The strength of any microscopy method lies in the ability of its applied contrast mechanism to visualise and quantify properties in biological structures without interfering with normal physiological behaviour. Second-harmonic generation (SHG) is one of the several available label-free nonlinear contrast mechanisms that can be utilised in the microscope. Since SHG requires a noncentrosymmetric media, only certain biological structures can inherently generate the signal. Collagen, starch granules and the thick myosin filaments of striated muscle are examples of biological structures that generate SHG. Investigating the SHG intensity dependence on the incident polarisation allows the relative magnitudes of the second-order nonlinear susceptibility tensor components to be determined. For example, collagen and muscle myosin can be modeled with cylindrical symmetry, which results in three surviving tensor components. Since the samples have different material composition the tensor component magnitudes and the resulting polarisation dependence differ drastically. In this work the outgoing polarisation of the generated second harmonic is also measured for higher accuracy fitting of data obtained from biological samples. The polarisation-in polarisation-out (PIPO) surface plots can be used to obtain values for the nonlinear susceptibility tensor components. In addition, birefringence in the fundamental beam and emitted second harmonic can be accounted for in the PIPO theory, thereby providing more accurate results of the nonlinear susceptibility tensors in birefringent biological structures. The birefringence in a single skeletal muscle fibre was determined to be Δn(1028 nm)=0.0018±0.0004 and Δn(514 nm)=0.0021±0.0003.