Abstract:
The apparatus according to the present invention is an apparatus for measuring width direction end position of a strip which passes through an enclosed space surrounded by a plurality of surfaces. The apparatus includes an antenna section which emits electromagnetic waves toward the width direction end and receives the electromagnetic waves reflected by the width direction end; a signal processing section for determining a position of the width direction end using the reflected electromagnetic waves; and a scattering plate for scattering electromagnetic waves which are incident thereon, wherein the antenna section is installed on a first surface which faces the width direction end a position of which is to be determined and the scattering plate is installed on a second surface which faces the first surface.

Description:
TECHNICAL FIELD 
       [0001]    The present invention relates to an apparatus for measuring width direction end position of a strip, an apparatus for measuring width direction central position of a strip and a microwave scattering plate. 
       BACKGROUND ART 
       [0002]    In production and treatment processes of strips such as steel strips, strips must be made by control to travel without meandering. Further, in coiling a strip, the end of the strip to be coiled must be kept at a fixed position with respect to the coiling position by control for a better shape of the coiled strip. For such a control, an apparatus for measuring width direction end position of a strip and an apparatus for measuring width direction central position of a strip are used in the production and treatment processes of strips. 
         [0003]    As an apparatus for measuring width direction end position of a strip and an apparatus for measuring width direction central position of a strip, an optical type, a pneumatic type, a capacitance type and the like are used. However, the optical type has a problem that it is sensitive to the environment such as steam and dust particles. The pneumatic type has a problem that it cannot achieve a high accuracy of detection. The capacitance type has a problem that it is not sufficiently stable. 
         [0004]    In order to solve the problems described above, the applicant has developed and commercialized an apparatus for measuring width direction end position of a strip and an apparatus for measuring width direction central position of a strip in which electromagnetic waves are used (hereinafter called an electromagnetic wave type) (Patent Document 1). In the electromagnetic wave type, electromagnetic waves are transmitted toward the end of a strip and reflected electromagnetic waves are detected to measure a distance toward the end. The electromagnetic wave type has advantages that it is not sensitive to the environment such as steam and dust particles, achieves a high accuracy of detection and is highly stable. Thanks to the above-described advantages, the electromagnetic wave type can be used with stability even in a hostile environment such as in heat treat furnaces. 
         [0005]    However, when the electromagnetic wave type is used in an enclosed space of predetermined dimensions or smaller such as in a narrow furnace, there arises a problem that noise is generated by electromagnetic waves reflected on inside surfaces of the enclosed space and the noise deteriorates accuracy of measurement of the electromagnetic wave type. Thus, a sufficiently high accuracy of measurement can hardly be assured when the electromagnetic wave type is used in an enclosed space of predetermined dimensions or smaller. 
         [0006]    Further, materials to absorb electromagnetic waves are used to prevent harmful effects of noise caused by electromagnetic waves such as microwaves (for example, Patent Document 2). However, such materials to absorb electromagnetic waves are poor in environmental resistance such as heat-resistance, and therefore cannot be used at elevated temperatures such as in a high-temperature furnace. 
       PRIOR ART DOCUMENTS 
     Patent Documents 
       [0000]    
       
