Abstract:
An optical sensing apparatus for use in a ring laser interferometer measuring a physical quantity of an object includes a ring laser cavity formed by several internal mirrors, of which at least two internal mirrors are partly light-transmitting. The ring laser cavity generates two laser beams of an identical wavelength, the two laser beams propagating in counter direction to each other in the ring laser cavity. External mirrors are disposed at a distance from the ring laser cavity, whereby portions of the two laser beams, which pass through the internal mirrors and travel on optical paths toward the external mirrors, are reflected back into the ring laser cavity. The apparatus further includes at least one platform for mounting the external mirrors.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention generally relates to an interferometer using a ring laser; and, particularly, a high accuracy interferometer including external cavity where two beams provided from a ring laser gyroscope through two mirrors are sent back to the ring laser by using external mirrors separated from the ring laser by a certain distance and the length of the external cavity is controlled by a physical quantity to be measured; and, more particularly, an interferometer where the physical quantity is measured by counting the number of pulses generated by interference of two beams propagating in opposite directions in the ring laser, such number being determined by the length of the external cavity. In the interferometer of the present invention, a lock-in zone is broadened by fixing the ring laser and increasing only back scattering of the ring laser so that the interferometer operates in the lock-in zone and the oscillating frequency of the interferometer rarely changes. 
     2. Description of the Related Art 
     There are various kinds of laser interferometers which commonly utilize the coherency of laser beams. In a laser interferometer, a laser beam from one source is split into two beams, one of which is made to propagate as a base wave and the other is modulated by a physical quantity to be measured. The two beams are later combined to generate interference fringes whose shape, number, variation in time and interval are assessed to identify the physical quantity such as refractive index, displacement, length and density. Alternatively, known interference fringes are projected to an object so that the shape or surface profile of the object is measured by analyzing the variation of the fringe shape. Typically, in order to get more accurate measurement results, each interference fringe is partitioned into fine sections with equal intervals so that the measurement results may be provided in digital form. 
     A ring laser gyroscope measures its angular velocity by counting the number of time-variations of beat resulting from a difference of oscillating frequencies of two counter propagating beams in a ring-shaped resonator. Specifically, when a ring laser gyroscope rotates, effective length of the resonator for a beam propagating in the same direction with the rotation is lengthened while that for the other beam propagating in the counter direction is shortened, which phenomenon is known as Sagnac effect. This difference in effective length results in difference of the center frequencies of the two beams so that addition of the two beams provides beat from which angular velocity can be measured in high accuracy. 
     The accuracy of the angular velocity of the ring laser gyroscope have reached around 0.001 degree/hour. When the ring laser gyroscope rotates below a certain angular velocity, the frequency difference between the two beams is very small so that the two beams oscillate at a same frequency. Such range of low angular velocities is called “lock-in zone,” which means that the two beams are locked in to each other. The locking-in of the beams results from the fact that mirrors in the ring laser gyroscope scatter part of each beam in the opposite direction from an original direction so that the scattered beam is added to the other beam propagating in the counter direction. This scattered beam is called “back scattering wave,” and as the intensity of the back scattering wave becomes larger, the lock-in zone becomes broader. When the ring laser gyroscope is operated in the lock-in zone, it is simply a ring laser because there is neither a frequency difference nor beat. The ring laser is constructed by making a resonator in the form of a polygon having 3, 4 or more sides by using mirrors. There are usually two beams with identical wavelength in the ring laser, one of them propagating clockwise and the other propagating counterclockwise. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is, therefore, to provide a high accuracy measurement system capable of measuring various physical quantities by using a ring laser and method for using the same. 
     Another object of the present invention is to provide an interferometer employing a ring laser where the effect of minute movement of the ring laser is minimized on the measurement. 
     In accordance with one aspect of the present invention, there is provided a ring laser interferometer including an external cavity ring laser where part of each of two beams propagating in opposite directions is outputted from the ring laser through a corresponding mirror and is injected back into the ring laser as back propagating wave by using an external mirror, thereby broadening the lock-in zone. In the ring laser interferometer of the present invention, the length of an optical path, that is, the distance between the external mirror and the ring laser is controlled by the physical quantity to be measured. Then the quantity is identified by counting variation rate in the number of interference fringes which are caused by intensity and phase changes of the two counter propagating waves according to the control of the optical path length. 
     By inserting an attenuator between the external mirror and the ring laser, the intensity of each back propagating wave can be controlled externally to operate the ring laser only in the lock-in zone. The physical quantities to be measured include displacement, length, position, temperature, refractive index or pressure. 
     The output from the inventive interferometer is variation rate in interference fringe which depends on intensity sum and difference, and phase difference, of the output beams of the two counter propagating waves, parts of which are fed back to suppress or compensate the effect of fluctuation in applied voltage or other external factors to enable high accuracy measurement. As the ring laser operates in the lock-in zone, the effect of minute movements of the laser on the measurement result can be minimized. 
     In accordance with one aspect of the present invention, there is provided an optical sensing apparatus for use in a ring laser interferometer for measuring physical quantity, comprising a ring laser cavity resonator; and at least one external mirror, wherein the ring laser cavity resonator includes a plurality of internal mirrors; the ring laser cavity includes two laser beams having a same wavelength and propagating in opposite direction to each other; part of each of the two counter propagating laser beams is transmitted through one of the internal mirrors; and is reflected by one of the external mirrors to generate two back propagating waves, each of which is injected to the ring laser cavity along path of the corresponding transmitted beam through the corresponding one of the selected internal mirrors; and the optical path from each of the selected internal mirrors to the corresponding external mirror is changed based on the physical quantity to be measured. 
