Analytical Fresnel imaging models for photon sieves

Flattened Gaussian focal spot with uniform phase produced by photon sieve

The equivalent pupil and the point spread function constitute the Fourier-Bessel transform relation. Based on this, we established the equivalent pupil function theory of rotating symmetric photon sieve and derived the Fourier transform of the flattened Gaussian function. The focal spot produced by this type of photon sieve exhibits a uniform intensity and phase distribution. According to the numerical results, the flattened Gaussian field distribution is consistent with the designed function. In addition, the nonuniformity in intensity and phase is approximately 1% and less than 1/170 wavelength, respectively.

Numerical simulation model of an optical filter using an optical vortex

Vortex beam has the potential to significantly improve the performance of lidar (light detection and ranging) and optical communication applications in which low signal-to-noise ratio (SNR) limits the detection/transmission range. The vortex beam method allows for spatially separating the coherent light (laser signal) from the incoherent light (the background radiation and multiple-scattered light) of the received signal. This paper presents results of a simulation model in which the optical vortex acts as an optical filter. We present instrument parameters that describe the filtering effect, e.g., the form of the vortex phase modulation function, the topological charge of the vortex and the focal length of a virtual Fresnel lens that is used for optical filtering. Preliminary experimental results show that the background radiation within the spectral filter bandwidth can be suppressed by as much as 95%. At the same time, we retain 97% of the coherent laser signal. Our simulation model will be used in future design of lidar instruments and optical communication systems in which the optical vortex method is used for optical filtering of the detected signals.

Amplitude Zone Plate in Adaptive Optics: Proposal of the Principle

One of the main elements in hardware-based adaptive optics systems is a deformable mirror. There is quite a large number of such mirrors based on different principles and exhibiting varying performance. They constitute a significant portion of the cost of the final optical devices. In this study, we consider the possibility of replacing an adaptive mirror with the adaptive amplitude Fresnel zone plate, implemented using a digital light-processing matrix. Since such matrices are widely used in mass industry products (light projectors), their costs in large batches are 1–2 orders of magnitude lower than the cost of inexpensive deformable mirrors. Numerical modeling for scanning an optical coherence tomography system with adaptive optics is presented. It is shown that wavefront distortions with high spatial frequencies and large amplitudes can be corrected using an amplitude Fresnel zone plate. The results are compared with piezoelectric and microelectromechanical system mirrors.

Trapezoid-kinoform zone plate lens - a solution for efficient focusing in hard X-ray optics

X-ray microscopes are powerful tools in the nano-inspection of materials owing to their ultra-high resolution at the molecular level. However, the focusing efficiency of binary zone plate lenses as key components in such probes is merely 5% in practice, hindering their application in advanced scientific research. Although kinoform zone plate lenses are in principle supposed to possess high efficiency beyond binary ones, little progress has been reported so far due to the shortage of both a theoretical calculation approach and greyscale lithography for generating fine three-dimensional (3D) kinoform zones of the lenses. This paper reports our theoretical work for a modified beam propagation method to compute the focusing performance and state-of-the-art 3D greyscale electron beam lithography for kinoform zone plate lenses. Three different zone shapes - binary, kinoform and top-flat kinoform (nicknamed the trapezoid-kinoform) - were compared both theoretically and experimentally. Theoretical calculations suggest, for the first time, that the trapezoid-kinoform zone plate gives rise to the highest focusing efficiency among the three lenses, which was proved by optical characterization of the fabricated lens with hard X-rays. As high as 40% of the focusing efficiency by Au trapezoid-kinoform lenses with resolution of 250 nm at 8 keV has been achieved, which is two times higher than that of binary zone plate lenses. The origin of the enhanced efficiency in the trapezoid-kinoform zone plate lens was explained by the joint contributions from both the refraction through the kinoform slope and the diffraction through the top flat part of the trapezoid-kinoform zone plate. Such a breakthrough in focusing efficiency sheds light on the further development of X-ray lenses with both high resolution and high efficiency.

Efficient computation of 2D point-spread functions for diffractive lenses

Diffractive lenses, such as Fresnel zone plates, photon sieves, and their modified versions, have been of significant recent interest in high-resolution imaging applications. As the advent of diffractive lens systems with different configurations expands, the fast and accurate simulation of these systems becomes crucial for both the design and image reconstruction tasks. Here we present a fast and accurate method for computing the 2D point-spread function (PSF) of an arbitrary diffractive lens. The method is based on the recently derived closed-form mathematical formula for the PSF and the transfer function of a diffractive lens. In the method, first, the samples of the transfer function are computed using the transmittance function of the diffractive lens, and then the inverse Fourier transform of this transfer function is computed to obtain the PSF. For accurate computation, the selection of the sampling parameters is handled with care, and simple selection rules are provided for this purpose. The developed method requires a single fast Fourier transform, and, therefore, has little computational complexity. Moreover, it is also applicable to any diffractive lens configuration with arbitrary-shaped structures and modulation. As a result, this fast and accurate PSF computation method enables efficient simulation, analysis, and development of diffractive lens systems under both focused and defocused settings.

Compressive spectral imaging with diffractive lenses

Compressive spectral imaging enables the reconstruction of an entire 3D spectral cube from a few multiplexed images. Here we develop a novel compressive spectral imaging technique using diffractive lenses. Our technique uses a coded aperture to spatially modulate the optical field from the scene and a diffractive lens such as a photon sieve for both dispersion and focusing. Measurement diversity is achieved by changing the focusing behavior of the diffractive lens. The 3D spectral cube is then reconstructed from highly compressed measurements taken with a monochrome detector. A fast sparse recovery method is developed to solve this large-scale inverse problem. The performance is illustrated for various scenarios with different compression ratios through simulations. The results demonstrate that promising reconstruction performance can be achieved at high compression levels. This opens up new possibilities for high-resolution spectral imaging with simpler and low cost designs.