Subpixel Detection of Spectrum Images by Photodiode Structures
The present paper is devoted to the issues of enhancing the photometer’s resolving power when the spectrum images are detected by linear image sensors on emission spectrometers. Here we focus our attention on the case where the size of a photodiode structure pixel exceeds the width of the point-spre...
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| Цитувати: | Subpixel detection of spectrum images by photodiode structures / A. Yegorov, V. Yegorov, S. Yegorov // Радиофизика и радиоастрономия. — 2009. — Т. 14, № 1. — С. 77-83. — Бібліогр.: 10 назв. — англ. |
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Yegorov, A. Yegorov, V. Yegorov, S. 2010-05-28T13:27:28Z 2010-05-28T13:27:28Z 2009 Subpixel detection of spectrum images by photodiode structures / A. Yegorov, V. Yegorov, S. Yegorov // Радиофизика и радиоастрономия. — 2009. — Т. 14, № 1. — С. 77-83. — Бібліогр.: 10 назв. — англ. 1027-9636 https://nasplib.isofts.kiev.ua/handle/123456789/8439 The present paper is devoted to the issues of enhancing the photometer’s resolving power when the spectrum images are detected by linear image sensors on emission spectrometers. Here we focus our attention on the case where the size of a photodiode structure pixel exceeds the width of the point-spread function of an optical device. It is shown that a combination of the parallel detection of all points of an image with its successive shift relative to a recording structure ensures proper recording of thus obtained image, hence the optical section of the device with an arbitrarily large sensor pixel having no loss of resolution. The problem pertaining to measurement data handling reduces to finding a solution to the inconsistent set of linear equations. An algorithm is suggested for solving the derived system of equations. The results illustrating the operation of this particular algorithm are herewith shown. Работа посвящена вопросам повышения разрешающей способности фотометра при регистрации изображений спектров фотодиодными линейками на эмиссионных спектрометрах. Рассматривается случай, когда размер пиксела фотодиодной структуры превосходит размеры пятна замытия оптического прибора. Показано, что сочетание параллельного способа регистрации всех точек изображения с последовательным его смещением относительно регистрирующей структуры позволяет зарегистрировать полученное таким образом изображение без потери разрешающей способности оптической части прибора при произвольно большом пикселе детектора. Задача обработки результатов измерений сводится к решению несовместной системы линейных уравнений. Предлагается алгоритм решения полученной системы уравнений и приводятся результаты, иллюстрирующие действие этого алгоритма. Робота присвячена питанням покращання роздільної здатності фотометра при реєстрації зображень спектрів лінійками фотодіодів на емісійних фотометрах. Розглянуто випадок, коли розмір піксела фотодіодної структури перевищує розміри плями розмитості оптичного приладу. Показано, що поєднання паралельного способу реєстрації усіх точок зображення з його послідовним зміщенням відносно фотодіодної структури дозволяє зареєструвати одержане таким чином зображення без втрати роздільної здатності оптичної частини приладу за довільно великого піксела детектора. Задача обробки результатів вимірювання зводиться до розв'язання несумісної системи лінійних рівнянь. Запропоновано алгоритм розв'язання одержаної системи рівнянь та наведено результати, що ілюструють дію цього алгоритму. en Радіоастрономічний інститут НАН України Статистическая радиофизика Subpixel Detection of Spectrum Images by Photodiode Structures Субпиксельная регистрация изображений спектров фотодиодными структурами Субпіксельна реєстрация зображень спектрів фотодіодними структурами Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Subpixel Detection of Spectrum Images by Photodiode Structures |
| spellingShingle |
Subpixel Detection of Spectrum Images by Photodiode Structures Yegorov, A. Yegorov, V. Yegorov, S. Статистическая радиофизика |
| title_short |
Subpixel Detection of Spectrum Images by Photodiode Structures |
| title_full |
Subpixel Detection of Spectrum Images by Photodiode Structures |
| title_fullStr |
Subpixel Detection of Spectrum Images by Photodiode Structures |
| title_full_unstemmed |
Subpixel Detection of Spectrum Images by Photodiode Structures |
| title_sort |
subpixel detection of spectrum images by photodiode structures |
| author |
Yegorov, A. Yegorov, V. Yegorov, S. |
| author_facet |
