A method for lens-free imaging of a sample or objects within the sample comprising: a) illuminating a sample located a distance z 1 away from a light source; b) obtaining a first plurality of images of the sample with a sensor disposed a distance z 2 away from the sample, wherein z 1>> z 2, wherein the plurality of images are obtained by changing the relative position of the light source, sensor, or sample in lateral shifts; c) adjusting the distance z 2; d) obtaining an additional plurality of images of the sample at the adjusted distance z 2, wherein the additional plurality of images at the adjusted distance z 2 are obtained by changing the relative position of the light source, sensor, or sample in lateral shifts; e) repeating operations c) and d) a plurality of times; f) generating a high-resolution pixel super-resolved hologram at each distance z 2 from the first plurality of images and the additional plurality of images at the adjusted distance z 2, which are lower resolution holograms spatially shifted with respect to each other; g) recovering lost phase information of the high-resolution pixel super-resolved hologram at a given z 2 distance comprising: i. analytically computing, using Transport of Intensity equation, an initial phase estimate at the given distance z2 based on two different measurements of the high resolution pixel super-resolved holograms at two different heights; ii. updating the phase estimate from (i) using forward propagation of an estimate of the complex optical wave at the given distance z 2 to a modified or adjusted z 2 distance, which generates new amplitude and phase information for the forward propagated complex wave; iii. wherein at the modified or adjusted z 2 distance, an amplitude of the super resolved hologram replaces the currently computed amplitude information of the forward propagated complex wave from (ii) and the new phase information is retained for next iterations; iv. forward propagating the complex estimated wave to reach a further modified or adjusted z 2 distance; v. repeating steps (iii) and (iv) among all or a sub-set of measured planes corresponding to different z 2 distances as a loop until convergence is achieved; and h) outputting a phase-recovered complex field at an object plane based on the recovered lost phase information obtained in (g) for one or more z 2 planes. a) illuminating a sample located a distance z 1 away from a light source; b) obtaining a first plurality of images of the sample with a sensor disposed a distance z 2 away from the sample, wherein z 1>> z 2, wherein the plurality of images are obtained by changing the relative position of the light source, sensor, or sample in lateral shifts; c) adjusting the distance z 2; d) obtaining an additional plurality of images of the sample at the adjusted distance z 2, wherein the additional plurality of images at the adjusted distance z 2 are obtained by changing the relative position of the light source, sensor, or sample in lateral shifts; e) repeating operations c) and d) a plurality of times; f) generating a high-resolution pixel super-resolved hologram at each distance z 2 from the first plurality of images and the additional plurality of images at the adjusted distance z 2, which are lower resolution holograms spatially shifted with respect to each other; g) recovering lost phase information of the high-resolution pixel super-resolved hologram at a given z 2 distance comprising: i. analytically computing, using Transport of Intensity equation, an initial phase estimate at the given distance z2 based on two different measurements of the high resolution pixel super-resolved holograms at two different heights; ii. updating the phase estimate from (i) using forward propagation of an estimate of the complex optical wave at the given distance z 2 to a modified or adjusted z 2 distance, which generates new amplitude and phase information for the forward propagated complex wave; iii. wherein at the modified or adjusted z 2 distance, an amplitude of the super resolved hologram replaces the currently computed amplitude information of the forward propagated complex wave from (ii) and the new phase information is retained for next iterations; iv. forward propagating the complex estimated wave to reach a further modified or adjusted z 2 distance; v. repeating steps (iii) and (iv) among all or a sub-set of measured planes corresponding to different z 2 distances as a loop until convergence is achieved; and i. analytically computing, using Transport of Intensity equation, an initial phase estimate at the given distance z2 based on two different measurements of the high resolution pixel super-resolved holograms at two different heights; ii. updating the phase estimate from (i) using forward propagation of an estimate of the complex optical wave at the given distance z 2 to a modified or adjusted z 2 distance, which generates new amplitude and phase information for the forward propagated complex wave; iii. wherein at the modified or adjusted z 2 distance, an amplitude of the super resolved hologram replaces the currently computed amplitude information of the forward propagated complex wave from (ii) and the new phase information is retained for next iterations; iv. forward propagating the complex estimated wave to reach a further modified or adjusted z 2 distance; v. repeating steps (iii) and (iv) among all or a sub-set of measured planes corresponding to different z 2 distances as a loop until convergence is achieved; and h) outputting a phase-recovered complex field at an object plane based on the recovered lost phase information obtained in (g) for one or more z 2 planes.