Consider the two following sets of two-dimensional systems:
\[\begin{array}{l} S_U(\mu_U) = (a = \{1, 1\}, \mu = \{ -\mu_U/2, \mu_U/2 \}), \\ S_V(a_1, a_2, \mu_V) = (a = \{a_1, a_2\}, \mu = \{ -\mu_V/2, \mu_V/2 \}). \end{array}\]
Define the trigonometric Prony map for each system:
\[\begin{cases} m_{U,k}(\mu_V) = e^{-2\pi i (-\mu_U/2) k \delta} + e^{-2\pi i (\mu_U/2) k \delta}, \\ m_{V,k}(a_1, a_2, \mu_V) = a_1 e^{-2\pi i (-\mu_V/2) k \delta} + a_2 e^{-2\pi i (\mu_V/2) k \delta}. \end{cases}\]
Define a scalar field in the \((a_1, a_2, \mu_V)\) space:
\[F(a_1, a_2, \mu_V) = \sqrt{\Delta m_0^2 + \Delta m_1^2 + \Delta m_2^2 + \Delta m_3^2}, \quad \Delta m_k = m_{U,k} - m_{V,k}.\]
You can see equipotential surfaces of the field on the following figure (\(\delta = 0.2\), \(\mu_U \in [0.1, 5]\))