基于二次相位光栅的三维显微成像系统优化设计
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摘要
人类从未停止过对微观世界的探索和观察。光学显微镜自400多年前问世以来,经历了日新月异的演变。当今,在显微镜的结构和种类飞速发展的同时,显微观测技术也在不断创新。如何观测到更清晰的物体,如何拍摄/重建出更真实的三维影像,成了光学、生物学、信息科学等多个学科共同研究的热点。
本文以基于二次相位光栅的三维显微成像系统为研究对象,以提高相位光栅的成像效率(文中的成像效率定义为相位光栅前3个(0,±1)衍射级的光能量相对于入射光总能量的比值)和光学系统的成像质量为目标,对基于二次相位光栅的三维显微成像系统的原理及光学系统设计方法、三维显微成像系统的误差分析、多阶相位光栅的成像效率分析、利用棱栅校正三维显微成像系统的色差等方面进行了系统的研究。
在三维显微成像系统的原理及光学系统设计方面,以衍射原理和相位光栅的工作原理为基础,设计了一种简单易行且低成本的离轴菲涅耳透镜,即二次相位光栅。该光栅由一组周期不等的圆弧形刻槽组成,可使入射光的波前产生迂回相位,于是光栅对入射光的不同衍射级有了不同的聚/离焦能力。基于该光栅的光学系统可以作为附件,与大多数商用显微镜的CCD端口联接,实时记录样品3-9个不同深度平面的像。该技术打破了大部分现有三维显微成像技术对于光源相干性的限制,从根源上减弱了由于强入射光导致的样品光漂白和光损伤等问题。并由于其捕捉图像的实时性,尤其适用于活体生物细胞成像,避免了细胞游动过快而导致的不同时刻错误图像采集问题。
为了观测到尽可能真实清晰的图像,提高相位光栅的成像效率和改善三维显微成像系统的成像质量,是本文研究的重点。为此分别针对相位光栅和三维显微成像系统进行了误差分析。首先,建立了三种典型加工误差(刻蚀深度误差、表面粗糙度和版图误差)的一维理论和仿真模型。计算结果表明,相位光栅的表面粗糙度和版图误差对各衍射级能量平衡的影响较小,但刻蚀深度误差决定了相位光栅前3个衍射级能量平衡的精度,必须严格予以控制。其次,系统分析了由二次相位光栅引起的三维显微成像系统的若干误差。研究结果表明,色差是影响光学系统成像质量的主要误差来源,必须加以校正。
在提高相位光栅的成像效率方面,基于二元光学的相关原理,建立了多阶(2,4,6)相位光栅的一维数学模型。通过对不同台阶数相位光栅成像效率的分析,得到了与之对应的光栅各台阶的深度和栅距等参数的优化值,为今后相位光栅的设计提供了方向。理论计算及仿真结果表明,优化参数的4阶相位光栅,其成像效率高达90.9%,比2阶相位光栅高了4.4%；而相应的,6阶相位光栅的成像效率增益仅为4.8%。因此,制作4阶相位光栅是提高光栅成像效率的有效途径之一。其次,简述了几种相位光栅加工方法,并由于刻蚀深度的精度要求比较高(几纳米),提出了一种潜在的薄膜沉积加工方法。
在提高光学系统的成像质量方面,校正色差是目前工作的重心之一。利用棱镜和光栅的组合——棱栅,通过设计其结构参数,可对一定波长范围的入射光进行较均匀的“预色散”,使得不同波长的光通过二次相位光栅后获得相同的衍射角,从而消除/减弱了色差。通过调节CCD相机的位置和一对棱栅之间的距离,开展一系列重复性实验,得到了一组优化的实验参数。并基于此,分别采用复合双色激光和白光,验证了一对平行排列的棱栅可有效地消除带宽约100nnm的色散现象。于是将一对棱栅与基于二次相位光栅的三维显微成像系统相结合,初步用于几种常见荧光团的模拟成像。实验表明,一对棱栅对各荧光团-1衍射级的色差进行了较成功的校正,提高了系统的成像质量。该技术亦适用于各种显微镜系统,且有望推广到9个平面同时成像系统的色差校正中。
基于上述研究,本论文在以下方面具有创新之处：1)建立了相位光栅加工误差分析的一维理论模型,系统研究了几种典型的加工误差对相位光栅成像效率及前3个衍射级能量平衡的影响,并分析了基于二次相位光栅的三维显微成像系统的主要误差来源：2)建立了多阶(2,4,6)相位光栅的一维数学模型,分析了光栅相位轮廓的细化(增加台阶数目)对成像效率的影响,并论证了优化参数下的4阶相位光栅,可在实现前3个衍射级能量平衡的前提下,将光栅的成像效率提高至90.9%；3)提出了利用棱栅(棱镜和光栅的组合元件)校正三维显微成像系统色差的方法,提高了光学系统的成像质量。
People have never stopped exploring and observing small systems like cells. Since the first optical microscope was invented400years ago, the microscope imaging techniques are constantly innovated. There is an increasing need to extend these techniques into the third dimension, so that dynamic interactions between two or more components can be studied in whole living cells.