Yegorov, A. Yegorov, V. Yegorov, S. |
| topic |
Статистическая радиофизика |
| topic_facet |
Статистическая радиофизика |
| publishDate |
2009 |
| language |
English |
| publisher |
Радіоастрономічний інститут НАН України |
| format |
Article |
| title_alt |
Субпиксельная регистрация изображений спектров фотодиодными структурами Субпіксельна реєстрация зображень спектрів фотодіодними структурами |
| description |
The present paper is devoted to the issues of enhancing the photometer’s resolving power when the spectrum images are detected by linear image sensors on emission spectrometers. Here we focus our attention on the case where the size of a photodiode structure pixel exceeds the width of the point-spread function of an optical device. It is shown that a combination of the parallel detection of all points of an image with its successive shift relative to a recording structure ensures proper recording of thus obtained image, hence the optical section of the device with an arbitrarily large sensor pixel having no loss of resolution. The problem pertaining to measurement data handling reduces to finding a solution to the inconsistent set of linear equations. An algorithm is suggested for solving the derived system of equations. The results illustrating the operation of this particular algorithm are herewith shown.
Работа посвящена вопросам повышения разрешающей способности фотометра при регистрации изображений спектров фотодиодными линейками на эмиссионных спектрометрах. Рассматривается случай, когда размер пиксела фотодиодной структуры превосходит размеры пятна замытия оптического прибора. Показано, что сочетание параллельного способа регистрации всех точек изображения с последовательным его смещением относительно регистрирующей структуры позволяет зарегистрировать полученное таким образом изображение без потери разрешающей способности оптической части прибора при произвольно большом пикселе детектора. Задача обработки результатов измерений сводится к решению несовместной системы линейных уравнений. Предлагается алгоритм решения полученной системы уравнений и приводятся результаты, иллюстрирующие действие этого алгоритма.
Робота присвячена питанням покращання роздільної здатності фотометра при реєстрації зображень спектрів лінійками фотодіодів на емісійних фотометрах. Розглянуто випадок, коли розмір піксела фотодіодної структури перевищує розміри плями розмитості оптичного приладу. Показано, що поєднання паралельного способу реєстрації усіх точок зображення з його послідовним зміщенням відносно фотодіодної структури дозволяє зареєструвати одержане таким чином зображення без втрати роздільної здатності оптичної частини приладу за довільно великого піксела детектора. Задача обробки результатів вимірювання зводиться до розв'язання несумісної системи лінійних рівнянь. Запропоновано алгоритм розв'язання одержаної системи рівнянь та наведено результати, що ілюструють дію цього алгоритму.
|
| issn |
1027-9636 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/8439 |
| citation_txt |
Subpixel detection of spectrum images by photodiode structures / A. Yegorov, V. Yegorov, S. Yegorov // Радиофизика и радиоастрономия. — 2009. — Т. 14, № 1. — С. 77-83. — Бібліогр.: 10 назв. — англ. |
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Радиофизика и радиоастрономия, 2009, т. 14, №1, с. 77-83
© A. Yegorov, V. Yegorov, S. Yegorov, 2009
Subpixel Detection of Spectrum Images by Photodiode Structures
A. Yegorov, V. Yegorov, and S. Yegorov
O. Ya. Usikov Institute for Radiophysics and Electronics of NAS of Ukraine,
12, Akad. Proskury St., Kharkiv, 61085, Ukraine
Received April 17, 2008
The present paper is devoted to the issues of enhancing the photometer’s resolving power when the
spectrum images are detected by linear image sensors on emission spectrometers. Here we focus our
attention on the case where the size of a photodiode structure pixel exceeds the width of the point-spread
function of an optical device. It is shown that a combination of the parallel detection of all points of an
image with its successive shift relative to a recording structure ensures proper recording of thus obtained
image, hence the optical section of the device with an arbitrarily large sensor pixel having no loss of
resolution. The problem pertaining to measurement data handling reduces to finding a solution to the
inconsistent set of linear equations. An algorithm is suggested for solving the derived system of equa-
tions. The results illustrating the operation of this particular algorithm are herewith shown.
