Manufacturing Technologies Toward Extreme Precision

International Journal of Extreme Manufacturing
TOPICAL REVIEW • OPEN ACCESS

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| IMMT International Journal of Extreme Manufacturing
Int. J. Extrem. Manuf. 1 (2019) 022001 (22pp) https://doi.org/10.1088/2631-7990/ab1ff1
Topical Review
Manufacturing technologies toward extreme

precision
Zhiyu Zhang1,2, Jiwang Yan2 and Tsunemoto Kuriyagawa3
1
Key Laboratory of Optical System Advanced Manufacturing Technology, Changchun Institute of Optics,
Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, People’s Republic of
China
2
Department of Mechanical Engineering, Keio University, Yokohama 223-8522, Japan
3
Department of Mechanical Systems Engineering, Tohoku University, Sendai 980-8575, Japan
E-mail: yan@mech.keio.ac.jp
Received 5 April 2019, revised 6 May 2019

Accepted for publication 8 May 2019
Published 18 June 2019
Abstract
Precision is one of the most important aspects of manufacturing. High precision creates high
quality, high performance, exchangeability, reliability, and added value for industrial products.
Over the past decades, remarkable advances have been achieved in the area of high-precision
manufacturing technologies, where the form accuracy approaches the nanometer level and
surface roughness the atomic level. These extremely high precision manufacturing technologies
enable the development of high-performance optical elements, semiconductor substrates,
biomedical parts, and so on, thereby enhancing the ability of human beings to explore the macro-
and microscopic mysteries and potentialities of the natural world. In this paper, state-of-the-art
high-precision material removal manufacturing technologies, especially ultraprecision cutting,
grinding, deterministic form correction polishing, and supersmooth polishing, are reviewed and
compared with insights into their principles, methodologies, and applications. The key issues in
extreme precision manufacturing that should be considered for future R&D are discussed.
Keywords: ultraprecision cutting, grinding, polishing, supersmooth surface, ultraprecision
measurement, extreme precision
(Some figures may appear in colour only in the online journal)
1. Introduction Subtractive manufacturing is undoubtedly the most

widely used process, in which a workpiece is shaped by
The term ‘manufacturing technologies’ refers to the processes removing material away from a bulk of material. The process
by which raw materials are transformed into final products. of removing unnecessary material from a workpiece is termed
The study of manufacturing technologies has been a part of machining. Mechanical machining is further divided into
human activity since ancient times. Three kinds of material cutting methods, such as turning, milling, drilling, etc, and
processing technologies have been developed in response abrasive machining methods, such as grinding, lapping, and
to manufacturing needs: (1) subtractive manufacturing, polishing.
(2) additive manufacturing, and (3) material forming. Additive manufacturing is a process by which a work-
piece is constructed by depositing material in layers such that
it becomes a predesigned shape. Three-dimensional (3D)
Original content from this work may be used under the terms printing is one of the common processes of additive manu-
of the Creative Commons Attribution 3.0 licence. Any
further distribution of this work must maintain attribution to the author(s) and facturing. Additive manufacturing is suitable for small-sized
the title of the work, journal citation and DOI. components containing enclosed features that cannot be
© 2019 The Author(s). Published by IOP Publishing Ltd on behalf of the IMMT
2631-8644/19/022001+22$33.00 1
Int. J. Extrem. Manuf. 1 (2019) 022001 Topical Review
Figure 1. Taniguchi chart to predict the development of machining accuracy.
machined by subtractive manufacturing. Material forming realize extreme ultraviolet (EUV) exposure, the total thick-
generally refers to methods that change the shape or internal/ ness variation of a 12 inch bare silicon (Si) wafer is required
external structure of the workpiece without changing the to be less than 200 nm; and the middle spatial frequency
material volume. These processes include casting, forging, roughness is required to be less than 0.1 nm [3]. In addition,
press/injection molding, stamping, and imprinting. Each of inertial confinement fusion (ICF) is a fusion energy research
the above-mentioned processes has its own advantages and project that attempts to initiate nuclear fusion reactions by
limitations. Therefore, manufacturing technology encom- heating and compressing a fuel target, typically in the form of
passes a very vast area and provides the tools that enable a pellet that contains a mixture of deuterium and tritium. To
fabrication of a broad range of products. compress and heat the fuel, energy is delivered to the outer
In this paper, we focus on subtractive manufacturing, i.e. layer of the target using high-energy laser beams. Each ICF
machining processes, because a huge number of diverse system requires more than 7000 pieces of high-precision,
engineering materials (metals, semiconductors, optical glas-
large optical components [4].
ses, ceramics, composite materials, and polymers) can be
In 1983, Taniguchi proposed a chart to predict the
machined; and a large variety of functional surfaces (with
development of achievable machining accuracy over time [5].
optical, mechanical, microfluidic, bionic, or electronic func-
The Taniguchi chart is considered to be the Moore’s law of
tions) can be achieved. Another reason for the focus on
the machining field. According to the chart, shown in figure 1,
subtractive manufacturing is that this method can achieve
extremely high precision which cannot be achieved by other normal machining by the year 2020 comes in at better than
methods. 200 nm accuracy. Precision machining comes in currently at
In recent years, various high-performance optics, optoe- about 5 nm capability. It is worth noting that ultraprecision
lectronics, and semiconductor products have emerged which machining (extremely accurate machining) can produce an
require manufacturing technologies of higher and higher accuracy of better than 0.3 nm, reaching atomic or molecular
precision. For example, the surface roughness of a substrate scale precision. The way to achieve this precision is either
used in a ring laser gyroscope is required to reach a roughness through the subtractive process (atom/molecule removal or
average (Ra) of <0.5 nm and a flatness of N<30 nm. The ion beam machining) or the additive process (atom/molecule
surface roughness of mirrors in deep ultraviolet (DUV) lasers deposition). Taniguchi’s predictions are very close to the
and ultrahigh power laser systems is required to reach an state-of-the-art (as of the year 2019) process and precision
Ra<0.2 nm and a flatness of N<60 nm [1, 2]. In order to levels, especially for ultraprecision machining accuracy.
2
Ultraprecision machining is the final processing method ultraviolet optics. In such a case, corrective polishing is
for obtaining high form accuracy and low surface roughness. needed. Polishing has been traditionally used for reducing the
In recent decades, ultraprecision machining has been surface roughness of a workpiece or changing the dimen-
demonstrated to be a deterministic method for achieving high sional or geometric accuracy of a workpiece by manual
accuracy and cost-effectiveness for the generation of func- control of pad pressure or dwelling time. However, in the
tional surfaces. At present, through multiaxis machining, field of ultraprecision machining, the polishing pressure and
optical or near-optical surface finish and micro/nanos- dwelling time can now be precisely controlled on a highly
tructures can be directly created in freeform surfaces. Appli- local zone on a workpiece surface, thus corrective polishing is
cations of ultraprecision machining have ranged from optics a common method used to achieve nanometric form accuracy.
to illumination, astronomy, automobiles, biomedical pro- A variety of corrective polishing techniques were
ducts, and so on. Ultraprecision machining technology plays developed to improve the surface form accuracy, such as
an important role in the construction of a nation’s industry computer-controlled optical surfacing (CCOS) [8], stressed-
and economy. lap polishing [9], bonnet polishing [10], and magnetorheo-
logical finishing (MRF) [11]. These methods use different
polishing tools and abrasive particles to improve the work-
2. Typical ultraprecision machining processes piece surface finish by means of mechanical, electro-
magnetical, chemical, or electrochemical actions. Another
At present, ultraprecision machining technologies can be nonmechanical method for ultraprecision form correction is
roughly divided into four categories: (1) ultraprecision cut- ion beam figuring (IBF) [12]. As will be discussed later in this
ting, (2) ultraprecision grinding, (3) corrective polishing, and paper, deterministic form correction has been widely used in
(4) supersmooth polishing. This section will provide a brief processing the optical elements with extreme precision, such
summary of the fundamentals of these technologies. as a large-aperture telescope and DUV/EUV lithography
optics.
2.1. Ultraprecision cutting
Ultraprecision cutting uses ultraprecision lathes and single-

