Dissertation submitted to the Combined Faculties for the Natural Sciences and for Mathematics of the Ruperto-Carola University of Heidelberg, Germany for the degree of Doctor of Natural Sciences Put forward by Diplom-Physicist: Kristina Irsch Born in: Merzig, Germany Oral examination: December 17, 2008 Polarization Modulation Using Wave Plates to Enhance Foveal Fixation Detection in Retinal Birefringence Scanning for Pediatric Vision Screening Purposes Referees: Prof. Dr. Josef Bille Prof. Dr. Christoph Cremer To My Teachers For Showing Me the Excitement and Joy of Ophthalmic Optics My Parents For Their Love and Abundant Support Zusammenfassung Um die beidäugige foveale Fixationserkennung mit Hilfe der binokularen „Retinal Birefringence Scanning“ (RBS)-Methode zu Seh-Screening Zwecken von Kleinkindern zu verbessern, wurde ein neues Verfahren entwickelt, welches auf der Verwendung eines rotierenden λ/2-Plättchens und eines festen Wellenplättchens beruht. Das rotierende λ/2- Plättchen ermöglicht differenzielle polarisationsempfindliche Detektion des Fixationssignals mit nur einem Detektor und überwindet damit Grenzen des vorherigen optisch-elektronischen Aufbaus mit zwei Photodetektoren. Mit Hilfe der festen Verzögerungsplatte kann dieses durch die doppelbrechende Eigenschaft der Henle-Faserschicht verursachte Fixationssignal quasi unabhängig von der störenden kornealen Doppelbrechung, welche von einem Auge zum anderen variiert, erfasst werden. Unter Zuhilfenahme gemessener Doppelbrechungswerte der Hornhaut von 300 repräsentativen menschlichen Augen wurde unter MATLAB ein Algorithmus und eine damit verbundene Computersoftware zur Optimierung der Eigenschaften beider Wellenplättchen entwickelt. Das Optimierungsverfahren bestand in der Maximierung des Fixationssignals bei gleichzeitiger Minimierung der inter- und intra- individuellen Variabilität aufgrund verschiedener Hornhautwerte. Rotiert man das λ/2- Plättchen mit 9/16 der Scan-Frequenz und verwendet man ein Wellenplättchen mit einer Verzögerung von 45° und einer Orientierung von 90°, so wird das Fixationssignal optimiert. Kombiniert mit der „Bull’s-Eye“-Methode zur Erkennung von Defokus eignet sich dieses computeroptimierte RBS-basierte Verfahren als gerätegestützte objektive Methode zur automatischen Erkennung eines Amblyopierisikos bei Kleinkindern, die Hauptursache des Sehverlustes im Kindesalter. Abstract To enhance foveal fixation detection while bypassing the deleterious effects of corneal birefringence in binocular retinal birefringence scanning (RBS) for pediatric vision screening purposes, a new RBS design was developed incorporating a double-pass spinning half wave plate (HWP) combined with a fixed double-pass retarder into the optical system. The spinning HWP enables essential differential polarization detection with only one detector, easing constraints on optical alignment and electronic balancing, and together with a fixed wave plate, this differential RBS signal can be detected essentially independent of various corneal retardances and azimuths. Utilizing the measured corneal birefringence from a dataset of 300 human eyes, an algorithm was developed in MATLAB for optimizing the properties of both wave plates to statistically maximize the RBS signal, while having the greatest independence from left and right eye corneal birefringence. Foveal fixation detection was optimized with the HWP spun 9/16 as fast as the circular scan, with the fixed retarder having a retardance of 45 degrees and fast axis at 90 degrees. Combined with bull’s-eye focus detection, this computer- optimized RBS design promises to provide an effective screening instrument for automatic identification of infants at risk for amblyopia, the leading cause of vision loss in childhood. “Life is like riding a bicycle. To keep your balance you must keep moving.” Albert Einstein Contents 1 Introduction.......................................................................................................................1 2 Vision Screening................................................................................................................4 2.1 Amblyopia ...................................................................................................................4 2.2 Traditional Screening Methods....................................................................................5 2.3 Newer Screening Modalities........................................................................................8 3 Polarization and the Eye ................................................................................................11 3.1 Polarization of Light ..................................................................................................11 3.1.1 Linearly Polarized Light .....................................................................................13 3.1.2 Circularly Polarized Light...................................................................................13 3.1.3 Elliptically Polarized Light .................................................................................14 3.2 Birefringence .............................................................................................................15 3.2.1 Wave Plates.........................................................................................................17 3.2.2 Form Birefringence.............................................................................................18 3.3 Müller- Stokes Matrix Calculus.................................................................................19 3.3.1 Stokes Vector Representation .............................................................................19 3.3.2 Müller Matrix Formalism....................................................................................23 3.3.3 Poincaré Sphere...................................................................................................23 3.4 Ocular Birefringence..................................................................................................25 3.4.1 Lenticular Birefringence .....................................................................................26 3.4.2 Corneal Birefringence.........................................................................................27 3.4.3 Retinal Birefringence ..........................................................................................29 4 Retinal Birefringence Scanning (RBS)..........................................................................32 4.1 Assessment of Foveal Fixation..................................................................................32 4.2 Pediatric Vision Screening Using Binocular RBS.....................................................34 4.2.1 Optical Design of RBS System...........................................................................35 4.2.2 Limitations and Problems ...................................................................................36 4.2.3 Hypotheses and Objectives .................................................................................39 5 Spinning Half Wave Plate Design for RBS...................................................................40 5.1 Phase-Shift Subtraction Technique............................................................................41 5.2 Modeling of RBS Using Wave Plates........................................................................43 5.2.1 Model of Ocular Birefringence...........................................................................43 5.2.2 Assessing the Influence of Corneal Birefringence on the RBS Signal...............53 5.2.3 Determination of Optimum Spinning Frequency of Double-Pass HWP ............56 5.2.4 Finding the Optimum Fixed Double-Pass Wave Plate .......................................63 5.2.5 Differential Polarization Subtraction with Optimized Spinning-HWP RBS Design ..........................................................................................................................75 6 Validation of RBS Computer Model.............................................................................78 6.1 Experimental Setup....................................................................................................78 6.1.1 Intermediate Eye Fixation Monitor.....................................................................78 6.1.2 Method of Determining the Retardance and Fast Axis Orientation of a Wave Plate..............................................................................................................................82 6.1.3 Method of Determining Corneal Birefringence..................................................84 6.2 Model Predictions with the Intermediate Eye Fixation Monitor ...............................86 6.2.1 Influence of Varying Corneal Birefringence on the RBS Signal........................86 6.2.2 Optimizing Foveal Fixation Detection with the Intermediate Eye Fixation Monitor ........................................................................................................................87 6.3 Verification with Human Subjects.............................................................................94 6.3.1 Model Predictions for Studied Eyes....................................................................94 6.3.2 Measured Data from Studied Eyes......................................................................97 6.3.3 Comparison of Measured Data and Predicted Results........................................99 7 Pediatric Vision Screener