Coating Impact on Flatness Calculator

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)