Abstract:
A rotating state detection apparatus comprising, an optical device for detecting coherent beams toward a plurality of positions on a diffraction grating present along a rotational direction of a rotating object, an interfering device for superposing diffraction beams of a specific order with each other, the diffraction beams being diffracted at the plurality of different positions on the diffraction grating, and light-receiving device for receiving the superposed beams obtained by the interfering device, and for photoelectrically converting interference fringes formed by the superposed beams.

Description:
This application is a continuation of application Ser. No. 883,052 filed on July 8, 1986, now abandoned. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a rotating state detection apparatus and, more particularly, to an apparatus which photoelectrically detects a rotational speed and angle of a rotating object by utilizing a beam diffracted by a diffraction grating, and which is suitable for e.g., a rotary encoder. 
     2. Related Background Art 
     Photoelectric rotary encoders are conventionally used as a means for detecting a rotational speed and variations therein of rotating mechanisms in office equipment, such as a floppy-disk drive computer and a printer, an NC machine tool, the capstan motor of a VTR, a rotating drum, and the like. 
     A method which adopts a photoelectric rotary encoder employs a so-called index scale system wherein a light projection means and a light-receiving means are arranged to oppose each other with a main scale and a stationary index scale sandwiched therebetween. The main scale is formed by arranging light-transmitting and light-shielding portions at equal angular intervals at the peripheral portion of a disk coupled to a rotating shaft. The index scale is formed by arranging light-transmitting and light-shielding portions at the same angular intervals as in the main scale. According to this method, a signal in synchronism with the pitch of the adjacent light-transmitting and light-shielding portions of both scales can be obtained as the main scale is rotated. The obtained signal is subjected to frequency analysis to detect variations in the rotational speed of the rotating shaft. The smaller the pitch of the light-transmitting and light-shielding portions on both scales, the higher the detection precision. However, when the scale pitch is small, the S/N ratio of the output signal from a light-receiving means is degraded by diffracted light, resulting in low precision. In order to prevent this, if a total number of light-transmitting and light-shielding portions of the main scale is fixed, and the intervals between the two portions are increased to a point at which the light-receiving means is free from the effects of the diffracted light, the diameter and thickness of the disk of the main scale are increased, resulting in an increase in the overall apparatus size. Therefore, the object to be rotated is overloaded. 
     SUMMARY OF THE INVENTION 
     The present invention has been made in view of the above conventional drawbacks. It is a first object of the present invention to provide a rotating state detection apparatus in which the load acting on a rotating object is decreased and which can perform measurement at high precision. 
     It is a second object of the present invention to provide a rotating state detection apparatus which satisfies the first object and in which the influence of mounting eccentricity caused upon mounting a measurement diffraction grating on a rotating object is eliminated. 
     It is a third object of the present invention to provide a rotating state detection apparatus which satisfies the first and second objects and which can perform detection with stable precision regardless of an environmental change such as a vibration or a temperature change. 
     In order to achieve the above objects, the rotating state detection apparatus according to the present invention comprises an optical means for directing coherent beams toward a plurality of positions on a diffraction grating present along a rotational direction of a rotating object, an interfering means for superposing diffraction beams of a specific order with each other, the diffraction beams being diffracted at the plurality of different positions on the diffraction grating, and a light-receiving means for receiving the superposed beams obtained by the interfering means, wherein interference fringes are photoelectrically converted by the light-receiving means thereby detecting the rotating object. 
     In particular, when coherent beams are directed toward two points on the rotating object which are substantially symmetrical with each other at least with respect to the center thereof, the eccentricity between the center of the diffraction grating and that of the rotating object can be removed, thereby allowing a highly precise measurement. 
