Abstract:
An apparatus and method of controlling optical loss in an optical switch to equalize optical power or loss in a group of optical signals in an optical transmission system relatively insensitive to mechanical vibration. In one embodiment a group of optical signals is input into an optical switch and selected optical signals are variably attenuated using synchronized control to two mirrors in order to provide more uniform power distribution among the group of optical signals without enhancing vibration sensitivity of the optical switch.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
   The present application is a continuation application of U.S. patent application Ser. No. 10/616,244, filed Jul. 8, 2003, now U.S. Pat. No. 6,904,195 and claims the benefit of U.S. Provisional Application No. 60/394,740, filed Jul. 9, 2002. 

   FIELD OF THE INVENTION 
   This invention relates to power balancing (or equalization) of optical power between channels of fiber optic transmission systems. More particularly, the invention relates to power balancing in an optical system using optical switches in fiber optic transmission systems to selectively attenuate optical signals passing through the optical switches. Still more particularly, some embodiments of the invention relate to power balancing of the various optical channels in optical transmission systems that transmit a multitude of optical signals by the technique of Wavelength Division Multiplexing (WDM). 
   BACKGROUND OF THE INVENTION 
   Fiber optic systems play an increasingly important role in transmission of signals. A common application uses WDM to combine many independent optical signals of different wavelengths onto one optical fiber for long distance transmission. Signals are routed through the network by demultiplexing signals from a group of input fibers into an individual fiber for each signal, directing the signals using a large cross-connect switch, then recombining the signals using wavelength multiplexers onto a group of output fibers. 
   Since excessively strong optical signals saturate optical amplifiers and reduce the gain available to weaker signals, desired signal to noise ratio is maintained in the network by keeping the optical power at each wavelength approximately the same. Consequently, loss at each wavelength must be carefully controlled across the network. 
   It is known that loss can be controlled by using programmable optical attenuators before or after the optical switch at the point where each optical signal is separate. However, these programmable optical attenuators add substantial cost, complexity and loss to the network. See “Optical Cross-Connect System In Broadband Networks: System Concept And Demonstrators Description”, Journal of Lightwave Technology, Vol. 11 (No. 5–6), May–June 1993, pp. 688–694, Johansson, S.; Lindblom, M.; Granestrand, P.; Lagerstrom, B.; Thylen, L. 
   An acousto-optic tunable filter (AOTF) can also be used in an optical network to equalize power levels as disclosed in, “MOSAIC: A Multiwavelength Optical Subcarrier Multiplexing Controlled Network”, IEEE Journal on Selected Areas in Communications, Special Issue on High Capacity Optical Networks, 16 (7), 1270–1285 (September 1998), Gaudino, R.; Len, M; Desa, G.; Shell, M.; Blumenthal, D. J. 
   An alternate method of balancing optical power in an optical network by detuning an optical switch in order to equalize optical loss or optical power was disclosed in pending U.S. patent application Ser. No. 09/855,765, “Wavelength Power Equalization by Attenuation in an Optical Switch”, which has issued as U.S. Pat. No. 6,697,547 B2. Balancing optical power is obtained by detuning one or more mirror electrodes in a MEMS-based switch using mirrors that rotate in two axes. 
   BRIEF SUMMARY OF THE INVENTION 
   According to one embodiment of the present invention, loss control in an optical network is obtained within a large optical switch having one or more two-dimensional arrays of movable mirrors for directing optical signals. Loss can be increased by detuning one or more mirrors away from the optimum angle for minimum loss. Because this approach generally results in unacceptable sensitivity to vibration, a technique is disclosed for detuning an input and output mirror with opposite vibration sensitivity to result in a system insensitive to vibration. 
   Other aspects and advantages of the invention will become apparent from the following detailed description taken in conjunction with the accompanying drawings which illustrate, by way of example, the principles of the invention. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention will be readily understood with reference to the accompanying drawings, wherein like reference numerals designate like structural elements, and in which: 
       FIG. 1  is a block diagram of an optical transmission system. 
       FIG. 2  is an illustration of the operation of power equalization and loss equalization. 
       FIG. 3  is a block diagram of an embodiment of an optical switch. 
       FIG. 4  illustrates how loss detuning increases sensitivity to vibration for minimum loss and loss detuning. 
       FIG. 5  illustrates a cross-section of the mirror geometry showing the mirror actuator. 
       FIG. 6  illustrates the switch geometry showing the relationship of the center of mass of the mirrors with respect to the hinges. 