Introduction
Optical image sensors offer a certain set of
parameters. In terms of the specific problem
to be solved a set of parameters is likely to
be variable. Specifically it includes resolution,
photometric accuracy, speed of response, etc.
In most cases the performance quality of ima-
ging optical system is evaluated by its resolving
power. The optical system resolution is deter-
mined by its point-spread function, which is a
sort of the system’s response to the δ-like ef-
fect at the input. For an optical device this ef-
fect is produced by a signal from a point source.
The dimensions and shape of the point source
image are largely dependent upon the diffrac-
tion phenomena at the device’s aperture, opti-
cal aberrations, sensor resolution and other
factors. The space resolution of image sensors
is primarily determined by the dimensions of an
elementary detecting cell. For the case of pho-
tographic plate, the role of an elementary cell is
played by the size of the photo-emulsion grain,
whereas for the linear image sensors and ma-
trices – by a photodiode element (pixel). The
typical dimensions of the photo-emulsion grain
and the pixels of solid-state charge-coupled
devices (CCD) are about the same order and
equal to ~10 мm. Therefore a transition from
photographic recording to the CCDs was not
followed by a noticeable change in resolution.
The fact that photo-materials used in photo-
and movie cameras are being rapidly replaced
by the CCDs and fall into disuse strongly sug-
gests that these latter are convenient in ser-
vice, operationally capable of being quickly
readjusted, computer-compatible, and in the end
they do offer lots of advantages [1, 2, 3].
By now, neither a widespread photo-emulsion
nor mass-produced CCDs are capable of pro-
viding a resolution limit of light-gathering op-
tics. The stronger the aperture ratio of the feed-
ing optics is, the smaller is the diffraction image
size of a luminous point [4]. For instance, with
an instrument aperture ratio equal to 1 this size
is on the order of an optical wavelength mag-
nitude. For a visible spectrum it will be around
0.5 μm, while for the ultraviolet it will accor-
dingly be several times smaller. The simplest
way of tackling this problem is to reduce the pixel
size at least by an order of magnitude, in which
case a great many technological difficulties are bound
to arise. Hence, some alternative methods are
to be found to deal with the above problem.
A. Yegorov, V. Yegorov, and S. Yegorov
78 Радиофизика и радиоастрономия, 2009, т. 14, №1
1. Treatment of the Problem
in a Spectral Representation
One of the ways to enhance the detector’s
resolving power is, e. g., optimum filtering based
upon the deconvolution filter that provides for
the rise in upper space frequencies. Note that
the greater is the signal-to-noise ratio within the
frequency range of interest, the stronger is the
effect produced by this particular filter. As a
result, this type of a filter cannot reconstruct
those portions of the spectrum of the signal to be
recorded, where the transfer function of the
sensor gets nulled.
To estimate the efficiency of this type of filte-
ring, consider the transfer function of a linear
image sensor whose pixel size is equal to w. In
this one-dimensional case, the module of Fourier
transform can be regarded as a sensor transfer
function of the sensitivity distribution along a pixel.
Once the sensitivity is uniform (constant), it can
be graphically shown as a rectangular pulse with
perfectly steep edges. The Fourier transform mod-
ule ( )G k of such a pulse is that of function
sin( )wk wkπ π (see curve 1 in Fig. 1 on a logarith-
mic scale, k means relative spatial frequency).
