Typical 3-D topography sensors for the measurement of surface
structures in the micro- and nanometre range are atomic force microscopes (AFMs),
tactile stylus instruments, confocal microscopes and white-light
interferometers. Each sensor shows its own transfer behaviour. In order to
investigate transfer characteristics as well as systematic measurement
effects, a multi-sensor measuring system is presented. With this measurement
system comparative measurements using five different topography sensors are
performed under identical conditions in a single set-up. In addition to the
concept of the multi-sensor measuring system and an overview of the
sensors used, surface profiles obtained from a fine chirp calibration standard are
presented to show the difficulties of an exact reconstruction of the surface
structure as well as the necessity of comparative measurements conducted with
different topography sensors. Furthermore, the suitability of the AFM as
reference sensor for high-precision measurements is shown by measuring the
surface structure of a blank Blu-ray disc.
Introduction
Schematic representation of the multi-sensor measuring system with
five different topography sensors (a) and a photograph of the measuring
system with active vibration damping on a steel plate reducing mechanical environmental vibrations (b).
The characterization of surface structures in the micro- and nanometre range
can be done by various types of topography sensors. The demands on
topography sensors with regard to accuracy and measurement speed increase
steadily. Currently the best-known method for three-dimensional topography
measurement with respect to its transfer behaviour is the tactile stylus
method, where the surface of the specimen is scanned with a stylus tip.
However, the tip may influence the sample to be measured and also limits the
measuring speed typically up to 1 mms-1.
Therefore, there are efforts to increase the measuring speed of
tactile sensors and to reduce the wear of the stylus tip
. present a microprobe
which allows tactile roughness measurements with a lateral scanning speed of
15 mms-1.
Optical methods such as confocal microscopy, coherence scanning
interferometry (CSI) and laser interferometry provide an alternative
. The advantage of these methods
is a fast and contactless measurement of the surface topography. Damages of
the measuring surface as well as maintenance costs and measuring deviations
due to worn probe tips are eliminated. For the compensation of disturbances
caused by external vibrations, different methods exist
. However,
depending on the surface topography, more or less systematic measurement
errors may also occur. Examples are artefacts known as batwings
, phase jumps resulting from the slope effect
in white-light interferometry and also laser
interferometry , artefacts from crosstalk between
neighbouring pinholes of a spinning disc of a confocal microscope
, and artefacts occurring by equal curvature of the
wavefront and the measuring surface . For an investigation
of these effects it is necessary to distinguish between the real and the
measured surface. Therefore, measurements are performed on specimens with a
known surface structure like a surface standard or by comparing the
measurement results with those of a reference sensor. An advantage of
comparative measurements with reference sensors in the same system
configuration is the feasibility of measurement of arbitrary surface
structures under identical environmental conditions. For this purpose a
multi-sensor measuring system has been developed in our lab
. Next to the investigation of different systematic
effects it is possible to characterize the transfer behaviour of our
self-assembled topography sensors with this measuring system. A similar
multi-sensor concept has already been pursued by and
. However, here the priority targets were the
extension of the measuring range and the coverage of metrological
requirements for different measuring objects through the use of different
optical and tactile sensors.
Multi-sensor set-up
The multi-sensor measuring system comprises two self-assembled optical sensors
(a Mirau interferometer and a fibre-coupled interferometric point sensor) as
well as three commercial sensors (an atomic force microscope, AFM; a confocal microscope; and a tactile
stylus instrument). The sensors are mounted on an L-shaped granite portal as
shown in Fig. . Each sensor is connected to the granite
portal by a vertically aligned linear stage. The linear stages provide a
vertical positioning of each sensor in a range of 100 mm. With two
horizontally aligned air bearing linear stages it is possible to position a
specimen in the measuring volume of the respective sensor. A lateral
measurement field of 150 mm× 100 mm is covered by all topography
sensors for comparative measurements. In addition, the xy linear stages are
used as scan axes for scanning a specimen surface horizontally as well as for
stitching of several measurement fields. The repeatability of the xy linear
stages is denoted by ±400nm in the x direction and ±50nm
in the y direction. Based on this positioning accuracy it is possible to measure
surfaces with stochastic structures without a reference point.
In order to compensate for environmental vibrations, several techniques are
employed. At higher frequencies vibrations are damped by the inertial mass of
the granite used and the lower frequency spectrum is covered by an active
vibration damping system shown in Fig. b.
The atomic force microscope (AFM) can measure the surface in the tactile
static mode and the contactless dynamic mode. In the more precise
dynamic mode the maximum rms value of the noise of the measured height values
is specified by 150 pm. The lateral deflection of the cantilever via
three internally installed coils results in a maximum diamond-shaped
measuring field of 110 µm× 110 µm and a square field of
79 µm× 79 µm. The maximum vertical deflection of the
cantilever is 22 µm. Besides the low noise of the height values
the lateral resolution of this sensor is much better than the resolution of
optical sensors based on microscopic imaging, as demonstrated by measuring
the surface of a Blu-ray disc in Sect. . For this reason,
the AFM generates a precise surface topography of the structures to be
measured and thus is qualified as a precision reference sensor for optical
topography sensors.