2.4. Supersmooth polishing
crystal diamond tools to machine a workpiece. As the tool-
workpiece interface is limited to a very small region As for ultraprecision optical elements, not only is high-
approaching a point, ultraprecision cutting is also referred to precision form accuracy required, but a supersmooth surface is
as single-point diamond turning (SPDT). The diamond tool indispensable. Some supersmooth polishing techniques have
edge can be sharpened to the nanometer scale, which enables been developed for the purpose of reducing surface roughness,
removal of an extremely thin layer of material and finally such as bowl-feed polishing [13], float polishing [14], elastic
realizes the generation of high form accuracy and a smooth emission machining (EEM) [15], microfluid jet polishing
surface. Ultraprecision cutting is suitable for processing (MFJP) [16], and use of the canon super smooth polisher [17].
ductile materials, such as nonferrous metals, plastics, and Moreover, it should be pointed out that the combination of
some infrared optical crystal materials. A form accuracy of supersmooth polishing and corrective polishing may be used in
less than 100 nm and a surface Ra of less than 1 nm can be the final finishing phase for optical elements with extreme
achieved by ultraprecision cutting [6]. precision where an extremely high level of surface form acc-
uracy and low surface roughness are required at the same time.
2.2. Ultraprecision grinding To date, there have been a number of review papers in
the precision manufacturing field written from different per-
Ultraprecision grinding uses ultraprecision grinders and
spectives [18–25]. There have also been several books pub-
grinding wheels with fine/ultrafine abrasive grains to obtain a
lished recently that review precision manufacturing
form accuracy of ∼100 nm and a surface Ra of ∼10 nm.
technologies [26–29]. However, much higher precision has
Ultraprecision grinding is suitable for processing hard and
been required in recent years, and advanced optics with more
brittle materials, such as fused silica, silicon carbide, cera-
mics, etc. The grinding wheel usually needs to be precisely complex surfaces, such as microstructured and freeform sur-
dressed to make the abrasive particles keep protruding from faces and optics with extremely small/large dimensions have
the wheel surface. After grinding, the grinding trace left on been attracting attention due to their unique optical perfor-
the ground surface is extremely fine; and the residual surface mance. Continuing improvements and new challenges in the
height is very small [7]. fabrication of large-aperture, extremely accurate, and super-
smooth aspheric optical surfaces, such as EUV lithography,
require the surface roughness of EUV mirrors to be machined
2.3. Corrective polishing
at the subangstrom level [30].
Although ultraprecision cutting and grinding can produce an Therefore, a comprehensive review of state-of-the-art
optical surface which can be directly used for infrared optics manufacturing technologies for achieving extreme precision
and even for visible lights, sometimes after ultraprecision is necessary. In this paper, we review the latest challenges for
cutting and grinding, the form error of the machined surface manufacturing technologies that have received extensive
cannot meet the high precision requirements, especially for attention in the high-precision optical fabrication and
3
optoelectronic engineering fields in recent years and identify aperture D, the angular resolution of the system can be
some future directions of R&D activities in this area. effectively improved; and the energy collection ability of the
system can be improved at the same time. Thus, more dim
objects of the universe can be observed. Therefore, large-
3. Advances in manufacturing precision aperture aspheric optical elements have been used more and
more widely in modern optical telescope systems.
3.1. Early developments In order to obtain high-resolution images, high form
Ultraprecision machining technology has important applica- accuracy as well as low surface roughness of less than 1 nm
tions in the field of optical components fabrication. Because Ra over an aperture range of several meters is required. For
optical elements need to manipulate light waves, the accurate example, the primary mirror of a very large telescope is an
manufacturing of their surfaces should be on the order of 8.2 m diameter mirror; and the level of form accuracy
optical wavelength. Therefore, the development of ultra- achieved is 18–43 nm root mean square (rms) for a surface
precision machining technology has been driven by the need roughness of 0.8–2 nm over the full aperture [36]. A 14 nm
for ultraprecision optical components. rms form error was achieved for the 8.2 m diameter mirror of
Ultraprecision cutting technology originated in the 1950s. the Japanese Subaru Telescope [37]. Moreover, the diameter
Ultraprecision cutting, i.e. SPDT technology, was first developed of the primary reflective mirror in the Hubble Space Tele-
in order to meet the processing requirements of aluminum mirrors scope (HST) is 2.4 m. The form accuracy achieved in the
[31]. With high processing efficiency and high surface finish, this effective aperture was 8 nm in rms [38–40].
technology has become the main processing method for optical Such rigorous requirements for form accuracy and sur-
mirrors, especially for batch processing of aluminum/copper face roughness are extremely difficult to achieve and cannot
mirrors. With the increasing requirements for processing accuracy be directly obtained even by ultraprecision turning or ultra-
during the past decades, ultraprecision cutting has been widely precision grinding methods. Normally, such optical elements
used for processing of nonferrous metals, nonelectrolytic plated need to be manufactured by ultraprecision turning (for ductile
nickel, soft and brittle optical crystals, and some optical plastics. materials) or grinding (for hard brittle materials) as the pre-
The surface roughness can reach the nanometer level, and the ceding process and ultimately manufactured by a subaperture
surface form accuracy can reach the submicron level [32–34]. corrective polishing process with iterative measurements and
Because it is difficult to process hard and brittle materials corrections of local form errors [41]. Sometimes, large-aper-
by ultraprecision cutting, diamond grinding is an alternative ture optics have to be decomposed into a number of smaller
used for machining glass and ceramics. In recent years, the pieces of segments, and each segment is machined individu-
development of on-machine dressing technology for grinding ally. After machining, the segments are then combined
wheels has caused ultraprecision grinding to play an impor- together and aligned by numerous high-precision actuators to
tant role in the processing of hard and brittle materials. achieve total form accuracy. In a word, astronomy is
However, grinding usually generates grinding marks on undoubtedly one of the main forces driving the development
the surface and internal material defects, i.e. subsurface of ultraprecision manufacturing engineering. Astronomers’
damage (SSD) inside the workpiece. Thus subsequent pol- need for large-aperture telescopes is constantly challenging
ishing is normally needed. For semiconductor wafers, such as the extreme-precision manufacturing capabilities of humans.
silicon, silicon carbide, and gallium nitride, which have plane The aforementioned large-aperture telescopes are mainly
surfaces, chemo-mechanical polishing (CMP) planarization is used to control visible light with a wavelength band between
generally required to remove the grinding marks and grind- 350 and 750 nm [42]. If light with a shorter wavelength needs to
ing-induced SSD after ultraprecision grinding. be controlled, the manufacturing accuracy of optical compo-
nents will become more stringent. Typical applications of short
wavelength optics are objective lenses in lithographic machines,
3.2. State-of-the-art precision level
alternatively called steppers, for semiconductor chip fabrication.
Advances in precision manufacturing have been greatly In recent decades, there has been rapid progress in the
driven by astronomy. Astronomy is an ancient science, which integrated circuit industry with more and more functionality
has a far-reaching and wide-ranging impact on human beings. being packed onto a single chip, which is largely being driven
The development of astronomy urgently requires the con- by the rapid progress of photolithography [43]. Photo-
struction of advanced experimental equipment. Astronomical lithography is the process of transferring geometric patterns
telescopes have always been the indispensable research tool on a mask to the surface of a Si wafer using a stepper. For a
to observe distant planets, galaxies, and other astronomical lithographic system, the line-width resolution R (minimum
objects. The angular resolution of a telescope optical system feature size) is determined by the Rayleigh formula [44]:
is determined by the working wavelength and the system
aperture. The relationship can be expressed as [35]: kl
R= , (2 )
NA
1.22l
a= , (1 )
D where λ is the wavelength of light, NA is the numerical
where α is the angular resolution, λ is the working wave- aperture (the brightness of the projection lens), and k is a
length, and D is the telescope aperture. By increasing the constant process factor.
4
Table 1. Precision levels and manufacturing methods for typical applications.
Form accuracy Surface roughness