Just for comparison, in the same figure shown
is curve 2 for the Fourier transform of a flat-edge
bell-shaped pulse. A Gaussian pulse was modeled
by an exponential normal-distribution function with
a unit amplitude and a half-width of ~0.4 w . The
width is specified by normalization conditions so
that an area beneath the Gaussian and rectangu-
lar pulses is the same. As evident from the com-
parison, the transfer function behavior for these
two cases is tangibly different. The module of the
sensor transfer characteristic in the high-space
frequency range for curve 1 is on many orders of
magnitude higher than that for curve 2. This dif-
ference gives good reason to expect that (in view
of the case of curve 1), as signal-to-noise ratios
are large, the sub-pixel resolution can certainly be
achieved through the use of the appropriate data
handling procedure. The great drawback of the
relationship shown by curve 1 are the dips on
some of space frequencies. This property is in-
herent to a sensor whose regular structure
is composed of similar-in-type photodiode ele-
ments. In some instances, a photographic plate
has a texture in which the size of a grain and
solid-state image sensor pixel, on the average,
identical. This may produce a more informative
image than a photodiode structure can, which is
caused by a certain spread in the size of photo-
emulsion grains and their random arrangement.
This is more pronounced in recording one-dimen-
sional objects, in particular, spectra [5]. In Fig. 2
curve 1 corresponds to an averaged module of
the transfer function of the sensor whose pixels
differ in size (a width 0.6w, 1w and 1.4 w).
Fig. 1. The transfer function G( k ) of the sensor with
a rectangular (1) and bell-shaped (2) sensitivity
distribution along a pixel
Fig. 2. Comparative characteristics of the transfer func-
tion of the sensor whose pixels are of different (1) and
similar (2) size. Scale of the axes being similar to Fig. 1
Subpixel Detection of Spectrum Images by Photodiode Structures
79Радиофизика и радиоастрономия, 2009, т. 14, №1
Fig. 2 indicates that oscillations of the total trans-
fer characteristic of this sensor are substantially
attenuated as against the sensor whose pixels are
of the same size with a half-width w (curve 2)
smoother curve can be plotted by adding to the
variety of values of pixel half-width. In practice,
this type a sensor could well be made feasible by
splitting a luminous flux into parallel beams and
recording one and the same image with the aid of
several sensors having different pixel dimensions.
A similar effect can be produced by the imaging
cameras of the same kind which are fitted with
optical channels of different magnification. Both of
these variants lead to significant sophistication of
photo-detecting equipment. The hardware realiza-
tion of this technique appears to be more simplified
in a sequential variant, which can only be utilized
for time-independent images.
Essentially, the sequential variant implies that,
as an optical image is being detected by a multi-
channel detector, this image is shifted with re-
spect to the image sensor pixels. This method
was referred to in [6] where a description was
given of using it during the photometric spectral
measurements, i. e. for a one-dimensional case.
A transition to a two-dimensional image does not
offer any crucial distinctions.
We have also followed this particular method
for the one-dimensional case when imaging emis-
sion spectra. On frequent occasions, a signal in
a high-transmission emission spectrometer is con-
siderably higher than the sensor’s dark current. In
this connection, a sufficient photometric accuracy
is achieved through short-term single exposures
on the order of 0.1 s. Yet, as a specimen under
study undergoes slow heating and evaporation, the
overall measurement period needs to be substan-
tially extended, occasionally, up to several minutes.
Thus, in most cases the spectral measurement time
involves a set of N-single exposures. We suggest
that each of the N exposures be made after the
spectrum has been shifted by a 1 N width of
a pixel. Technically, this procedure is quite feasible,
e. g., by turning a plane-parallel plate mounted right
behind the spectrograph slit. In this case using the
spectral curve allows to get the counts-off whose
number will be N times greater than that usual.
The shifting of the spectrum relative to a linear
image sensor just within a single pixel during suc-
cessive exposures not only improves the photomet-
ric accuracy, as the measurement data are being
properly handled, but also makes it possible for the
spectral device to take the full advantage of its
entire resolving power even if that device offers
relatively wide pixels of a detecting linear image
sensor. In a number of cases, this additional poten-
tial of the system may even prove to be more use-
ful than the photometric accuracy itself.
