Performance evaluation of a sensorless adaptive optics multiphoton microscope

A wavefront sensorless adaptive optics technique was combined with a custom‐made multiphoton microscope to correct for specimen‐induced aberrations. A liquid‐crystal‐on‐silicon (LCoS) modulator was used to systematically generate Zernike modes during image recording. The performance of the instrument was evaluated in samples providing different nonlinear signals and the benefit of correcting higher order aberrations was always noticeable (in both contrast and resolution). The optimum aberration pattern was stable in time for the samples here involved. For a particular depth location within the sample, the wavefront to be precompensated was independent on the size of the imaged area (up to ～360 × 360 μm²). The mode combination optimizing the recorded image depended on the Zernike correction control sequence; however, the final images hardly differed. At deeper locations, a noticeable dominance of spherical aberration was found. The influence of other aberration terms was also compared to the effect of the spherical aberration.     

Measurement of specimen-induced aberrations of biological samples using phase stepping interferometry

Confocal or multiphoton microscopes, which deliver optical sections and three‐dimensional (3D) images of thick specimens, are widely used in biology. These techniques, however, are sensitive to aberrations that may originate from the refractive index structure of the specimen itself. The aberrations cause reduced signal intensity and the 3D resolution of the instrument is compromised. It has been suggested to correct for aberrations in confocal microscopes using adaptive optics. In order to define the design specifications for such adaptive optics systems, one has to know the amount of aberrations present for typical applications such as with biological samples. We have built a phase stepping interferometer microscope that directly measures the aberration of the wavefront. The modal content of the wavefront is extracted by employing Zernike mode decomposition. Results for typical biological specimens are presented. It was found for all samples investigated that higher order Zernike modes give only a small contribution to the overall aberration. Therefore, these higher order modes can be neglected in future adaptive optics sensing and correction schemes implemented into confocal or multiphoton microscopes, leading to more efficient designs.     

人眼波前像差客观测量的研究

分析波动光学中人眼像差的产生机理和波前像差的表示方式。运用Zernike多项式表示人眼波前像差函数,研究Zernike多项式与人眼波像差的对应关系以及一些高级像差对人眼成像质量的影响。通过对自适应光学中Zernike多项式重建波前理论的研究,重点分析了应用Hartmann-Shack波前传感器测量人眼客观像差并用变形反射镜矫正人眼像差的解决方案。对提高正常眼睛的视力和人眼屈光矫正手术具有重要的实验和临床价值。     

Adaptive optics in spinning disk microscopy: improved contrast and brightness by a simple and fast method

Multiconfocal microscopy gives a good compromise between fast imaging and reasonable resolution. However, the low intensity of live fluorescent emitters is a major limitation to this technique. Aberrations induced by the optical setup, especially the mismatch of the refractive index and the biological sample itself, distort the point spread function and further reduce the amount of detected photons. Altogether, this leads to impaired image quality, preventing accurate analysis of molecular processes in biological samples and imaging deep in the sample. The amount of detected fluorescence can be improved with adaptive optics. Here, we used a compact adaptive optics module (adaptive optics box for sectioning optical microscopy), which was specifically designed for spinning disk confocal microscopy. The module overcomes undesired anomalies by correcting for most of the aberrations in confocal imaging. Existing aberration detection methods require prior illumination, which bleaches the sample. To avoid multiple exposures of the sample, we established an experimental model describing the depth dependence of major aberrations. This model allows us to correct for those aberrations when performing a z‐stack, gradually increasing the amplitude of the correction with depth. It does not require illumination of the sample for aberration detection, thus minimizing photobleaching and phototoxicity. With this model, we improved both signal‐to‐background ratio and image contrast. Here, we present comparative studies on a variety of biological samples.     

Specimen-induced distortions in light microscopy

Specimen‐induced aberrations affect the imaging properties in optical 3D microscopy, especially when high numerical aperture lenses are used. Studies on aberrations are often properly concerned with the degradation of image quality such as compromised resolution or reduced signal intensity. Apart from these, aberration effects can also introduce geometric image distortions. The effects, discussed here are particularly strong when thick biological specimens are investigated. Using a high numerical aperture interferometer, we measured wavefront aberrations in transmission mode and quantified geometric distortions associated with specimen‐induced aberrations. This assessment for a range of biological specimens allows estimation of the accuracy of spatial measurements. The results show that high‐resolution spatial measurements can be significantly compromised by specimen‐induced aberrations.     