         Patent Document 1: JP4416798B 
         Patent Document 2: JP2008-277363A 
       
     
       SUMMARY OF INVENTION 
     Problem to be Solved by the Invention 
       [0009]    Accordingly, there is a need for an apparatus for measuring width direction end position of a strip and an apparatus for measuring width direction central position of a strip which use electromagnetic waves and can assure a sufficiently high accuracy of measurement in an enclosed space of predetermined or smaller dimensions such as in a narrow furnace. Further, there is a need for a member to absorb electromagnetic waves which replaces materials to absorb electromagnetic waves and which is good in environmental resistance. 
       Means for Solving the Problem 
       [0010]    An apparatus for measuring width direction end position of a strip according to the first aspect of the present invention is an apparatus for measuring width direction end position of a strip which passes through an enclosed space surrounded by a plurality of surfaces. The apparatus for measuring width direction end position of a strip according to the present aspect includes an antenna section which emits electromagnetic waves toward the width direction end and receives the electromagnetic waves reflected by the width direction end; a signal processing section for determining a position of the width direction end using the reflected electromagnetic waves; and a scattering plate for scattering electromagnetic waves which are incident thereon, wherein the antenna section is installed on a first surface which faces the width direction end a position of which is to be determined and the scattering plate is installed on a second surface which faces the first surface. 
         [0011]    Since the apparatus for measuring width direction end position of a strip according to the present aspect is provided with the scattering plate on the surface of the enclosed space, which faces the surface on which the antenna section in installed, electromagnetic waves which have been emitted by the antenna section, reflected by the opposite surface and return again to the antenna section can be remarkably reduced. Accordingly, in the apparatus for measuring width direction end position of a strip according to the present aspect, noise caused by reflected electromagnetic waves in an enclosed space smaller than predetermined dimensions can be remarkably reduced over a wide range of distance between the surface on which the antennas section is installed and the end of an object to be measured, and therefore a sufficient accuracy of measurement can be ensured in the enclosed space of predetermined or smaller dimensions. 
         [0012]    In an embodiment of the present aspect, the scattering plate is corrugated. 
         [0013]    In the present embodiment, electromagnetic waves which have reached the scattering plate are reflected in directions which are different from the direction in which electromagnetic waves incident onto a flat plate installed in place of the scattering plate at the same position would be specularly reflected by the flat plate, and therefore electromagnetic waves which travel in the direction in which electromagnetic waves incident onto the flat plate installed in place of the scattering plate at the same position would be specularly reflected can be remarkably reduced. Accordingly, noise of the measuring apparatus caused by reflected electromagnetic waves can be remarkably reduced. Further, the scattering plat which is corrugated can be easily made from metal such as steel by working. 
         [0014]    In another embodiment of the present aspect, the scattering plate is provided with a set of cone- or pyramid-shaped projections or cone- or pyramid-shaped depressions arranged thereon. 
         [0015]    In the present embodiment, electromagnetic waves which have reached the scattering plate are uniformly scattered around cone- or pyramid-shaped projections or cone- or pyramid-shaped depressions, and therefore electromagnetic waves which travel in the direction in which electromagnetic waves incident onto a flat plate installed in place of the scattering plate at the same position would be specularly reflected can be remarkably reduced. Accordingly, noise of the measuring apparatus caused by reflected electromagnetic waves can be remarkably reduced. 
         [0016]    An apparatus for measuring width direction central position of a strip according to the second aspect of the present invention is an apparatus for measuring width direction central position of a strip which passes through an enclosed space surrounded by a plurality of surfaces. The apparatus includes a first antenna section which emits electromagnetic waves toward one of the width direction ends and receives the electromagnetic waves reflected by the one of the width direction ends; a second antenna section which emits electromagnetic waves toward the other of the width direction ends and receives the electromagnetic waves reflected by the other of the width direction ends; a signal processing section for determining a width direction central position of the strip by determining positions of both width direction ends using data obtained from the reflected electromagnetic waves; and scattering plates for scattering electromagnetic waves which are incident thereon, wherein the first antenna section is installed on a first surface of the enclosed space, which faces the one of the width direction end, the second antenna section is installed on a second surface of the enclosed space, which faces the other of the width direction ends and the scattering plates are installed respectively around the first antenna section on the first surface and around the second antenna section on the second surface. 
         [0017]    The apparatus for measuring width direction central position of a strip according to the present aspect is provided with the scattering plates which are installed respectively around the second antenna section on the second surface facing the first surface on which the first antenna section is installed and around the first antenna section on the first surface facing the second surface on which the second antenna section is installed, and therefore electromagnetic waves which have been emitted by the first and second antenna sections and reflected by the opposite surfaces and return again to the first and second antenna sections can be remarkably reduced. Accordingly, in the apparatus for measuring width direction central position of a strip according to the present aspect, noise caused by reflected electromagnetic waves in an enclosed space smaller than predetermined dimensions can be remarkably reduced over a wide range of distance between one of the surfaces on which the first and second antennas sections are installed and the corresponding end of an object to be measured, and therefore a sufficient accuracy of measurement can be ensured in the enclosed space of predetermined or smaller dimensions. 
         [0018]    A scattering plate according to the third aspect of the present invention is a scattering plate for scattering microwaves which are incident thereon, wherein the scattering plate is corrugated. 
         [0019]    In the scattering plate according to the present aspect, electromagnetic waves which travel in the direction in which electromagnetic waves incident onto a flat plate installed in place of the scattering plate at the same position would be specularly reflected can be remarkably reduced. Further, the scattering plate according to the present aspect can be made from metal, and therefore is good in environmental resistance such as heat-resistance 
         [0020]    In an embodiment of the present aspect, a length of a face of the corrugation is more than a half of the wavelength of the microwaves. 
         [0021]    In the present embodiment, microwaves are efficiently scattered. If the length of the face of the corrugation is less than a half of the wavelength of the frequency of the microwaves, scattering effect thorough reflection on the face might not be obtained. 
         [0022]    In another embodiment of the present aspect, an angle of incidence of the microwaves with respect to a face of the corrugation ranges from 20 degrees to 45 degrees. 
         [0023]    In the present embodiment, microwaves which are incident onto the face of the corrugation are scattered in directions completely different from the incidence direction, and therefore the microwaves are efficiently scattered. 
         [0024]    A scattering plate according to the fourth aspect of the present invention is a scattering plate for scattering microwaves which are incident thereon, wherein the scattering plate is provided with a set of cone- or pyramid-shaped projections or cone- or pyramid-shaped depressions thereon. 
         [0025]    In the scattering plate according to the present aspect, electromagnetic waves which travel in the direction in which electromagnetic waves incident onto a flat plate installed in place of the scattering plate at the same position would be specularly reflected can be remarkably reduced. Further, the scattering plate according to the present aspect can be made from metal, and therefore is good in environmental resistance such as heat-resistance 
         [0026]    In an embodiment of the present aspect, a length of a surface of a cone or a pyramid is more than a half of the wavelength of the microwaves. 
         [0027]    In the present embodiment, microwaves are efficiently scattered. If the length of a surface of a cone or a pyramid is less than a half of the wavelength of the microwaves, scattering effect thorough reflection on the face might not be obtained. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0028]      FIG. 1  illustrates an apparatus for measuring width direction central position of a strip; 
           [0029]      FIG. 2  shows a configuration of the signal processing unit for the left end in the signal processing section of the apparatus for measuring width direction central position of a strip according to the present embodiment; 
           [0030]      FIG. 3  shows an apparatus for measuring width direction edge position of a strip according to an embodiment of the present invention, installed in an enclosed space; 
           [0031]      FIG. 4  shows a strip passing through a furnace as an enclosed space; 
           [0032]      FIG. 5  shows a strip in a furnace and an apparatus for measuring width direction edge position of a strip according to an embodiment of the present invention, installed in the furnace; 
           [0033]      FIG. 6  illustrates a detection area of an apparatus for measuring width direction edge position of a strip according to an embodiment of the present invention, installed in a furnace; 
           [0034]      FIG. 7  illustrates an experiment to determine how electromagnetic waves which are emitted by an apparatus for measuring width direction edge position of a strip according to an embodiment of the present invention and reflected by a plate affect the apparatus; 
           [0035]      FIG. 8A  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 5 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 ; 
           [0036]      FIG. 8B  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 10 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 ; 
           [0037]      FIG. 8C  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 15 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 ; 
           [0038]      FIG. 8D  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 20 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 ; 
           [0039]      FIG. 8E  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 25 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 ; 
           [0040]      FIG. 8F  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 30 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 ; 
           [0041]      FIG. 8G  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 35 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 ; 
           [0042]      FIG. 8H  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 40 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 ; 
           [0043]      FIG. 8I  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 45 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 ; 
           [0044]      FIG. 9  illustrates an experiment to determine how electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention and reflected by a scattering plate which is corrugated affect the apparatus; 
           [0045]      FIG. 10  illustrates an experiment to determine how electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention and reflected by a scattering plate provided with a set of cone- or pyramid-shaped projections affect the apparatus; 
           [0046]      FIG. 11A  shows plan views of scattering plates in which cone- or pyramid-shaped projections are arranged on a plane; 
           [0047]      FIG. 11B  shows perspective drawings of scattering plates provided respectively with cone- or pyramid-shaped projections and with cone- or pyramid-shaped depressions thereon; 
           [0048]      FIG. 12  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by the scattering plate which is corrugated and received by the apparatus in the experiment described in connection with  FIG. 9 ; 
           [0049]      FIG. 13  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by the scattering plate provided with a set of cone- or pyramid-shaped projections and received by the apparatus in the experiment described in connection with  FIG. 1 ; 
           [0050]      FIG. 14  illustrates an experiment to determine how electromagnetic waves which are reflected by a furnace wall affect the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention when a position of the strip is changed in the furnace; 
           [0051]      FIG. 15  shows measurements of the end position obtained by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention when a scattering plate is not used in the experiment shown in  FIG. 14 ; 
           [0052]      FIG. 16  shows measurements of the end position obtained by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention when the scattering plate which is corrugated is used in the experiment shown in  FIG. 14 ; 
           [0053]      FIG. 17  shows measurements of the end position obtained by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention when the scattering plate provided with a set of cone- or pyramid-shaped projections is used in the experiment shown in  FIG. 14 ; and 
           [0054]      FIG. 18  shows an apparatus for measuring width direction central position of a strip according to an embodiment of the present invention, installed in an enclosed space. 
       
