Diffraction theory applied to X‐ray imaging with clessidra prism array lenses

Clessidra (hourglass) lenses, i.e. two large prisms each composed of smaller identical prisms or prism‐like objects, can focus X‐rays. As these lenses have a periodic structure perpendicular to the incident radiation, they will diffract the beam like a diffraction grating. Refraction in the prisms is responsible for blazing, i.e. for the concentration of the diffracted intensity into only a few diffraction peaks. It is found that the diffraction of coherent radiation in clessidra lenses needs to be treated in the Fresnel, or near‐field, regime. Here, diffraction theory is applied appropriately to the clessidra structure in order to show that blazing in a perfect structure with partly curved prisms can indeed concentrate the diffracted intensity into only one peak. When the lens is entirely composed of identical perfect prisms, small secondary peaks are found. Nevertheless, the loss in intensity in the central peak will not lead to any significant widening of this peak. Clessidras with perfect prisms illuminated by full coherent X‐ray radiation can then provide spatial resolutions, which are consistent with the increased aperture, and which are far below the height of the single small prisms.     

Diffraction of partially coherent X‐rays in clessidra prism arrays

When small triangular prisms are arranged in arrays which have an overall appearance like an hourglass (in Italian: clessidra) they can focus X‐rays owing to a combined action of diffraction and refraction. From the optical point of view these objects can be regarded as a Fresnel variant of concave transmission lenses. Consequently they can provide larger apertures than purely refractive lenses. However, one has to recognize that clessidra lenses will strongly diffract as the lens structure is periodic in the direction perpendicular to the incident beam. In experiments the diffraction is reduced because it is difficult to illuminate the large apertures with a full spatially coherent wavefront. So the illumination is at best partially coherent. In order to interpret available experimental data for this condition, diffraction theory has been applied appropriately to the clessidra structure, taking into account the limited spatial coherence. The agreement between the theoretical simulations and experimental data is very good, keeping the lens properties at their projected values and allowing for only two free model parameters. The first is the lateral spatial coherence; the second is a lens defect, a rounding of all edges and tips in the structure. Both values obtained from the simulations have been found to be in agreement with expectations.     

Large‐aperture prism‐array lens for high‐energy X‐ray focusing

A new prism‐array lens for high‐energy X‐ray focusing has been constructed using an array of different prisms obtained from different parabolic structures by removal of passive parts of material leading to a multiple of 2π phase variation. Under the thin‐lens approximation the phase changes caused by this lens for a plane wave are exactly the same as those caused by a parabolic lens without any additional corrections when they have the same focal length, which will provide good focusing; at the same time, the total transmission and effective aperture of this lens are both larger than those of a compound kinoform lens with the same focal length, geometrical aperture and feature size. This geometry can have a large aperture that is not limited by the feature size of the lens. Prototype nickel lenses with an aperture of 1.77 mm and focal length of 3 m were fabricated by LIGA technology, and were tested using CCD camera and knife‐edge scan method at the X‐ray Imaging and Biomedical Application Beamline BL13W1 at Shanghai Synchrotron Radiation Facility, and provided a focal width of 7.7 µm and a photon flux gain of 14 at an X‐ray energy of 50 keV.     

基于反转光楔和泽尼克多项式的共形光学设计

采用一对反向旋转的累斯莱棱镜可以实现对目标视场的动态扫描,并应用一对内表面为泽尼克边缘矢高表面的透镜对共形光学整流罩引入的主要像差进行校正,剩余像差则由累斯莱棱镜内表面进行补充校正.设计实例中,通过比较光学系统校正前后的成像质量以验证这种校正方法的有效性.     

On the use of clessidra prism arrays in long‐focal‐length X‐ray focusing

Clessidra (hour‐glass) X‐ray lenses have an overall shape of an old hour glass, in which two opposing larger triangular prisms are formed of smaller identical prisms or prism‐like objects. In these lenses, absorbing and otherwise optically inactive material was removed with a material‐removal strategy similar to that used by Fresnel in the lighthouse lens construction. It is verified that when the single prism rows are incoherently illuminated they can be operated as independent micro‐lenses with coinciding image positions for efficient X‐ray beam concentration. Experimental data for the line width and the refraction efficiency in one‐dimensional focusing are consistent with the expectations. Imperfections in the structures produced by state‐of‐the‐art deep X‐ray lithography directed only 35% of the incident intensity away from the image and widened it by just 10% to 125 µm. An array of micro‐lenses with easily feasible prism sizes is proposed as an efficient retrofit for the refocusing optics in an existing beamline, where it would provide seven‐fold flux enhancement.     

