WO2019037020A1 - 基于非再入型二次扭曲(nrqd)光栅和棱栅的四维多平面宽带成像系统 - Google Patents

基于非再入型二次扭曲(nrqd)光栅和棱栅的四维多平面宽带成像系统 Download PDF

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WO2019037020A1
WO2019037020A1 PCT/CN2017/098805 CN2017098805W WO2019037020A1 WO 2019037020 A1 WO2019037020 A1 WO 2019037020A1 CN 2017098805 W CN2017098805 W CN 2017098805W WO 2019037020 A1 WO2019037020 A1 WO 2019037020A1
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grating
nrqd
optical
imaging system
imaging
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PCT/CN2017/098805
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English (en)
French (fr)
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冯艳
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冯艳
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Priority to US16/465,451 priority Critical patent/US11054627B2/en
Priority to PCT/CN2017/098805 priority patent/WO2019037020A1/zh
Priority to EP17922765.7A priority patent/EP3528254A4/en
Priority to CN201780049763.7A priority patent/CN109716434B/zh
Priority to JP2019548508A priority patent/JP2020514809A/ja
Publication of WO2019037020A1 publication Critical patent/WO2019037020A1/zh

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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B21/00—Microscopes
    • G02B21/36—Microscopes arranged for photographic purposes or projection purposes or digital imaging or video purposes including associated control and data processing arrangements
    • G02B21/361—Optical details, e.g. image relay to the camera or image sensor
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/42—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect
    • G02B27/4233—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect having a diffractive element [DOE] contributing to a non-imaging application
    • G02B27/4238—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect having a diffractive element [DOE] contributing to a non-imaging application in optical recording or readout devices
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B21/00—Microscopes
    • G02B21/16—Microscopes adapted for ultraviolet illumination ; Fluorescence microscopes
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/42—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/42—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect
    • G02B27/4205—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect having a diffractive optical element [DOE] contributing to image formation, e.g. whereby modulation transfer function MTF or optical aberrations are relevant
    • G02B27/4211—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect having a diffractive optical element [DOE] contributing to image formation, e.g. whereby modulation transfer function MTF or optical aberrations are relevant correcting chromatic aberrations
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/42—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect
    • G02B27/4272—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect having plural diffractive elements positioned sequentially along the optical path
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/42—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect
    • G02B27/4272—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect having plural diffractive elements positioned sequentially along the optical path
    • G02B27/4277—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect having plural diffractive elements positioned sequentially along the optical path being separated by an air space
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B5/00—Optical elements other than lenses
    • G02B5/18—Diffraction gratings
    • G02B5/1814—Diffraction gratings structurally combined with one or more further optical elements, e.g. lenses, mirrors, prisms or other diffraction gratings
    • G—PHYSICS
    • G11—INFORMATION STORAGE
    • G11B—INFORMATION STORAGE BASED ON RELATIVE MOVEMENT BETWEEN RECORD CARRIER AND TRANSDUCER
    • G11B7/00—Recording or reproducing by optical means, e.g. recording using a thermal beam of optical radiation by modifying optical properties or the physical structure, reproducing using an optical beam at lower power by sensing optical properties; Record carriers therefor
    • G11B7/12—Heads, e.g. forming of the optical beam spot or modulation of the optical beam
    • G11B7/135—Means for guiding the beam from the source to the record carrier or from the record carrier to the detector
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
    • G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
    • G03H1/02—Details of features involved during the holographic process; Replication of holograms without interference recording
    • G03H1/024—Hologram nature or properties
    • G03H1/0248—Volume holograms

Definitions

  • the invention relates to an optical system which can be used for four-dimensional (4D: three-dimensional + time) multi-plane wide-band imaging, which can transmit four-dimensional wavefront information between object space and image space, that is, simultaneously capture multi-color images of multiple object planes And imaging it on the same image plane; or recording the chromatic aberration correction image of a single object plane on a series of image planes according to the reversible principle of the optical path.
  • the technology can be flexibly combined with a variety of modern technologies, including microscopy, astronomical optics, optical data storage, biomedical imaging, wavefront analysis, and virtual/augmented reality, with broad applications in academic research and industry. .
  • DOE diffractive optical element
  • a three-dimensional imaging system based on the element can simultaneously image different object planes on the same image plane, or simultaneously image the same object plane on different image planes.
  • DOE diffractive optical element
  • some of the previously proposed chromatic aberration correction schemes can operate on a multi-color beam that is incident, outputting a pre-dispersed parallel beam, and can be used with diffractive optical element (DOE)-based optics without excessive loss of luminous flux.
  • DOE diffractive optical element
  • the original three-dimensional narrowband imaging system included a diffractive optical element (DOE), a lens system (consisting of one or more lenses), a narrowband bandpass filter, and some imaging devices (such as a light source and camera).
  • DOE diffractive optical element
  • a basic design schematic of a narrowband three-dimensional imaging system is depicted in Figure 1, in which multiple object planes with a spacing of ⁇ z can be simultaneously imaged in the same image plane, and a diffractive optical element (DOE), or quadratically distorted:
  • the QD) grating is placed at a telecentric position such that the images formed by the various faces have the same magnification (PADalgarno, et al. Multiplane imaging and three dimensional nanoscale particle tracking in biological microscopy. Optics Express 18(2), 877 -884 (2010)).
  • the equivalent focal length f g of the mth diffraction order of the QD grating can be expressed as:
  • R is the radius of the QD grating and W 20 is the standard coefficient of defocus.
  • f g values equal in magnitude and opposite sign.
  • the spacing ⁇ z of each object surface can be expressed as:
  • f eff is the effective combined focal length of the lens assembly system
  • M is the magnification of the microscope objective
  • ⁇ is the wavelength of the incident light
  • d 0 is the center period of the QD grating.
  • the maximum dispersion s g formed on a QD grating can be given by:
  • ⁇ is the bandwidth of the incident light spectrum.
  • a dispersive device is added to the three-dimensional imaging system to correct for non-zero diffraction order chromatic aberrations caused by QD gratings and to reduce optical energy losses.
  • Blanchard and Grinway first proposed a chromatic aberration correction scheme, which uses a pair of reflective blazed gratings and a folded-shaped optical path, which successively introduce opposite dispersions to compensate each other to achieve chromatic aberration correction, as shown in Fig. 2. Show (PMBlanchard and AH Greenaway, 'Broadband simultaneous multiplane imaging', Optics Communications 183(1), 29-36 (2000)).
  • the degree of dispersion can be controlled by changing the distance between the two blazed gratings, but due to the folded optical path, changing the grating spacing tends to cause a corresponding adjustment of the angle and position of several optical components, so the system becomes so complicated that It is difficult to integrate with user equipment, which limits the practicality of the solution.
  • a diffractive optical element DOE of the type described above ie a secondary distortion (QD) grating
  • a secondary distortion (QD) grating consists of a series of concentric arcs which may be alternating transparent/opaque (amplitude type) or different optical thicknesses (phase type) ).
  • QD secondary distortion
  • a Cartesian coordinate system is established, where the origin is the geometric center of the QD grating, the x axis is perpendicular to the reticle of the QD grating, and the y axis is parallel to the reticle.
  • Figure 3 shows that the origin is the geometric center of the QD grating
  • the x axis is perpendicular to the reticle of the QD grating
  • the y axis is parallel to the reticle.
  • Equation (5) defaults to a circular QD grating, but the design principle is applicable to any shape of QD grating.
  • the radius C n of the nth concentric arc line of the QD grating can be expressed as:
  • Equation (8) determines the accuracy in QD grating mask layout processing.
  • the QD grating produces an additional phase to the incident light, the so-called detour phase.
  • the meandering phase is caused by the secondary distortion of the QD grating reticle in a direction perpendicular to the original reticle direction (ie, perpendicular to the y-axis direction in FIG. 3), rather than the general grating due to the etch depth (ie, optical thickness).
  • the phase difference caused by the difference.
  • the meandering phase difference ⁇ m acting on the wavefront can be expressed as:
  • Equation (9) shows that the QD grating produces different phase delays for different diffraction orders, so that each non-zero diffraction order has different focusing capabilities.
  • each incident wavelength determines a corresponding image center position when illuminated with a broadband source. Therefore, if the image position difference caused by the different wavelengths is not corrected, the multi-color images corresponding to the non-zero diffraction orders will generate dispersion.
  • the non-periodic reticle offset feature inherent in the secondary distortion (QD) grating the light of different wavelengths corresponds to different grating periods, and the diffraction angles of the light of each wavelength after passing through the QD grating are equal, and the chromatic aberration can be corrected. .
  • a custom optical system can output a collimated and pre-dispersed beam according to the periodic variation of the QD grating, so that beams of different colors can be "dispersed" to the position of the corresponding period of the grating (to obtain the same diffraction). Angle), whereby the dispersion is corrected.
  • Figure 5 shows a basic design diagram of a three-plane multi-color imaging system in which two paste-made prisms are placed along the optical axis, back to back (ie, opposite each other's grating faces), using a photovoltaic element (Thorlabs). In the optical path system. Light near the center wavelength of 532 nm does not shift when passing through the rib system, and the longer and shorter wavelengths of the multi-color beam are first dispersed by the first rib and then collimated by the second rib.
  • the imaging quality of the above optical system is also affected by the image overlap caused by the reentry-type reticle of the QD grating and the wavelength-dependent QD grating focal length.
  • re-entrant grooves refer to Fresnel zone tapes which are larger than a semicircle appearing in the QD grating mask layout.
  • the optical parameters of the QD grating and the ridge system cannot be matched. Therefore, the optical path of the imaging device is long (about 1.3 meters in total length, as shown in Fig. 7), so that the camera can only record one image corresponding to a single diffraction order at a time. Such a system cannot even achieve the goal of simultaneous imaging of the original multi-plane/multi-diffraction stage.
  • the imaging system is not compatible with other technologies, such as microscopy, due to various inaccuracies, including inaccurate calibration of unstable long optical paths and processing defects of the ribs and their bases.
  • reentry phenomenon ( Figure 6) Shown).
  • This reentry phenomenon may be beneficial for other applications, but in the present invention this phenomenon is a forbidden zone for QD grating design.
  • the reentrant type of reticle usually causes image overlap, and the pre-dispersion generated by the ribs cannot correspond to the exact position of the grating, resulting in reduced performance of the 4D imaging system or even no imaging at all.
  • "re-entrant grooves” refer to Fresnel zone tapes which are larger than a semicircle appearing in the QD grating mask layout.
  • NRQD grating non-reentry quadratically distorted grating
  • the present invention establishes a four-dimensional multi-plane broadband imaging system without scanning, in order to improve imaging time resolution without affecting image space.
  • the technique can transmit four-dimensional wavefront information between the object space and the image space, that is, simultaneously capture multi-color images of multiple object planes and image them in the same image plane; or according to the reversible principle of optical paths, the color difference of a single object plane The corrected image is simultaneously recorded on a series of image planes.
  • the four-dimensional multi-planar broadband imaging system includes the following optical components ( Figure 8):
  • Non-reentry type secondary distortion (NRQD) grating that is, a QD grating without reentry type reticle, for generating focal length and spatial position corresponding to each diffraction order in a multi-element optical system;
  • NQD Non-reentry type secondary distortion
  • NQD non-reentry secondary distortion
  • a lens system for effectively correcting an optical system focal length corresponding to each diffraction order of a non-reentry secondary distortion (NRQD) grating, and adjusting the optical path to meet the design requirements of the ridge system, and
  • NQD non-reentry secondary distortion
  • the NRQD grating can be designed with a combined mask layout of more than one NRQD arc pattern, so that the focal planes of multiple object planes (more than 3) are reasonably distributed on the same image plane.
  • the NRQD grating can be finely machined to obtain a multi-stage (digital) or continuous (analog) profile structure.
  • NRQD gratings can be used including, but not limited to, periodically distributed grooved structures having different transmittance, reflectivity, optical thickness, or polarization sensitivity.
  • the rib is a combined optical component of grating and prism.
  • the design of the ribs can be defined by the scribe line density of the grating structure: when the refractive index of the rib base material is 1.4 to 1.5, the scribe line density ranges from 100 to 800 lines per mm; When the refractive index of the base material is 1.5 to 1.6, the scribe line density ranges from 100 to 900 lines per mm; when the refractive index of the prism base material is 1.6 to 1.7, the scribe line density ranges from 100 to 1200 lines per mm; When the refractive index of the prismatic base material is greater than 1.7, the scribe line density ranges from 100 to 1400 lines per millimeter.
  • the ribs used in the present invention may be volume phase holographic (VPH) ribs.
  • the refractive index of the blazed/VPH grating and the prism constituting the prism structure may be different.
  • More than one pair of ribs can be used to correct for broadband light dispersion caused by more than one NRQD grating.
  • the ribs can be placed anywhere as long as the theoretically expected pre-dispersion and re-alignment can be achieved in the full incident light band.