     And also, there is provided an interferometer comprising the optical sensing apparatus described above, at least one platforms for changing the optical paths; a counting unit for counting the number of pulses of a waveform given by variation rate in time of the waveform generated by the intensity difference between the two counter propagating waves in the ring laser cavity based on the change of the optical paths, wherein the physical quantity to be measured is determined from the counted number of the pulses. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The aforementioned aspect and other features of the invention are explained in the following description, taken in conjunction with the accompanying drawings wherein: 
     FIG. 1 shows a diagram of the structure of an external cavity ring laser having an ordinary four mirror ring laser with an external mirror; 
     FIG. 2 represents a 3 dimensional plot of Eq. (14) with axis of (l 1 −l 2 )/λ a  and (l 1 +l 2 )/2λ a ; 
     FIGS. 3A and 3B depict schematic diagrams of a ring laser interferometer stabilizing circuit; 
     FIG. 4 illustrates a graphical diagram of time functions defined on a optical path between the external mirror and the ring laser; 
     FIGS. 5A and 5B show waveforms illustrating the values of Eqs. (21) and (22), respectively; 
     FIG. 6 represents waveform in case only one of l 1  and l 2  is varied by an object or in case both of l 1  and l 2  are varied independently; 
     FIG. 7 depicts a plot of the optical path when the two external mirrors are moved by a single platform along an object; 
     FIG. 8 illustrates graphical diagrams of variation in time for the variables in Eq. (23), an output of a difference amplifier and an input voltage of piezo transducers when the stabilizing circuit operates; 
     FIG. 9 shows graphical diagrams of variation in time for variables in Eq. (23), an output of a difference amplifier and an input voltage of piezo transducers when the stabilizing circuit does not operate; 
     FIG. 10 represents a structural diagram of a ring laser interferometer with accordance to the present invention; 
     FIGS. 11A and 11B depict structural diagrams of the optical unit of the ring laser interferometer which is not affected by rotation of the ring laser itself; and 
     FIGS. 12A and 12B illustrate structural diagrams of the optical sensing unit of the interferometer. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1 shows a basic structure of an optical sensing unit of the present invention, which is constructed by adding external mirrors  106  and  107  to a conventional four mirror ring laser  105 . In case the transmissivity of internal mirrors  101  to  104  in a ring laser  105  is not 0, part of each of counter propagating beams in the ring laser  105 , that is, clockwise (“CW”) propagating beam  117  and counterclockwise (“CCW”) propagating beam  116 , is transmitted out through the internal mirrors  101  to  104 . For example, part of the CW propagating beam  117  is transmitted through mirrors  101  and  102  to become beams  108  and  113 , respectively. Similarly, part of the CCW propagating beam  116  is transmitted through mirrors  101  and  102  to become beams  112  and  109 , respectively. Two beams are selected, one of which is from the CCW  116  and the other of which is from the CW  117 . For example, the beam  108  originated from the beam  117  is selected out of the beams  108  and  112  transmitted through the mirror  101  and the beam  109  originated from the beam  116  is selected out of the beams  109  and  113  transmitted through the mirror  102 . Then, each of the two selected transmitted beams  108  and  109  is returned by using the external mirrors  106  and  107  as the beams  110  and  111  respectively, to the ring laser  105 . And each of the returning beams  110  and  111  travels functions as a back propagating wave. 
     The amplitudes of the back propagating waves  110  and  111  can be controlled by providing optical attenuators  118  and  119  in the optical paths. When the ring laser  105  is fixed and the back travelling waves enters the ring laser  105  by using the external mirrors  106  and  107 , intensity difference between the other beams  112  and  113  transmitted respectively from the external mirrors  106  and  107  is a function of the distances l 1  and l 2  between the external mirrors  106 ,  107  and its corresponding internal mirrors  101  and  102 , respectively. Each of the external mirrors  106  and  107  is mounted, respectively, on platforms  149  and  150  which can be moved in the direction of the transmitted beams  108  and  109  or of the back propagating waves  110  and  111  as needed. Under the condition that the moving speeds of the external mirrors  106  and  107  are below several cm/sec, I 1 −I 2 , I 1  and I 2  representing the intensity of the transmitted beams  112  and  113 , respectively, is determined as follows:                  I   1     -     I   2       =           2      M         α   ~     -     β   ~              [         M   1            1   -         Ω   ~     2       Ω   0   2             +       (         b   ~        M     +     M   2       )            Ω   ~       Ω   0           ]       +       2      δ         α   ~     -     β   ~                   Eq   .                (   1   )                                  
     where {tilde over (α)} and {tilde over (β)} are obtained by dividing imaginary parts of self and cross saturation coefficients of nonlinear polarizability of gain medium in the ring laser  105  with normalized pumping parameter(η−1)/η of the ring laser; δ represents relative difference between the pumping parameters of the two counter propagating beams  116  and  117 ; {tilde over (Ω)} represents the angular velocity of the ring laser  105 ; and M, M 1  and M 2  are functions defined by the back propagating beams  110  and  111  from the external mirrors  106  and  107  and back propagating beams  114  and  115  produced by the internal mirrors  101  to  104 . Specifically, M, M 1  and M 2  are as follows:              M   =       1   2                m   ~     1   2     +     2          m   ~     1            m   ~     2          cos        (       θ   1     -     θ   2       )         +       m   ~     2   2                   Eq   .                (   2   )                   M   1     =             m   ~     1   2     -       m   ~     2   2         4      M                     and             Eq   .                (   3   )                   M   2     =             m   ~     1            m   ~     2         2      M            sin        (       θ   1     -     θ   2       )                 Eq   .                (   4   )                                  
     In Eqs. (2) to (4), {tilde over (m)} 1  and {tilde over (m)} 2  are obtained by dividing the intensities of the back propagating waves produced by the external mirror and the internal mirrors with Δω=(ω(η−1))/Q, that is, the line width of the ring laser. 
     
       
           {tilde over (m)}   1   e   −iθ     1     =m   1   (ext)   e   −iξ     1     +m   1   (int)   e   −iε     1     Eq. (5) 
       
     
     
       
           {tilde over (m)}   2   e   −iθ     2     =m   2   (ext)   e   −iξ     2     +m   2   (int)   e   −iε     2     Eq. (6) 
       
     
     In Eqs. (5) and (6), θ i  (i=1, 2) is phase of the overall back propagating waves given to the ring laser; m i   (ext)  and m i   (int)  (i=1, 2) are amplitudes of light which travels back or is scattered from the external mirrors and the internal mirrors, respectively, divided by Δω, wherein m i   (ext) m i   (int) . ε i (i=1,2) is a phase of the back scattering waves produced by internal mirrors; and ξ i (i=1,2) is a phase determined by the distance between the external mirrors and the ring laser. And Ω 0  is a rotational angular velocity corresponding to the lock-in frequency and can be determined as follows:                Ω   0     =             b   ~     2          M   2       +     2        b   ~          MM   2       +     M   3   2                 Eq   .                (   7   )                                  