A simple x‐ray monochromator based on an alligator lens

Alligator lenses, i.e. two inclined arrays of sawteeth or prisms, which face each other, can focus x‐rays with photon energies >4 keV. The inclination angle can be changed easily, and thus either the focal length for fixed photon energy or the photon energy in a fixed slit position can be varied. The material distribution in this condition is approximately parabolic along the teeth axis, hence it is of the shape required for aberration‐free focusing at a given photon energy. As the refractive index varies significantly with photon energy in the x‐ray range, these lenses suffer from chromatic aberrations, if illuminated with white x‐rays. In combination with a slit such a lens can therefore be used as an easily insertable inline monochromator. In this work, a simple universal function for the dependence of the transmission on the photon energy was derived for this application. The required tolerances for the shape of the sawteeth are found to be compatible with standard workshop machining procedures. A laboratory‐made lens of Plexiglas is shown to increase the flux density in a laboratory setup by a factor of 3, i.e. 50% of the expected result for a perfect lens. The discrepancy can be consistently ascribed to macroscopic defects of the sawteeth tips. Expectations for the performance of these lenses as monochromators at synchrotron radiation sources are presented. A single Be alligator lens is expected to provide tuning between at least 8 keV and 20 keV photon energy with a bandpass of 6%, sufficient for XRF and SAXS experiments. Consequently, such a lens pair is all that is needed for building simple synchrotron radiation beamlines for special x‐ray experiments. Copyright © 2004 John Wiley & Sons, Ltd.     

On aberrations in saw‐tooth refractive X‐ray lenses and on their removal

The X‐ray lens, which is composed of opposing canted saw‐tooth structures, originally assembled from cut‐out pieces from long‐playing records, is understood by recognizing that an incident plane X‐ray wave will traverse a varying number of triangular prisms in them. The refraction will deflect any beam towards the prism tips and the variation of the deflection angle, which grows linearly with the number of traversed prisms, can result in X‐ray focusing. The structure offers focusing flexibility by simply changing the taper angle. This report will discuss the aberrations arising in the saw‐tooth structure in its simplest form with identical prisms. It is found that the saw‐tooth structures in low‐Z materials with focal length below 1 m provide less flux density in the focal spot than stacks of one‐dimensionally focusing refractive lenses with identical transmission function. This is due to excessive aberrations in the regular structure, which are absent in stacks of concave lenses, and which limit the focusing to spot sizes of just submicrometre dimensions, as measured experimentally for some lenses. It will be shown that this limitation can be overcome by appropriately modifying the prism shape. Then the image size could be reduced by about an order of magnitude to the diffraction limit with competitive numbers even below 0.1 µm. Microfabrication techniques are identified as the appropriate means for producing the structures.     

曲面和平面菲涅尔透镜的像差比较

通过一个大尺寸菲涅尔透镜的设计,比较了曲面菲涅尔透镜和平面菲涅尔透镜在光学像差方面的差异。从应用角度看,菲涅尔透镜设计属于准直系统,一般采用平面结构,但由于其成像要求的特殊性,通过运用P-W方法进行分析和比较,结果表明：曲面的设计较之于平面更具优势,并在ZEMAX中分别对2种菲涅尔透镜进行建模,验证了结果的正确性。但这不表明曲面菲涅尔透镜在像差方面一定比平面菲涅尔透镜更具优势,它还与实际应用场合有关,为此,提出了不同的结构参数设计。     

