Beam arrangement with limited projections based on tunable diode laser absorption spectroscopy is the key to achieving a more accurate two-dimensional reconstruction of the combustion field. Using fractional calculus theory, a beam optimization method based on fractional Tikhonov regularization is proposed. The beam arrangement function based on fractional Tikhonov regularization is established by extending the standard Tikhonov regularization to fractional modes. The optimal beam arrangement is chosen by using genetic algorithm for different orders in the range of (0,1). Using 20 laser beams scanning the characteristic absorption spectrum of H₂O in the near-infrared band 7185.6 cm^-1, and modeling calculations in a 10×10 element discrete tomography domain. Comparing the reconstruction results of the five beam arrangements for different Gaussian distribution models, the beam arrangement based on fractional Tikhonov regularization shows more obvious advantages. This proposed design method will be valuable for the theoretical study of the optimal design of two-dimensional measurement beams based on the tunable diode laser absorption spectroscopy technique, which can promote the application of this technique in the two-dimensional reconstruction of complex engine combustion fields and combustion efficiency improvement.