A method of estimating chordal holdup values of gas, oil, and water (εG, εO, εW) for tomographic imaging of a three-phase flow through a volume, including: providing an X-ray source for irradiating through said volume and X-ray sensors for discriminating between a first and a second radiation bands, conducting first calibration measurements (IGS, IOS, IWS) of said first radiation band, conducting second calibration measurements (IGH, IOH, IWH) of said second radiation band, arranging a mixture of two or more fluids, irradiating said volume and conducting X-ray measurements (IS, IH) in said radiation bands, establishing a relationship between a function of holdup values f(εG, εW) of at least gas and water and said X-ray measurements (IS, IH), searching holdup values (εG, εW) that minimize said function of holdup values f(εG, εW) under the constraints of the sum of said holdup values is more than or equal to zero and less than or equal to one, i.e. that 0≦εG+εW≦1.