General equations for the null-screen test for aspherical surfaces with deformation coefficients.

Area of Science:

• Optical Engineering
• Surface Metrology

Background:

• Testing fast aspherical surfaces is crucial for optical system performance.
• Conventional methods for null screen design can be complex and computationally intensive.

Purpose of the Study:

• To present a modified, simplified approach for calculating null screens for testing fast convex/concave aspherical surfaces.
• To introduce aberration polynomials into the sagitta equation for straightforward null screen generation.

Main Methods:

• Incorporation of the aberration polynomial into the sagitta equation.
• Development of computationally simple equations for null screen calculation.
• Validation using a fast aspherical convex condenser lens (f/0.18).

Main Results:

• The modified approach allows for simple and computationally efficient null screen generation.
• Validation demonstrated a percentage error smaller than 1.3% in surface shape coefficient recovery.
• The method is easy to implement programmatically.

Conclusions:

• The presented modified approach offers a significant improvement in the ease and efficiency of null screen calculation for aspherical surface testing.
• This method is suitable for testing challenging optical components like fast aspherical lenses.
• The accuracy achieved validates the practical applicability of this computational approach.