Computational out-of-focus imaging increases the space–bandwidth product in lens-based coherent microscopy

The space–bandwidth product (SBP) of modern objective lenses is often significantly larger than the pixel count of opto-electronic image sensor chips, and, therefore, much of the information transmitted by the optical system cannot be adequately sampled or digitized. To resolve this mismatch, microscopes are in general designed to maintain the resolution of the optical system while significantly wasting the field of view (FOV) and SBP of the objective lens. We introduce a wide-field and high-resolution coherent imaging method that uses a stack of out-of-focus images to provide much better utilization of the SBP of an objective lens. We demonstrate our approach on a benchtop microscope by using a demagnification camera adapter to match the active area of the image sensor chip to the FOV of an objective lens. We show that the resulting spatial undersampling caused by capturing a large FOV can be mitigated through an iterative pixel super-resolution algorithm that uses e.g., ∼three to five slightly out-of-focus images, yielding an ∼8-fold increase in the SBP of the microscope. Furthermore, the same pixel super-resolution algorithm also achieves phase retrieval, revealing the optical phase information of the specimen. We compared our method against traditional off-axis and phase-shifting digital holographic microscopy modalities and demonstrated at least 3-fold reduction in the number of images required to achieve the same SBP. This technique could be used to maximize the throughput and SBP of lens-based coherent imaging and holography systems and inspire new microscopy designs that benefit from the inherent autofocusing steps of a scanning microscope to increase its SBP.