Design and Calibration of an Optical Micro Motion Sensing System for Micromanipulation Tasks

Abstract

An optical sensing system has been developed using a pair of orthogonally placed position sensitive detectors (PSD) to track 3D displacement of a microsurgical instrument tip in real-time. An infrared (IR) diode is used to illuminate the workspace. A ball is attached to the tip of an intraocular shaft to reflect IR rays onto the PSDs. Instrument tip position is then calculated from the centroid positions of reflected IR light on the respective PSDs. The system can be used to assess the accuracy of hand-held microsurgical instruments and operator performance in micromanipulation tasks, such as microsurgeries. In order to eliminate inherent nonlinearity of the PSDs and lenses, calibration is performed using a feedforward neural network. After calibration, percentage RMS error is reduced from about 5.46 % to about 0.16%. The system RMS noise is about 0.7 mum. The sampling rate of the system is 250 Hz.

Full text

Abstract- An optical sensing system has been developed using
a pair of orthogonally placed position sensitive detectors (PSD)
to track 3D displacement of a microsurgical instrument tip in
real-time. An infrared (IR) diode is used to illuminate the
workspace. A ball is attached to the tip of an intraocular shaft
to reflect IR rays onto the PSDs. Instrument tip position is then
calculated from the centroid positions of reflected IR light on
the respective PSDs. The system can be used to assess the
accuracy of hand-held microsurgical instruments and operator
performance in micromanipulation tasks, such as
microsurgeries. In order to eliminate inherent nonlinearity of
the PSDs and lenses, calibration is performed using a
feedforward neural network. After calibration, percentage
RMS error is reduced from about 5.46 % to about 0.16%. The
system RMS noise is about 0.7 µm. The sampling rate of the
system is 250 Hz.
Keywords – Position Sensitive Detectors, resolution, lenses,
microsurgery, neural network
I. INTRODUCTION
Vitreoretinal microsurgery and some cell
micromanipulation tasks are fields that require very high
tool positioning accuracy. In vitreoretinal microsurgery,
there appears to be a consensus for the accuracy requirement
of 10 µm [1] whilst cell micromanipulation tasks require
accuracy ranging from micrometers to nanometers
depending on the applications.
Many involuntary and inadvertent components are present
in normal human hand movement. These include
physiological tremor [2], jerk [3]and low frequency drift [4].
It has been reported that the vector magnitude of
physiological tremor during the most delicate part of the
procedure is measured to be 38 µm RMS [5].
Intelligent hand-held instruments have been or are being
developed [6] to cancel tremor during microsurgery. We are
also developing a similar instrument in our laboratory. In
Tun Latt Win is with the school of Mechanical and Aerospace
Engineering, Nanyang T echnol ogical Univer sity, S ingapor e (phon e: 65-
9021-1975; fax: 65- 6793 5921; e-mail: wintunlatt@ntu.edu.sg ).
U-Xuan Tan is with the school of Mechanical and Aerospace
Engineering, Nanyang T echnological University, Singapore (e-mail:
TANU0002@ntu.edu.sg ).
Cheng Yap Shee is with the school of Mechanical and Aerospace
Engineering, Nanyang T echnological University, Singapore (e-mail:
cyshee@ntu.edu.sg )
Wei Tech Ang is with the school of Mechanical and Aerospace
Engineering, Nanyang T echnological University, Singapore (e-mail:
wtang@ntu.edu.sg ).
order to evaluate accuracy of such systems, more accurate
systems need to be developed.
There are many commercial systems commonly used in
tracking surgical instruments, including Optotrak (Northern
Digital, Waterloo, Canada), Isotrack II (Polhemus,
Colchester, Vt.) and miniBIRD. But, these systems cannot
provide adequate accuracy and resolution for microsurgery
and some cell micromanipulation applications.
