Buchdahl's glass dispersion coefficients calculated from Schott equation constants

Area of Science:

• Optical Engineering
• Materials Science
• Computational Physics

Background:

• Accurate modeling of optical materials is crucial for lens design.
• Schott and Buchdahl dispersion models are widely used but can be complex to evaluate.
• Evaluating dispersion coefficients at arbitrary wavelengths is computationally intensive.

Purpose of the Study:

• To develop a rapid method for evaluating Buchdahl's dispersion coefficients.
• To enable calculations at any arbitrary base wavelength using Schott equation constants.
• To simplify the application of Buchdahl's dispersion model in optical design.

Main Methods:

• Applied Buchdahl's chromatic coordinate transformation to the Schott equation for refractive index.
• Utilized a Taylor series expansion of the transformed Schott equation.
• Equated the expansion to the square of the Buchdahl dispersion model and matched terms up to fourth order.

Main Results:

• Derived analytical equations for Buchdahl's dispersion coefficients.
• The method allows for efficient calculation at any specified base wavelength.
• Validated the accuracy of the derived coefficients against established models.

Conclusions:

• The presented method offers a computationally efficient approach to determine Buchdahl's dispersion coefficients.
• This facilitates faster optical design and analysis using the Schott and Buchdahl dispersion models.
• The technique is broadly applicable for optical materials characterization.