A further reference sensor is the confocal microscope. A rotating multi-pinhole
disc generates the confocal effect by filtering the light of an LED
light source and the light field in the image plane. During one rotation a
complete image of the surface to be measured is detected by an areal CCD
camera. The depth scan required for the topography measurement is done by
changing the distance between the microscope objective and specimen by a stepwise
motion of the objective using a piezoelectric-driven stage. At each step the
camera detects an image of the surface. The confocal sensor provides a
measurement field of 320 µm× 320 µm by a total magnification
of 23. At a numerical aperture (AN) of 0.95 the lateral optical
resolution is approximately 320 nm using the Rayleigh criterion for
conventional optical microscopy. By the confocal effect the lateral optical
resolution is improved compared to classical light microscopy
. As a result of the optical
magnification and the pixel pitch of the camera the lateral sampling interval
in the object plane is approximately 320 nm. Based on the Shannon
criterion, grating structures with a period larger than 640 nm can be
reconstructed. The vertical resolution is specified with a noise level of
2 nm. To obtain an overview of the surface to be measured it is
possible to generate conventional microscopic images besides the confocal
measurement mode. Due to the high AN and the different working
principle compared to interferometric sensors, the confocal microscope is an
appropriate optical reference sensor.
The third reference sensor is the tactile stylus instrument. In particular,
tactile measurements of surface contour and roughness can be obtained with
this sensor. A stylus tip is brought into contact with the surface of the
specimen and scans a line of 26 mm in the y direction with a scan
velocity in a range of 0.1 to 1 mms-1 (for the coordinates see
Fig. ). Height differences of the surface structure
result in deflection of the tip which is measured. In combination with the
x axis, several parallel profiles can be scanned and combined to a 3-D
topography. The accuracy of the measured height information is specified by
the residual value Rz0 according to ; see
Table .
Scanning speed values and related Rz0 according to ,
Lc = 0.25 mm, Lc / Ls = 100.
Rz0 (nm)≤30≤50≤80vs (mms-1)0.10.51.0
Self-assembled Mirau interferometer measuring a chirp standard provided by Physikalisch-Technische Bundesanstalt (PTB).
In addition to the three reference sensors, two different self-assembled
interferometric topography sensors are integrated in the multi-sensor system.
One of these 3-D sensors is the Mirau interferometer shown in
Fig. . With this interferometer the transfer characteristics
of white-light interferometers are investigated as an example, including the
investigation of artefacts like the batwing effect . A special feature of this Mirau interferometer is its ability to
simply adapt the spectral characteristics of the light source and to perform
depth scans of up to 100 mm using a stepper-motor-driven linear axis
instead of an additional piezo-driven positioning system. Using a linear depth
scan in combination with a CMOS camera with a USB3.0 interface, high-speed
measurements are possible. At full resolution
(2048 pixels× 2048 pixels) the camera captures 90 frames per seconds
(fps) or 360 fps with a resolution of
512 pixels× 2048 pixels. For signal analysis different algorithms are
used. In addition to the determination of the height values by detecting the
position of the envelope, the more precise phase evaluation is inter alia obtained
by a lock-in algorithm (LT algorithm) or frequency domain analysis
.
Fibre-coupled interferometric–confocal high-speed
distance sensor using a 1550 nm laser source.
Figure shows the practical realization of a fibre-coupled
interferometric–confocal high-speed sensor . The
fundamental principle of this sensor is based on a Michelson interferometer.
A laser beam with a wavelength λL of 1550 nm
propagating from the end face of the optical fibre is divided by a beam
splitter in a measurement and a reference beam with the intensities
Im and Ir. The modulation of the optical path length
by an ultrasonic transducer, which actuates the reference mirror, allows a
phase detection to calculate the height value h(x,y). Neglecting the
offset, the two-beam interference equation takes the form
ΔI(t)=2ImIrcos4πλLz^acos2πfat-hx,y.
Here z^a and fa represent the amplitude and
frequency of the oscillating reference mirror. For each period of the
oscillating mirror, two height values result. Therefore, the oscillation
frequency fa of 58 kHz used yields 116 000 height values per
second. This high acquisition rate allows a movement speed of the horizontal
scan axis up to 100 mms-1 as demonstrated using a sinusoidal
standard . However, if a lower scan velocity is used,
the high acquisition rate can be utilized to filter and improve the accuracy
of the height values. In order to generate a 3-D topography of the surface to
be measured, the air bearing xy linear stages are used as scan axes. With
AN of approximately 0.4, the lateral resolution is about
2.3 µm according to the Rayleigh criterion. However, the
single-mode optical fibre acts as a pinhole of a confocal microscope
, improving the lateral resolution and
suppressing stray light.
