Knife-edge Scanning Microscope Using An Ultra-precision 3

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KESM Using a Diamond Turning Lathe Knife-Edge Scanning Microscope Using an Ultra-Precision 3-Axis CNC Diamond Turning Lathe Bruce H. McCormick1, Marian Wiercigroch2, and David Mayerich1 1 Texas A&M University College Station, TX, 77843-3112, USA 2 University of Aberdeen, Aberdeen AB24 3UE, Scotland, UK Abstract A knife-edge scanning microscope (KESM) is comprised of three components: (1) a precision CNC (computer numerical controlled) nanomachining system, which uses a diamond knife to section a workpiece containing plastic-embedded tissue, such as small-animal brains; (2) an image capture system, for imaging newly cut tissue as it passes over the edge of the knife and is concurrently imaged in turn by a microscope objective, the microscope’s optical train, and a linescan camera; and (3) a cluster computer/storage area network, for data compression, segmentation, three-dimensional reconstruction, and visualization of the tissue and storage of both the image and reconstructed data. Here we focus on the nanomachining component, for which we propose using an ultra-precision three-axis CNC lathe designed for single-point diamond turning. These instruments, adapted as described below, promise to provide reliable, chatter-free sectioning over extended periods of time. Chatter-free operation is a critical prerequisite for three-dimensional imaging of embedded brain tissue at a cubic-voxel sampling at 300nm linear resolution. In this new design, a continuous section, or tape, of the freshly sectioned tissue is not only scanned as it passes over the diamond knife edge, but also can be spooled and stored for subsequent analysis. This tape can then be processed or edited selectively offline. For example, the tape can be counter-stained, then scanned selectively, and used to “paint” a 3D reconstruction of neurons and glial cells in the tissue -- merging these diverse types of information. Alternatively, having chosen a 6mm-wide diamond knife, one can extract a tape of consecutive ultra-thin sections (~0.5m thick) of entire mouse brains in transverse section and, as above, process and examine the tape offline. 1. Overview The original KESM [McCormick and Mayerich, 2004, 1] is capable of volume digitizing a complete mouse brain at 300nm sampling resolution within 100 hours. The brain specimen is embedded in a plastic block (~1cm3) and mounted atop a three-axis CNC ultra-precision positioning stage (Fig. 1a). A custom diamond knife, mounted rigidly to a massive granite bridge overhanging the three-axis stage, serially cuts consecutive thin sections from the block. Parallel light rays from an intense white light source are reflected by the bottom facet of the knife, providing a narrow stripe of intense bright field illumination of the tissue section. A microscope objective, aligned perpendicular to the top facet of the knife, images the sectioned tissue as it flows over the knife edge (Fig. 1b). Thus the diamond knife serves dual purposes: It is both the Bruce H. McCormick © Page 1 5/19/2005 KESM Using a Diamond Turning Lathe tool for physical sectioning and an optical prism in the collimator of the microscope. A highsensitivity line-scan camera images the newly-cut thin section within 20m of the knife-edge, prior to subsequent extraction of the tissue ribbon (Fig. 1c). The CNC nanomachining capabilities the instrument insures that the stack of images generated from successive sections is kept in registration. Finally, the digital video signal from the line-scan camera is passed through image acquisition boards and stored for subsequent analysis in a cluster computing system. The current cluster consists of 5 servers, each dual processor (1.1-1.5 GHz), 2GB of memory, with a combined 1 TB hard drive capacity. The servers are linked by a Cisco gigabit/s switch. ne se ct io Granite bridge Th in K ni fe n /li gh t ca -s n Li Illumination from Objective light source (40X Nikon Fluor) Tank tip Knife 3D precision stage Specimen block Line-scan imaging Knife / light assembly on cti ire d g ttin Cu Brain specimen Knife edge Plastic block Fig. 1. (a, left) Photo of the KESM showing line-scan/microscope assembly, knife/light assembly, granite bridge, and 3D precision stage. (b, center) Specimen undergoing sectioning by knife-edge scanner (thickness of section is not drawn to scale); (c, right) Close-up photo of the line-scan/ microscope assembly and the knife/light assembly. Mouse brain is embedded in plastic and molded to aluminum specimen ring. The prototype KESM has been validated on Golgi- and Nissl-stained mouse brain specimens, and is currently producing high-quality 2D and 3D data. Nissl staining targets the RNA in the cytoplasm of all neurons, as well as the DNA in all cell bodies. As a result, all cell bodies are visible, but the dendritic arbors and axons remain unstained. Thus, Nissl staining allows us to reconstruct the distribution of all cell bodies in the mouse brain, and in particular their distribution within the six layers of the cerebral cortex. 2(a) shows a coronal slice (10X magnification objective) of a Nissl-stained mouse brain containing the lateral ventricle, hippocampus and ventral part of the cortex. Different layers of the mouse brain are clearly visible as changes in cell density. Enlarged views in 2(b-c) show the lateral ventricle, running through the central area of the brain, and the hippocampus. With this objective (10X), the individual cells that outline the lateral ventricle can also be seen. Bruce H. McCormick © Page 2 5/19/2005 KESM Using a Diamond Turning Lathe Fig. 2. (a, top) KESM scan of Nissl-stained ribbon of a mouse brain using a 10X objective (coronal section). (b, left) Close-up of the lateral ventricle. (c, middle) Close-up of the hippocampus. (d, right) Staircase cutting of a specimen block into ribbons (section thickness not drawn to scale). A ribbon image is split into image stacks (denoted by circled numerals) and off-loaded to cluster nodes for processing and storage. In a CNC linear ultra-microtome, as used in the KESM prototype instrument, the impact of the diamond knife upon the workpiece block generates transient knife oscillations, which can induce chatter in the sectioning or cutting process. In an adequately