     When the lengths of the optical paths of the plurality of diffraction beams emitted by a light source are set to be the same, an optical system stable against external influences such as a temperature change and a vibration can be provided. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic block diagram of a rotating state detection apparatus according to an embodiment of the present invention; 
     FIG. 2 is a vector diagram for explaining the relationship between a beam incident on the diffraction grating and a diffraction beam reflected thereby; 
     FIG. 3 is a view for explaining an eccentricity between the center of the radial grating and that of a rotating object which are used in the present invention; 
     FIG. 4 is a partial view for explaining a modification of the rotating state detection apparatus shown in FIG. 1; and 
     FIG. 5 is a schematic block diagram of a rotating state detection apparatus according to another embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1 is a schematic block diagram of a rotating state detection apparatus according to an embodiment of the present invention. 
     In FIG. 1, the apparatus has a coherent beam light source 1 such as a laser, a collimator lens 2, and a polarizing beam splitter 3. The polarizing beam splitter 3 is arranged such that its polarizing axis is inclined at 45° with respect to the linearly polarized light emitted by the laser 1. λ/4 plates 4 1 , 4 2 , and 4 3  are arranged such that their polarizing axes are respectively inclined at 45° with respect to the linearly polarized light reflected and transmitted by the polarizing beam splitter 3. More specifically, the λ/4 plate 4 1  is arranged such that its polarizing axis is inclined at 45° with respect to the direction of linear polarization of the beam reflected by the polarizing beam splitter 3. The λ/4 plate 4 2  is arranged such that its polarizing axis is inclined at 45° with respect to the direction of linear polarization of the beam transmitted through the polarizing beam splitter 3. The λ/4 plate 4 3  is arranged such that its polarizing axis is inclined at 45° with respect to either the direction of linear polarization of the beam transmitted through the polarizing beam splitter 3, or the direction of linear polarization of the beam reflected by the polarizing beam splitter 3. The apparatus also has a reflecting mirror 5, cylindrical lenses 6 1 , 6 2 , 6 1  &#39;, and 6 2  &#39;, and reflecting mirrors 7 and 7&#39;. A radial grating 8 has grating patterns consisting of e.g, light-transmitting portions and light-reflecting portions at equal angular intervals arranged on a disk. A rotating shaft 9 of a rotating object (not shown), a beam splitter 10, and light-receiving elements 12 and 12&#39; are also provided. Polarizing plates 11 and 11&#39; are arranged such that their directions of polarization form an angle of 45° with respect to each other. 
     The beam emitted by the laser 1 is collimated by the collimator lens 2, and a substantially parallel beam obtained is incident on the polarizing beam splitter 3. The polarizing beam splitter 3 is arranged such that its direction of polarization is inclined at 45° with respect to the direction of linear polarization of the laser 1, and splits the beam from the laser 1 into a reflected beam and a transmitted beam of substantially the same intensity. The two split beams respectively pass the [O/4 plates 4 1  and 4 2  and are circularly polarized. Among them, the transmitted beam which passed the λ/4 plate 4 2  is linearly incident on a position M1 of the radial grating 8 through the cylindrical lens 6 1 . The reflected which beam passed the λ/4 plate 4 1  is linearly incident on a position M2 of the radial grating 8 through the reflecting mirror 5 and the cylindrical lens 6 1  &#39;. The cylindrical lenses 6 1  and 6 1  &#39; are arranged as needed to linearly guide the beam in a direction perpendicular to the radial direction of the radial grating 8. With this linear radiation, a pitch error of the diffraction grating, which consists of light-transmitting and light-reflecting portions on the radial grating 8 corresponding to the portion irradiated by the beam, can be decreased. The portions M1 and M2 on the radial grating 8 irradiated with the beams are set to be substantially symmetrical with respect to the center of rotation of a rotating object (not shown). 
     The beam incident on the radial grating 8 is reflected and diffracted by the diffraction grating patterns of the radial grating 8. The diffraction angle θ m  of the reflected diffraction beams L and L&#39; of the mth order is represented by the following equation: 
     
