Intraocular Lens Calculations

Foreword
Preface
Acknowledgments
Contents
Part I: Introduction
	1: The History of the IOL Power Club: 2005–2025
		2004: The Origins of the IOL Power Club—How It All Started
			The Club and By-Laws
		2005: First IPC Meeting—San Sebastian, Spain, September 6–8, Abba Londres y de Inglaterra Hotel
			First Meeting
		2006: Second IPC Meeting—Carmel, CA, March 22–25, Pine Inn Hotel
		2007: First Independent IPC EC Meeting—San Diego, CA April 28 Croce’s Restaurant
		2007: Third IPC Meeting—Århus, Denmark, September 4–6, Hotel Royal
		2008: Fourth IPC Meeting—St. Pete Beach, FL, November 12–16, Tradewinds Island Grand Resort
		2009: Second IPC Executive Committee Independant Meeting—St. Helena, CA, April 7–9
		2009: Fifth IPC Meeting—Roses, Spain, September 8–11, Vistabella Hotel
		2010: Sixth IPC Meeting—Venice, Italy, August 30 to September 2 Splendid Hotel
		2011: Third EC Independent Meeting Santa Monica, CA March 29-April 2 Le Merigot Hotel
		2011: Seventh IPC Meeting—Würzburg, Germany, September 22–25 Steinberg Schloss Hotel
		2012: Eighth IPC Meeting—Memphis and Nashville, TN, April 25–29, The Hermitage Hotel, Nashville, The Peabody Hotel, Memphis
		2013: Ninth IPC Meeting—Haarlem, the Netherlands, October 9–12, Amrâth Grand Hotel Frans Hals
		First IPC Member Business Meeting
		2014: Tenth IPC Meeting—Fort Lauderdale, FL, October 8–11, Il Lugano Hotel and Pelican Grand Hotel
		2015: 11th IPC Meeting—San Sebastian, Spain, September 9–12, Londres Hotel
		2016: 12th IPC Meeting—New Orleans, LA, May 10–13 Royal Sonesta Hotel
		2017: 13th IPC Meeting—Athens, Greece, September 8–16 Grand Britannia Hotel
		2018: 14th IPC Meeting—St. Pete Beach, FL, October 22–25 Tradewinds Island Grand Resort
		2018: ESCRS—IPC IOL Power Calculation Course, September 23, Vienna, Austria
		2019: IPC EC Fourth Independant Meeting—La Jolla, CA, May 6–7 La Valencia Hotel
		2019: 15th IPC Meeting—Napa, CA, October 8–11, Archer Hotel
		2021: 16th IPC Meeting—Carmel, CA, July 28–31 Pine Inn Hotel (Site of our Second Meeting in 2006)
		2022: 17th IPC Meeting—Stresa, Italy, September 21–24 Princess Regina Hotel
		2023: 18th IPC Meeting—Palm Springs, CA, November 8–11 Hotel Zoso Palm Springs
		2024: 19th IPC Meeting—Rockland, ME, April 9–12 Rockland Harbor Hotel, Maine Lighthouse Museum and Farnsworth Museum
		2025: 20th Anniversary IPC Meeting—Santa Barbara, CA, April 29-May 2
	2: American History of IOL Power Calculation
		Introduction
		Personal Ultrasound History
		First American Ultrasound IOL Power Calculation
		Personal Formula History
		Earliest Calculators and Computers
		The First Dedicated IOL Power A-Scan: The Invention of the Applanation Method
		Early IOL Power Studies
		The EyeLab
		Ultrasound Velocities for Axial Length Measurement
		Getting the Word Out
		Conclusion
		References
Part II: Basic Science
	3: Gaussian Optics
		Fundamental Hypotheses
		Classical Study in Paraxial Optics
			Paraxial Trace Through a Spherical Surface
			Lagrange–Helmholtz Relation
			Centered System
			Principal Points and Focal Lengths
			Nodal Points
			Relation of Conjugation and Transverse Magnification
			Dioptric Power
			Magnification
			Combination of Two Systems
			Single Lens
			Entrance and Exit Pupils
		Matrix Method in Paraxial Optics
			Elementary Matrices
				(a) Vergence of a Spherical Surface
				(b) Refraction Matrix
				(c) Translation Matrix
			Centered Systems
				(a) Transfer Matrix of a Centered System
				(b) Vergence of a Centered System
				(c) Conjugate Matrix
				(d) Homographic Relation
			Cardinal Elements
			Limits of Paraxial Approximation for the Eye
			Schematic Eye
		References
	4: Exact Optics
		Introduction
		Optical Materials and Geometry
			The Index of Refraction
		Beyond Paraxial Optics
			Seidel Aberrations
			Wavefront Aberrations
		Wave Optics for Image-Forming Optical Systems
			The Quality of an Optical System
		Conclusions
		References
	5: Pseudophakic Eye Models
		Introduction
		Schematic Eye Models
			Paraxial Models
				Reduced Paraxial Models
				Simplified Paraxial Models
				Exact Paraxial Models
			Finite Eye Models
				Comparison of Finite Model Eyes
		Computational Eye Models
			Pseudophakic Eye Models
			Personalized Pseudophakic Eye Models
			IOL Power Calculation
			Pseudophakic Finite Element Models
		Physical Eye Models
		Conclusions