stiff CNC precision linear planer (of which the prototype KESM ultramicrotome is a special case), these vibrations are both minimized and dampened quickly, avoiding chatter. Our experience with the KESM prototype suggests that for stable, reliable chatter-free sectioning over long machining times (~ 100 hrs), the diamond knife should cut tissue continuously with only very gradual changes of the cutting velocity. The cutting speed can be constrained to be uniform, or slowly varying, in two different machining systems: (1) a linear planer, using consecutive strokes to section a long block workpiece, or (2) a lathe, turning a cylindrical workpiece. In either machining system the tool/workpiece/stage or spindle compliance must be extremely stiff (ideally within tolerances of 40N/µm), so that knife oscillations are minimized and may be dampened quickly. For long cutting strokes with either machine, the tissues must fill the workpiece envelope efficiently, whether by potting together multiple small-animal brains or by potting one slab of a larger animal brain. We are continuing to explore optimal chatter-abating strategies for the linear planer design, using the KESM prototype. In this report we will examine lathe-based sectioning exclusively; in this design we anticipate that sectioning will be chatter-free. 2. T-configuration of the lathe A new class of CNC machine, the ultra-precision three-axis CNC lathe, designed for single-point diamond turning, has been introduced recently for manufacturing micro-photonics components [2]. These machines are used to manufacture freeform optical surfaces (e.g., aspherical lenses). Moore Nanotech Systems LLC and Precitech, Inc., both in Keene, NH, are the only two manufacturers in the United States of ultra-precision three-axis CNC lathes. As illustrative of these lathes, we consider the Nanotech 220UPL, made by Moore Nanotech Systems, LLC, Keene, NH, USA (Fig. 3). The two axes (X and Z) in this machine are mounted in a T-axis orientation (Fig. 4a). A heavy-duty air-bearing spindle (C-axis), with its integral angular encoder, is mounted above the X-axis machine slide (Fig. 4b.). The cylindrical workpiece is typically held by a vacuum chuck. These machines use the slow-slide servo method, whose main features have been described by Tohme and Lowe [3]: Bruce H. McCormick © Page 3 5/19/2005 KESM Using a Diamond Turning Lathe       Two linear machine slides (X-axis and Z-axis), both of which use hydrostatic bearings for improved damping and stiffness Position-controlled air-bearing spindle (C-axis). The Professional Instruments ISO 5.5 heavy-duty spindle is used in these instruments. Direct-drive motors on all axes Friction-free bearings on all axes High-resolution feedback systems High-bandwidth closed position loops Fig. 3. Nanotech 220 UPL ultra-precision diamond turning lathe: (a, left) Cabinet and control console; (b, right) with door open, showing lathe spindle [from Moore Nanotechnology Systems LLC website brochure]; (c) close-up of workpiece held by spindle chuck. Fig. 4. (a, left) Base and slides from a current state-of-the-art single point diamond turning machine Model shown is a Moore Nanotech 330UP [4]; (b, right) Slow slide servo, showing the mounting of the heavy-duty spindle on the X-slide. In the scanning application, the direction of spindle rotation is counter-clockwise, as viewed from the front, opposite that illustrated in the figure [3]. 3. Lathe specifications System specifications for the Nonotech 220 UPL ultra-precision three-axis CNC lathe are summarized in Table 3.1. The key parameters that affect three-dimensional microscopy are summarized in Table 3.2, which also summarizes the minimum machine specifications dictated by the needs of high-resolution three-dimensional microscopy at 300nm resolution. Bruce H. McCormick © Page 4 5/19/2005 KESM Using a Diamond Turning Lathe Table 3.1. Lathe specifications Specification (December 2003) System/Control Configuration Control System Nanotech 220 UPL (Moore Nanotechnology Systems LLC) (before modification) Description Vibration Isolation Three-axis CNC lathe, T-configuration Delta Tau PMAC-2 Turbo® @ 80MHz CNC motion controller. (Remote diagnostics and modem included with base machine) Natural granite, supported in a fabricated steel frame. Protective stainless steel apron Passive air isolation system Machine Slides Type Travel Feed rate (maximum) Drive System Feedback type X- and Z-Axes Preloaded hydrostatic oil bearing design 200mm (8”) 1500mm/min Brushless DC linear motor Laser holographic linear scale (mounted athermally) Work-holding Spindle Manufacturer and Model Type Speed Range* Load Capacity (radial) Axial Stiffness Radial Stiffness Drive Swing Capacity HeavyDuty Option Professional Instruments ISO 5.5 heavy-duty spindle Fully constrained groove-compensated air bearing 50 to 6000 rpm 57Kg (125lbs) @ spindle nose 140N/m (800,000 lbs/in) @ 8.3 bar (120 psi) 87N/m (500,000 labs/in) @ 8.3 bar (120 psi) Frameless, brushless DC motor 220mm dia.(heavy duty spindle) Base Machine Operating Requirements Power 230VAC, 3 phase, 50-60 Hz, 25 amp Air 8.4 bar (120 psi) / 8 CFM Floor Space 1.3m wide x 1.3m deep x 1.6m high. Floor-mounted control pendant not included. Weight Approx. 1,360 Kg Bruce H. McCormick © Page 5 5/19/2005 KESM Using a Diamond Turning Lathe Table 3.2. Critical lathe specifications governing the KESM application Specification Minimum KESM requirement Machine Slide (X- and Y-Axes) Travel 100mm Feed rate 15mm/min (maximum) (spiral turning at 5mm dia, not positioning) Feedback 50nm Resolution Straightness in Reproducibility, not straightness, critical direction is required Work-holding Spindle (Heavy-Duty Option) Speed Range 5 to 50 rpm (maximum) (tangential velocity of 13.2mm/s at surface of 50mm and 5mmdiametercylinders, respectively; slower is preferable) Load Capacity Axial Stiffness (See Section 4 below) Radial Stiffness (See Section 4 below) Motion Accuracy Axial: ≤ 50nm Radial: ≤ 50nm Rotary C-axis Positioning Control Speed Range 50 rpm (maximum) Resolution of the 0.42 arc-seconds = 50nm @ encoder and its 25mm radius (rads) electronics Positioning accuracy Reproducibility, not absolute positional accuracy, required Nanotech 220 UPL (Moore Nanotechnology Systems LLC) 200mm 1500mm/min 34 picometer (0.034nm) 0.2m over full travel 50 to 6000 