Correcting flat mirrors with surface stress: analytical stress fields.

Area of Science:

• Optics
• Materials Science
• Mechanical Engineering

Background:

• Accurate fabrication of thin mirrors is crucial for advanced space telescopes.
• Surface stress application offers a method to correct residual height errors in fabricated mirrors.

Purpose of the Study:

• To present surface stress fields capable of correcting arbitrary height errors in thin, flat plates.
• To evaluate the efficacy of different stress field configurations for mirror surface correction.

Main Methods:

• Developing two surface stress fields for exact height error correction in thin plates.
• Representing stress fields as Zernike polynomial combinations for round plates.
• Simulating stress application on a measured glass wafer with known height errors.

Main Results:

• Equibiaxial stress alone is insufficient for exact height error correction in round plates.
• Exact correction requires all three components of surface stress.
• A measured 3.64 μm RMS height error on a glass wafer was reduced to 0.34 μm RMS using an optimized equibiaxial stress field.
• Using all three stress components resulted in exact correction with 2.5x lower RMS stress compared to equibiaxial stress alone.

Conclusions:

• Precise surface deformation of thin mirrors can be achieved using controlled surface stress.
• A full three-component stress field is necessary for exact correction of arbitrary surface errors.
• This technique holds promise for fabricating high-precision optics for next-generation space telescopes.