     In the present invention, the ring laser is fixed and the back propagating waves are injected into the ring laser by the external mirrors. In this case, because {tilde over (Ω)}=0, δ is very small and the center frequency of the ring laser is rarely changed by the back propagating waves. Thus, {tilde over (b)}=0 and Eq. (2) may be simplified as follows:                  I   1     -     I   2       =           m   ~     1   2     -       m   ~     2   2         2        (       α   ~     -     β   ~       )          (       Ω   0     +     Ω   1       )                 Eq   .                (   8   )                                  
     wherein  1  is first perturbation constant of  0  given as follows:                Ω   0     =       1   2                m   ~     1   2     -     2          m   ~     1            m   ~     2          cos        (       θ   1     -     θ   2       )         +       m   ~     2   2                   Eq   .                (   9   )                                  
     Ω 0  is not less than 0 and its maximum and minimum values are given as {tilde over (m)} 1 +{tilde over (m)} 2  and |{tilde over (m)} 1 −{tilde over (m)} 2 | when cos(θ 1 −θ 2 ) equals 1 and −1, respectively. When l 1  and l 2  denote the distances between the ring laser and the two external mirrors, respectively, and l 0  denotes the distance between two neighboring mirrors in the ring laser, ξ 1 =ξ 1   (0) +2k(l 1 −l 0 )(ξ 1   (0)  is the initial value of ξ 1 ; k=2πn/λ a  is a wave number where n is the diffraction coefficient of a medium filling the space between the ring laser and the external mirrors; and λ a  is the wavelength of the ring laser output beam in the air) and ξ 2 ξ 2   (0) −2l 2 k(ξ 2   (0)  is the initial value of ξ 2 ). In addition, if m 1   (ext) =m 2   ext) =m (ext)  and m 1   (int) =m 2   (int) =m (int)  and Ω 1  is much smaller than Ω 0 , when the medium is air(n=1), Eq. (6) may be simplified as follows:                  I   1     -     I   2       =       C       Ω   0          (       α   ~     -     β   ~       )            sin                   π        (       2                       l   1     -     l   2         λ   a         -     ζ   1       )          sin                   π        (       2                       l   1     +     l   2         λ   a         -     ζ   2       )                 Eq   .                (   10   )                                  
     wherein C is a constant which is defined as a multiplication of m (ext)  and m (int) , and ξ i (i=1, 2) is phase component which is defined by difference and sum of ε i (i=1,2), ξ i   (0)  (i=1, 2) and kl 0 . The phase difference φ between two counter propagating beams  116  and  117 , caused by the back propagating waves  110  and  111  from the external mirrors  106  and  107 , is as follows:              φ   =     π   +         tan     -   1       [                     m   ~     1          cos        (     θ   1     )         -         m   ~     2          cos        (     θ   2     )                   m   ~     1          sin        (     θ   1     )         -         m   ~     2          sin        (     θ   2     )                     ]                 Eq   .                (   11   )                                  
     The phase difference above in Eq. (11) can be detected by making two projection beams from one mirror of the ring laser interfere each other. If we let I a  and I b  be the intensities of the two projection beams, I Fringe , a signal produced from the interference of the two projection beams is given as follows:                I   Fringe     =       I   a     +     I   b     +     2            I   a          I   b              cos        (     φ   +     φ   0       )                   Eq   .                (   12   )                                  
     wherein φ 0  is a phase value caused in the course of making two beams interfere. As Eq. ( 12) is a function of φ, it depends on the values of l 1  and l 2 . Thus, by measuring the variation of the interference fringe, i.e the change of I Fringe  due to change of l 1  and l 2 , the variation of l 1  or l 2  can be measured. In case there is no back propagating waves caused by the external mirrors in the ring laser, the intensities of the two counter propagating beams are almost identical with each other. Defining this intensity as I 0 , I 0  is given as follows:                I   0     =     1       α   ~     +     β   ~                 Eq   .                (   13   )                                  
     If we normalize Eq. (10) by dividing by I 0 , we get the following equation.                    I   1     -     I   2         I   0       =         C        (       α   ~     +     β   ~       )           Ω   0          (       α   ~     -     β   ~       )            sin                   π        (       2                       l   1     -     l   2         λ   a         -     ζ   1       )          sin                   π   (       2                       l   1     +     l   2         λ   a         -       ζ   2             )                     Eq   .                (   14   )                                  
     Since {tilde over (α)} and {tilde over (β)} are values representing the characteristic of the oscillating medium in the ring laser, and thus are not related to l 1  and l 2 , Eqs. (10) and (14) represents waveforms of the same shape. The Eq. (14) includes four operating regions. In the first operating region, one of l 1  and l 2  varies and in the second operating region, l 1 −l 2  is constant. And in the third operating region, l 1 +l 2  is constant and in the fourth operating region, both of l 1  and l 2  varies. In the second operating region, that is, in the case l 1 −l 2  is constant, the Eq (10) will be represented by a function of l 1 +l 2 . In the third region, that is l 1 +l 2  is constant, the Eq (10) will be represented by a function of l 1 −l 2 . 
     FIG. 2 shows a 3 dimensional plot of the Eq. (14) , which has two axes of (l 1 −l 2 )/λ a  and (l 1 +l 2 )/2λ a . In FIG. 2, there is provided the operating region of the interferometer when l 1 −l 2  or l 1 +l 2  is constant. It is important to achieve as large value for the Eq. (14) as possible by placing the range of (l 1 −l 2 )/λ a  on a line CD  122  or a line C′D′  123  in case of the constant l 1 −l 2  and by placing the range of (l 1 +l 2 )/2λ a  on a line AB  120  or a line A′B′  121  in case of the constant l 1 −l 2 /2λ a . That is, measurement accuracy is improved when the peak value of the waveform of the intensity difference between two counter propagating waves is maximized. FIGS. 3A and 3B are schematic diagrams of the optical sensing unit and the optical stabilization unit of the ring laser interferometer to measure physical quantity of the object by using Eq. (10) in accordance with the present invention. FIG. 3A is a schematic diagram where one of l 1  or l 2  varies by the physical quantity to be measured or the external mirrors are moved simultaneously to make l 1 −l 2  constant. FIG. 3B is a schematic diagram where event two external mirrors are moved interactively to make l 1 +l 2  constant. 
     In FIG. 3A, The beam  108  is part of the two counter propagating beams in the ring laser  105  are transmitted through one mirror  101  of the two neighboring mirrors  101  and  102  in the ring laser  105 . The transmitted beam  108  is reflected by the external mirror  106  separated by l 1  from the ring laser  105  to thereby reverse its travel direction. Thus, the transmitted beam  108  becomes the back propagating wave  110  returning to the ring laser  105  through the mirror  101 . The transmitted beam  112  is detected by a photo detector  124  which outputs a voltage proportional to the intensity of the transmitted beam  112 . The output of the photo detector  124  is amplified by a pre-amplifier  128  and then applied to one of input terminals  143  of a difference amplifier  130 . 
     Similarly to the transmitted beam  108 , the transmitted beam  109  through the mirror  102  is reflected by the external mirror  107  separated by l 2  from the ring laser  105  to thereby inverse its travel direction. Thus, the transmitted beam  109  becomes the back propagating wave  111  back to the ring laser  105  through the mirror  102 . The transmitted beam  113  is detected by a photo-detector  125  which outputs voltage proportional to the intensity of the transmitted beam  113 . The output of the photo-detector  125  is amplified by a pre-amplifier  129  and then applied to the other input terminal  144  of the difference amplifier  130 . The photo-detector  125  has characteristic identical to the photo-detector  124 . And also the pre-amplifier  129  has identical characteristic with the pre-amplifier  129 . 