2. Treatment of the Problem
in a Coordinate Representation
In [6], we have earlier referred to, no description
is given of an algorithm for solving this particular
problem. In searching for an adequate algorithm
we have been looking into the inherent potentialities
of utilizing spectral and coordinate representation
of a signal. In our specific case, the signal is an
irregular sequence of peaks against the dark current
and other photodetector noise. The shape of the
peaks is governed by intensity distribution within
a spectral line. As the spectrometer optical unit res-
olution increases, the above shape of the peaks tends
to a δ-function. The δ-like signal has a wide spec-
trum that decreases with frequency. In our instance,
the noise can be considered as white. Therefore the
signal-to-noise ratio in a HF region tends to diminish.
In order to solve a number of spectrometric prob-
lems we have employed an algorithm whose essen-
tial features can be appreciated from the following
simplified examination. Let two data files (obtained
while shifting a linear image sensor by a pixel half-
width) be sequentially recorded. Here we have the
case where 2.N = The whole problem is to find
an array of a doubled length, which corresponds
to the double resolution of the linear image sensor.
The solution to this problem is found in terms of a set
of linear equations like:
,M X B⋅ = (1)
where
110.....000
011.....000
................. ,
000.....110
000.....011
M
⎛ ⎞
⎜ ⎟
⎜ ⎟
⎜ ⎟=
⎜ ⎟
⎜ ⎟
⎜ ⎟⎝ ⎠
A. Yegorov, V. Yegorov, and S. Yegorov
80 Радиофизика и радиоастрономия, 2009, т. 14, №1
X is the sought vector, B is the measurement
data vector.
In vector B the even and odd components
are related to two exposures taken as the linear
image sensor is shifted by a pixel half-width.
If the half-width of the line is considerably smaller
than that of a pixel, then it is not improbable that
the resolving power might be increased many times
ever rather than twice as much. In this case N
is set equal to a greater number than 2 and, ac-
cordingly, a quantity of unities in the rows of matrix
M tends to grow.
It should be noted that system (1) is undefined
even though noises are unavailable, because the
number of unknowns is always greater by one than
that of equations. However, this difficulty can be
overcome through the use of numerous a priori
data provided by spectral measurements. This sit-
uation allows writing additional equations and find
a correct solution to the system. If the half-width
of a spectral line is well smaller than the pixel
width, then the resolving power might as well be
raised by several folds rather than by a factor of 2
only. One of the conceivable versions of a priori
data can be afforded by the magnitudes of the
spectral curve in the gaps between the above lines.
In general an emission spectrum tends to exhibit
a wavelength-dependent (λ-dependent) non-uni-
form distribution of spectral density (Fig. 3). This
is one realization of the ТМН lamp spectrum.
In between the spectral lines the curve for the
wavelength-dependent luminous flux intensity for
the emission spectrum is relatively flat. In this case,
the entire spectrum can be broken down into the
areas whose beginnings and ends lie in the domains
between the spectral lines. Using the interpolation
formula in these domains yields small errors for
interpolated values, which can be employed as
a priori data. Given the value of the function
is assigned at both ends of the measuring interval
we arrive at the overdetermined sets of equations
whose matrices assume the following form:
1000.....0000
1100.....0000
0110.....0000
.
.................
0000.....0011
0000.....0001
M
⎛ ⎞
⎜ ⎟
⎜ ⎟
⎜ ⎟
= ⎜ ⎟
⎜ ⎟
⎜ ⎟
⎜ ⎟⎜ ⎟⎝ ⎠
(2)
With a redundant number of equations it would
be advisable to seek an adequate solution with a
least-squares procedure [7, 8]. In this case the
problem is to find a solution to the following system:
,T TM M X M B⋅ ⋅ = ⋅ (3)
where the upper index T denotes the transposition
of matrix M.
For the case (2) matrix TM M⋅ is written as:
2100....0000
1210....0000
0121....0000 .
.................
