I struggled with finding the mathematical explanation behind this transformation, so hopefully this helps someone. It is explained in the second paragraph of the background of this paper:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2572624/
The way I understood it is that for illumina infinium arrays the two channels:
Cy5 = Red = A allele = X signal Cy3 = Green = B allele = Y signal
The raw data is analyzed like this in GenomeStudio
The raw X and Y signal from each allele is normalized to account for background signal, etc using a proprietary illumina algorithm
These normalized X and Y signals for each sample can be plotted on a cartesian coordinate system to get this type of plot in GenomeStudio:
- More commonly, the "polar transformation" of these values are shown with R plotted against theta like this:
- R is the intensities. R for a sample is the sum of normalized X and Y (R= X+ Y)
- Theta is the B allele frequency and is calculated by: (2/pi)*arctan(normalized Y/ normalized X)
You can check this math by selecting "filter rows" in the "Full Data Table" and making Theta, R, X, and Y visible for every SNP in GenomeStudio then plugging in X and Y to the formulas in 3.
I'm afraid basic statistics is not bioinformatics. Where did you get the data? Only the file generator knows for sure what theta and R mean, but it sounds like minor allele frequency and some correlation. A log ratio sounds like an effect likelihood. Maybe you want those to be high? Plot them as a function of position, and post a picture please.