     The output waveform of the difference amplifier  130  is proportional to I 1 −I 2  of the Eq. (10) and part of the output of the difference amplifier  130  is directly measured by a control and display unit  171 . Regulated voltage supplies  126  and  127  are coupled to one input  136  of a piezo transducer  141  and one input  137  of the piezo transducer  142 , where the applied voltage from the regulated voltage supplies  126  and  127  control the piezo transducers  141  and  142  finely so that the difference amplifier  130  outputs a maximum peak waveform. By this fine control, the operating range of the difference amplifier  130  is on the line CD  122 , the line C′D′  123 , the line AB  120 , or the line A′B′  121 . The selection of range of the CD  122  or the C′D′  123 , or the AB  120  or the A′B′  121  depends on the polarization of the inputs  134  and  136  and the inputs  135  and  137  of the piezo transducers  141  and  142 . The remaining part of the output of the difference amplifier  130  is integrated by an integrator  131 . The integrated output is amplified by the output amplifier  132 . The output of the output amplifier  132  is applied to the other input terminal  134  of the piezo transducer  141  attached on the external mirror  108  or the other input terminal  135  of the piezo transducer  142  attached on the external mirror  109 . The inputs to one of the piezo transducers  141  and  142  stabilize the ring laser  105  so as to make I 1 −I 2  zero, that is, minimize the difference between the intensities of the two counter propagating beams in the ring laser  105 . 
     If the optical path for only one of l 1  and l 2  is varied by an object, the output of the output amplifier  132  is applied only to the piezo transducer associated with the variation, e.g., the transducer  141 . If l 1 −l 2  is constant, the output of the output amplifier  132  is applied to both of the piezo transducers  141  and  142 . The integrator  131  separates the difference amplifier  130  from the output amplifier  132  and maintains for a predetermined time the output voltage of the output amplifier  132  applied to the piezo transducers  141  and  142  based on the output variation of the difference amplifier  130  so as to stabilize the interferometer and make accurate measurement. If there is not the integrator, measurement accuracy is degraded since the output of the difference amplifier  130  stays at constant value only in average. The output  133  of the output amplifier  132  is also applied to the control and display unit  171  of the interferometer in order to discharge the integrator  131  when the voltage of the integrator  131  reaches a predetermined level. In case l 1 −l 2  or l 1 +l 2  is constant, it is possible to supply the voltage by using selected one of the regulated voltage supplies  126  and  127  because the absolute value of the voltage applied from the regulated voltage supply  126  to the piezo transducer  141  should be equal to the absolute value of the voltage applied from the regulated voltage supply  127  to the piezo transducer  142 . When the distances between the external mirrors  106  and  107  and the ring laser  105  are varied based on the physical quantity to be measured, the piezo transducers  141  and  142  attached on, respectively, the external mirrors  106  and  107  achieve stabilization of the interferometer by suppressing the variation of l 1 −l 2  occurring due to disturbance generated in the ring laser  105 . 
     Depending on constriction and expansion of the piezo transducers  141  and  142  based on the output of the output amplifier  132 , the external mirrors  106  and  107  are moved in the direction of the transmitted beams  108  and  109  or the direction of the back propagating wave  110  and  111 . Such that the distances between the external mirrors  106  and  107  and the ring laser  105  remain constant. The control and display unit  171  of the interferometer is coupled to the remaining input  145  of the integrator  131  to discharge the integrator  131  and coupled to the remaining input  146  of the output amplifier  132  to reset the output amplifier  132 . The optical attenuator  118  placed within the optical path constructed by the mirror  101  and the external mirror  106  is to make the amplitudes of the back propagating waves from the external mirrors  106  and  107  identical with each other. The stabilization circuit  172  includes the photo detectors  124  and  125 , the pre-amplifiers  128  and  129 , the regulated voltage supplies  126  and  127 , the difference amplifier  130 , the integrator  131  and the output amplifier  132 . 
     FIG. 3B is identical to FIG. 3A except that the two mirrors  106  and  107  moves relatively so that l 1 +l 2  is constant. The amplification rate of the pre-amplifiers  128  and  129  is controlled to compensate difference between  1  and l 2  due to the difference between transmission rates of the mirrors  101  and  102 . 
     FIG. 4 depicts time functions defined on the optical path between the external mirrors and the ring laser of the interferometer in accordance with the present invention. Since the optical path  147  or  148  varies depending on the physical quantity to be measured, the length thereof can be represented by the time function. l 1 (t) represents the distance between the mirror  101  of the ring laser  105  and the external mirror  106  when the voltage applied to the piezo transducer  141  is 0, x 1 (t) represents the distance between the mirror  101  of the ring laser  105  and the external mirror  106  when the voltage applied to the piezo transducer  141  is not 0, and x′ 1 (t) represents the distance between the platform  149  on which the external mirror  106  is mounted and the external mirror  106 . l 1 (t) can be expressed as follows: 
       l   1 ( t )= x   1 ( t )+ x′   1 ( t )  Eq. (15) 
     In Eq. (15), the positive direction of x 1 (t) is defined as opposite to that of x′ 1 (t). Similarly as l 1 (t) represented by Eq. (15), l 2 (t) can be expressed as follows: 
     
       
           l   2 ( t )= x   2 ( t ) +x   2 ( t )  Eq. (16) 
       
     
     In Eqs. (15) and (16), x 1 (t) and x 2 (t) are the distances between the ring laser  105  and the external mirrors  106  and  107  and are identical to l 1  and l 2  in Eqs. (10) and (14), respectively. In Eqs. (15) and (16), x′ 1 (t) and x′ 2  (t) are 0 at t=0 and then l 1 (0)=x 1 (0) l 2 (0)=x 2 (0). It may be preferable to set l 1 (0) and l 2 (0), respectively, as the distance between the ring laser  105  and the front side  151  of the platform  149  and the distance between the ring laser  105  and the front side  152  of the platform  150 , respectively, and initially place the external mirror  106  at the same plane with the front side  151  of the platform  149  and the external mirror  107  at the same plane with the front side  152  of the platform  150 . On the other hand, while t is not 0, the piezo transducer  141  operates to stabilize the interferometer and then x′ 1 (t) and x′ 2 (t) are product of voltage V 1 (t) applied to the piezo transducer  141  and conversion coefficient k p1 (mm/volt) of the piezo transducer  141  and product of voltage V 2 (t) applied to the piezo transducer  142  and conversion coefficient k p2 (mm/volt) of the piezo transducer  142 , respectively. 
       x   i ( t ) =k   pi   V   i ( t )  Eq. (17) 
     where i is 1 or 2. Addition of Eqs. (15) and (16) and substitution Eq (17) result in 
     
       
           x   1 ( t )+ x   2 ( t )=( l   1 ( t ) +l   2 ( t ))−( k   p1   V   1 ( t )+ k   p2   V   2 ( t ))  Eq. (18) 
       
     
     and substraction Eq. (16) from Eq. (15) and substitution Eq. (17) result in 
     
       
           x   1 ( t )− x   2 ( t )=( l   1 ( t )− l   2 ( t ))− k   p1   V   1 ( t )− k   p2   V   2 ( t ))  Eq. ( 19)   
       
     
     When l 1 −l 2  is constant, that is, both of the external  106  and  107  are placed on the selected one of platforms and moved in same direction, it is possible to let V 1 (t)=V 2 (t)=V(t) since input voltages for one of the piezo transducers from the output amplifier  132  and the regulated voltage supplies  126  and  127  are identical to those for the other piezo transducer so that the following equation can be obtained. 