rpm 55kg (120 lbs) 140 N/m (800,000 lbs/in) @ 8.3 bar (120 psi) 87 N/m (500,000 labs/in) @ 8.3 bar (120 psi) Axial: ≤ 50nm Radial: ≤ 50nm 2,000 rpm 0.063 arc-seconds 2 arc-seconds The encoding specifications of the spindle and rotary C-axis position encoding for the KESM application assume a maximum cylinder diameter of 50mm. Cylinders of larger diameter require excessive machining times (with presently available line-scan cameras), unless section thinness (300nm) and/or the section sampling interval (300nm) are compromised. Contemporary highsensitivity line-scan cameras are limited in line rate to either 44kHz (4096 pixels) or 88kHz (2048 pixels). Both cameras yield identical data rates of 180MB/s, with 1B/voxel. The critical Bruce H. McCormick © Page 6 5/19/2005 KESM Using a Diamond Turning Lathe specifications governing this KESM application (Table 3.2 above) will still suffice even when high-resolution line-scan cameras of higher data rates become available; the spindle merely rotates faster. The Nanotech 220 UPL machine has adequate resolution in its C-axis encoder to allow machining cylinders (e.g., brain slices) of 220mm diameter, the maximum swing capacity of the instrument, while maintaining a sampling resolution of 300nm. 4. The workpiece: packing brains into cylinders For illustration we will confine our discussion to packing mouse brains into the cylindrical work piece, though comparable methods can be used with rat brain and other mammalian brain tissue. We will assume the following nominal dimensions for the mouse brain: 12.5mm A-P, 9mm M-L, and 6mm D-V. However, the anterior portion of the mouse brain resembles a nose cone, with the olfactory lobes anterior at the apex of the cone. In the packing arrangements described below, we approximate the mouse brain by a truncated cone of elliptical cross-section. 4.1. Packing arrangements Mice brains can be packed into a cylinder in three symmetrical arrangements such that transverse (coronal) or sagittal sectioning is preserved: The brains can be (1) packed radially, like spokes of a wheel (Fig. 5); (2) packed axially; or (3) packed circumferentially into a cylinder. For each of these packing arrangements, either cylindrical turning or face turning can be used, for a total of 6 combinations of packing arrangement and sectioning axis. Fig. 5. Radial packing of mouse brains into a cylinder. Here the A-P axes of the brains are radial, like spokes of a wheel. These arrangements give the nearest equivalent to transverse (or coronal) sectioning for cylindrical turning. For face turning, these arrangements give sagittal sectioning. (Illustration by W. Koh). 4.2. Molds for potting brains into cylinders Radial assembly of mouse brains and concentric metal shank into a cylindrical workpiece For cylindrical turning, yielding quasi-transverse sectioning, the participating mice brains would be potted individually into truncated pie-shaped volumes, and then molded and assembled like a clock face within a shallow stiff cylinder. A metal shank (~10mm diameter), to fit the vacuum chuck of the lathe and to stiffen the work piece, would be potted at the center of the mold with the assembled mice molded concentrically about it. Bruce H. McCormick © Page 7 5/19/2005 KESM Using a Diamond Turning Lathe Clam-shell assembly of a cylindrical workpiece As an example, consider axial packing of mouse brains into a cylinder (Fig. 5 above). First we cast in plastic a bottom half-height cylinder with indentations for the mice brains. Then we insert the individual mice brains, and cover the mice brains with a symmetrically indented top halfcylinder lowered into a cylindrical mold; after which we insert the metal shank and harden the potted assembly. 5. Nanomachining using a cylindrical grid system 5.1. Nanomachining modes Apart from appropriate offsets, the lathe dictates that nanomachining is conducted in cylindrical coordinates: X (radial displacement), Z (axial displacement), and  (angular position of the spindle). Both cylindrical turning or face turning are conducted in this coordinate system, though the offsets will differ, reflecting the 90º rotation of the tool holder and possible fine tuning of adjustments between these two modes of machining. Three nanomachining programs We distinguish three nanomachining programs, applicable to both cylindrical and face turning: (1) band (ring) turning, where successive bands (rings) are machined at the width of the knife; (2) spiral turning, stepping one knife-width per revolution; and (3) bidirectional spiral turning, as in (2), but reversing direction of the spiral after each traversal of the workpiece. These are the only machining variants that ensure that the tissue ribbon is uniform in thickness. The third variant, bidirectional spiral cutting, will not be discussed further here, as any roll or yaw misalignment of the diamond knife (see Section 8.1 below) would leave a double helix of ridges induced by the knife ends on the workpiece surface. Trim cutting The workpiece, containing the packing of the brains into a cylinder, is first trim cut to avoid damage or dulling the diamond knife used in sectioning. The trim cutting can be best performed using a single point diamond knife, which can generate a surface finish of less than 100nm PV. Maximum depth of cut Band (ring) turning over many successive spindle revolutions is attractive in that (1) the tissue ribbon so generated is long, and (2) transient vibrations induced into the cutting process by the start of a new cut are minimized, hence minimizing the potential for inducing chatter. However, a deep trench can disturb the scanning process, as the edge of the diamond knife can rub against the wall of the trench, contributing a ragged edge to the tissue ribbon as it is cut or torn by the cutting process. The maximum depth of trench is not known, though experience with the prototype KESM suggests that this depth is 30-100m, or 100-333 revolutions at 300nm depth increment per revolution. Similar restrictions apply to spiral turning. Staircase cutting of the cylinder can be used to minimize trench depth (Fig. 2d). 