剪切干涉测量中基于Zernike多项式的自适应波前重建

提出一种剪切干涉测量中被测波前重建的新方法，该方法基于Zernike多项式最小二乘拟合的基本原理，通过自适应的方式来确定波前重建表达式。推导出剪切相位Zernike多项式系数与被测波前Zernike多项式系数的直接转换矩阵，提出了自适应确定多项式级次的新算法，给出了相应的波前重建数学模型。对算法进行了计算机模拟，并应用于实际剪切干涉测量，结果证明该方法具有可靠的波前重建精度。     

Phase correction of laser radiation with the use of adaptive optical systems at the Russian Federal Nuclear Center—Institute of Experimental Physics

Results obtained at the Institute of Laser Physics Research (which is part of the Russian Federal Nuclear Center — Institute of Experimental Physics) on phase correction of pulsed and continuous wave laser radiation by closed-loop adaptive optical systems (AOS) with flexible deformable mirrors are described. With the help of a conventional AOS including a Hartmann-Shack wavefront sensor and an adaptive mirror having a 220 × 220 mm aperture, aberrations of the beam of a powerful pulsed laser facility called Luch have been reduced by an order of magnitude. The development of special software for reconstruction of singular wavefronts by the Hartmann-Shack sensor has allowed us to perform the correction of a doughnut-shaped Laguerre-Gaussian vortex laser beam in an AOS with a bimorph mirror and to focus it into a bright axial spot that drastically increases the Strehl ratio. Adaptive optical systems have been developed where the adaptive mirror control is ensured by searching for an extremum of a chosen criterion functional with the help of a stochastic parallel gradient algorithm rather than by means of wavefront measurements. Embedding of microcontrollers into the control unit has allowed us to reach an AOS bandwidth of 5 kHz and to demonstrate the dynamic phase correction of tip-tilts and higher aberrations of the wavefront caused by turbulence induced by heating of the beam propagation path under laboratory conditions.     

利用Zernike多项式分析超薄镜热变形

利用圆域上正交基-Zernike多项式拟合镜面温度场,将温度场转化为较有意义的模式,采用有限元方法进行了热变形的计算,其中针对空间大口径超薄镜面建立镜面模型,且暂不考虑重力,另外因超薄镜厚度很小,也不考虑轴向温度梯度的影响。通过计算利用Zernike多项式得到温度场产生的热变形,得到了不同温度模式产生的不同像差形式:即对于不同的温度场模式—温度整体变化(平移),一端凉且一端热(倾斜),中心与边缘温度不同(离焦热模式),以及像散热模式,彗差热模式,球差热模式导致的热变形分别主要表现为像差离焦,倾斜,离焦,倾斜,倾斜,球差。不同热模式在相同温差下产生的变形有数量级的差别,能够产生较大变形量的温度模式有离焦,彗差和球差,这意味着超薄镜对这些温度场比较敏感。计算和总结表明,利用Zernike多项式分解温度场,可以对热变形规律进行有效的分析,解决了镜面温度分布随时间变化使得热分析较为不准确的困难。     

The influence of objective lens aberrations in energy-loss spectrometry

The conditions under which the energy resolution and collection efficiency in electron energy-loss spectrometry are limited by the spherical and chromatic aberrations of the objective lens have been studied. It is shown that, for the optimum settings of the pre-spectrometer optics, the energy resolution will be of the same order in diffraction mode as it is in magnification mode. The influence of the aberrations on the practice of energy-loss spectroscopy is discussed, and it is demonstrated that the chromatic aberration can act as a broadband filter for energy-loss electrons.     

Zernike多项式拟合方法及应用

由于Zernike多项式的各项与光学像差有相应的对应关系,用Zernike多项式对镜面面形数据进行处理的方法已经广泛应用于工程项目、光学系统设计软件和干涉检查等.用Zernike多项式作为光学和结构分析程序间的接口工具是非常方便和成熟的.本文阐述了Zernike多项式及其拟合方法和应用流程,并应用它作为数据接口工具实现了光机热各分析模块间的数据转换,并在某空间相机系统集成分析中得到应用.     