		References
	6: Data Analysis in IOL Power Calculations
		Designing the Sample to be Analyzed
		Selecting the Data to be Reported
		Analyzing the Data
		References
	7: Demographics of Biometry
		Introduction
		Methods
		Results
			Sex-Related Differences
			Racial Differences
			Age-Related Trends
			Corneal Astigmatism
			Correlation Among Biometry Variables
			Inter-Eye Variation
		Conclusion
		References
Part III: Measurements
	8: Clinical Refraction
		Basic Clinical Refraction
		Key Points in Subjective Refraction
		Refraction in the Presence of a Monofocal IOL
		Refraction in the Presence of Multifocal IOLs
		Refraction in the Presence of Extended-Depth-of-Focus (EdoF) IOL
		Summary
		References
	9: Ultrasound Biometry
		Basic Principles of A-Scan Echography
		Measurement Technique
			Immersion Technique
			Contact Technique
		A-Scan Pattern of the Phakic Eye
			Identifying the Echospikes
			Setting the Appropriate Velocities
			Errors in Axial Length Measurement and the Final Refraction
		Axial Length Measurement of the Challenging Eye
			The Aphakic Eye
			The Pseudophakic Eye
			The Eye with Silicone-Filled Vitreous
		Avoiding Errors in Axial Length Measurement
			Avoiding Shorter Axial Length Measurement
			Avoiding Longer Axial Length Measurement
			Detecting Significant Intraocular Pathology
		References
	10: Optical Biometry
		History of Optical Biometry
			Ultrasound Biometry
			Partial Coherence Interferometry (PCI)
			Ultrasound Biometry vs. PCI
		Concept of PCI
			Optical Low-Coherence Reflectometry (OLCR)
		Advancements of PCI
		Introduction of OCT-Based Biometry
			Time-Domain OCT
			Spectral-Domain OCT
			Swept-Source SD-OCT
		OCT and Dense Cataracts
		Optical Biometry: Cornea
		Intraoperative OCT
		References
	11: Axial Length Measurement
		Introduction
		Basic Science
			Axial Length Measurements
			Ultrasound (US) Biometry
				Optical Biometry (Interferometry)
				Refractive Indices (RIs)
				Scaling Formulas
		Definitions of Commonly Used Terms.
			Coherence
			Group RI
		History
			Lenstar
				Sum-of-Segments AL
		Segments
			Summary of Segments
		Areas for Potential Improvement
		Chapter Summary
		References
	12: Technology of SS-OCT Biometer: Argos Biometer
		Background
		Challenges
			Large Coherence Length
			Swept-Source Biometer
				Early Work and Breakthrough
		Argos SS-OCT Biometer
			Basic Performance
			High Success Rate
				ERV Mode
			True Axial Length
		Future of SS-OCT with Tunable VCSEL
		References
	13: Influence of Anterior Chamber Depth, Lens Thickness, and Corneal Diameter on Intraocular Lens Power Calculation
		Introduction
		Intraocular Lens Power Calculation Formulas
			Performance of Different Formulas
		Refractive Prediction Errors after Cataract Surgery
		Preoperative Evaluation
			Anterior Chamber Depth
			Lens Thickness
			Corneal Diameter
			Agreement Between Measurement Techniques
			Population Means
		Influence of Anterior Chamber Depth on Intraocular Lens Power Calculation
		Influence of Lens Thickness on Intraocular Lens Power Calculation
		Influence of Corneal Diameter on Intraocular Lens Power Calculation
		The Case of Toric Intraocular Lenses
		Future Perspectives
		References
	14: Keratometry
		Keratometry
			Instrumentation
			The Calculation of Power from Curvature
			Asphericity and Ray Tracing
			Clinical Studies Using Scheimpflug Data
			Notes on the Stiles–Crawford Effect
		References
	15: Corneal Topography and Tomography
		Introduction
		Technologies
			Reflection Topography
			Elevation Topography
		Measurements
			Axial and Tangential Radii
			Metrics
				Curvature Metrics
				Elevation Metrics
				Refractive Power Metrics
			Precision and Agreement
		Software
			Surgical Planning Information (Fig. 15.6)
			IOL Calculation
			Toric IOL Calculations
			Post-surgical Analysis
		IOL Selection
			Corneal Optical Quality
			Corneal Anatomical Quality
		IOL Power Calculation
			Important Concepts
			Parameters for IOL Calculations
				Sim K
				Equivalent K Reading (EKR)
				Total Corneal Power
				Radii of Curvature
				Central Corneal Elevation Data
				Corneal Asphericity and Spherical Aberration
				Axis of Reference
		Toric IOL Calculation
			Regular and Irregular Astigmatism
			Measured and Estimated Total Astigmatism
		References
	16: The A-Scan Biometer
		Basic Technology
		Physical Principles of A-Scan Ultrasound