A0模态Lamb波聚焦透镜的结构设计及实验研究

基于折射率的弯曲波透镜多在板结构上打孔或挖槽,这种设计破坏了原有的结构,降低了板的刚度和稳定性。鉴于此,通过在板表面镶嵌棱柱的方式设计了A0模态Lamb波的聚焦透镜。首先,详细讨论了棱柱的结构参数对Lamb波带隙的影响机理,获取了波速与结构尺寸的定量关系,并实现了透镜的结构设计;其次,有限元仿真了该聚焦透镜的工作性能,包括聚焦位置、焦点处能量分布、聚焦尺寸、工作带宽等;最后,通过实验验证了该透镜设计的正确性。研究结果表明,设计的透镜能够使弯曲波聚焦在预先设定位置,且在不改变结构参数的情况下具有一定的工作频率带宽。该透镜设计方法具有聚焦性能优越、刚度强、易于加工等优点,为声聚焦透镜在无损检测、能量收集等领域的实际应用提供了参考。     

Spherical reflectors as laser-beam expanders

Lasers emit a narrow beam of light which, for many applications, is often required to be expanded and then collimated. A common type of device used for this purpose is a lens telescope in which a pin-hole is placed at the common focal point of the two lenses. In dye laser cavities, dispersion through a number of prisms gives an expanded beam. The divergence of a laser beam can also be achieved by a convex reflecting surface like a polished steel ball. Here the capability of a small steel ball as an inexpensive, simple and convenient laser-beam expander has been investigated experimentally. It has been shown, with the help of shearing interferograms and Ronchigrams, that the aberrations introduced from on-axis as well as off-axis illumination of the ball are less than 1/4 of a fringe.     

基于改进哈特曼法的眼镜片全孔径屈光度测量

自由曲面镜片的发展和普及,对现有的屈光度测量方法提出了挑战,也要求新的测量方法具有更高的精度以及更好的可靠性。因此,介绍了传统哈特曼检测法测量眼镜片屈光度的测量原理并提出了一种改进方法,对球面单焦点镜片和散光镜片进行仿真测量的屈光度误差均在1%以内。对改进方法与传统方法测量所得到的渐进多焦点自由曲面镜片屈光度分布图的分析结果表明,改进哈特曼检测法相比于传统哈特曼检测法具有测量范围大,精度高的特点,能够准确反映眼镜片的屈光度分布特征。     

大孔径变焦投影镜头设计

为了实现某一大孔径定焦投影镜头作为初始结构, 经过优化设计后成为大孔径变焦投影镜头, 根据设计目标的DMD对角线尺寸, 利用AUTOCAD对选择的定焦距系统的初始结构尺寸进行测绘, 初步选择各镜材料, 规划成5组元变焦系统, 利用各种操作数对镜头的基本参数和外形尺寸进行限制, 并合理利用2个非球面, 在光学设计软件Zemax与CODE V中往返优化, 得到一款在可见光波段内, 短焦距为14.61 mm、视场角为60°、F数为1.5, 长焦距为29.31 mm、视场角为30°、F数为1.6的变焦投影镜头。设计结果表明:各视场的传递函数(MTF)值在截至频率60 lp/mm处不低于0.46, 各焦距处的弥散角不超出1.6', 镜头具有良好的像质。该镜头系统由11块透镜和1块平行平板组成, 其中透镜2使用了非球面镜, 该镜头片数较少, 透镜折射率不高, 材料容易选择。     

Experimental Results of Radar Sounding of Subsurface Oil-Polluted Areas

We present experimental estimates of the possibility to use an adapted ground penetrating radar (GPR) for mapping subsurface zones (lenses) polluted by oil products as a result of ecological accidents. The radar was tested at the site of a large lens with air kerosene at a depth of about 6 m. On the basis of comparison of radar measurements and geological data obtained by well-boring it is shown that use of GPRs for mapping subsurface lenses with oil products is expedient.     

基于曲面传感器的大孔径1300万像素手机镜头设计

设计了一款由5片塑料非球面透镜组成的1 300万像素大孔径手机镜头。将曲面传感器引入镜头设计,在不增加镜片数量以及保证大光圈的基础上改善了边缘像质,解决了边缘失光问题。系统采用1/3英寸(4.8 mm×3.6 mm),长宽比为4:3的曲面传感器。该镜头的焦距为3.5 mm,F数为1.55,视场角为74°,全视场调制传递函数(MTF)均大于0.4,最大畸变小于3.5%,相对照度大于55%,可以获得良好的成像效果。镜头公差灵敏度较低,能满足加工条件。     

