8
XII INTERNATIONAL CONFERENCE AND SEMINAR EDM’2011, SECTION IX, JUNE 30 - JULY 4, ERLAGOL 354 The Optical System for the Three-channel Pyrometric Device of Two Spectral Ratios Eugene V. Sypin, Member, IEEE, Nadezhda Y. Tupikina, Graduate Student Member, IEEE, Evgeniy S. Povernov, Member, IEEE Biysk Technological Institute (branch), Altai State Technical University after I.I. Polzunov, Biysk, Russia Abstract – The article describes the possible implementation scheme for the three-channel optical pyrometric device of two spectral ratios. For device designing preference is given to the scheme with interference bandpass optical filters. In addition to this, dimensional analysis of the optical system was fulfilled and preliminary values of the optical filter sizes, optical filters arrangement and photodetectors arrangement were obtained. Index Terms Pyrometric device, optical system, interference optical filter. I. INTRODUCTION HE OPTICAL-ELECTRONIC devices and systems laboratory (Biysk Technological Institute) is carrying out the work aimed at development of optical-electronic devices to determine the early stage of the explosion in the gas-dispersed systems [1]–[4]. One area of this work is associated with the improving noise immunity of the developed devices under external optical noise interference. In the previous studies the hardware redundancy and the software redundancy are proposed to use to improve the noise immunity of the designed devices [5]. The redundancy can be realized for the device by using several spectral ratios channels. Previously a block diagram for the three-channel pyrometric device of two spectral ratios was proposed (see Fig. 1). 1 – lens; 2 – a device for light flow separation; 3, 4, 5 – optical filters; 6, 7, 8 – optical radiation receivers; 9, 10, 11 – amplifiers; 12 – signals processing unit Fig. 1. The block diagram for the three-channel pyrometric device of two spectral ratios For convenience all components of the block diagram can be divided into two parts: the optical part components (in Fig. 1 marked by the dashed line) and the electronic part components. In this article we will discuss the optical system development of the device. The optical system is an important part of the device. The main functions of the optical system are [6]: providing of the required energy relations and the obtaining of the required image quality; separation of the useful optical signal (optical filtering). The optical system can include various components (lenses, mirrors, etc.). The choice of these components should be reasonable and promote the implementation of the basic optical system functions. II. PROBLEM DEFINITION So the aim of work was formulated: to develop a block diagram of the optical system for the three-channel pyrometric device of two spectral ratios and to carry out the dimensional analysis for device designed. The following tasks should be performed to achieve this aim. 1. To consider the possible structural schemes of the optical system for the device. 2. To choose the optimal block structural scheme of the optical system for the device according to the following criteria: the ability of simultaneous selection of narrow spectral bands, the minimum loss of the signal power when it passes through the optical system, the minimum external dimension of the optical system. 3. To fulfill the dimensional analysis of the optical system for the device based on the chosen structure. III. POSSIBLE SCHEMES FOR CONSTRUCTION OF OPTICAL SYSTEM The optical system should provide a selection of three narrow spectral bands. This problem can be solved by the receiving optical system when separate lens for each of the device channels is used. But these optical systems are characterized by the parallax. The parallax arises because of the objects can be observed at different angles for each channel. In addition to this, there is the problem of overlapping images observed by different lenses. When the receiving system is single for all channels, additional devices need to be used. And the separation of the optical flux can be realized in the following ways: T ISBN 978-1-61284-795-5/11/$26.00 ©2011 IEEE

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XII INTERNATIONAL CONFERENCE AND SEMINAR EDM’2011, SECTION IX, JUNE 30 - JULY 4, ERLAGOL

354

The Optical System for the Three-channel Pyrometric Device of Two Spectral Ratios

Eugene V. Sypin, Member, IEEE, Nadezhda Y. Tupikina, Graduate Student Member, IEEE,

Evgeniy S. Povernov, Member, IEEE Biysk Technological Institute (branch), Altai State Technical University after I.I. Polzunov, Biysk, Russia

Abstract – The article describes the possible implementation scheme for the three-channel optical pyrometric device of two spectral ratios. For device designing preference is given to the scheme with interference bandpass optical filters. In addition to this, dimensional analysis of the optical system was fulfilled and preliminary values of the optical filter sizes, optical filters arrangement and photodetectors arrangement were obtained.