    
    
     DESCRIPTION OF EMBODIMENTS 
       [0055]      FIG. 1  illustrates an apparatus for measuring width direction central position of a strip. A scattering plate is not shown in  FIG. 1 , and therefore the apparatus of the electromagnetic wave type shown in  FIG. 1  is identical with that described in Patent Document 1. The scattering plate will be described in detail later. 
         [0056]    A cold-rolled steel strip  201  runs between a furnace wall  301 R and a furnace wall  301 L of a continuous annealing furnace as an enclosed space. The enclosed space is a space which extends a certain distance in the longitudinal direction of the strip  201  and is formed by surfaces which surround the strip  201 . The enclosed space has openings as an entrance and an exit of the strip. In the drawing, the horizontal direction indicates to the width direction of the cold-rolled steel strip  201 , and the cold-rolled steel strip  201  runs from the near side to the far side. 
         [0057]    On the furnace wall  301 R on the right side, a microwave transmitting antenna  101 R and a microwave receiving antenna  103 R are provided such that microwaves transmitted by the microwave transmitting antenna  101 R is reflected by the right end of the cold-rolled steel strip  201  and received by the microwave receiving antenna  103 R. Similarly, on the furnace wall  301 L on the left side, a microwave transmitting antenna  101  L and a microwave receiving antenna  103  L are provided such that microwaves transmitted by the microwave transmitting antenna  101  L is reflected by the left end of the cold-rolled steel strip  201  and received by the microwave receiving antenna  103  L. 
         [0058]    When time between transmission of microwaves and reception of the reflected waves is represented as t and velocity of the microwaves is represented as c, a distance to an object which has reflected the microwaves can be obtained as below. 
         [0000]        t·c/ 2 
         [0059]    The microwave transmitting antenna  101 R and the microwave receiving antenna  103 R are connected to a signal processing unit for the right end  105 R. The signal processing unit for the right end  105 R generates microwaves and delivers them to the microwave transmitting antenna  101 R, converts microwaves received by the microwave receiving antenna  103 R into an electric signal, measures time t between transmission of microwaves and reception of the reflected waves by processing the electric signal and calculates a distance to the right end of the cold-rolled steel strip  201  based on the time t to determine a position of the right end of the cold-rolled steel strip  201 . Similarly, the microwave transmitting antenna  101 L and the microwave receiving antenna  103  L are connected to a signal processing unit for the left end  105  L. The signal processing unit for the left end  105 L generates microwaves and delivers them to the microwave transmitting antenna  101 L, converts microwaves received by the microwave receiving antenna  103 L into an electric signal, measures time t between transmission of microwaves and reception of the reflected waves by processing the electric signal and calculates a distance to the left end of the cold-rolled steel strip  201  based on the time t to determine a position of the left end of the cold-rolled steel strip  201 . Signal from the signal processing unit for the right end  105 R and signal from the signal processing unit for the left end  105  L are delivered to a signal processing unit for the central position of the strip  107 . The signal processing unit for the central position of the strip  107  detects a width direction central position of the cold-rolled steel strip  201  as the midpoint between the position of the right end and the position of the left end. A combination of the signal processing unit for the right end  105 R, the signal processing unit for the left end  105 L and the signal processing unit for the central position of the strip  107  is referred to as a signal processing section. 
         [0060]    In the above-described apparatus for measuring width direction central position of a strip, a group of the microwave transmitting antenna and the microwave receiving antenna on the right side and the signal processing unit for the right end or a group of the microwave transmitting antenna and the microwave receiving antenna on the left side and the signal processing unit for the left end forms an apparatus for measuring width direction end position of a strip. Each group can be made to function independently for measuring the right or left end position of the strip. 
         [0061]      FIG. 2  shows a configuration of the signal processing unit for the left end in the signal processing section of the apparatus for measuring width direction central position of a strip according to the present embodiment.  FIG. 2  and the description thereof are identical with those described in Patent Document 1. 
         [0062]    A clock generator  501  generates a clock signal with a frequency f 1 . This clock signal enters an M-sequence signal generator  505  and is converted into an M-sequence pseudo-random signal. The term “pseudo-random signal” as used in the text of specification and in the claims refers to a signal that has a periodicity when viewed for a long time but can be considered a random signal when viewed for a short time. An M-sequence signal is universally known as a typical pseudo-random signal composed of two values, “1” and “0,” and an example of how such a signal is formed is described in JP-H06-16080B. The wave number of the pulses included in one period of this M-sequence signal is designated as N. The output M 1  of the M-sequence signal generator  505  is split in two parts, one of which enters a power amplifier  513 , is power-amplified, and is emitted as microwaves from the transmitting antenna  101 L. 
         [0063]    A clock generator  503  generates a clock signal with a frequency f 2 . This frequency f 2  is set slightly lower than the frequency f 1 . This clock signal enters an M-sequence signal generator  507  and is converted into an M-sequence pseudo-random signal. Since the M-sequence signal generator  505  and M-sequence signal generator  507  are made up of exactly the same circuitry, the repeat pattern of the output from the M-sequence signal generator  13  and that of the output from M-sequence signal generator  14  are identical with each other, and the only difference is the frequency. 
         [0064]    The output M 2  of the M-sequence signal generator  507  is split in two parts, one of which enters a multiplier  509  and is multiplied by the output M 1  of the M-sequence signal generator  505 . The output of the multiplier  509  enters a low-pass filter  517 , where the high-frequency component is removed. The output of this low-pass filter  517  is a triangular wave. The timing with which the output of this low-pass filter  517  reaches its maximum value is detected by a maximum value detection circuit  521 , pulses are generated with this timing, and these are used as reference signals. If the period of the reference signals is designated as T A , the difference in wave number between the signal M 1  and the signal M 2  included in this period T A  is the wave number N of exactly one period. Specifically, this relationship is expressed as follows: 
         [0000]        T   A   ·f 1 =T   A   ·f 2 +N    
         [0000]    From this, the following is obtained. 
         [0000]        T   A   =N /( f 1 −f 2)  (1)
 
