The phase problem is inherent to crystallographic, astronomical and optical 
imaging where only the intensity of the scattered signal is detected and the 
phase information is lost and must somehow be recovered to reconstruct the 
object's structure. Modern imaging techniques at the molecular scale rely on 
utilizing novel coherent light sources like X-ray free electron lasers for the 
ultimate goal of visualizing such objects as individual biomolecules rather than 
crystals. Here, unlike in the case of crystals where structures can be solved by 
model building and phase refinement, the phase distribution of the wave 
scattered by an individual molecule must directly be recovered. There are two 
well-known solutions to the phase problem: holography and coherent diffraction 
imaging (CDI). Both techniques have their pros and cons. In holography, the 
reconstruction of the scattered complex-valued object wave is directly provided 
by a well-defined reference wave that must cover the entire detector area which 
often is an experimental challenge. CDI provides the highest possible, only 
wavelength limited, resolution, but the phase recovery is an iterative process 
which requires some pre-defined information about the object and whose outcome 
is not always uniquely-defined. Moreover, the diffraction patterns must be 
recorded under oversampling conditions, a pre-requisite to be able to solve the 
phase problem. Here, we report how holography and CDI can be merged into one 
superior technique: holographic coherent diffraction imaging (HCDI). An inline 
hologram can be recorded by employing a modified CDI experimental scheme. We 
demonstrate that the amplitude of the Fourier transform of an inline hologram is 
related to the complex-valued visibility, thus providing information on both, 
the amplitude and the phase of the scattered wave in the plane of the 
diffraction pattern. With the phase information available, the condition of 
oversampling the diffraction patterns can be relaxed, and the phase problem can 
be solved in a fast and unambiguous manner. We demonstrate the reconstruction of 
various diffraction patterns of objects recorded with visible light as well as 
with low-energy electrons. Although we have demonstrated our HCDI method using 
laser light and low-energy electrons, it can also be applied to any other 
coherent radiation such as X-rays or high-energy electrons.