MultiSpectral Optoacoustic Tomography (MSOT) is a fast developing imaging modality, combining the high resolution and penetration depth of ultrasound with the excellent contrast from optical imaging of tissue. Absorption and scattering of the near infrared excitation light modulates the spectral profile of light as it propagates deep into biological tissue, meaning the images obtained provide only qualitative insight into the distribution of tissue chromophores. The goal of this work is to accurately recover the spectral profile of excitation light by modelling light fluence in the data reconstruction, to enable quantitative imaging. We worked with a commercial small animal MSOT scanner and developed our light fluence correction for its' cylindrical geometry. Optoacoustic image reconstruction pinpoints the sources of acoustic waves detected by the transducers and returns the initial pressure amplitude at these points. This pressure is the product of the dimensionless Grüneisen parameter, the absorption coefficient and the light fluence. Under the condition of constant Grüneisen parameter and well modelled light fluence, there is a linear relationship between the initial pressure amplitude measured in the optoacoustic image and the absorption coefficient. We were able to reproduce this linear relationship in different physical regions of an agarose gel phantom containing targets of known optical absorption coefficient, demonstrating that our light fluence model was working. We also demonstrate promising results of light fluence correction effects on in vivo data.