Topography and profile of a blank Blu-ray disc measured with the AFM .
Comparative measurements
At first, the result of a topography measurement on a blank Blu-ray disc
(Verbatim BD-RW SL 25 GB) measured by the AFM is presented to underpin the
suitability of this instrument as a high-resolution reference sensor.
Figure shows the measured topography as well as a
2-D profile of the structure. The tracks of the Blu-ray disc with trapezoidal
grooves are well-resolved. The measured track pitch of 324 nm and
groove depth of 24 nm correspond to the reported values of
320 and 20 nm.
In order to be able to resolve this fine surface structure, the cantilever
EBD-HAR made of HDC/DLC (high-density carbon/diamond-like carbon) by
Nanotools is used. With an opening angle below 8∘ this cantilever is
particularly suitable for measurements of steep edges and fine structures.
The air bearing xy linear axes were also lowered prior to the measurement
in order to minimize the influence of vibrations caused by the air stream.
For comparison, a high-resolution Linnik interferometer with a AN
of 0.9 and a blue LED light source with a centre wavelength of 460 nm
resolves the tracks of the disc too but not as detailed as the AFM
.
Profile of the PTB chirp standard measured by the tactile stylus instrument GD26.
Profiles of the fine chirp structure obtained by various topography
sensors: (a)50× Mirau interferometer with a AN
of 0.55 (phase evaluation using the LT algorithm) and a central wavelength
of 590 nm, (b) unwrapped profile from (a), (c) confocal microscope,
(d) high-speed sensor with two different scan velocities (blue:
0.1 mms-1; red: 1 mms-1), (e) AFM with a Tap190Al-G
cantilever and (f) contact stylus instrument with a scan velocity of
0.5 mms-1 by using a probe according to DIN EN ISO 3274
(2 µm tip radius and an aperture angle of 60∘).
In order to show the necessity of comparison measurements with various
topography sensors, measurement results of these sensors are juxtaposed using
a chirp structure manufactured by PTB (Physikalisch-Technische Bundesanstalt,
Germany). An overview of the surface structure of the chirp standard results
from the profile measured by the tactile stylus instrument; see
Fig. . The standard is divided into a coarse and a fine
chirp structure. Both sinusoidal microstructures are specified with a
peak-to-peak amplitude of 400 nm. In the case of the coarse chirp the
spatial wavelengths are in a range of 91 to 10 µm and in a range of 12 to 4.3 µm
for the fine chirp . Such a chirp calibration standard can
be used to describe the transfer behaviour at different spatial wavelengths
. To represent the measured amplitude as a
function of the spatial wavelength, the so-called instrument transfer
function (ITF) can be used . With the knowledge about the
real structure, the transfer function is estimated.
Figure a shows the measurement result of the Mirau
interferometer with AN of 0.55 and a magnification of 50×.
In addition to the chirp structure, artefacts occur at the steepest slopes of
the structure. These artefacts are phase jumps caused by height displacements
occurring as a result of envelope evaluation, which in turn results from a
too-low lateral resolution related to low-pass filtering of the fringes
.
By unwrapping this profile the phase jumps are
removed as presented in Fig. b. This effect does not
appear in the result of the confocal microscope, as it is shown in
Fig. c. However, the profile indicates a stronger low-pass
filtering of the structure compared to the Mirau interferometer. When looking
at the profiles, it is striking that there is only a one-sided constriction
of the profile at the centre. In theory, double-sided constrictions are to be
expected in a low-pass-filtered profile. A possible reason for this effect is
indicated by an AFM measurement. Figure e shows the chirp
profile measured by the AFM in the dynamic mode using a Tap190Al-G cantilever
from BudgetSensors. Again, there is also a one-sided constriction with a
height reduction of approx. 40 nm. In addition, the upper peaks of
the sinusoidal structure in the centre of the chirp standard are tapered,
resulting in a sharp-combed chirp structure. Therefore, the top levels are
more affected by low-pass filtering compared to the bottom levels. To achieve
high accuracy in the determination of the transfer behaviour of a topography
sensor, the profile measured by AFM can be used as a reference representing
the original course of the chirp structure.
In the further three subsections the transfer behaviour of the tactile stylus
instrument, the fibre-coupled high-speed sensor and the confocal microscope
is investigated in more detail.
Tactile stylus instrument
For the measurement of the fine chirp structure with the tactile stylus
instrument, a probe with a 2 µm tip radius and a cone angle of
60∘ according to is used. Compared to the lateral
resolution of the interferometric high-speed sensor (see
Fig. d), similar low-pass filtering of the measured chirp
structure is expected. However, the measured stylus profile in
Fig. f shows a fairly good reproduction of the reference
structure. Deviations to the structure measured by the AFM are inter alia
formed by the lateral sampling distance of 0.5 µm, measuring
deviations given by the residual value up to 50 nm according to
Table and the dilatation coming from the stylus tip. Due
to the mechanical contact of the tip and the surface to be measured, no
low-pass filtering of the upper tapered peaks appears and the real shape is
reproduced nearly correctly.