To address the above issues, Riviere, C.N et al. developed
ASAP (Apparatus to Sense Accuracy of Position) and
MADRID (Measurement Apparatus to Distinguish
Rotational and Irrotational Displacement) [7-9] systems to
track microsurgical instrument motion in micro-scale. PSDs
and lenses formed the main components of these systems
whereby the accuracy is limited by nonlinearity inherent in
PSDs and lenses.
It is well known that lens introduces distortion. PSD also
introduces distortion effects that vary fr om PSD to PSD
(Figure 1) and these distortion effects play a significant part
at submicron and nanometer levels. The overall nonlinearity
is the combination of distortion effects from the lenses and
PSDs.
Figure 1. Distortion effect of PSDs
Accuracy is worse without calibration because of the
imperfect alignment and assembly of the components. If
accuracy and resolution can be improved by eliminating
inherent nonlinearity and increasing signal to noise ratio
respectively, the optical Micro Motion Sensing System
(M2S2) can be extended to evaluate the accuracy of cell
micromanipulation systems. This motivates us to develop a
better tracking system and calibration method to eliminate
nonlinearity.
Design and Calibration of an Optical Micro Motion Sensing System
for Micromanipulation Tasks
T. L. Win, U. X. Tan, C. Y. Shee and W. T. Ang, Member, IEEE
2007 IEEE International Conference on
Robotics and Automation
Roma, Italy, 10-14 April 2007
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II. METHODOLOGY
A. System Development
We propose to use PSDs, instead of expensive high
resolution and speed cameras as PSDs offer adequate high
accuracy and frequency response at a lower and affordable
cost. While CCD camera’s resolution is limited by the
number of pixels, that of PSD is limited by the noise floor of
the system. There are four output electrodes for a two-
dimensional PSD - two for each axis. The current produced
at an electrode depends on the intensity and position of the
light spot on the PSD. With regards to an electrode pair, the
electrode located nearer to the light spot centroid will
produce more current than the other. With this phenomenon,
the position of the light spot centroid can be calculated once
the current produced is known. Our system consists of two
PSDs, three lenses, one IR diode, a white reflective ball and
a data acquisition (DAQ) system as shown in Figure 2. and
Figur e 3. Th e overall system block diagram is shown in
Figure 4.
Figure 2. Schematic Diagram (Top View) of the system
A white reflective ball (Diameter=6mm) from Gutermann
(Art. 773891), which is to be tracked, is attached to a non-
reflective black color rod of 1 mm in diameter. IR light is
shined onto the workspace containing the ball so that IR
light reflected by the ball would impinge on the PSDs. The
light spot positions on the respective PSDs are affected by
the ball position.
Two PSD modules (DL100-7PCBA3) each with a 10mm
square sensing area from Pacific Silicon Sensor Inc are used
in our system and placed orth ogonally to each other (Figur e
2. and Figure 3. ). There are four bipolar analog voltages
outputs from each PSD module - X position (Xdiff) and Y
position (Ydiff) of the light spot centroid as well as the total
X current (Xsum) and Y current (Ysum). The schematic
diagram of a PSD module is shown in Figure 5. The sum
outputs (Xsum, Ysum) are used to normalize the difference
outputs (Xdiff and Ydiff) so that the X and Y positions become
independent of fluctuations in light spot intensity. The
position calculation is shown in the equations below.
Normalized X position = (X1-X2)/(X1+X2) = Xdiff /Xsum
Normalized Y position = (Y1-Y2)/(Y1+Y2) = Ydiff /Ysum
Figure 3. Micro Motion Sensing System (MMSS)
Figure 4. Overall block diagram of the system (MMSS)
Figure 5. Schematic Diagram of a DL100-7PCBA3 PSD module.