         sin θ.sub.m =m λ/p                            (1) 
    
     where p is the pitch of the diffraction gratings at the portion irradiated with the beam, and λ is the wavelength of the beam. 
     Assume that the radial grating 8 is rotated at an angular speed ω. Then, a peripheral speed at the incident positions M1 and M2 is v=rω, where r is the distance from the center of rotation of the radial grating 8 to the incident positions M1 and M2. 
     When the beam incident on the positions M1 and M2 is represented as ki in wave vector representation, the reflected diffraction beams L and L&#39; are represented as ks and k&#39;s in wave vector representations, and the peripheral speed of the radial grating 8 at the positions M1 and M2 is represented as v by vector representation, their relationship is as shown in FIG. 2. Therefore, the frequencies of the reflected diffraction beams L and L&#39; are subjected to so-called Doppler shift by amounts Δf and Δf&#39;, respectively, represented by equation (2): ##EQU1## Where . represents the vector inner product. 
     The beams are reflected by the reflecting mirrors 7 and 7&#39; to be incident on the positions M1 and M2 again through the cylindrical lenses 6 2  and 6 2  &#39;. Then, the beams are diffracted again at the positions M1 and M2. In this case, these reflected diffraction beams of the mth order are subjected to Doppler shift again by the amounts represented by equation (2) and return to the initial optical paths. Therefore, the frequency of the beam which is re-diffracted at the position M1 and which returns to the initial optical path is subjected to Doppler shift by an amount 2Δf, and the frequency of the beam which is re-diffracted at the position M2 and which returns to the initial optical path is subjected to Doppler shift by an amount of -2Δf. 
     When the beam re-diffracted at the position M1 returns to the initial optical path and is transmitted through the λ/4 plate 4 2  again, it is linearly polarized thereby such that its direction of linear polarization is rotated through 90° when compared to the original incident beam, and is reflected by the polarizing beam splitter 3. Similarly, when the beam re-diffracted at the position M2 returns to the initial optical path and is transmitted through the λ/4 plate 4 1  again, it is linearly polarized thereby such that its direction of linear polarization is rotated through 90° when compared to the original incident beam, and is transmitted through the polarizing beam splitter 3. Thus, the beams rediffracted at the positions M1 and M2 are superposed on each other. After the superposed beam passes the λ/4 plate 4 3  and is split by the beam splitter 10 into two beams, the beams are transmitted through the polarizing plates 11 and 11&#39;, and are incident on the light-receiving elements 12 and 12&#39;. 
     In this manner, since the two beams subjected to Doppler shift of frequency by 2Δf and -2Δf are superposed, the frequency of the output signals of the light-receiving elements 12 and 12&#39; is: 2Δf-(-2Δf)=4Δf. More particularly, the frequency F of the output signals from the light-receiving elements 12 and 12&#39; is: F=4Δf=4fωsin θ m  /λ. Substitution of equation (1) into this equation yields: F=4mrω/p. Since p=rΔΨ and ΔΨ=2π/N, 
     
         F=2mNω/π                                          (3) 
    
     where N is the total number of the grating patterns on the radial grating 8 and ΔΨ is the pitch of the equal angular intervals. Since n=FΔt and θ=ωΔt, 
     
         n=2mNθ/π                                          (4) 
    
