# Coating Impact on Flatness Calculator

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### Coating Type:Anti-Reflective (AR) Highly-Reflective (HR)

Surface Flatness After Coating (PV), SF2: --

Percentage Change in Surface Flatness: --

Note: Assumes coating on one side only

Equations and Corresponding Legend: $$R = \frac{1}{6} \left( \frac{\left( \frac{E_s \times t_s ^3}{1 - v_s} \right ) + \left( \frac{E_c \times t_c ^3}{1 - v_c} \right )}{\sigma \times t_c \times \left( t_c + t_s \right )} \right )$$ $$\text{SF}_2 = \text{SF}_1 \left[\text{waves} \right] \times \frac{\text{SF}_1 \left[ \large{ \unicode[Cambria Math]{x03BC}} \normalsize{\text{m} } \right ]}{\text{SF}_1 \left[ \large{ \unicode[Cambria Math]{x03BC}} \normalsize{\text{m} } \right ] + \frac{D^2}{8R}}$$ $$\% \text{Change} = 100 \% \times \left | \frac{\text{SF}_1 - \text{SF}_2}{\text{SF}_1} \right |$$

 R Radius of Curvature [µm] D Substrate Diameter [µm] Es Substrate Elasticity Modulus [Pa] Ec Coating Elasticity Modulus [Pa] ts Substrate Thickness [µm] tc Coating Thickness [µm] vs Substrate Poisson’s Ratio (unitless) vc Coating Poisson’s Ratio (unitless) σ Coating Stress (MPa) SF1 Surface Flatness Before Coating (waves or µm) SF2 Surface Flatness After Coating (waves or µm)

The calculator is based on the following assumptions:

• Mechanical properties of coating materials are averaged from the bulk values
• Coating stress for a particular coating technology is approximated from historical data
• Stress-induced deformation is assumed to be spherical
• It is assumed that R >> D

## Description

Many modern-day optical coating technologies, such as magnetron sputtering and ion beam sputtering, involve high-energy material deposition. While these techniques can create coatings with distinct advantages, they can impart a significant amount of stress on the coating and substrate. This stress can lead to issues with surface flatness, impacting the transmitted or reflected wavefront error of coated optics.

This calculator approximates the impact of coating-induced stress on the surface flatness of a coated optic.

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