  • the four-dimensional multi-planar broadband imaging system of the present invention is compatible with a variety of commercial microscopes, including fluorescence, light/dark fields, phase contrast, differential interference contrast (DIC), and structured light illumination.
  • the system can also be used for uniform illumination of a single broadband source simultaneously in multiple planes.
  • the technology can be flexibly combined with a variety of modern technologies, including microscopy, astronomical optics, optical data storage, biomedical imaging, wavefront analysis, and virtual/augmented reality, and will be widely used in academic research and industry. Applications.
  • Figure 1 shows a basic design schematic of a three-dimensional narrowband imaging system.
  • Figure 2 shows an early schematic diagram of a chromatic aberration correction scheme by pre-dispersion of the beam before entering the QD grating.
  • Figure 3 shows a schematic diagram of the QD grating structure in an x-y Cartesian coordinate system.
  • Figure 4 depicts the pre-dispersion and collimation of incident broadband light prior to entering the QD grating, which corrects the dispersion caused by the QD grating.
  • Figure 5 shows a basic design schematic of a multicolor imaging system based on QD gratings and ridges.
  • the imaging system (40) comprises: a dispersing device (10) between a collimated optical path of a pair of achromatic lenses (42), (44), a multi-color light source (32) , a QD grating (46), a multimode fiber (34), and a CCD detection device (not shown).
  • Figure 6 shows a mask partial pattern of a QD grating with reentrant scribe lines for British Patent GB 2504188.
  • Figure 7 shows the long optical path of an imaging system based on QD gratings and ridges.
  • Figure 8 is a schematic illustration of a four dimensional multi-plane broadband imaging system.
  • the apparatus includes: one or more non-reentry quadratically distorted (NRQD) gratings (5) that can generate focal lengths and spatial positions corresponding to respective diffraction orders, thereby implementing multiple object/image planes (2) Real-time transmission of wavefront information between the same image/object plane (7); ridge system that limits lateral dispersion of images caused by chromatic aberration by dispersing incident light into a bundle of parallel light arranged horizontally according to spectral components (4) ); a lens system (3) for adjusting the optical path, and a photodetecting device (6).
  • NQD non-reentry quadratically distorted
  • a plurality of objects/image planes (2), a lens system (3), a ridge system (4), an NRQD grating (5), a photodetecting device (6), and a single image/object plane (7) ) are all located on the same optical axis (1).
  • Figure 9 is a schematic diagram of an optical path model of a single rib, showing the path of light from air into the ribs and then back into the air (in this case, the blazed diffraction level is +1).
  • Figure 10 shows the wedge/blaze angle design of the prism at different unbiased wavelengths when B270 Schott glass is used as the substrate material.
  • the number of reticle lines (lines/mm) of the blazed grating is identified in the legend, which correspond to the respective connecting lines from bottom to top in the figure.
  • Figure 11 shows the "bright rainbow". This is the first time that the imaging technique of the present invention successfully records all three diffraction-order four-dimensional broadband images in a single photograph, and the image quality is not adversely affected by the difference in focal length of the NRQD grating for different wavelengths of light. .
  • Figure 12 shows a pseudo color image obtained by passing white light through a series of bandpass filters: (i) Correcting chromatic aberration without using a ridge system.
  • the non-central wavelength corresponds to the severe dispersion of each image point due to chromatic aberration, the focal length difference of QD grating to different wavelengths of light, and the image overlap blur caused by the reentry scribe line of QD grating; (ii) the use of ridge system Correct the color difference.
  • the dispersion phenomenon is effectively corrected, but the image points corresponding to the non-central wavelength are still dispersed.
  • the phenomenon of image point dispersion is caused by the difference in focal length of the QD grating for different wavelengths of light and the image overlap blur caused by the reentry scribe line of the QD grating; (iii) optimal focusing for each color, and the chromatic aberration is not corrected by using the ridge system .
  • Figure 13 shows a four-dimensional, three-plane broadband image of an eGFP fluorophore obtained by simulated microscopic imaging experiments with a combination of white light and a series of bandpass filters with or without rib-corrected chromatic aberration.
  • Figure 14 shows a four-dimensional, three-plane broadband microscopic image of a fluorescent bead with or without rib-corrected chromatic aberration.
  • Figure 15 shows a bright field four-dimensional three-plane broadband microscopic image of human cervical cancer (HeLa) living cells.
  • the pitch ( ⁇ z, see equation (2)) of each focused image plane is 2.3 ⁇ m, and the spectral bandwidth is 525 ⁇ 39 nm.
  • Figure 16 shows the design of an NRQD grating mask layout incorporating phase contrast imaging and multiplanar imaging principles for four-dimensional, three-plane broadband phase contrast microscopy.
  • Figure 17 shows the wedge/blaze angle design of the prism at different unbiased wavelengths when quartz glass is used as the substrate material.
  • the number of reticle lines (lines/mm) of the blazed grating is identified in the legend, which correspond to the respective connecting lines from bottom to top in the figure.
  • Figure 18 shows the wedge/blaze angle design of the prism at different unbiased wavelengths when N-BAF10 Schott glass is used as the substrate material.
  • the number of reticle lines (lines/mm) of the blazed grating is identified in the legend, which correspond to the respective connecting lines from bottom to top in the figure.
  • Figure 19 shows a schematic diagram of the design of an NRQD grating mask layout with a "cross" structure that allows nine different object planes to be simultaneously imaged and presented separately on the same image plane.
  • Figure 20 shows the wedge/blaze angle design of the prism at different unbiased wavelengths when N-SF11 Schott glass is used as the substrate material.
  • the number of reticle lines (lines/mm) of the blazed grating is identified in the legend, which correspond to the respective connecting lines from bottom to top in the figure.
  • the core challenge in designing this optical system is the system design of the NRQD grating and ribs, as well as the good parameter matching of the NRQD grating-edge combination system.
  • the center period d 0 and the defocus factor W 20 of the NRQD grating must be designed very carefully.
  • the central period which determines the diffraction angle, determines the spacing between images recorded by an image detecting device such as a camera.
  • the lens system is introduced and further combined with other parameters of the NRQD grating, such as the incident light band, the radius, the refractive index of the base material, and the etching depth, thereby preliminarily establishing the optical path design prototype of the NRQD grating-lens combination system.
  • other parameters of the NRQD grating such as the incident light band, the radius, the refractive index of the base material, and the etching depth
  • the reentrant reticle may appear "mistaken" in the mask layout of the QD grating, or the minimum period d mtn (formula (8)) of the NRQD grating may become too small.
  • d mtn formula (8)
  • the operability of the grating design parameters is poor, and the grating cannot be flexibly designed. Instead, it is necessary to check whether there is a reentry type reticle after all calculations of the layout design program are completed. Even more inconvenient, this algorithm can only generate "arc" type engraved lines, but can not generate any other form of combined engraved structure, such as "cross” type engraved lines (see “Example 3" for details).
  • the improved design of the NRQD grating is greatly limited. In the present invention, based on the two-dimensional mathematical model of the NRQD grating, we have written a series of codes using Mathematica and Matlab software for the parameter design of the mask layout.
  • a masking program developed by AutoCAD software is used to perform mask layout drawing of the NRQD raster. Potential design flaws in the mask layout are easier to spot during this visual rendering process. In addition, the runtime of the mask generation code is significantly reduced, and it may take only a few minutes for an experienced AutoCAD user. Further, regardless of Whether a single NRQD raster layout or a composite layout of several NRQD gratings can be generated and flexibly operated to accommodate more imaging requirements. As more gratings are stacked, the energy loss of the optical system is greater.
  • a mask layout having an arbitrary combination of reticle structures can be designed and fabricated, thereby avoiding system light energy loss caused by superimposing two or more NRQD gratings, and truly realizing 9 or more planes. Simultaneous imaging.
  • the dispersion produced by more than one NRQD grating or a single NRQD grating with a combined mask layout can be corrected by using more than one pair of ribs.
  • the dashed lines in the figure indicate the normal direction (PN) of the prism, the normal direction of the outer surface of the grating (GN), and the normal direction of the blazed surface (FN).
  • the symbol rule is: when measuring the angle from the normal to the incident surface, the angle in the counterclockwise direction is represented by a positive value.
  • Such a rib can be obtained by processing a grating structure on the surface of the prism. At the moment we focus only on a simple but practical ridge design, rather than a complete display of the details of the optical path tracking mathematical model of the rib.
  • the diffraction angle ⁇ can be given by:
  • Equation (10) defaults that the two optical elements (gratings and prisms) that make up the ribs have the same refractive index n, however their refractive indices may be different. The refractive index of each element can be easily changed based on the same prism light path model.
  • the optical path tracking mathematical model of the prism According to the optical path tracking mathematical model of the prism, a series of graph functions about the prism design parameters can be obtained.
  • the main design parameters of the prism such as the wedge angle, the blaze angle, and the number of lines of the blazed grating, can be obtained from a corresponding set of graph functions. select.
  • the parameter selection of the ribs is optimized according to the design parameters of the NRQD grating and the imaging requirements of the optical system.
  • the Zemax software was used for optical path tracking simulation to finally verify the design of the ribs.
  • the layer design optimization parameters of the ribs are optimized, and it can be confirmed that the parameters of the NRQD grating and the ribs are well matched, and the performance of the entire optical system is optimized. So far, a custom NRQD-based grating and rib-based four-dimensional multi-plane broadband imaging system has been established.
  • the ribs used in the same imaging system may be of any type, nor are they limited to the same design, and the position in the optical system may be arbitrary as long as the amount of pre-dispersion required to correct the chromatic aberration can be Fully implemented.
  • the optical system can be customized and used in a variety of applications, and can be flexibly combined with a variety of modern technologies, including microscopy, astronomical optics, optical data storage, biomedical imaging, wavefront Analysis and virtual/augmented reality.
  • this optical system for four-dimensional multi-plane broadband imaging.
  • the optical device can also be used to record a broadband light/image of a single object plane on a series of image planes.
  • optical system design parameters mentioned in the following embodiments are only used to illustrate the feasibility of the present invention, rather than the definition of each parameter. It is obvious that experienced people can fine tune the parameters without affecting the normal operation of the system.
  • Embodiment 1 Four-dimensional three-plane broadband imaging simulation experiment
  • a continuous white laser (Fianium supercontinuum source SC450-PP-HE, available in wavelengths from approximately 450 nm to over 1750 nm) was coupled to the imaging system through a single mode fiber (Thorlabs P1-488PM).
  • a simple optical system (Fig. 5) that has been used before: a small hole with a diameter of about 3 mm is used as the aperture stop; two achromatic lenses with a focal length of 250 mm are spaced 200 mm apart to form an equal size ( A combined optical system with a magnification of 1) and an equivalent focal length of 208 mm.
  • the NRQD grating is processed on quartz glass with a refractive index of about 1.46, the nominal axial period (ie, the center period) is 50 ⁇ m, the curvature parameter W 20 is 50 times the wavelength, and the radius is 10 mm;
  • the focal length of the NRQD grating at the first diffraction order is ⁇ 1898 mm.
  • the NRQD grating is 208 mm from the second principal plane of the combined lens system (about 42 mm from the second lens), the images corresponding to the respective diffraction orders have the same magnification. Based on the different focusing capabilities of the NRQD grating for each diffraction order, the optical system enables simultaneous multi-plane imaging.
  • the custom parameters of the ribs are described as a set of graph functions by establishing a pair of optical path models of the same structure and back-to-back placement (the grating blazed faces are opposite).
  • the main design parameters such as the wedge angle of the prism, the blazed angle and the number of lines of the blazed grating can be selected from the chart function according to the actual needs of the optical system.
  • the prisms customized in this example have a base material of Schott B270 glass having a refractive index of about 1.53 and a cross-sectional dimension of 25 mm x 25 mm. According to the graph function shown in Fig.
  • the wedge angle and the blaze angle (corresponding to E and E' in Fig. 9, respectively) can be selected to be 17.5°, and the number of reticle lines of the blazed grating. It is 300 lines/mm.
  • the structure of the blazed grating can be machined on the hypotenuse of a right-angle prism with the wedge angle of the prism equal to the blazed angle of the grating.
  • a custom rib can split an incident parallel polychromatic light into a set of parallel beams by wavelength, and the "width" of the outgoing beam ( The degree to which the incident light is separated by the grating can be controlled by changing the pitch of the two gratings. It should be noted that we only need to pay attention to the distance between the two gratings, and their specific position between the two achromatic lenses is not important.
  • the imaging experiment Before carrying out the imaging experiment, it is necessary to rationally design the spacing of each image on the image plane (camera chip), so as to use the camera's photosensitive chip as efficiently as possible while avoiding the coincidence of multi-planar images.
  • the camera used in this example is Andor Zyla 4.2s CMOS with an image resolution of 2048 ⁇ 2048 and a pixel size of 6.5 ⁇ m, so the size of the sensor chip is 13.3 ⁇ 13.3 mm 2 .
  • the magnification of the optical system is 1:1
  • the diffraction angle of the first diffraction order is about 0.6°, thereby obtaining three images (corresponding to a zero diffraction order and a ⁇ 1 diffraction order, respectively).