     
       
           x′   1 ( t )+ x′   2 ( t )=( k   p1   +k   p2 ) V ( t )=2 k   p   V ( t )  Eq. (20) 
       
     
     where k p  is the average of k p1  and k p2 . And also, since the two optical paths moves same distance simultaneously by the selected platform, l 1 (t)+l 2 (t)=2l(t), and since sin term(let it be C′) including l 1 −l 2  is constant when l 1 −l 2  is constant. Thereby, Eq. (10) can be expressed as follows:                  I   1     -     I   2       =         CC   ′         Ω   0          (       α   ~     -     β   ~       )            sin                   π        (       2        l        (   t   )         -         k   p          V        (   t   )             λ   a     /   2       -     ζ   2       )                 Eq   .                (   21   )                                  
     To apply Eq. (21) to the interferometer, the external mirrors  106  and  107  identical with each other are driven by single platform. 
     In order to maintain l 1 +l 2  constant, the two external mirrors interact each other and l 1  and l 2  are moved in same direction in the structure as shown in FIG.  3 B. Accordingly, x′ 1 (t) and x′ 2 (t) should be moved in the same direction. Thus, because the input voltage applied to the piezo transducer  141  should have opposite polarity compared to the input voltage applied to the piezo transducer  142 , V 1 (t)=−V 2 (t)=V(t). Provided l 1 (t)−l 2 (t)=2Δl(t), then Eq. (10) can be expressed as follows:                  I   1     -     I   2       =         CC   ″         Ω   0          (       α   ~     -     β   ~       )            sin                   π        (       2      Δ                   l        (   t   )         -         k   p          V        (   t   )             λ   a     /   2       -     ζ   1       )                 Eq   .                (   22   )                                  
     where C″ represents the constant sin term including l 1 +l 2 . 
     In Eqs. (10) and (14), where one of l 1  and l 2  is varied according to the object and the other is used as a reference optical path, the initial value applied to the piezo transducer is effective. And it is preferable to measure the object by measuring the variation quantity of the interference fringes given by Eq. (12)rather than by Eq. (10). FIGS. 5A and 5B illustrate waveforms for Eqs. (21) and (22), respectively, showing the cross sections of the waveform shown in FIGS. 2A and 2B. The waveforms are plotted using N 1  and N 2 , multiples of λ a /2. Neglecting the term m 1   (ext)  since m 1   (ext)  is much smaller than m 1   (int) , then {tilde over (m)} 1 ≃m i   (ext) θ i ≃ξ i . Thus, cos(θ 1 −θ 2 )is defined as a function of l 1 +l 2 . Therefore, if l 1 +l 2  is constant, then cos(θ 1 −θ 2 )is constant and Ω 0  is substantially constant. This why the waveform shape in FIG. 5A is different from that in FIG.  5 B. 
     Where l 1 −l 2  is constant, the waveform shape is of a pinnacle as shown in FIG. 5A due to effect of Ω 0 . And where l 1 +l 2  is substantially constant, the waveform shape is of sine wave as shown in FIG.  5 B. As shown in Eqs. (21) and (22), each of the waveforms in FIGS. 5A and 5B has a period of λ a /2, a half wavelength of the output beam of the ring laser. Since 2 pulses  156  and  157  or  158  and  159  are counted during this period, the pulse width is λ a /4. The number of the pulses is counted to thereby measure various physical quantities given by the variation of l 1 +l 2  or l 1 −l 2 . 
     FIG. 6 is a waveform where, by the object to be measured, only one of l 1  and l 2  is varied or both l 1  and l 2  are varied independently each other. In this case, it is difficult to count the pulses because the waveform of Eq. (10) is complex. Therefore, variation of the optical paths is measured by measuring the variation of the interference fringe waveform given by Eq. 12 during the measurement period as described above. 
     FIG. 7 depicts a function defined on the optical path as similar as shown in FIG. 4, which illustrates the variation of the optical path when the two external mirrors on single platform are moved depending on the object. Since the output of the output amplifier  132  is 0 when the measurement system is turned on at t=0, the voltage applied to the piezo transducers  141  and  142  is then accordingly 0 and thereby the external mirrors  106  and  107  are not moved. Here, the distance between the internal mirror  101  and the external mirror  106  is l 1 (t) and the distance between the internal mirror  102  and the external mirror  107  is l 2 (t). Because the disturbance occurred to the ring laser  105  at instance of turning on the measurement system, the voltage output of the difference amplifier  130  is generated to be not 0 and such voltage output is integrated by the integrator  131 . The voltage output of the integrator  131  is applied to the piezo transducers  141  and  142  after amplified by the output amplifier  132 . The piezo transducers  141  and  142  are contracted or expanded based on the applied voltage thereto. And then the external mirrors  106  and  107  are moved by the contraction or expansion of the piezo transducers  141  and  142 . By the movement of the external mirrors  106  and  107 , the disturbance in the ring laser  105  is reduced and the output voltage of the difference amplifier  130  is also reduced. Accordingly, although increase of the output voltage of the integrator  131  slows down, substantial output voltage increase makes the external mirrors  106  and  107  move to reduce the disturbance in the ring laser  105  and finally the output of the difference amplifier  130  reached 0 after time t 1 . While the output of the difference amplifier  130  is 0, the output of the integrator  131  does not change and then the voltage applied to the piezo transducers  141  and  142  do not change so that contraction or expansion of the piezo transducers  141  and  142  is stopped and the positions of the external mirrors  106  and  107  does not change. Subsequently, the difference amplifier  130 , the integrator  131 , the output amplifier  132  and the piezo transducers  141  and  142  construct a negative feedback loop to stabilize the measuring system. Thus, the external mirrors moves in direction opposite to the moving direction of the platform to maintain the length of the optical path constant. The distances that the external mirrors  106  and  107  are moved by the piezo transducers  141  and  142  during time t=0 to t=t 1  are represented by x′ 1 (t) and x′ 2 (t), respectively. x′ 1 (t) and x′ 2 (t) are determined based on the voltage applied to the piezo transducers  141  and  142  and thus are calculated by measuring that voltage. At time t==t 1 , the distance between the internal mirror  101  in the ring laser  105  and the external mirror  106  is x 1 (t 1 ) and the distance between the internal mirror  102  in the ring laser  106  and the external mirror  106  is x 2 (t 2 ). If the platform  152  is moved by the object to be measured at t=t 1  and this movement is stopped at t=t 2 , x′ 1 (t) and x′ 2 (t) are can be calculated by achieving the voltage applied to the piezo transducers  141  and  142  since the external mirrors  106  and  107  are moved by the piezo transducers  141  and  142  to make the output of the difference amplifier  130  for stabilization of the system. And the distance between the internal mirror  101  in the ring laser  105  and the external mirror  106  is x 1 (t 2 ) and the distance between the internal mirror  102  in the ring laser  105  and the external mirror  107  is x 2 (t 2 ). In this system, when l 1 (t 1 )=l 1 (0)=x 1 (0), l 2 (t 1 )=l 2 (0)=x 2 (0), 2x(t 1 )=x 1 (t 1 )+x 2 (t 1 ), 2x(t 2 )=x 1 (t 2 )+x 2 (t 2 ), 2x′(t 1 )=x′ 1 (t 1 )+x′ 2 (t 1 ), 2x′(t 2 )=x′ 1 (t 2 )+x′ 2 (t 2 ), 2l(t 1 )=l 1 (t 1 )+l 2 (t 1 ) and 2l(t 2 )=l 1 (t 2 )+l 2 (t 2 ), the distance that the platform is moved is l(t 2 )-−l(t 1 ) and expressed as follows: 
     
       
           l ( t   2 )− l ( t   1 )=[ x ( t   2 )− x ( t   1 )]+[ x′ ( t   2 )− x ′( t   1 )]  Eq. (23) 
       
     
     The waveforms of the input/output values of the blocks shown in FIG. 3 generated when the platform varies depending on the moving speed of the platform. Since the optical path difference is not great when refractive index, temperature, stress or pressure is measured, the moving speed of the platform is made as slow as the operating speed of the stabilization circuit. Since the optical path difference is great when displacement or distance is measured, the moving speed of the platform is made fast and the interferometer operates without the stabilization circuit. 