Index Terms – Pyrometric device, optical system, interference optical filter.

I. INTRODUCTION

HE OPTICAL-ELECTRONIC devices and systems laboratory (Biysk Technological Institute) is carrying

out the work aimed at development of optical-electronic devices to determine the early stage of the explosion in the gas-dispersed systems [1]–[4]. One area of this work is associated with the improving noise immunity of the developed devices under external optical noise interference. In the previous studies the hardware redundancy and the software redundancy are proposed to use to improve the noise immunity of the designed devices [5]. The redundancy can be realized for the device by using several spectral ratios channels.

Previously a block diagram for the three-channel pyrometric device of two spectral ratios was proposed (see Fig. 1).

1 – lens; 2 – a device for light flow separation;

3, 4, 5 – optical filters; 6, 7, 8 – optical radiation receivers; 9, 10, 11 – amplifiers; 12 – signals processing unit

Fig. 1. The block diagram for the three-channel pyrometric device of two spectral ratios

For convenience all components of the block diagram can be divided into two parts: the optical part components (in Fig. 1 marked by the dashed line) and the electronic

part components. In this article we will discuss the optical system development of the device.

The optical system is an important part of the device. The main functions of the optical system are [6]: � providing of the required energy relations and

the obtaining of the required image quality; � separation of the useful optical signal (optical

filtering). The optical system can include various components

(lenses, mirrors, etc.). The choice of these components should be reasonable and promote the implementation of the basic optical system functions.

II. PROBLEM DEFINITION

So the aim of work was formulated: to develop a block diagram of the optical system for the three-channel pyrometric device of two spectral ratios and to carry out the dimensional analysis for device designed. The following tasks should be performed to achieve this aim.

1. To consider the possible structural schemes of the optical system for the device.

2. To choose the optimal block structural scheme of the optical system for the device according to the following criteria: � the ability of simultaneous selection of narrow

spectral bands, � the minimum loss of the signal power when it

passes through the optical system, � the minimum external dimension of the optical

system. 3. To fulfill the dimensional analysis of the optical

system for the device based on the chosen structure.

III. POSSIBLE SCHEMES FOR CONSTRUCTION OF OPTICAL SYSTEM

The optical system should provide a selection of three narrow spectral bands. This problem can be solved by the receiving optical system when separate lens for each of the device channels is used. But these optical systems are characterized by the parallax. The parallax arises because of the objects can be observed at different angles for each channel. In addition to this, there is the problem of overlapping images observed by different lenses.

When the receiving system is single for all channels, additional devices need to be used. And the separation of the optical flux can be realized in the following ways:

T

ISBN 978-1-61284-795-5/11/$26.00 ©2011 IEEE

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SYPIN, TYPIKINA and POVERNOV: THE OPTICAL SYSTEM FOR THE…

355

� without dividing the optical flux (the design with changeable optical filters); � the power separation of optical flux with

filtration followed; � the spectral separation of the optical flux. The design with movable elements (changeable optical

filters) reduces the device reliability and is not desirable. Also in this separation method of the optical flux registration of signals from the radiation source takes place at different times. This leads to decrease in the performance of the device as a whole and requires the synchronization of signals by channels.

The power separation of optical flux has been previously used for designing of the devices [7, 8]. The power separation of optical flux was performed using the semitransparent mirror fixed at an angle to the optical axis of the system. But use of the semitransparent mirror in the optical system of the device decreases flux at each photodetector by two times and for the three channels at least by 3 times. It is necessary to use the signal spectral separation to eliminate attenuation of the signal.

The possible realization scheme of the optical system for the three-channel pyrometric device of two spectral ratios with beam splitters is shown in Figure 2.

