  We show that if $A$ is a set of mutually orthogonal exponentials with respect
to the unit disk then $|A \cap [-R, R]^2| \lesssim_\varepsilon
R^{3/5+\varepsilon}$ holds. This improves the previous bound of $R^{2/3}$ by
Iosevich--Kolountzakis. The main new ingredient in the proof is a variant of
Marstrand's projection theorem.