5.2. Cylindrical grid systems The scanning process maps sampled voxel values to a cylindrical grid system, one voxel to each vertex in the grid system. The three-dimensional position rijk of each vertex (i, j, k ) in the grid system must be specified. Ideally we would like to keep the voxel dimensions uniformly 300nm, that is, i rijk   j rijk  k rijk , where i rijk  ri 1 jk  rijk ,  j rijk  rij 1k  rijk ,  k rijk  rijk 1  rijk , though strict adherence to these constraints is impossible for a cylindrical grid system. In our scanning the width of voxel is held constant, as the number of pixels along the knife edge is Bruce H. McCormick © Page 8 5/19/2005 KESM Using a Diamond Turning Lathe fixed by the sensor geometry (typically 2048 pixels per knife width). Likewise, the thickness of the tissue, X for cylindrical turning and Z for face turning, is maintained constant during the cutting process. Hence the only free variable is the angular position sampling interval,  . Piecewise cylindrical grid systems Maintaining a uniform cylindrical grid system throughout the workpiece entails significant oversampling during scanning of the workpiece, both lengthening the scanning duration and contributing additional computational cost during the three-dimensional reconstruction process. Accordingly, a piecewise-cylindrical grid system will be used for data acquisition. As illustrated in Fig. 6a, a piecewise-cylindrical grid system (consisting of concentric cylindrical grid systems) is defined by two vectors:  D  [ D0 , D1 ,, Dm ] of successively increasing diameters, D0  D1   Dm , defining the successive start (end) of a new uniform cylindrical grid system; and  Δθ  [1 , 2 ,, m ] of angular sampling increments used uniformly within each concentric cylindrical grid system (i.e., i between diameters Di-1 and Di ). How should the vector D be selected? A large value of m impedes reconstruction, while a small value of m insures significant over-sampling of the workpiece. One handle on this issue is to insist that the tissue ribbon sampling interval, Di i / 2 , at the outer diameter of each concentric cylinder, is uniform, here taken as 300nm, while at the inner surface of each cylinder is oversampled by less than 10% (Fig. 6b): ( Di i  Di 1 ) / Di i  0.1 . For example, using cylindrical turning of a workpiece with 40mm outer diameter, Dm , and inner diameter, D0 , of 10mm, we derive D  [10,11.1,,36, 40] mm and Δθ  [11.8,11.1,,3.09] arc-seconds . As the rotary C-axis positioning control has an encoder resolution of 0.063 are-seconds, these  tolerances are easily held. The same D and Δθ vectors can also be used with spiral turning. Bruce H. McCormick © Page 9 5/19/2005 KESM Using a Diamond Turning Lathe Fig. 6. Piecewise-cylindrical grid system consisting of concentric cylindrical grid systems and over-sampling constrain on successive concentric diameters of the piecewise-cylindrical grid system. 6. Scanning times and data storage requirements 6.1. Scanning times We will refer to the ribbon of tissue cut by the diamond knife as its tape. Because the tape is so extremely thin (typically 0.3-0.5m), the integrated tape length can be extremely long. Its length l is given by l m r Douter / 2  Dinner / 2 2 rdr  m  r D 4 2 outer 2  Dinner  where r is the radial cutting step per revolution, and Dinner ( Douter ) is the inner (outer) diameter of the cylindrical stock. Here the length of the cylindrical stock is measured by m, the integral number of knife widths along the machined stock (cylinder length). The tissue ribbon is both thickened and shortened by the cutting process. The compression factor  measures the shortening of the tissue ribbon per unit stoke length, as a result of the thickening of the ribbon by the cutting process by the inverse factor 1  . For example, a cylindrical workpiece of outer diameter Douter  40mm , inner diameter Dinner  10mm , cylindrical length 6.25mm, m  10 for a knife width of 0.625mm (the field of view of a 40X water-immersion objective), turned in steps of r  0.3m per rotation, and assuming a compression factor   0.8 , yields an integrated tape length (assuming no breaks) of 31km. The scanning time  can be computed from the integrated tape length l (after compression bu the cutting process) by the formula Bruce H. McCormick © Page 10 5/19/2005 KESM Using a Diamond Turning Lathe   l /( LRcamera  y) . Here LRcamera is the line rate of the line scan camera and y is the incremental sampling distance along the circumference of the cylinder. For example, consider a cylinder of 40mm diameter and 6.25mm axial length. In this example, the time T to machine the brain-embedded portion of the mice brains is given by T  31km /(88kH x 300nm)  1.2 x 106 s  14da. Using the 4096-pixel camera, but with the Olympus 20X objective, we would achieve an identical time. Alternatively we can realize shorter times by packing fewer mouse brains into smaller cylinders. 6.2. Data storage requirements Let us assume an average volume of 320mm2 for the plastic-embedded mouse brain. Our cubic 3 voxel size is 300nm on edge, or 1mm3  300nm   37 x109 voxels / cubic mm . Accordingly the number of voxels per mouse brain (on average), after suppressing unwanted image data from the tissue-free embedding plastic, is given by: Voxels/mouse brain = 11.9 Teravoxels; or, at one byte/voxel, 11.9 TB. Consider the mouse brain embedded in a block 15mm (A-P) x 9mm (M-L) x 6mm (D-V), for a total of 810mm3. In this exercise only 320mm3/810mm3 = 38% of the block is brain tissue; the remaining portion of the block is clear plastic. However it is relatively straightforward to strip off the scanned data generated by the clear embedding plastic, so while the embedding plastic figures prominently in computing scanning time, it plays virtually no role in computing data storage requirements. 