refering now to fig1 of the drawings there is illustrated a two degree of freedom permanent magnet gyroscope and associated control circuitry 10 for an inertial sensing instrument . the drive motor includes a permanent magnet rotor 12 and a two phase stator having windings designated φa and φb . a trapezoidal shaped optical pattern consisting of a reflective segment 11 and a nonreflective segment 13 is formed on gyro rotor 12 . the formed optical pattern in a flattened representation is shown in fig3 . two optical sensors 14 and 18 are positioned around the outer circumference of rotor 12 at a 90 ° separation . the permanent magnet two degree of freedom gyro consists of the spin motor which includes the permanent magnet rotor 12 , the two phase stator windings φa , φb , torquer windings t1 , t2 , and two optical pickoffs 14 , 18 . the reflective segment 11 and nonreflective segment 13 correspond to the locations of the magnetic north and south poles of the rotor . as shown in fig4 each optical sensors 14 and 18 includes a light source 15 and 19 and a light sensor 16 and 20 respectively . each light source 15 and 19 of the optical pickoff is directed at the rotor 12 striking either the reflective 11 or nonreflective 13 portion of the optical pattern . if light strikes a reflective segment 11 of the optical pattern then the associated light sensor 16 , 20 will receive reflected light and be activated to produce a dc current . if the light from a source 15 , 19 strikes a nonreflective portion 13 of rotor 12 , than the associated light sensor 16 , 20 will not be activated . the dc current generated by an activated light sensor 16 , 20 is squared and buffered producing an output which is either plus 15 volts for a reflective surface or 0 volts for a nonreflective surface . when rotor 12 is spinning , the output square wave frequency is proportional to the rotor speed , while the zero crossing of the square wave approximately represents the instantaneous position of the rotor poles . the two phases of the permanent magnet motor are positioned 90 ° in space with respect to each other while the two pickoff sensors are also separated by 90 °. therefore , each buffered output of the pickoff sensor 14 , 18 is associated with one phase of the stator and is used to provide the timing information for motor commutation . the outputs of optical sensors 14 and 18 which represent pole locations , serve as commands to commutator switches 30 and 32 . the output of the commutator switches 30 , 32 are fed to drivers 40 and 42 respectively . in a manner well known in the art drivers 40 and 42 drive their associated stator windings φa , φb . as the rotor 12 of the permanent magnet motor accelerates from rest , the buffered output from the optical sensor is a square wave whose frequency is proportional to wheel speed . the output of either sensor 14 or 18 can be used to generate the dc voltage using a frequency to dc voltage converter 44 . as shown in fig4 the resulting dc voltage from converter 44 , which is proportional to rotor speed , is fed to a comparator 46 for comparison with a dc voltage input speed command signal . this results in a dc error signal at the output of comparator 46 , which is fed to a loop control circuit 48 where it is integrated to provide velocity and position feedback information . the velocity and position feedback signal is amplitude and phase adjusted to compensate for the rotor wheel dynamics . the conditioned signal from loop control circuit 48 is then fed to both commutator switches 30 and 32 whose outputs feed the drivers 40 and 42 . operation of the permanent magnet motor is always in a two phase drive mode providing maximum torque capability . with an optical pattern as shown in fig3 when the rotor 12 rotates about its spin axis and is not displaced in relation to a spin reference axis which may also be referred to as the center axis of the stator , light will strike a nonreflective segment 50 % of the time and a reflective segment 50 % of the time . when an input rate is applied to the gyro causing an angular displacement or tilt of the rotor 12 in relation to a spin reference axis , light will be reflected either above or below the midpoint of the trapezoidal pattern . light will no longer strike the reflective and nonreflective surfaces of rotor 12 for an equal amount of time . the sensor , 14 or 18 associated with the axis about which the rotor is displaced senses the reflective or nonreflective segments for different amounts of time resulting in a square wave which does not have a 50 % duty cycle . the outputs from comparators 60 and 62 are differentially combined with the signals from a constant pulse width generators 64 and 66 in differential amplifiers 68 and 70 . the resulting output from differential amplifier 68 or 70 is is fed to pulse width to dc voltage converter 72 or 74 to provide an error signal which through a torquer winding amplifier 76 or 78 provides a current output to either torquer winding t1 or t2 to drive rotor 12 to a null position . refering now to fig1 and 3 the spin axis about which the rotor 12 is driven is designated as the x axis , light sensor 14 is positioned along the z axis and senses displacement of the spinning rotor 12 about the y axis . light sensor 18 is positioned along the