Abstract
Lensless imaging is a high potential and currently intensely targeted research goal, in view of those fields of applications for which aberration-free high-resolution lenses are not available, for example for x-ray imaging. A recently proposed (direct inversion) variant of lensless imaging combines the advantages of two classical routes toward lensless imaging, the high-resolution characteristics of iterative object reconstruction, and the direct and deterministic nature of holographic reconstruction. Here, we use a simple standard optical setup using visible wavelength, a lithographic test object and a phase-shifting reference object to demonstrate the approach. Importantly, we show that a phase-shifting reference object, instead of the absorption mask proposed earlier, is sufficient for object reconstruction. This is relevant in view of the much easier implementation in future x-ray applications.
Export citation and abstract BibTeX RIS
GENERAL SCIENTIFIC SUMMARY Introduction and background. In our everyday world just as in most physics laboratories, optical images are formed by mirrors or by lenses, in optical instruments ranging from digital cameras and glasses to microscopes or telescopes. There are cases, however, when lenses or mirrors are not practical or simply not available in sufficient quality. Figure errors or aberrations can lead to image distortion and can limit the sharpness or resolution of images.
Main results. Using a simple optical test bench, as can be found in many undergraduate lab courses, it has been shown that images can be computed numerically from the diffracted radiation collected by a CCD camera behind the object, in a direct and fast one-step calculation. Replacing lenses or mirrors by a computer algorithm, or 'lens-less imaging' as it is called, is currently being studied intensively by several reasearch groups world wide. The present work is based on a deterministic algorithm which is able to calculate the image in a single mathematical step, in contrast to iterative algorithms which rely on random numbers to seed the calculation. There is one constraint which makes it possible to directly calculate the image: the unknown object to be imaged must be placed in a rectangular mask, acting like a frame to the object. This was predicted and first shown just recently.
Wider implications. With the generalization of the present work this stringent requirement can be relaxed, and very thin transparent frames can be used instead of absorbing frames. This is exactly what is needed if one wants to apply lens-less imaging where it is most urgently needed: to high photon energy radiation like x-rays which passes most materials with little attenuation, and for which high resolution lenses are not available in sufficient quality. Sharper images at the nanoscale can be envisioned by replacing lenses by a computer algorithm.