卢卡斯光子筛的聚焦特性研究

介绍了一种基于卢卡斯数编码设计的轴上四焦点光子筛,其各焦距分布与黄金分割比密切相关.实验上利用相移数字全息验证了设计器件具有轴上四焦点聚焦特性,测量结果表明:轴向焦距和横向焦斑光强分布与理论设计值一致.该振幅型光子筛具有体积小、重量轻、易加工等优点,可应用于X波段显微和生物细胞阵列成像等领域.

Focusing properties of Lucas sieves

A kind of optical diffractive element named photon sieve, which is essentially Fresnel zone plate in which the transmissive rings are replaced with a large number of randomly distributed isolated pinholes, can be used to focus X-ray and extreme ultraviolet lithography spectrum into spots with sizes smaller than the diameter of the smallest circular pinhole. However, both the traditional photon sieves and Fibonacci sieves have no more than two axial foci. In order to break this limitation, the Lucas sequence is introduced into the design of photon sieves, and thus producing four axial foci. With respect to the previous Fibonacci sequence, Lucas sequence has the same recursion relation as well as the same eigenvalue of golden mean γ=(1 + √5)/2. The only difference between them is the first two initial seeds. Based on Fresnel-Kichhoff diffraction theory, the simulation results show that there exist four focal spots with approximately equal intensity along the optical axis on condition that the hole diameters are set to be 1.16 times the underlying Fresnel zone width. Then in order to verify the validity of our proposed model, a Lucas sieve of diameter 12.11 mm and referred focal length 180 mm is fabricated by photolithography and its focusing properties are precisely measured by the in-line phase-shifting digital holography. In experiment, a quarter wave plate is used to realize two-step phase-shift interferences, and obtain the quad-focal length by auto-focusing algorithm in holography. Meanwhile, the quad-focal spots can also be calculated through the diffraction propagation of reconstructed object wave. Compared with the theoretical values, the measurement results indicate that the maximum deviation of quad-focal lengths is less than 0.9%, and the relative errors of the full width at half maximum of four Airy spots are all less than 5%. The experimental results agree well with the theoretical analysis results. Owing to the advantages of small volume, little weight and easy processing, Lucas sieve has great potential in X-ray microscopy, array imaging for living biological cell and especially in the next generation of synchrotron light sources.