  Direct visualization of electronic-structure symmetry within each crystalline
unit cell is a new technique for complex electronic matter research. By
studying the Bragg peaks in Fourier transforms of electronic structure images,
and particularly by resolving both the real and imaginary components of the
Bragg amplitudes, distinct types of intra-unit cell symmetry breaking can be
studied. However, establishing the precise symmetry point of each unit cell in
real space is crucial in defining the phase for such Bragg-peak Fourier
analysis. Exemplary of this challenge is the high temperature superconductor
Bi2Sr2CaCu2O8+d for which the surface Bi atom locations are observable, while
it is the invisible Cu atoms that define the relevant CuO2 unit-cell symmetry
point. Here we demonstrate, by imaging with picometer precision the electronic
impurity states at individual Zn atoms substituted at Cu sites, that the phase
established using the Bi lattice produces a ~2% (2pi) error relative to the
actual Cu lattice. Such a phase assignment error would not diminish reliability
in the determination of intra-unit-cell rotational symmetry breaking at the
CuO2 plane. Moreover, this type of impurity atom substitution at the relevant
symmetry site can be of general utility in phase determination for Bragg-peak
Fourier analysis of intra-unit-cell symmetry.
