Coating Impact on Flatness Calculator

View All Technical Tools

Surface Flatness Before Coating, SF1:

Wavelength for Flatness Specification (nm):

Substrate Thickness, t_s (mm):

Substrate Diameter, D (mm):

Substrate Material:

Coating Type:

Coating Technology Used:

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]
E_s	Substrate Elasticity Modulus [Pa]
E_c	Coating Elasticity Modulus [Pa]
t_s	Substrate Thickness [µm]
t_c	Coating Thickness [µm]
v_s	Substrate Poisson’s Ratio (unitless)
v_c	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.