Section of the chirp profile with the shortest spatial wavelength
measured by the AFM (blue line) and a fitted concentric circle (red line)
with a radius of 3.99 µm, using the software MountainsMap. The additional
blue dashed line illustrates a sine with the spatial wavelength
Λmin′ and the amplitude z^FC,0′.
The radius of curvature RFC,min at the smallest spatial
wavelength Λmin of the nominal sinusoidal chirp structure
is
RFC,min=Λmin2z^FC,04π2≈1.83µm,
where Λmin=3.8µm (see
Fig. ) and the amplitude z^FC,0 is equal
to 200 nm. Because the structure is sharp-combed instead of
sinusoidal, the radius of curvature of the grooves is assumed to be
reasonably greater than 1.83 µm. This assumption is confirmed by
the reference measurement of the AFM plotted in Fig. .
Next to the area of the smallest spatial wavelengths (blue curve), a fitted
concentric circle with a radius of 4 µm (red curve) is depicted,
which was created using the analysis software MountainsMap. An explanation
for the difference between the calculated value of 1.83 µm and the
empirically determined value of 4 µm is given by the sharp-combed
structure. The sharp-combed profile almost resembles a rectified sine
function of twice the period of the nominal sinusoidal chirp structure. Thus,
the period Λmin′ of the sine to calculate the
radius RFC,min′ corresponds to twice the period
Λmin with twice the amplitude:
RFC,min′=Λmin′2z^FC,0′4π2=Λmin22z^FC,0π2≈3.7µm,
as it is graphically illustrated by the dashed blue line in
Fig. . Hence, the grooves can be measured using a stylus
instrument with a tip radius of 2 µm. In the case of an optical
sensor, low-pass filtering of the structure occurs due to the limited
lateral-resolution capabilities, resulting in a double-sided constriction as a
simulation shows . On the other hand, when using a tactile
measuring method, a one-sided constriction of the grooves is to be expected,
because the intrusion between two peaks is first limited before the peaks are
no longer resolvable.
In all measured profiles, the smallest period of the chirp structure is
3.8 µm. This leads to the conclusion that there is a deviation
from the nominal sinusoidal structure of the 4.3 µm period.
Optical high-speed sensor
Median filtered profiles of the fine chirp structure obtained by the
high-speed sensor with two different lateral scan velocities (blue:
0.1 mms-1; red: 1 mms-1) are shown in
Fig. d. Higher scan velocities such as
80 mms-1 are also possible as presented by
. Both profiles of the high-speed sensor show a similar
but stronger low-pass filter effect than the profile of the confocal
microscope. In the profile measured at a higher scanning speed there is a
stronger low-pass-filtering effect, which is due to an additional averaging
over the surface heights caused by the scanning motion. The sawtooth-like
structure of both profiles is probably the result of a maladjusted sensor and
needs further investigation.
Comparison of different profiles of the fine chirp structure: (a) profile
measured by AFM (blue) and the same profile filtered with a sliding average filter
based on a rectangular impulse response function with a pulse width of
1.85 µm (red), and (b) comparison of the filtered profile (red)
from (a) and the structure measured by the interferometric high-speed sensor (blue).
In order to demonstrate the suitability of the measurement results of the AFM
as a reference for the characterization of the transfer behaviour of the
optical sensors, a simple example is presented in
Fig. . To simulate the low-pass-filtering effect of
the optical sensors a sliding average filter convolving the profile with a
rectangular function is used:
hc(nyΔy)=1Nwhafm(nyΔy)⋅rect(nyΔy),
with the sampling interval Δy, and a window length of the filter
Nw∈N, ny∈N and
rect(nyΔy)=1for0≤nyΔy≤ΔyNw-10fornyΔy≥NwΔy.
Employing the low-pass filtering according to Eq. ()
to hafm, with different parametrization of the minimum beam
waist, yields the best match for a width of the rectangular function of
NwΔy=1.85µm shown in
Fig. a.
Through the comparison of this filtered structure with
the profile measured by the interferometric high-speed sensor, a good
congruence is observed, especially for the constriction of the upper and
lower peaks; see Fig. b. A mathematical description
of the focused laser beam of the high-speed sensor is possible assuming a
Gaussian beam. Therefore, the minimal radius of the laser spot is equal to
the smallest waist w0 of the Gaussian beam :
w0=λLπarcsinAN.
