The goal of MSE is to use custom patterns having multiple spatial frequency components, and extract the attenuated spatial frequency components remitted from the sample. First, multifrequency illumination patterns are projected onto a sample at different phases and a camera detects the remitted light. Each spatial frequency component in the custom pattern is simultaneously attenuated by the sample. We can express our series of raw intensity images as a vector ($I$), which is the product of the Fourier series coefficients of each frame with the reflectance at each spatial frequency component, shown in Eq. (2). Here, $C$ represents the frequency amplitude and phase maps for each projected pattern (i.e., the Fourier coefficient matrix). For consistency, we express each frequency component as a real-valued sinusoid, although single complex exponentials (analytical expression) can also be used. $R$ represents the amplitude attenuation for each frequency component in the reflectance maps. $k$ and $p$ are the indices for the Fourier component and projected pattern, and $m$ and $n$ are the total number of projected patterns and Fourier components, respectively. Display Formula
$Ip(x,y)=Ck,p(x,y)*Rk(x,y)\u2192Rk(x,y)=Cp,k(x,y)\u22121*Ip(x,y),Ip(x,y)=[I1(x,y)\vdots Im(x,y)]Rk(x,y)=[R1(x,y)\vdots Rn(x,y)],Cp,k(x,y)=[C1,1(x,y)cos[\omega x,y,1+\varphi 1(x,y)]\u2026C1,n(x,y)cos[\omega x,y,n+\varphi 1(x,y)]\vdots \ddots \vdots Cm,1(x,y)cos[\omega x,y,1+\varphi m(x,y)]\cdots Cm,n(x,y)cos[\omega x,y,n+\varphi m(x,y)]].$(2)