Optical interference matrix is an effective way to calculate reflectivity in multilayer thin film.
The matrix method is usually employed for calculation of reflection coefficient.
The reflectance in multilayers is calculated by the optical admittance (Y ) which is the ratio of the total tangential magnetic (C) and electric fields (B).
I am not familiar with the matrix method - but does it work correctly when the wavelength of the light is similar to the thickness of the layers? Now you have to take wavelength and constructive and destructive interference effectgs into account.
Briefly, in the transfer matrix method each layer in the multylayers system, along with the two semiinfinite media on top and botom of the system, are desribed by relatively simple matrix with dimension 2x2. The elements in the matrix include optical constants and thickness of the layer, angle of incidence and wavelength, of course. When you ascribe to each layer a matrix, you have to multiply all matrices and you will obtained again 2x2 matrix. Transmitance and reflectance are nothing but elements of the final matrix. Hopefuly, now it is more clearly.
There is the optical analysis of solar cell layers by the TCAD Silvaco. You can use it to calculate the reflectance of the multi layer structure.
For anti reflection coating you can make the layer optical path thickness = lambda/4 so that the the bounced radiation from back surface has a path difference of lambda/2 to sum destructively with the reflected radiation from the front surface. In this way one builds an interference filter for cancelling the reflected waves from the front and back surfaces. This concept can be applied for each layer. So, the thickness of the layer = lambd0/4 n , with n is the refractive index and lambda0 is the free space wavelength.
But is this concept is not used you can calculate the reflected radiation from the front surface and from the interfaces and the final reflecting surface between the anti reflective coating and the active layer.
If you assume that the incident radiation flux is Fi, then the reflected from the front surface R1= roh1^2 Fi, with roh1 is the reflection coefficient at the front surface.
The reflected from the the second surface R2= roh2^2 (1- roh1^2)Fi,
The characteristic matrix method is a much effective way to calculate the reflectance of a multilayer system as you can be able to program it using matlab or any other programming language you are familiar with.