Distortion compensation technique for high resolution microscopy
The paper represents the technique for distortion compensation in digital images from high resolution optical microscopes. This technique is based on approximation of necessary pixel shifts as a power function that can be identified using small set of data from distorted digital images of diffractio...
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| Published in: | Semiconductor Physics Quantum Electronics & Optoelectronics |
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| Date: | 2003 |
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| Format: | Article |
| Language: | English |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2003
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| Cite this: | Distortion compensation technique for high resolution microscopy / V.N. Borovytsky // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2003. — Т. 6, № 4. — С. 517-519. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860043235218423808 |
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| author | Borovytsky, V.N. |
| author_facet | Borovytsky, V.N. |
| citation_txt | Distortion compensation technique for high resolution microscopy / V.N. Borovytsky // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2003. — Т. 6, № 4. — С. 517-519. — Бібліогр.: 8 назв. — англ. |
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| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | The paper represents the technique for distortion compensation in digital images from high resolution optical microscopes. This technique is based on approximation of necessary pixel shifts as a power function that can be identified using small set of data from distorted digital images of diffraction gratings. The experimental studies confirmed efficiency of the proposed technique for decreasing distortion till a level of spatial discretization.
|
| first_indexed | 2025-12-07T16:57:23Z |
| format | Article |
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517© 2003, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Semiconductor Physics, Quantum Electronics & Optoelectronics. 2003. V. 6, N 4. P. 517-519.
PACS: 07.07.D.42.79.P.Q
Distortion compensation technique
for high resolution microscopy
V.N. Borovytsky
Information Software Systems Ltd, 15 Bozhenko str., 03680 Kyiv, Ukraine
Abstract. The paper represents the technique for distortion compensation in digital images
from high resolution optical microscopes. This technique is based on approximation of
necessary pixel shifts as a power function that can be identified using small set of data from
distorted digital images of diffraction gratings. The experimental studies confirmed efficiency
of the proposed technique for decreasing distortion till a level of spatial discretization.
Keywords: distortion, optical microscope, digital image, pixel shift.
Paper received 20.11.03; accepted for publication 11.12.03.
1. Introduction
Optical microscopy has a wide field of applications in-
cluding medicine, material science, semiconductor indus-
try, machine building and etc [1,2]. Implementation of
digital cameras and image processing software is one of
the most perspective tendencies in optical microscopy [1].
Digital cameras installed on microscopes and attached
to personal computers with image processing software
make possible fast and effective capturing, saving, trans-
mitting and processing of digital images [1].
Modern digital cameras have more than million pho-
tosensitive cells that are located with sub-micron accu-
racy in image plane of a microscope [3]. Thus small im-
age corruptions caused by distortion of microscope op-
tics become visible in digital images even a human ob-
server can not see these small distortion. Good micro-
scope optics has distortion in range 1�2 % and it can
dramatically reduce precision of measuring locations
and dimensions of large objects in digital images [2]. Thus
the problem of distortion compensation becomes actual
for optical microscopy.
2. Analysis of known techniques for distortion
compensation
The known techniques for distortion compensation are
based on operations like pixel shifts depending on pixel
coordinates [4�6]. The necessary shifts are calculated
using a distorted images of two dimensional periodical
test-objects � grids, matrices of circles, boxes, points and
etc. But direct application of these techniques for high
resolution optical microscopy is difficult. First, two di-
mensional test-objects with micron dimensions of elements
and sub-micron accuracy of their locations are extremely
expensive and they are not widely used in microscopy
laboratories. Second, digital images produced by opti-
cal microscopes have sufficient non-uniformity of inten-
sity distribution. It introduces errors in binarization of a
whole digital image and as a results pixel shift value can
not be calculated for each pixel in a digital image. Third,
for calculation of necessary pixel shifts and their appli-
cation to digital images a user has to purchase the expen-
sive software packages for microscopy such as Image Pro,
Clemex, ASIS, Matrox Image Library and the others.
Due to the mentioned reasons the distortion compensa-
tion using the known techniques becomes expensive and
complicated procedure.