Applications (nm rms) (nm rms) Manufacturing methods
Eye glasses 2000 10 Hot press or injection
Illumination optics 300 2 Grinding+polishing
Projector optics 300 1 Precision grinding+polishing
Photo optics, consumer devices 100 1 Ultraprecision grinding+polishing
Space optics 20 0.5 Corrective polishing+supersmooth polishing
DUV projection lithography 2 0.3 Corrective polishing+supersmooth polishing
system
EUV projection lithography 0.1 0.05 Corrective polishing+supersmooth polishing
system
In order to create finer patterns, a light source providing a the contemporary era [59–64]. Table 1 lists some precision
shorter wavelength is needed. The state-of-the-art lithography levels and manufacturing methods for typical applications.
tools use DUV light from argon fluoride (ArF) excimer lasers In the semiconductor industry, another need for an
with wavelengths of 193 nm, which has enabled transistor atomic level surface finish is CMP of bare Si wafers. In
feature sizes to shrink below 10 nm [45]. A typical projection general, Si wafers are polished using an elastic polisher and a
system consists of 28 fused silica lenses, and 7 of them are slurry made from ultrafine silicon dioxide (SiO2) particles
aspherical lenses with a maximum diameter of 280 mm [46]. (approximately 10 nm in size) suspended in an alkaline
It should be noted that, in the case of lithography optics, the solution of approximately 10 pH. The Si wafers are required
specification for surface roughness measurement is further to be polished to a high-quality surface with a surface
subdivided into middle spatial frequency range (MSFR), high roughness of 0.1 nm Ra and a flatness of about 1 μm in the
spatial frequency range (HSFR), and extended HSFR 12 inch range without any resultant defect from the former
[47, 48]. Carl Zeiss has investigated the influence of errors in processes.
different frequency bands on the performance of optical Overall, in order to achieve such high flatness and surface
systems [49]. The surface form error causes image distortion finish, the resolution of surface material removal must reach
and introduces various aberrations. The MSFR error causes the atomic or subatomic level. The manufacturing process is
small-angle scattering and flares, which will affect the ima- accompanied by many unprecedented subatomic level phe-
ging contrast. The HSFR error will cause large-angle scat- nomena. Therefore, clarifying the new principles and the
tering and reduce the refractivity of the lenses [50]. Therefore, physical and chemical phenomena of the nanometric- and
the errors of every spatial frequency, namely surface form atomic-level manufacturing processes is the fundamental
accuracy, waviness, and roughness, should be precisely requirement for the manufacturing of the above-mentioned
controlled to the nanometer level. optical elements.
According to the previous research results, the surface
form accuracy of each DUV lens should be 2 nm rms; and the
MSFR error should be 0.3 nm rms [51–56]. As the diameter 4. New developments in ultraprecision
of an atom is 0.1–0.2 nm, the atoms on the surface need to be manufacturing
removed layer by layer if the size fluctuation range of the
machined surface is in the subnanometer order, which is the 4.1. Ultraprecision cutting
ultimate target processing accuracy, namely, atomic-level
accuracy. 4.1.1. Materials to cut. Ultraprecision cutting has become
Even higher precision is required. Extreme ultraviolet one of the most important methods used for the direct
lithography is the latest lithography technology using an EUV machining of ductile materials, such as aluminum, copper,
wavelength of 13.5 nm [57]. The reflective projection system copper alloy, silver, gold, electroless plated nickel, and
in an EUV lithographic machine has the highest accuracy of acrylic plastic, to optical quality without the need for a
the reflective optical systems. The wavefront error of the all- subsequent polishing process. These materials are very
reflective EUV mirror system is required to be 1 nm, and thus difficult to machine into a mirror surface by abrasive
the accuracy of a single mirror element is required to reach machining processes because they are soft, and the
the 0.1 nm level. The MSFR, which determines the flare level abrasives scratch the finished surface. In addition, this
of the system, is critical in overall EUV lithography. An process is unable to produce high levels of flatness at the
extremely smooth surface should be polished with MSFR edges of the machined surface.
roughness down to 0.05 nm rms [58]. It means that manu- On the other hand, some hard and brittle materials, such
facturing technology and metrology should close the loop for as Si and germanium (Ge) can also be finished to a surface
form accuracy control on the subatomic level. Therefore, the roughness of a few nm Ra. Gerchman and Mclain [65]
manufacturing of the EUV mirrors is full of tough challenges, published their results of early work on the machining of Ge
representing the highest level of ultraprecision machining in in which they diamond-turned Ge to a surface roughness of
5
Figure 2. Schematic diagrams for (a) brittle-regime cutting and (b) ductile-regime cutting.
5–6 nm Ra. The machined samples were 50 mm in diameter