         [0065]    The microwaves reflected by the end of the cold-rolled steel strip  201  are received by the microwave receiving antenna  103 L and amplified by a power amplifier  515 . The output signal M 1 ′ of the power amplifier  515  enters a multiplier  511  and is multiplied by the output signal M 2  of the M-sequence signal generator  507 . The output of the multiplier  511  enters a low-pass filter  519 , where the high-frequency component is removed. The output of this low-pass filter  519  is a triangular wave. The timing with which the output of this low-pass filter  519  reaches its maximum value is detected by a maximum value detection circuit  523 , pulses are generated at this timing, and these are used as detection signals. 
         [0066]    If the time period from the time at which microwaves are emitted by the microwave transmitting antenna  101 L to the time at which the reflected waves are detected by the receiving antenna  103 L is designated as Δt, and the difference between the time at which a detection signal is generated and the time at which a reference signal is generated is designated as τ, then the wave number of the signal M 2  generated during the period τ is lower than the wave number of the signal M 1  generated during the period τ by the wave number of the signal M 1  generated during the period Δt. Accordingly, the following equation holds true. 
         [0000]      τ· f 2 =τ·f 1 −Δt·f 1
 
         [0000]    From this, the following is obtained: 
         [0000]      Δ t =( f 1 −f 2)·τ c/f 1  (2)
 
         [0000]    A time difference detection circuit  25  performs this calculation and determines Δt. 
         [0067]    If the velocity of the microwaves is designated as c, the distance x between the transmitting antenna  101 L or the receiving antenna  103 L and the edge of the cold-rolled steel strip  201  is calculated from the following equation 
         [0000]        x =( f 1 −f 2)·τ· c /(2 ·f 1)  (3)
 
         [0000]    Thus, the position of the edge of the cold-rolled steel strip  201  is determined. A distance computation circuit  527  performs this calculation to determine the distance x. 
         [0068]    With this means, only signals having the same waveform as the M-sequence signals generated by the M-sequence signal generator  505  and M-sequence signal generator  507  are valid. Therefore, noise can be eliminated almost completely, and even in cases where the power of the reflected waves is very small, the reflected wave signal can be obtained at a high S/N ratio. 
         [0069]    In cases where microwaves from the microwave transmitting antenna  101 R in  FIG. 1  are detected by the microwave receiving antenna  103 L, or in cases where microwaves from the microwave transmitting antenna  101 L are detected by the microwave receiving antenna  103 R, detection error caused by mixture of the two signals can be prevented by having the waveform of the M sequence used in the right-side edge position measurement apparatus  105 R be separate from the pattern of the M sequence used in the left-side edge position measurement apparatus  105 L. 
         [0070]      FIG. 3  shows an apparatus for measuring width direction edge position of a strip according to an embodiment of the present invention, installed in an enclosed space. In the description below, the enclosed space is a furnace. However, the enclosed space can be a passage like a throat or the like besides furnaces. 
         [0071]    In  FIG. 3 , electromagnetic waves emitted by the transmitting antenna  101 L provided on the furnace wall  301 L are reflected by the edge of the strip  201  and then received by the receiving antenna  103 L. The transmitting antenna  101 L and the receiving antenna  103 L are installed such that the electric field plane of the electromagnetic waves is parallel to the plane of the strip  201 . Electromagnetic waves reflected by the edge of the strip  201  are used as signal for measurement of a distance to the edge of the strip  201 , and therefore they are represented as S in  FIG. 3 . On the other hand, some of the electromagnetic waves emitted by the transmitting antenna  101 L reach the furnace wall  301 R facing the furnace wall  301 L, are reflected by the furnace wall  301 R and are received by the receiving antenna  103 L. Electromagnetic waves reflected by the furnace wall  301 R are noise in measurement of a distance to the edge of the strip  201  using electromagnetic waves reflected by the edge of the strip  201 , and therefore the electromagnetic waves reflected by the furnace wall  301 R are represented as N in  FIG. 3 . In order to obtain a higher SN ratio (a signal to noise ratio), influence of noise N generated by reflection on the furnace wall  301 R must be reduced. 
         [0072]    Free space propagation loss T of reflected power of electromagnetic waves is represented by the following expression. 
         [0000]    
       
         
           
             T 
             = 
             
               10 
                
               
                 
                   log 
                    
                   
                     ( 
                     
                       
                         4 
                          
                         π 
                          
                         
                             
                         
                          
                         D 
                       
                       λ 
                     
                     ) 
                   
                 
                 2 
               
             
           
         
       