     where n is the number of waves of the output signal from the light-receiving element during a time Δt, and θ is the rotational angle of the radial grating 8 during the time Δt. As a result, the rotational angle θ of the radial grating 8 can be calculated in accordance with equation (4) by counting the number n of waves of the output signal from the light-receiving element. 
     It is preferable that the rotational direction be detected upon detection of the rotational angle. Therefore, in this embodiment, as is known in conventional photoelectric rotary encoders, a plurality of light-receiving elements are prepared and arranged such that the signals therefrom are 90° out of phase, and a signal representing the rotational direction is derived from the 90°-phase difference signals generated upon rotation. 
     In this embodiment, the 90°-phase difference between the output signals from the light-receiving elements 12 and 12&#39; is obtained by a combination of a polarizing beam splitter, a [O/4 plate, and a polarizing plate. More specifically, the light beams re-diffracted at the positions M1 and M2 and returned to the initial paths are respectively reflected by and transmitted through polarizing beam splitter 3 to be superposed with each other, and are then transmitted through the [O/4 plate 4 3  to provide linearly polarized light. The direction of the polarized light changes upon rotation of the radial grating 8. When the directions of polarization of the polarizing plates 11 and 11&#39;, which are respectively provided before the light-receiving elements 12 and 12&#39;, are shifted from each other by 45°, the 90°-phase difference is provided between the output signals from the light-receiving elements 12 and 12&#39;. For example, as shown in FIG. 1, the output signals from the light-receiving signals 12 and 12&#39; are subjected to waveform shaping to detect the rotational direction of the rotating object, and counted by the counter, thereby obtaining the rotational angle. 
     If this embodiment is adopted as a rotational speedometer which obtains only a rotational speed, the polarizing beam splitter 3 shown in FIG. 1 can be a half mirror, and the [O/4 plates 4 1 , 4 2 , and 4 3 , the polarizing plates 11 and 11&#39;, the beam splitter 10, and the light-receiving element 12 are not needed. 
     FIG. 3 is a view for explaining the radial grating 8 shown in FIG. 1, incident positions M1 and M2 of the two beams on the radial grating 8, and the center of rotation of the rotating object. 
     In this embodiment, the two points of positions M1 and M2 that are substantially symmetrical with respect to the center 0 of the radial grating 8 and to the center of rotation 0&#39; of the rotating object are set as the measurement points, in order to decrease the influence of the eccentricity between the center 0 of the radial grating 8 and the center of rotation 0&#39; of the rotating object. More particularly, it is difficult due to mechanical difficulties to completely coincide the center 0 of the radial grating 8 with the center of rotation 0&#39; of the rotating object, and a certain degree of eccentricity is inevitably present therebetween. For example, when an eccentricity a is present between the center 0 of the radial grating 8 and the center of rotation 0&#39; of the object to be rotated, as shown in FIG. 3, the Doppler shift of frequency at the measurement point M1, which is distant from the center of rotation by r, changes from r/(r+a) to r/(r-a) when compared to the case wherein no eccentricity is present. Meanwhile, the Doppler shift of frequency at the measurement point M2, which is symmetrical to the position M1 with respect to the center of rotation, changes from r/(r-a) to r/(r+a) in the opposite manner to that at the position M1. Therefore, the two points M1 and M2 are measured simultaneously, thereby decreasing the influence of the eccentricity. 
     FIG. 4 is a partial perspective view of a rotating state detection apparatus according to another embodiment of the present invention, and shows portions of the radial grating 8 shown in FIG. 1 to which beams are incident. The same reference numerals in FIG. 3 denote the same elements as in FIG. 1. The transmitted diffraction beams of the ±mth orders, which are incident on the positions M1 and M2 on the radial grating 8, are incident again on the radial grating 8 through cylindrical lenses 6 2  and 6 2  &#39;, λ/4 plates 4 2  and 4 2  &#39;, and corner cube reflecting mirrors 13 and 13&#39;, in order to obtain the same effect as the embodiment shown in FIG. 1. 
     More particularly, the second embodiment utilizes a transmitted diffraction beam, whereas the first embodiment utilizes a reflected diffraction beam. Furthermore, in this embodiment, the corner cube reflecting mirrors 13 and 13&#39; are used in place of usual reflecting mirrors, and reflect the beams diffracted at the positions M1 and M2 of the radial grating 8 to allow them to be constantly incident again in the vicinity of the positions M1 and M2. In other words, in this embodiment, even if the diffraction angles of the beams diffracted at the positions M1 and M2 of the radial grating 8 are changed due to the change in &amp;he oscillation wavelength of the laser resulting from the ambient temperature change, the diffraction beams can be constantly returned to positions in the vicinity of the positions M1 and M2 because of the known characteristics of the corner cube reflecting mirrors. An optical element or an optical system other than a corner cube reflecting mirror can be constituted to have the same characteristics. With the arrangement having such characteristics, a semiconductor laser can be used as a light source, resulting in a decrease in size of the overall apparatus and in the manufacturing costs. 
     In the apparatus shown in FIGS. 1 to 4, the beams diffracted at the positions M1 and M2 of the radial grating 8 and respectively transmitted and reflected are incident again on the positions M1 and M2. However, the beams diffracted at the positions M1 and M2 of the radial grating 8 and respectively transmitted and reflected can be superposed with each other directly, so that interference fringes are obtained and detected by a light-receiving element. In this case, the two superposed beams are respectively diffracted only once and subjected to Doppler shift. Therefore, the output signal from the light-receiving element is: Δf-(-Δf)=2Δf. Namely, the frequency F of the output signal from the light-receiving signal is : F=2Δf=2rω sin θ m  /λ, and equation (4) can be replaced by equation (4)&#39;: 
     
         n=mNθ/π                                           (4)&#39; 
    
