A lens-free microscope system (10, 50, 70) for imaging a sample containing micro-objects comprising: a sample holder configured to hold the sample; a portable electronic device having an imaging sensor array and at least one processor therein; an extension configured to be secured to the portable electronic device adjacent to the imaging sensor array; a spatial filter disposed within the extension at a distance z 1 from the sample holder on first side of the sample holder, the spatial filter comprising an aperture configured to allow the passage of illumination; wherein the imaging sensor array having an active area is disposed within the portable electronic device and located at a distance z 2 from the sample holder on a second, opposite side of the sample holder, wherein z 2 <<z 1; an illumination source disposed within the extension and configured to illuminate the sample through the aperture, the spatial filter being interposed between the illumination source and the sample holder; and wherein the at least one processor is configured to execute image processing software to receive image frames from the imaging sensor array containing raw hologram amplitude images of the micro-objects, the raw hologram amplitude images comprising amplitude information, wherein the image processing software is further configured to recover lost hologram phase information of the micro-objects of interest using an iterative reconstruction algorithm to digitally reconstruct a microscope-quality image of the micro-objects having a field-of-view equal to the active area of the imaging sensor array using the recovered lost hologram phase information and the amplitude information. a sample holder configured to hold the sample; a portable electronic device having an imaging sensor array and at least one processor therein; an extension configured to be secured to the portable electronic device adjacent to the imaging sensor array; a spatial filter disposed within the extension at a distance z 1 from the sample holder on first side of the sample holder, the spatial filter comprising an aperture configured to allow the passage of illumination; wherein the imaging sensor array having an active area is disposed within the portable electronic device and located at a distance z 2 from the sample holder on a second, opposite side of the sample holder, wherein z 2 <<z 1; an illumination source disposed within the extension and configured to illuminate the sample through the aperture, the spatial filter being interposed between the illumination source and the sample holder; and wherein the at least one processor is configured to execute image processing software to receive image frames from the imaging sensor array containing raw hologram amplitude images of the micro-objects, the raw hologram amplitude images comprising amplitude information, wherein the image processing software is further configured to recover lost hologram phase information of the micro-objects of interest using an iterative reconstruction algorithm to digitally reconstruct a microscope-quality image of the micro-objects having a field-of-view equal to the active area of the imaging sensor array using the recovered lost hologram phase information and the amplitude information.