1 – collecting lens, 2, 5 – beam splitters;

3, 6, 8 – optical band pass filters; 4, 7, 9 – photodetectors Fig. 2. The optical system for three-channel pyrometric device of two

spectral ratios with beam splitters arranged at the different angles to the optical axis

This scheme shows that the optical flux from the radiation source through the lens 1 is partially reflected by the beam splitter 2, passes through the filter 3 and arrives at the photodetector 4. The beam splitter 2 is arranged at an angle of 135� to the axis of the optical system and the part of the optical flux passes through it on the beam splitters 5. The beam splitter 5 is arranged at an angle of 45� the axis of the optical system. The part of the optical flux (reflected beam splitter 5) through the filter 6 arrives at the photodetector 7 and the passed optical flux through the filter 8 – to the photodetector 9. Optical filters in the suggested optical system are of bandpass type.

Fig. 3 shows the signals at the input of the optical system (black outline), the signals after passing beamsplitter 2 and beamsplitter 5 (gray areas in Fig. 3) and the signals arriving at the photodetectors of 4, 5 and 9 (blue, green and red outline, respectively).

Fig. 3. The signal at the input of the optical system of three-channel pyrometric device of two spectral ratios and the signals after passing

through the optical elements of optical systems with beamsplitters

The angle between the optical axis and beamsplitter 2 was chosen taking into account the previously performed calculations for the elements arrangement in the similar systems with semitransparent mirror [7]. The angle of 135� is optimal for minimizing the external dimensions of the optical system and reducing the reflection of the optical flux back through the lens 1. The beamsplitter 4 should have an angle of 45� or 135� to the axis of the optical system; the arrangement with another angle can lead to increasing of the dimensions or the reflecting of the optical flux at the beamsplitter 2.

A collecting biconvex lens was chosen as the objective of the optical system for the three-channel pyrometric device of two spectral ratios. Later complication of the receiving optical system may be required. For example, the use of the condenser to increase the signal to noise ratio at the photodetector output or the use of additional devices to reduce the aberration of the optical system may be required.

The lens is to be chosen by two parameters: the diameter and focal length. The diameter of the lens should be as small as possible to approximate the area of full radiation to the lens and as large as possible to receive more energy from a point radiator or an area radiator for the photodetector. The previous calculations showed that it is not reasonable to increase lens diameter above 100 mm [7].

The scheme in Fig. 2 can be somewhat modified if you put the beamsplitter 4 as well as the beamsplitter 2 at an angle of 135� to the optical axis of the system (Fig. 4).

The same angle to the optical axis of the system arrangement of beamsplitters can somewhat reduce the external dimensions of the optical system. The form of the signals at the optical system output will be similar to the signals shown in Fig. 3.

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XII INTERNATIONAL CONFERENCE AND SEMINAR EDM’2011, SECTION IX, JUNE 30 - JULY 4, ERLAGOL 356

1 - collecting lens, 2, 5 - beam splitters;

3, 6, 8 - optical band pass filters; 4, 7, 9 - photodetectors Fig. 4. The optical system for three-channel pyrometric device of two spectral ratios with beam splitters arranged at the same angles to the

optical axis

The use of beamsplitters requires the using of optical filters to select narrow spectral band that increases the quantity of elements in optical system. The quantity of the elements used can be decreased by the replacing beamsplitters with the interference bandpass filters. The advanced optical system of the device with bandpass interference filters is shown in Fig. 5.

1 - collecting lens, 2, 4, 6 - optical band pass filters;

3, 5, 7 - photodetectors Fig. 5. The optical system for three-channel pyrometric device of two

spectral ratios with interference bandpass filters

In this scheme the selection of the narrow spectral bands is performed by bandpass interference filters (2, 4, 6). Both filter 2 and filter 4 are arranged at an angle of 135° to the optical axis of the system. The signals arriving at the photodetectors are shown in Fig. 6.

The advantages of the scheme shown in Fig. 5 are the reduced quantity of the elements. Reduction of the quantity of the elements leads to reducing of the power losses of the radiation passing through the optical system. Therefore, the optical system with the bandpass interference filters was chosen to design the three-channel pyrometric device of two spectral ratios.