     In the above embodiment, coherent beams are directly incident on the diffraction grating. However, the coherent beams can be incident on the diffraction grating through a reflecting mirror or the like. Alternatively, the entire optical system can be inclined by the diffraction angle of the diffraction beam or the diffraction angle of light of a specific order with respect to a plane of the diffraction grating, and the coherent beams can be obliquely incident on the diffraction grating. 
     As described in the above embodiment, when a laser or the like is used as a coherent beam light source, the beam therefrom often has predetermined polarizing characteristics. Therefore, when a polarizing beam splitter as a light splitter as well as a λ/4 plate and the like is also used with a specific consideration to its optical arrangement, the coherent beams emitted from the laser can be effectively utilized. For this reason, a polarizing beam splitter is preferably used as the beam splitter. 
     FIG. 5 is a schematic block diagram of a rotating state detection apparatus according to another embodiment of the present invention. In FIG. 5, the apparatus has a coherent beam light source 1 such as a laser, a collimator lens 2, and a polarizing beam splitter 3 as a beam splitting means. The polarizing beam splitter 3 is arranged such that its polarizing axis is inclined at 45° with respect to the direction of linear polarized light from the laser 1. The apparatus also has cylindrical lenses 6 1 , 6 2 , 6 1  &#39;, and 6 2  &#39;, λ/4 plates f 1 , 4 2 , 4 3 , 4 4 , and 4 5 , reflecting mirrors 14 and 14&#39;, corner cube reflecting mirrors 13 and 13&#39;, a radial grating 8, and a rotating shaft 9 of a rotating object (not shown). The radial grating 8 is a diffraction grating obtained by arranging a plurality of grating patterns consisting of light-transmitting and light-transmitting portions at equal angular intervals on a disk. The apparatus also has a λ/2 plate 15, a beam splitter 10, polarizing plates 11 and 11&#39;, and light-receiving elements 12 and 12&#39;. The polarizing plates 11 and 11&#39; are arranged such that their direction of polarization are inclined at 45° with respect to each other. 
     The beam emitted by the laser 1 is collimated by the collimator lens 2. A substantially parallel beam obtained is then incident on the polarizing splitter 3. The polarizing beam splitter 3 is arranged such that its polarizing axis is inclined at 45° with respect to the direction of the linear polarization of the laser 1. Therefore, the beam 1 from the laser 1 is split by the polarizing beam splitter 3 into a reflected beam and a transmitted beam of substantially the same light intensity. Among them the transmitted beam is linearly incident at a position M1 on the radial grating 8 through the cylindrical lens 6 1  as a first radiation means. The reflected beam is linearly polarized by the λ/2 plate 15 such that its direction of polarization is rotated through 90° from the beam before polarization, is transmitted through the polarizing beam splitter 3&#39;, is converted into circularly polarized light by the λ/4 plate 4 5 , is reflected by the reflecting mirror 14&#39;, and passes through the λ/4 plate 4 5  again to become a linearly polarized beam perpendicular to the beam incident on the polarizing beam splitter 3&#39;. This beam is then reflected by the polarizing beam splitter 3&#39;, and is linearly incident, through the cylindrical lens 6 1 , as a second radiation means, on a position M2 of the radial grating 8 substantially symmetrical to the point M1 thereon with respect to the center of rotation thereof. The cylindrical lenses 6 1  and 6 1  &#39; are arranged so as to perform linear radiation in directions perpendicular to the radial direction of the radial grating 8. With this linear radiation, the influence of a pitch error of the light-transmitting and light-reflecting portions on the radial grating 8, which corresponds to the portion irradiated with the beam, can be decreased. The beam incident on the radial grating 8 is diffracted and reflected by the diffraction grating of the radial grating 8. 
     The diffraction angle λ m  of the reflected diffraction beams L and L&#39; of the mth order can be represented by equation (1) described above, where is the pitch of the grating patterns at the incident portion of the beam. Assume that the radial grating 8 is rotated at an angular speed ω, and that peripheral speed at the incident positions M1 and M2 is v=rω, where r is the distance from the center of rotation of the radial grating 8 to the incident position M1 and M2. Assuming that the beam incident on the positions M1 and M2 is represented as kl in wave vector representation, the reflected diffraction beams L and L&#39; are represented as ks and k&#39;s in wave vector representations, and the peripheral speed of the radial grating 8 at the positions M1 and M2 is represented as v in vector representation, the relationship among ki, ks, ks&#39;, and v is as shown in FIG. 2. Therefore, the frequencies of the reflected diffraction beams L and L&#39; are subjected to so-called Doppler shift by amounts Δf and Δf&#39;, respectively, represented by equation (2) described above. 
     The beam reflected by a first optical means comprising the corner cube reflecting mirror 13 is incident on the point M1 again through the cylindrical lens 6 2  and the λ/4 plate 4 1 . Similarly, the beam reflected by a second optical means comprising the corner cube reflecting mirror 13&#39; is incident on the point M2 again through the cylindrical lens 6 2  &#39; and the λ/4 plate 4 2 . 
