Why galaxy surveys mix up their Fourier modes—and how to unmix them

Galaxy surveys measure light from our past, not from a frozen moment in time. This breaks the standard assumption that different Fourier modes don't talk to each other—lensing, redshift, and time evolution create "mode-mixing" that confuses analysis. The authors reframe the problem: instead of Fourier-transforming galaxy positions, transform observer positions, recovering a diagonal power spectrum that naturally handles integrated effects like gravitational lensing and the Integrated Sachs-Wolfe effect without extra complications.