Ultra-broadband extreme-ultraviolet lensless imaging of extended complex structures

Lensless imaging is an elegant approach to high-resolution microscopy, which is rapidly gaining popularity in applications where imaging optics are problematic. However, current lensless imaging methods require objects to be placed within a well-defined support structure, while the light source needs to have a narrow, stable, and accurately known spectrum. Here we introduce a general approach to lensless imaging without spectral bandwidth limitations or sample requirements. We use two time-delayed coherent light pulses, and show that scanning the pulse-to-pulse time delay allows the reconstruction of diffraction-limited images for all spectral components in the pulse. Moreover, an iterative phase retrieval algorithm is introduced, which uses these spectrally resolved Fresnel diffraction patterns to obtain high-resolution images of complex extended objects without any support requirements. We demonstrate this two-pulse imaging method with octave-spanning visible light sources (in both transmission and reflection geometries), and with broadband extreme-ultraviolet radiation from a high-harmonic source. This demonstrates that our approach enables effective use of low-flux ultra-broadband sources, such as table-top soft-X-ray systems, for high-resolution imaging.