In this dissertation, we demonstrate a simple, on axis multi-plane imaging technology that delivers real time3D imaging over cellular volumes. Our technique utilizes a quadratically-distorted phase grating (QD grating), in the form of an off axis-Fresnel zone plate that, by introducing a detour phase term, imparts an equal but opposing focal power in the positive and negative diffracted orders, thus providing a ability to image multiple (3-9) object planes simultaneously on a single image plane. The QD grating can be used in simple attachments which are fully compatible with commercial microscopes and standard camera systems, to record wide-field images focused simultaneously on multiple specimen depths. Thus the biggest advantage of this technique is that various light sources could be used, rather than coherent light source limited in most of other3D imaging techniques, which avoids the cell bleaching and/or damaged. Furthermore, simultaneity in measurement is important in applications for studies of rapidly changing objects in cell-biology (e.g. organelle and flagella dynamics), fluid-flow problems and other high-speed,3D tracking applications.
However, maximizing the optical efficiency and improving the image quality are crucial in most modern microscope imaging applications. When using QD grating, the first challenge is to maximize photometric efficiency in the usable diffraction orders, by reducing the intensity in the unused higher orders, without compromising QD grating performance or functionality; the second challenge is to diminish chromatic aberration induced in non-zero diffraction orders of QD grating.
In order to assess the influence of errors and thus find dominant ones to mitigate a comprehensive error budget, in the form of theoretical analyses, computer simulations and ray-tracing, is established. The analysis presented shows that with achievable accuracies, the plotting error, the residual surface roughness, the thickness of the spectral filters and QD grating substrate, the misplacing of the grating (both lateral and axial) and the delivery of images in the±1diffraction order do not produce significant image defects. And the axial spacing and location of the in-focus images are altered slightly by the use of thick lenses and the aberrations introduced by other optics. The influence on the ability to balance the energy in the multi-focal images arises from the slight change in the NA of the imaging system between diffraction orders of the QD grating. For narrow-spectral bands the etch depth error dominates other errors, but the analysis here was in1D and we expect this effect to be less in2D QD gratings. The most serious error in fluorescence imaging arises from the wavelength-dependent diffraction angle of the±1diffraction orders. In multi-focal imaging this effect may be largely corrected by pre-dispersing the light before it strikes the QD grating.
Based on some principles of binary optics, it is demonstrated that grating efficiency could be improved by multi-etch fabrication, using theoretical models of gratings based on an analytical solution to the optimisation of the multi-level phase conditions. Under the conditions of refractive index n=1.46(fused silica) and wavelength of incident light λ=600nm, a set of optimised parameters of grating structure are obtained, which achieve a balanced intensity distribution between diffraction orders and maximum value of grating efficiency. Under these conditions each order contains28.84%,30.3%and30.45%of the flux, when the grating is single (binary-level), double (4-level) and triple (6-level) etched, separately. So we may conclude that double etches is good enough because little efficiency gain would be obtained in3etch levels. And the results are particularly beneficial when using multiple QD gratings, where diffraction losses cumulate. For example,9-plane simultaneously imaging, using dual back-to-back QD gratings would result in higher order losses of25.14%for binary-level grating compared to17.37%for4-level grating. Then some grating fabrication methods are explored, and film deposition technology might be our potential grating fabrication method due to the high accuracy of film thickness. However, for the long term, any process that allows the production of a continuous surface profile (grey level rather than discrete levels), or very-precise alignment of etches on the same side of the substrate (alignment better than about2microns), would offer new opportunities.