3. The proposed technique for distortion com-
pensation
To overcome the disadvantages of the known techniques
the new interesting approach has been found. The core
idea of this approach is identification of pixel shift func-
tion using a small set of data from distorted images of a
diffraction gratings. This pixel shift function in form of a
displace mask for Adobe PhotoShop can be implemented
to distorted images to reduce distortion [4,7]. The com-
pensation procedure requires the following operations:
518
SQO, 6(4), 2003
V.N. Borovytsky: Distortion compensation technique for high resolution microscopy
1. A set of digital images of vertical and horizontal
diffraction gratings has to be prepared. The diffraction
gratings with spatial periods of 300�1000 lines per mm
are widely used in optical laboratories. They are not very
expensive and they have sub-micron accuracy of line
width, pitch and location.
2. The center zone in these images is considered as a
reference one. In this zone an average value of spatial
period of gratings in number of pixels can be calculated.
It has to note that distortion appears in boundary zones
of digital images [2, 4, 8]. The central zone of image can
be considered as a zone without distortion.
3. For the boundary zone necessary pixels shifts
should be identified for a number of pixels. These pixel
shifts are equal to difference of pixel coordinated in a dis-
torted digital image and in a non distorted one (Fig. 1):
( )
( ) ,,
1,
O
O
O
ypnyyyxy
x
pn
y
xx
y
y
xxyxx
Y
Y
−⋅=−=∆
⋅
−
⋅
=−⋅=−=∆
(1)
where ∆x(x,y) , ∆y(x,y) � the necessary pixel shifst as a
function of pixel coordinates in a distorted digital image,
x, y � the coordinates of the pixel in a distorted digital
image,
xO, yO � the coordinates of the pixel in a non-dis-
torted digital image,
n, pY � the number of lines from a center of the digital
image till the point (x,y) and the average value of spatial
period in pixel of grating (Fig. 1).
4. The pixel shift function can be identified using the
set of data about necessary pixel shifts in various pixels
of digital images. The best fit power function is good
formula for approximation of the pixel shift function be-
cause according to optical theory the geometrical distor-
tion can be characterized by a power function with axial
symmetry [8]. It is obvious that this axial symmetry re-
mains only in case of square shape of photosensitive cells
and equal spatial periods along axises OX and OY in a
digital camera. The regression analysis of the data (1)
helps to calculate the parameters of the pixel shift func-
tions:
( )
( )
PB
PA
d
yx
Byxy
d
yx
Ayxx
+
⋅⋅=∆
+
⋅⋅=∆
22
22
2,
2,
(2)
where A, B, PA, PB � the parameters of the pixel shift
functions that have to be calculated during search the
best fit function for the data set (1), d � diagonal of a
digital image:
22
MM yxd +=
xM, yM � the dimensions of a digital image in pixels.
5. The pixel shift functions (2) can be represented in
form of a pixel displace mask for the widely used image
processing software package Adobe PhotoShop [7]. This
displace mask uses different color channels for coding
necessary pixel shifts in horizontal and vertical direc-
tions:
( )( )
( )( )
255
5.0,5.0128int
5.0,5.0128int
,
,
,
=
⋅−⋅−∆⋅+=
⋅−⋅−∆⋅+=
ji
MMji
MMji
b
yyxxykg
yyxxxkr
(3)
where ri,j , gi,j , bi,j � the color values of i, j � pixels of 24-
bit color displace mask for distortion compensation [7],
i, j � the pixel coordinates, k � the coefficient for getting
values in range [�128, +128], int( ) � the function for
conversion of real values into integer ones.
Generation of a pixel displace mask (3) can be done
by any mathematical software packages such as
MathCAD, MatLab only once for each combination of a
microscope optics and a digital camera.
6. The generated displace mask (3) has to be applied
to the distorted digital images. Adobe PhotoShop makes
this operation quickly. This operation can be easily ap-
plied for a set of distorted digital images.
