Using special algorithms, scientists have significantly improved computational imaging in lensless microscopes. The algorithms were used not only to generate the image, but also to improve the optical signal, making it possible to obtain images with higher resolution using only mathematical methods, without making any physical changes to the microscope. Scientists from Saint Petersburg National Research University of Information Technology, Mechanics and Optics (ITMO University) and Tampere University of Technology used computational superresolution phase retrieval from phase-coded diffraction patterns to artificially expand the field of view and consequently the resolution of the image. Scientists confirmed the efficiency of the superresolution sparse phase amplitude retrieval algorithm in simulations and physical experiments. They showed that high-level superresolution could be achieved with a superresolution factor of up to four; i.e., the pixel size of the reconstructed object was four times smaller than the pixel size of the sensor. In comparison with the wavelength, the achieved superresolution was up to two-thirds the wavelength. Both simulation tests and experiments demonstrated good-quality imaging for superresolution and a significant advantage over diffraction-limited resolution. “We used the mathematical method of sparse representation of signal. A simple example may help understand how it works,” said ITMO researcher Nikolay Petrov. “Imagine that you have a grid paper and you choose a square area of 8 × 8. If you register the signal in this 8 × 8 square, then the retrieved image will be discretized in the same way. But if the signal meets certain requirements of sparsity, you can potentially use the same 8 × 8 signal to restore all the missing information regarding the same object, but with a smaller discrete mesh of 16 × 16 or even 32 × 32. At the same time, the resolution will increase twofold or fourfold correspondingly. “Moreover, our computational algorithm expands the signal beyond the registration area. This essentially implies the appearance of extra pixels around our 8 × 8 square, which therefore expands the field of view." Using this approach, scientists were able to improve image resolution without any modifications in the quality of the image sensor and other microscope components. The ability to improve performance without the need to change the equipment could lead to significant cost savings. “What seems to be the trend in this area of research is the simplification and optimization of optical systems,” said Tampere researcher Igor Shevkunov. “To achieve even more optimization, we need to remove the spatial light modulator (SLM) from the system and reduce the amount of filters. One of the obvious paths to achieve these goals is to use a single filter with sequential movement. This will make our lensless computational microscope even cheaper, as the spatial light modulator is the most expensive element in such systems.” Lensless computational microscopy can be used to visualize transparent objects or measure their shape in 3D. These microscopes have no lenses or objectives that focus light on an image sensor. Instead they rely on measuring diffraction patterns that result from illuminating an object with laser or LED light. The image obtained from these patterns is generated using a computational approach. Improvement of lensless computational microscopy could further research in biology, chemistry, medicine and other fields. The research was published in Optica, a publication of The Optical Society (doi: 10.1364/OPTICA.4.000786).