Lensless microscopy by multiplane recordings: sub-micrometer, diffraction-limited, wide field-of-view imaging.

Lensless microscopy is attractive because lenses are often large, heavy and expensive. We report diffraction-limited, sub-micrometer resolution in a lensless imaging system that does not need a reference wave and imposes few restrictions on the density of the sample. We use measurements of the intensity of light scattered by the sample at multiple heights above the sample and a modified Gerchberg-Saxton algorithm to reconstruct the phase of the optical field. We introduce a pixel-splitting algorithm that increases resolution beyond the size of the sensor pixels, and implement high-dynamic-range measurements. The resolution depends on the numerical aperture of the first measurement height only, while the field of view is limited by the last measurement height only. As a result, resolution and field of view can be controlled independently. The pixel-splitting algorithm also allows imaging with light of low spatial coherence, and we show that such low coherence is beneficial for a larger field of view. Using illumination from three LEDs, we produce full-color images of biological samples. Finally, we provide a detailed analysis of the limiting factors of this lensless microscopy system. The good performance demonstrated here can allow lensless systems to replace conventional microscope objectives in some situations.