  • a high-power continuous white laser (Fianium SC450-PP-HE) is passed through a series of 20nm bandwidth, 20nm steps, and a center wavelength from 450nm to 650nm.
  • the filter (Thorlabs)
  • 11 sets of spectra with a bandwidth of 20 nm were simulated.
  • the grayscale image of each band is sequentially acquired by an sCMOS camera (Andor Zyla 4.2), and the total luminous flux of the corresponding image points of each band is normalized using ImageJ software.
  • the pseudo-color images of the last 11 bands (center wavelengths from 450 nm to 650 nm, step size 20 nm, bandwidth of 20 nm per band) are combined to form a multi-color image.
  • the brilliant rainbow demonstrates the first successful use of NRQD grating and ribbed four-dimensional imaging technology for real-time multi-plane broadband imaging.
  • the brilliant rainbow reveals the core optics.
  • the system of the present invention can be used for simultaneous imaging of three planes of achromatic (this example), but the old system proposed by Feng Yan et al. in 2013 can only record one of the three diffraction orders for each photograph.
  • the focus position of the imaging system in this example is only unbiased/center wavelength of the system in the first three diffraction orders.
  • the focal length of 530nm is determined, and on this basis, the simulation imaging experiment with/without prism correction color difference is carried out. It is obvious that in the brilliant rainbow, the dispersion of the image points of the non-zero diffraction orders deviating from the center wavelength band (520 nm to 540 nm) is effectively alleviated, while the image points of the zero diffraction order are not affected by the NRQD grating and the ridge grid.
  • the rainbow experiment is only used to simulate the effect of four-dimensional multi-plane broadband imaging, only a relatively small prism spacing is selected in this example: 140 mm.
  • the 140mm prism spacing can only be used to correct the dispersion with a bandwidth of about 100nm (the incident light bandwidth in this case is 220nm). Therefore, as shown in FIG. 11, the first diffraction order image still has residual dispersion. In fact, chromatic aberration correction over a wider bandwidth range can be achieved simply by using a larger rib spacing.
  • the present invention simulates a set of fluorophore microscopic imaging experiments and selects eGFP, a fluorophore widely used in cell biology, as an imaging model for simulation experiments.
  • the optical system is focused and calibrated using the corresponding filters such that the wavelength of the corresponding central image point matches the peak wavelength of the fluorophore 520 nm. Due to the optimized design of the optical system, there is no image overlap blur caused by the QD grating reentry type reticle, and the influence of the NRQD grating on the focal length difference of different wavelengths of light can be ignored. In this example, the position of the light source is fixed, only Focus on the image corresponding to the zero diffraction order. Through a set of bandpass filters with wavelengths in the fluorophore emission spectrum, a series of pixels with a bandwidth of 20 nm are acquired, and the image points corresponding to each filter (band) are very clear.
  • each filter (band) corresponding to the image point is normalized by the total luminous flux corresponding to the image point of the fluorophore peak band, and then the emission spectrum profile of the fluorophore is simulated.
  • the luminous flux corresponding to each pixel in each band is weighted by a corresponding coefficient.
  • the images corresponding to the respective bands are merged together, and the simulated eGFP fluorophore image points simultaneously imaged by the three planes before and after the prism correction color difference are respectively obtained.
  • the three-plane broadband image simulating the eGFP fluorophore is simultaneously recorded, although there is still a very small amount of residual chromatic aberration in the red band (as shown in the upper image of Figure 13).
  • the invention has successfully developed a four-dimensional multi-plane wide-band imaging system based on NRQD grating and rib grid.
  • a chromatic aberration-correcting, high-efficiency, simple and practical three-plane simultaneous imaging is realized. Due to the high temporal resolution, the optical system can be expected to be used to measure dynamic processes, such as tracking individual particles.
  • the results of simulated imaging experiments obtained under the same conditions as the actual imaging can be used as a reference standard for post-image processing, and a non-zero diffraction order image when reconstructing a four-dimensional image using images of multiple planes.
  • the aberrations are corrected to obtain a more accurate 4D image.
  • Example 2 Four-dimensional three-plane broadband multimode microscopic imaging
  • the efficiency of the grating is defined as the ratio of the sum of the optical energy of each diffraction order measured to the total energy of the incident light.
  • the grooved structures of the periodic distribution have different transmittances, different reflectivities, different optical thicknesses or different polarization sensitivities.
  • the dispersion caused by the NRQD grating is not only effectively controlled, but also greatly increases the luminous flux of the imaging system.
  • the four-dimensional multi-planar broadband imaging device can be easily attached as an accessory to the camera port of a commercial microscope to record four-dimensional multi-color images of multiple object planes in real time, and can be used in various imaging modes such as fluorescence, bright field, phase contrast, and differential Interference difference (DIC), knot Light-emitting lighting, etc.
  • DIC differential Interference difference
  • the four-dimensional multi-planar broadband microscopy imaging system does not require narrow-band filters and complex optical path adjustments, it is well suited for biomicroscopic imaging applications where the luminous flux is very limited and the measured object is constantly changing.
  • This technique is also suitable for image localization and tracking, as well as image reconstruction of full-field, three-dimensional deconvolution-based z-stack samples.
  • the z-direction spacing between multiple planar images can vary from any small to several microns.
  • Four-dimensional multi-planar broadband fluorescence microscopy imaging has become an important application of this technology due to the use of four-dimensional multi-planar broadband imaging technology to capture the full-band optical information of the fluorophore emission spectrum.
  • the four-dimensional multi-planar broadband imaging technology is coupled to the camera port of a commercial microscope to capture and record the four-dimensional light field information of the microscopic sample.
  • the four-dimensional three-plane broadband microscopic imaging of fluorescent beads is taken as an example to demonstrate the optical performance of the imaging system.
  • the first step in the imaging experiment was to prepare a fluorescent pellet sample.
  • the coverslips (BRAND, 470820) were sonicated in acetone and 1 M NaOH solution for 30 min, then rinsed with ultrapure water multiple times (more than 2 times, if necessary with sonication). Finally, these coverslips were blown dry with nitrogen. Due to the good viscosity and optical properties of polyvinyl alcohol (PVA: Polyvinyl Acetate, 81381 Sigma-Aldrich), it was selected as a carrier for carrying fluorescent beads. A 30% aqueous PVA solution was prepared by dissolving PVA powder in water, stirring and heating to 100 °C.
  • the 1:10 dilution of the fluorescent sphere suspension (Invitrogen, F8827, 2 ⁇ m, 505/515) was then thoroughly mixed with the PVA aqueous solution at a ratio of 1:10.
  • the ultrasonic vibration, vortex mixing and 70 °C water bath heating were repeated during the mixing. Etc. operation to avoid agglomeration of the fluorescent sphere itself, and to maintain a certain solubility of the PVA to be thoroughly mixed with the fluorescent beads.
  • 100 ul of the dispersed fluorescent sphere/PVA solution was carefully dropped onto a clean coverslip (if a film of uniform thickness was required, it could be spin-coated using a homogenizer), and then placed in an oven at 45 ° C for several minutes.
  • the imaging experiment was based on the Olympus IX73 microscope (100-fold oil mirror). By designing the optical device, three different planes of the sample can be simultaneously imaged on the same image plane and chromatic aberration correction.
  • the unbiased (center) wavelength of the NRQD grating and prism combination system is designed according to the peak wavelength of the fluorophore emission spectrum.
  • a four-dimensional three-plane wide-band fluorescence microscopy imaging system was designed, and the distance ( ⁇ z) between the three object planes was 2.3 ⁇ m.
  • the NRQD grating is placed in the Fourier plane of the lens system, but the absolute position of the ribs need not be strictly defined.
  • the fluorophore sample was excited by a laser having a wavelength of 473 nm.
  • the emitted light is then filtered using a bandpass filter (Thorlabs, FB550-40) to form an 80 nm emission spectral bandwidth ([Delta][lambda]).
  • the grating pitch should be set to 108 mm.
  • Fig. 14 Images were acquired by an sCMOS camera (Andor Zyla 4.2) with an exposure time of 50 ms and then processed by ImageJ software. Before and after the prism correction color difference, the first three diffraction orders of the NRQD grating correspond to The images of the three object planes are shown in Fig. 14. Here, a single photographing is performed to simultaneously image three different planes of the fluorescent beads, and the dispersion phenomenon of the first diffraction order is effectively corrected.
  • the four-dimensional multi-planar broadband microscopic imaging technique of the present invention can also be used for multi-plane simultaneous imaging of multiple fluorophores.
  • a series of NRQD gratings each grating is designed for different operating wavelengths
  • multiple pairs of ribs, and dichroic patches placed between a particular NRQD grating and its corresponding camera in a series of Multi-planar focused images of multiple fluorophores are simultaneously recorded on the color camera separately.
  • the fluorescence is separated by a dichroic sheet such that the short-wavelength fluorescence emitted by the fluorophore is received by one camera and the long-wavelength fluorescence is received by the other camera, the fluorescence of the different wavelength bands emitted by these fluorophores can be simultaneously three-dimensionally
  • the ground is imaged separately on two separate cameras.
  • a third type of fluorophore having an emission wavelength peak wavelength at an intermediate wavelength is selected so that the emitted fluorescence can be simultaneously detected three-dimensionally by the above two cameras.
  • the images that coincide on the two cameras are then derived from the fluorescence emitted by the fluorophore with the emission spectrum in the middle band, and the remaining images on each camera are derived from the short- or long-wavelength fluorescence, respectively.
  • the luminescence emits light is separated by a series of dichroic patches and each camera can receive fluorescence in a certain band.
  • the light emitted by the fluorophores of a plurality of different bands can be simultaneously multi-planarly imaged on a series of independent cameras. Since the light emitted by each fluorophore can be imaged simultaneously in multiple planes, it is possible to conduct an in-depth study of the dynamic interaction phenomenon of four-dimensional achromaticity between multiple components of cells.
  • HeLa Human cervical cancer
  • DMEM fetal bovine serum
  • the cells were seeded in 35 mm glass bottom culture dishes (Shengyou Biotechnology). To be cultured until the cells are in good condition, the cells are washed several times (usually 3 times) with PBS buffer before the bright field microscopy, and replaced with new medium.
  • the optical setup of this experiment was consistent with the parameters of the simulation experiment in Example 1, except that an NRQD grating with a center period of 30 ⁇ m was used (other parameters were unchanged) and the prism spacing was changed to 176 mm.
  • the four-dimensional multi-planar broadband imaging system of the present invention can be flexibly applied to a variety of different microscopic imaging modes at low cost, including light/dark fields, fluorescence, phase contrast, differential interference contrast (DIC), and structured light illumination.
  • a curved and partially displaced NRQD grating structure is used to combine the four-dimensional multi-planar broadband imaging technique with the phase contrast microscopy imaging pattern, as shown in Figure 16 (Y.Feng, et al.'Multi -mode microscopy using diffractive optical elements', Engineering Review 31(2), 133-139 (2011)).
  • the internal grating structure is shifted by a quarter cycle, so that the +1 diffraction order is generated.
  • Phase shift and -1 diffraction order generation The phase shift is such that the phase of the diffracted reference beam is delayed or advanced based on different diffraction orders (zero diffraction orders are unaffected).
  • the NRQD grating used in this example is processed on quartz glass with a refractive index of about 1.46, the nominal axial period (ie, the center period) is 32 ⁇ m, the curvature parameter W 20 is 150 times the wavelength, and the radius is 10 mm, so when incident When the center wavelength of the light is 620 nm, the focal length of the NRQD grating at the first diffraction order is ⁇ 538 mm.
  • the prism light path model as shown in Fig. 17
  • the wedge angle and the blaze angle can be selected.
  • the distance ( ⁇ z) between the three focused object planes can be obtained to be 12.3 ⁇ m.
  • the optical system enables four-dimensional multi-planar broadband microscopy/tracking of transparent and fast moving objects (such as motion measurement of human sperm cells) over a large scale, providing a new perspective for in-depth study of biodynamics.
  • a four-dimensional multi-planar broadband imaging system is used for the differential interference contrast (DIC) microscopic imaging mode. Imaging experiments can be performed based on the Olympus IX73 microscope. By configuring the microscope system, three different object planes can simultaneously achieve differential interference contrast (DIC) microscopic imaging of the corrected chromatic aberration on the same image plane.
  • DIC differential interference contrast
  • the NRQD grating used in this example is processed on quartz glass with a refractive index of about 1.46, the nominal axial period (ie, the center period) is 30 ⁇ m, the curvature parameter W 20 is 50 times the wavelength, and the radius is 10 mm, so when incident When the center wavelength of light is 479 nm, the focal length of the NRQD grating at the first diffraction order is ⁇ 2088 mm.
  • the chart function obtained by the prism light path model (as shown in Fig. 18), when the base material of the prism is N-BAF10 (SCHOTT) glass with a refractive index of ⁇ 1.68 and the unbiased wavelength of the prism is 479 nm, it can be selected.