		Major Components of a Biometer
			The Probe and Its Transducer
			The Sensitivity Setting
			The Velocity Setting
			The Electronic Gates
			Data Analysis and IOL Calculation
		Choosing the Appropriate Ultrasound Biometer
		Commonly Used Ultrasound Biometers
		References
	17: ZEISS IOLMaster 700
		Introduction
		SWEPT Source Biometry®
			OCT Technology
			Unique Fixation Check
		Distance Independent Telecentric 3-Zone Keratometry
		Additional Measurements
			Angle Alpha- and Kappa-Chords
			Corneal and Pupil Diameter
		Total Keratometry: Replacing Assumptions with Measurements
			Principle of Total Keratometry
			Precision of Total Keratometry Measurements
			Clinical Results with Total Keratometry in Non-toric and Toric IOL Power Calculation
			Clinical Performance of Total Keratometry in Post-corneal Refractive Surgery Eyes
		Central Topography: Starting Your Workflow with More Insights
		Markerless Toric IOL Alignment
		IOL Power Calculation
		ZEISS Cataract Workflow
		References
	18: Digital Solutions in the Cataract Workflow from ZEISS
		Introduction
		ZEISS FORUM
			Streamline the Workflow
			Decide with Confidence
			Simplify the Environment
		ZEISS EQ Workplace
			Preoperative Surgical Planning
				Data Review
				IOL Calculation
				IOL Ordering
				Surgery Preparation
				Documentation
				Individual Constant Personalization
			Intraoperative Assistance.
				Surgery Preparation and Digital Toric Alignment
		ZEISS VERACITY Surgery Planner
			Preoperative Surgical Planning
				Configurability
				Electronic Medical Record (EMR) Integration
				Diagnostic Device Integration
				Patient Questionnaire
				Data Validation and Alerts
				Suggestions
				IOL Calculations
				Automated Constant Optimization
				Arcuate Incisions
				Surgical Plan
				Surgery Scheduling
				Documentation
			Intraoperative Assistance
				Digital Toric Alignment
				OR Display
				Automated Operative Note
			Postoperative Data Analytics
		ZEISS CALLISTO eye
		Summary
		References
	19: Biometry Measurements Using a New Large Coherence Length Swept-Source Optical Coherence Tomography
		Repeatability and Reproducibility of the Argos Measurements
		Comparing the Argos Measurements to the IOLMaster 500 and Lenstar Biometers
		Acquisition Rate
		The Value of Using Multiple Indices of Refraction
		References
	20: Argos Verion Image-Guided System
		Astigmatism Correction
		Argos and Verion Digital Marking
		References
	21: Optical Biometer OA-2000
		Introduction
		Axial Length Measurement
		Clinical Cases
		Measurement of Corneal Radius of Curvature and Topography
		Important Indices of Cornea for Cataract Surgery
		IOL Calculation and Toric Calculation
		References
	22: ANTERION Swept-Source OCT Biometer
		Background: Swept-Source OCT Imaging for the Anterior Segment of the Eye
		Clinical Applications of Anterior Segment OCT as Implemented on ANTERION
		Biometry and IOL Power Calculations with ANTERION
		Study Results
		Summary
		References
	23: The NIDEK Cataract Suite: The OPD-Scan III Multifunction Diagnostic Device and the AL-Scan Optical Biometer
		OPD-Scan III
		AL-Scan Optical Biometer
		Putting It All Together
		References
	24: Aladdin Optical Biometer
		Introduction
		Measuring of Eye Parameters
			Repeatability and Reproducibility
		Assessing of Corneal Surface Regularity
		Keratoconus Screening
		Pupillometric Analysis
		Analysis of Corneal Quality of Vision
		Formulas for Calculating the Power of the IOL
		Conventional Formulas for Calculating the Power of Spherical Lenses
		Toric Lens Calculator
		Special Formulas for Calculating Lens Power in the Case of Patients Who Have Undergone Refractive Surgery
		Barrett Calculator
		Olsen Calculator
		Printed Reports
	25: Haag-Streit Biometers: Eyestar 900 and Lenstar 900
		Introduction
		Swept-Source OCT-Based Biometry and Tomography with Mandala Scan Technology
		Swept-Source OCT Biometry of the Entire Eye
		Swept-Source OCT Topography
		Zernike Analysis and Vision Simulation
		Reflective Dual-Zone Keratometry
		Other Standard Parameters and Displays
		Usability and Patient Comfort
		AC Suite and More
		Summary
		Lenstar, the All-in-One Cataract Planning Platform
			Introduction
		Summary
	26: The Pentacam Family
		Introduction
		History and Basic Principle
		Some Basic Questions
			Is Pure Keratometry and Axial Length Enough for IOL Power Calculation Today?