For the high-speed sensor a minimum spot radius of 1.2 µm is
therefore assumed. The half rectangular width used for the sliding filter
corresponds to the radius of the laser spot and should be equal to
1.2 µm. However, the radius of the presented filtered structure
(Fig. b) is approx. 0.9 µm. This is (about
25 %) smaller than the theoretical value. This discrepancy supports
a smaller diameter of the laser spot and an accompanying improvement of the
lateral resolution by the confocal effect caused by the single-mode
fibre used. The scale of this value corresponds to the improvement (27 %)
of the lateral single-point resolution between a confocal and a conventional
microscope described in . Besides small deviations in the
determination of the filter width, a further reason can be a higher numerical
aperture. In addition, the result obtained by filtering the AFM profile
confirms the theory of one-sided constrictions by low-pass filtering using
optical topography sensors.
Transfer characteristics of the confocal microscope: (a) comparison
of the chirp profile measured by confocal microscope (blue curve) and filtered
profile according to Eq. () with an additional
discretization by the camera pixels (red curve), (b) comparison of the
measured profile of the confocal microscope (blue curve) to a reconstructed profile (red curve),
(c) ITF resulting from the measured height
of rectangular gratings with various spatial wavelengths in relation to the
results of the AFM (see Table ) with the spatial
wavelength Λ50% equal to twice the spatial wavelength
ΛR according to the Rayleigh criterion, and (d) comparison
of the profile obtained with the confocal microscope (blue) and a filtered profile (red)
according to Eq. () with a filter width of 3ΛR.
Confocal microscope
Using the confocal
microscope with a numerical aperture AN of 0.95 and an LED light source with a
central wavelength λconf of 500 nm,
a well-resolved profile of the fine chirp structure is expected.
However, the Nyquist–Shannon sampling criterion is not satisfied
by the equivalent camera pixel pitch of 320 nm, and the surface
structure is not completely resolved as shown in Fig. c. A
first approach to investigate the low-pass behaviour of the confocal
microscope is to convolve the reference structure hafm measured
by the AFM with the normalized point spread function (PSF) of the confocal
microscope:
hc(y)=hafm(y)⋅PSFconf(y).
Here, the PSFconf corresponds to the square of the
PSFconv of a conventional microscope
and is described by
PSFconf(y)=PSFconv2(y)=J12πλconfANy2πλconfANy4,
with the Bessel function J1 of the first kind and order. Following
the convolution according to Eq. () the
discretization due to the camera pixels is considered by an additional
filtering according to Eq. , where
NwΔy is the equivalent pixel width of 320 nm.
Therefore, every Nwth point is taken from the filtered result. As shown in
Fig. a, there is a significant deviation between
the filtered and the measured profile. A further approach is to rebuild the
image formation. Appropriate procedures are presented by
as well as for confocal microscopy
using transmitted and reflected light. For the calculation of the intensities
a simulation program introduced by is used, which is based
on the Richards–Wolf model . Here, the measured AFM
profile builds the input surface to rebuild the intensities I(nyΔy,nzΔz) with the lateral sampling interval Δy equal
to 20 nm. The discretization of the camera pixels is achieved by
averaging the resulting intensities Iconf(y,z) covering a
single camera pixel:
Iconf(lΔỹ,nzΔz)=1Nw∑i=1NwIconf(lΔyi,nzΔz),
with the pixel index l∈N, the number of intensity samples
Nw covered by a single pixel and the equivalent camera resolution
Δỹ=NwΔy=320nm.
Equation () is applied to each image of index
nz recorded during the depth scan with step size of Δz.
By using a Gaussian fit algorithm to approximate the intensity along the z
axis, a height profile is reconstructed. However, a significant deviation
between this simulated and the measured profile still remains, as it is shown
in Fig. b. This deviation is slightly smaller
compared to Fig. a and can be a result of
aberrations of the optical system which are not considered in the image
formation model.
A favoured characterization of the transfer behaviour is given by the ITF,
which describes the ratio of the measured and the true amplitude of a surface
structure with respect to the spatial frequency. In the work of
the theoretical ITF is compared with experimental
results using a white-light interferometer to demonstrate the transfer
behaviour for incoherent illumination as well as for coherent illumination by
using a Fizeau interferometer. compare multiple ITFs of a
laser scanning confocal microscope using various measurements on a chirp profile
of different slope angles and amplitudes, using an AFM as reference
instrument. A further application example is the characterization of a
phase-shifting interferometer by an ITF created by measurements on a Siemens star
with a structure height of about 50 nm. A
theoretical investigation of the transfer behaviour of white-light
interferometers using the ITF is given by .
Comparison of height differences depending on various spatial
period lengths Λ measured by AFM and confocal microscope using
a RS-N standard manufactured by Simetrics.
In order to obtain the ITF, various measurements are performed with the
confocal microscope on a Simetrics RS-N standard, as presented in
Table . This standard covers different rectangular
gratings of various fundamental spatial frequencies Λ-1. The
precision of the measured step height is increased by averaging 10 repeated
measurement results for each spatial wavelength. As reference height, the
measuring results of the AFM are used. The resulting ITF shows a decrease
below a grating period of 3 µm, as displayed in
Fig. c. From the course
of the curve a wavelength Λ50% of 925 nm is obtained, which is
related to a decrease of 50 % of the real amplitude. As defined in
and for coherence scanning interferometry,
Λ50% equals twice the spatial wavelength
ΛR pursuant to the Rayleigh criterion:
Λ50%=2ΛR=1.22λconfANχ.
