Hello Sebastien,

Thank you so much for clarifying the creation of the transmission matrix. That explains a lot about why I was having some difficulty. I've followed your suggestions and attempting to recreate the TM for focusing, without a scattering medium present, does yield a focus on the detector (though the SLM profile doesn't look exactly like a quadratic lens profile). However, when I incorporate the scattering medium, I'm not seeing much of a change between the initial image and the "focused" image. Do you have any intuition as to why this might be the case?

Thanks,
Chris.

I'm attempting to reproduce the work of Popoff et al. (primarily "Controlling light through optical disordered media: transmission matrix approach" New Journal of Physics 13 (2011) 123021). Using roughly the same setup as depicted in Figure 1 of that paper (i.e. not using a reference arm and using the SLM in phase only modulation mode), I have measured the observed transmission matrix (TM) and then determined the actual TM via singular value decomposition.

However, I am now trying to use that TM to engineer a particular field at my detector (e.g. a focus) or sense (e.g. detect a pattern portrayed on the SLM) but am running into some trouble. My primary confusion seems to come from how to use this TM. Using Eq. 16 in said paper, I can calculate the the input field needed to yield a desired output field. The TM is a complex matrix, the field is complex and when I do this calculation, I yield another complex matrix (after reshaping). Since, I'm using an SLM to engineer the phase, then I extract the associated phase profile and display that on the SLM.

Unfortunately, this does not seem to yield the desired result at the detector plane. Any suggestions or tips would be greatly appreciated.

Thanks,
Chris.