     
         [0000]    Unit of free space propagation loss T is dB. D represents propagated distance while λ represents wavelength of the electromagnetic waves. Since free space propagation loss T increases in proportion to square of propagated distance, noise caused by reflected electromagnetic waves is negligible when the propagated distance is great. 
         [0073]      FIG. 4  shows a strip passing through a furnace as an enclosed space. 
         [0074]      FIG. 4  shows a cross section perpendicular to the plane of the strip. The furnace has furnace walls  301 T and  301 B which are parallel to the plane of the strip  201  and furnace walls  301 L and  301 R which are perpendicular to the plane of the strip  201 . In the cross section shown in  FIG. 4 , length in the direction parallel to the plane of the strip of the furnace wall  301 T and that of the furnace wall  301 B are A, while length in the direction perpendicular to the plane of the strip of the furnace wall  301 L and that of the furnace wall  301 R is B. If A is smaller than 2000 mm or B is smaller than 1000 mm, an influence of electromagnetic waves reflected on the furnace wall surfaces (inner surfaces of the enclosed space) cannot be ignored. The reason that an influence of noise becomes greater when A is smaller than a predetermined value has been described in connection with  FIG. 3 . The reason that an influence of noise becomes greater when B is smaller than a predetermined value will be described later. 
         [0075]      FIG. 5  shows a strip in a furnace and an apparatus for measuring width direction edge position of a strip according to an embodiment of the present invention, installed in the furnace. 
         [0076]      FIG. 5  shows a cross section perpendicular to the plane of the strip. In  FIG. 5 , a transmission area into which electromagnetic waves are transmitted by a transmitting antenna  101 L installed on a furnace wall surface  301 L is represented as T. Further, a reception area from which electromagnetic waves are received by a receiving antenna  103 L installed on the furnace wall surface  301 L is represented as R. The area in which the transmission area T and the reception area R overlap each other is a detection area D of the apparatus for measuring width direction edge position of a strip. 
         [0077]      FIG. 6  illustrates a detection area of the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, installed in a furnace. 
         [0078]    By way of example, when frequency of the carrier wave is 10 GHz and directional gain is 20 dBi, the transmission area and reception area corresponds to approximately 23 degrees (main lobe). As shown in  FIG. 6 , width in the vertical direction of the detection area is approximately 700 mm when the distance in the horizontal direction is 2000 mm. 
         [0079]      FIG. 7  illustrates an experiment to determine how electromagnetic waves which are emitted by an apparatus for measuring width direction edge position of a strip according to an embodiment of the present invention and reflected by a plate affect the apparatus. Electromagnetic waves reflected by the plate correspond to noise as described in connection with  FIG. 4  and should preferably be minimized. 
         [0080]    As shown in  FIG. 7(   a ), the plate is 600 mm square and the plate is initially set at a distance of 500 mm from transmitting and receiving antennas such that the plate is parallel to the apertures of the transmitting and receiving antennas. In the above-described arrangement, electromagnetic waves which have been emitted by the transmitting antenna  101  and reflected by plate  401  are detected by the receiving antenna  103 . 
         [0081]    Then, as shown in  FIG. 7(   b ), the plate  401  is inclined with respect to the apertures of the transmitting and receiving antennas, and in the above-described arrangement, electromagnetic waves which have been emitted by the transmitting antenna  101  of the apparatus for measuring width direction edge position and reflected by the plate  401  are detected by the receiving antenna  103 . Detection is performed at each five degrees from 5 degrees to 45 degrees of angle of inclination. Thus, detection is performed at nine kinds of angles of inclination. The plane of the plate  401  at 0 degree of angle of inclination is referred to as a reference plane. The reference plane is parallel to the apertures of the transmitting and receiving antennas. When electromagnetic waves travel in a direction perpendicular to the reference plate and are incident onto the plate  401 , angle of incidence of the electromagnetic waves is equal to angle of inclination of the plate  401 . 
         [0082]      FIG. 8A  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 5 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 . 
         [0083]    In  FIGS. 8A to 8I , the horizontal axis represents frequency of the carrier wave while the vertical axis represents intensity of received electromagnetic waves. Intensity of electromagnetic waves reflected by a plate at each angle of inclination is represented by a solid line, while intensity of electromagnetic waves reflected by a plate at an angle of inclination of 0 degree is represented by a dotted line as reference. In each drawing, values in unit of dB shown with frequencies represent those of intensity of electromagnetic waves at corresponding frequencies which are reflected by a plate at each angle of inclination. 
         [0084]    According to  FIG. 8A , in the case of frequency of the carrier wave of 10 GHz, the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 5 degrees is smaller than the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 0 degree by approximately 1.5 dB. 
         [0085]      FIG. 8B  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 10 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 . 
         [0086]    According to  FIG. 8B , in the case of frequency of the carrier wave of 10 GHz, the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 10 degrees is smaller than the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 0 degree by approximately 3.9 dB. 
         [0087]      FIG. 8C  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 15 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 . 
         [0088]    According to  FIG. 8C , in the case of frequency of the carrier wave of 10 GHz, the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 15 degrees is smaller than the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 0 degree by approximately 7.0 dB. 
         [0089]      FIG. 8D  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 20 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 . 
         [0090]    According to  FIG. 8D , in the case of frequency of the carrier wave of 10 GHz, the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 20 degrees is smaller than the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 0 degree by approximately 15.2 dB. 
         [0091]      FIG. 8E  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 25 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 . 
         [0092]    According to  FIG. 8E , in the case of frequency of the carrier wave of 10 GHz, the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 25 degrees is smaller than the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 0 degree by approximately 21.4 dB. 
         [0093]      FIG. 8F  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 30 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 . 
         [0094]    According to  FIG. 8F , in the case of frequency of the carrier wave of 10 GHz, the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 30 degrees is smaller than the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 0 degree by approximately 22.7 dB. 