     In this case, these beams of the mth order which are reflected and diffracted at the positions M1 and M2 are subjected to Doppler shift again by the amounts represented by equation (2) and return to the initial optical paths. As a result, the frequency of the beam R1 which is re-diffracted at the point M1 and which returns to the initial optical path is subjected to Doppler shift by an amount 2Δf, and the frequency of the beam R2 which is re-diffracted at the point M2 and which returns to the initial optical path is subjected to Doppler shift&amp; by an amount of -2Δf. 
     In this manner, the beam R1 is re-diffracted at the point M1 through the λ/4 plate 4 1  and returns to the initial optical path. Therefore, the beam R1 becomes linearly polarized light having a direction of polarization perpendicular to the direction of polarization of the incident beam, and is reflected by the polarizing beam splitter 3. The beam R1 is then reflected by the reflecting mirror 14 through the λ/4 plate 4 4  and passes through the λ/4 plate 4 4  again. Then, the polarizing direction of the beam R1 is rotated through 90° again by the λ/4 plate 4 4  and is transmitted through the polarizing beam splitter 3. The direction of polarization of the beam R1 is further rotated through 90° by the λ/2 plate 15, and is reflected by the polarizing beam splitter 3&#39;. Meanwhile, the beam R2 is re-diffracted at the point 
     M2 through the λ/4 plate 4 2  and returns to the initial optical path. Therefore, the beam R2 becomes linearly polarized light having a direction of polarization perpendicular to the direction of polarization of the incident beam, and is transmitted through the polarizing beam splitter 3&#39;. Then, the two beams R1 and R2 re-diffracted at the points M1 and M2 are guided to a position P on the polarizing beam splitter 3&#39; by first and second light-guide means, respectively, and are superposed with each other. The superposed beam is passed through the λ/4 plate 4 3 , and is split into two beams by the beam splitter 10. The split beams are incident on the light-receiving elements 12 and 12&#39; through the polarizing plates 11 and 11&#39;. 
     In this manner, since the two beams R1 and R2 subjected to Doppler shift of frequency by 2Δf and -2Δf are superposed, the frequency of the output signals of the light-receiving elements 12 and 12&#39; is: 2Δf-(-2Δf)=4Δf. More particularly, the frequency F of the output signals from the light-receiving elements 12 and 12&#39; is: F=4Δf=4fω sinθ m  /λ. Substitution of equation (1) into this equation yields: F=4mrω/p. Since n=FΔt and θ=ωΔt, equations (3) and (4) described above are obtained where N is the total number of the grating patterns on the radial grating 8,ΔΨ is the pitch of the equal angular intervals, n is the number of waves of the output signal from the light receiving element during a time Δt, and θ is the rotational angle of the radial grating 8 during the time Δt. As a result, the rotational angle θ of the radial grating 8 can be calculated in accordance with equation (4) by counting the number n of waves of the output signal from the light-receiving element. 
     It is preferable that the rotational direction be detected upon detection of the rotational angle. Therefore, in this embodiment, as in the first embodiment and as is known in conventional photoelectric rotary encoders, a plurality of light-receiving elements are prepared and arranged such that the signals therefrom are 90° C. out of phase, and a signal representing the rotational direction is derived from the 90°-phase difference signals generated upon rotation. 
     In this embodiment, the 90°-phase difference between the output signals from the light-receiving elements 12 and 12&#39; is obtained by a combination of a polarizing beam splitter, a λ/4 plate, and a polarizing plate. More specifically, the light beams re-diffracted at the positions M1 and M2 and returned to the initial paths are respectively reflected by and transmitted through polarizing beam splitter 3&#39; to be superposed with each other, and are then transmitted through the λ/4 plate 9 to provide linearly polarized light. The direction of the polarized light is changed upon rotation of the radial grating 8. When the directions of polarization of the polarizing plates 11 and 11&#39;, which are respectively provided before the light-receiving elements 12 and 12&#39;, are shifted from each other by 45°, the 90°-phase difference is provided between the output signals from the light-receiving elements 12 and 12&#39;. For example, as shown in FIG. 1, the output signals from the light-receiving signals 12 and 12&#39; are subjected to waveform shaping to detect the rotational direction of the rotating object, and counted by the counter, thereby obtaining the rotational angle. 
     If this embodiment is adopted as a rotational speedometer which obtains only a rotational speed, the polarizing beam splitter 3 shown in FIG. 1 can be a half mirror, and the λ/4 plates 4 1 , 4 2 , 4 3 , 4 4 , and 4 5 , the polarizing plates 11 and 11&#39;, the beam splitter 10, and the light-receiving elment 12 are not needed. 