Fig. 6. The signal at the input of the optical system of three-channel pyrometric device of two spectral ratios with interference bandpass

filters and the signals arriving to the photodetectors

IV. DIMENSIONAL ANALYSIS OF THE OPTICAL SYSTEM

The source data for dimension analysis of the optical system are: � diameter of collecting lens (D) and its focal

length (F); � diameter of the detectors sensitive area (L). In

the calculation, we assume that the photodetectors used in the optical system of the device have the circular sensitive area in all channels, and sizes of the sensitive area are equal for all photodetectors. � arrangement of the photodetectors in the back

focal plane of a collecting lens symmetrical relative to the optical axis of the lens. This provides the maximum area size of the total radiation and a sufficiently large angular field of the device. � the optical filters are arranged at an angle of

135� to the positive direction of the x-axis [7]. In the calculations and the plotting it is necessary to

consider all possible positions of points in the device field of view. Therefore, we assume that the image projected by a lens is not a point, but a certain set of the points located on the sensitive area of the photodetector. Thus, for calculations the light beam formed by a lens in the space can be considered as a direct truncated cone.

When performing the dimension analysis of the optical system it is required to find the size of filters (the height and width) and their position relative to the collecting lens and the photodetectors position in the optical system. Let us consider the filter thickness (t) to be a known value. Most interference filters manufactured by Photooptik-Filtry (for photometry) have thickness of 5–6 mm [9].

Calculation of the position and sizes is carried out consecutively for all filters. The following conditions are imposed on the position of the filters and their sizes (Fig. 5). � Filter 4 should not intersect the light beam

formed by lens 1 on the interval between the lens and the filter 2. � Filter 6 should not intersect the light beam in the

interval between filter 2 and photodetector 3.

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SYPIN, TYPIKINA and POVERNOV: THE OPTICAL SYSTEM FOR THE…

357

� Filters of 2, 4 and 6 should not touch each other. � Filter 2 should not be located to the left of the

plane of the lens 1.

A. Calculation of Geometric Dimensions of Optical Filter 2

Filter 2 should completely overlap the light beam formed by the lens 1. Therefore, position of the filter 2 in the optical system and its external dimensions determine points E and C1 (Fig. 7). These points are the points of intersection of the front and back planes of the filter with �1� and �2� generators of light cone formed by the lens, respectively.

The angle of the filter arrangement was determined earlier when the structural scheme of the optical system was chosen. This angle to the positive direction of the x-axis is equal to 135�.

Fig. 7. The explanations for the calculation of the geometric dimensions and the arrangement of the optical bandpass filter 2 in the optical system

of three-channel pyrometric device of two spectral ratios with interference bandpass filters and the signals arriving at the

photodetectors

To perform the calculation we introduce the additional point of K1 - a point of intersection of the front plane of the filter with the x-axis. At this point, the optical axis will be reflected at the angle of 90�.

It is necessary that optical filter 2 completely overlaps the light beam formed by lens 1 and the condition of arrangement a filter at an angle of 135� to the optical axis of the system implies that the segment OK1 technically cannot be less than 2D . Therefore, the K1 point has coordinates 12

1sDxK �� , where s0

1�Ky 1 is

manufacturing clearance, defined as the minimum distance from the filter 2 to the lens 1. Further, we will designate the coordinates with x and y letter; the subscript will designate the point to which this coordinate applies.

The optical filter 2 and the light beam formed by lens 1 form an ellipse at the intersection. The projection of the ellipse to the XOZ plane and YOZ plane will represent a circle and the projection to the XOY plane will represent the segment (z-axis perpendicular to the plane of the figure, the positive direction to the viewer).

It is necessary to find the length of the segment projected to the XOY plane in order to determine the height of filter 2.

� � � �22fsfsF yyxxH ���� , (1)

where (xs, ys) and (xf, yf) are coordinates of the beginning and ending of the projected segment.

It is necessary to find the diameter of the circle projected to the XOZ plane or the YOZ plane in order to determine the width. The equality of circles follows from the filter arrangement at an angle of 135� to the optical axis of the system. Thus, the width of the filter can be defined as the height projection to the y-axis

� �2

1135180sin ������ FFF HHW � . (2)

Let us find the coordinates of the E point and C1 point. E point is the intersection of O1B line and EC line. Therefore, it is necessary to set up the equations of these lines and to find their point of intersection in order to determine coordinates of these points.