Based on the assumption that this relation is valid also for confocal
microscopy, ΛR equals 462.5 nm. If χ equals 1,
ΛR corresponds to the theoretical optical lateral
resolution according to the Rayleigh criterion. However, here the empirical
relation results in a multiplication with χ=1.45, which is a consequence
of the deviation between the experimentally determined ΛR and
the theoretical optical resolution.
Due to a comparison of the profile measured by the confocal microscope with a
filtered AFM profile (according to Eq. ), using
various filter widths yields the best match for a sliding average with a width
of 3ΛR as shown in Fig. d.
Here, the ITF at 3ΛR corresponds to 0.75. Based on the
results of the three different methods presented here to characterize the
transfer behaviour of the confocal microscope, the latter method based on the
experimentally determined ITF proved to be most suitable. This probably may
be explained by optical aberrations of the confocal system due to imperfect
optical components and maladjustment.
Conclusions
The multi-sensor measuring system makes it possible to conduct comparative
measurements with various sensors at equal environmental conditions. In
addition to the determination of the transfer characteristics of
self-assembled sensors, the investigation of reference sensors is also
possible. As a result of different working principles of the topography
sensors used, artefacts or other deviations can be identified by comparative
measurements. Since the measuring volume tracking is not fully implemented
yet, the profiles shown in Fig. are not measured on the exact
same location on the specimen surface. For precise
characterization of the transfer behaviour of a topography sensor, comparative
measurements at equal locations are required. To reach this, further steps
are essential. This includes the software implementation of all sensors in a
common C ++ program and the proper calibration of the spatial deviations
between the individual locations of the measurement fields of the sensors. In
addition to positioning by the air bearing xy axes, the spatial conformity
of the measurement fields can be increased by correlation of measured
topographies. The desired maximum lateral deviation is 1 µm.
The accuracy of the height measurement of each reference sensor is characterized
by different parameters for different instruments, namely the rms value for
the AFM, the noise level for the confocal microscope and the residual value
Rz0 for the stylus instrument. To ensure comparability, it is
necessary to characterize both the individual reference sensors and the
self-assembled topography sensors using the same parameter based on measurements
on well-known surfaces.
As presented, the results of the AFM can be used as reference data for the
characterization of other sensors. For a theoretical and numerical analysis
of the measurement results of optical sensors, the results of the AFM can be
used as input data to a simulation program introduced in ,
which is based on Kirchhoff theory and the Richards–Wolf model
.
Measurements at the same chirp structure using different topography sensors
show the necessity of comparison measurements. Insight into the transfer
behaviour of the sensors in the multi-sensor application is achieved by
comparison of their chirp standard measurement results to those of the AFM.
Therefore, the one-sided constrictions of the profiles measured by the optical
sensors are explained by a sharp-combed structure instead of the originally
assumed sinusoidal structure. Due to the sharp-combed structure the
calculated nominal radius of curvature, based on the assumption of a
sinusoidal structure, is too small. Thus the fine chirp profile is resolvable
using the tactile stylus instrument with a tip radius of 2 µm. In
spite of a lateral sampling interval of 500 nm the structure of the
chirp standard is almost correctly measured. The presented comparative
measurements between tactile and optical sensors indicate that depending on
the surface structure of the measuring object, both techniques feature unique
advantages, which are not available in a single-sensor system.
The multi-sensor measuring system is currently undergoing further development.
As a final target, an automatic procedure for comparative measurements is
intended as well as the continuous testing and improvement of the topography
sensors.
Data availability
The underlying measurement data are not publicly available
and can be requested from the authors if required.
Competing interests
The authors declare that they have no conflict of
interest.
Special issue statement
This article is part of the special issue “Sensors and
Measurement Systems 2018”. It is a result of the “Sensoren und Messsysteme
2018, 19. ITG-/GMA-Fachtagung”, Nürnberg, Germany, from 26 June 2018 to
27 June 2018.
Acknowledgements
The authors gratefully acknowledge the financial support of this project by
the DFG (Deutsche Forschungsgemeinschaft) under grant no. INST159/59-1 and
thank the company Mahr for providing the stylus instrument GD26.
Edited by: Rainer Tutsch
Reviewed by: two anonymous referees
ReferencesBlu-ray Disc Association: White Paper Blu-ray Disc format: General, 5th
Edition, available at: http://www.blu-raydisc.com, last access: 10 August 2018.
Brand, U., Doering, L., Gao, S., Ahbe, T., Buetefisch, S., Li, Z., Felgner,
A.,
Meess, R., Hiller, K., Peiner, E., Frank, T., and Halle, A.:
Sensors and calibration standards
for precise hardness and topography measurements in micro-and nanotechnology,
in: Micro-Nano-Integration; 6. GMM-Workshop; Proceedings of, 1–5 pp., VDE,
2016.