			Does One Formula for Every Purpose Exist?
			Every IOL for Every Patient?
		Every Patient Is an Individuum = Customization
			Corneal Morphology Assessment
			The More Complex Corneas: How to Deal with It?
			Corneal Optical and Anterior Chamber Properties Assessment
			Centration of Optical Elements and Pupil Diameter
			Total Eye Visual Performance
		IOL Power Calculation Formulas in the Pentacam
			Monofocal IOL Formulas for Virgin Corneas
			Toric IOL Formulas for Virgin Corneas
			IOL Formulas for Patients After Corneal Laser Refractive Surgery and RK (Radial Keratotomy)
		The Post-op Visual Assessment
		Summary and Take-Home Message
		References
	27: GALILEI G6 Lens Professional
		Overview
		Hardware
		Dual-Scheimpflug Concept
		Axial Biometry by Optical A-Scan
		Conversion of Optical Distances to Geometrical Distances
		Total Corneal Power (TCP)
		Technical Specifications (Table 27.1)
		Study Results
		Software
		Summary
		References
	28: CASIA2: Anterior Segment 3D Swept-Source OCT
		Introduction
		Various Functions for Cataract Surgery
		IOL Screening on Pre-op Cataract
		IOL Power Calculation on Pre-op Cataract
		Toric IOL Calculation and Axis Registration Support on Pre-op Cataract
		Lens Analysis Function
		Post-op Cataract
		Direct Observation of Toric Axis Marking Dots
		Various Functions for Other Clinical Fields
		Functions for ICL®
		Trend Analysis
		Wider and Deeper Image with Averaging
		STAR360°
		References
	29: CSO MS-39: Principles and Applications
		Introduction
		Technical Features of MS-39
		Acquisition
		Section
			Lens Biometry
			Pupillography
			Topography
		IOL Module
		Toric IOL Marker
		References
	30: IOL Power Calculations with ORA Intraoperative Aberrometer
		Talbot-Moiré Aberrometer
		IOL Power Calculation
		Using ORA
		Results
		Surgeon Benefits
		Summary
		References
	31: Cassini Corneal Topographer
		Introduction
		Cassini Basic Principle
		Surgical Planning with Cassini
			Monofocal IOLs
			Toric IOLs
			Multifocal IOLs
			FLACS
		Ocular Surface Diagnostics (Tear Film)
		Conclusion
		References
Part IV: Calculation Methods
	32: An Overview of Intraocular Lens Power Calculation Methods
		Historical Methods
			Standard Lens Method
			The Refraction Method
		Theoretical Formulas
			2-Variables Thin-Lens Vergence Formula: Third Generation Theoretical Formulas
				Hoffer Q and Hoffer QST
				Holladay 1 and Holladay 2 Formulas
				SRK/T
			Relationship Between the Third-Generation Formulas and Axial Length
				Fam Adjusted
				Wang-Koch Adjustment
				The T2 Formula
				Haigis Formula
			Regression Versus Theoretical Models
			Thin Lens Formula
			The Impact of Optical Biometry
				Ladas Super Formula (LSF) 1.0
				Kane Formula
				Panacea
				VRF-G
				Castrop
			Thick Lens Formula
				Barrett Universal II (BUII) Formula
				Næser Formula
				EVO
				PEARL-DGS
			Ray Tracing
				Olsen Formula
				Okulix
				CSO Method
		Regression Methods
		Artificial Intelligence (AI)
			Radial Basis Function (RBF)
			BART
			Ladas Super Formula (LSF) 2.0
		Intraoperative Aberrometry
			ORA
		Conclusion
		References
	33: Outcomes Review of Intraocular Lens Power Calculation Formulas
		In Memory of Wolfgang Haigis
			Modification
			Application
			Further Review
		Subgroup Analyses
			The Long and Short of It
				Short Eyes
				Review (Short Axial Lengths)
				Medium Axial Length
				Review (Medium Axial Lengths)
				Very Long Axial Length (>26.0 mm)
				Review (Long Axial Lengths)
			Other Parameters
				Flat Cornea (<42.0D) & Steep Cornea (>48.0D)
				Ametropia
				Ray Tracing and Intraoperative Aberrometry
				Even More Parameters
				Elderly
		Conclusion
		References
	34: ELP Estimation
		ELP Estimation
		Methods to Estimate the ELP
		Beware the Unusual Eyes!
