Hi forum members,

Could you please shed some light for me on the measurement of TM, for the case of a multimode fibre?

- Is it absolutely critical to use a orthorgonal basis in the input? As for the case of a MMF, can I use random patterns as per the paper below. My thinking is along this
- Use some set of random patterns and measure a TM.
- Apply SVD on the TM, find SVs (say 98% of the total power)
- Use a bigger set of random patterns, measure again the TM
- Apply SVD again, check the SVs... when the number of SVs is stable it indicates that all of the modes has been activated (assuming large NA input)

Can it be done that way? Here the paper they used the random pattern but they just say that 900 patterns is enough.

https://arxiv.org/ftp/arxiv/papers/1806/1806.09315.pdf

- The TM for a multimode fibre should ideally has the rank of N (number of macro pixel on the SLM)? It is because I think the basic vectors of both left and right singular matrices are the same fibre modes, so that the TM would be an square vector of rank N.

My question is: After obtaining the TM, should I apply SVD on such TM and try to reduce it to a leaner version (less noisy) of the TM before testing the stuffs such as focusing or imaging?

- I was told that if I do the SVD directly on the intensities obtained from different input (basically not applying the 4-phase or off-axis technique to extract the complex field pattern but just use the intensity vectors as column of the "intensity TM"), the number of SVs will be roughly twice the number of modes. I could not find any paper which actually did this but just wonder if it is something obvious that someone here can give me some light on? For the case of TM matrix measured on the complex field pattern then the number of SVs is the number of modes as shown in this paper

https://www.osapublishing.org/ol/fulltext.cfm?uri=ol-37-21-4558&id=244834

Thank you very much for your help.