The equation of the O1B line is written as:

22Dx

FDLy ��

�� . (3)

The E� line is arranged at an angle of 135° to the optical axis of the system and passes through K1 point; therefore, its equation is written as:

11 KK yxxy ���� . (4) To find the coordinates of E point the system of

equations (3) and (4) are solved for xE and yE:

12

211

��

���

FDL

Dyxx

KK

E ; (5)

11 KKEE yxxy ���� . (6) The C1 point lies on the intersection of O2A line and

E1�1 line. The equation of O2A line is

22Dx

FLDy ��

�� . (7)

The E1�1 line is the back plane of the filter 2; it is parallel to the EC line, the equation of which has been found previously (4). The displacement of the E1�1 line relative to the EC line on the axes can be found if thickness of the filter (the segment CC' (t)) is known. Since the filter is arranged at an angle of 135° to the positive direction of the x-axis, the EE' segment (filter thickness) is arranged at an angle 45° to the positive direction of the x-axis.

)45sin()45cos(11

�� �������� ttyxxy KK ,

211

tyxxy KK ����� . Thus, coordinates of the �1 point are as follows:

12

22

11

1

��

����

FLD

Dtyxx

KK

C ;

21111

tyxxy KKCC ����� .

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XII INTERNATIONAL CONFERENCE AND SEMINAR EDM’2011, SECTION IX, JUNE 30 - JULY 4, ERLAGOL 358

It is obviuous that the coordinates of C point can be determined via coordinates of the C1 point as follows:

� �2

135cos11

txtxx CCC ������ � ;

� �2

135sin11

tytyy CCC ������ � .

Thus, the height of filter 2 can be determined by the formula (1), where (xs, ys) are coordinates of the E point and (xf, yf) are coordinates of the C point. Then, the filter width can be determined according to the formula (2).

B. Calculation of Geometric Dimensions of Optical Filter 4

Since it is necessary that filter 4 completely overlaps the light beam reflected by the filter 2, the position of the filter 4 in the optical system and its dimensions determine the E' point and the �'1 point. This points are the intersection points of the front plane and back plane of filter 4 with the generators of the light cone reflected by filter 2 (Fig. 8). The mounting angle of the filter 4, as well as the mounting angle of the filter 2 is equal to 135° to the positive direction of x-axis.

Fig. 8. The explanations for the calculation of the geometric dimensions and the arrangement of the optical bandpass filter 4 in the optical system

of three-channel pyrometric device of two spectral ratios with interference bandpass filters and the signals arriving to the

photodetectors

The ME' segment should be different from zero. In this case filter 4 does not overlap the light beam formed by lens. Let us designate this segment length as s2. M point is the intersection point of the light cone formed by lens 1 and the light cone reflected by optical filter 2, i.e. it is a intersection point of the EA' line and the O2A line.

Therefore, the equation of EA' line is written as:

EE

EK

EK

EK

EK yxxLx

xxFx

xLx

xxFy ��

��

�����

��

����

22 1

1

1

1 . (8)

The equation of the O2A line has been found earlier (4). The system of equations (3) and (8) should be solved for (xM; yM) in order determine the coordinates of the M point.

EK

EK

EE

EK

EK

M

xLx

yxFF

LD

yxxLx

yxFD

x

��

���

����

����

22

22

1

1

1

1

; (9)

22Dx

FLDy MM ��

�� . (10)

The coordinates of the E' point can be found by the known coordinates of the M point:

sin2' ��� sxx ME ; (11) cos2' ��� syy ME . (12)

where is the angle between the generator of the light cone reflected by the filter 2, and its height.

Tangent of the angle can be found as:

F

LD

tg 22�

� . (13)

Because the filter 4 forms with the positive direction of the x-axis angle of 135� the light cone formed by the lens and light cone reflected by the light filter 2 are identical. Therefore, it can be virtually imagined that the reflected light cone is formed by lens rotated an angle of 90� relatively to the initial position of the lens. Photodetector 5 should be located in the back focal plane of the virtual lens. Thus, the length of the following segments will be known:

FPO �'' ;

2'''' 12

DOOOO �� ;

111 ' KxKOOK �� . To find the coordinates of the C'1 point it is necessary to

find equations of the E1'C1' line and the O'1B' line, on the intersection of which this point lies. Let us find the equation of the E1'C1' line. The E1'C1' line lies at an angle of 135� to the optical axis of the system and passes through the E1' point, which is shifted relatively to the E' point on the thickness of the filter (t). The coordinates of the E' point have been found previously (11)–(12).

