and Q=0.3 and a test ellipsoid with (a) R=8+R mm and Q=0.3 or (b) R=8 mm and Q=0.3+Q. Each experiment compares 5 fits to the reference ellipsoid and 5 fits to the test one, simulating two sets of five repeated noisy mesurements (10 m standard deviation at each point of the ellipsoid). For each amount of change of R or Q, we simulated 1000 experiments, and the proportion of detected significant differences is plotted. Circles: Proportion of trials where MANOVA identified a significant change. Squares: Proportion of trials where the Student’s t test identified a significant change, either in radius or in asphericity. Triangles: Same as squares but applying the Bonferroni correction. This correction is needed because when we perform two simultaneous statistical tests on the same data, the probability of false positives increases about two times, so we must divide the significance threshold by two. MANOVA does not use previous knowledge about the correlation between the two variables, and therefore it is the method of choice in order to check the significance of measurements, when the instrument is not characterized. However, if the correlation specific to a given instrument is well known from a careful 253
ANNEX A characterization, other statistical methods that make use of this previous knowledge can be implemented, increasing further the sensitivity of the tests. A.5.3. Implications of the results The presence of strong correlations between radius and asphericities describing a surface has important implications in the detection of changes in conic surfaces. Certain combination of changes in the asphericity and radius along the correlation line can be interpreted as a change in the surface that does not really exist, while changes in radius and asphericities of the same magnitude but in the perpendicular direction can describe certainly significant changes in the surface. This is particularly important in physiological optics where conic surfaces are used to describe the surfaces of the ocular component. Studies of the geometry of crystalline lens reveal correlations between radius and asphericity (Manns et al., 2004) which may be overinterpreted as a particular feature of the lens, in association with development, growth or aging. However, our results indicate that this is actually a consequence of the fit. Similarly, the impact of corneal treatments on corneal geometry and optical quality is usually assessed in terms of changes in radius of curvature and asphericity (Marcos et al., 2003, Perez-Escudero et al., 2009b). Current efforts in refractive surgery aim at not inducing changes in corneal asphericity to prevent the induction of spherical aberration. Statistical analysis of the significancy of these changes should take into account the existing correlations between radius and asphericity in the statistical analysis of possible induced changes in asphericity. A.6. CONCLUSIONS There is an important degree of correlation between radius and asphericitiy, observed in repeated measurements with different instruments (Scheimpflug imaging topographer, Placido disk videokeatoscope, non-contact optical profilometer). This strong correlation holds across different measurement conditions: anterior surface and posterior surface of the cornea, and intraocular lens. Simulations show that this correlation effect is produced even by subtle measurement noise or surface variability (as with the profilometer, Fig. A.5). Measurement noise and surface variability will always be present experimentally, and we therefore can conclude that when fitting surface measurements to conics or conic-based surfaces the retrieved R and Q parameters will be usually correlated. It is clear from the examples and also from the simulations, that when reporting the results of conic fittings, as those routinely used in ocular biometry, radius and asphericity cannot be treated separately: a correct description of the surface needs both parameters. We have proposed to use the statistical test MANOVA to study corneal changes. This test increases the sensitivity of the analysis, detecting changes about 4 times smaller than the separate analysis in R and Q. 254
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Doctoral thesis Corneal Ablation an
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Contents Corneal Ablation and Conta
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2.2.1. Fitting surfaces............
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5.3.3. Ablation efficiency factors
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10.5. DISCUSSION...................
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We thank José Antonio Sánchez-Gil
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BOZR Back Optic Zone Radius BCVA Be
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INTRODUCTION 1.1. MOTIVATION The fr
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INTRODUCTION 1.2. THE OPTICAL SYSTE
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INTRODUCTION Myopia is a very commo
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INTRODUCTION a point focus: the dif
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INTRODUCTION system, and tilt repre
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INTRODUCTION term Z 0 2 stands for
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INTRODUCTION which image was shadow
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INTRODUCTION The defocus Zernike te
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INTRODUCTION 1.4.6.3. Internal Aber
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INTRODUCTION 1.5.2.3. Alternating v
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INTRODUCTION and further-more, at l
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INTRODUCTION alcohol is used to loo
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INTRODUCTION changes in reflectivit
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INTRODUCTION Marcos et al. (Marcos
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INTRODUCTION 1.7.3. Ablation effici
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INTRODUCTION corneal surface may be
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INTRODUCTION Algorithm design: The
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INTRODUCTION contact lenses the fie
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INTRODUCTION 1.10.1. Tear studies A
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INTRODUCTION there are still many u
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INTRODUCTION 6. Evaluation and unde
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METHODS 2Chapter Chapter 2 - Method
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METHODS 2.1. MEASUREMENT OF OPTICAL
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METHODS In both profilometers, cust
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METHODS The measurement method that
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METHODS Fig. 2. 9. Set of points in
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METHODS Slit lamp Scheimpflug Camer
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METHODS representing the deviation
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METHODS 2.2.2.2. Ablation pattern f
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METHODS direction. These calculatio
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METHODS eye through the whole pupil
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METHODS (1993) power thresholds for
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METHODS alignment (frontal-illumina
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METHODS Fig. 2. 24. Example frame f
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METHODS 4) New image processing too
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METHODS Fig. 2. 28. Corrected entra
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METHODS Badal lens, corresponds to
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METHODS Each VA measurement consist
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REFRACTIVE SURGERY PMMA MODEL 3.1.