(
(
x
x
O,
,
y
y
O)
)
Fig. 1. Digital images of gratings with distortion (dark color)
and without it (bright color). The pixel coordinates (x, y) in a
distorted image correspond to the pixel coordinates (xO, yO) in a
non-distorted one, data for distortion compensation is done by
collection of this information from various pixels marked as black
points in a distorted image.
V.N. Borovytsky: Distortion compensation technique for high resolution microscopy
519SQO, 6(4), 2003
Conclusions
The proposed distortion compensation techniques is
based on identification of pixel shift function using a small
set of data from distorted digital images of diffraction
gratings (1�3). The experimental studies have confirmed
that this technique makes possible to reduce a geometri-
cal distortion in high resolution microscopy from 0.6 %
till 0.055 % (Fig. 2).
References
1. W. G. Hand, A practical guide to digital microscopy //
Photonics Spectra, No10. p.100-104 (2001).
2. G.E. Skvortzov, V.A. Panov, N.I. Polakov, L.A. Fedin, Mic-
roscopes. � L.: Mashinostroenie, 1969.
3. B. L. Benamati, In search of ultimate Image Sensor // Photonics
Spectra, No 9. p. 132�136 (2001).
4. Harri Ojanen, Automatic coorection of Lens distortion using
digital image processing // Preprint of the State University of
New Jersey, Mathematical department, Rutgers. Preprint lo-
cation is www.math.rutgers.edu/~ojanen/
5. X. Wang, R. Ning, Accurate and efficient image intensifier
distortion correction algorithm for volume tomo graphic
angionaphy // Optical Engineering, 37(3). p. 997-983 (1998).
6. V. Krzyzanek, Analysis of continiously distortted quasi-peri-
odic images: two-dimensional reconstruction of S-layers of
cyanobacteria // Optical Engineering, 39(4), p. 872-878 (2000).
7. A.D.Greenberd, S.Greenberd, Fundamental PhotoShop,
Berkeley: Osborne McGraw-Hill, 1997.
8. B.N. Begynov, N.P. Zakaznov, Theory of optical systems. �
M.: Mashinostroenie, 1973.
a
b
Fig. 2. Boundary fragments of digital images before (a) and after
(b) distortion compensation (fragment dimensions in pixels � width
3040×height 230 � corresponds to a field in an object plane �
0.23×0.018 mm, image fragments are scaled in horizontal direc-
tion to make distortion 0.6 % visible, a black reference lines
indicates how gratings images differs from straight lines before
and after distortion compensation).
|
| id | nasplib_isofts_kiev_ua-123456789-118079 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2025-12-07T16:57:23Z |
| publishDate | 2003 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Borovytsky, V.N. 2017-05-28T16:37:17Z 2017-05-28T16:37:17Z 2003 Distortion compensation technique for high resolution microscopy / V.N. Borovytsky // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2003. — Т. 6, № 4. — С. 517-519. — Бібліогр.: 8 назв. — англ. 1560-8034 PACS: 07.07.D.42.79.P.Q https://nasplib.isofts.kiev.ua/handle/123456789/118079 The paper represents the technique for distortion compensation in digital images from high resolution optical microscopes. This technique is based on approximation of necessary pixel shifts as a power function that can be identified using small set of data from distorted digital images of diffraction gratings. The experimental studies confirmed efficiency of the proposed technique for decreasing distortion till a level of spatial discretization. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Distortion compensation technique for high resolution microscopy Article published earlier |
| spellingShingle | Distortion compensation technique for high resolution microscopy Borovytsky, V.N. |
| title | Distortion compensation technique for high resolution microscopy |
| title_full | Distortion compensation technique for high resolution microscopy |
| title_fullStr | Distortion compensation technique for high resolution microscopy |
| title_full_unstemmed | Distortion compensation technique for high resolution microscopy |
| title_short | Distortion compensation technique for high resolution microscopy |
| title_sort | distortion compensation technique for high resolution microscopy |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/118079 |
| work_keys_str_mv | AT borovytskyvn distortioncompensationtechniqueforhighresolutionmicroscopy |