We present an improved method for recording a synthesized Fourier hologram under incoherent white-light illumination. The advantage of the method is that the number of real projections needed for generating the hologram is significantly reduced. The new method, designated as synthetic projection holography, is demonstrated experimentally. We show that the synthetic projection holography barely affects the reconstructed images. However, by increasing the number of observed projections one can improve the synthetic projection hologram quality.