The fatty acid elongase 1 (FAE1) gene catalyzes the initial condensation step in the elongation pathway of VLCFA (very long chain fatty acid) biosynthesis and is thus a key gene in erucic acid biosynthesis. Based on a worldwide collection of 62 accessions representing 14 tribes, 31 genera, 51 species, 4 subspecies and 7 varieties, we conducted a phylogenetic reconstruction and correlation analysis between genetic variations in the FAE1 gene and the erucic acid trait, attempting to gain insight into the evolutionary patterns and the correlations between genetic variations in FAE1 and trait variations. The five clear, deeply diverged clades detected in the phylogenetic reconstruction are largely congruent with a previous multiple gene-derived phylogeny. The Ka/Ks ratio (<1) and overall low level of nucleotide diversity in the FAE1 gene suggest that purifying selection is the major evolutionary force acting on this gene. Sequence variations in FAE1 show a strong correlation with the content of erucic acid in seeds, suggesting a causal link between the two. Furthermore, we detected 16 mutations that were fixed between the low and high phenotypes of the FAE1 gene, which constitute candidate active sites in this gene for altering the content of erucic acid in seeds. Our findings begin to shed light on the evolutionary pattern of this important gene and represent the first step in elucidating how the sequence variations impact the production of erucic acid in plants.

It was found that binary phase diffractive optical element (DOE) with non-π phase difference had higher diffraction efficiency and adjustable zero-order intensity than a 0-π one. However, existing design methods are all based on the simulated annealing algorithm and thus computationally expensive. In this paper, a simple and efficient method using the iterative Fourier transform algorithm (IFTA) is proposed. In this method, the target pattern is first modified via reducing the zero-order intensity. Then, the IFTA is adopted to design the conventional 0-π DOE. Subsequently, the phase distribution remains unchanged and the phase difference is carefully adjusted to increase the zero-order intensity so that the reconstructed pattern is consistent with the target. To verify this method, several typical DOEs for beam splitting were designed and fabricated, and the result showed that the proposed method is effective.

This paper presents an approach that is capable of producing a color image using a single composite diffractive optical element (CDOE). In this approach, the imaging function of a DOE and the spectral deflection characteristics of a grating were combined together to obtain a color image at a certain position. The DOE was designed specially to image the red, green, and blue lights at the same distance along an optical axis, and the grating was designed to overlay the images to an off-axis position. We report the details of the design process of the DOE and the grating, and the relationship between the various parameters of the CDOE. Following the design and numerical simulations, a CDOE was fabricated, and imaging experiments were carried out. Both the numerical simulations and the experimental verifications demonstrated a successful operation of this new approach. As a platform based on coaxial illumination and off-axis imaging, this system is featured with simple structures and no cross-talk of the light fields, which has huge potentials in applications such as holographic imaging.

Divergent light illumination can effectively increase the diffraction angle of holographic projection. However, the achieved maximum image size is limited to the geometric enlargement of the hologram size with the existing double-sampling Fresnel diffraction algorithm. In this paper, an effective method for further magnifying the image is proposed. The theoretical maximum size under divergent illumination is first analyzed. On this basis, a virtual intermediate plane is introduced between the source plane and the image plane. Then three-step diffraction calculation is performed to evaluate the Fresnel diffraction between the hologram plane and the image plane so that the sampling interval on the image plane is related to the position of the virtual plane and can be flexibly tuned. Consequently, the achieved image size can be further enlarged. The feasibility of the proposed method is demonstrated by simulations and experiments.

Microlens arrays (MLAs) are key optical components in laser beam homogenization. However, due to imperfect surface profiles resulting from microfabrication, the functionalities of MLAs in beam modulation could be compromised to some extent. In order to address this issue, the effects of surface profile mismatches between ideal and fabricated MLAs on beam homogenization were analyzed. Four types of surface profile errors of MLAs were modeled theoretically and numerical simulations were conducted to quantitatively estimate the effects of these profile errors on beam homogenization. In addition, experiments were conducted to validate the simulation results, revealing that profile errors leading to optical deviations located on the apex of microlenses affected beam homogenization less than deviations located further away from it. This study can provide references for the further applications of MLAs in beam homogenization.

Conventional iterative phase retrieval suffers from an inherent phase ambiguity due to limited measurement intensity. Multimodal amplitude modulation introduces physical constraints to tackle the underdetermination challenge. However, the time overhead caused by mask switching slows down the imaging speed. To increase imaging speed, we report an accelerated coded phase retrieval method by optimizing modulation masks. Compared to existing methods that require at least four patterns as inputs, the proposed method requires only three mask modulations to robustly reconstruct complex objects. The transparent pixels of the two masks partially overlap, constituting a strong constraint on the objective function. An additional random mask increases the difference between diffraction intensity patterns and ensures that the algorithm converges. The proposed method of efficient modulation using pure amplitude elements may open the door to short-wavelength high-speed complex amplitude imaging. Numerical simulations and proof-of-principle experiments have verified the feasibility of this method.