     In this embodiment, the laser 1 as the light source is preferably a semiconductor laser since a semiconductor laser is small in size, low in price, and has a high output. The wavelength of a semiconductor laser changes in accordance with the ambient temperature change. When the wavelength of the laser changes, the diffraction angle θ m  changes, as apparent from equation (1) representing diffraction conditions. Furthermore, when an eccentricity is present between the center of the radial grating 12 and the center of the rotating object, the pitch p of the grating patterns at the measurement points M1 and M2 changes. As a result, the diffraction θ m  also changes, as apparent from equation (1) representing diffraction conditions. However, in this embodiment, the corner cube reflecting mirrors 13 and 13&#39; (shown in FIG. 4) are used as the reflecting mirrors for the diffraction beams L and L&#39;. Therefore, even if the diffraction angle θ m  changes, the beams reflected by the corner cube reflecting mirrors 13 and 13&#39; always return to the initial optical path. In short, errors caused by the change in the wavelength of the light source or the eccentricity due to the change in the diffraction angle are removed by the corner cube reflecting mirrors 13 and 13&#39;. 
     In this embodiment, the length of the optical path extending from the laser 1 and reaching the light-receiving elements 12 and 12&#39; through the incident position M1 and the corner cube reflecting mirror 13, i.e., the first optical path (indicated by a solid line in FIG. 5), and the length of the optical path extending from the laser 1 and reaching the light-receiving elements 12 and 12&#39; through the incident position M2 and the corner cube reflecting mirror 13&#39; i.e., the second optical path (indicated by a dotted line in FIG. 5), are optically the same, thus providing a so-called common path interferometer. Therefore, the system is stable against external influences such as a vibration or a temperature change. 
     In the embodiments described above, two diffraction beams of the mth order are used. However, two diffraction beams of ±mth orders or of different orders can be used. 
     The diffraction grating used in the embodiments consists of light-transmitting and light-reflecting portions. However, so-called amplitude-type diffraction gratings which include diffraction gratings consisting of light-transmitting and light shielding portions can be adopted. Furthermore, so-called phase-type diffraction gratings consisting of uneven relief patterns or gradient reflective indexes, and holograms can also be adopted. A phase-type diffraction grating, more particularly, a diffraction grating having a relief pattern can be obtained on a mass-production line, and is thus suitable for the present invention from an economical view point. 
     Since the phase-type diffraction grating has a higher diffraction efficiency than an amplitude-type diffraction grating, it can increase the light use efficiency of the laser light, and can use an inexpensive light-receiving element having a low-output laser and/or low sensitivity. In other words, a high-sensitivity, high-precision rotating state detection apparatus can be provided. Furthermore, in view of a further increase in the diffraction efficiency, a brased diffraction grating or a volume hologram that can increase the intensity of the diffraction beam of a specific order is also suited. 
     According to the present invention, interference fringes formed by interference between the diffraction beams obtained from two positions of a radial grating substantially symmetrical to each other with respect to its center is used, in order to remove the eccentricity between the center of the rotating object and the center of the radial grating. It must be noted that the condition of the substantial symmetry of the two points with respect to the center is most preferably employed when measurement precision is to be increased. Depending upon the specifications of a specific apparatus used, the eccentricity can be removed to a certain degree only by utilizing the diffraction beams obtained from a plurality of different points. As described above, a method can be employed wherein two diffraction beams diffracted at two different positions are allowed to interfere with each other. However, another method can also be employed wherein diffraction beams diffracted at three or more different points are allowed to interfere with each other and are superposed on each other The apparatus can be modified in accordance with the method employed. 
     In the embodiment shown in FIG. 5, a constitution of a common path interferometer is employed so as to provide an apparatus stable against external influences such as a vibration and a temperature change. The application of the common path interferometer in the system of the present invention is not limited to that shown in FIG. 5, but can be modified in any other manner provided that the first and second optical paths described above have the same lengths. 
     In the embodiments described above, linear radiation is obtained using a cylindrical lens for the purpose of decreasing the pitch error of the diffraction grating patterns. However, such linear radiation is not necessary depending on the specifications of a specific apparatus used. 
     According to the rotating state detection apparatus of the present invention, a small, high-precision rotary encoder wherein a rotating object is subjected to a small load and eccentricity between the center of the radial grating and the center of rotation of the rotating object is decreased can be achieved. When the apparatus has a constitution of a common path interferometer, a rotary encoder which is stable against external influences such as a vibration and a temperature change can be achieved. 
     In a conventional photoelectric rotary encoder employing an index scale system, the relationship corresponding to equation (4), among the number n of waves in an output signal from the light-receiving element, the total number N of the grating patterns of the main scale, and the rotational angle θ, is: 
     
