Spectroscopy is a popular technique for identifying and quantifying fluorophores in fluorescent materials. However,quantifying the fluorophore of interest can be challenging when the material also contains other fluorophores (baseline), particularly if the emission spectrum of the baseline is not well-defined and overlaps with that of the fluorophore of interest. In this work, we propose a method that is free from any prior assumptions about the baseline by utilizing fluorescence signals at multiple excitation wavelengths. Despite the nonlinearity of the model, a closed-form expression of the least squares estimator is also derived. To evaluate our method, we consider the practical case of estimating the contributions of two forms of protop...