Voltage signals from each output of the PSD modules are
sampled and digitized at 16 bits, 16.67 kHz using the PD2-
MF-150 data acquisition card from United Electronic
Industries, Inc. Shielded cables are used to connect every
PSD module output to the data acquisition card for better
noise suppression. The power and signal cables are also
separated to eliminate coupling of power line noise and
signals. The digitized samples are first filtered with an 8th
PSDs
Ball to be
detected
Bi-convex Lenses
Reflected Lights
Lens used to
converge
divergi ng IR
lights
PSD modules are
placed inside
X1 Y1
X2 Y2
(
Ydif
f
)
(
Ysu
m
)
(
Xdif
f
)
(
Xsu
m
)
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order Butterworth low-pass software filter having a cutoff
frequency of 15Hz and subsequently averaged every 67
samples. Thus, the sampling rate is 16.67k/67=248Hz. The
unfiltered and filtered signal noise is about 10mV and less
than 0.5mV respectively. After averaging, the filtered
signals are used to compute the respective normalized
position values - x1, z1, y2 and z2. Finally, the normalized
values are applied to the input of a feedforward neural
network to obtain the absolute position x, y and z.
Bi-convex lenses (Diameter=25.4mm, f=25.4mm) from
Thorlabs (LB1761-B) are used to focus the reflected IR light
onto the PSDs. These anti-reflection lenses also reduce
surface reflection to maximize the IR light intensity striking
the PSDs. Without the bi-convex lenses, the reflected IR
light would impinge on the PSDs in such a manner that the
position of the ball position cannot be determined correctly.
The system resolution is determined by the signal to noise
ratio (SNR). Higher system SNR would offer better
resolution. The intensity and wavelength of reflected IR light
striking the PSDs are important factors in increasing SNR.
The intensity must be high enough whilst the IR light
wavelength must fall within the most sensitive region of the
PSD spectral response. We choose OD-669 IR diode from
Opto Diode Corp. as the IR light source because it has the
highest power output and its peak emission wavelength is
within the most sensitive region of the PSD spectral
response. Since radiation of IR light from OD-669 is
diverging, an aspheric condenser lens (D=27mm,
EFL=13mm) from Edmund Optics is placed in front of the
IR diode to converge the IR rays onto the workspace. The
lens also enhances the IR intensity by more than 2 times.
The IR diode is strobed at 500Hz (Duty cycle=50%) thereby
increasing the maximum current limit of the IR diode. This
results in a higher IR emission intensity and thereby,
improving the SNR. The strobe timing of the IR diode is
controlled with a PIC microcontroller via a field effect
transistor (FET).
B. System Calibration
Calibration of the system can be performed by various
approaches such as physical modeling, brute force method in
which look-up table (LUT) and interpolation are used, neural
network, etc. Physical modeling can give the best accuracy if
done accurately and that requires thorough understanding of
the physical behavior of each individual component. LUT
with interpolation method requires calibration data points be
stored in memory and needs more data points for higher
accuracy.
We propose to employ a multilayer neural network
approach for this application because it eliminates the need
to know individual component’s behavior; uses a reasonable
span of time for a trained network to determine the output
and can approximate any arbitrary continuous function to
any desired degree of accuracy [10].
The calibration data points are obtained by moving the
ball being tracked to known locations and using the
corresponding values from th e two PSDs. Movement of th e
ball is automatically done by controlling motorized precision
stages using software developed in-house. X-Y-Z stepper-
motorized precision translation stages (8MT173-20 from
Standa) are used for our calibration. According to the
specifications, 1 step movement of the stepper motors is
equivalent to 1.8 degrees rotational and 1.25 micrometer
translational movement respectively. The step angle
accuracy is 5%. Since our data points spacing is 500
micrometers which is an integer multiple of 1.25
micrometers, the accuracy is 1.25*0.05= 62 nanometers. The
travel range is 20mm. The calibration setup for the system is
shown in Figure 6.
Figure 6. MMSS system and its calibration setup
The exact region of workspace is not initially known due
to imperfect alignment and assembly of the PSDs and lenses.
A 20mm cubical region is initially scanned with a step
increment of 1mm between two successive points to cover
the workspace region. The 20mm cubical region is large
enough for estimating the workspace region based on our
knowledge of the system configuration and sensing area of
the PSDs.
Matlab is then used to plot these initial calibration data
points in a 3 dimensional graph to determine the workspace
region.