         n=Nθ/2π                                           (5) 
    
     Therefore, the rotational angle Δθ per wave is: 
     
         Δθ=2π/N (radian)                            (6) 
    
     In contrast to this, in this embodiment, 
     
         Δθ=π/2mN (radian)                           (7) 
    
     from equation (4). Therefore, according to this embodiment, the detection of a rotational angle can be performed with a precision 4m times that of the conventional encoder, even if it uses a scale of the same split number as the conventional encoder. 
     In the conventional photoelectric rotary encoders, the lower limit of a gap between the light-transmitting and light-shielding portions is about 10 μm in view of the influence of the light diffraction. 
     When the rotational angle detection precision of, e.g., 30 seconds is to be obtained, the split number N of the main scale must be N=360×60×60/30=43,200 from equation (6). When the gap between the light-transmitted and light-shielding portions at the outermost periphery of the main scale is 10 μm, the diameter of the main scale must be 0.01 mm×43,200/π=137.5 mm. 
     In constrast to this, according to this embodiment, the split number of the radial grating can be 1/4m to obtain the same rotational angle detection precision as the conventional encoder. When diffracted light of the orders of ±1 (m=1) is used, the split number of the patterns of the radial grating 8 can be 43,200/4=10,800 to provide a rotational angle detection precision of 30 seconds. The gap between the light-transmitting and light shielding portions can be small if a diffracted laser beam is used as in this embodiment. Therefore, if this gap is 4 μm, the diameter of the radial grating can be 0.004 mm×10,800/π=13.75 mm. In other words, according to this embodiment, the diameter of the radial grating can be less than 1/10 that of the conventional one to obtain the same rotational angle detection precision as the conventional photoelectric rotary encoders employing the index scale system. As a result, the load acting on the rotating object becomes much smaller than in the conventional encoder, and accurate measurement can be performed.