     FIG. 8 offers the variations of respective variables in Eq. (23), the output of the output amplifier  132  and the voltage applied to the piezo transducers  141  and  142  when the stabilization circuit operates, that is, the moving speed of the platform is slower than the transducing speed of the piezo transducers  141  and  142 . As described above, when the measuring system is turned on at time t=0, the output of the output amplifier  132  is 0, the voltage applied to the piezo transducers  141  and  142  is 0 and then the external mirror  106  and  107  are not moved. At instance of turning the measuring system, negative voltage is generated at the difference amplifier  130  due to the disturbance occurred in the ring laser  105  and this negative voltage is applied to the piezo transducers  141  and  142  after amplified by the output amplifier  132 . Thus, the piezo transducers  141  and  142  are contracted by the negative voltage and then the external mirrors  106  and  107  attached on the piezo transducers  141  and  142 , respectively, are moved in the direction away from the ring laser  105 . Therefore, although l(t)=l(0), x(t) becomes larger than the x(0) by x′(t). Due to that movement, the disturbance in the ring laser  105  is reduced and the output voltage of the difference amplifier  130  is also reduced. And, accordingly, although increase of the output voltage of the integrator  131  slows down, substantial output voltage increase makes the external mirrors  106  and  107  move to reduce the disturbance in the ring laser  105  and finally the output of the difference amplifier  130  reached 0. When the output of the difference amplifier  130  is 0, the output of the integrator  131  does not change and the voltage applied to the piezo transducers  141  and  142  do not change so that the contraction of the piezo transducers  141  and  142  is stopped and the positions of the external mirrors  106  and  107  are not changed. That is, x′(t 1 ) and x(t 1 ) are maintained as constants so that the ring laser  105  stays on stable state. 
     If the platform is moved in the direction away from the ring laser  105  at time t=t 1 +τ, the output of the output amplifier  130  is increased and subsequently the piezo transducers  141  and  142  are expanded so that the external mirrors  106  and  107  are moved toward the ring laser  105 . As the platform further is moved, the output of the difference amplifier  130  is maintained as a constant by the negative feedback and the output of the integrator  131  increases. And then the output of the output amplifier  132  increases so that the external mirrors  106  and  107  are further moved toward the ring laser  105 . When the output of the output amplifier  132  reaches the voltage that expands the piezo transducers  141  and  142  by λ a /2, that is, the voltage V m  where x′(t) becomes λ a /2, the integrator  131  is discharged instantaneously and then the output of the output amplifier  132  is reduced to a value near 0 instantaneously. Therefore, the piezo transducers  141  and  142  moves by λ a /2 during the discharge of the integrator  131  from λ a /2 expanded state to normal state (non-expanded or non-contracted). During the discharge period, the stabilization circuit does not operates and the output of the difference amplifier  132  is the waveform  164  corresponding to the half wavelength as shown in FIG.  5 . The time period  165  should be longer than that of the lock-in frequency given by the external mirrors. The stabilization circuit operates the piezo transducers to set off the movement of the platform and then x(t) does not change till the output of the output amplifier  132  reaches the V m  and only x′(t) changes by λ a /2 equal to the distance that the platform is moved. Thus, as the integrator is discharged, x′(t) is reduced to 0 passing λ a /4 and accordingly x(t) is reduced to x(t 1 +τ)+λ a /4 and subsequently to x(t 1 +τ)+λ a /2. When the discharge is completed, the output of the difference amplifier  132  increase to compensate the disturbance of the ring laser  105  so that the interferometer is stabilized by the operation of the stabilization circuit, and therefore as the movement of the platform continues those operations described above are repeated. x(t) increases by λ a /2 during the discharge period. If the movement of the platform is stopped at t=t 2 , then the output of the difference amplifier  130  is made to 0 by the operation of the stabilization circuit and then the voltages of the integrator  131  and the output amplifier  132  so that the interferometer is stabilized. If the number of the output waveforms of the difference amplifier  130  generated during the movement of the platform is m, then Eq. (23) can be represented as follows:                  l        (     t   2     )       -     l        (     t   1     )         =       m          λ   a     4       +     [         x   ′          (     t   2     )       -       x   ′          (     t   1     )         ]               Eq   .                (   24   )                                  
     FIG. 9 is a timing diagram illustrating the variation in time for the variables in Eq. (23) and variations for the output of the difference amplifier  130  and the voltage applied to the piezo transducers in case the measurement is made when the moving speed of the platform is faster than the transducing speed of the piezo transducers and the stabilization circuit does not operates. As similarly as in FIG. 8, the measuring system is turned on at t=0. However, if the platform is moved faster than the transducing speed of the piezo transducers at t=t 1 +τ after the interferometer is stabilized, the output of the difference amplifier  130  continuously increases and then the output of the integrator  131  accordingly increases because the disturbance of the ring laser  105  increases with acceleration. Thus, the output of the output amplifier  132  reaches the voltage V m  expanding the piezo transducers by λ a /2. Accordingly, the integrator  131  is discharged instantaneously, then the output of the output amplifier  132  is reduces to 0 instantaneously, and the difference amplifier  130  outputs a waveform  255  corresponding to a half wavelength given in FIG.  5 . After that because the moving speed of the platform is fast so that the stabilization circuit does not operates, the waveform given in FIG. 5 is generated at the output of the difference amplifier  130 . Upon stopping the movement of the platform, the stabilization circuit operates to result in the waveforms as shown in FIG.  8 . 