Corle, T. R. and Kino, G. S.: Confocal scanning optical microscopy and
related
imaging systems, Academic Press, 1996.
Dabbs, T. and Glass, M.: Fiber-optic confocal microscope: FOCON, Appl. Optics, 31, 3030–3035, 1992.
de Groot, P.: Principles of interference microscopy for the measurement of
surface topography, Adv. Opt. Photonics, 7, 1–65, 2015.
de Groot, P. and de Lega, X. C.: Interpreting interferometric height
measurements using the instrument transfer function, in: Fringe 2005,
30–37 pp., Springer, 2006.
de Groot, P., de Lega, X. C., Kramer, J., and Turzhitsky, M.: Determination
of
fringe order in white-light interference microscopy, Appl. Optics, 41,
4571–4578, 2002.
DIN EN ISO 25178-604: Geometrical product specification (GPS) – Surface
texture: Areal – Part 604: Nominal characteristics of non-contact
(coherence scanning interferometry) instruments, 2013.
DIN EN ISO 3274: Geometrical Product Specifications (GPS) – Surface
texture:
Profile method – Nominal characteristics of contact (stylus) Instruments,
1996.Doering, L., Brand, U., Bütefisch, S., Ahbe, T., Weimann, T., Peiner, E.,
and Frank, T.: High-speed microprobe for roughness measurements in
high-aspect-ratio microstructures, Meas. Sci. Technol., 28,
034009, 10.1088/1361-6501/28/3/034009, 2017.
Fewer, D., Hewlett, S., McCabe, E., and Hegarty, J.: Direct-view microscopy:
experimental investigation of the dependence of the optical sectioning
characteristics on pinhole-array configuration, J. Microsc., 187,
54–61, 1997.Fujii, A., Suzuki, H., and Yanagi, K.: Development of measurement standards
for
verifying functional performance of surface texture measuring instruments,
J. Phys. Conf. Ser., IOP
Publishing, 311, 012009, 10.1088/1742-6596/311/1/012009, 2011.Giusca, C. L. and Leach, R. K.: Calibration of the scales of areal surface
topography measuring instruments: part 3. Resolution, Meas. Sci.
Technol., 24, 105010, 10.1088/0957-0233/24/10/105010, 2013.
Gu, M. and Sheppard, C.: Signal level of the fibre-optical confocal scanning
microscope, J. Mod. Optic., 38, 1621–1630, 1991.
Hagemeier, S. and Lehmann, P.: Multisensorisches Messsystem zur Untersuchung
der Übertragungseigenschaften von Topographiesensoren (Multisensor
measuring system for investigating the transfer characteristics of topography
sensors), tm-Technisches Messen, 85, 380–394, 2018a.
Hagemeier, S. and Lehmann, P.: Vergleichbarkeit des
Übertragungsverhaltens
optischer 3D-Sensoren an Kanten und Mikrostrukturen (Comparability of the
transfer behavior of 3D optical sensors at edges and microstructures), 2.
VDI-Fachtagung Multisensorik in der Fertigungsmesstechnik, VDI-Berichte Nr.
2326, 199–212, 2018b.Hagemeier, S., Tereschenko, S., and Lehmann, P.: High-speed laser
interferometric distance sensor with reference mirror oscillating at
ultrasonic frequencies, tm-Technisches Messen, 10.1515/teme-2019-0012, 2019.
Harasaki, A. and Wyant, J. C.: Fringe modulation skewing effect in
white-light
vertical scanning interferometry, Appl. Optics, 39, 2101–2106, 2000.Jordan, H.-J., Wegner, M., and Tiziani, H.: Highly accurate non-contact
characterization of engineering surfaces using confocal microscopy,
Meas. Sci. Technol., 9, 1142, 10.1088/0957-0233/9/7/023, 1998.
Kimura, S. and Wilson, T.: Confocal scanning optical microscope using
single-mode fiber for signal detection, Appl. Optics, 30, 2143–2150, 1991.Kiselev, I., Kiselev, E. I., Drexel, M., and Hauptmannl, M.: Noise robustness
of interferometric surface topography evaluation methods. Correlogram
correlation, Surface Topography: Metrology and Properties, 5, 045008, 10.1088/2051-672x/aa9459, 2017.
Kogelnik, H. and Li, T.: Laser beams and resonators, Appl. Optics, 5,
1550–1567, 1966.
Krüger-Sehm, R., Bakucz, P., Jung, L., and Wilhelms, H.:
Chirp-Kalibriernormale für Oberflächenmessgeräte (Chirp
calibration standards for surface measuring instruments), tm-Technisches
Messen, 74, 572–576, 2007.Lehmann, P., Tereschenko, S., and Xie, W.: Fundamental aspects of resolution
and precision in vertical scanning white-light interferometry, Surface
Topography: Metrology and Properties, 4, 024004, 10.1088/2051-672X/4/2/024004, 2016.