7. Chatter generation and its avoidance From the machining point of view, the prototype KESM can be classified as a small-scale planing machine, which uses a single point cutting tool. Preliminary cutting tests have shown that the major obstacle to obtain robust data is generation of self-excited oscillations (mechanical chatter) during the cutting process, when sequential layers are being removed from the specimen. The exact explanation of this phenomenon has yet to be further studied, but it is clear now, that the regeneration effect and free oscillations caused by the sudden nature of the tool engagement into the specimen, play paramount roles. To grasp a sufficient understanding of the main problems involved, a brief discussion of the cutting mechanics based on [5] is given below. Generally a cutting process results in dynamic interactions between the machine tool, the cutting tool, and the workpiece, and therefore its mathematical model should take into account its kinematics, dynamics, geometry of the chip formation, and the mechanical and the thermodynamic properties of both the workpiece and the cutting tool. The mechanics of chip formation is recognized even more now than before as a key issue in a further development of machining technologies. The physical complexity in describing and analyzing a cutting process comes from the interwoven phenomena such as elasto-plastic deformations in the cutting zones, variable friction force acting on the cutting tool, heat generation and transfer, adhesion and diffusion, and material phase transformations, to name but a few. A schematic showing three main deformation zones and listing all important phenomena influencing the mechanics in the cutting process is given in Figure 8(a). Understanding the relationships between these Bruce H. McCormick © Page 11 5/19/2005 KESM Using a Diamond Turning Lathe phenomena is critical for an adequate modeling of a specific cutting process. It is important to note that most of the phenomena (e.g. friction) are strongly nonlinear and interdependent. First studies on chatter date back to 1907, when the first significant work was published on metal cutting mechanics [6], however, the real breakthrough was achieve in mid-1940s when the first physical model of the chip formation was established [7]. Figure 8(b) shows this model, which is called the orthogonal cutting model. Here, the uncut layer (initial depth of cut), h0, of the workpiece in the form of a continuous chip is seen to be removed along the shear plane. Subsequently, the chip of thickness h flows along the face of the tool, where it encounters friction on the tool-chip interface. The width of the chip remains unchanged, hence the stress field can be considered in two dimensions. The cutting force, Fc, and the thrust force, Ft, determine the vector R, which represents the resistance of the material being cut acting on the cutting tool. In stationary cutting conditions, this force is compensated by the resultant force generated in the shear stress field, and the friction on the rake surface. Fig. 7. (a) Three main deformation zones with all important physical phenomena influencing the cutting process; (b) physical model of orthogonal cutting developed by Merchant [7]. The chip formation mechanism is controlled by instant cutting parameters such as feed, velocity and depth of cut. Any variation in these parameters almost instantaneously changes the force loading on the cutting tool and consequently the chip and the workpiece surface geometry. If these alterations of the chip geometry (e.g., thickness) start to be periodic, the appearance of chatter is imminent. The first attempts to describe chatter were made by Arnold [8]; however, a convincing mathematical model and analysis were given by Tobias and Fishwick [9]. In general, chatter can be classified as primary and secondary. Another classification distinguishes frictional, regenerative, mode-coupling, and thermo-mechanical chatter. As can be seen from Section 1, some good data has been obtained on the original KESM [1] as slight alterations of the cutting velocity for each pass have partially suppressed the chatter, however, not to extend that KESM can be used reliably over long time intervals without further modification. The main modification is to produce a chatter-free operation by increasing the stiffness and producing a continuous chip. This can be achieved by employing an ultra-precision three-axis CNC lathe designed for single point diamond turning, where the angular and axial motion accuracy is around 8nm and the machine has subnanometer slide feedback resolution. Details of this new design are given in the sections to follow. Bruce H. McCormick © Page 12 5/19/2005 KESM Using a Diamond Turning Lathe 8. Holders for the diamond knife and the microscope objective The design for the tool holder for the diamond knife (Section 8.1) and the microscope objective (Section 8.2) are described below in the context of cylindrical turning. However, when these holders are rotated as a unit 90º about the Y-axis, they are positioned correctly for face turning of the workpiece. 8.1. Diamond knife tool holder The standard tool holder, with modifications as described below, will be fitted to the diamond knife (Fig. 8.) The tool holder allows vertical (Y-axis) adjustment of knife, while providing an extremely stiff mounting (40 N/m). The diamond knife, considered as a boat, has 6 degrees of freedom (dof), three positional and three rotational, relative to linear array sensor back-projected onto the object plane of the microscope objective. In the Cartesian frame defined by the threeaxis lathe, the position of the knife is provided by the two linear axes (X and Z) of the machine, and the vertical adjustment (Y) of the tool holder. These motions suffice for single-point machining with a pointed diamond tool. Fig.8. Standard tool holder used for single point diamond nanomachining (Moore Nanotechnology Systems LLC). To accommodate the finite width, thickness, and extent of the knife, three rotational adjustments for cylindrical turning are required, ideally: yaw (about the X-axis, in machine-based coordinates); pitch (about the Z-axis); and roll (about the Y-axis), as illustrated in Fig. 9. In this machine-based Cartesian coordinate frame, the ideal knife orientation has 0º yaw, an approximately -2º pitch (the clearance angle between the bottom facet of the diamond knife and the plane of the workpiece), and a 0º roll. The tolerances required for these orientation adjustments vary considerably. We illustrate by assuming three-dimensional sampling at 300nm resolution, and a knife width of 0.625mm (2048 pixels), which accommodates the field-of-view Bruce H. McCormick © Page 13 5/19/2005 KESM Using a Diamond Turning Lathe of the Nikon 40X water-immersion objective. Furthermore, we will assume that the objective/line-scan camera has been aligned properly so that the knife edge is centered and fills the objective’s field of view. We image a narrow band of tissue parallel to the knife edge, 300nm x 32 lines = 9.6m wide, and displaced from the knife edge by 20m or less (Fig. 10a). Fig.9. Diamond knife alignment, showing (a) yaw and (b) pitch rotational adjustments. Fig.10. Yaw correction: (a) at the camera, showing the sensor array of the line-scan camera back-projected onto the newly-cut section adjacent to the knife edge. Pitch is the least critical of these orientation adjustments. The requirement here is to keep all 32 TDI registers on focus, or within (say) one-third of sampling increment over displacement divided by the back-projected band of 32 registers. Here   300nm is the sampling increment.  