Purpose: An analytic method to design excitation and emission filters of a multispectral fluorescence imaging system is proposed and was demonstrated in an application to poultry fecal inspection Methods: A mathematical model of a multispectral imaging system is proposed and its system parameters, such as excitation and emission filters, were optimally determined by linear discriminant analysis (LDA). An alternating scheme was proposed for numerical implementation. Fluorescence characteristics of organic materials and feces of poultry carcasses are analyzed by LDA to design the optimal excitation and emission filters for poultry fecal inspection. Results: The most appropriate excitation filter was UV-A (about 360 nm) and blue light source (about 460 nm) and band-pass filter was 660-670 nm. The classification accuracy and false positive are 98.4% and 2.5%, respectively. Conclusions: The proposed method is applicable to other agricultural products which are distinguishable by their spectral properties.