变焦距投影光学系统中的远心光路设计

介绍了含有棱镜系统的数字光处理器（DLP）投影仪连续变焦距远心镜头的设计。通过对DLP投影镜头与数字微反射镜器件之间的全反射棱镜系统进行分析，发现采用像方远心光路设计方法，可使投影系统产生的杂光大大减少。进一步研究变焦距系统远心光路的结构特征，得出了使系统在整个变焦过程中都处于远心位置的光阑轴向位移方程。借助给光阑固联一个透镜（与补偿组共同补偿变倍组）所产生的像面移动，得到了变焦曲线平缓、光焦度分配均匀且成像质量较好的投影镜头。     

液体透镜在变焦系统中的应用

利用液体透镜进行变焦系统设计可以大幅降低系统的复杂程度,本文介绍和讨论了该项技术的研究和应用现状。首先,基于液体透镜的分类即渐变折射率透镜和变曲率透镜介绍了几种主要液体透镜的原理和特点,给出了具有代表性的ARCTIC透镜系列和Optotune透镜系列的设计参数和优点。然后,对液体透镜技术在变焦系统中的应用进行了分析,描述了其在变焦眼镜、手机相机、内窥镜和显微镜等诸多领域中应用的现状和优势。最后,利用液体透镜设计了一种长焦距变焦系统,该系统可实现2.5倍的可见光变焦。     

Compound Fresnel Zone Lens Conformal to Truncated Cone: Antenna Application

A millimeter wave antenna consisting of two Fresnel zone plate lenses, plane and conical, is examined numerically by use of the vector diffraction theory. The lenses are of Wood-Wiltse (double-dielectric) or Soret (half-open) type, and are designed for the frequency of 117 GHz. The lenses are made conformal to a truncated circular cone with a base diameter of 500 mm and a plateau diameter of 250 mm. Designs for two opening semi-angles, 45° and 75° each of them with a particular lens thickness are presented. For the angle of 90° the cone lens becomes a plane ring lens, which in combination with the plateau zone lens forms a plane lens of size equal to the cone base diameter. Illuminated by directive feeds set at a focal distance of 525 mm from the cone apex, the double-dielectric and half-open compound and plane lenses, form three pairs of Fresnel zone lens antennas, the co-polar and cross-polar radiation characteristics of which have been compared numerically. The double-dielectric lens antennas examined are about 5 dB superior in gain to the half-open lens antennas, which has a gain of approximately 45 dBi. Because all lenses are of equal transverse aperture, the corresponding lens antennas exhibit the same −3 dB beamwidth of about 0.33 degrees. The plane zone lens antenna is very thin and simple. Instead, the antenna comprising a 3-D compound Fresnel zone lens is thicker but can be made conformal to a specific surface shape and possesses more levels of design and optimization freedom.     

衍射光学透镜的设计

介绍一种衍射光学透镜的通用设计方法，它适用于大的相对孔径和任意的物像共轭距离，同时考虑了透镜基板厚度的影响．设计的结果，用激光写入法加工成透镜，其成像质量达到衍射极限．     

一款超薄800万像素手机镜头的设计

为了满足市场对超薄手机镜头的要求,运用光学软件CODEV,结合非球面理论,设计一款新的超薄800万像素手机镜头。该镜头由4片非球面塑料镜片,1片滤光镜片和1片保护玻璃组成,其中第1片透镜是正透镜,第2片镜片是负透镜,第3片镜片是正透镜,第4片镜片是负透镜,且光阑位于第1片透镜的前面。镜头光圈值F为2.4,视场角2为65.5,焦距为3.731 5 mm,后焦距0.31 mm,镜头总长度为4.6 mm,在最高频率1/2处大多数视场的MTF值均大于0.5,畸变小于2% 。     

Modified nodal point method for the measurement of the large focal length of lenses

Some modifications have been suggested to the nodal slide and microscope method to suit the focal length measurement of large focal length lenses. In this procedure, the experimental set-up has to be accommodated on the two usual optical benches in line, and the position of the nodal point of the lens under test is easily located by introducing an extra lens of comparatively shorter focal length between the test lens and microscope. The results of the measurement of ‘f’ for a few lenses, and the experimental parameters, are presented.