  • the wedge angle and the blaze angle (corresponding to E and E' in Fig. 9, respectively) were 44.8°, and the number of reticle lines of the blazed grating was 1000 lines/mm.
  • Two achromatic lenses with a focal length of 150 mm are spaced apart from each other by 130 mm to form a combined optical system of equal magnification (magnification of 1) and equivalent focal length of 132 mm.
  • a bandpass filter Thins, MF479-40
  • ⁇ output bandwidth
  • the distance ( ⁇ z) between the three focused object planes is 839 nm.
  • the contrast of the multi-planar image can be adjusted.
  • four-dimensional three-plane wide-band differential interference contrast (DIC) microscopic imaging can obtain more edge structure details of three different planes of the sample under test, and there is no artificial light. gosh.
  • DIC differential interference contrast
  • the 4D multi-planar broadband imaging system can be used as an accessory to the microscope, perfectly compatible with commercial microscopes and camera systems, or integrated into the optical path system of the microscope to achieve a customized new microscope.
  • Embodiment 3 Four-dimensional nine-plane broadband imaging
  • the NRQD grating we discussed above consists of a series of concentric arc reticle lines (not more than a semicircle) with unequal radii.
  • the grating reticle lines of these arc structures produce a meandering phase to the incident light, which can be derived from 3 different objects. Planar objects are simultaneously imaged and appear on the same image plane separately from each other.
  • the NRQD raster layouts of the two "arc" structures (the "arc” structure shown in Figure 3) can be vertically combined with each other to design a new NRQD grating.
  • the mask layout, the so-called "cross" structure layout (as shown in Figure 19).
  • NRQD gratings In the case where a certain loss of light energy has no serious influence on the imaging performance of the system, two NRQD gratings (hereinafter referred to as "arc" NRQD gratings) of an "arc" structure which are orthogonally superposed with each other may be used instead of using one having the same An NRQD grating of the "cross" structure of the design parameters (hereinafter referred to as "cross" NRQD grating).
  • cross NRQD grating
  • the imaging system can only be used for real time on five focused object planes. Imaging.
  • the curvature ratio (W 20 ) of two mutually perpendicular "arc" NRQD gratings constituting the "cross" NRQD grating combined mask layout should be 1:3 (as shown in the figure). 19)).
  • the "plane" NRQD grating achieves the object plane spacing ( ⁇ z, see equation (2)) via the optical system, which should be three times the object plane spacing achieved by another "arc” NRQD grating.
  • the field of view of the image plane and the object plane is determined only by the physical size or pupil size of the image sensing device. Therefore, the field of view obtained by a multifocal microscopic imaging device developed by a similar principle in the industry is about 35x35 square micron (60 times magnification) or about 20x20 square micron (100 times magnification) (S. Abrahamsson, et al.
  • two pairs of ribs can be used: one pair of ribs is used as described above; and the other pair of ribs should be rotated 90° around the optical axis to correct The dispersion of the "circular arc" structure rotated by 90° in the NRQD grating to the broadband incident light.
  • the two pairs of ribs can be designed by a chart function (e.g., Figures 10, 17, and 18) depending on the choice of glass type for the rib base material.
  • the parameters of the ribs can be selected according to the chart function shown in FIG.
  • Each of the ribs in the optical system can have the same or different design, depending largely on the design of the optical path. And as long as theoretically expected pre-dispersion and re-alignment can be achieved in the full incident light band, the ribs can be placed anywhere in the optical system. It is pointed out here that the working band of the prism and the four-dimensional multi-plane broadband imaging system is not limited to the spectral range of visible light, but can be applied to the invisible light band, and the optical design principle is completely consistent with the foregoing.
  • the efficiency of the grating is defined as the ratio of the sum of the optical energy of each diffraction order measured to the total energy of the incident light.
  • High optical efficiency NRQD gratings and ribs are indispensable for 4D multi-planar broadband imaging, especially when measuring/tracking fast moving target objects, weak optical signals or noisy backgrounds usually give the light energy of each image. Very low.
  • the limited optical energy needs to be uniformly "distributed" to nine images, and the correction of the broadband light dispersion caused by the NRQD grating requires two pairs of ribs, thereby improving the optical efficiency of each optical component while Reducing the optical loss of the system has a decisive influence on the imaging performance of the optical system.
  • We have previously studied the method of multi-step engraving to quantify the phase profile of a grating into multiple steps to improve optical efficiency Feng Yan, “Optimization Design of 3D Microscopic Imaging System Based on Secondary Phase Grating”, China Science Ph.D. Thesis of Technology University, 2013).
  • the NRQD grating can be finely processed to obtain a multi-stage (digital type) or continuous (analog type) cross-sectional structure.
  • a common prism a combination of a grating and a prism
  • VPH volume phase holographic
  • the structure of the ribs is similar to a sandwich, that is, a holographic grating has a prism on each side (Y. Feng, et al. 'Optical system', UK Patent Application No. GB2504188-A, (2013)).
  • the prisms on either side of the VPH grating are used to provide the grating with the correct angle of incidence and diffraction angle to maximize optical efficiency.
  • the refractive index of the blazed/VPH grating and the prism constituting the prism structure may be different.