Three‐dimensional optical transfer functions in the aberration‐corrected scanning transmission electron microscope

In the scanning transmission electron microscope, hardware aberration correctors can now correct for the positive spherical aberration of round electron lenses. These correctors make use of nonround optics such as hexapoles or octupoles, leading to the limiting aberrations often being of a nonround type. Here we explore the effect of a number of potential limiting aberrations on the imaging performance of the scanning transmission electron microscope through their resulting optical transfer functions. In particular, the response of the optical transfer function to changes in defocus are examined, given that this is the final aberration to be tuned just before image acquisition. The resulting three‐dimensional optical transfer functions also allow an assessment of the performance of a system for focal‐series experiments or optical sectioning applications.     

137单元变形镜性能测试及校正能力实验

自制了一个137单元分立促动器的连续镜面式变形镜,用于自适应光学相关技术的研究。首先,利用Zygo激光干涉仪对变形镜的静态性能进行了测试,包括面形测试、单个促动器的响应测试和耦合测试;然后,针对变形镜的校正能力,分别进行了Zernike多项式拟合和展平测试,并利用自适应光学实验平台实验验证了变形镜的校正能力;最后,利用搭建的快速响应测量平台测试了变形镜及其驱动电路的动态响应性能。测试及实验表明,137单元变形镜静态展平后的面形RMS值优于λ/50,PV值优于0.18λ（λ=632.8 nm）;能够对前7阶Zernike多项式进行较好的拟合和校正;变形镜及其高压驱动器的动态响应优于1 kHz;该变形镜能使系统的Strehl ratio从小于0.1提高到优于0.9,明显改善了系统的成像能力。     

Breaking the spherical and chromatic aberration barrier in transmission electron microscopy

Since the invention of transmission electron microscopy (TEM) in 1932 (Z. Physik 78 (1932) 318) engineering improvements have advanced system resolutions to levels that are now limited only by the two fundamental aberrations of electron lenses; spherical and chromatic aberration (Z. Phys. 101 (1936) 593). Since both aberrations scale with the dimensions of the lens, research resolution requirements are pushing the designs to lenses with only a few mm space in the pole-piece gap for the specimen. This is in conflict with the demand for more and more space at the specimen, necessary in order to enable novel techniques in TEM, such as He-cooled cryo electron microscopy, 3D-reconstruction through tomography (Science 302 (2003) 1396) TEM in gaseous environments, or in situ experiments (Nature 427 (2004) 426). All these techniques will only be able to achieve Angstrom resolution when the aberration barriers have been overcome. The spherical aberration barrier has recently been broken by introducing spherical aberration correctors (Nature 392 (1998) 392, 418 (2002) 617), but the correction of the remaining chromatic aberrations have proved to be too difficult for the present state of technology (Optik 57 (1980) 73). Here we present an alternative and successful method to eliminate the chromatic blur, which consists of monochromating the TEM beam (Inst. Phys. Conf. Ser. 161 (1999) 191). We show directly interpretable resolutions well below 1A for the first time, which is significantly better than any TEM operating at 200 KV has reached before.     

Imaging with low-voltage scanning transmission electron microscopy: a quantitative analysis

A dedicated specimen holder has been designed to perform low-voltage scanning transmission electron microscopy in dark field mode. Different test samples, namely InGaAs/GaAs quantum wells, InGaAs nanowires and thick InGaAs layers, have been analysed to test the reliability of the model based on the proportionality to the specimen mass-thickness, generally used for image intensity interpretation of scattering contrast processes. We found that size of the probe, absorption and channelling must be taken into account to give a quantitative interpretation of image intensity. We develop a simple procedure to evaluate the probe-size effect and to obtain a quantitative indication of the absorption coefficient. Possible artefacts induced by channelling are pointed out. With the developed procedure, the low voltage approach can be successfully applied for quantitative compositional analysis. The method is then applied to the estimation of the In content in the core of InGaAs/GaAs core-shell nanowires.     

Optical Property Analyses of Plant Cells for Adaptive Optics Microscopy

In astronomy, adaptive optics (AO) can be used to cancel aberrations caused by atmospheric turbulence and to perform diffraction-limited observation of astronomical objects from the ground. AO can also be applied to microscopy, to cancel aberrations caused by cellular structures and to perform high-resolution live imaging. As a step toward the application of AO to microscopy, here we analyzed the optical properties of plant cells. We used leaves of the moss Physcomitrella patens, which have a single layer of cells and are thus suitable for optical analysis. Observation of the cells with bright field and phase contrast microscopy, and image degradation analysis using fluorescent beads demonstrated that chloroplasts provide the main source of optical degradations. Unexpectedly, the cell wall, which was thought to be a major obstacle, has only a minor effect. Such information provides the basis for the application of AO to microscopy for the observation of plant cells.     