         [0095]      FIG. 8G  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 35 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 . 
         [0096]    According to  FIG. 8G , in the case of frequency of the carrier wave of 10 GHz, the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 35 degrees is smaller than the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 0 degree by approximately 33.5 dB. 
         [0097]      FIG. 8H  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 40 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 . 
         [0098]    According to  FIG. 8H , in the case of frequency of the carrier wave of 10 GHz, the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 40 degrees is smaller than the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 0 degree by approximately 23.9 dB. 
         [0099]      FIG. 8I  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by a plate at an angle of inclination of 45 degrees and received by the apparatus in the experiment described in connection with  FIG. 7 . 
         [0100]    According to  FIG. 8I , in the case of frequency of the carrier wave of 10 GHz, the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 45 degrees is smaller than the intensity of electromagnetic waves reflected by the plate at an angle of inclination of 0 degree by approximately 18.8 dB. 
         [0101]    According to the results shown in  FIGS. 8A to 8I , intensity of electromagnetic waves which are received by the receiving antenna  103  and correspond to noise reflected by the plate  401  is relatively small when the angle of inclination is between 20 degrees and 45 degrees inclusive. 
         [0102]      FIG. 9  illustrates an experiment to determine how electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention and reflected by a scattering plate which is corrugated affect the apparatus. 
         [0103]      FIG. 9(   a ) shows an arrangement of transmitting and receiving antennas of the apparatus for measuring width direction edge position of a strip and the scattering plate  111 A. 
         [0104]    The scattering plate  111 A which is corrugated on a surface is 600 mm square. The scattering plate  111 A is set at a distance of 500 mm from the transmitting and receiving antennas such that it is parallel to the apertures of the transmitting and receiving antennas. In the text of specification and the claims, a scattering plate means a plate which reflect electromagnetic waves incident onto the plate in a direction which is different from the direction in which the electromagnetic would be specularly reflected when the plate were flat. In the above-described arrangement, electromagnetic waves which have been emitted by the transmitting antenna of the apparatus for measuring width direction edge position and reflected by the scattering plate  111 A which is corrugated are detected by the receiving antenna. A size of the scattering plate  111 A substantially corresponds to the detection area of the transmitting and receiving antennas shown in  FIG. 6 . 
         [0105]      FIG. 9(   b ) shows a cross section of the corrugation of the scattering plate  111 A. The cross section is perpendicular to the direction of the ridges and troughs of the corrugation. According to the results shown in  FIGS. 8A to 8I , in the corrugation an angle of inclination of a face with respect to the bottom is preferably between 20 degrees and 45 degrees inclusive. In the present embodiment, an angle of inclination of a face with respect to the bottom is set to 30 degrees. The scattering plate  111 A is made from metal such as steel by working. A length of the face S of the corrugation should be more than a half of the wavelength corresponding to the frequency of the carrier wave. In the text of specification and the claims, a length of the face S of the corrugation refers to a distance between adjacent ridge and trough in a cross section perpendicular to the direction of the ridge or trough of the corrugation. If the length of the face S is less than a half of the wavelength of the frequency of the carrier wave, scattering effect thorough reflection on the face might not be obtained. When the frequency of the carrier wave is 10 GHz, the wavelength is 30 mm, and therefore the length of the face S should be 15 mm or more. 
         [0106]      FIG. 9(   c ) illustrates reflection by the corrugation shown in  FIG. 9(   b ) of electromagnetic waves in the direction perpendicular to the apertures of the transmitting and receiving antennas. As shown in  FIG. 9(   c ), electromagnetic waves in the direction perpendicular to the apertures of the transmitting and receiving antennas are reflected by a face of the corrugation at an angle of 60 degrees with respect to the direction. 
         [0107]      FIG. 10  illustrates an experiment to determine how electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention and reflected by a scattering plate provided with a set of cone- or pyramid-shaped projections affect the apparatus. 
         [0108]      FIG. 10(   a ) shows an arrangement of the transmitting and receiving antennas of the apparatus for measuring width direction edge position of a strip and the scattering plate  111 B. 
         [0109]    The scattering plate  111 B provided with cone- or pyramid-shaped projections on its surface, is 600 mm square. The scattering plate  111 B is set at a distance of 500 mm from the transmitting and receiving antennas such that it is parallel to the apertures of the transmitting and receiving antennas. In the above-described arrangement, electromagnetic waves which have been emitted by the transmitting antenna of the apparatus for measuring width direction edge position and reflected by the scattering plate  111 B provided with cone- or pyramid-shaped projections on its surface are detected by the receiving antenna. A size of the scattering plate  111 B substantially corresponds to the detection area of the transmitting and receiving antennas shown in  FIG. 6 . 
         [0110]      FIG. 10(   b ) shows a cross section of a cone-shaped projection of the scattering plate  111 B. The cross section contains the central axis of the cone-shaped projection (the axis of rotational symmetry of the cone). The scattering plate  111 B is made from metal such as steel by working. A length of the conical surface S should be more than a half of the wavelength corresponding to the frequency of the carrier wave. In the text of specification and the claims, a length of a surface of a cone or a pyramid refers to the minimum distance between the top and the bottom of thereof. A length of the conical surface corresponds to a cone distance. If the length of the surface S is less than a half of the wavelength of the frequency of the carrier wave, scattering effect thorough reflection on the surface might not be obtained. When the frequency of the carrier wave is 10 GHz, the wavelength is 30 mm, and therefore the length of the surface S should be 15 mm or more. 
         [0111]      FIG. 10(   c ) illustrates reflection by the cone- or pyramid-shaped projection shown in  FIG. 10(   b ) of electromagnetic waves travelling in the direction perpendicular to the apertures of the transmitting and receiving antennas. As shown in  FIG. 10(   c ), electromagnetic waves travelling in the direction perpendicular to the apertures of the transmitting and receiving antennas are reflected by the conical surface of the cone-shaped projection at an angle of 30 degrees with respect to the direction and at any angle around the central axis. 
