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## Transmission Matrix: Measuring and Utilizing 2 years 6 months ago #66

 sanjiv OFFLINE New Member Posts: 14 Karma: 0 Hi I am a beginner in Matlab. I would like to simulate a transmission matrix in matlab. Can I get some papers/resources from which I can simulate it from the perspective of Matlab. Could anyone please help me.

## Transmission Matrix: Measuring and Utilizing 2 years 6 months ago #67

 sebastien.popoff OFFLINE Administrator Posts: 29 Thank you received: 10 Karma: 3 Hi Sanjiv, That depends on what kind of transmission matrix you want to simulate and what for. The easiest matrix is a Gaussian complex random matrix: T = randn(n,m)+j*randn(n,m) This matrix would not conserve the energy nor it will make appear the effect of mesoscopic correlations. However, it is valid in most cases: if you consider a subpart of a full transmission matrix (which is usually the case when only one polarization is controlled/measured and with a limited numerical aperture) and when the discretization of the field is such that the elements correspond to different speckle grains (and thus are considered uncorrelated). If you want to simulate the full transmission matrix of a slab or a disordered wire, then the singular values of the matrix has to follow the bimodal distribution. You would then have to generate a diagonal matrix with values that follow the distribution and then multiply on both side by unitary random matrices. Again, I cannot go in much details if I do not know more about what you want to do.

## Transmission Matrix: Measuring and Utilizing 2 years 6 months ago #71

 sanjiv OFFLINE New Member Posts: 14 Karma: 0 Thanks Sebastien. I succeeded in making a transmission matrix by T=rand(m,n)+1i*rand(m,n); and performing SVD and normalization. However I am interested in modeling a scattering medium which is combination of two operator first operator is a Random phase scattering matrix followed by a free space propagation. This is one layer and there are N such layers. Can you suggest me how can I do it in Matlab ?

## Transmission Matrix: Measuring and Utilizing 1 year 8 months ago #89

 jian29ye4 OFFLINE New Member Posts: 3 Karma: 0 [quote="sebastien.popoff" post=33】 The matrix is measured in the Hadamard basis, meaning that the first output complex field measured corresponds to the first Hadamard vector in input, not to the first pixel of the SLM. Of course you need to perform a change the basis to obtain the TM in the pixel basis (this is the matrix you want). [/quote] Hi, Sebastien. May I know how to exactly change the basis??

## Transmission Matrix: Measuring and Utilizing 1 year 8 months ago #91

 sebastien.popoff OFFLINE Administrator Posts: 29 Thank you received: 10 Karma: 3 Hi Jian, The change of basis you need to perform depends on the basis you use for the measurements, so only you can know. If you use a Hadamard basis, then you need to multiply by the inverse of the Hadamard matrix (which is conveniently a Hadamard matrix) to retrieve the matrix in the pixel basis. What you measure is T' = T \times Ha with Ha the Hadamard matrix and T the transmission matrix. So you need the operation T = T' \times (Ha)^-1 to get T. en.wikipedia.org/wiki/Hadamard_matrix Best, Sebastien
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