		The C-Constant
		Error Propagation Model
		References
	35: Anterior Chamber Depth and IOL Calculations
		Impact of Postoperative ACD
		Postoperative ACD Prediction
		Problems of Intraoperative ACD Measurements
		Postoperative ACD Shift
		ACD Shift in Plate Haptics IOL Vs Standard Three-Piece Open-Loop Haptics IOL of the Same Acrylic Material [36, 37]
		ACD Shift in Single-Piece Open-Loop haptics IOL Vs Three-Piece Open-Loop Haptics IOL of the Same Acrylic Material [42]
		ACD Shift in Single Piece Open-Loop Haptics IOL Vs Plate Haptics IOL of the Same Acrylic Material [46]
		Postoperative ACD Shift and Rhexis Shape and Size
		Postoperative ACD Shift and Capsular Shrinkage
		Summary
		References
	36: IOL Constant Optimization
		Accuracy vs Precision
		Factors That Affect the IOL Constant
		The Methodology for Deriving IOL Constants
			Data and Sample Size Requirements
			Optimization of Single-Variable IOL Power Formulae
			IOL Formulae Requiring a Different Approach to Optimizing Their Constant(s)
		Conclusions
		References
	37: Barrett Formulas: Strategies to Improve IOL Power Prediction
		Barrett Universal II (BUII)
		Classical vs. Segmental AL
		CAL vs. SAL Holladay 1
		CAL vs. SAL BUII
		Validation of BUII SAL (Barrett True AL Formula)
			Comparison of Standard BUII Formula Based on CAL to Haigis, Hoffer Q, Holladay 1, and SRK/T
			Comparison of Standard BUII Formula Based on CAL to the New Barrett True AL Formula Based on SAL
		Summary
		Measurements
		Additional Parameters
		New Parameters
		Post-Refractive Formulas
		Formula for Unexpected Refractive Outcome
		References
	38: The Castrop IOL Formula
		References
	39: CSO IOL Calculation Module
		Basic Concepts
		Prediction of the IOL Position
		Performing the IOL Power Calculation
		Examples of Application
		References
	40: Emmetropia Verifying Optical (EVO) Formula
		History
		Description
		Axial Length
		Corneal Power
		Lens Geometry
		Effective Lens Position
		Performance
		Toric Prediction
		Post-Myopic Laser Vision Correction
		Conclusion
		References
	41: The Haigis Formula
		The Thin Lens Formula
		Effect of Lens Geometry on IOL Position
		Calculations According to Haigis
		Optimization of Constants
			Single Optimization (Optimization of a0 Only)
			Triple Optimization (optimization of a0, a1, and a2)
		Clinical Measurements
			Methods
			Results
		In Summary
		References
			Additional Sources
	42: Hill-RBF: Improving IOL Power Selection by Artificial Intelligence
		Accuracy
		Artificial Intelligence for IOL Power Selection
		Making the Most of What’s Available
		Developing a Real-World Artificial Intelligence Calculator
		Boundary Models
		First Prospective Study
		Availability to the Worldwide Ophthalmic Community
		Current Accuracy
		New Applications for Increased Sensitivity and Accuracy
		Challenges
		Summary
		References
	43: Hoffer Formulas
		Introduction
		The Hoffer-Colenbrander Formula [First Generation]
		Adding the First AL-Dependent ACD [Second Generation]
		The Hoffer Q Formula [Third Generation]
		The Hoffer H Formula [Fourth Generation]
		The Hoffer H-5 Formula [Fifth Generation]
		The Hoffer QST Formula 2020 [Using Artificial Intelligence]
		References
	44: Holladay Formulas
		Introduction
		Basic Math and Science
		Brief History of IOL Power Formulas
		Holladay 1 Formula
		Holladay 2 Formula
		Axial Length Adjustment
		Formula Performance
		References
	45: Intraoperative Aberrometry
		Intraoperative Refractive Biometry: Aphakic Method
			Intraoperative Aberrometry
				Technologies
				Measurement
		Intraoperative Aberrometry for IOL Power Calculation
			Normal Eyes
			Long Eyes
			Short Eyes
			Eyes with Previous Corneal Refractive Surgery
		Intraoperative Aberrometry for Astigmatism Correction