         [0112]      FIG. 11A  shows plan views of scattering plates in which cone-shaped projections are arranged on a plane. FIG.  11 A(a) shows a plan view of a scattering plate in which cones are arranged on a plane such that the positions of the central axes of the cones form vertices of regular triangles. FIG.  11 A(b) shows a plan view of a scattering plate in which cones provided with hexagonal bottoms are arranged on a plane such that the positions of the central axes of the cones similarly form vertices of regular triangles. 
         [0113]      FIG. 11B  shows perspective drawings of scattering plates provided respectively with cone-shaped projections and with cone-shaped depressions thereon. FIG.  11 B(a) is a perspective drawing of a scattering plate provided with cone-shaped projections thereon while  FIG. 11(   b ) is a perspective drawing of a scattering plate provided with cone-shaped depressions thereon. The scattering plate provided with cone-shaped depressions thereon has a similar degree of effectiveness to the scattering plate provided with cone-shaped projections thereon. 
         [0114]    The above-described scattering plate which is corrugated and the above-described scattering plate provided with cone- or pyramid-shaped projections or with cone- or pyramid-shaped depressions thereon are made from metal such as steel by working as described above, and therefore are good in environmental resistance such as heat-resistance and can be widely used. 
         [0115]      FIG. 12  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by the scattering plate which is corrugated and received by the apparatus in the experiment described in connection with  FIG. 9 . 
         [0116]    In  FIG. 12 , the horizontal axis represents frequency of the carrier wave while the vertical axis represents intensity of received electromagnetic waves. Intensity of electromagnetic waves reflected by the scattering plate is represented by a solid line, while intensity of electromagnetic waves reflected in the absence of the scattering plate is represented by a dotted line as reference. When the intensity of electromagnetic waves reflected by the scattering plate is compared with the intensity of electromagnetic waves reflected in the absence of the scattering plate in  FIG. 12 , the former is smaller than the latter by approximately 20.7 dB at the frequency of the carrier wave of 9 GHz, by approximately 18.1 dB at the frequency of the carrier wave of 10 GHz and by approximately 13.5 dB at the frequency of the carrier wave of 11 GHz. 
         [0117]      FIG. 13  shows intensity of electromagnetic waves which are emitted by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention, reflected by the scattering plate provided with a set of cone- or pyramid-shaped projections and received by the apparatus in the experiment described in connection with  FIG. 10 . 
         [0118]    In  FIG. 13 , the horizontal axis represents frequency of the carrier wave while the vertical axis represents intensity of received electromagnetic waves. Intensity of electromagnetic waves reflected by the scattering plate is represented by a solid line, while intensity of electromagnetic waves reflected in the absence of the scattering plate is represented by a dotted line as reference. When the intensity of electromagnetic waves reflected by the scattering plate is compared with the intensity of electromagnetic waves reflected in the absence of the scattering plate in  FIG. 13 , the former is smaller than the latter by approximately 16.1 dB at the frequency of the carrier wave of 9 GHz, by approximately 22.6 dB at the frequency of the carrier wave of 10 GHz and by approximately 21.7 dB at the frequency of the carrier wave of 11 GHz. 
         [0119]      FIG. 14  illustrates an experiment to determine how electromagnetic waves which are reflected by a furnace wall affect the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention when a position of the strip is changed in the furnace. 
         [0120]      FIG. 14(   a ) shows a cross section of an experimental arrangement, which is parallel to the plane of the strip while  FIG. 14(   b ) shows a cross section of the experimental arrangement, which is perpendicular to the plane of the strip. The experimental arrangement includes a furnace section and a strip drive unit. The furnace section has a furnace wall surface section  301 T′, a furnace wall surface section  301 B′, a furnace wall surface section  301 L′ and a furnace wall surface section  301 R′. The furnace wall surface section  301 T′ and furnace wall surface section  301 B′ are parallel to the plane of the strip. The furnace wall surface section  301 L′ and furnace wall surface section  301 R′ are perpendicular to the plane of the strip. Length of the furnace wall surface section  301 T′ and that of the furnace wall surface section  301 B′ in the width direction and in the longitudinal direction of the strip are 2000 mm, respectively. Length of the furnace wall surface section  301 L′ and that of the furnace wall surface  301 R′ in the direction perpendicular to the plane of the strip are 700 mm, respectively. The strip drive unit  601  moves a strip section  201 ′ in the strip width direction in the furnace section. Thickness of the strip is 1 mm. The transmitting antenna  101 L and the receiving antenna  103 L of the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention are installed on the furnace wall surface section  301 L′ and electromagnetic waves which have been emitted by the transmitting antenna  101 L are received by the receiving antenna  103 L. 
         [0121]      FIG. 15  shows measurements of the end position obtained by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention when a scattering plate is not used in the experiment shown in  FIG. 14 . 
         [0122]    The horizontal axis of  FIG. 15  represents distance between the left end of the strip section  201 ′ and the furnace wall surface section  301 L′ in  FIG. 14 . The vertical axis of  FIG. 15  represents measurement of the distance obtained by the apparatus for measuring width direction edge position of a strip according to the present embodiment (scale on the left side) and difference between the measurement of the distance and the real value of the distance (scale on the right side). In  FIG. 15 , the measurement of the distance is represented as a thin solid line while the difference is represented as a thick solid line. 
         [0123]    According to  FIG. 15 , the maximum value of the difference of the measurement of the distance is approximately 45 mm. According to  FIG. 15 , the difference of the measurement of the distance becomes greater when the distance between the left end of the strip section  201 ′ and the furnace wall surface section  301 L′ is 300 mm or less. It is estimated that the reason is that electromagnetic waves reflected by the furnace wall surface on the opposite side travel leftward in  FIG. 14  along the strip section  201 ′ which extends to a position which is relatively close to the receiving antenna  103 L while being repeatedly reflected between the strip section  201 ′ and the furnace wall surface section  301 T′ and between the strip section  201 ′ and the furnace wall surface section  301 B′ and reach the receiving antenna  103 L. It is supposed that electromagnetic waves reflected by the furnace wall surface on the opposite side can hardly travel leftward in  FIG. 14  along the strip section  201 ′ while being repeatedly reflected between the strip section  201 ′ and the furnace wall surface section  301 T′ and between the strip section  201 ′ and the furnace wall surface section  301 B′ and can hardly reach the receiving antenna  103 L if length B in the direction perpendicular to the plane of the strip of the furnace wall surface  301 L (corresponding to furnace wall surface section  301 L′ in  FIG. 14 ) and the furnace wall surface  301 R (corresponding to furnace wall surface section  301 R′ in  FIG. 14 ) in  FIG. 4  is 1000 mm or greater. Accordingly, is estimated that an influence of noise caused by the reflected electromagnetic waves is small if length B is 1000 mm or greater. 
