How to convert polar meshgrid to Cartesian meshgrid?

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I prepared a Cartesian meshgrid (10x10) and then converted it to polar. After doing some calculations and filling all 100 elements of the matrix now I want to see the final picture back in Cartesian coordinates. So, I want to map every single index of that 10x10 matrix to its Cartesian counterpart. How can I do that?

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