Lehmann, P., Xie, W., Allendorf, B., and Tereschenko, S.: Coherence scanning
and phase imaging optical interference microscopy at the lateral resolution
limit, Opt. Express, 26, 7376–7389, 2018.
Lin, S. K., Lin, I. C., and Tsai, D. P.: Characterization of nano recorded
marks at different writing strategies on phase-change recording layer of
optical disks, Opt. Express, 14, 4452–4458, 2006.
Martínez-Corral, M.: Point spread function engineering in confocal
scanning microscopy, SPIE Proceedings, 5182, 112–123, 2003.
Mauch, F., Lyda, W., Gronle, M., and Osten, W.: Improved signal model for
confocal sensors accounting for object depending artifacts, Opt. Express,
20, 19936–19945, 2012.
Meinders, E. R., Mijiritskii, A. V., van Pieterson, L., and Wuttig, M.:
Optical
Data Storage: Phase-change media and recording, vol. 4, Springer Science &
Business Media, 2006.Morrison, E.: The development of a prototype high-speed stylus profilometer
and
its application to rapid 3D surface measurement, Nanotechnology, 7, 37–42, 10.1088/0957-4484/7/1/005, 1996.
Richards, B. and Wolf, E.: Electromagnetic diffraction in optical systems,
II.
Structure of the image field in an aplanatic system, Proc. R. Soc. Lond. A,
253, 358–379, 1959.Schake, M. and Lehmann, P.: Perturbation resistant RGB-interferometry with
pulsed LED illumination, SPIE Proceedings, 10678, 1067805-01–1067805-12, 10.1117/12.2306221, 2018.
Schake, M., Schulz, M., and Lehmann, P.: High-resolution fiber-coupled
interferometric point sensor for micro-and nano-metrology, tm-Technisches
Messen, 82, 367–376, 2015.Schulz, M. and Lehmann, P.: Measurement of distance changes using a
fibre-coupled common-path interferometer with mechanical path length
modulation, Meas. Sci. Technol., 24, 065202, 10.1088/0957-0233/24/6/065202, 2013.
Schulz, M. and Lehmann, P.: Fasergekoppelter High-Speed-Sensor zum Messen
optischer Funktionsflächen, 18. GMA/ITG-Fachtagung Sensoren und
Messsysteme, 411–417, 2016.Seewig, J., Raid, I., Wiehr, C., and George, B. A.: Robust evaluation of
intensity curves measured by confocal microscopies, SPIE Proceedings, 8788,
87880T, 10.1117/12.2020551, 2013.Seewig, J., Eifler, M., and Wiora, G.: Unambiguous evaluation of a chirp
measurement standard, Surface Topography: Metrology and Properties, 2,
045003, 10.1088/2051-672X/2/4/045003, 2014.
Sheppard, C. and Choudhury, A.: Image formation in the scanning microscope,
Op. Acta, 24, 1051–1073, 1977.
Tereschenko, S.: Digitale Analyse periodischer und transienter Messsignale
anhand von Beispielen aus der optischen Präzisionsmesstechnik, Ph.D.
thesis, University of Kassel, Germany, 2018.
Tereschenko, S., Lehmann, P., Zellmer, L., and Brueckner-Foit, A.: Passive
vibration compensation in scanning white-light interferometry, Appl.
Optics, 55, 6172–6182, 2016.
VDI/VDE 2655-1.3: Optical measurement of microtopography – Calibration of
interference microscopes for form measurement, part 1.3, 2018.
Weckenmann, A.: Koordinatenmesstechnik: flexible Strategien für
funktions-und fertigungsgerechtes Prüfen, Hanser, 2012.
Wiedenhöfer, T.: Multisensor-Koordinatenmesstechnik zur Erfassung
dimensioneller Messgrößen, tm-Technisches Messen, 78, 150–155, 2011.
Wilson, T.: Confocal microscopy, Academic Press London, 1990.Xiao, G., Corle, T. R., and Kino, G.: Real-time confocal scanning optical
microscope, Appl. Phys. Lett., 53, 716–718, 1988.
Xie, W.: Transfer Characteristics of White Light Interferometers and Confocal
Microscopes, Ph.D. thesis, University of Kassel, Germany, 2017.Xie, W., Hagemeier, S., Woidt, C., Hillmer, H., and Lehmann, P.: Influences
of
edges and steep slopes in 3d interference and confocal microscopy, SPIE
Proceedings, 9890, 98900X, 10.1117/12.2228307 2016.Xie, W., Hagemeier, S., Bischoff, J., Mastylo, R., Manske, E., and Lehmann,
P.:
Transfer characteristics of optical profilers with respect to rectangular
edge and step height measurement, SPIE Proceedings, 10329, 1032916, 10.1117/12.2270185, 2017.