� �2

135cos '''1txtxx EEE ������ � ;

� �2

135sin '''1tytyy EEE ������ � .

Then the equation of the E1'C1' line can be written as: 2'' tyxxy EE ����� . (14)

Equation of the O'1B' line is

11 22222

22KK xDx

DLFx

DLFy �

��

�� ��

���

�� .(15)

Thus, it is necessary to solve the system of equations (13) and (14) for � �

11 '' ; CC yx in order to determine the coordinates of C'1.

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SYPIN, TYPIKINA and POVERNOV: THE OPTICAL SYSTEM FOR THE…

359

1

22

22

22

''

'

11

1

��

������

�� ��

��

DLF

tyxxDxDL

F

x

EEKK

C ;

2''''1 tyxxy EECC ����� . Sizes of filter 4 can be calculated in the same manner as

sizes of filter 2 by formulas (1) and (2), where (xs, ys) are the coordinates of the E' point and (xf, yf) are the coordinates of the C ' point. The coordinates of the C ' point can be obviously determined through the coordinates of the C'1 point as follows:

� �2

135180cos11 '''

txtxx CCC ������ �� ;

� �2

135180sin11 '''

tytyy CCC ������� � .

The following condition should be observed to avoid touching filter 4 and photodetector 5: y-coordinate of the C'1 point must be greater than the y-coordinate of the B' point.

''1 BC yy � , or

� �11' KC xFy ��� ,

11 'CK yxF �� . (16) The coordinates of the K2 point should be found to

determine the position of photodetector 7. K2 point is the intersection point of the front (reflecting) plane of the filter 4 with the O'P' line. It is followed from he condition of the detectors arrangement that . The coordinate is found from the condition that K

12 KK xx �

2 point lies on the E'S' line. The E'S' line lies at an angle of 135� to the optical axis and passes through the E' point. The coordinates of the E' point have been found earlier (11) - (12).

''22 EEKK yxxy ���� . (17)

C. Calculation of Geometric Dimensions of Optical Filter 2

The position of filter 6 in the optical system and dimensions of the filter are determined by the E'' point and the K3 point (Fig. 9). E'' point is intersection point of the plane of optical filter 6 with the generator of the light cone reflected at the filter 4. K3 point is the intersection point of the plane of the filter 6 and the doubly reflected optical axis.

Because the filter 4 is arranged at 90� to the x-axis, it has the form of the light beam reflected at the filter 4. If the filter is of circular form, its diameter is determined as:

� �''32 EKF yyD ��� . (18)

M1 point is the intersection point of the light cone reflected by light filter 2 and the light cone reflected by light filter 4, i.e. it is the intersection point of the O'1B '

line and the E'B'' line. The equation of the O'1B ' line has been found previously (15). Let us find the equation of the E'B'' line taking into account the coordinates of the points through which it passes.

Fig. 9. The explanations for calculation of the geometric dimensions and the arrangement of the optical bandpass filter 6 in the optical system of three-channel pyrometric device of two spectral ratios with interference

bandpass filters and the signals arriving at the photodetectors

Thus, the equation of the E'B'' line is written as:

'''

'

'

'

2

2

2

2 22EE

EK

EK

EK

EKyx

xyF

yLyx

xyF

yLyy ��

��

����

��

���

(19) Thus, the system of equations (15) and (19)

for � �11

; MM yx is solved to determine the coordinates of the M1 point

22

2

222

2

'

'

'''

'

2

2

112

2

1

DLF

xyF

yLy

xDxDLFyx

xyF

yLy

x

EK

EK

KKEEEK

EK

M

��

��

��

���

�� ��

����

��

��

1111 22222

KKMM xDxDL

FxDL

Fy ���

�� ��

���

�� .

Let us find the coordinates of the E'' point and the K3 point. The coordinate of the K3 point is (17),

and the coordinate is found from the condition that the surface of the optical filter 6 and photodetector 7 touches, i.e.

23 KK yy �

3Kx

tyFKKOKx KK �����23 321 .

