We successfully extend the standard Fibonacci zone plates with two on-axis foci to the generalized Fibonacci photon sieves (GFiPS) with multiple on-axis foci. We also propose the direct and inverse design methods based on the characteristic roots of the recursion relation of the generalized Fibonacci sequences. By switching the transparent and opaque zones, according to the generalized Fibonacci sequences, we not only realize adjustable multifocal distances but also fulfill the adjustable compression ratio of focal spots in different directions.

Extreme ultraviolet (EUV) light is difficult to focus due to strong absorption of most materials. Photon sieves (PS), rather than Fresnel zone plates (FZP), can focus EUV to smaller spot and suppress the higher orders of secondary maxima by several orders of magnitude. The number of pinholes used in PS is far more than that of transparent rings used in FZP, providing a great flexibility to manipulate structured focusing in EUV. In this work we investigate the Fermat-spiral PS to produce focused vortices with different topological charges. Experiment at the wavelength of 46.9 nm is carried out and multi-planar coherent diffractive imaging is used to retrieve the phase map of the focused EUV vortices. These results show the enormous potential of PS for manipulating EUV light. This study not only provides a compact, affordable substitute to focusing vortices where transmissive optics materials are unavailable, but also provides a route of converting various complex light manipulation ranging from visible light to EUV and soft x-ray.

Multi-wavelength imaging diffraction system is a promising phase imaging technology due to its advantages of no mechanical movement and low complexity. In a multi-wavelength focused system, spectral bandwidth and dispersion correction are critical for high resolution reconstruction. Here, an optical setup for the multi-wavelength lensless diffraction imaging system with adaptive dispersion correction is proposed. Three beams with different wavelengths are adopted to illuminate the test object, and then the diffraction patterns are recorded by a image sensor. The chromatic correction is successfully realized by a robust refocusing technique. High-resolution images can be finally retrieved through phase retrieval algorithm. The effectiveness and reliability of our method is demonstrated in numerical simulation and experiments. The proposed method has the potential to be an alternative technology for quantitative biological imaging.

Multi-wavelength diffraction imaging is a lensless, high-resolution imaging technology. To avoid multiple exposures and enable high-speed data collection, here an innovative setup for the single-exposure multi-wavelength diffraction imaging based on a blazed grating is proposed. Since the blazed angle varies with the wavelength, the diffraction patterns for the individual wavelengths can be separated from each other and recorded in a single measurement at one time. A method of high-precision position alignment between different wavelength patterns is proposed in our system to achieve good image quality and high resolution. Experiments on a phase-only USAF resolution target and biological samples were carried out to verify the effectiveness of our proposed method. This proposed setup has such advantages as a simpler structure, fast recording, and algorithm robustness.

Compared to off-axis holography, phase-shifting technology takes full use of the space-bandwidth product of the detector array. Here we introduce the Chinese Taiji into diffractive lenses and generate the phase-shifting focal spots, which not only can be used for a spherical reference wave, but also make it possible to realize the lensless Fourier-transform holography. The experimental results of a 1951 U.S. Air Force resolution test target verify the validity of the above theory in the optical region. Owing to the amplitude-only diffractive lenses, these kinds of lenses will have great potential in x-ray holography or biochemical microscopy for the next generation of synchrotron radiation and free electron lasers in the future.

Phase shifting is the key technique in in-line digital holography, but traditional phase shifters have their own limitations in short wavelength regions. Here, phase-shifting Greek-ladder sieves with amplitude-only modulation are introduced into in-line digital holography, which are essentially a kind of diffraction lens with three-dimensional array diffraction-limited foci. In the in-line digital holographic experiment, we design two kinds of sieves by lithography and verify the validity of their phase-shifting function by measuring a 1951 U.S. Air Force resolution test target and three-dimensional array foci. With advantages of high resolving power, low cost, and no limitations at shorter wavelengths, phase-shifting Greek-ladder sieves have great potential in X-ray holography or biochemical microscopy for the next generation of synchrotron light sources.