Accordingly, an adjustment tolerance of pitchmin  13 rad  0.01rad  0.570 suffices. 32 Bruce H. McCormick © Page 14 5/19/2005 KESM Using a Diamond Turning Lathe Roll must be adjusted so that the knife edge lies horizontal and flat against the workpiece. Here we would like the radial increment between the two ends of the knife to be within one-third of  the sampling increment: rollmin  13 rad  0.33x103 rad  1.1 arc minutes . 1024 Yaw misalignment induces a rotation of the band across the top facet of the diamond knife thereby displacing one end of the sampled tape or band; that is, it would forces the tape outside of the object plane of the objective field of view. As the object plane is at approximately 45º to the X-axis, the minimum yaw adjustment is therefore: yawmin  2 rollmin  1.6 arc minutes . In the knife-edge scanning microscope, pitch is predetermined by the design of the knife bracket and by the desired clearance angle of the knife, which is typically 2º. Roll is corrected by incrementally rotating the tool holder. Yaw is corrected by deflecting one of the prongs of a “tuning fork” adjustment, using a sliding-block arrangement for micro-calibration (Fig. 10b). 8.2. Microscope objective holder The microscope objective is screwed into the objective holder, a U-shaped vertically aligned structure surrounding the tool holder and, like the tool holder, the objective is also mounted on the Z-slide (Fig. 11). The objective is positioned above the knife so that its optical train is not blocked by the diamond knife tool holder. The objective and the knife use separate mounts to minimize vibration coupling between these two components. As the objective holder is subjected to little vibration, its stiffness is far less critical than for the tool holder. The mounting for the microscope objective is best visualized in a local Cartesian frame: X’. Y’, and Z’, where the machine’s Cartesian frame is rotated 45º counterclockwise about the Z-axis, and thus the Y’-lies along the optical axis of the objective (Fig. 11), while the X’-Y’ plane parallels the top facet of the diamond knife. Once the knife has been adjusted, the objective must be focused. The objective’s field of view is centered over the knife edge by displacement of a small two-axis (X’ and Y’) stage in the X’-Y’ plane (Fig. 11) that moves parallel to the top facet of the knife. All these adjustments can be made very small. A two-axis micrometer-driven twoaxis stage with locking suffices to meet these tolerances. Bruce H. McCormick © Page 15 5/19/2005 KESM Using a Diamond Turning Lathe Fig. 11. Schematic of microscope objective holder and X’, Y’, Z’ Cartesian fame for describing microscope positioning. 9. Cutting under water The newly cut tissue is imaged under water to improve optical resolution. Axons in the mouse brain average 300nm in diameter [Braitenberg and Shutz, 1998], illustrating the importance of enhancing optical resolution. Hence water-immersion objectives must be used exclusively. The working distance of the water-immersion Nikon 40X objective is 2mm. Rays leaving the objective’s field of view (0.625mm dia.) in the image plane and entering the front face of objective must pass only through water; this constraint defines a minimum truncated cone that must always be water-filled. A 2mm-high truncated cone in front of the objective is filled with water by drip flow. Excess water is captured in a spill pan beneath the work piece. Further benefits of using a water trap and pump include: (1) preventing the newly cut ribbon of tissue from buckling, and (2) providing for smooth extraction of this ribbon prior to storing the tissue. In the design illustrated in Fig. 12, the water trap is established only after the newly cut tissue is sharply in focus. At this point the water trap has (1) a wide entrance channel opening to its upper, anterior chamber; and (2) an exit channel directly over the top facet of the knife in the lower, posterior chamber. A hydrostatic (water) bearing is established between the tissue ribbon and the channel in the water trap over the ribbon. To achieve a stable rate of flow, water is pumped under pressure into the exit channel through small orifices in the underside of the upper water trap and evacuated by forcibly pumping the lower chamber. Water flow flattens the ribbon and pulls it along through the channel at approximately 26mm/s, which defines the uniform maximum scanning data rate. Bruce H. McCormick © Page 16 5/19/2005 KESM Using a Diamond Turning Lathe Fig. 12. Ribbon extraction module 10. Optical train/camera mounting An identical mounting for the knife and microscope objective, apart from a 90º rotation about the Y-axis, can be used both cylindrical and face turning. However the coupling between the objective and the remaining optical train of the microscope/camera is not identical for these two cases. We will discuss these two cases separately. Nonetheless, apart from a change of prism, the optical train of the microscope/camera can be mounted on a manual stage, parallel to the Z-axis slide, which in turn is rigidly mounted to the granite base. This arrangement allows both cylindrical or face turning, upon appropriate translation of the Z-axis stage. Cylindrical turning Immediately after leaving the objective, the optical train is bent 90º to become parallel to the Zaxis. Fig. 13a shows the optical coupling between the objective, with its attached 90º prism, and the remaining optical train of the microscope, which are linked by an extensible baffle. The 10mm or so Z-axis displacements made while turning tissue can be accommodated by the infinity optics of the objective. Face turning The tool holder and the objective holder can be jointly rotated 90º about the Y-axis, so