0000....0012
TM M
⎛ ⎞
⎜ ⎟
⎜ ⎟
⎜ ⎟⋅ =
⎜ ⎟
⎜ ⎟
⎜ ⎟⎝ ⎠
(4)
For large spectrum portions the dimensionality of
M runs up to several thousands. However, as this
particular matrix is of co-diagonal type, the sys-
tem in question is solved with no difficulties what-
soever. It is easy to make sure that the numerical
value of the determinant of the square matrix (4)
of size m m× always is equal to 1.m + With the
proviso that
Fig. 3. Atomic emission spectrum I(n) of gas-discharge
tube, n is the number of a pixel of a recording linear
image sensor
Subpixel Detection of Spectrum Images by Photodiode Structures
81Радиофизика и радиоастрономия, 2009, т. 14, №1
,Tb M B= ⋅
the components of vector b will make the sum
of two adjacent components of vector B:
1.i i ib B B += +
Using the above designations the solution of sys-
tem (3) can be given as:
1 ,
T
X K b
M M
= ⋅ ⋅
⋅
(5)
where the matrix of coefficients K, which can be
referred to as weighting ones, is formed using the
mathematico-deductive method with no computa-
tional procedures whatsoever. As an example, for
the set of equations with four unknowns we have:
4 3 2 1
3 6 4 2
.
2 4 6 3
1 2 3 4
K
− −⎛ ⎞
⎜ ⎟− −⎜ ⎟=
⎜ ⎟− −
⎜ ⎟
− −⎝ ⎠
As regards the sets of equations with other m,
matrix K has a different dimensionality and other
values of the elements. However, in spite of this
the common properties they share are as follows:
1) matrix K regardless of its dimensionality
is symmetric with respect to the diagonal;
2) the magnitude of the elements is linearly
decreasing to the modulus with an increase in
distance from the diagonal element;
3) along the rows and the columns there oc-
curs an alternating sequence.
The above-mentioned common properties will
suffice for generating matrix K of any dimension-
ality. This strategy allows the fast algorithm to be
implemented in solving this particular problem.
Moreover, the computational difficulties over
solving equation (3) are substantially reduced when
splitting the spectrum interval to be reconstructed
into a set of areas “jointed” by their ends. In cal-
culating the values of the components of vector X
from expression (5), a row of matrix K is multiplied
by vector b derived from measurement data. Owing
to the second property of matrix K a maximal con-
tribution to value iX is made by i-th and ( 1)i ± -th
elements of the measurement data vector. The data
from measuring vector iB with indices 2,i ±
3, ...i ± have a slight impact upon value .iX For
the same reason the impact of the noise compo-
nent vector b is likewise insignificant.
3. Experimental Results
The algorithm described enables one to arrive
at an accurate solution in the case where the
noise is nonexistent and the transfer function of
the measuring system remains unchanged for two
successive exposures. In the real experimental
environments it is quite a challenge to provide for
steady-state regimes. What is more, the noises
are, in fact, apt to provide non-recurrent data.
This gives rise to the oscillation of vector X, which
is similar to the one described in [9], where diffe-
rent smoothing procedures for suppressing those
oscillations are suggested.
We have made use of this algorithm for a two-
fold definition of the spectrum image using the
experimental setup comprising of the ISP-51
spectrograph and a recording system based upon
the ILX511 multi-cell sensor (SONY company)
whose pixel width is 14 μm. The spectrogtaph has
an aperture ratio of 1:5.5. It can be used to provide
an image of a glowing spot 6.6 μm in diameter the
diffraction limit for a 0.5 μm light wave. This diam-
eter is two time smaller than the pixel size of multi-
cell sensor ILX511. To shift the spectrum image
relative to photodetector, a plane-parallel quarz plate
of ~2 mm thick was placed in between the slit and
collimator of spectrograph in close proximity to the
slit. This plate was rotated in the exposure latitudes
with a spacing of around 34 10−⋅ radian. With this
plate rotation a spectrum image was displaced by
an amount nearly equal to the tenth fraction of the
pixel width. In this way the number of samples we
had obtained on the spectrogram was on the order
greater than was considered to be the case. In
preprocessing an already recorded array the mea-
sured data were subjected to smoothing out and
normalizing. Using the smoothed-out spectrogram
A. Yegorov, V. Yegorov, and S. Yegorov
82 Радиофизика и радиоастрономия, 2009, т. 14, №1
a series of averaged values was derived with a
spacing strictly equal to the half of the pixel width.