  • the present invention has been theoretically verified that the VPH ridge system improves the optical efficiency of the system while its chromatic aberration correction performance is very similar to that of the conventional ribs previously used.
  • the grooves of the VPH grating can be directly machined to the prism surface at a suitable angle, which may avoid the use of a second prism, further reducing the system's optical energy loss. In-depth research on the chromatic aberration correction scheme is still in progress.

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Abstract

一个四维(4D:3D+时间)多平面宽带成像系统可以实时记录3D多平面多色像。该成像系统包括：一个或多个可生成各个衍射级对应的焦距和空间位置的非再入型二次扭曲(non-reentry quadratically distorted：NRQD)光栅(5)，从而实现在多个物/像平面(2)和同一个像/物平面(7)之间实时传送波前信息；通过将入射光分散成一束按照光谱成分横向排列的平行光，限制色差引起的图像横向弥散的棱栅系统(4)；用于调整光路的透镜系统(3)，以及光检测器件(6)。在该光学系统中，多个物/像平面(2)、透镜系统(3)、棱栅系统(4)、NRQD光栅(5)、光检测器件(6)、以及单个像/物平面(7)都位于同一个光轴(1)。这个简单、易用且集成化高的光学系统可以满足多种不同的需要，有广阔的应用前景。

Description

基于非再入型二次扭曲(NRQD)光栅和棱栅的四维多平面宽带成像系统 技术领域
本发明涉及到一个可用于四维(4D:三维+时间)多平面宽带成像的光学系统，其可在物空间与像空间之间传送四维波前信息，即同时捕捉多个物平面的多色像并将其成像于同一个像平面；或根据光路可逆原理，将单一物平面的色差校正像同时记录在一系列的像平面上。该技术可以灵活地与多种现代技术相结合，其中包括显微术、天文光学、光数据存储、生物医学成像、波前分析以及虚拟/增强现实，在学术研究和工业界将有广阔的应用。
背景技术
近年来涌现出的超分辨显微成像技术已经突破了衍射极限。相对于图像空间分辨率的突破，高时间分辨率成像依然存在挑战。多个平面同时成像的可能性被越来越广泛地研究，这类技术拟在细胞生物学、流体问题及三维追踪等领域实现对快速变化对象的实时成像。基于一种新型的衍射光学元件(diffractive optical element，简称DOE)——离轴菲涅耳波带片，最早由布兰卡德和格林恩韦发明了一套三维成像系统，通过使用一个简单的共轴光学装置，该系统可实现三个平面同时成像(A.H.Greenaway and P.M.Blanchard,‘Three-dimensional imaging system’,International application published under the patent cooperation treaty(PCT),PCT/GB99/00658,(1999))。这种衍射光学元件(DOE)就像一个具有多组焦距的镜片，但利用了衍射原理成像而不是折射原理，使其不同的衍射级具有不同的聚焦能力。因此，基于该元件的三维成像系统可以将不同的物平面同时成像在同一个像平面上，或将同一个物平面同时成像在不同的像平面上。然而，由于非零衍射级固有的色散性质，为了限制色差，过去基于该衍射光学元件(DOE)的技术只能用于窄带成像，因此减少了系统的光通量并限制了其早期在生物显微成像中的应用。尤其当样品处的光源强度原本就微弱的时候，光通量对成像质量的影响更甚。在理论上，之前提出的一些色差校正方案可对入射的多色光束进行操作，输出一个预色散的平行光束，从而在不过多损失光通量的情况下，可与基于衍射光学元件(DOE)的光学系统联用实现多色成像(P.M.Blanchard and A.H.Greenaway,‘Broadband simultaneous multiplane imaging’,Optics Communications 183(1),29-36(2000)；Y.Feng,et al.‘Optical system’,UK Patent Application No.GB2504188-A,(2013))。但在实际应用中，由于核心光学元件和光学系统的设计不完善，这些方案仅限于色差校正的测试实验，而不是用于真正的三维宽带成像。因此在本发明中，我们将致力于系统设计核心光学元件，并搭建光栅-棱栅参数良好匹配的成像系统，使得该 光学装置的性能得到有力的改进，并可与多种技术联用(如显微术、天文光学、光数据存储、生物医学成像、波前分析以及虚拟/增强现实)，从而在多个领域实现四维多平面宽带成像。
1.原有的三维窄带成像系统及存在的问题
最初的三维窄带成像系统包括一个衍射光学元件(DOE)、一个透镜系统(由一个或多个透镜组成)、一个窄带带通滤波片、以及一些用于成像的设备(比如光源和相机)。一个窄带三维成像系统的基础设计示意图如图1描述，其中间距为Δz的多个物平面可同时成像在同一个像平面，且衍射光学元件(DOE)，或称为二次扭曲(quadratically distorted：QD)光栅，被放在远心位置上使得各个面所成的像有相同的放大率(P.A.Dalgarno,et al.Multiplane imaging and three dimensional nanoscale particle tracking in biological microscopy.Optics Express 18(2),877-884(2010))。
QD光栅的第m衍射级的等效焦距fg可以被表示为：
Figure PCTCN2017098805-appb-000001
这里R是QD光栅的半径，W20是标准的离焦系数(coefficient of defocus)。在任一衍射级m上，等效焦距fg的值大小相等且符号相反。
各物面的间距Δz可以表示为：
Figure PCTCN2017098805-appb-000002
这里feff是透镜组合系统的有效组合焦距，M是显微镜物镜的放大倍率。
因此相机平面上各图像的中心间距Δd可以写成：
Figure PCTCN2017098805-appb-000003
这里λ是入射光的波长，d0是QD光栅的中心周期。
理论上，QD光栅上形成的最大色散sg可以由下式给出：
Figure PCTCN2017098805-appb-000004
这里Δλ是入射光频谱的带宽。
出于对宽带成像和光通量的实际需求，一个色散装置被加入该三维成像系统，以便对QD光栅引起的非零衍射级色差进行校正并减小光能损失。布兰卡德和格林恩韦早期提出了一种色差校正方案，其使用一对反射式闪耀光栅和折叠形的光路，先后引入相反的色散进行相互补偿从而达到色差校正的目的，如图2所示(P.M.Blanchard and A.H.Greenaway,‘Broadband simultaneous multiplane imaging’,Optics Communications 183(1),29-36(2000))。通过改变两个闪耀光栅之间的距离可以对色散的程度进行控制，但是由于折叠型的光路，改变光栅间距势必会引起若干光学元件的角度和位置的相应调节，因此系统变得很复杂以致于难以与用户设备集成，从而限制了该方案的实用性。
冯艳等人提出使用一对棱栅(光栅和棱镜的组合元件)校正色差的方案，但是由于核心光学元件的设计不完善，且光栅-棱栅系统的参数不匹配，导致了其早期的成像装置无法实现三个平面的同时成像，甚至无法和显微镜联用(Y.Feng,et al.‘Optical system’,UK Patent Application No.GB2504188-A,(2013))。因此这种粗糙的光栅-棱栅系统很难真正用于成像，细节见“二次扭曲(QD)光栅和棱栅组合系统”部分。
2.衍射光学元件DOE(二次扭曲光栅)的基本原理
上文所述类型的衍射光学元件DOE(即二次扭曲(QD)光栅)由一系列同心圆弧构成，这些圆弧可以是交替的透明/不透明(振幅型)或不同的光学厚度(相位型)。对于一个单次刻蚀(双层或者二元)的QD光栅，建立一个笛卡尔坐标系，其中原点为QD光栅的几何中心，x轴垂直于QD光栅的刻线，y轴平行于刻线，如图3所示。这里定义整数n为每一条圆弧刻线的位置序列数：n＝0对应于QD光栅的原点，且n值(依序)由正值变为负值，即其符号方向与x轴方向相反。
QD光栅的弧形刻线设计满足下式：
Figure PCTCN2017098805-appb-000005
式中x和y是QD光栅平面上相对于原点的笛卡尔坐标，d0是QD光栅的中心周期，W20是标准的离焦系数(coefficient of defocus)，λ是入射光的波长，R是QD光栅(中心位于光轴)的半径。这里式(5)默认了QD光栅为圆形，但设计原理对任何形状的QD光栅都适用。
因此QD光栅的第n条同心圆弧刻线的半径Cn可以表示为：
Figure PCTCN2017098805-appb-000006
因为QD光栅不同位置的周期不是固定常数，沿x坐标轴某位置的周期d与该位置的x坐标值 之间的关系如下：
Figure PCTCN2017098805-appb-000007
因此当x＝-R时，QD光栅的最小周期为：
Figure PCTCN2017098805-appb-000008
式(8)决定了QD光栅掩膜版图加工中的精度。
这里QD光栅对入射光产生了一个附加的相位，即所谓的迂回相位(detour phase)。该迂回相位是由于QD光栅刻线在垂直于原刻线方向(即垂直于图3中的y轴方向)产生二次扭曲所导致的，而不是一般的光栅由于刻蚀深度(即光学厚度)不同所导致的相位差。对于第m衍射级，作用于波前的迂回相位差φm可以表示为：
Figure PCTCN2017098805-appb-000009
式(9)表明了QD光栅对于不同的衍射级，产生了不同的相位延迟，从而使各非零衍射级具有了不同的聚焦能力。
3.二次扭曲(QD)光栅和棱栅组合系统
由于光栅的衍射角依赖于波长，而各衍射级中心的间距依赖于衍射角，在使用宽带光源照明时，每一个入射波长都决定了一个相应的图像中心位置。因此如果不纠正不同的波长导致的图像位置差异，对应于非零衍射级的各多色图像就会产生色散。利用二次扭曲(QD)光栅固有的非周期性刻线偏移特征，令不同波长的光对应于不同的光栅周期，则各波长的光经过QD光栅后产生的衍射角相等，即可校正色差。如图4所示，根据QD光栅的周期变化，一个定制的光学系统可以输出准直且预色散的光束，使不同颜色的光束可“分散”到光栅相应周期所在的位置(以获得相同的衍射角)，由此色散即被校正。
使用一对棱栅，即一种闪耀光栅和棱镜的组合元件，冯艳等人提出了一种色差校正方案(Y.Feng,et al.‘Optical system’,UK Patent Application No.GB2504188-A,(2013))。为了证实该方案的可行性，两个商用的光学元件成品：1个楔角为18°8'、基底材料为N-BK7的棱镜和1个闪耀角为17°30'、线数为300线/毫米、基底材料为B270的透射式闪耀光栅(均购于Edmund Optics)，被粘合在一起。 尽管粘合过程不够精确导致了两个棱栅的工作参数不尽相同，该系统依然可以提供一个接近532nm的无偏波长。图5展示了三平面多色成像系统的基础设计示意图，其中两个粘贴制成的棱栅沿着光轴方向、背靠背放置(即彼此的光栅面相对)在使用光电元件(Thorlabs)搭建成的光路系统中。接近中心波长532nm的光在通过棱栅系统时没有偏移，而多色光束中较长和较短波长的光则先被第1个棱栅分散，再被第2个棱栅准直。
然而，除了色散，上述光学系统的成像质量还会受到以下因素的影响：QD光栅的再入型刻线造成的图像重叠和依赖波长的QD光栅焦距。这里“再入型刻线(re-entrant grooves)”是指在QD光栅掩膜版图中出现的大于半圆的菲涅耳波带片刻线。尽管棱栅组合可以有效地缓解色差引起的弥散，但由于使用了未经系统设计且具有再入型刻线的QD光栅(如图6所示)，成像质量依然较差(Y.Feng,et al.‘Optical system’,UK Patent Application No.GB2504188-A,(2013))。进一步地，由于棱栅也缺乏理论设计，从而使得QD光栅和棱栅系统的光学参数无法匹配。因此该成像装置的光路很长(全长约1.3米，如图7所示)，以致于相机每次只能记录对应于单个衍射级的一幅图像。这样的系统甚至连最初的多平面/多衍射级同时成像的目标都无法实现。此外，由于各种误差，包括对不稳定的长光路的校准不精确和棱栅及其底座的加工缺陷等，该成像系统无法和其它技术兼容使用，比如显微技术。
发明内容
在本发明中，我们将系统设计并使用不具有再入型刻线的QD光栅，从而改善图像质量。与此同时，一个棱栅的Mathematica光路设计模型将被建立，因此实现了从理论上定制棱栅的参数。通过使用设计完善的光栅-棱栅系统，我们的四维多平面宽带成像设备可以成功地与其它技术联用，例如显微技术，实现高质量成像。