with spherical surfaces. The material removal rate in diamond
turning was given in terms of a tool feed of 2.5 μm per
revolution of the workpiece together with a 25 μm depth of
cut. More recently, Shore [66] has reported that material
removal rates on the order of 2–4 mm3 per minute have been
obtained in diamond turning of Ge optics with a 100 mm
diameter. The tool life (expressed as the effective cutting
distance of the tool) when producing optical surfaces (<1 nm
Ra) at these removal rates was in excess of 12 km. More
detail on this subject is provided in the next section.
Every sword has two edges, and diamond cutting is no
exception. A diamond tool wears at a very high rate during
the cutting process of ferrous materials [67–69]. In general, a
diamond tool cannot be used for turning steels, irons,
titanium, and pure nickel. This is due primarily to the Figure 3. Schematic of laser-assisted cutting by directly heating the
graphitization of diamond induced by the catalytic reaction cutting zone. Reprinted from [73], Copyright 2015, with permission
from The Society of Manufacturing Engineers.
with the ferrous materials even at ambient temperatures.
4.1.2. Ductile-regime cutting of brittle materials. In recent machining even though the undeformed chip thickness is
decades, research efforts have focused on the ultraprecision smaller than tc. Therefore, keeping the cutting tool edge sharp
diamond turning of hard and brittle materials. It is well known and reducing the tool wear rate plays a significant role in the
that the surface roughness and SSD caused by diamond application of ductile-regime cutting technologies. While tool
turning of a hard and brittle material could be reduced as the wear cannot be completely avoided, it can be minimized to
undeformed chip thickness t is reduced to the submicron scale some extent if the temperature rise is suppressed and the
or smaller. There exists a critical value for t below which lubrication of the tool-workpiece interface is improved [71].
surface damage does not occur. This critical value is known Laser-assisted cutting was recently reported to be a
as the critical undeformed chip thickness (tc). The process of potential method for realizing low tool wear ductile cutting of
machining hard and brittle materials in such a mode is called some hard and brittle materials. Traditionally, the heat-
ductile-regime machining. When the undeformed chip assisted cutting techniques were applied in such a way that
thickness is larger than tc, however, cracks are generated, the heating zone was in front of the cutting tool, softening
forming fractured cutting chips. These two different materials prior to chip formation. In 2005, Patten et al
machining regimes are schematically shown in figure 2 [72, 73] proposed micro laser-assisted machining (μ-LAM),
[70]. The brittle-ductile transition is originated from a tensile as shown in figure 3, where the laser beam passes directly
to compressive stress state transition in the cutting region due through the cutting tool and heats the cutting zone. After that,
to the effect of edge radius. In order to improve the surface Ravindra et al [74] investigated the ductile mode material
finish in diamond turning of hard and brittle materials, it is removal and high-pressure phase transformation in silicon
desirable to machine them in a ductile-regime way in that during the μ-LAM process. Their results demonstrated that
continuous cutting chips are formed, thus leaving a crack-free the optimized laser power condition resulted in a greater
surface. critical depth of cut and a nearly damage-free or cured
Ductile-regime cutting can be realized by reducing the diamond structure silicon (Si-I), similar to that of the original
undeformed chip thickness to a certain value. The cutting workpiece phase.
performance is strongly determined by the conditions of the Using alternative tool materials is another challenge. As
cutting tool edge [69]. If the diamond tool edge wears diamond tools are prone to graphitization at high temperature,
severely, ductile-regime cutting will change to brittle-regime they are not suitable for carbon alloy cutting. Wei et al [75]
6
Figure 4. Schematic diagrams for the microgrooving process for fabricating Fresnel lenses on single-crystal Ge and a surface topography of
the machined lens. Reproduced from [80]. © IOP Publishing Ltd. All rights reserved.
investigated laser-assisted cutting with a sapphire tool that has 4.1.4. Ultrasonic-vibration assisted cutting. Hardened steel is
high heat resistance. a common die material developed for molding plastic and
glass optical elements. However, conventional diamond
cutting is not applicable to steel materials due to the
4.1.3. Microstructure cutting. Microstructures with a high extremely severe chemical tool wear [82]. In the last few
aspect ratio, such as V-grooves, pyramids, and microlens decades, ultrasonic vibration cutting technology has been
arrays, can enhance the functionality of surfaces in many successfully applied to difficult-to-cut materials [83, 84].
ways. Such microstructured optics are used in various optical Shamoto et al [85] proposed the elliptical vibration cutting
applications for imaging, illumination, or light concentration (EVC) method, as shown in figure 6. The feasibility of cutting
[76–79]. One example is the Fresnel lens, which can be steel with diamond tools was verified by applying EVC.
machined by diamond turning with the tool path matching the Moreover, the vibration amplitude of the EVC is actively
contour of the structure. For example, the microgrooving controlled while machining. Thus, the depth of cut can be
changed rapidly just like using a fast tool servo (FTS). This
process was performed on single-crystal Ge for fabricating
technology combines the advantages of EVC and FTS, which
infrared Fresnel lenses [80], where a sharply pointed diamond
enables fabrication of micro/nanostructures on difficult-to-cut
tool was used to generate the micro-Fresnel structures under
materials [86]. The EVC system developed was applied
three-axis ultraprecision numerical control, as shown in to sculpture arbitrary micro-/nanostructures by vibration
figure 4. By adopting a small angle between the cutting amplitude control. Subsequently, a nanometer-scale sculpture
edge and the tangent of the objective surface, this method was fabricated on a hardened steel surface. Figure 7 shows an
enabled the uniform thinning of the undeformed chip example of a machined angle grid surface with a height of 1 μm
thickness to the nanometric range and thus provided and a wavelength of 150 μm on hardened steel [87].
complete ductile regime machining of brittle materials. A
Fresnel lens, which has a form error of 0.5 μm and a surface
4.1.5. Fly cutting of large crystals. Fly cutting is an
roughness of 20–50 nm Ry was successfully fabricated during
intermittent cutting process in which a diamond tool is
a single tool pass.
mounted to the end of a spindle to intermittently cut a
Another example of microstructure cutting on hard and
workpiece [88–91]. This process has important applications
brittle material is the machining for spherical and hexagonal in the production of large flat surfaces. Figure 8 is an example
concave microlens arrays on a single-crystal Si wafer by STS of fly cutting of potassium dihydrogen phosphate (KDP)
diamond turning, as shown in figure 5 [81]. The rapid crystal which has excellent nonlinear optical properties [4].
fabrication of microlens arrays on the surface of single crystal Potassium dihydrogen phosphate crystal is a typical soft,
Si was realized by the sectional cutting method where the brittle material which has poor processing properties, such as
follow-up error of the tool servo was suppressed. Microlens easy deliquescence and mechanical anisotropy [92]. This
arrays with a form error of ∼300 nm peak-to-valley (PV) and makes it one of the most difficult to cut materials.
a surface roughness of ∼6 nm Sa were successfully Ultraprecision fly cutting has proven to be an effective
fabricated. processing method to fabricate large-sized KDP crystals. The
7
Figure 5. Spherical and hexagonal microlens arrays on a single-crystal Si wafer machined by slow tool servo diamond turning. Reprinted
from [81], Copyright 2017, with permission from Elsevier.
Figure 7. Machined angle grid surface with a height of 1 μm and a

Figure 6. Amplitude control sculpturing method in elliptical wavelength of 150 μm. Reproduced from [87]. CC BY 3.0.
vibration cutting. Reprinted from [85], Copyright 1994, with
permission from CIRP.
subwavelength gratings [97–102]. Jones et al [103] presented
a focused-ion-beam fabricated diamond tool for producing
flatness of large KDP crystals was machined within 500 nm, submicron structures through a roll-based mastering method.
and the surface roughness reached 1 nm Ra [93–95]. Burr formation was minimized, and the surface quality of the
Recently, the fly cutting method has also been equipped product was improved by optimizing the tool shape and the
with a slow FTS to fabricate hybrid structural surfaces on microcutting conditions. Liu et al [104] suggested that a
freeform surfaces [96]. higher cutting speed was the most critical factor influencing
the mold accuracy. The experimental result demonstrated that
through the strict control of cutting parameters, diamond
4.1.6. Diamond turning of roll-to-roll imprinting molds. turning was an effective approach for ensuring the continual
Diamond turning of high-precision molds is a vital process mass production of subwavelength gratings. Moreover,
for the roll-to-roll resin imprinting process used in fabricating Terabayashi et al [105] proposed a method for machining
8
initiation. In most cases, the critical chip thickness in grinding

is different from that in cutting due to the significant
difference in the edge geometries between a diamond cutting
tool and abrasive grains. Several investigations about the
critical depth of cut brittle materials have been conducted by
indentation and scratching. A simple equation was developed
for the calculation of the critical depth of cut in grinding in
terms of material properties [111]
⎛ E ⎞ ⎛ K ⎞2
dc = 0.15 ⎜ ⎟ ⎜ c ⎟ , (3 )
⎝ H ⎠⎝ H ⎠
where E is Young’s modulus, Kc is fracture toughness, and H