We then trained the neural network using calibration data
points spaced 0.5mm apart for the range of 6.5mm in each
axis. Therefore, total number of calibration points used is
13x13x13=2197. The training data is limited within a 6.5
mm cubical region to attain accurate neural network output
since the degree of nonlinearity outside the said region is too
high. This high degree of nonlinearity is assumed to be due
to the imperfect alignment and distortion effects of lenses
and PSDs. As such, the useful working region is limited to
6.5mm cubical region although 10mm square sensing area
Motorized precision
translation stages
Reflective ball Vibrati on isolation ta ble
Lenses
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PSDs is used. The normalized positions obtained at each
calibration point and their corresponding absolute positions
are used as training and target values respectively for neural
network training. The network was also trained in a similar
manner using calibration points with 1 mm spacing.
In order to improve the quality of the acquired data, after
every step movement, sufficient time is provided for
mechanical vibrations generated by the motion of the
motorized stages to settle down before acquiring data. In
addition, the system including the motorized stages is placed
on an anti-vibration table to suppress floor emanated
vibrations.
In order to ensure that calibration is not affected by
temperature, the system is switched on for about 50 minutes
before commencing calibration so that the IR diode attained
a steady operating temperature state.
C. Software Implementation and Integration
LabVIEW, a signal acquisition, measurement and analysis
software from National Instrument Corporation, is used to
acquire, filter, and process signals from the PSDs. Neural
network function is implemented in C language and
integrated within the LabVIEW based program developed.
Since acquisition takes place continuously while the IR
diode is strobing, the acquired signals contained voltage
values whilst the IR diode was switched on (ON-time) and
off (OFF-time). However, only voltage values acquired
during ON-time contained relevant position information of
the ball being tracked. Therefore, acquired voltage values
are separated and only ON-time values used for subsequent
processing. The segregation of ON-time and OFF-time
voltage values is carried out using a software threshold
approach described hereafter .
In this approach, a transistor-transistor logic (TTL) signal
having the same switching frequency and phase as the signal
controlling the IR diode is used as the reference signal. TTL
is about 5V and 0V during ON-time and OFF-time
respectively. A data acquisition channel is used to acquire
the TTL signal and subsequently, compared with a
predefined threshold value of 4V.
One scan is defined as a period during which sampling
takes place channel after channel for all active data
acquisition channels. In a scan, if the acquired TTL value is
above the threshold, all voltage values acquir ed during that
scan are regarded as ON-time values and used for
processing. On the other hand, if the TTL value is below the
threshold, all acquired voltage values are considered as OFF-
time values and not used for processing.
There is a fixed amount of time-delay between sampling
of each successive channel. So, there is a possibility that
some channels’ values are OFF-time values while the TTL
signal indicates ON-time. To make sure that only ON-time
values are used in processing, the first scan of any IR diode
switching cycle in which the TTL signal indicates ON-time
is not used.
D. Mapping by a Feedforward Neural Network
We propose a multilayer artificial neural network model
because PSD calibration is a nonlinear problem that cannot
be solved using a single layer network [11]. The
determination of proper network architecture for the PSD
system calibration is ambiguous like other neural network
applications. The best architecture and algorithm for a
particular problem can only be evaluated by experimentation
and there are no fixed rules to determine the ideal network
model for a problem. However, variations in architecture
and algorithm affect only the convergence time of the
solution.
The network model we employed includes 4 input
neurons, and 3 output neur ons. The number of neurons in the
hidden layers and the number of layers are varied to achieve
the best accuracy. Four neurons are used in the input layer
because there are four inputs; x1, y1, y2 and z2. Three
neurons are used in the output layer for the three
coordinates; x, y and z. Transfer functions of all the layers
are log-sigmoid except for the output layer, which is a linear
function. The block diagram of the model is shown in Figure
7.