原理上，在垂直于光轴的像平面上的多个图像对应于由QD光栅结构决定的各个衍射级。因此，QD光栅结构的系统设计是非常重要的。为了把这种QD光栅用于四维多平面成像系统，除了布兰卡德和格林恩韦提出的波带片基本设计理论之外，我们更关注于QD光栅的掩膜图形绘制设计。由式(6)和(7)可知，当x＝R时，周期d最大而刻线半径Cn最小。这意味着Cn可能成为负值，而d值可能相当大。在这种情况下，QD光栅掩膜图形中将出现若干条超过半圆的弧形刻线(甚至完整的圆环刻线都可能出现)，我们将其称为“再入现象”(如图6所示)。这种再入现象也许对其它一些应用领域有益处，但在本发明中该现象是QD光栅设计的禁区。因为再入型的刻线通常会造成图像重叠，并且由棱栅产生的预色散无法对应到光栅的准确位置，从而导致4D成像系统的性能降低甚至完全无法成像。这里“再入型刻线(re-entrant grooves)”是指在QD光栅掩膜版图中出现的大于半圆 的菲涅耳波带片刻线。为了指定专用于我们的光学系统的衍射光学元件，我们将不存在再入型刻线的QD光栅定义为非再入型二次扭曲(non-reentry quadratically distorted)光栅，简称为NRQD光栅。
通过引入系统设计的非再入型二次扭曲(NRQD)光栅和棱栅，本发明建立了一个无需扫描的四维多平面宽带成像系统，以期在提高成像时间分辨率的同时，不影响图像的空间分辨率。该技术可在物空间与像空间之间传送四维波前信息，即同时捕捉多个物平面的多色像并将其成像于同一个像平面；或根据光路可逆原理，将单一物平面的色差校正像同时记录在一系列的像平面上。该四维多平面宽带成像系统包括以下光学元件(图8)：
非再入型二次扭曲(NRQD)光栅，即不存在再入型刻线的QD光栅，用于在多元件光学系统中生成各个衍射级对应的焦距和空间位置；
成对的棱栅，用于在空间中基于波长对光路进行调控，从而校正非再入型二次扭曲(NRQD)光栅引起的宽带光色散；
透镜系统，用于有效地修正非再入型二次扭曲(NRQD)光栅各衍射级对应的光学系统焦距，并且对光路进行调控以满足棱栅系统的设计需要，以及
光检测器件。
NRQD光栅可以通过多于一个NRQD圆弧版型的组合掩膜版图进行设计，从而使多个物平面(多于3个)的聚焦像合理分布在同一个像平面上。
为了获得更高的光学效率，NRQD光栅可以被精细加工，得到多级(数字型)或连续(模拟型)的剖面结构。
多种类型的NRQD光栅都可以被使用，包括(但不限于)周期分布的刻槽结构呈不同的透射率、反射率、光学厚度或偏振敏感性。
棱栅是一种光栅和棱镜的组合光学元件，为了适用于四维多平面宽带成像系统的宽带光色差校正，我们通过建立Mathematica光路模型对其进行设计。在本发明中，棱栅的设计可以由其光栅结构的刻线密度进行界定：当棱栅基底材料的折射率为1.4～1.5时，刻线密度范围是100到800线每毫米；当棱栅基底材料的折射率为1.5～1.6时，刻线密度范围是100到900线每毫米；当棱栅基底材料的折射率为1.6～1.7时，刻线密度范围是100到1200线每毫米；当棱栅基底材料的折射率大于1.7时，刻线密度范围是100到1400线每毫米。
本发明中使用的棱栅可以是体相位全息(volume phase holographic(VPH))棱栅。
组成棱栅结构的闪耀/VPH光栅和棱镜的折射率可以不相同。
可以使用多于一对的棱栅，对多于一个的NRQD光栅所引起的宽带光色散进行校正。
只要能在全入射光波段实现理论预期的预色散和重新准直，棱栅可以被放在任何位置。
本发明的四维多平面宽带成像系统可以与多种模式的商用显微镜兼容，其中包括荧光、明/暗场、相衬、微分干涉差(DIC)和结构光照明。
通过将单一的宽带照明光源聚焦在一系列不同的平面上，该系统还可用于单一宽带光源在多个平面的同时均匀照明。
该技术可以灵活地与多种现代技术相结合，其中包括显微术、天文光学、光数据存储、生物医学成像、波前分析以及虚拟/增强现实，并将在学术研究和工业界都有广阔的应用。
附图说明
图1展示了三维窄带成像系统的基本设计示意图。
图2展示了一个早期的通过对进入QD光栅之前的光束进行预色散的色差校正方案示意图。
图3展示了在x-y笛卡尔坐标系中的QD光栅结构示意图。
图4描述了对进入QD光栅之前的入射宽带光进行预色散和准直，可校正QD光栅引起的色散。
图5展示了基于QD光栅和棱栅的多色成像系统的基础设计示意图。如专利GB2504188-A中的描述，成像系统(40)包括：在一对消色差透镜(42)、(44)的准直光路之间的色散装置(10)，一束多色光源(32)，一个QD光栅(46)，一个多模光纤(34)，和CCD检测装置(图中未展示)。
图6展示了用于英国专利GB2504188的具有再入型刻线的QD光栅的掩膜局部图形。
图7展示了基于QD光栅和棱栅的成像系统的长光路。
图8是四维多平面宽带成像系统的示意图。该装置包括：一个或多个可生成各个衍射级对应的焦距和空间位置的非再入型二次扭曲(non-reentry quadratically distorted：NRQD)光栅(5)，从而实现在多个物/像平面(2)和同一个像/物平面(7)之间实时传送波前信息；通过将入射光分散成一束按照光谱成分横向排列的平行光，限制色差引起的图像横向弥散的棱栅系统(4)；用于调整光路的透镜系统(3)，以及光检测器件(6)。在该光学系统中，多个物/像平面(2)、透镜系统(3)、棱栅系统(4)、NRQD光栅(5)、光检测器件(6)、以及单个像/物平面(7)都位于同一个光轴(1)。
图9是单个棱栅的光路模型示意图，展示了光线从空气进入棱栅、然后再返回空气中的路径(本例中闪耀衍射级为+1)。
图10展示了当B270肖特玻璃作为基底材料时，棱栅在不同无偏波长时的楔角/闪耀角设计。图例中标识了闪耀光栅的刻线数(线/毫米)，先后分别对应着图中从下到上的各条联接线。
图11展示了“艳的彩虹”。这是本发明的成像技术第一次在单次拍照中，成功地记录所有3个衍射级的四维宽带图像，并且图像质量没有受到NRQD光栅对不同波长的光产生的焦距差异带来的负面影响。
图12展示了白光通过一系列带通滤波片后得到的伪彩色图像：(i)未使用棱栅系统校正色差。图中非中心波长对应各像点的严重弥散现象源于色差、QD光栅对不同波长光的焦距差异、以及QD光栅的再入型刻线造成的图像重叠模糊；(ii)使用了棱栅系统校正色差。色散现象被有效校正，但非中心波长对应的各像点依然弥散。该像点弥散现象源于QD光栅对不同波长光的焦距差异、以及QD光栅的再入型刻线造成的图像重叠模糊；(iii)针对每个颜色进行优化聚焦，未使用棱栅系统校正色差。
图13展示了有/无棱栅校正色差时，通过白光和一系列带通滤波片的组合，模拟显微成像实验得到的eGFP荧光团的四维三平面宽带图像。
图14展示了有/无棱栅校正色差的荧光小球的四维三平面宽带显微图像。
图15展示了人体宫颈癌(HeLa)活体细胞的明场四维三平面宽带显微图像。各聚焦像平面的间距(Δz,见公式(2))是2.3μm，光谱带宽为525±39nm。
图16展示了结合相衬成像模式和多平面成像原理的NRQD光栅掩膜版图的设计，可以用于四维三平面宽带相衬显微成像。
图17展示了当石英玻璃作为基底材料时，棱栅在不同无偏波长时的楔角/闪耀角设计。图例中标识了闪耀光栅的刻线数(线/毫米)，先后分别对应着图中从下到上的各条联接线。
图18展示了当N-BAF10肖特玻璃作为基底材料时，棱栅在不同无偏波长时的楔角/闪耀角设计。图例中标识了闪耀光栅的刻线数(线/毫米)，先后分别对应着图中从下到上的各条联接线。
图19展示了有“交叉”结构的NRQD光栅掩膜版图的设计示意图，该版图设计可实现将九个不同物平面同时成像并彼此分离地呈现在同一个像平面上。
图20展示了当N-SF11肖特玻璃作为基底材料时，棱栅在不同无偏波长时的楔角/闪耀角设计。图例中标识了闪耀光栅的刻线数(线/毫米)，先后分别对应着图中从下到上的各条联接线。
具体实施方式
设计该光学系统的核心挑战是NRQD光栅和棱栅的系统设计，以及NRQD光栅-棱栅组合系统的良好参数匹配。在实践中，为了避免出现再入型刻线，继而避免图像重叠，必须非常小心地设计NRQD光栅的中心周期d0和离焦系数W20。尤其是中心周期，其决定了衍射角，从而决定了图像检测装置(如相机)所记录的图像之间的间隔。然后引入透镜系统，并进一步结合NRQD光栅的其它参数，例如入射光波段、半径、基底材料的折射率以及刻蚀深度，由此初步建立NRQD光栅-透镜组合系统的光路设计雏型。为了设计出精细的四维多平面宽带成像系统，还需要精心选择棱栅的参数，从而在实现其校正色差的功能的基础上，结合已经得到的NRQD光栅-透镜组合系统的设计雏型，最终优化设计出NRQD光栅-透镜-棱栅的组合光学系统。由于光学系统中的各参数彼此影响，因此通常需要进行反复的优化才能确定最终的设计参数。而在这个过程中，再入型刻线可能会“失误”地出现在QD光栅的掩膜版图中，或NRQD光栅的最小周期dmtn(公式(8))可能变得过于小，这些情况将导致NRQD光栅的错误设计或更高难度/成本的加工。因此，在将“优化的”参数投入实验之前，对上述两个的因素进行最终检查是必要的。值得一提的是，基于同样的原理，所谓“优化的”光路设计参数在实际应用中是可变的、有多种选择的。
基于夫朗禾费衍射和傅立叶光学的相关理论，NRQD光栅的二维数学模型被建立起来，由此我们可以深入研究NRQD光栅的成像原理并改进NRQD光栅的设计(例如NRQD光栅掩膜版图的设计，以及其加工参数的设计：包括优化的刻蚀深度)。根据泽尼克多项式，在本发明之前，曾有一个Matlab程序被开发并用于QD光栅的掩膜版图设计。然而，由于该算法的复杂性及其相对较长的运行时间(通常多于10个小时)，且掩膜版图绘制的过程是不可见的，导致常常出现由于光栅初始设计参数选择不当而造成的再入型刻线。因此该方法对光栅设计参数的可操作性较差，无法灵活设计光栅，而是必须在版图设计程序的所有计算都结束后再检查是否有再入型刻线存在。更不方便的是，这种算法只能生成“圆弧”型刻线，而不能生成其它任何形式的组合型刻线结构，例如“交叉”型刻线(细节见“实施例3”)，极大限制了NRQD光栅的改进设计。在本发明中，根据NRQD光栅的二维数学模型，我们用Mathematica和Matlab软件编写了一系列代码，用于掩膜版图的参数设计。然后基于这些参数，使用AutoCAD软件开发的绘图程序进行NRQD光栅的掩膜版图绘制。在这个可视化的绘制过程中，掩膜版图中潜在的设计缺陷较容易被发现。除此之外，掩膜生成代码的运行时间也大幅缩短，对于一个有经验的AutoCAD使用者可能只需几分钟。更进一步地，无论 是单个NRQD光栅版图还是几个NRQD光栅的复合版图都可以被生成和灵活操作，以便适用于更多的成像要求。由于越多的光栅被叠加使用，光学系统的能量损失就越多。在本发明中，一个拥有任意组合刻线结构的掩膜版图可以被设计并制作，从而避免了叠加2个或多个NRQD光栅造成的系统光能损失，真正有效地实现9个或更多平面同时成像。在任何情况下，多于一个NRQD光栅或单个具有组合掩膜版图的NRQD光栅所产生的色散，可以通过使用多于一对的棱栅进行校正。
基于特劳布的设计，我们建立了单个棱栅的光路模型(W.A.Traub,‘Constant-dispersion grism spectrometer for channeled spectra’,Journal of the Optical Society of America A 7(9),1779-1791(1990))。如图9所示，以箭头标记的一束光线先后以A角度进入棱镜、折射、以α角度到达光栅、最后以衍射角β进入空气中(这里标记的是+1衍射级)。图中的虚线分别表示棱镜的法线方向(PN)、光栅的外表面法线方向(GN)和闪耀面法线方向(FN)。符号规则是：从法线到入射面测量角度时，逆时针方向的角度用正值表示。可以通过在棱镜表面加工一个光栅结构得到这样一个棱栅。目前我们仅专注于一个简单但实用的棱栅设计，而不是完整地展示棱栅的光路追踪数学模型的细节。
对于图9所示的棱栅模型，其衍射角β可由下式给出：
Figure PCTCN2017098805-appb-000010
式中m是衍射级次，λ是入射波长，d是光栅周期，n是棱栅基底材料的折射率。相对于零衍射级，正的衍射级位于顺时针方向，而负的衍射级位于逆时针方向。公式(10)默认了组成棱栅的两个光学元件(光栅和棱镜)有相同的折射率n，然而它们的折射率可以不相同。基于相同的棱栅光路模型，可以容易地更改各元件的折射率。
根据棱栅的光路追踪数学模型，可以得到一系列关于棱栅设计参数的图表函数。在实际应用中，结合棱栅基底玻璃材料和无偏波长的选择，棱栅的主要设计参数，如楔角、闪耀角、以及闪耀光栅的刻线数，可以从相应的一组图表函数中选择。进一步地，根据NRQD光栅的设计参数和光学系统的成像要求，对棱栅的参数选择进行优化。此外，还使用Zemax软件进行光路追踪模拟，从而最终验证棱栅的设计。通过上述步骤对棱栅设计参数进行层层优化选择，可以确认NRQD光栅和棱栅的参数实现了良好的匹配，且整个光学系统的性能得到了优化。至此，一个定制的基于NRQD光栅和棱栅的四维多平面宽带成像系统就建立起来了。理论上，在同一个成像系统中使用的棱栅可以是任意类型，也不限于采用相同的设计，并且在光学系统中的位置也可以是任意的，只要校正色差所需的预色散量可以被充分实现即可。
在本发明中，我们建立了一系列基于Mathematica和Matlab软件的核心光学元件以及NRQD光栅和棱栅组合系统的设计的数学模型。在这些理论模型的指导下，光学系统可被定制并用于多种场合，并可以灵活地与多种现代技术相结合，其中包括显微术、天文光学、光数据存储、生物医学成像、波前分析以及虚拟/增强现实。这里我们将列举一些该光学系统用于四维多平面宽带成像的例子。根据光路可逆原理，该光学装置还可用于将单一物平面的宽带光/像记录在一系列的像平面上。一个有经验的人士有可能在不脱离本发明范围的情况下，对光学系统的若干设计参数进行改动。因此，以下实施例中提到的光学系统设计参数仅用于例证本发明的可行性，而非对各参数的限定。很显然有经验的人士可以对各参数进行微调而不影响系统正常运行。
实施例1:四维三平面宽带成像仿真实验
如上文所述，我们已经展示了四维多平面宽带成像系统的原理和设计。在将该技术用于实际成像之前，我们首先开展了一些仿真的四维多平面宽带成像实验，以此定性地验证理论模型和光学装置，进而检验该技术在实际应用中的潜在性能和实效。
为了模拟成像环境，将一束连续白激光(Fianium超连续光源SC450-PP-HE，可用波长范围从大约450nm到1750nm以上)通过一根单模光纤(Thorlabs P1-488PM)联接到成像系统中。这里搭建了一个之前用过的简单的光学系统(图5)：使用了一个直径约为3mm的小孔作为孔径光阑；两个焦距为250mm的消色差透镜彼此间隔200mm，形成一个等大(放大倍率为1)、等效焦距为208mm的组合光学系统。在此例中，NRQD光栅加工在折射率约为1.46的石英玻璃上，其名义上的轴向周期(即中心周期)为50μm，曲率参数W20为50倍波长，半径为10mm；因此当入射光波长为527nm时，该NRQD光栅在第一衍射级的焦距为±1898mm。当NRQD光栅距离组合透镜系统的第二主平面208mm(距离第二个透镜约42mm)时，各衍射级对应的像具有相同的放大率。基于NRQD光栅对各衍射级的不同聚焦能力，该光学系统可实现多平面同时成像。