         [0124]      FIG. 16  shows measurements of the end position obtained by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention when the scattering plate which is corrugated is used in the experiment shown in  FIG. 14 . 
         [0125]    In the experimental arrangement shown in  FIG. 14 , the scattering plate  111 A a face of which is corrugated as shown in  FIG. 9  was installed at the area on the furnace wall surface section  301 R′, which faces the transmitting and receiving antennas and the experiment was carried out. A size of the scattering plate  111 A substantially corresponds to the detection area of the transmitting and receiving antennas which is shown in  FIG. 6 . 
         [0126]    The horizontal axis of  FIG. 16  represents distance between the left end of the strip section  201 ′ and the furnace wall surface section  301 L′ in  FIG. 14 . The vertical axis of  FIG. 16  represents measurement of the distance obtained by the apparatus for measuring width direction edge position of a strip according to the present embodiment (scale on the left side) and difference between the measurement of the distance and the real value of the distance (scale on the right side). In  FIG. 16 , the measurement of the distance is represented as a thin solid line while the difference is represented as a thick solid line. 
         [0127]    According to  FIG. 16 , the maximum value of the difference of the measurement of the distance is approximately 19 mm. When compared with data in  FIG. 15 , in  FIG. 16  the difference of the measurement of the distance is much smaller when the distance between the left end of the strip section  201 ′ and the furnace wall surface section  301 L′ is 300 mm or less. 
         [0128]      FIG. 17  shows measurements of the end position obtained by the apparatus for measuring width direction edge position of a strip according to the embodiment of the present invention when the scattering plate provided with a set of cone- or pyramid-shaped projections is used in the experiment shown in  FIG. 14 . 
         [0129]    In the experimental arrangement shown in  FIG. 14 , the scattering plate  111 B provided with a set of cone- or pyramid-shaped projections thereon as shown in  FIG. 10  was installed at the area on the furnace wall section  301 R′, which faces the transmitting and receiving antennas and the experiment was carried out. A size of the scattering plate  111 B substantially corresponds to the detection area of the transmitting and receiving antennas which is shown in  FIG. 6 . 
         [0130]    The horizontal axis of  FIG. 17  represents distance between the left end of the strip section  201 ′ and the furnace wall surface section  301 L′ in  FIG. 14 . The vertical axis of  FIG. 17  represents measurement of the distance obtained by the apparatus for measuring width direction edge position of a strip according to the present embodiment (scale on the left side) and difference between the measurement of the distance and the real value of the distance (scale on the right side). In  FIG. 17 , the measurement of the distance is represented as a thin solid line while the difference is represented as a thick solid line. 
         [0131]    According to  FIG. 17 , the maximum value of the difference of the measurement of the distance is approximately 13 mm. When compared with data in  FIG. 15 , in  FIG. 17  the difference of the measurement of the distance is much smaller over the whole range of the distance between the left end of the strip section  201 ′ and the furnace wall surface section  301 L′. 
         [0132]    Based on the results of the experiments shown in  FIGS. 15 to 17 , the inventors have newly obtained the findings that in measurement of the end position of a strip in a furnace accuracy of measurement can be remarkably improved over a wide range of distance between the surface ( 301 L′) on which the antennas are installed and the end of an object ( 201 ′) to be measured when a scattering plate is installed on the surface ( 301 R′) facing the surface ( 301 L′) on which the antennas are installed. In the absence of a scattering plate, difference of measurement of the distance between the left end of the strip section  201 ′ and the furnace wall surface section  301 L′ is relatively great when the distance is 300 mm or less. Such a great difference can also be remarkably reduced. It is estimated that the reason is that the installed scattering plate  111 A or  111 B remarkably reduces electromagnetic waves which are reflected by the furnace wall surface section  301 R′ facing the surface on which the transmitting antenna is installed, travel leftward in  FIG. 14  along the strip section  201 ′ while being repeatedly reflected between the strip section  201 ′ and the furnace wall surface section  301 T′ and between the strip section  201 ′ and the furnace wall surface section  301 B′ and reach the receiving antenna  103 L. 
         [0133]      FIG. 18  shows an apparatus for measuring width direction central position of a strip according to an embodiment of the present invention, installed in an enclosed space. 
         [0134]      FIG. 18(   a ) shows the whole arrangement of the apparatus for measuring width direction central position of a strip according to the present embodiment. The arrangement except for a scattering plate is identical with that described in connection with  FIG. 1 . A strip  201  runs through the enclosed space. A transmitting antenna  101 L and a receiving antenna  103 L for measuring a position of one of the width direction ends of the strip  201  are installed on a surface  301 L of the enclosed space, which faces the one of the width direction ends. A scattering plate  111 R for reducing electromagnetic waves received by the receiving antenna  103 L as noise is installed on a surface  301 R which faces the surface  301 L of the enclosed space. A transmitting antenna  101 R and a receiving antenna  103 R for measuring a position of the other of the width direction ends of the strip  201  are installed on a surface  301 R of the enclosed space. A scattering plate  111 L for reducing electromagnetic waves received by the receiving antenna  103 R as noise is installed on the surface  301 L which faces the surface  301 R of the enclosed space. The scattering plates  111 R and  111 L are made of metal such as steel and are corrugated or provided with a set of cone- or pyramid-shaped projections. 
         [0135]      FIG. 18(   b ) shows the scattering plate  111 L provided on the surface  301 L of the enclosed space. The scattering plate  111 L is installed around the transmitting antenna  101 L and the receiving antenna  103 L. Electromagnetic waves which have been emitted by the transmitting antenna  101 R installed on the surface  301 R and have reached the scattering plate  111 L installed on the surface  301 L are reflected or scattered in directions different from the incidence direction and do not travel toward the receiving antenna  103 R installed on the surface  301 R. On the other hand, electromagnetic waves which have been emitted by the transmitting antenna  101 R installed on the surface  301 R and have reached the transmitting antenna  101 L and the receiving antenna  103 L installed on the surface  301 L are absorbed without being reflected. The reason is that the transmitting antenna  101 L and the receiving antenna  103 L are connected respectively to a power amplifier  513  and a power amplifier  515  and are terminated with an impedance of 50 ohms. Accordingly, noise received by the receiving antenna  103 R installed on the surface  301 R is remarkably reduced compared with the case in which the scattering plate  111 L is not installed.