The condition for touching surfaces of the filter 6 and the photodetector 7 is required to ensure the smallest possible size of filters and reduce the cost of the optical system.

The E'' point is the intersection point of the E'B'' line and the

3Kxx � line; therefore, its coordinates can be

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XII INTERNATIONAL CONFERENCE AND SEMINAR EDM’2011, SECTION IX, JUNE 30 - JULY 4, ERLAGOL 360

determined by substituting 3'' KE xx � in the equation of the

E’B’’ line (19). Thus, the E’’ point coordinates are

3'' KE xx � ,

'''

'

'''

'

''

2

2

2

2 22EE

EK

EK

EEK

EK

E yxxyF

yLyx

xyF

yLyy ��

��

����

��

���

The following condition should be observed to

eliminate the intersection of optical filter 6 and the light beam reflected at filter 2: x-coordinate of the E’’ point must be greater than the x-coordinate of the M1 point

1'' ME xx � , (20) The fulfillment of condition (20) ensures the

manufacturing clearance of s3 (segment M1E’’). Therefore,

�cos3'' 1��� sxx ME , (21)

where � is the angle between the generator of the light cone reflected by filter 4 and its height. Since in the considered optical system the photodetectors with the same area of the sensitive surface are used in all channels, it is obvious that the � angle is equal to the angle � (13).

Taking into account expression (21) condition (20) can be written as:

03 �s . (22)

D. Preliminary Calculation of Optical System

The performed dimensional analysis of the optical system allows finding the size of the optical filters, the positions of the optical filters and the positions of the detectors.

The dimensional analysis was performed for the following parameters of the optical system: � diameter of the input lens – 60 mm; � focal length of the lens – 100 mm; � sensitive area diameter of the detectors – 10 mm; � thickness of used filters – 6 mm; � manufacturing clearance – s1 = s2 = 5 mm.

TABLE I CALCULATED ARRANGEMENT OF THE OPTICAL FILTERS

Designation of optical filter

Coordinates of optical filter characteristic points

2 E (6.67; 28.33) �1 (58.79; -15.30) 4 E' (21.21; -29.85) �'1 (41.57; -58.70) 6 E'' (50.36; -37.14) K3 (50.36; -43.64)

The performed dimensional analysis allows determining the position and the size of all filters by calculated coordinates for the following points (Tab. I): � E and �1 for optical filter 2; � E’ and �’1 for optical filter 4; � E’’ and K3 for optical filter 6. The dimensions of the optical filters can be calculated

by (1) and (2) – for optical filters 2 and 4. Diameter of light filter 6 is determined by the formula (18). Calculated geometric dimensions of optical filters are shown in Tab. 2.

TABLE II CALCULATED GEOMETRIC DIMENSIONS OF

THE OPTICAL FILTERS Designation of optical filter Size (height�width), mm 2 67.71�47.88 4 34.81�24.61 6 diameter of 13

The position of the photodetectors in the optical system is characterized by the points of optical axis passing through a photodetector. There are points of P, P' and P'' (Fig. 7)–(Fig. 9). The coordinates of these points are given in Tab. 3.

TABLE III CALCULATED POSITION OF THE PHOTODETECTORS

Point name Coordinates P (0; 100) P' (35; -65) P'' (21.36; -43.64)

The calculations and the chosen initial parameters

should be checked for correctness. For this purpose verify conditions (16) and (22).

Substituting the coordinates of the points to the condition (16), we obtain:

� �30.1533100 ��� ; 30.48100 � .

The manufacturing clearance of s3 can be calculated by formula (21). According to the calculations s3 = 3.30 mm. It suggests that the selected initial data for the calculation allows correctly implementing the optical system of the three-channel pyrometric device of two spectral ratios with spectral interference bandpass filters.

The calculation was performed in computerized manner. Therefore, the similar calculation can be performed for other initial parameters of this optical system.

VI. CONCLUSION

The set aim of the work was accomplished. The structural scheme of the three-channel optical pyrometric device of two spectral ratios was designed; the dimensional analysis for the device designed was carried out. During the work following tasks were performed:

1. The possible structural schemes of the optical system for the device are considered with beam splitters and with interference bandpass filters.