     FIG. 10 is a schematic diagram showing system structure of the ring laser interferometer of the present invention. In the optical sensing unit  174 , the transmitted beams  169  and  168  are selected, which are generated by transmitting the counter propagating beams in the ring laser  218  through the selected mirrors  219  and  220 . The beam  169  is collimated to a collimated beam by the beam collimator  170  and enters the external mirror  187  via the optical attenuator  180  and a beam splitter  181 . The beam  168  is reflected by the external mirror  189  attached on the piezo transducer  190  via the beam collimator  221  and again reflected by the external mirror  222  to be parallel with the beam  169  to enter the external mirror  187 . The beam  169  is reflected by the external mirror  187  and part of the reflected beam is splitted by the beam splitter  181 . Part of the split beam is converted to current by the photo detector  186  and then, after amplified by the amplifier  209 , enters the system controller  210 . And the remaining part of the split beam enters the ring laser through the mirror  219  along the original path. The beam  168  is reflected by the external mirror  187  and then split by the beam splitter  181 . Part of the split beam is converted to current by the photo detector  185  and then, after amplified by the amplifier  208 , enters the system controller  210 . And the remaining part of the split beam enters the ring laser  218  through the mirror  220  along the original path. The photo detectors  185  and  186  detect the disturbance occurred on the optical path, e.g., measurement error due to extinction of the beams. The external mirror  187  and the piezo transducer  188  attached thereon are mounted on the platform  153  so as to move based on the physical quantity to be measured. 
     The piezo transducer  190  attached on the external mirror  189  is for controlling the difference amplifier  213  to have maximum difference between its highest voltage output and its lowest voltage output. 
     Since the cavity of the ring laser  105  is on the plasma state, the beam transmitted through the mirror  219  includes incoherent stray beam  166  due to the gas plasma in addition to the counter propagating waves to make it difficult to measure I 1 −I 2 . Therefore, it is possible to make accurate measurement for l 1 l 2  by subtracting the stray beam from I 1  and I 2  after measuring the intensity of the stray beam  166  separately. The photo detectors  193  and  194  measure the intensity of the stray beam  166 . The two counter propagating beams  167  is detected by the photo detectors  192  and  195  and then the intensity of the stray beam  166  is subtracted therefrom by the difference amplifier  211  and  212  to achieve accurate values of I 1  and I 2 . Then, the outputs of the difference amplifier  211  and  212  are applied to another difference amplifier  213  to achieve accurate value of I 1 −I 2 , the difference value of the two counter propagating beams. 
     The output of the difference amplifier  213  is applied to the output amplifier  215  via the integrator  214 . The output  226  of the output amplifier  215  is applied to the piezo transducer  188  attached on the external mirror  187  to stabilize the ring laser  218  and applied to a comparator  205  to discharge the integrator  214  by using the system controller  210  when it is equal to or higher than the reference voltage V m . 
     The two counter propagating beams through another mirror  223  in the ring laser  218  are combined by the beam combining prism  196  and the cosine component  197  of the combined beam is applied to the amplifier  201  via the photo detector  199  and the sine component  198  is applied to the amplifier  202  via the photo detector  199 . The outputs of the amplifiers  201  and  202  are applied to the counter  203  to be used for measurement of the variation of the interference fringes given in Eq. (12). Since it is possible to detect the moving direction of the interference fringes by detecting the cosine and sine components, it is also possible to measure the moving direction of the platform. The counter  203  counts the number of the pulses of the output waveform of the difference amplifier  213 . And the system controller  210  controls the counter  203 . The output of the counter  203  is applied to the computer  204  for computing and displaying, which is capable of achieving accurate measurement by compensating the physical quantity to be measured by using the accurate refractive index of the physical quantity to be measured, if necessary. It is possible to compensate the accuracy of the physical quantity to be measured by measuring continuously the refractive index associated with measurement environment by using the devices shown in FIG. 12 simultaneously. 
     Parts of the outputs of the difference amplifiers  211  and  212  are combined by a sum amplifier  216 . The output of which includes information for the variation of the cavity length in the ring laser  218  due to temperature change. The output of the sum amplifier  216  drives the piezo transducer  225  attached on another mirror  224  in the ring laser  218  or the cooling device  227 , e.g., a fan, for reducing the change of temperature in the ring laser  218  to compensate the effect of the temperature change in the ring laser  218 . A timer  206  is used to control the time constant of the integrator  214 . 
     The output of the signal oscillator  207  is an alternating current signal of a constant frequency that is equal to or lower than the resonance frequency of the piezo transducer, and is applied to the other input terminal of the output amplifier  215  via the system controller  210 . The output of the signal oscillator  207  vibrates the external mirror prior to measurement. This vibration reduces the measurement error due to diffractive beam generated by grating formed by standing interference fringe generated by interference of the two counter propagating beams on the dielectric coating surface of the internal mirrors  219 ,  220 ,  223  and  224 . That is, the standing interference fringe on the internal mirrors is eliminated by dispersing the phases of the two counter propagating beams. 
     The control and display unit  171  is constructed by the system controller  210 , the photo detectors  199 ,  200 ,  185  and  186 , the amplifiers  201 ,  202 ,  208  and  209 , the counter  203 , the computer  204 , the comparator  205 , the timer  206  and the signal oscillator  207  to perform operation control of the whole system, signal processing and display of measurement result. The stabilization circuit  173  includes the sum amplifier  216  and the output amplifier  217  in addition to, as shown in FIG. 3, the photo detectors  192 ,  193 ,  194  and  195 , the difference amplifier  211 ,  212  and  213 , the regulated voltage supply  191 , the integrator  214 . The stabilization circuit  173  also compensates the variation of the cavity length in the ring laser  218  due to the environmental changes. Since it is possible to construct all components in the optical sensing unit  174  and the photo detectors as a mono block  175  except for the external mirror mounted on the moving platform  153 , the interferometer can be constructed by three blocks, this fixed mono block, electronic circuit block and the external mirror-associated block. 
     FIGS. 111A and 11B offer the structures of the optical unit of the ring laser interferometer using the ring laser having the cavity structure in which the two counter propagating waves propagate to set off the Sagnac effect due to rotation of the ring laser itself. FIG. 11A shows the case the two external mirrors are moved independently and FIG. 11B shows the case the two external mirrors are on the single platform, that is, the optical path is controlled by the single external mirror  259 . In FIG. 11A, the ring laser  263  includes four mirrors  233 ,  234 ,  235  and  236  positioned to make the two counter propagating waves  261  and  262  crossed each other. 
     The transmitted beam  264  through the mirror  235  is reflected from the mirror  237 , collimated by the beam collimator  238 , reflected, after passing the beam attenuator  239 , on the corner cube retroreflector  230  of inner angle 90° or an alternative element and enters, via the beam splitter  242 , the external mirror  244  perpendicularly. The reflected beam from the external mirror  244  is split by the beam splitter  242 . Part  248  of the split beam is applied to the photo detector to detect the disturbance occurred on the propagation path of the beam  264  and remaining part of the split beam enters the mirror  235  with the direction opposite to the original propagation path. 
     The transmitted beam  266  through the mirror  236  is reflected on the mirror  246 , collimated by the beam collimator  247 , reflected on the corner cube retroreflector  241  and enters, via the beam splitter  243 , the external mirror  245  perpendicularly. The reflected beam  269  through the external mirror  245  is split by the beam splitter  243 . Part  249  of the split beam  266  is applied to the photo detector to detect the disturbance occurred on the propagation path of the beam  266  and remaining part enters the external mirror  236  with the direction opposite to the original propagation path. 