Because QD gratings are dispersive, the images may be chromatically smeared if the dispersion is not corrected. In most of our former applications, due to the need to limit chromatic distortion, the QD grating-based technique is narrow band, limiting the incident spectral bandwidth, restricting photon flux and hindering application to multiple-fluorophore life science imaging. So we demonstrate an optically and ergonomically-efficient correction in this dissertation-using of a pair of grisms (a grating combined with a prism, both are commercially-available) in multi-plane polychromatic imaging, exploiting the inherent chirp of the QD grating to achieve a near-complete correction of the principal chromatic defects in the3D imaging by simply changing the grism separation in an unfolded, axial, optical system. It is this configuration, in which first-order diffraction of a selected wavelength (mid visible in this case) occurs for an un-deviated beam, that is exploited here to provide a simplified chromatic control system. It is shown that a collimated output beam with easily-varied chromatic shear is achieved by this grism pair. We assess this chromatic shear produced as a function of the grism separation by measuring the angle at which two different laser wavelengths are brought to focus as a function of the grism separation. We then successfully correct the dispersion in3D imaging of a compact polychromatic source using QD grating. For further application, we simulate the performance of the grism correction to the full bandwidth of the fluorophore imaging. The results show that for eGFP and Cy5the dispersion are nearly corrected, though for the broader bandwidth mCherry, there is evidence of some residual chromatic smearing manifest in some low-brightness "wings". Further exploration would be focused on the chromatic correction in9-plane imaging system and a more compact optical alignment to be compatible with commercial microscopes.
In conclusion, the highlights of innovation of this work are following:1) Novel error budget methods-1D mathematical models of phase grating fabrication errors have been established, and influence of both fabrication errors and system errors induced by QD grating are assessed.2)1D mathematical models of multi-level (2,4,6) phase grating with balanced intensity distribution between diffraction orders have been established, which illustrate that4.4%efficiency gain is obtained when the QD grating is double etched (4-level) with optimised parameters.3) An innovated technique to correct chromatic smearing in QD grating based3D imaging system, using a simple, linear, grism (grating and prism) pair without compromising image quality.
本文以基于二次相位光栅的三维显微成像系统为研究对象,以提高相位光栅的成像效率(文中的成像效率定义为相位光栅前3个(0,±1)衍射级的光能量相对于入射光总能量的比值)和光学系统的成像质量为目标,对基于二次相位光栅的三维显微成像系统的原理及光学系统设计方法、三维显微成像系统的误差分析、多阶相位光栅的成像效率分析、利用棱栅校正三维显微成像系统的色差等方面进行了系统的研究。
在三维显微成像系统的原理及光学系统设计方面,以衍射原理和相位光栅的工作原理为基础,设计了一种简单易行且低成本的离轴菲涅耳透镜,即二次相位光栅。该光栅由一组周期不等的圆弧形刻槽组成,可使入射光的波前产生迂回相位,于是光栅对入射光的不同衍射级有了不同的聚/离焦能力。基于该光栅的光学系统可以作为附件,与大多数商用显微镜的CCD端口联接,实时记录样品3-9个不同深度平面的像。该技术打破了大部分现有三维显微成像技术对于光源相干性的限制,从根源上减弱了由于强入射光导致的样品光漂白和光损伤等问题。并由于其捕捉图像的实时性,尤其适用于活体生物细胞成像,避免了细胞游动过快而导致的不同时刻错误图像采集问题。