			Regular Astigmatism
			Astigmatism After Corneal Refractive Surgery
		Conclusion
		References
	46: Kane Formula
		Toric Formula
		Keratoconus Formula
		References
	47: Ladas Super Formula: Origin and Evolution with AI
		Introduction
		LSF 1.0
		LSF 2.0. The Introduction of AI
		Automation of the Process and Next Steps
		Conclusion
		References
	48: Norrby Formulas for IOL Power Calculation
		Prologue
		Data
		Norrby Thick Lens Formula
		Norrby Thin Lens Formula
		Norrby Regression Formula
		Calculations for Other IOL Models
		Toric Calculation with Norrby Formulas
		Future
		Epilogue
		References
	49: OKULIX Raytracing Software
		Background: Raytracing?
		IOL Selection in OKULIX
		Input Parameters for IOL Calculation
			Axial Length Data
			Corneal Data
			IOL Data
		Benefits: Applications and Comparisons
			IOL Calculation in Eyes After Corneal Surgery
			Very Long Eyes
			Impact of IOL Shape Factor Variations
			Comparison with the “Big Data” Approach
		Additional Tools
		Limitations
			Accuracy of Refraction
			Accuracy of Placido/Scheimpflug Tomographers
			Accuracy of OCT Tomographers
			IOL Manufacturing Tolerances
		Conclusions and Future Developments
		References
	50: The Olsen Formula
		The Olsen Formula
			PhacoOptics® Software
				Data Entry
				Data Quality Is the Key
			Formula Validation
			Own History of Calculation Accuracy
			Recent Clinical Studies
		References
	51: Panacea IOL Calculator
		Introduction
		IOL Panacea Formula and Toric Calculator
			Axial Length
			Effective Lens Position
			Total Corneal Power
				Posterior-Anterior Relation/Gullstrand Ratio
				Corneal Asphericity and Spherical Aberration
				Corneal Multifocality
		Availability
		Conclusion
		References
	52: The PEARL-DGS Formula
		History of the PEARL-DGS Formula
		Description of the Current PEARL-DGS Formula
			General Principles
			Sum-of-Segments AL Calculation
			Optical Principles
			Posterior Corneal Radius Prediction
			TILP Back-Calculation
			TILP Prediction
			Predicted SE Calculation
			Corneal Index Optimization
			Extreme AL Adjustment in the Multiple Regression Algorithm
			Formula Development for IOLs with Unknown Geometry
			Prediction for IOLs with Unknown Geometry and No Available Data
		Performances of the PEARL Formula
		Perspectives
		References
	53: SRK Formula History
		1977–1980
			Collaboration Examples
			Preoperative ACD (ACDPRE)
		1980: SRK Is Born
			Paper Summary: Retzlaff
			Paper Summary: Sanders Kraff
		Early 1980s
		Late 1980s SRK II
		Secret Formulas
		1990 SRK/T
		SRK/T Development
		SRK/T Accuracy Comparison: Independent Data Sets
		SRK/T Accuracy Comparison 1990
		SRK/T Errata
		Closing Remarks and Thoughts
		References
	54: The T2 Formula
		Introduction
		Non-physiological Behaviour in the SRK/T Formula
		Non-physiological Behaviour in the Calculation of Corrected Axial Length
		Non-physiological Behaviour in the Calculation of Corneal Height
		Clinical Significance of the Corneal Height Cusp
		Solution to the SRK/T Cusp: The T2 Formula
		Evaluation of the T2 Formula
		Conclusion
		References
	55: The VRF and VRF-G Formulas
		Investigation of Formula
		Investigation of Estimated Lens Position
		CACD Constant of VRF Formula
		Evaluation of VRF Formula
			The VRF-G Formula
		Investigation of Formulas
		Evaluation of the Formula
		References
	56: Calculation of Phakic and Pseudophakic Additional Lenses
		Introduction to Phakic and Pseudophakic Additional Lenses
		Calculation of Additional Lenses
			Clinical Example 1
			Clinical Example 2
		Calculation of Toric Additional Lenses
			Clinical Example 3
		Simplification for a Thin Lens Model of the Cornea
		Simplification Using Linear Modeling
		References
	57: Online IOL Power Calculators