     As similarly as described above with reference to FIG.  3 , the piezo transducers  270  and  271  attached on the external mirrors  244  and  245 , respectively, are used to stabilize the interferometer and the other transmitted beams through the mirror  235  and  236  are applied to the difference amplifier and summation amplifier(not shown) via the photo detectors to measure I 1 −I 2  and I 1 +I 2 . 
     As similarly as the piezo transducer  225  in FIG. 6, the piezo transducer  250  attached on the external mirror  233  is used to compensate the variation of the cavity length in the ring laser  263  due to the environmental changes, e.g., temperature. As similarly as the beam combining prism  96  in FIG. 10, the beam combining prism attached to the mirror  234  is used to measure the variation of the interference fringe due to the interference between the two counter propagating beams  261  and  262  in the ring laser  263 . 
     The measurement of the physical quantity is enabled by fixing the piezo transducers  270  and  271  attached on the external mirrors  244  and  245 , respectively, and moving the platform  273  and  274  on which the corner cube retroreflector  240  and  241  or an alternative element is mounted. Depending upon the kind of the physical quantity to be measured, the corner cube retroreflectors  240  and  241  are moved simultaneously or separately or only one of them is moved. The propagation direction of the transmitted beam  264  reflected on the mirror  237  is parallel with the moving direction of the platform and perpendicular to the sectional surface  278  of the corner cube retroreflector  240 . It will be preferable that the sectional surface  278  of the corner cube retroreflector  240  is parallel with the external mirror  244 . The propagation direction of the transmitted beam  266  reflected on the mirror  246  is parallel with the moving direction of the platform  274  and perpendicular to the sectional surface  279  of the corner cube retroreflector  241 . It will be also preferable that the sectional surface  279  of the corner cube retroreflector  241  is parallel with the external mirror  245 . It is possible to construct the reference optical path by using only one of the corner cube retroreflectors and move the external mirror based on the physical quantity to be measured in FIG.  11 B. And it is also possible to construct the reference optical path by using the external mirror and move the corner cube retroreflector based on the physical quantity to be measured. 
     In FIG. 11B, the transmitted beam  265  through the mirror  235  is collimated by the beam collimator  238 , reflected, via the attenuator  239 , on the mirror  253 , again reflected on one side of the two-side mirror  256  and enters the external mirror  259  via the corner cube retroreflector  257  and the beam splitter  258 . Part of the beam  268  reflected on the external mirror  259  is applied to the photo detector by the beam splitter  258  and the remaining part enters the ring laser  263  through the mirror  235  along the direction opposite to the original propagation path. 
     The transmitted beam  267  through the mirror  236  is collimated by the beam collimator  247 , reflected from the mirror  252 , again reflected on the other side of the two-side mirror  256  and enters the external mirror  259  via the corner cube retroreflector  257  and the beam splitter  258 . Part of the beam  269  reflected on the external mirror  259  is applied to the photo detector by the beam splitter  258  and the remaining part enters the ring laser  263  through the mirror  236  along the direction opposite to the original propagation path. The transmitted beams  265  and  267  propagate parallel to each other after reflected on the two-side mirror  256 . And the transmitted beams  265  and  267  should be parallel with the moving direction of the platform  275  on which the corner cube retroreflector  257  is mounted. The front furnace  272  of the corner cube retroreflector  257  should be parallel to the external mirror  259 . The piezo transducer  272  attached on the mirror  253  is used to control, by using the regulated voltage supply, the difference amplifier to have maximum difference between the highest voltage output and the lowest voltage output, that is, maximum peak waveform. The piezo transducer  260  attached on the external mirror  259  is used to stabilize the interferometer as the corner cube retroreflector  257  is moved by the platform  275 . 
     The piezo transducer  250  attached on the mirror  233  is used to compensate the variation of the cavity length in the ring laser  263  due to the measurement environment changes. The beam combining prism  251  attached on the mirror  234  is used to measure the variation of the interference fringe due to the interference between the two counter propagating beams  261  and  262  in the ring laser  263 . 
     The corner cube retroreflector  240 ,  241  and  257  are constructed by joining two mirror  283  and  284  to have the inner angle 90° and inner reflecting sides. The incident beam  285  is reflected on the mirrors  283  and  284  to be the beam  286  which is parallel with the incident beam  285  and on the same plane. The mirrors  246 ,  252 ,  253  are able to rotate to make the beams  268  and  269  parallel. The polarization direction of the two counter propagating waves in the ring laser  263  should be identical with each other. In FIGS. 11A and 11B, all parts may be constructed as mono-blocks  281  and  282  except for the corner cube retroreflector  240 ,  241  and  257  or the alternative elements and the platform  273 ,  274  and  275 . 
     FIGS. 12A and 12B provide the structure of the optical sensing unit of the inventive interferometer capable of changing the only one of optical paths on l 1  and l 2  by the object without changing the physical distance between the mirror in the ring laser and the external mirror. FIG. 12A depicts the case l 1  includes the measurement cell. FIG. 12B depicts the case l 1  does not include the measurement cell. 
     In FIG. 12A, the transmitted beam through the mirror  288  in the ring laser  287  produced from the two counter propagating beams in the ring laser  287  enters the external mirror  290  and the transmitted beams through the mirror  289  in the ring laser  287  enters the external mirror  293 . The external mirrors  290  and  293  are aligned to have the incident beams thereto and the reflected beams therefrom be parallel with each other and on the same plane. The measurement cell  298  is divided as a vacuum section  297  through which the reference beam is transmitted and another vacuum section  296  which will be fill with the gas corresponding to the physical quantity to be measured and through which the measuring beam is transmitted. The gas corresponding to the physical quantity to be measured is injected passing the stopper  299 . The piezo transducer  291  is attached on the external mirror  290  and initially stabilized by the regulated voltage supply  292 . And the piezo transducer  294  is attached on the external mirror  293  and initially stabilized by the regulated voltage supply  295 . When the interferometer is turned on at t=0, the ring laser is stabilized by the initial voltage of the regulated voltage supply and the output amplifier. If the gas corresponding to the physical quantity to be measured is injected at t=t 1 , then thereby the optical path is changed and the output based on Eq. (12) is generated. 
     FIG. 12B is the case the reference beam does not transmit through the measurement cell  300  which is vacuum and later the gas is injected thereto. 
     The output of the inventive interferometer is the variation rate of the interference fringe due to the intensity sum, the intensity difference and the phase difference, between the two counter propagating wave. Part of that output is fedback negatively to suppress or set off the variations of output beam intensity and frequency of the ring laser, due to input voltage change and other environmental effect so that accurate measurement can be achieved. And the effect of the minute movement of the ring laser on the measurement is minimized by operating the ring laser within the lock-in zone. 
     While the present invention has been shown and described with respect to the particular embodiments, it will be apparent to those skilled in the art that many changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.