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CHAPTER 3 optimization of refractiv
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CHAPTER 3 These data demonstrate th
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CHAPTER 3 regression line, since it
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CHAPTER 3 Figure 3.3 shows one of t
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CHAPTER 3 Ablation efficiency facto
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CHAPTER 3 considering the same set
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CHAPTER 3 3.5.3 Impact of correctio
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ABLATION PROPERTIES OF FILOFOCON A
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OPTIMIZED LASER PLATFORMS 5.1 ABSTR
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CHAPTER 5 pulses. Fluence, repetiti
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CHAPTER 5 ablations. The slit-confo
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CHAPTER 5 (Anera et al., 2003): d S
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CHAPTER 5 asymmetries also appeared
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CHAPTER 5 5.3.4. Ablation patterns
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CHAPTER 5 a) b) : 6.5 mm c) Fig. 5.
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CHAPTER 5 achieve proper reflection
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CHAPTER 5 Both the ablation algorit
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HYBRID PORCINE/PLASTIC MODEL 6.1. A
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CHAPTER 6 6.3.1. Hybrid porcine-pla
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CHAPTER 6 is detected. Therefore, i
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CHAPTER 6 no preferential orientati
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ANTERIOR AND POSTERIOR CORNEAL ELEV
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Page 177 and 178: ANTERIOR AND POSTERIOR CORNEAL ELEV
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Page 187: SOFT CONTACT LENS FITTING USING MOD
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Page 194: ON-EYE OPTICAL PERFORMANCE OF RIGID
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Page 212: SOFT MONOFOCAL AND MULTIFOCAL CONTA
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Page 220 and 221: CORRELATION BETWEEN RADIUS AND ASPH
Page 230: CONCLUSIONS Conclusions This thesis
Page 233 and 234: CONCLUSIONS 5We have developed a pr
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Page 240 and 241: CONCLUSIONS FUTURE RESEARCH LINES T
Page 242 and 243: CONCLUSIONS LIST OF PUBLICATIONS AN
Page 244 and 245: REFERENCES References AIZAWA, D., S
Page 246 and 247: REFERENCES PHOTODECOMPOSITION (APD)
Page 248 and 249: REFERENCES DORRONSORO, C., CANO, D.
Page 250 and 251: REFERENCES GISPETS, J., ARJONA, M.
Page 252 and 253: REFERENCES KOPF, M., YI, F., ISKAND
Page 254 and 255: REFERENCES MARCOS, S., DORRONSORO,
Page 256 and 257: REFERENCES NOVO, A., PAVLOPOULOS, G
Page 258 and 259: REFERENCES SAKIMOTO, T., ROSENBLATT
Page 260: REFERENCES WANG, L., DAI, E., KOCH,
Page 263 and 264: RESÚMENES pacientes reales fue com
Page 265 and 266: RESÚMENES experimentales de cirug
Page 267 and 268: RESÚMENES cada punto de las cornea
Page 269 and 270: RESÚMENES plástico medidas anteri
Page 272 and 273: RESÚMENES 8 Evaluación óptica de
Page 274 and 275: RESÚMENES 9 Prestaciones ópticas
Page 276 and 277: RESÚMENES 10 Calidad óptica y cal
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RESÚMENES A Correlación entre rad
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CONCLUSIONES clínicos. La descripc
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CONCLUSIONES 12 Las superficies ocu
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CONCLUSIONES IMPLICACIONES DE ESTA
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CONCLUSIONES contribuyen a la compr
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(y muchísimo más difícil). Me da
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