“…In optical coherence tomography (OCT), low coherence spectroscopy (LCS) and low coherence interferometry (LCI), light from a low coherence source interact with a sample and a Michelson interferometer is used to extract depth-dependent information about the sample from the backscattered light [9]. In spectroscopic OCT (S-OCT) and LCS, broadband illumination and spectrally sensitive signal detection allows for characterisation of spectrally resolved absorption and scattering properties [6] which have been used to quantify media composition from absorption [10][11][12][13][14] and, when combined with Mie scattering models, to quantify particle size [4,5,[14][15][16][17][18][19][20][21]. The use of inverse problem approaches to analyse particle size distribution in a sample is prevalent in systems using forward-scattering of light (see for example: [22,23]) but is less common in backscattered light techniques such as OCT where it is known as inverse S-OCT (IS-OCT) [19,20,[24][25][26] In this paper, we briefly review the theory of S-OCT to show where each of the existing IS-OCT techniques are derived from [19,20,[24][25][26] before extending the technique presented in [26], that used Lambert-Beer's law to describe the time frequency distributions, to backscattering spectra from Mie theory.…”