is hardness. The critical chip thickness can be estimated from
equation (1).
Figure 8. Schematic of the processing of large-aperture KDP crystal
by fly cutting. [4] 2016. Reprinted by permission of the publisher To achieve ductile mode grinding, a diamond wheel
(Taylor & Francis Ltd, http://tandfonline.com). having fine/ultrafine grains is critical [112]. Essentially,
truing/dressing the wheel surface to make a uniform
two-directional wavy microgrooves by using a slow tool protrusion of grains is a key point for ductile mode grinding.
servo (STS) system. As shown in figure 9, microgrooving
experiments using a two-axis STS system were conducted on 4.2.2. Grinding kinematics. In recent years, several grinding
cylindrical oxygen-free copper roller molds to machine kinematics, including cross-grinding, parallel grinding, and
various wavy microgrooves. The resulting form accuracy on wheel-axis adaptive grinding, have been developed for the
the roll mold was at the ∼1 μm level and surface roughness precision grinding of curved surfaces [113–115]. Cross-
was at the ∼10 nm level. The machined roller mold was used grinding is the most common grinding technique for large
for ultraviolet resin imprinting, and high-precision replication convex surfaces. As shown in figure 10(a), the rotational
of the two-directional wavy structures was realized. These direction of the workpiece and the cutting direction of the
structures are very useful for reducing fluid drag. wheel are perpendicular at the grinding point. The wheel wear
is concentrated at the contact point. Therefore, it is difficult to
4.2. Ultraprecision grinding obtain a high form of accuracy when the workpiece is very
hard and the size is large. Parallel grinding employs an arc-
Ultraprecision grinding is primarily used to generate high- shaped grinding wheel, where the grinding spindle is tilted
quality, functional surfaces made of difficult-to-machine with respect to the workpiece axis [113]. As shown in
materials, such as hard and brittle materials. Through the figure 10(b), the grinding point moves along the grinding
multipoint cutting actions of ultrafine abrasive grains, ultra- wheel, thus the wheel wear could be dispersed over a large
precision grinding can generate parts with high surface finish, area, which is helpful for improving form accuracy. However,
high form accuracy, and high surface integrity at reduced tool the form accuracy of the grinding wheel must be high for
wear, compared to diamond cutting. parallel grinding, which is a critical issue.
Wheel-axis adaptive grinding means the wheel axis
4.2.1. Ductile mode grinding. The fracture toughness of hard always changes to keep the wheel normal to the workpiece
and brittle materials, such as glass, is very small, only surface [116]. As shown in figure 10(c), the grinding point
10−2–10−3 of the metal materials [106]. Therefore, cracks remains constant during grinding as a result of the tool-axis
appear easily during the grinding of hard and brittle materials. rotation. This grinding mode has a very low requirement of
In recent decades, it has been established that the wheel form accuracy. However, wheel wears rapidly at the
ultraprecision machine enabling an extremely small feed fixed grinding point, which introduces a gradually increased
rate can achieve ultraprecision mirror surface grinding, which form error on the ground surface.
is similar to the grinding of metal materials. Thus, the
transition from brittle-to-ductile material removal is 4.2.3. In-process dressing technologies. In order to reduce
considered to be of great importance for ultraprecision the surface roughness and SSD on ground wafers, grinding
grinding. Until now, intensive research efforts have been wheels with smaller diamond grains are desirable. However,
focused on the ductile grinding of a variety of hard and brittle when the size of diamond grains decreases to micron scale
materials, such as Si [107], silicon carbide (SiC) [108], and with a high concentration, it is very difficult for the wheel to
optical glasses [109, 110]. maintain sufficient self-dressing ability [117].
The critical depth of cut (critical chip thickness in a 3D To solve this problem, the electrolytic in-process
model) for ductile-brittle transition is the most critical dressing (ELID) grinding method was proposed. The ELID
parameter to produce a ductile ground surface. Ductile continuously exposes new sharp abrasive grains by dissolving
grinding of hard and brittle materials requires a maximum the bond material (mainly cast iron) around the abrasive
chip thickness not exceeding the critical value for crack grains [118]. As shown in figure 11, the wheel surface had
9
Figure 9. Slow-tool-servo turning for two-directional wavy microgrooves. Reproduced with permission from. Reproduced with permission
from [105].
Figure 10. Relative motion between wheel and workpiece: (a) cross-grinding method, (b) parallel grinding method, and (c) wheel-axis
adaptive grinding. [116] 2016 © Springer-Verlag London. With permission of Springer.
an increase in conductivity of the wheel surface. Thus, the

electrolysis could be restarted and the oxide layer regenerated.
By this manner, the protrusion of the grains remains constant
during grinding.
In 1985, ELID grinding of ceramics was reported using
metal-bond diamond wheels with grain sizes smaller than 30
μm [119]. Afterward, the ELID technique was further
improved. In 1995, ELID grinding experiments on silicon
wafers were conducted with a 5 nm grain size iron-bonded
diamond grinding wheel. A superfine surface with Ra 3.29 Å
was successfully achieved [120]. In recent years, ELID has
become an important manufacturing process for hard-to-
Figure 11. Principle of ELID grinding. Reproduced with permission
machine materials, although several technical barriers have
from [118]. been reported for ELID grinding to achieve extreme precision
[121]. For example, the material removal rate in ELID
good conductivity at the predressing stage. The conductivity grinding of Si wafers is low compared to conventional wafer
of the wheel surface was reduced with the growth of the oxide grinding. As the wheels are dressed during the grinding
layer thickness. However, the oxide layer became worn along process, the wheel wear must be precisely compensated for in
with the grinding action. The wear of the oxide layer caused order to obtain high dimensional accuracy. Thus, it is difficult
10
Figure 12. Manufacturing process of the CMG wheel. Reprinted from [130], Copyright 2012, with permission from Elsevier.
for ELID grinding to achieve high wafer flatness. In addition, machined on binderless WC as well as SiC. The edge
the oxide layer on the ground surface has been reported to be radius of the V-grooves and pyramids was less than
a problem with ELID grinding [122]. 1 μm [139].
In addition to ELID, there are a variety of other in- Figure 13 shows the schematic of grinding microgrooves
process dressing methods, such as electrochemical in-process [140]. The flat diamond grinding wheel is trued into a
controlled dressing (ECD) [123], laser dressing [124], laser- V-shaped microtip. The wheel moves horizontally along the
assisted dressing [125], water-jet in-process dressing [126], cutting direction. Yin et al [141] developed a V-groove
ultrasonic dressing [127], and electrical discharge dressing grinding process by applying ELID and microtruing opera-
[128]. These methods all have their advantages and problems tions. The minimum wheel tip radius of 8.2 μm was achieved
and need to be studied further prior to application in by microtruing the grinding wheel in a diameter of 305 mm.
ultraprecision grinding. Finally, a corner radius of V-groove ranging from 15 to
25.8 μm could be realized on a Ge surface. The grinding
4.2.4. Chemo-mechanical grinding technology. Diamond method developed was used in the fabrication of a large Ge
grinding induces grinding marks and SSD in the form of immersion grating element for the SUBARU Telescope.
crystal defects and amorphous layers [129]. Those defects can
be removed in the subsequent CMP process [130]. As an 4.2.6. Grinding for large optics. The next generation of
alternative, Zhou et al [131] proposed the chemo-mechanical- ground-based telescopes requires hundreds of meter-scale,
grinding (CMG) process, which combines the advantages of off-axis reflective mirrors. To fulfill the fabrication demands,
both grinding and polishing. The CMG is a fixed abrasive the Cranfield BoX™ grinding machine was developed to
process integrating chemical reaction and mechanical provide meter-scale grinding capability for optics at high
grinding into one process and shows advantages against material removal rates while minimizing levels of SSD
CMP in efficiency, geometric controllability, and waste [142–145]. The high loop stiffness of the BoX™ machine was
disposal. Figure 12 shows the manufacturing process of the demonstrated by the absence of edge roll-off and chipping, as
CMG wheel [132]. The experimental results indicated that well as the microlevel SSD layer. In the grinding of the
the CMG process could achieve supersurface finishing European extremely large telescope 1.45 m freeform
comparable to that obtained from CMP by decreasing the ZERODUR® segments, an rms form deviation of <1 mm
wheel abrasive hardness and introducing chemical reactions for error-compensated grinding with a surface roughness of
with the workpiece surface [133, 134]. The application of between 100 and 200 nm Ra was achieved [146].
CMG in the processing of crystalline materials, such as Zhang et al [116] developed an ultrasonic-vibration-
silicon [135], quartz glass [136], and sapphire [137] have assisted, fix-point grinding technology. In-process compensa-
been reported. A major issue in CMG is the relatively low tion of surface form error was developed based on the wheel
material removal rate. wear prediction and modification of the tool path. Using the
grinding strategies developed, a 2 m SiC mirror blank, as
4.2.5. Microstructure grinding. Microstructures on shown in figure 14, was ground to a form accuracy of 2 μm
nonferrous metals can be machined by single-point diamond in rms.
machining [6]; grinding is preferred for processing hard
materials, especially ceramics such as fused quartz glass, SiC, 4.3. Corrective polishing
and tungsten carbide (WC). A number of such grinding
processes have been developed in recent years. For example, 4.3.1. Computer-controlled optical surfacing. The form
Guo et al [138] proposed an ultrasonic-vibration-assisted accuracy of the workpiece finished by cutting and grinding
grinding technique to fabricate microstructured surfaces. The is determined by the high-precision spatial motion trajectory
experimental results indicated that the introduction of of the ultraprecision machine tools. In theory, the accuracy of
ultrasonic vibration was able to both improve the surface a workpiece surface cannot exceed that of the machine tools.
finish and the edge sharpness of the microstructures. Micro- In the 1970s, Rupp proposed the CCOS process [147].
V-groove arrays and pyramid arrays were successfully As shown in figure 15, a polishing tool with a smaller
11
Figure 13. Schematic of microgrinding of microgroove. [140]

