Knife-Edge Scanning Microscope Using an Ultra-Precision 3 ... · objective, aligned perpendicular to the top facet of the knife, images the sectioned tissue as it ... design, using

KESM Using a Diamond Turning Lathe

Bruce H. McCormick © Page 1 5/19/2005

Knife-Edge Scanning Microscope Using an Ultra-Precision 3-Axis CNC Diamond Turning Lathe

Bruce H. McCormick1, Marian Wiercigroch

2, and David Mayerich

1

1Texas A&M University

College Station, TX, 77843-3112, USA 2University 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 line-

scan 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 (~0.5m 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



tool for physical sectioning and an optical prism in the collimator of the microscope. A high-

sensitivity line-scan camera images the newly-cut thin section within 20m 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.

Granite

bridge

3D precision stage

Tank

Line-scan

Knife

/light

Knife

edge

Line-scan

imaging

Plastic

block

Knife / light

assembly

Cutting dire

ction

Brain

specimen

Objective

(40X Nikon Fluor)

Thin

sec

tion

Illumination fromlight source

Knife tip

Specimen block

Granite

bridge

3D precision stage

Tank

Line-scan

Knife

/light

Knife

edge

Line-scan

imaging

Plastic

block

Knife / light

assembly

Cutting dire

ction

Brain

specimen

Objective

(40X Nikon Fluor)

Thin

sec

tion

Illumination fromlight source

Knife tip

Specimen 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.



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]:



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.



Table 3.1. Lathe specifications

Specification

(December 2003) Nanotech

220 UPL

(Moore Nanotechnology Systems LLC)

(before modification)

System/Control Description

Configuration Three-axis CNC lathe, T-configuration

Control System Delta Tau PMAC-2 Turbo® @ 80MHz CNC motion controller.

(Remote diagnostics and modem included with base machine)

Base Natural granite, supported in a fabricated steel frame.

Protective stainless steel apron

Vibration Isolation Passive air isolation system

Machine Slides X- and Z-Axes

Type Preloaded hydrostatic oil bearing design

Travel 200mm (8”)

Feed rate (maximum) 1500mm/min

Drive System Brushless DC linear motor

Feedback type Laser holographic linear scale (mounted athermally)

Work-holding Spindle HeavyDuty Option

Manufacturer and Model Professional Instruments ISO 5.5 heavy-duty spindle

Type Fully constrained groove-compensated air bearing

Speed Range* 50 to 6000 rpm

Load Capacity (radial) 57Kg (125lbs) @ spindle nose

Axial Stiffness 140N/m (800,000 lbs/in) @ 8.3 bar (120 psi)

Radial Stiffness 87N/m (500,000 labs/in) @ 8.3 bar (120 psi)

Drive Frameless, brushless DC motor

Swing Capacity 220mm dia.(heavy duty spindle)

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



Table 3.2. Critical lathe specifications governing the KESM application

Specification Minimum KESM requirement Nanotech

220 UPL

(Moore Nanotechnology Systems

LLC)

Machine Slide (X- and Y-Axes)

Travel 100mm 200mm

Feed rate

(maximum)

15mm/min

(spiral turning at 5mm dia, not

positioning)

1500mm/min

Feedback

Resolution

50nm 34 picometer (0.034nm)

Straightness in

critical direction

Reproducibility, not straightness,

is required 0.2m over full travel

Work-holding Spindle (Heavy-Duty Option)

Speed Range

(maximum)

5 to 50 rpm

(tangential velocity of 13.2mm/s

at surface of 50mm and 5mm-

diametercylinders, respectively;

slower is preferable)

50 to 6000 rpm

Load Capacity 55kg (120 lbs)

Axial Stiffness (See Section 4 below) 140 N/m

(800,000 lbs/in) @ 8.3 bar (120

psi)

Radial Stiffness (See Section 4 below) 87 N/m (500,000 labs/in) @ 8.3

bar (120 psi)

Motion Accuracy Axial: ≤ 50nm

Radial: ≤ 50nm

Axial: ≤ 50nm

Radial: ≤ 50nm

Rotary C-axis Positioning Control

Speed Range

(maximum)

50 rpm 2,000 rpm

Resolution of the

encoder and its

electronics

0.42 arc-seconds = 50nm @

25mm radius (rads)

0.063 arc-seconds

Positioning accuracy Reproducibility, not absolute

positional accuracy, required 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 high-

sensitivity 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



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.



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 half-

cylinder 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 30-100m, 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 ijkr 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 ijk j ijk k ijk r r r , where 1 1 1, ,i ijk i jk ijk j ijk ij k ijk k ijk ijk ijk r r r r r r r r r ,

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



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 over-

sampling 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:

0 1[ , , , ]mD D DD of successively increasing diameters,

0 1 mD D D , defining the

successive start (end) of a new uniform cylindrical grid system; and

1 2[ , , , ]m Δθ of angular sampling increments used uniformly within each

concentric cylindrical grid system (i.e., -1 between diameters andi i iD D ).

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, / 2i iD , at the outer diameter of each concentric

cylinder, is uniform, here taken as 300nm, while at the inner surface of each cylinder is over-

sampled by less than 10% (Fig. 6b):

1( ) / 0.1i i i i iD D D .

For example, using cylindrical turning of a workpiece with 40mm outer diameter, mD , and inner

diameter, 0D , of 10mm, we derive [10,11.1, ,36,40] mmD and

[11.8,11.1, ,3.09] arc-secondsΔθ . 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.



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 0.3-0.5m), the integrated tape length can be extremely long. Its length

l is given by

/ 2

2 2

/ 2

24

outer

inner

D

outer inner

D

m ml rdr D D

r r

where r is the radial cutting step per revolution, and innerD ( outerD ) 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 factor1 . For example, a cylindrical workpiece of outer

diameter 40outerD mm , inner diameter 10innerD mm , cylindrical length 6.25mm, 10m for a

knife width of 0.625mm (the field of view of a 40X water-immersion objective), turned in steps

of 0.3r 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



/( )cameral LR y .

HerecameraLR 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

6 31 /(88 300 ) 1.2 10 14 . T km kH x nm x s da

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

voxel size is 300nm on edge, or 33 91 300 37 10 /mm nm x 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 320mm

3/810mm

3 = 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



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.



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 three-

axis 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



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 = 9.6m wide, and displaced from the knife edge by 20m 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 01min 3

0.01 0.5732

pitch rad rad

suffices.



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: 31min 3

0.33 10 1.11024

roll rad x rad arc minutes

.

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: min min2 1.6yaw roll 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 two-

axis stage with locking suffices to meet these tolerances.



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.



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 Z-

axis. 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.



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



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 Z-

axis 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, outerSD , 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



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 immuno-

histochemical 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



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/.

http://www.brainatlas.org/

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