We propose differential holography as a method to overcome the long-standing forward-scattering problem in photoelectron holography and related techniques for the three-dimensional imaging of atoms. Atomic images reconstructed from experimental and theoretical Cu 3p holograms from Cu(001) demonstrate that this method suppresses strong forward-scattering effects so as to yield more accurate three-dimensional images of side-and back-scattering atoms.PACS numbers: 61.14. -x, 42.40.-i Holography [1] is a method of recording both the amplitudes and phases of waves scattered by an object illuminated with coherent radiation, and using this information to directly construct a three-dimensional image of the object. Szöke [2] first suggested that coherent outgoing waves from atomically-localized sources of photoelectrons, fluorescent x-rays, and γ-rays could be used to achieve atomic-scale holography. This idea was initially demonstrated theoretically for the case of photoelectrons by Barton [3], and then extended into a multienergy format by Barton and Terminello and by Tong and co-workers [4]. By now several experimental approaches to such atomic-resolution holography have been demonstrated, including photoelectrons [5,6,7,8] Among these methods, photoelectron holography (PH) has the advantages of being capable of studying the local atomic structure around each type of emitter without requiring long-range order and of distinguishing emitters through core-level binding-energy shifts [8]. Photoelectron holograms also show strong modulations of up to ±50%, so such effects are easily measurable. However, PH can suffer from serious image aberrations due to the strength of electron scattering. The atomic scattering factor f is a highly anisotropic function of scattering angle, and can depend strongly on electron kinetic energy E k . In particular, as E k increases above a few hundred eV, f becomes more and more significant in the forward direction, resulting in a strong forward-scattering (FS) peak [16] that can induce image aberrations. Beyond this, PH also can suffer from multiple-scattering (MS) effects due to the scattering strength.Various reconstruction algorithms and measurement methods [4,5,7,17] have been proposed to correct for the anisotropic f and MS effects, some of which can be summarized viawhere U is the image intensity at position r, χ is the normalized 3D hologram, and the function or operator W permits describing the difference between algorithms, with W =1 in the original multi-energy formulations [4]. One alternative algorithm [5] sets W = f −1 k, θ k r so as to divide out the anisotropic f , where θ k r is the angle between r and k. In another algorithm [7] based on the more ideal electron back scattering (BS), a window function for W that limits the integral in Eq. (1) to be in a small cone ofk around −r is chosen to emphasize the imaging of BS atoms. Although successful in several applications [7,18], it is difficult to apply this smallcone method to many systems where the imaging of FS or even side...