© Springer Nature Singapore Pte Ltd, 2018. With permission of
Springer.
Figure 15. Schematic diagram of the CCOS.
figure 16(b), the high points in the polishing tool covered area,
which suffer greater pressure, were removed first so that the high
frequency surface errors were eliminated.
Computer-controlled optical surfacing uses an iterative
approach to achieve the desired surface precision. First, the
error distribution of the workpiece surface is obtained by
accurate measurement. Then, the local dwell time of the
polishing tool on the workpiece is calculated. After that, the
polishing tool is controlled to correct the local surface errors
on the workpiece surface. By sufficient rounds of error
correction, extremely high-precision surfaces with a smooth
surface could be achieved even using low-precision machine
Figure 14. Mounting of a 2 m SiC mirror blank onto a machining tools [148].
center for surface grinding. [116] 2016 © Springer-Verlag London.
One of the early applications of the CCOS technology is
With permission of Springer.
the manufacture of the HST [150], and today CCOS is being
widely used in the manufacture of high-precision large
diameter than the workpiece is controlled to pass through the
aspheric optical surfaces.
workpiece surface and polish off a certain amount of material
In CCOS, the polishing tool makes the physical contact
at each individual point.
and removes material from the workpiece. Thus, tool
As shown in figure 16(a), the feed speed along the tool path
development is an especially complex task, especially for
is purposefully changed to control the dwell time (polishing
aspheric (or freeform) optics manufacturing. Local curvatures
time) at each point [149]. The polishing tool is controlled to ride
of an aspheric surface vary as a function of position on a
on the high regions to cut off the peaks, while skipping the low
workpiece; however, the CCOS uses a rigid polishing tool
regions without removing the material there. Therefore, a low
whose shape cannot change during polishing. When polishing
frequency surface error can be corrected, as shown in
a large aspheric surface, a rigid polishing tool cannot follow
figure 16(a). Theoretically, the amount of material removed is
the curvature changes at different areas of the surface,
determined by the local dwell time and tool impact function
resulting in the inconsistency of material removal rate and
(TIF). The TIF means the spatial removal amount of polishing
low efficiency of surface error convergence. In order to
tool in unit time. The material removed is a convolution of the
improve the performance of a rigid polishing tool, several
removal function and the dwell time, given as follows:
flexible contact polishing methods were proposed to maintain
H (x , y) = R (x , y)**D (x , y) , (4 ) good contact with the workpiece surface. These methods
include stressed-lap polishing [151], bonnet polishing [152],
where H(x, y) is the desired removal function, R(x, y) is the TIF and rigid conformal (RC) tool polishing [153], which will be
per unit time, and D(x, y) is the dwell time function. As shown in reviewed as follows.
12
Figure 16. Figuring and smoothing through CCOS. Reprinted from [148], Copyright 1987, with permission from Elsevier.
Figure 17. The schematic diagram of stressed-lap polishing technology. Reproduced with permission from [155].
Figure 19. The schematic diagrams of the ‘precession’ motion in

bonnet polishing.
Figure 18. Top view of the stressed lap. Reproduced with permission the polishing tool [163]. The air pressure in the air bonnet can
from [155]. be adjusted in real time, and the outside of the air bonnet is
covered with a layer of polishing cloth. The flexible air
bonnet coincides with the workpiece surface.
4.3.2. Stressed-lap polishing. As early as 1984, Angle et al The second principle of bonnet polishing is to use a kind
[154] proposed that the polishing tool should be actively of motion called ‘precession,’ which is different from the
deformed in order to reproduce the subaperture shape of the ‘rotation’ and ‘translation’ of a traditional polishing tool
aspheric mirror corresponding to the pad position on the [164–166]. The precession motion is divided into two parts:
mirror surface, as shown in figure 17 [156]. Based on this (1) the air bonnet rotates around the normal direction of the
concept, several stressed laps were designed to change their tool and (2) the air bonnet rotates around the normal direction
shape in-process to coincide with the mirror surface during of the workpiece at a certain angle, as shown in figure 18. Due
polishing [157–160]. Figure 18 shows one design of a to the precession motion, bonnet polishing can homogenize
stressed lap in which the deformation of the pad surface is the motion trajectory, thus improving the machined surface
achieved by drawing steel wire using a servo motor [155]. roughness.
Stressed-lap polishing has significant advantages in the Bonnet polishing is a kind of flexible polishing, which is
polishing of superlarge astronomical telescopes. One characterized by high determinacy of TIF and high conv-
example is that an 8.4 m diameter primary mirror in the ergence efficiency. However, due to the use of a spherical air
Giant Magellan Telescope (GMT) project was processed by bonnet, the contact area with the workpiece is small; and the
the Steward Observatory Mirror Lab at the University of material removal efficiency is low.
Arizona [161]. Stressed-lap polishing with a diameter of 1 m
was developed. After polishing, full surface roughness and
form accuracy reached 20 nm Ra and less than 1 μm, 4.3.4. Rigid conformal lap polishing. In 2009, Kim and Burge
respectively [162]. proposed a rigid conformal polishing tool that conforms to the
aspheric shape yet maintains stability to provide natural
4.3.3. Bonnet polishing. As shown in figure 19, the first smoothing for high spatial-frequency errors on the workpiece
principle of bonnet polishing is to use a flexible air bonnet as [167–169]. The tool uses an elastic rubber paste called
13
Figure 20. Three-dimensional schematic of rigid conformal lap