		Online Calculators for Spherical and Toric IOL Power
			ASCRS Post-refractive IOL Calculator
			Barrett Formula Website (Fig. 57.1)
			Cooke K6 Formula Website (Fig. 57.2)
			EVO Formula Website (Fig. 57.3)
			Hoffer QST Formula Website (Fig. 57.4)
			Holladay 2 Formula (Fig. 57.5)
			Kane Formula Website (Fig. 57.6)
			Karmona Formula Website (Fig. 57.7)
			Ladas Formula Calculator (Fig. 57.8)
			Nallasamy Formula Website (Fig. 57.9)
			PEARL DGS Formula Website (Fig. 57.10)
			RBF 3.0 Calculator Website (Fig. 57.11)
			PRINTOUTS
			ESCRS all Formula Calculator (Fig. 57.13)
		Online Calculators for Toric IOL Power
			ASSORT Web Calculators
		Free Downloadable Apps for Spherical and Toric IOL Power
			Panacea Formula
		Appendix
		Reference
	58: Power Calculations for Spherical and Toric Phakic IOLs
		Introduction
		Stigmatic PIOL Power Calculations
			Russian Method
			van der Heijde’s Method
			Holladay’s Method
		Astigmatic PIOL Power Calculations
			Sarver’s Method
			Astigmatic Decomposition
			Effectivity
		Phakic IOL Calculations
			Ideal IOL Power
			Predicted PO Refraction
			Calculating the elp Value
			Refractive Surprise Exchange Calculation
			Sample Calculation
		Discussion
		References
Part V: Toric IOL Calculations
	59: Astigmatism Notation: Dealing with Vectors
		Spherocylinder Formats
		Corneal Spherocylinder Formats
		Refractive Spherocylinder Formats
		Refractions and Aberrations
		Comparing Corneal and Refractive Astigmatisms
		Dioptric Vector Formats
		Næser’s Polar Value System
		Other Vector Formats
		Statistical Analysis
		Terminology
		Practical Calculation of Surgically Induced Refractive Change
		Calculating the Corneal SIA for a Temporal Incision
		References
	60: Astigmatism of the Cornea
		Corneal Astigmatism Based on Anterior Corneal Measurement
		Contribution of Posterior Corneal Astigmatism to Total Corneal Astigmatism
		Corneal Astigmatism Changes with Aging
		Higher-Order Aberrations of the Cornea
		Future Directions/Needs
		Conclusion
		References
	61: Lens and IOL Tilt
		Tilt and Visual Quality
		Measurement of Tilt
			Cross Section-Based Imaging
			Purkinje Reflexes
		Physiological Tilt
		Prediction of Post-operative Tilt
		Factors Influencing Tilt
			Capsulorrhexis
			Pseudoexfoliation
			IOL Material and Design
			After-Cataract
			IOL Implantation Outside the Capsular Bag
			Combined Surgery
		Effect of Tilt on Refraction
		Summary
		References
	62: Toric Calculations
		Keratometric Astigmatism and Total Corneal Astigmatism
		Solving the ACD Issue
		The Influence of IOL Tilt
		Current Toric Calculators
			Abulafia-Koch Toric Calculator
			Barrett Toric Calculator
			Barrett True-K Toric Calculator
			EVO 2.0 Toric Calculator
			Goggin Keratometry Adjustor Calculator
			Holladay Toric Calculator
			Johnson & Johnson Toric Calculator
			Kane Toric Calculator
			Næser-Savini Toric Calculator
			Rayner Toric Calculator
			Zeiss Toric Calculator
		Results
		References
Part VI: Special Situations
	63: IOL Power Calculation in Long Eye
		Factors Contributing to Challenges in IOL Power Calculation in Long Eyes
			Posterior Staphyloma
			Calculation of Axial Length Matching US Data: The IOL Master Calibration
			Extrapolation Issue in Extreme Long Eyes
			Principal Plane Shift in Negative-Power IOLs
		IOL Power Calculation Formulas for Long Eyes
			Axial Length Adjustment Methods (Wang-Koch Adjustment)
			Super Formula
			Barrett Universal II Formula
			Hill-RBF Formula
			Olsen Formula
			Kane Formula
			EVO Formula
			Panacea IOL Calculator
			Pearl-DGS Calculator
		Refractive Accuracy of IOL Formulas in Long Eyes
			IOL Power Prediction Accuracy
			Comparison of Refractive Accuracy Among Formulas
		Conclusion
		References