对于棱栅参数的设计，通过建立一对结构相同且背靠背放置(光栅闪耀面相对)的棱栅的光路模型，将棱栅的定制参数描述为一组图表函数。在使用特定光学玻璃和特定无偏波长的情况下，棱栅的楔角、闪耀角和闪耀光栅的刻线数等主要设计参数可根据光学系统的实际需求，从图表函数中选择。本例中所定制的棱栅，基底材料为折射率约1.53的肖特B270玻璃，截面尺寸为25mm×25mm。根据图10所示的图表函数，当棱栅的无偏波长为527nm时，可以选择楔角和闪耀角(分别对应于图9中的E和E')为17.5°，闪耀光栅的刻线数目为300线/毫米。这里闪耀光栅的结构可被加工在一个直角棱镜的斜边上，棱镜的楔角和光栅的闪耀角相等。在一个类似图5所示的简易光学系统中，定制的棱栅可以将一束入射的平行多色光按照波长分散成一组平行光束，且出射光束的“宽度”(可 以理解为入射光被棱栅分离的程度)可以通过改变两个棱栅的间距进行控制。需要说明的是，我们只需关注两个棱栅之间的距离，而它们在两个消色差透镜之间的具体位置并不重要。
在开展成像实验之前，还需合理设计各个像在像平面(相机芯片)上的间距，从而在避免多平面图像重合的前提下，尽可能有效地利用相机的感光芯片。根据相机感光芯片的物理尺寸，需要在芯片上对多个(2～9)像的位置和尺寸进行合理安排。此例中使用的相机为Andor Zyla 4.2sCMOS，其图像分辨率为2048×2048，像素尺寸为6.5μm，因此感光芯片的尺寸为13.3×13.3mm2。基于物方远心光路系统设计(光学系统的放大率为1:1)，我们使用上文中已选择的光学参数搭建了一个实时三平面宽带成像系统。当光线垂直入射，使用设计波长为527nm且中心周期为50μm的NRQD光栅时，第一衍射级的衍射角约为0.6°，从而得到3个像(分别对应零衍射级和±1衍射级)的中心间距为2.18mm，这也是保证3个像彼此不重叠的最小间距。因此3个像共占据相机的横向尺寸为3×2.18mm＝6.54mm，大约为相机感光芯片宽度的50％，故该光路设计比较合理。
为了展示四维多平面宽带成像系统对整个可见光范围的成像性能，将高功率的连续白激光(Fianium SC450-PP-HE)先后通过一系列20nm带宽、20nm步长、中心波长从450nm到650nm的带通滤波片(Thorlabs)，模拟出11组带宽为20nm的光谱。然后通过调节光纤光源的位置，模拟出分别对应于3个物平面的不同物距。每个波段的灰度图像由sCMOS相机(Andor Zyla 4.2)依次采集，再使用ImageJ软件将各个波段对应像点的总光通量进行归一化。然后通过Mathematica软件计算每个波段的中心波长对应的RGB值、对每一幅图进行兼容RGB的归一化、每幅图可生成分别对应R、G、B标准的伪彩色图、最终再将每幅图对应的3张伪彩色图合并成1张伪彩色图。该图即对应于某一中心波长的伪彩色图，至此完成了对单个波段图像的伪彩色处理。最后11个波段(中心波长从450nm到650nm，步长为20nm，每个波段的带宽为20nm)的伪彩色图像被合并在一起，形成了一幅多色图像。由于该实验展示了各个颜色呈彩虹顺序排列的现象，发明者冯艳用她的名字命名该实验——艳的彩虹，其特指在有/无棱栅校正色差的情况下，宽带光经过NRQD光栅后形成的多平面多色图像。灰度格式的彩虹图像如图11所示。
艳的彩虹展示了基于NRQD光栅和棱栅的四维成像技术首次成功地用于实时多平面宽带成像。与冯艳等人在2013年提出的类似的光学设计(Y.Feng,et al.‘Optical system’,UK Patent Application No.GB2504188-A,(2013))相比较，艳的彩虹揭示了核心光学元件和成像系统的优化设计所带来的若干优势。首先，本发明的系统完全可以用于消色差的3个平面(本例)同时成像，但冯艳等人在2013年提出的旧系统每次拍照仅能记录3个衍射级中某一个衍射级对应的单个平面的像(如图12所示)，而不能在相机芯片上同时记录3个平面的像。其次，本发明的系统通过设计合理 的NRQD光栅和棱栅的参数，成功地减轻了由NRQD光栅对不同波长的光产生的焦距差异而引发的像点弥散，而不需要像冯艳等人之前做的那样：根据每个波段的中心波长对应的焦距分别移动光源的位置，从而使相机记录到一系列聚焦点像(如图12(iii)所示)。由于不需要通过重置各个波长的光纤光源位置，来补偿NRQD光栅对不同波长光的焦距差异，此例中的成像系统在前3个衍射级的各焦点位置仅由系统无偏/中心波长～530nm的焦距决定，并在此基础上分别开展有/无棱栅校正色差的仿真成像实验。很明显，在艳的彩虹中，各个偏离中心波段(520nm～540nm)的非零衍射级的像点的弥散现象被有效地缓解了，而零衍射级的像点没有受到NRQD光栅和棱栅的影响(除了光能量降低)。不同于艳的彩虹，尽管色散已经被有效校正，图12(ii)所示的偏离中心波段的各像点依然弥散；这正是由于影响图像质量的因素还包括QD光栅的再入型刻线(见图6)造成的图像重叠模糊，以及依赖波长的NRQD光栅焦距。而且，为了适应QD光栅对每个颜色(波长)的光所产生的焦距的线性变化，人为地调节各个颜色的光源位置以便找到最优焦距(图12(iii))，在实际的成像实验中是不可行的。因此，为了实现有效的四维多平面宽带成像，合理设计不存在再入型刻线的QD光栅(即NRQD光栅)是必备条件，且应该通过建立数学模型并进行参数验证，对基于NRQD光栅、棱栅和消色差双胶合透镜的光学系统进行优化的设计。
这里需要指出的是，由于彩虹实验只是用于模拟四维多平面宽带成像的效果，此例中仅选取了一个相对较小的棱栅间距：140mm。而根据我们建立的数学模型，140mm的棱栅间距仅可用于校正带宽约为100nm的色散(本例中的入射光带宽为220nm)。因此如图11所示，第一衍射级图像依然存在残余的色散。事实上，可以简单地通过使用更大的棱栅间距，以获得更大带宽范围的色差校正。我们正在建立一个更为精致的四维多平面宽带成像系统的数学模型，其中包括分析更多的光学像差，例如球差和彗差。
为了进一步展示四维多平面宽带成像系统的实用性，本发明模拟了一组荧光团显微成像实验，并选择了eGFP这种在细胞生物学中广泛应用的荧光团作为仿真实验的成像模型。在不使用显微镜的情况下，通过下述方法模拟荧光团的四维多平面宽带成像实验：即白光经过一系列带宽为20nm的带通滤波片后，得到一组特定波段的光谱(就像截取了某一部分光谱的彩虹实验)；然后将一组像点按照荧光团的发射光谱排列(以20nm为步长，波长范围从480nm到600nm)，并模拟荧光团发射光谱的能量分布，对各像点的强度进行加权修正。利用相应的滤波片对光学系统进行对焦和校准，使得相应中心像点的波长与荧光团的峰值波长520nm相匹配。由于光学系统的优化设计，因此不存在QD光栅再入型刻线导致的图像重叠模糊，也可忽略NRQD光栅对不同波长光的焦距差异带来的影响，本例中固定了光源的位置，仅聚焦于零衍射级对应的像。通过一组波长在荧光团发射谱范围的带通滤波片，采集到一系列带宽为20nm的像点，每个滤波片(波段)对应的像点非常清晰。 然后对这些像点进行处理：首先通过荧光团峰值波段对应像点的总光通量将每个滤波片(波段)对应像点的总光通量进行归一化，然后再模拟荧光团的发射光谱轮廓，将各波段对应像点的光通量按相应的系数加权。如图13所示，各波段对应的图像合并在一起，分别得到了棱栅校正色差前后的三个平面同时成像的模拟eGFP荧光团像点。我们看到，模拟eGFP荧光团的三平面宽带像被同时地记录下来，尽管在红色波段范围依然存在极少量的残余色差(如图13中的上图所示)。
本发明已经成功地研制出了基于NRQD光栅和棱栅的四维多平面宽带成像系统，第一次实现了校正色差的、高效率的、简单实用的、三个平面同时成像。由于高的时间分辨率，该光学系统可以被预期用于测量动态的过程，例如追踪单个粒子。在与实际成像同等条件下(例如相同的波段和光能量分布)得到的模拟成像实验结果，可以在使用多个平面的像重建四维图像时，作为后期图像处理的参照标准，对非零衍射级像的像差进行校正，从而得到更准确的四维图像。
实施例2:四维三平面宽带多模式显微成像
尽管一些现代的光学显微技术已经实现了超高的空间分辨率，每一次拍照依然只能得到样品在某一个焦平面的信息，也就是二维(2D)信息。而生物样品，例如活细胞，是三维(3D)且不断变化的，因此在基础的生物学研究以及临床诊断治疗领域，越来越多地需要对生物样品的三维观察并对其体结构进行分析。目前大多数的3D显微成像技术都依赖于沿着样品深度方向扫描的时耗式方法，严重限制了对光学敏感样品的成像和对生物样品动态过程的观测，在需要追踪快速动态过程的时候尤其如此。而且不幸的是，空间和时间分辨率彼此对立，为了看到更细致的结构总是以牺牲时间分辨率为代价。因此需要开发新的高时间分辨成像技术，在不受空间分辨率约束的情况下，高帧率记录被测样品的三维动态信息。
在本发明中，我们建立了一个高时间分辨率、高效率且简单实用的四维多平面宽带成像系统，其可以灵活地与多种现代技术相结合，其中包括显微术、天文光学、光数据存储、生物医学成像、波前分析以及虚拟/增强现实。这里光栅的效率被定义为：被测量各衍射级的光能量总和与入射光总能量的比值。通过高精度的光栅加工(如多层刻蚀)，可得到多级(数字型)或连续(模拟型)的光栅剖面结构，从而优化了NRQD光栅的光学效率。根据成像应用的不同需求，多种类型的NRQD光栅可被使用：周期分布的刻槽结构呈不同的透射率、不同的反射率、不同的光学厚度或不同的偏振敏感性。通过优化的定制棱栅代替窄带滤波片，NRQD光栅引起的色散现象不仅被有效地控制，还大幅提高了成像系统的光通量。下面将展示四维多平面宽带成像技术与显微成像技术相结合的若干应用实例。该四维多平面宽带成像装置可作为附件简易地联接在商用显微镜的相机端口，实时记录多个物平面的四维多色像，并可用于多种成像模式，如荧光、明场、相衬、微分干涉差(DIC)、结 构光照明等。由于该四维多平面宽带显微成像系统不需要窄带滤波片和复杂的光路调节，非常适合(可用于成像的)光通量十分有限而被测物体持续变化的生物显微成像应用。该技术也适用于对粒子的定位和追踪，以及全场、三维的基于去卷积的z叠层样品的图像重建。多个平面图像之间的z向间距可以从任意小到若干微米变化。
荧光小球的四维三平面宽带显微成像
由于使用四维多平面宽带成像技术可以采集到荧光团发射光谱的全波段光信息，四维多平面宽带荧光显微成像成为该技术的一个重要应用。四维多平面宽带成像技术与显微技术结合使用时，其简易且集成化的光学装置被联接在商用显微镜的相机端口，捕捉并记录显微样品的四维光场信息。这里以荧光小球的四维三平面宽带显微成像为例，展示该成像系统的光学性能。
成像实验的第一步是制备荧光小球样品。盖玻片(BRAND,470820)先后在丙酮和1M NaOH溶液中超声30min，然后用超纯水冲洗多次(多于2次，必要时超声处理)。最后将这些盖玻片用氮气吹干。由于聚乙烯醇(PVA：Polyvinyl Acetate,81381Sigma-Aldrich)的良好黏度和光学性能，选择其作为承载荧光小球的载体。通过将PVA粉末溶解于水中，搅拌并加热到100℃，制得30％的PVA水溶液。然后将按1:10稀释的荧光球悬浮液(Invitrogen,F8827,2μm,505/515)与PVA水溶液按1:10的比例充分混合，混合过程中重复超声震动、漩涡混匀以及70℃水浴加热等操作，以避免荧光球自身发生团聚，并可使PVA保持一定的溶解性从而与荧光小球充分混合。最后取100ul分散好的荧光球/PVA溶液小心地滴到干净的盖玻片上(如果需要得到厚度均匀的薄膜，可以使用匀胶机进行旋转涂膜)，再置于45℃烘箱干燥数分钟。使用显微镜对干燥后的样品进行快速的检查，发现各荧光小球单一(非团聚)地、接近随机均匀分布地被固定在PVA胶体中。为了避免样品产生光分解(尽管很少发生)，将其保存在黑暗避光处。
成像实验基于奥林巴斯IX73显微镜(100倍油镜)开展，通过设计光学装置，使样品的3个不同平面可同时成像在同一个像平面上并实现色差校正。为了完整展示荧光小球的发射光谱，NRQD光栅和棱栅组合系统的无偏(中心)波长按照荧光团发射光谱的峰值波长来设计。根据实施例1中的光学参数，设计搭建了四维三平面宽带荧光显微成像系统，其3个物平面之间的距离(Δz)为2.3μm。在该成像系统中，将NRQD光栅置于透镜系统的傅立叶平面，但棱栅的绝对位置不需严格定义。荧光团样品被波长为473nm的激光激发。然后使用一个带通滤波片(Thorlabs,FB550-40)对发射光进行滤波，从而形成80nm的发射光谱带宽(Δλ)。根据数学模型，为了校正该宽带光经过NRQD光栅时产生的色散，应将棱栅间距设置为108mm。图像由sCMOS相机(Andor Zyla 4.2)采集，曝光时间为50ms，然后通过ImageJ软件进行处理。棱栅校正色差前后，NRQD光栅前3个衍射级对应的 3个物平面的图像如图14所示。这里看到单次拍照可将荧光小球的3个不同平面同时成像，且第一衍射级的色散现象被有效地校正了。
本发明的四维多平面宽带显微成像技术还可以用于多种荧光团的多平面同时成像。通过使用一系列NRQD光栅(每个光栅被设计用于不同的工作波长)、多对棱栅、以及放置于特定NRQD光栅和其对应的相机之间的二向色性片，可以在一系列单色相机上分别地同时记录多种荧光团的多平面聚焦像。正如之前举过的一个例子(Y.Feng,et al.‘Chromatically-corrected,high-efficiency,multi-colour,multi-plane 3D imaging’,Optics Express 20(18),20705-20714(2012))，如果荧光被二向色性片分开，使得荧光团发出的短波长的荧光被一个相机接收，而长波长的荧光被另一个相机接收，那么这些荧光团发出的不同波段的荧光可以被同时地三维地分别成像在两个独立的相机上。然后选择第三种发射光峰值波长处于中间波长的荧光团，使其发出的荧光可同时地三维地被上述两个相机检测到。于是在两个相机上重合的图像就来源于发射光谱位于中间波段的荧光团发出的荧光，而每个相机上其余的图像则分别来源于上述短波长或长波长的荧光。根据相似的原理，如果使用多于2个NRQD光栅和多于2对棱栅，且如果荧光团发出的光被一系列二向色性片分开并使得每个相机都能接收某个波段的荧光，那么多个不同波段的荧光团发射的光可以被同时地多平面地分别成像在一系列独立的相机上。由于每个荧光团发射的光都可以被同时地多平面地成像，使得人们对细胞多组分之间的四维消色差的动态交互现象的深入研究成为可能。
