Recommended coordinate systems for thin spherocylindrical lenses

Area of Science:

• Optometry and Vision Science
• Optical Engineering
• Mathematical Optics

Background:

• Thin spherocylindrical lenses can be represented as vectors in a vector space.
• Existing coordinate systems for lenses include those based on the lens power matrix and the Humphrey Vision Analyzer.
• Understanding lens combinations is crucial for accurate vision correction.

Purpose of the Study:

• To highlight the utility of a specific Cartesian coordinate system derived from the Humphrey Vision Analyzer.
• To demonstrate how this system simplifies lens addition trigonometry.
• To show the system's effectiveness in preserving symmetry for sets of spherical, Jackson crossed-cylinder, and cylindrical lenses.

Main Methods:

• Utilizing a Cartesian coordinate system associated with the Humphrey Vision Analyzer.
• Employing a related cylindrical coordinate system.
• Applying vector space principles to lens representation and addition.
• Analyzing the symmetry of lens sets within the chosen coordinate system.

Main Results:

• The chosen Cartesian and related cylindrical coordinate systems simplify the trigonometry of adding lenses.
• This coordinate system preserves symmetry when depicting sets of spherical lenses, Jackson crossed-cylinders, and cylindrical lenses.
• The study discusses suitable coordinates for lens-based statistical analysis.

Conclusions:

• A specific Cartesian coordinate system, related to the Humphrey Vision Analyzer, offers significant advantages for lens calculations.
• This system simplifies complex trigonometric operations in lens addition and enhances the visualization of lens sets.
• Extending the lens vector space to general optical systems is not straightforward.