Figure 7. Nonlinear mapping provided by a multilayer feedforward neural
network
III. RESULTS
The improvement in linearity after the calibration using a
neural network is shown in figure 8(b) and 9(b). The amoun t
of improvement is shown in Table I. All results presented in
the tables are obtained from the neural network trained using
points with 0.5mm spacing. The neural network consists of
4, 20, and 20 neurons in the first, second, and third hidden
layers respectively and 3 neurons in the output layer. The
results obtained using training points having 1mm spacing
are not as good as those shown in the tables.
Percentage errors (RMSE (%) and Maximum Error (%))
are calculated over the range of 6.5mm cubical region. To
determine the measurement errors at each point, measured
values at these locations are subtracted from their respective
true values. True values are known by moving the ball to be
tracked to known locations using the motorized stages.
Then, average RMS error and maximum error values are
calculated using errors at all the points. The RMS errors
calculated within different sizes of cubical regions are
shown in Table II.
Multilayer
Feedforward
Neural
Network
x1, z1,
y2
and z2
values
x, y and z
position
of
reflective
ba
ll
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(a)
(b)
Figure 8. 3D Comparison for the amount of non-linearity (a) before
calibration, a nd (b) after neural network calibration.
In order to determine resolution of the system, a one
minute recording of a stationary ball position is obtained.
The RMS noise is found to be 0.7µm.
The resolution of the system with a larger ball (diameter
10mm) is also tested. The RMS noise for a one minute
position recording is discovered to be 0.5µm.
(a)
(b)
Figure 9. 2D Comparison for the amount of non-linearity (a) before
calibration, a nd (b) after neural network calibration.
TABLE I. ERROR DUE TO NONLINEARITY BEFORE CALIBRATION AND
AFTER CALIBRATION (%)
6500
RMSE
Before Calibration After Calibration
RMSE (µm) 354.89 10.22
(%)
6500
RMSE 5.46 0.16
Maximum Error (µm) 1483.10 74.40
(%)
6500
MaxError 22.82 1.14
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TABLE II. RMS ERROR CALCULATED WITHIN DIFFERENT SIZES OF
CUBICAL REGION
Cubica l Regi on (mm3) RMSE (µm)
1.5 3.49
2.5 3.99
3.5 4.70
4.5 5.40
5.5 6.39
6.5 10.22
IV. DISCUSSION
The RMSE values stated in Table II show that errors
increase with larger working region. This suggests that
nonlinearity is less severe near to the center of the
workspace and manipulation tasks should be performed near
to the centre for better tracking accuracy.
RMS noise is lesser with a bigger ball as more reflected
IR rays are produced thereby increasing the intensity of the
IR light striking the PSDs. Although a smaller ball size is
preferred for microsurgical trainings, some applications that
require better resolution and where the ball size is not a
major concern, can use a larger diameter ball.
Since the system employs optical approach, line-of-sight
between PSDs and the ball has to be maintained. This
hampers the use of this system for tracking in actual
microsurgical operations. However, for accuracy evaluation
of microsurgical instruments or performance of surgeons,
the setup can be arranged such that the IR light path between
PSDs an d the ball will not be blocked.
Comparing to other similar systems [7-8], our system
offers better performance in terms of sampling rate and
resolution. The sampling rate of our system is 250 Hz while
other similar systems are 150 Hz. The resolution of our
system is 0.7µm while other systems are in the region of
1µm. Comparison of accuracy against other systems cannot
be made because other systems do not describe overall
system accuracy.
V. CONCLUSION
We have developed a real-time optical micro-motion
sensing system that utilized a multi-layer feedforward neural
network approach for its nonlinear calibration. The results
suggested that nonlinearity is eliminated thereby greatly
improving the linearity. More subsequent experiments
involving varying architectures and calibration data is
expected t o yield better results. The future work includes
improving resolution by providing additional light sources
and utilizing better IR reflective material for the ball (such
as gold).
VI. ACKNOWLEDGMENT
Intelligent Handheld Instrument for Microsurgery &
Biotech Micromanipulation project is funded by Agency for
Science, Technology & Research (A*STAR) and the
College of Engineering, Nanyang Technological University.
The authors thank them for the financial support of this
work.
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