	64: IOL Power Calculation in the  Short Eye
		Introduction
		Definition
		Short Eye Classification
		Characteristic Features of Short Eyes
		Biometry in the Short Eye
		Results in Short Eyes
		Poly-pseudophakia: Piggy-Back Lens
		High-Power Intraocular Lenses
		Visual Acuities Obtained
		Conclusions
		References
	65: IOL Power Calculation After Corneal Refractive Surgery
		Introduction
		Corneal Refractive Surgery
		Sources of Error
		Solutions
			Correct ELP Calculation
			Correct Keratometry Calculation
		Calculation Methods
			Methods Requiring Clinical History Data (Original Keratometry and/or Refractive Change)
			Methods Not Requiring Clinical History Data (Original Keratometry and/or Refractive Change)
				Methods that Don’t Use Posterior Corneal Measurement
				Methods that Use Posterior Corneal Measurement
		Calculation After Radial Keratotomy
		Availability of These Methods
		References
	66: IOL Power Calculation in Keratoconus
		Approaches to IOL Power Calculation in Keratoconus
		New Methods for IOL Power Calculation in Keratoconus
		Conclusion
		References
	67: Patient-Specific Eye Models for Intraocular Lens Power Calculation in Irregular Corneas
		The Current Landscape for IOL Power Calculation in Keratoconus
		IOL Power Calculation After Keratoplasty (Penetrating or Posterior Lamellar)
		Present-Day Strategies for IOL Power Calculation After Corneal Refractive Surgery
		Behind the Need for Change in Odd-Corneas: Three-Dimensional Corneal Shape
		Patient-Specific IOL Power Calculation: Ray Tracing
		Redefining the Refractive Target: Matching the Ideal IOL in Keratoconus and Surgically Modified Patients
		Personalized Surgical Planning
		Appendix 1 Patient-Specific Ray-Tracing Eye Model (ZEMAX)
		Appendix 2 Optical Aberrations and Image Quality Metrics
		References
	68: IOL Calculation in Vitreoretinal Pathology and Surgery
		Introduction
		Axial Length Measurement
			Macular Thickening
			Macula-Off Retinal Detachment
			Scleral Buckling
			Vitrectomized Eyes
			Silicone Oil
		Bad Fixation and Macular Screening
		Vitreous Humor Optics
		Silicone Oil and Refraction
		IOL Position, Tilt and Centration
		IOL Calculation in the Vitrectomized Eye
		IOL Calculation in Phacovitrectomy
		References
	69: IOL Power Calculation in Keratoplasty
		Factors Limiting IOL Power Calculation Accuracy in Eyes Undergoing Simultaneous Cataract Surgery and Corneal Transplantation (Triple Procedure)
		Methods Available to Limit Refractive Surprises
			Triple Procedures (Simultaneous Keratoplasty + Cataract Extraction + IOL Implantation)
			Aphakic Eyes (Eyes Which Have Undergone Keratoplasty and Cataract Surgery and Have Been Left Aphakic)
			Pseudophakic Eyes (Eyes Which Have Undergone Keratoplasty and Have Been Left Pseudophakic with a Significant Residual Refractive Error)
			Transplanted Corneas Which Still Have Cataract (Eyes Which Have Undergone Keratoplasty But Still Have to Undergo Cataract Surgery)
		Management of Refractive Surprises
		Summary
		References
	70: IOL Power Choice in Children
		IOL Formula Accuracy
		The Growth of the Eye
		The Choice of Initial Postoperative Refraction
		References
	71: Out-of-the-Bag Implantation IOL Power
		Introduction
		Clinical Situations
			Capsular Damage
			Zonular Damage
		Out-of-the-Bag IOL Implantation
			Posterior Chamber
				Sulcus Support
					Sulcus IOL Power
				Scleral Fixation
					Fixation Point
					Scleral Fixated IOL Power
					Refractive Results
					Sulcus Fixation IOL
			Iris Plane
				Iris Claw IOL
					Iris Claw IOL Power
				Iris Sutured
					Iris Sutured IOL Power
			Anterior Chamber
				Anterior Chamber IOL Power
		References
	72: Fellow Eye Calculation
		Fellow Eye Calculation
		Case Study
		Comments
		References
Index