The improvement in the AFM image after applying a Lucy- Richardon
deconvolution algorithm using a new technique for estimating the AFM
tip shape from the square sample
AHMED AHTAIBA
Electrical and Electronic Engineering Department
Sirte University
Sirte
LIBYA
Abstract: - The images measured using AFM are distorted because of the influence of the tip geometry. This
influence let the images do not accurately represent the real shape of the measured particles or cells. Therefore,
it is necessary to reconstruct the AFM tip shape. This paper proposed a new approach (impulse response
technique) to reconstruct the tip shape from a square sample. Once the tip shape is known, erosion or
deconvolution process has been carried out between the estimated tip shape and the distorted image. The
experimental results and the computer simulations validate the performance of the proposed approach in which
it illustrates that the AFM image accuracy has been greatly improved. Also, we have compared the proposed
algorithm with the blind tip estimation algorithm using computer simulations and real AFM images, and our
algorithm has given better results. It is worth mentioning here that the blind tip estimation is the industrial and
research standard algorithm for the restoration of AFM images.
Key-Words: - AFM, image restoration, tip estimation, Square sample, deconvolution.
Received: June 11, 2022. Revised: August 16, 2023. Accepted: September 17, 2023. Published: October 4, 2023.
1 Introduction
The Atomic Force Microscope (AFM) is very
important instrument for use in nanotechnology and
biology since it can be used to measure a variety of
objects such as nano-particles and cells.. An AFM
image is represented as the distorted sample due to
the convolution effect, which produced by the finite
size of the AFM tip. The image restoration problem
has been studied by many researchers in terms of
determining the cantilever tip shape for the AFM
and then using it to restore the AFM images using a
deconvolution algorithm. This formulation of the
image restoration problem ignores the other
parameters that affect the image acquisition process
in the AFM such as the scanning speed, the response
of the x, y and z piezo materials, and the bandwidth
of the feedback loop system. As is well-known in
digital image processing theory, the impulse
response of a linear time invariant system “fully
characterises” this system. This implies that our
proposed algorithm aim of finding the impulse
response of the AFM should take all these
parameters inherently into consideration and should
produce better and more faithful image
restoration algorithm than those that already exist in
the literature.
The first essential step in front-end digital image
processing systems is that of capturing digital
images. Many distortions occur during the image
acquisition process and these distortions should be
eliminated or alleviated using image restoration
algorithms. Examples of systems where these
distortions occur are in astronomical imaging using
telescopes, confocal microscopy, computed
tomography (CT) scanners and many other
applications. These are similar research problems to
the image restoration of AFM images [7-9].
In this paper we proposed a new method ( impulse
response technique), which is suitable for estimating
the AFM tip from the AFM image of the square
sample. Computer simulation and experimental
results have been used for estimating the AFM tip
shape. Then, in computer simulation an erosion
operation has been used between the estimated
AFM tip and the AFM image for obtaining more
accurate an AFM image. In experimental results, a
Lucy- Richardson deconvolution algorithm [1-2]
has been used between the estimated AFM tip and
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DOI: 10.37394/232014.2023.19.11
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the AFM image for improving the distorted AFM
image.
2 AFM tip estimation
This paper presents a new technique for estimating
the AFM tip shape from the square sample using an
impulse response method. The proposed approach
uses a tip characterizer ( square sample) [3-5]. The
AFM image of the square sample is considered as a
convolution effect between the shape of the sample
and the tip. Thus, the AFM tip can be reconstructed
by eliminating the effects of the tip characterizer
topography from the AFM image of the square
sample. We have used a tip characterizer consists of
a standard square sample and the impulse response
approach for eliminating the effects of the tip
characterizer geometry from the AFM image. In this
paper we will show that the proposed approach of
using an impulse response method is effective for
estimating 3-D tip geometry, which then can be
used in the restoration of more accurate AFM
images.
2.1 Computer Simulation
In computer simulation, we constructed the
computer models for AFM tip and the sample in
which the tip has a pyramidal shape and the sample
has square shape as depicted in Fig 1(a) and 1(b),
respectively. The image of the square sample is
represented by a dilation operation between the
square sample and a pyramidal tip. It is clear from
Fig. 1(c) that after applying a dilation operation
between the sample and tip, the AFM image is
distorted by AFM tip and does not accurately
represent the sample. In order to improve AFM
image, it is necessary to obtain information about
the AFM tip shape. Once the tip shape is known, the
opposite operation of the dilation which is the
erosion can be applied between the distorted AFM
image and the reconstructed tip to remove this
distortion.