the alignment procedure for these two is the same. Immediately after leaving the objective, the optical train is bent 45º in the Y-Z plane to be again parallel to the Z-axis. Fig. 13b. shows the coupling by an extensible baffle between the objective, with its attached 45º prism, and the remaining optical train of the microscope. Mounting the remaining optical train The microscope optical train (field and relay lenses, etc.) are mounted rigidly to a granite block adjacent to the Z-slide. A plan view of the stainless steel apron covering the granite base is shown in Fig. 13c for the Moore Nanotech 220 UPL. The position of the optical train/camera support is indicated. This mounting is independent whether cylindrical or face-plate machining is used. Bruce H. McCormick © Page 17 5/19/2005 KESM Using a Diamond Turning Lathe Fig. 13. Folded optics of the objective and residual optical train (including camera). (a, left) For cylindrical nanomachining: coupling via a 90º prism through an extensible baffle; (b, right) face-plate nanomachining: coupling via a 45º prism through an extensible baffle 11. Epi-illumination Bright-field illumination of the sectioned tissue is provided by two alternative types of light source, as described below. The EXFO X-Cite 120 light source, using a metal halide lamp, has a typical life of 1500hrs. A water-filled light pipe with integral mounted illumination optics is used to transport the intense white light from the light source to the back face of the diamond knife, where it is reflected by the lower facet of the diamond knife. This light source has been used successfully in the original KESM. Nokia Superluminescent LEDs in multiple colors provide the for excitation illumination for fluorescence microscopy. These narrow-band light sources avoid the unwanted diffraction bands seen along the knife edge when laser illumination is used. These superluminescent LEDs are more energy, in that the excitation illumination is narrow band that no excitation filter need be used. 12. Generating high-resolution brain atlases A particularly attractive use of the ultra-precision three-axis CNC diamond turning lathe is for the generation of three-dimensional brain atlases. Such atlases can be specialized to show gene expression, in similar manner to the Allen Institute Atlas [10.], but at finer resolution. To illustrate, consider a cylinder with radially symmetric spacing of mice brains (Fig. 5). We now use a diamond knife of width (6mm) equal to the full length of the machined portion of the cylinder. As above, we section the work-piece at 300nm thickness. Our integrated tape length, l , however, is now a mere 3.9 kilometers (as m = 1, not 10, as in Section 6.1). Examining the tape offline, one sees quasi-transverse sections, observed serially from posterior to anterior, cycling repeatedly through the 11 mice brains embedded in the work-piece cylinder (Fig. 14a). Currently, a tape spool of 3.9km length is not a convenient storage medium for most types of editing, particularly as a spool prevents subsequent selective counter-staining. An alternative format for storage lays down consecutive strips of tape on glass plates, 250mm x 250mm (Fig. 14b). For the 6mm tape width, 40 bands of tape can be laid down on each plate, for an integrated Bruce H. McCormick © Page 18 5/19/2005 KESM Using a Diamond Turning Lathe tape length of 40 x 250mm = 10m per glass plate. With this technique an entire 3.9km tape can be transferred to 390 glass plates, which in turn can then be selectively cross-stained and examined at any time. These glass plates can be stored in a robotic-actuated storage vault, with 400 slots (one per glass plate) at 5mm spacing. The vault would require 2m of working height (or length). Fig. 14. Storage formats for high-resolution brain atlases. (a, left) Tape format showing transverse mice brain sections; (b, right) archival glass plate format, each plate holding 40 tape widths of 250mm length. 13. Section extraction, collection, and archival storage Extraction of the section tape, even for ribbon widths as small as 0.625mm, is relatively simple, at least in principle. As described above, the holder for the knife/objective is mounted on the Zaxis slide. The tape-extraction mechanism and associated take-up reel for tape collection are also mounted on the Z-axis slide, adjacent to the knife/objective holder (Fig. 15). The same section extraction and collection arrangement can be used without change for either cylindrical or face cutting. Two difficulties complicate the design, however. (1) Successive sections, although generated in long ribbons (typically ~100 circumferences of the cylindrical workpiece for cylindrical turning), eventually must terminate. Accordingly, the extraction process must be self-feeding, restarting anew as the leader of each newly cut section appears. (2) The tool holder of the lathe (Fig. 8), though built for exceptional rigidity and stiffness, blocks the natural linear trajectory of the ribbon. Here a bend in the ribbon trajectory, though undesirable, is inevitable. The key issue is to insure that the successive long ribbons of sectioned tissue are preserved in order, without twisting, bunching, or dimensional distortion. Our constant (100%) line-sampling procedure insures that tape is produced at a constant velocity. Accordingly, the tape feed must advance the tape at approximately 88kHz x 300nm = 26.4mm/s. What size spool suffices if all the collected tape of tissue is wound on one spool? Consider the radial packing of mouse brains illustrated in Fig. 5. This cylinder generates a 31km tape from the sectioned tissue (that is, 39 km prior to compression by the cutting process). Assuming that the inner diameter of the take-up spool is 25mm, we calculate from the formula of Section 6.1 that the spooled ribbon reaches a diameter of 125mm. Even though the cutting process both thickens the tape and shortens it, the outer spool diameter, SDouter , as computed above, must remain invariant, in view of the volume incompressibility of the embedding plastic. Figure 15. Mounting of the tape extraction mechanism and associated take-up reel on the Z-slide Bruce H. McCormick © Page 19 5/19/2005 KESM Using a Diamond Turning Lathe 14. Counter-staining, secondary scanning, and painting the 3D reconstructed tissue Collecting and