2. The structural scheme with the bandpass interference filters was chosen for the device design. The chosen scheme is provided: � the ability of simultaneous selection of narrow

spectral bands, � the minimum loss of the signal power when it

passes through the optical system, � the minimum external dimension of the optical

system. 3. The dimensional analysis of the optical system for the device was fulfilled and the size of filters and the coordinates of their arrangement were obtained.

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The calculations performed will be used in the subsequent design of the three-channel pyrometric device of two spectral ratios.

REFERENCES [1] Detection and suppression of methane and coal dust in the initial

stage of its development / Remezov A.V., Shevelev, Yu.A., Leonov G.V., Sypin E.V., Belousov A.M., Kirpichnikov A.N., Kharitonov V.G. / / Ugol. - 2005. - N 9 (955). - p.31-34. (in Russian)

[2] Sensor of fire coordinates on CCD-array / Pavlov A.N., Terentiev S.A., Povernov E.S., Sypin E.V., Leonov G.V. / / Polzunovsky Gazette. 2006. � 2-2. p. 121-126. (in Russian)

[3] Research of Possible Construction Variants of the Multichannel Ignition Center Detection Device at the Early Stage / Tupikina N.U., Pavlov A.N., Povernov E.S., Barishnikova E.V., Uskova I.A., Sypin E.V. // International Workshop and Tutorials on Electron Devices and Materials, EDM - Proceedings. 2008. P. 207-210.

[4] Building a high-speed multithreshold pyrometric device of temperature object control / Gerasimov D.V., Pavlov A.N., Sypin E.V. / / Sensors and Systems. 2010. � 8. p. 51-54. (in Russian)

[5] Increased immunity to optical interference for the three-channel pyrometer spectral ratio gauge of detecting the fire source in the gas-media / Tupikina N.Y., Sypin E.V. / / Measurement, automation and modeling in industry and scientific research (IAMP-2010) - Proceedings. 2010. P. 191-194. (in Russian)

[6] Yakushenkov Y.G. Theory and calculation of optical-electronic devices: Textbook for university students. – Moscow: Logos, 1999. – 480p. (in Russian).

[7] Sypin E.V. First stage explosion development detection optical-electonic device in gas-dispersed systems // Ph.D. thesis – Biysk: 2007 – 144p. (in Russian).

[8] Design of optical systems with cylindrical lenses for pyrometric sensor of determining the coordinates of the fire source / Terentiev S.A., Sypin. E.V., Kulyavtsev E.Y., Kuimov R.I., Kazantsev V.G. // Bulletin of the Scientific Center for safety in coal industry. - 2010. - � 1. - p. 126-132. (in Russian)

[9] Photooptic-filters [Electronic resource] // Web Site of Ltd "Photooptic-filters". – http://www.photooptic-filters.com/

Eugene V. Sypin was born on February 20, 1971. He received an engineer degree (equivalent to M.S.) on speciality “Informational measuring technique and technology” from the Altay Polytechnical Institute, Altay Territory, Russian Federation in 1994 and the PhD degree in optic-electronic devices and systems from the Altay State Technical University in 2007. Since 1994 he has been working as a staff senior lecturer in the Biysk Technological Institute. Since 2009 up to now he has been working as a staff professor in the Biysk Technological Institute. Since 1998 up to now he is the head of the Laboratory for Methods and Means of Digital Information Processing in this Institute. His research interests include Control Systems, Industrial Electronics, Industry Applications, Instrumentation and Measurement, Systems of Protection Against Explosions, Optical-Electronic Devices and Systems.

Nadezhda Y. Tupikina is a post-graduate student of the Measurement Methods and Tools Chair in the Biysk Technological Institute, specialty “Instruments and methods to control the environment, substances, materials and products". Currently she is an engineer in the Student Scientific Research Sector of this Institute.

Evgeniy S. Povernov was born on February 16, 1978 in Biysk. In 2000 he received an engineer degree (equivalent to M.S.) on speciality “Informational measuring technique and technology” from the Altay Technical University, Russia. Currently, he works as a head of the Center for High-Tech Educational Process Support Facilities in the Biysk Technological Institute. His research interests include development of measuring and control devices, digital electronics.