为了观测到尽可能真实清晰的图像,提高相位光栅的成像效率和改善三维显微成像系统的成像质量,是本文研究的重点。为此分别针对相位光栅和三维显微成像系统进行了误差分析。首先,建立了三种典型加工误差(刻蚀深度误差、表面粗糙度和版图误差)的一维理论和仿真模型。计算结果表明,相位光栅的表面粗糙度和版图误差对各衍射级能量平衡的影响较小,但刻蚀深度误差决定了相位光栅前3个衍射级能量平衡的精度,必须严格予以控制。其次,系统分析了由二次相位光栅引起的三维显微成像系统的若干误差。研究结果表明,色差是影响光学系统成像质量的主要误差来源,必须加以校正。
在提高相位光栅的成像效率方面,基于二元光学的相关原理,建立了多阶(2,4,6)相位光栅的一维数学模型。通过对不同台阶数相位光栅成像效率的分析,得到了与之对应的光栅各台阶的深度和栅距等参数的优化值,为今后相位光栅的设计提供了方向。理论计算及仿真结果表明,优化参数的4阶相位光栅,其成像效率高达90.9%,比2阶相位光栅高了4.4%；而相应的,6阶相位光栅的成像效率增益仅为4.8%。因此,制作4阶相位光栅是提高光栅成像效率的有效途径之一。其次,简述了几种相位光栅加工方法,并由于刻蚀深度的精度要求比较高(几纳米),提出了一种潜在的薄膜沉积加工方法。
在提高光学系统的成像质量方面,校正色差是目前工作的重心之一。利用棱镜和光栅的组合——棱栅,通过设计其结构参数,可对一定波长范围的入射光进行较均匀的“预色散”,使得不同波长的光通过二次相位光栅后获得相同的衍射角,从而消除/减弱了色差。通过调节CCD相机的位置和一对棱栅之间的距离,开展一系列重复性实验,得到了一组优化的实验参数。并基于此,分别采用复合双色激光和白光,验证了一对平行排列的棱栅可有效地消除带宽约100nnm的色散现象。于是将一对棱栅与基于二次相位光栅的三维显微成像系统相结合,初步用于几种常见荧光团的模拟成像。实验表明,一对棱栅对各荧光团-1衍射级的色差进行了较成功的校正,提高了系统的成像质量。该技术亦适用于各种显微镜系统,且有望推广到9个平面同时成像系统的色差校正中。
基于上述研究,本论文在以下方面具有创新之处：1)建立了相位光栅加工误差分析的一维理论模型,系统研究了几种典型的加工误差对相位光栅成像效率及前3个衍射级能量平衡的影响,并分析了基于二次相位光栅的三维显微成像系统的主要误差来源：2)建立了多阶(2,4,6)相位光栅的一维数学模型,分析了光栅相位轮廓的细化(增加台阶数目)对成像效率的影响,并论证了优化参数下的4阶相位光栅,可在实现前3个衍射级能量平衡的前提下,将光栅的成像效率提高至90.9%；3)提出了利用棱栅(棱镜和光栅的组合元件)校正三维显微成像系统色差的方法,提高了光学系统的成像质量。
People have never stopped exploring and observing small systems like cells. Since the first optical microscope was invented400years ago, the microscope imaging techniques are constantly innovated. There is an increasing need to extend these techniques into the third dimension, so that dynamic interactions between two or more components can be studied in whole living cells.
In this dissertation, we demonstrate a simple, on axis multi-plane imaging technology that delivers real time3D imaging over cellular volumes. Our technique utilizes a quadratically-distorted phase grating (QD grating), in the form of an off axis-Fresnel zone plate that, by introducing a detour phase term, imparts an equal but opposing focal power in the positive and negative diffracted orders, thus providing a ability to image multiple (3-9) object planes simultaneously on a single image plane. The QD grating can be used in simple attachments which are fully compatible with commercial microscopes and standard camera systems, to record wide-field images focused simultaneously on multiple specimen depths. Thus the biggest advantage of this technique is that various light sources could be used, rather than coherent light source limited in most of other3D imaging techniques, which avoids the cell bleaching and/or damaged. Furthermore, simultaneity in measurement is important in applications for studies of rapidly changing objects in cell-biology (e.g. organelle and flagella dynamics), fluid-flow problems and other high-speed,3D tracking applications.
However, maximizing the optical efficiency and improving the image quality are crucial in most modern microscope imaging applications. When using QD grating, the first challenge is to maximize photometric efficiency in the usable diffraction orders, by reducing the intensity in the unused higher orders, without compromising QD grating performance or functionality; the second challenge is to diminish chromatic aberration induced in non-zero diffraction orders of QD grating.
