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We present a new technique for removing twin image in in-line digital Fourierholography using a combination of Fourier transformations. Instead of recordingonly a Fourier transform hologram of the object, we propose to record acombined Fourier transform hologram by simultaneously recording the hologram ofthe Fourier transform and the inverse Fourier transform of the object withsuitable weighting coefficients. Twin image is eliminated by appropriateinverse combined Fourier transformation and proper choice of the weightingcoefficients. An optical configuration is presented for recording combinedFourier transform holograms. Simulations demonstrate the feasibility of twinimage elimination. The hologram reconstruction is sensitive to phaseaberrations of the object, thereby opening a way for holographic phase sensing.

Twin image elimination in digital holography by combination of Fourier transformations