  Lensless microscopy with coherent or partially coherent light sources is a
well known imaging technique, commonly referred as digital in-line holographic
microscopy. In the established methods, both the spatial and temporal coherence
of light play a crucial role in determining the resolution of reconstructed
object. We report lensless microscopy with a spatially extended white LED, a
light source of low spatial and very low temporal coherence. The wave-field
propagation between two parallel planes can be obtained using a convolution
operation, where the convolution kernel depends on the object-sensor distance
and the characteristics of the light source. For a light source of unknown
characteristics, this kernel is an unknown function. In the proposed
reconstruction method, we decompose an unknown convolution kernel of very large
size (128 X 128) into a small unknown light-source-specific kernel (size 9 X 9)
and a known light-source-independent kernel (size 128 X 128). This drastically
reduces the number of parameters to be estimated at the system identification
step, which has been performed here by one time imaging of the known
microscopic objects. Final unknown object estimation has been performed using
the upper-bound constrained deconvolution. A lateral resolution of ~1-2
micrometer has been demonstrated.
