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ransmitted-light coherence-controlled holographic microscope (CCHM) based on an off-axis achromatic and space-invariant interferometer with a diffractive beamsplitter has been designed, constructed and tested. It is capable to image objects illuminated by light sources of arbitrary degree of temporal and spatial coherence. Off-axis image-plane hologram is recorded and the image complex amplitude (intensity and phase) is reconstructed numerically using fast Fourier transform algorithms. Phase image represents the optical path difference between the object and the reference arms caused by presence of an object. Therefore, it is a quantitative phase contrast image. Intensity image is confocal-like. Optical sectioning effect induced by an extended, spatial incoherent light source is equivalent to a conventional confocal image. CCHM is therefore capable to image objects under a diffusive layer or immersed in a turbid media. Spatial and temporal incoherence of illumination makes the optical sectioning effect stronger compared to a confocal imaging process. Object wave reconstruction from the only one recorded interference pattern ensures high resistance to vibrations and medium or ambience fluctuations. The frame rate is not limited by any component of the optical setup. Only the detector and computer speeds limit the frame rate. CCHM therefore allows observation of rapidly varying phenomena. CCHM makes the ex-post numerical refocusing possible within the coherence volume. Coherence degree of the light source in CCHM can be adapted to the object and to the required image properties. More coherent illumination provides wider range of numerical refocusing. On the other hand, a lower degree of coherence makes the optical sectioning stronger, i.e. the optical sections are thiner, it reduces coherence-noise and it makes it possible to separate the ballistic light. In addition to the ballistic light separation, CCHM enables us to separate the diffused light. Multi-colour-light