X-ray omni microscopy

The science of wave‐field phase retrieval and phase measurement is sufficiently mature to permit the routine reconstruction, over a given plane, of the complex wave‐function associated with certain coherent forward‐propagating scalar wave‐fields. This reconstruction gives total knowledge of the information that has been encoded in the complex wave‐field by passage through a sample of interest. Such total knowledge is powerful, because it permits the emulation in software of the subsequent action of an infinite variety of coherent imaging systems. Such ‘virtual optics’, in which software forms a natural extension of the ‘hardware optics’ in an imaging system, may be useful in contexts such as quantitative atom and X‐ray imaging, in which optical elements such as beam‐splitters and lenses can be realized in software rather than optical hardware. Here, we develop the requisite theory to describe such hybrid virtual‐physical imaging systems, which we term ‘omni optics’ because of their infinite flexibility. We then give an experimental demonstration of these ideas by showing that a lensless X‐ray point projection microscope can, when equipped with the appropriate software, emulate an infinite variety of optical imaging systems including those which yield interferograms, Zernike phase contrast, Schlieren imaging and diffraction‐enhanced imaging.     

On the complex three-dimensional amplitude point spread function of lenses and microscope objectives: theoretical aspects, simulations and measurements by digital holography

The point spread function is widely used to characterize the three‐dimensional imaging capabilities of an optical system. Usually, attention is paid only to the intensity point spread function, whereas the phase point spread function is most often neglected because the phase information is not retrieved in noninterferometric imaging systems. However, phase point spread functions are needed to evaluate phase‐sensitive imaging systems and we believe that phase data can play an essential role in the full aberrations' characterization. In this paper, standard diffraction models have been used for the computation of the complex amplitude point spread function. In particular, the Debye vectorial model has been used to compute the amplitude point spread function of ×63/0.85 and ×100/1.3 microscope objectives, exemplifying the phase point spread function specific for each polarization component of the electromagnetic field. The effect of aberrations on the phase point spread function is then analyzed for a microscope objective used under nondesigned conditions, by developing the Gibson model ( Gibson & Lanni, 1991 ), modified to compute the three‐dimensional amplitude point spread function in amplitude and phase. The results have revealed a novel anomalous phase behaviour in the presence of spherical aberration, providing access to the quantification of the aberrations. This work mainly proposes a method to measure the complex three‐dimensional amplitude point spread function of an optical imaging system. The approach consists in measuring and interpreting the amplitude point spread function by evaluating in amplitude and phase the image of a single emitting point, a 60‐nm‐diameter tip of a Near Field Scanning Optical Microscopy fibre, with an original digital holographic experimental setup. A single hologram gives access to the transverse amplitude point spread function. The three‐dimensional amplitude point spread function is obtained by performing an axial scan of the Near Field Scanning Optical Microscopy fibre. The phase measurements accuracy is equivalent to λ/60 when the measurement is performed in air. The method capability is demonstrated on an Achroplan ×20 microscope objective with 0.4 numerical aperture. A more complete study on a ×100 microscope objective with 1.3 numerical aperture is also presented, in which measurements performed with our setup are compared with the prediction of an analytical aberrations model.     

基于阻尼最小二乘算法的计算机辅助装调方法

对于具有中心遮拦的光学系统装调,需要将获得的波前进行拟合求取低阶像差。但是Zernike圆多项式在环域上已不具有正交性,不能正确的计算低阶像差。而Zernike环多项式在环域上具有正交性,可以解决这个问题。基于阻尼最小二乘法的算法原理,运用MatLab实现了计算机辅助装调。文中对卡塞格林光学系统进行了模拟实验,验证了使用Zernike环多项式进行拟合的辅助装调程序的正确性。同时,对于辅助装调程序的应用范围也做出了分析。     

High-energy x-ray microbeam with total-reflection mirror optics

Total-reflection mirror optics for high-energy x-ray microfocusing have been developed, and tested in the energy range of 30-100 keV at beamline 20XU of Synchrotron Radiation Facility SPring-8. The optical system consists of a Kirkpatrick-Baez-type [J. Opt. Soc. Am. 38, 766 (1548)] focusing optics with aspherical total-reflection mirrors for the purpose of reducing the spherical aberrations. A focused beam size of 0.35 x 0.4 microm(2) has been achieved at an x-ray energy of 80 keV, and the measured spot size was less than 1 microm in the x-ray energy region below 90 keV.