saving the actual tissue that has been sectioned and scanned offers several unique advantages. Data acquired from the knife-edge scanning (in the primary scanning) can be used to create a 3D reconstruction of the tissue microstructure. The collected sections can then be selectively counter-stained offline, especially with advanced techniques such as immunohistochemical and protein gene-expression stains. The ribbon can then be given a selective secondary scanning. The secondary data sets, morphed appropriately to match the dataset of the primary scan, would provide additional information not found in the initially stained tissue. This additional information can then be “painted” onto the reconstructed neurons, which allows us to identify, for example, gene expression on a neuron-by-neuron basis. Also, as the section ribbon is so exceedingly thin (300nm), neurons in a reconstructed region are built from a multi-layer (multi-deck sandwich) of diversely counter-stained tissue sections, painting multi-colored rings around each neurite. It is this additional information which is “painted” on the neurons and glial cells of the reconstructed tissue. 15. Conclusion and the foreseeable future Here we have established that an ultra-precision 3-axis CNC diamond turning lathe can provide (1) a tractable and attractive nanomachining system for a second-generation knife-edge scanning microscope (KESM). The other two KESM components--that is, (2) the image capture system and (3) the cluster computer/storage area network--continue design concepts already proven in the prototype KESM. The current limiting challenge for knife-edge scanning is to ensure that sectioning of the embedded tissue is always chatter-free. In this second-generation design of our KESM instrument, we have specified exceptional and exacting precautions to ensure chatter-free operation. The stability and stiffness of the cutting process in the ultra-precision 3-axis CNC diamond turning lathe is unsurpassed by any other machining system that can section tissue at comparable rates. We have presented designs that scan whole mouse brains at the rate of approximately one brain per day, while maintaining a sampling resolution of 300nm. At present no alternative technology matches this rate of data acquisition. Furthermore, the ultra-precision 3-axis CNC diamond turning lathe should provide a stable platform for acquisition of mammalian brain volume data sets for many years to come. The data-rate limitation on scanning brain microstructure is determined currently by the line rate of available high-sensitivity line-scan cameras. When faster cameras become available, the spindle speeds of the lathe can be increased accordingly. No further accommodation, aside from additional epi-illumination (which is already abundant), is required. In this new design the diamond knife and the microscope objective are co-mounted in a combined joint tool/objective holder, which can then be rotated 90º to accommodate either cylindrical or face turning and concurrent scanning. The tool/objective holder is built upon the tool holder routinely used in the Moore Nanotech 220 UPL. Learning from experience with the prototype KESM, we have in this new design assigned the burden for relative alignment of the Bruce H. McCormick © Page 20 5/19/2005 KESM Using a Diamond Turning Lathe knife and objective predominantly to the adjustments of the microscope objective. The six degrees of freedom (6 dof) in the alignment between the knife and the objective are accommodated more effectively by the optical objective than by the knife, as the knife must be clamped rigidly with stiffness comparable to that of the lathe, typically to tolerances of 40N/µm, to avoid the onset of chatter. The objective mounting is not faced with providing comparable stiffness. The future will undoubtedly bring line-scan cameras of higher data-rate (e.g., CMOS area-scan cameras are currently available), more use of multi-spectral imaging in bright-field microscopy, improved objective optics, and significant new ways to stain tissue en bloc, including the use of transgenic animals with GFP and other protein stains, and lipophilic membrane stains (e.g., osmium tetroxide) that stain 100% of all neurons. Concurrently, cluster computers and storage area networks are continuing their relentless drive toward higher performance. A KESM, based upon nanomachining using the proven ultra-precision 3-axis CNC diamond turning lathe, can meet these challenges and provide a new generation of three-dimensional light microscope. This second-generation KESM potentially can generate 15 terabytes of data per day, a virtual fire hose of brain microstructure data. Perhaps even more significant in the long run, the KESM design presented here should allow us to scan, at a neuronal level of detail, not only the rat but also even larger mammalian brains, including primate and human brain slices. References [1] B.H. McCormick and D.M. Mayerich, “Three-dimension imaging using knife-edge scanning microscopy,” Microsc. Microanal,10 (Suppl. 2), pp.1466-1467, 2004. [2] M. A. Davies, C. Evans, S. R. Patterson, R. Vohra, and B. C. Bergner, “Lithographic and micromachining techniques for optical component fabrication II,” edited by E.-B. Kiev, H. P.Herzig, Proc. of SPIE, Vol. 5183, 2003. [3] Y.E. Tohme and J.A. Lowe, “Machining of freeform optical surfaces by slow slide servo method,” Moore Nanotechnology Systems LLC, PPT presentation, 2004. [4]. G. Chapman, “Ultra-precision machining systems: an enabling technology for perfect surfaces,” Moore Nanotechnology Systems LLC [5] M. Wiercigroch and E. Budak, “Sources of nonlinearities, chatter generation and suppression in metal cutting,” Phil. Trans. R. Soc. Lond. A, vol. 359, pp. 663-693, 2001. [6] F.M. Taylor, “On the art of cutting metals”, Trans ASME, vol. 28, pp. 31-248, 1907. [7] E.M. Merchant, “Mechanics of the metal cutting process. I. Orthogonal cutting and a type 2 chip,” J. Appl. Phys., vol. 16, pp. 267-275, 1945. [8] R.N. Arnold, “Mechanism of tool vibration in cutting steel”, Proc. Mech. Engrs, vol. 154, pp. 261-276, 1946. [9] S.A. Tobias and W. Fishwick, “The chatter of lathe tools under orthogonal cutting conditions,” Trans. ASME, pp. 1079-1088, 1958. [10] Allen Brain Atlas, http://www.brainatlas.org/. Bruce H. McCormick © Page 21 5/19/2005