y axis and senses displacement of the spinning rotor 12 about the z axis . fig3 shows various voltage outputs for a positive , zero , and a negative displacement of rotor 12 about the z axis as sensed by a sensor 18 . in fig2 for a counterclockwise angular displacement of the rotor 12 about the z axis pulse v1a is on for less than 180 °, for no rotation of rotor 12 about the z axis v1a is on for 180 ° and for clockwise displacement about the z axis v1a is on for more than 180 °. these differences in v1a caused by the trapezoidal pattern scanned by the sensor 18 as rotor 12 spins , indicate the displacement of rotor 12 about the z axis . as shown in fig6 the signal v1a is compared with a constant pulse width signal v2a , from constant pulse width generator 64 , and the difference v3a is converted to a dc signal v4a which is amplified and utilized for energizing torquer winding t2 , to torque rotor 12 to a null position . sensor 14 detects angular displacement of rotor 12 about the y axis and provides an output signal after comparator 60 of v1b . as shown in fig7 signal v1b is processed , as described above for v1a , to energizing torquer winding t1 to torque rotor 12 to null . referring to the circuitry in fig4 which is similar to the circuitry shown and described in copending u . s . patent application no . 921 , 491 and which is herein incorporated by reference , the outputs from sensors 14 and 18 provide commutation timing signals for two phase control of commutator switches 30 and 32 . the input to commutators 30 and 32 is a dc error signal which is obtained by differentially combining a speed command signal with a feedback signal , obtained from sensor 18 . in fig5 there is shown more detail of the portion of the circuit which senses and counteracts the angular displacement of rotor 12 about the y or z axis . the output of sensor 18 is a pulse v1a and output of light sensor 14 is a pulse v1b . when the rotor 12 is rotating at constant speed , the width of pulse v1a is a function of displacement about the z axis and the width of pulse v1b is a function of displacement of rotor 12 about the y axis . pulses v1a and v1b activate constant pulse width generators 64 or 66 , respectively . the output of the constant pulse width generator is a pulse v2a or v2b having a width equal to v1a or v1b when there is no displacement around the y or z axis . pulses v2a and v2b are 50 % duty cycle pulses . v2a is compared with v1a to provide a differential output v3a which through a pulsewidth to dc voltage converter 72 drives torquer winding t2 . likewise , constant pulsewidth v2b is compared with pulse v1b to provide a difference signal v3b which feeds a pulsewidth to dc voltage converter 74 which provides dc output v4b . this dc output v4b feeds amplifier 78 which drives torquer winding t1 . fig6 shows waveform outputs for voltages v1a , v2a , v3a and v4a for positive displacement about the z axis . fig7 shows voltage outputs v1b , v2b , v3b and v4b for displacement of rotor 12 about the y axis . in the preferred embodiment the optical pattern formed on the gyro rotor 12 has a trapezoidal waveshape . the light source is directed at the midpoint of the trapezoidal waveshape so that as the rotor 12 spins at a constant rate about the x - axis and is not displaced about the y and z axes , light will strike a reflective segment for the same amount of time as it strikes a nonreflective segment , resulting in a 50 % duty cycle square wave . when an input rate is applied to displace the gyro , causing an angular displacement or tilt of the rotor about either the y axis or z axis , the light will strike above or below the midpoint of the trapezoidal waveshape depending upon the polarity of the displacement . the light will no longer strike the reflective and nonreflective surfaces for an equal amount of time . the resulting buffered sensor outputs contain angular displacement information . the angular displacement information is then extracted and phase and amplitude adjusted to deliver the amount of current to the torquers to maintain a closed loop operation . extracting this displacement information requires sensing a small change in the duty cycle of the sensor generated square wave outputs . in order to improve resolution , a constant pulsewidth v2a or v2b is subtracted from the square wave . each output v1a , v1b triggers a constant pulsewidth generator circuit and is also an input to a differential amplifier . the output of the pulsewidth generator circuits are combined in differential amplifiers with the sensor outputs to produce a difference signal . the difference signal contains the angular displacement information necessary to close the two cross - axes loops . the v3a and v3b outputs are then converted to dc levels v4a and v4b which are proportional to the width of v3a and v3b . the v3a output is shown in fig6 for a positive input rate which results in a pulse whose width is smaller than the width of the constant pulse , resulting in a positive dc output v4a . the v3b output is shown for a negative input rate which results in a pulse whose width is larger than the width of the constant width pulse , resulting in a negative dc output v4b . these dc outputs are frequency compensated and amplified to drive the torquer windings t2 and t1 .