structure. Reproduced with permission from [153]. © 2010 Optical
Society of America.
Figure 21. Mechanisms of MRF polishing and its material removal
mechanism. Reproduced with permission from [173].
Silly-Putty® as the deformed layer of the polishing tool, as
shown in figure 20. Silly-Putty is an organosilicon polymer
and a nonlinear viscoelastic non-Newtonian fluid [170]. The
fluid has both flexibility and rigidity for different time scales.
Under long-term stress, it shows the fluidity of liquid; under
high-frequency stress, it shows the rigidity of solid.
Therefore, the rigid conformal polishing tool has not only
the ability of a flexible polishing tool for a nonspherical
surface but also the smoothing effect of a rigid polishing tool.
Compared with CCOS methods, rigid conformal lap
balances the advantages and disadvantages of various
processing methods. Therefore, it has various advantages,
such as excellent TIF stability, high material removal rate, and Figure 22. The tool impact function of MRF. Reproduced with
good physical smoothing ability. Moreover, rigid conformal permission from [179]. © 2011 Optical Society of America.
lap can provide a supersmooth surface finish with <1 nm rms.
This may eliminate the need for the final touch-up step for a
supersmooth surface finish. Because of these competitive magnetorheological fluids increases instantaneously, becom-
advantages, the rigid conformal lap polishing is very suitable ing viscoplastic Bingham medium under the action of a high-
for processing large aperture aspheric mirrors with high intensity gradient magnetic field. When the Bingham medium
steepness and large deviation. The Steward Observatory passes through the narrow gap formed by the workpiece and
Mirror Lab of the University of Arizona successfully applied the polishing wheel, it generates a great shear force at the
this technology to the GMT 8.4 m primary mirror fabrica- contact area, thus removing the surface material of the
tion [171]. workpiece.
Magnetorheological finishing is a deterministic polishing
process because the polishing tool will not dull or wear
4.3.5. Magnetorheological finishing. The aforementioned
[174–178]. The shape, the size, and the hardness of the
polishing methods made changes to the polishing tool but
flexible polishing belt can be controlled by adjustment of
did not change the polishing fluid or abrasives, thus it was
the magnetic field intensity at the polishing zone. Therefore,
difficult to ensure long-term stability of the TIF because of the
poor consistency of particle concentration in polishing the material removal consistency of MRF is greatly improved
regions. In order to solve this problem, MRF was developed. compared with CCOS.
Magnetorheological finishing was originally proposed by Figure 22 is the TIF shape of the MRF, which looks like
Kordonski et al in the former Soviet Union [172]. The a bullet [179]. Such a TIF has only one peak value and is very
working principle of MRF is illustrated in figure 21 [173]. helpful for the convergence of surface error. However, the
The magnetorheological fluid is composed of base fluid, TIF of MRF is very small compared with traditional large
surfactant, magnetic particles, and polishing particles. Mag- polishing tools. Therefore, the material removal rate is low
netorheological fluid flows out of the nozzle and moves along and the processing time of MRF is bound to be very long for
the polishing wheel to the top area. The viscosity of large-aperture optical surfaces.
14
Figure 24. Schematic of atom removal process in EEM. Reproduced

with permission from [189]. © American Vacuum Society.
Figure 23. Schematic of the principle of ion beam figuring. [184]

2015 © Springer-Verlag London. With permission of Springer.
4.3.6. Ion beam figuring. The aforementioned polishing

methods are all contact processes. The polishing tools exert
a certain degree of pressure on the workpiece surface, which
leads to print-through of the structure of a light weighted
mirror [180]. Moreover, when the polishing tool moves to the
mirror edge, the polishing area becomes smaller and the
pressure increases, which inevitably leads to the edge roll-off
phenomenon [181].
As a noncontact and nonmechanical process, IBF has
been successfully applied in the polishing of space mirrors
since the 1970s [182, 183]. Figure 23 shows the working
principle of IBF [184]. IBF is a method of bombarding high-
energy ions (generally argon ions) into the machined surface Figure 25. Principle of microfluid jet polishing. Reprinted from
and removing materials by physical sputtering at the atomic [190], Copyright 2013, with permission from Elsevier.
level. One of the main advantages of IBF is the contactless
nature of an ion beam as a polishing tool, which eliminates most cases, silica particles with submicron diameters are used
the edge roll-off effects of mechanical tools. Because the as abrasives.
energy distribution of an ion beam can be accurately Kanaoka [189] investigated the smoothing performance
controlled, excellent stability of atomic-level removal can of rotating-sphere EEM for processing ULE® and ZERODUR
be achieved [185–187]. materials for EUV optics. It was demonstrated that the rms
There are, however, a few trade-offs to these benefits. surface roughness converged to a constant value of 0.1 nm
The deterministic removal of this method depends heavily on after removal of a certain depth of material. The surface
the stability of the ion source and the environmental stability roughness can thus be reduced to 0.1 nm rms or better,
of the vacuum chamber. The material removal efficiency of fulfilling the requirements of the EUV optics.
IBF is very low compared to mechanical methods due to
atomic-level material removal characteristics. 4.4.2. Microfluid jet polishing. In order to achieve
supersmooth lenses for 193 nm projection lithography
systems, Ma et al [190] proposed a supersmooth polishing
4.4. Supersmooth polishing method called MFJP, which combined the principles of float
polishing, CCOS, and abrasive jet polishing. As shown in
4.4.1. Elastic emission machining. EEM was first proposed figure 25, the polishing slurry outflowed from the spray holes
as a polishing method by Mori et al about 40 years ago [188]. of the polishing head, lifting the polishing tool a certain
EEM is a noncontact machining method that involves passing distance through the dynamic pressure caused by the motion
a flow of fine powder particles in pure water across the of the polishing slurry. The chemical reaction between the
workpiece surface. As shown in figure 24, the particles workpiece and the fine powder particles results in the removal
supplied in a flow of pure water and the topmost atoms of the of the topmost atoms from the workpiece surface.
work surface are chemically removed at the atomic level. A 100 mm diameter (95% effective aperture) fused silica
Hence, the work surface can be finished without defects. In flat optical element was polished using the MFJP method.
15
Figure 26. (a) Low, (b) mid-, and (c) high-spatial frequency PSD data. Reprinted from [190], Copyright 2013, with permission from Elsevier.
Testing results showed that the low-spatial form accuracy

improved from 3.624 to 3.393 nm in rms, and the midspatial
frequency surface roughness improved from 0.477 to 0.309 nm
in rms. The high-spatial frequency surface roughness improved
from 0.167 to 0.0802 nm in Rq. The power spectral density
curve before and after supersmoothing uniform polishing is also
shown in figure 26, in which the mid- and high-spatial
frequency roughness was significantly improved; but the low-
spatial surface form was not obviously changed.
5. On-machine measurement (OMM) and