人体宫颈癌(HeLa)活体细胞的四维三平面宽带明场显微成像
人体宫颈癌(HeLa)活体细胞在37℃、5％的CO2培养箱中培养，细胞培养所使用的培养基DMEM(Hyclone,U.S.A.)添加了10％的胎牛血清(Hyclone,U.S.A.)。细胞接种于35mm玻璃底培养皿中(Shengyou Biotechnology)。待培养至细胞状态良好，在进行明场显微成像前，再将细胞用PBS缓冲液洗几次(一般3次)，并换上新的培养基。除了使用一个中心周期为30μm的NRQD光栅(其它参数不变)并将棱栅间距改为176mm，本实验的光学设置都与实施例1中的仿真实验的参数一致。另外，这里使用了新的带通滤波片(Thorlabs,MF525-39)获得了78nm的输出光谱带宽(Δλ)。最后通过使用奥林巴斯IX73显微镜装置(100倍油镜)，在未经滤波的白光卤素灯照明条件下，对HeLa活体细胞进行四维三平面宽带明场显微成像。
HeLa活体细胞的四维三平面宽带明场显微图像如图15所示，可见该细胞的3个不同平面的像有显著的差别且细胞的形状和尺寸在非零衍射级图像中没有失真。尽管这些图像不是十足的清晰，各物平面依然可以认为是被良好聚焦的，原因在于3个物平面的间距Δz＝2.3μm过大，导致视场深 度已经超出了细胞的轴向尺寸。进一步的实验将会针对较小的物平面间距(Δz约为1μm)开展，从而可以捕捉到细胞内部结构的更多细节。
四维三平面宽带相衬显微成像
本发明的四维多平面宽带成像系统可以低成本地灵活运用于多种不同的显微成像模式，其中包括明/暗场、荧光、相衬、微分干涉差(DIC)、以及结构光照明。在本例中，使用了弯曲并部分移位的NRQD光栅结构，从而将四维多平面宽带成像技术与相衬显微成像模式相结合，如图16所示(Y.Feng,et al.‘Multi-mode microscopy using diffractive optical elements’,Engineering Review 31(2),133-139(2011))。以NRQD光栅的外圈结构作为参考，对其内部的光栅结构做四分之一周期的移位，于是+1衍射级产生
Figure PCTCN2017098805-appb-000011
的相移且-1衍射级产生
Figure PCTCN2017098805-appb-000012
的相移，从而基于不同的衍射级(零衍射级不受影响)，将衍射参考光束的相位进行了延迟或提前。
本例中使用的NRQD光栅加工在折射率约为1.46的石英玻璃上，其名义上的轴向周期(即中心周期)为32μm，曲率参数W20为150倍波长，半径为10mm，因此当入射光的中心波长为620nm时，该NRQD光栅在第一衍射级的焦距为±538mm。根据由棱栅光路模型得到的图表函数(如图17所示)，当棱栅的基底材料为折射率～1.46的石英玻璃且棱栅的无偏波长为620nm时，可以选择楔角和闪耀角(分别对应于图9中的E和E')为15.7°，闪耀光栅的刻线数目为200线/毫米。两个焦距为300mm的消色差透镜彼此间隔250mm，形成一个等大(放大倍率为1)、等效焦距为257mm的组合光学系统。使用一个带通滤波片(Thorlabs,MF620-52)以输出带宽(Δλ)为104nm的光谱，将棱栅间距设置为189mm可校正该宽带光经过NRQD光栅时所产生的色散。根据上述光路设计，并采用100倍油浸物镜，可以得到3个聚焦的物平面之间的距离(Δz)为12.3μm。该光学系统可在较大尺度范围实现对透明且快速运动的物体进行四维多平面宽带显微成像/追踪(如人体精子细胞的运动测量)，为深入研究生物动力学提供了新的视角。
四维三平面宽带微分干涉差(DIC)显微成像
本例中将四维多平面宽带成像系统用于微分干涉差(DIC)显微成像模式。成像实验可基于奥林巴斯IX73显微镜开展，通过配置显微镜系统，使3个不同的物平面可在同一个像平面上同时实现校正色差的微分干涉差(DIC)显微成像。
本例中使用的NRQD光栅加工在折射率约为1.46的石英玻璃上，其名义上的轴向周期(即中心周期)为30μm，曲率参数W20为50倍波长，半径为10mm，因此当入射光的中心波长为479nm时，该NRQD光栅在第一衍射级的焦距为±2088mm。根据由棱栅光路模型得到的图表函数(如图18所 示)，当棱栅的基底材料为折射率～1.68的N-BAF10(SCHOTT)玻璃且棱栅的无偏波长为479nm时，可以选择楔角和闪耀角(分别对应于图9中的E和E')为44.8°，闪耀光栅的刻线数目为1000线/毫米。两个焦距为150mm的消色差透镜彼此间隔130mm，形成一个等大(放大倍率为1)、等效焦距为132mm的组合光学系统。使用一个带通滤波片(Thorlabs,MF479-40)以输出带宽(Δλ)为80nm的光谱，将棱栅间距设置为108mm可校正该宽带光经过NRQD光栅时所产生的色散。根据上述光路设计，并采用100倍油浸物镜，可以得到3个聚焦的物平面之间的距离(Δz)为839nm。通过配置诺马斯基棱镜或者四分之一波带片(必要时)，多平面像的对比度可以被调节。与四维三平面宽带相衬显微成像相比较，四维三平面宽带微分干涉差(DIC)显微成像可以得到被测样品3个不同平面的更多的边缘结构细节，且不存在人为造成的光晕。
小结
四维多平面宽带成像技术与多种显微成像模式相结合的应用实例，已经充分证实了该技术的有效性和实用性。由于其简单易用且集成化高，该四维多平面宽带成像系统可以作为显微镜的附件使用，与商用显微镜和相机系统完美兼容；也可以集成到显微镜的光路系统，从而实现一个定制的新型显微镜。
实施例3:四维九平面宽带成像
上文中我们讨论的NRQD光栅是由一系列半径不等的同心圆弧刻线(不超过半圆)组成，这些圆弧结构的光栅刻线对入射光产生迂回相位，从而可以将来自3个不同物平面的物体同时成像并彼此分离地呈现在同一个像平面上。为了同时记录更多平面(最多9个)的像，可以将两个“圆弧”结构的NRQD光栅版图(“圆弧”结构如图3所示)彼此垂直组合，设计成一个新的NRQD光栅的掩膜版图，即所谓的“交叉”结构版图(如图19所示)。在损失一定的光能量对系统成像性能影响不严重的情况下，可使用两个彼此正交叠加的“圆弧”结构的NRQD光栅(以下简称“圆弧”NRQD光栅)，代替使用一个具有相同设计参数的“交叉”结构的NRQD光栅(以下简称“交叉”NRQD光栅)。然而，在实际的成像应用中，光学效率往往是影响光学系统成像性能的重要因素之一。因此，为了高效地实现四维九平面宽带成像，必须致力于“交叉”NRQD光栅的组合掩膜版图设计以及简单的色差校正方案，使得系统的宽带光能量可以被高光学效率地利用。
通过对“交叉”NRQD光栅的刻槽结构(如曲率、周期和刻蚀深度)和两组同心圆弧的圆心位置进行优化设计，可实现能量均衡分布在各个平面(最多9个)的像以九宫格的排列形式同时呈现在像平面上。特别地，当一个“交叉”NRQD光栅的掩膜版图由两个结构相同的“圆弧”NRQD光栅的掩膜版图彼此垂直组合而成时，该成像系统只能对5个聚焦的物平面实时成像。这是由于两个结 构相同的“圆弧”NRQD光栅在九宫格四个对角处产生的焦距大小相等且符号相反，使得能量彼此抵消，最终造成对角处的四个像的消失。为了同时记录9个等距物平面的聚焦像，构成“交叉”NRQD光栅组合掩膜版图的两个彼此垂直的“圆弧”NRQD光栅的曲率比(W20)应为1:3(如图19所示)。进一步推演可得，其中一个“圆弧”NRQD光栅经由光学系统实现的物平面间距(Δz,见公式(2))，应为另一个“圆弧”NRQD光栅所实现的物平面间距的3倍。对于放大率为1:1的远心四维多平面宽带成像系统，像面和物面的视场(field of view)仅由图像检测装置的物理尺寸或光阑尺寸决定。因此，相比较于业内同行基于类似原理开发的多焦面显微成像设备所得到的视场——约35x35平方微米(60倍放大率)或约20x20平方微米(100倍放大率)(S.Abrahamsson,et al.‘Fast multicolor 3D imaging using aberration-corrected multifocus microscopy’,Nature Methods 10,60–63(2013))，本发明的四维九平面宽带成像系统和显微成像技术相结合时，在同等成像条件下(如光源、显微镜配置、待测样品质量等)，可实现的视场要大得多。
对“交叉”NRQD光栅引起的宽带光色散进行校正，可以使用两对棱栅：其中一对棱栅的使用如前文所述；而另一对棱栅应绕光轴旋转90°，以便校正“交叉”NRQD光栅中旋转了90°的“圆弧”结构对宽带入射光所产生的色散。基于前文讨论的棱栅光路模型(图9)，两对棱栅可以通过图表函数(例如图10、图17和图18)进行设计，具体参数取决于对棱栅基底材料的玻璃种类的选择。在一些需要高折射率光学玻璃的特殊情况下，比如N-SF11(SCHOTT)玻璃，棱栅的参数可以根据图20所示的图表函数进行选择。光学系统中的每个棱栅可以有相同或不同的设计，很大程度上取决于光路的设计。并且只要能在全入射光波段实现理论预期的预色散和重新准直，棱栅可以被放在光学系统中的任何位置。这里特别指出，棱栅以及四维多平面宽带成像系统的工作波段不仅限于可见光的光谱范围，而是可以推广应用于不可见光波段，且光学设计原理和前文所述完全一致。
在本发明中，光栅的效率被定义为：被测量各衍射级的光能量总和与入射光总能量的比值。高光学效率的NRQD光栅和棱栅都是四维多平面宽带成像所不可或缺的，特别在测量/追踪快速运动的目标物体时，微弱的光信号或嘈杂的背景通常使各个像得到的光能量很低。尤其对于四维九平面宽带成像系统，有限的光能量需要被均匀“分配”到九个像上，且校正NRQD光栅引起的宽带光色散需要两对棱栅，因此提高各光学元件的光学效率，同时减少系统的光损耗，对光学系统的成像性能有决定性的影响。我们之前已经研究了通过多次套刻，将光栅的相位轮廓量化为多台阶状，从而提高光学效率的方法(冯艳，“基于二次相位光栅的三维显微成像系统优化设计”，中国科学技术大学博士学位论文,2013)。因此，为了获得更高的光学效率，NRQD光栅可以被精细加工，得到多级(数字型)或连续(模拟型)的剖面结构。提高色差校正装置的光学效率，可以通过使用体相位全息(volume phase holographic:VPH)棱栅代替普通的棱栅(一个光栅和一个棱镜的组合元件)。这种VPH 棱栅的结构类似三明治，即一个全息光栅的两边各有一个棱镜(Y.Feng,et al.‘Optical system’,UK Patent Application No.GB2504188-A,(2013))。VPH光栅两侧的棱镜是用于给光栅提供正确的入射角和衍射角，从而将光学效率最大化。组成棱栅结构的闪耀/VPH光栅和棱镜的折射率可以不相同。本发明已经从理论上验证了：VPH棱栅系统在提高系统光学效率的同时，其色差校正性能和之前使用的普通棱栅非常相似。通过超快激光刻印技术，VPH光栅的刻槽可以直接以合适的角度被加工在棱镜表面，这样做可能可以避免使用第二个棱镜，从而进一步降低系统的光能损耗。关于色差校正方案的深入研究还在进行中。

Claims (13)

  1. 四维多平面宽带成像系统，包括以下光学元件：
    非再入型二次扭曲(NRQD)光栅，即不存在再入型刻线的QD光栅，用于在多元件光学系统中生成各个衍射级对应的焦距和空间位置；
    成对的棱栅，用于在空间中基于波长对光路进行调控，从而校正非再入型二次扭曲(NRQD)光栅引起的宽带光色散；
    透镜系统，用于有效地修正非再入型二次扭曲(NRQD)光栅各衍射级对应的光学系统焦距，并且对光路进行调控以满足棱栅系统的设计需要，以及
    光检测器件。
  2. 在权利要求1提出的四维多平面宽带成像系统中，NRQD光栅通过多于一个NRQD圆弧版型的组合掩膜版图进行设计，从而使多个物平面(多于3个)的聚焦像合理分布在同一个像平面上。
  3. 在权利要求1或2提出的四维多平面宽带成像系统中，NRQD光栅是多级(数字型)或连续(模拟型)的剖面结构。
  4. 在权利要求1、2或3提出的四维多平面宽带成像系统中，多种类型的NRQD光栅被使用：周期分布的刻槽结构呈不同的透射率、不同的反射率、不同的光学厚度或不同的偏振敏感性。
  5. 在权利要求1提出的四维多平面宽带成像系统中，棱栅是体相位全息(volume phase holographic(VPH))棱栅。
  6. 在权利要求1提出的四维多平面宽带成像系统中，棱栅的设计可以由其光栅结构的刻线密度进行界定：当棱栅基底材料的折射率为1.4～1.5时，刻线密度范围是100到800线每毫米。
  7. 在权利要求1提出的四维多平面宽带成像系统中，棱栅的设计可以由其光栅结构的刻线密度进行界定：当棱栅基底材料的折射率为1.5～1.6时，刻线密度范围是100到900线每毫米。
  8. 在权利要求1提出的四维多平面宽带成像系统中，棱栅的设计可以由其光栅结构的刻线密度进行界定：当棱栅基底材料的折射率为1.6～1.7时，刻线密度范围是100到1200线每毫米。
  9. 在权利要求1提出的四维多平面宽带成像系统中，棱栅的设计可以由其光栅结构的刻线密度进行界定：当棱栅基底材料的折射率大于1.7时，刻线密度范围是100到1400线每毫米。
  10. 在权利要求1或5提出的四维多平面宽带成像系统中，组成棱栅结构的光栅和棱镜的折射率不相同。
  11. 在权利要求1、2或5提出的四维多平面宽带成像系统中，使用多于一对的棱栅，对多于一个的NRQD光栅所引起的宽带光色散进行校正。
  12. 权利要求1、2或5提出的四维多平面宽带成像系统，可以与多种模式的商用显微镜兼容，其中包括荧光、明/暗场、相衬、微分干涉差(DIC)和结构光照明。
  13. 权利要求1、2或5提出的四维多平面宽带成像系统，可以灵活地与多种现代技术相结合，其中包括显微术、天文光学、光数据存储、生物医学成像、波前分析以及虚拟/增强现实。
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