In order to assess the influence of errors and thus find dominant ones to mitigate a comprehensive error budget, in the form of theoretical analyses, computer simulations and ray-tracing, is established. The analysis presented shows that with achievable accuracies, the plotting error, the residual surface roughness, the thickness of the spectral filters and QD grating substrate, the misplacing of the grating (both lateral and axial) and the delivery of images in the±1diffraction order do not produce significant image defects. And the axial spacing and location of the in-focus images are altered slightly by the use of thick lenses and the aberrations introduced by other optics. The influence on the ability to balance the energy in the multi-focal images arises from the slight change in the NA of the imaging system between diffraction orders of the QD grating. For narrow-spectral bands the etch depth error dominates other errors, but the analysis here was in1D and we expect this effect to be less in2D QD gratings. The most serious error in fluorescence imaging arises from the wavelength-dependent diffraction angle of the±1diffraction orders. In multi-focal imaging this effect may be largely corrected by pre-dispersing the light before it strikes the QD grating.
Based on some principles of binary optics, it is demonstrated that grating efficiency could be improved by multi-etch fabrication, using theoretical models of gratings based on an analytical solution to the optimisation of the multi-level phase conditions. Under the conditions of refractive index n=1.46(fused silica) and wavelength of incident light λ=600nm, a set of optimised parameters of grating structure are obtained, which achieve a balanced intensity distribution between diffraction orders and maximum value of grating efficiency. Under these conditions each order contains28.84%,30.3%and30.45%of the flux, when the grating is single (binary-level), double (4-level) and triple (6-level) etched, separately. So we may conclude that double etches is good enough because little efficiency gain would be obtained in3etch levels. And the results are particularly beneficial when using multiple QD gratings, where diffraction losses cumulate. For example,9-plane simultaneously imaging, using dual back-to-back QD gratings would result in higher order losses of25.14%for binary-level grating compared to17.37%for4-level grating. Then some grating fabrication methods are explored, and film deposition technology might be our potential grating fabrication method due to the high accuracy of film thickness. However, for the long term, any process that allows the production of a continuous surface profile (grey level rather than discrete levels), or very-precise alignment of etches on the same side of the substrate (alignment better than about2microns), would offer new opportunities.
Because QD gratings are dispersive, the images may be chromatically smeared if the dispersion is not corrected. In most of our former applications, due to the need to limit chromatic distortion, the QD grating-based technique is narrow band, limiting the incident spectral bandwidth, restricting photon flux and hindering application to multiple-fluorophore life science imaging. So we demonstrate an optically and ergonomically-efficient correction in this dissertation-using of a pair of grisms (a grating combined with a prism, both are commercially-available) in multi-plane polychromatic imaging, exploiting the inherent chirp of the QD grating to achieve a near-complete correction of the principal chromatic defects in the3D imaging by simply changing the grism separation in an unfolded, axial, optical system. It is this configuration, in which first-order diffraction of a selected wavelength (mid visible in this case) occurs for an un-deviated beam, that is exploited here to provide a simplified chromatic control system. It is shown that a collimated output beam with easily-varied chromatic shear is achieved by this grism pair. We assess this chromatic shear produced as a function of the grism separation by measuring the angle at which two different laser wavelengths are brought to focus as a function of the grism separation. We then successfully correct the dispersion in3D imaging of a compact polychromatic source using QD grating. For further application, we simulate the performance of the grism correction to the full bandwidth of the fluorophore imaging. The results show that for eGFP and Cy5the dispersion are nearly corrected, though for the broader bandwidth mCherry, there is evidence of some residual chromatic smearing manifest in some low-brightness "wings". Further exploration would be focused on the chromatic correction in9-plane imaging system and a more compact optical alignment to be compatible with commercial microscopes.
In conclusion, the highlights of innovation of this work are following:1) Novel error budget methods-1D mathematical models of phase grating fabrication errors have been established, and influence of both fabrication errors and system errors induced by QD grating are assessed.2)1D mathematical models of multi-level (2,4,6) phase grating with balanced intensity distribution between diffraction orders have been established, which illustrate that4.4%efficiency gain is obtained when the QD grating is double etched (4-level) with optimised parameters.3) An innovated technique to correct chromatic smearing in QD grating based3D imaging system, using a simple, linear, grism (grating and prism) pair without compromising image quality.
引文
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