Then, we threshold the image of the square sample
as shown in Fig. 1(c). The goal of thresholding is to
segment the grey level image into two regions,
background and objects. The optimal threshold
value can be considered as a grey level that
separates an object region and a background region
without compromising the object integrity [6].
Fig.1. Shows the Simulation results of impulse response
technique using square sample.
Next, we determined the outer boundary of the
square using the edge canny detection which is
known to many as the optimal edge detector. Once
the outer boundary is known as illustrated in Fig
1(d). The pixels that belong to the image of the
square are eliminated and the tip data that are
available around the eliminated square have been
moved to the centre of square. The resultant image
which illustrated in Fig. 2. is the impulse response
of the AFM.
Fig. 2. Illustrates the Simulation results of the 3D image
of reconstructed tip.
Fig. 3(a) and 3(b) illustrates the three dimensional
image of the square sample and the reconstructed
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image after applying an erosion operation,
respectively. An erosion operation has been carried
out between the reconstructed AFM tip and the
dilated image of the square. The result of an erosion
operation, which represents the reconstructed image
is improved.
3 Experimental Results
3.1 Experimental results for estimating 3-D
AFM tip
The three- dimensional impulse response of the
AFM could be determined by performing the
following steps. Measuring a standard AFM
calibration sample using the AFM, shown in
Fig 4(a), that contains a square with a priori
faithfully known dimension. The 2-D
topographical image produced by AFM for the
sample contains the square profile, but this is
broadened due to the convolution between the
tip and the square. Digital image processing
such as the thresholding and canny edge
detection have been used to determine the exact
location of the square in the image as illustrated
in Fig 4(b) and 4(c), respectively. As the height
of the square is a priori known and those pixels
that represent the square has been eliminated by
moving the inherent image distortions that have
been introduced due to convolution effect to the
centre of the image of the square. The resultant
image which is considered as the three-
dimensional AFM tip using the impulse
response method is illustrated in Fig 4(d).
Fig.4. Shows the experimental results of impulse
response technique using a real sample that contains
squares.
4 Restoration of experimental AFM
images
The first essential step in front-end digital image
processing systems is that of capturing digital
images. Many distortions occur during the image
acquisition process and these distortions should be
eliminated or alleviated using image restoration
algorithms. Examples of systems where these
distortions occur are in astronomical imaging using
telescopes, confocal microscopy, computed
tomography (CT) scanners and many other
applications. These are similar research problems to
the image restoration of AFM images [7-9].
Restoration of subsequent images produced by the
AFM can be carried out by performing a
deconvolution process between the raw AFM image
that is acquired and the impulse response that was
found as detailed in the previous section. Many
algorithms can be used such as the Wiener,
Regularized filter, Lucy- Richardon, and Blind
deconvolution algorithms[10-11].
Fig. 5(a) and 5(b) illustrate the blurred AFM image
and the AFM image after applying the
deconvolution process, respectively. As a result the
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)(b
Fig. 3. Depicts the simulation results of impulse
response technique using an erosion process.
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AFM image after applying the deconvolution
algorithm is improved by removing the effects of
the AFM tip from the blurred image.
Fig. 5. Illustrates the experimental results of impulse
response technique using a Lucy- Richardson
deconvolution for reconstructing a real sample that
contains squares.
Fig. 6(a) depicts the AFM image of a real sample
that contains pillars measured using the Atomic
Force Microscope in our lab. Where Fig. 6(b)
illustrates the AFM image after applying a Lucy-
Richardson deconvolution ( the restorated image). It
is clear that from the restorated AFM image the
distortion is eliminated and the image is sharper
than the blurred AFM image.
Fig. 6. depicts Comparison between the Experimental
AFM image and the restorated AFM image.
Fig. 7. the AFM image of a selected square from
a real sample that contains squares is shown on the
left. The restorated AFM image after applying a
Lucy- Richardon deconvolution algorithm is
depicted on the right. As a result the distortion in the
resorted image is reduced compared with the
original image.
Fig. 7. Illustrates the experimental results of impulse
response technique using a Lucy-Richardson
deconvolution to restore the image of a real square
sample.
4 Conclusion
In this paper, A real sample that contains pillars
has been measured using an AFM. The original
image was captured in contact mode AFM when the
tip scans the sample.
The tip estimation technique using square sample
has been demonstrated to be a useful tool in
restorating the AFM images. Both the computer
simulation and experimental results have shown the
improvement in the AFM image after applying an
erosion operation and a Lucy- Richardon
deconvolution algorithm.
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Contribution of Individual Authors to the
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Policy)
The author contributed in the present research, at all
stages from the formulation of the problem to the
final findings and solution.
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Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The author has no conflict of interest to declare that
is relevant to the content of this article.
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