Retrace error calibration for interferometric measurements using an unknown optical system.

Area of Science:

• Optical Engineering
• Metrology
• Interferometry

Background:

• Classical interferometric null tests require identical measurement and reference beam paths to prevent retrace errors.
• Existing methods to correct retrace errors, such as computer-generated holograms (CGHs), are often costly and time-consuming.
• Mathematical treatments of retrace errors typically require detailed optical designs of interferometer components, which are often unavailable for commercial off-the-shelf assemblies.

Purpose of the Study:

• To introduce a flexible and broadly applicable mathematical model for accounting for retrace errors in interferometry.
• To present a method that eliminates the need for specific optical designs of interferometer components, particularly transmission spheres.
• To enable the use of standard, off-the-shelf optical assemblies in interferometric measurements without compromising accuracy.

Main Methods:

• Introduction of the Black Box Model (BBM), a mathematical model based on point characteristic functions.
• Application of the BBM within the framework of Tilted Wave Interferometry (TWI).
• Utilizing an extended calibration method to adapt the BBM to the behavior of real interferometers, bypassing the need for optical designs.

Main Results:

• The Black Box Model effectively accounts for retrace errors in interferometric measurements.
• The extended calibration method allows the BBM to be applied without requiring knowledge of the interferometer's internal optical design.
• This approach enables accurate interferometry using standard, commercially available optical components.

Conclusions:

• The Black Box Model offers a versatile and practical solution for managing retrace errors in interferometry.
• The method significantly reduces the cost and complexity associated with correcting retrace errors.
• This technique broadens the applicability of interferometry, especially when using standard optical assemblies with undisclosed designs.