Fig. 4 shows a scaled-up fragment of the spec-
trum shown in Fig. 3 on the interval between the
357-th and 398-th pixel.
Fig. 5 shows the same fragment with a dou-
bled resolution as obtained by the effect of the
algorithm described above.
4. Conclusions
The comparison between the initial and pro-
cessed graphic data illustrated in Fig. 4 and Fig. 5
is a convincing proof of the merit of our approach
to the problem of subpixel resolution in spectral
investigations. This allows to get rid of the inter-
fering impact of adjacent spectral lines and obvia-
te an adverse phase effect in photometric mea-
surements of spectra. This particular effect was
studied by the authors in [10].
Basically, the algorithm that has been scruti-
nized might as well be used to increase the reso-
lution of the recording system up to the diffraction
optical resolution of the device in the case of
arbitrary dimensions of an image sensor pixel. If
half-width of a spectral line is greater than the
pixel width, then this method is found to be on a
losing side in terms of getting an appropriate re-
solving power. The applicability scope of this tech-
nique is strongly dependent upon the behavior of
the signal-to-noise ratio with an increase in the
signal space frequency.
References
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Fig. 5. The result from processing the measurement
data. rX and r are the array and number of the
processed data
Fig. 4. The fragment of the spectrum shown in Fig. 3
prior to its processing. Scale of the axes being similar
to Fig. 3
Subpixel Detection of Spectrum Images by Photodiode Structures
83Радиофизика и радиоастрономия, 2009, т. 14, №1
Субпиксельная регистрация
изображений спектров фотодиодными
структурами
А. Д. Егоров, В. А. Егоров, С. А. Егоров
Работа посвящена вопросам повышения
разрешающей способности фотометра при ре-
гистрации изображений спектров фотодиодны-
ми линейками на эмиссионных спектрометрах.
Рассматривается случай, когда размер пиксела
фотодиодной структуры превосходит размеры
пятна замытия оптического прибора. Показано,
что сочетание параллельного способа регист-
рации всех точек изображения с последователь-
ным его смещением относительно регистриру-
ющей структуры позволяет зарегистрировать
полученное таким образом изображение без
потери разрешающей способности оптической
части прибора при произвольно большом пик-
селе детектора. Задача обработки результатов
измерений сводится к решению несовместной
системы линейных уравнений. Предлагается
алгоритм решения полученной системы урав-
нений и приводятся результаты, иллюстрирую-
щие действие этого алгоритма.
Субпіксельна реєстрация
зображень спектрів фотодіодними
структурами
А. Д. Єгоров, В. А. Єгоров, С. А. Єгоров
Робота присвячена питанням покращення
роздільної здатності фотометра при реєстрації
зображень спектрів лінійками фотодіодів на
емісійних фотометрах. Розглядається випадок,
коли розмір піксела фотодіодної структури
перевищує розміри плями розмитості оптич-
ного приладу. Показано, що поєднання пара-
лельного способу реєстрації усіх точок зобра-
ження з його послідовним зміщенням відносно
фотодіодної структури дозволяє зареєструвати
одержане таким чином зображення без втра-
ти роздільної здатності оптичної частини при-
ладу за довільно великого піксела детектора.
Задача обробки результатів вимірювання зво-
диться до розв’язання несумісної системи
лінійних рівнянь. Пропонується алгоритм роз-
в’язання одержаної системи рівнянь та наво-
дяться результати, що ілюструють дію цього
алгоритму.
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