compensation
For the form error correction process, the precise measure-

ment of the machined surface is an essential step. Metrology
Figure 27. Schematic of the two-probe measurement system
is the most important supporting technology for ultraprecision mounted on an ultraprecision lathe. Reproduced with permission
manufacturing. Without ultraprecision metrology, there will from [195].
be no advance in the precision level of manufacturing.
Typical surface metrology methods for ultraprecision surfaces
include contact/noncontact profilometer, laser interferometer, proposed an OMM system based on capacitive displacement
white light interferometer microscope, and atomic force sensors for high-precision optical surfaces. A 92% of full
microscope. However, most of the above-mentioned mea- aperture measurement of a spherical aluminum mirror with a
surement methods are off-machine methods. Because of the diameter of 300 mm was carried out, and the complete
remounting process, off-machine measurements reduce measurement of the form error required only 5 min. Zou et al
manufacturing efficiency and may cause measurement error [193] developed a chromatic confocal sensor to achieve
due to workpiece remounting and/or environmental changes. noncontact measurement with nanometer-level accuracy for
In order to solve these problems, on-machine metrology and an ultraprecision turning machine and is capable of recon-
error compensation based on the measurement result is structing the 3D surface topography of flat, spherical, and
expected.
aspheric surfaces. Li et al [194] integrated a dispersed refer-
There are several methods of realizing OMMs. A
ence interferometer on an ultraprecision turning machine. Yan
touching probe, i.e. the so-called linear variable differential
et al used a white-light interferometer for nanometer level
transformer, is always installed on a commercial diamond
turning machine. Other methods include laser and chromatic precision on-machine profiling of curved diamond cutting
confocal probes, which are noncontact and nondestructive tools [195]. Both theoretical and experimental investigation
methods for surface measurement. For example, Chen et al was conducted to prove the validity and effectiveness of the
[191] presented an OMM approach using a sapphire proposed calibration methodology. In addition, as shown in
microprobe of 0.5 μm in radius for the grinding of tungsten figure 27, Yu et al [196] proposed an OMM system using two
carbide aspheric molds. The overall form error after grinding optical probes to rapidly reconstruct the surface form from the
was obtained by subtracting the target form from the actual radial and axial directions. Thus, a two-step compensation
ground form. The aspheric surface had a high form accuracy strategy to generate a modified tool path was developed. The
of 0.177 μm after three compensation cycles. Li et al [192] results show that the OMM system and compensation strategy
16
Nagayama et al [197] proposed a new process flow

which includes error correction and prediction, as shown in
figure 28. The flow is composed of four steps: (1)
program optimization, (2) tool alignment error correction,
(3) machining error modification, and (4) form error predic-
tion. In this flow, all of the main error factors are optimized in
Steps (1), (2), and (3) based on error analysis; and the form
error of the finished surface is predicted in step (4). All of the
error corrections are carried out, and the finished form error is
predicted before machining. In this way, a very high form
Figure 28. Diagrams of the correction/prediction machining flow. accuracy can be obtained in a single cycle. Figures 29(a) and
Reproduced from [196]. CC BY 4.0.
(b) show the simulation and experiment results of form errors
under different conditions. In the simulation, the form error
was predicted to be reduced by 80% with correction steps (1),
(2), and (3), compared to the case of machining without any
corrections. The results of the experiment agree well with the
simulated results. Figure 29(c) shows the 3D topography of
the surface machined after all of the correction steps. A 10 nm
level sinusoidal wave grid was successfully fabricated on a
single crystal Si wafer by STS turning, and the form accuracy
was 8 nm PV [196].
6. Summary and outlook
Improving form accuracy and surface finish is the permanent

pursuit of high-value-added manufacturing technologies.
With the demands of the next generation EUV lithography,
space optics and laser fusion technology, ultraprecision
machining technologies are now stepping from the nanometer
scale towards the atomic scale. In the past decades, remark-
able advances have been achieved in the area of high-preci-
sion manufacturing technologies based on the significant
developments in machine building technology, tooling tech-
nology, measurement and control technologies. Future R&D
issues towards extreme precision manufacturing can be
Figure 29. Results of simulation and experiment of form errors under summarized as follows.
different conditions of correction/prediction machining. Reproduced
from [196]. CC BY 4.0.
(1) Material removal mechanisms at the atomic scale
The theoretical clarification of the basic principles
in the material removal process at the atomic level is
were effective for improving the form accuracy while
essential for optimizing existing manufacturing tech-
simultaneously enhancing the machining efficiency. nologies and developing new technologies. In the early
The error compensation strategy is a very important
1990s, Japanese scholars used extremely sharpened
issue. For example, in diamond turning, a typical machining single-crystal diamond tools to investigate experimen-
cycle consists of three steps: programming to generate tool tally the minimum chip thickness for metal cutting and
paths, tool alignment step for tool-workpiece alignment, and demonstrated that a cutting thickness of 1 nm was
machining for surface generation. A number of factors cause possible. Cutting experiments in scanning electron
workpiece form errors during each step of the process. In a microscopes and nanoindentation tests have been also
conventional process flow, the form error is corrected by used to clarify the nanoscale phenomena of machining.
using feedback correction, thus only a specific error factor is Such fundamental research will be still important in the
compensated for based on the experimentally measured form future for challenging the ultimate dimensional accur-
error. The machining-measurement cycle must be repeated acy of ultraprecision cutting. In recent years, molecular
many times because the form error decreases gradually in dynamics simulation has been applied to study the
each cycle; and it is extremely difficult and time-consuming nanometric and atomic scale cutting, grinding, and
to reduce the form error completely. polishing processes, which has made it easier for us to
17
reveal a material removal mechanism and investigate [8] Jones R 1986 Computer-controlled optical surfacing with
the machinability of various materials at small scales. orbital tool motion Opt. Eng. 25 256785
(2) Surface/subsurface evaluation for extreme-precision [9] Anderson D et al 1992 Stressed-lap polishing of 3.5-m f/1.5
and 1.8-m f/1.0 mirrors Proc. SPIE 1531 260–9
machining [10] Walker D et al 2006 Use of the ‘precessions’™ process for
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[12] Allen L 1995 Progress in ion figuring large optics Proc. SPIE
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such as potential microcracks, phase transformations, [13] Dietz R and Bennett J 1996 Bowl feed technique for
and residual stresses, which cannot be directly mea- producing super smooth optical surfaces J. Appl. Opt. 5
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International Journal of Extreme Manufacturing

TOPICAL REVIEW • OPEN ACCESS

- A simplified FEM analysis on the static

This content was downloaded from IP address 81.23.183.148 on 22/01/2021 at 07:46

Int. J. Extrem. Manuf. 1 (2019) 022001 (22pp) https://doi.org/10.1088/2631-7990/ab1ff1

Manufacturing technologies toward extreme

Received 5 April 2019, revised 6 May 2019

(Some ﬁgures may appear in colour only in the online journal)

1. Introduction Subtractive manufacturing is undoubtedly the most

Figure 1. Taniguchi chart to predict the development of machining accuracy.

Ultraprecision cutting uses ultraprecision lathes and single-

Table 1. Precision levels and manufacturing methods for typical applications.

Form accuracy Surface roughness

5–6 nm Ra. The machined samples were 50 mm in diameter

Figure 7. Machined angle grid surface with a height of 1 μm and a

initiation. In most cases, the critical chip thickness in grinding

where E is Young’s modulus, Kc is fracture toughness, and H

an increase in conductivity of the wheel surface. Thus, the

Figure 13. Schematic of microgrinding of microgroove. [140]

Figure 15. Schematic diagram of the CCOS.

Figure 19. The schematic diagrams of the ‘precession’ motion in

Figure 20. Three-dimensional schematic of rigid conformal lap

Figure 24. Schematic of atom removal process in EEM. Reproduced

Figure 23. Schematic of the principle of ion beam ﬁguring. [184]

4.3.6. Ion beam figuring. The aforementioned polishing

Testing results showed that the low-spatial form accuracy

5. On-machine measurement (OMM) and

For the form error correction process, the precise measure-

Nagayama et al [197] proposed a new process ﬂow

6. Summary and outlook

Improving form accuracy and surface ﬁnish is the permanent

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