       FIG. 7  illustrates insertion loss in an optical switch at the point of optical alignment for minimum loss, with (a) a contour plot for input and output mirror angle offsets (b) a contour plot for input and output frame angle offsets. 
       FIG. 8  illustrates insertion loss in an optical switch at the point of optical alignment for minimum loss, with linear plots for (a) input and output mirror angle coupled by vibration, and (b) input and output frame angle coupled by vibration. 
       FIG. 9  illustrates insertion loss in a switch with a single misaligned input mirror, showing insertion loss contour plots with varied input and output mirror angle offsets, and a linear plot with input and output mirror angles coupled by vibration. 
       FIG. 10  illustrates insertion loss in a switch with input and output mirrors misaligned equally in the same direction, showing an insertion loss contour plot for varied input and output mirror angle offsets, and a linear plot with input and output mirror angles coupled by vibration. 
       FIG. 11  illustrates insertion loss in a switch with input and output mirrors misaligned in the same direction, showing an insertion loss contour plot for varied input and output frame angles, and a linear plot with input and output frame angles coupled by vibration. 
       FIG. 12  illustrates insertion loss in a switch with input and output mirrors misaligned in opposite directions, showing an insertion loss contour plot for varied input and output mirror angle offsets, and a linear plot with input and output mirror angles coupled by vibration. 
       FIG. 13  illustrates insertion loss in a switch with input and output frames misaligned in different directions, showing a contour plot for input and output frame angle offsets, and a linear plot with input and output frame angles coupled by vibration 
       FIG. 14  shows a switch with input and output mirrors misaligned in the same direction by a different amount to compensate for different mirror hinge strengths, showing a contour plot for input and output mirror angle offsets, and a linear plot with input and output mirror angles coupled by vibration. 
       FIG. 15  shows measured vibration sensitivity of a switch when (a) loss detuning using a single mirror and when two mirrors are incorrectly offset so there is no vibration suppression and (b) when using two mirrors offset correctly for vibration suppression, and when using two frames offset correctly for vibration suppression. 
       FIG. 16  shows a dither pattern for measuring present alignment of the switch in order to calculate alignment adjustment 
       FIG. 17  shows a method of taking power measurements used to determine the optimum switch alignment for a particular mirror or frame angle. 
       FIG. 18  shows a control algorithm for feedback stabilization at the point of low vibration sensitivity. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   With reference first to  FIG. 1(   a ), one embodiment of the present invention for optical loss control in an optical network  100 , using an optical switch composed of two dimensional arrays of movable mirrors, is shown and described. Each fiber  101   a  through  101   n  in input fiber array  101  carries one or more optical signals multiplexed using wavelength division multiplexing (WDM). While  FIG. 1(   a ) illustrates an embodiment for a WDM application, it will be appreciated that this invention may be applied to optical switches used in other applications. At least one of the fibers comprising array  101 , e.g., fiber  101   a,  carries more than one optical signal, each signal being at a different wavelength. The wavelengths are separated by wavelength demultiplexers  102   a  through  102   n  such that each constituent signal is passed to and carried by a single optical fiber comprising fiber array  110 . Each signal from the wavelength demultiplexers  102   a  through  102   n  can be individually directed by optical cross-connect switch  103   a  fiber in fiber array  112  to any of the wavelength multiplexer  104   a  through  104   j  (n&lt;j; or n=j; or n&gt;j), where it is combined with signals at other wavelengths, again by WDM, onto an output fiber  106   a  through  106   j  of output fiber array  106 . 
   The optical power of each output wavelength from output of switch  103  is monitored by optical tap/detector combination  105   a  through  105   t  (t&lt;nj; or t=nj; or t&gt;nj) that splits of some of the optical power and measures the power level with a photo detector. A preferred integrated tap/detector is model IPD-10 from Santec, Inc. (Japan). A control and processor circuitry  107  (e.g., microprocessor TMS320C6211, Texas Instruments, Dallas, Tex.) can be used for control of the mirrors within switch  103  to equalize optical loss or power levels by adjusting the alignment of the mirrors, as will be further described below. 
   With reference next to  FIG. 2 , the concept of power balancing in an optical network is illustrated. In  FIG. 2(   a ), loss in increased for connections through the optical cross-connect switch  103  such that all of the outputs have equal power. The signal strength on the input fibers in the example of  FIG. 2(   a ) is arbitrary, and selected for illustrative purposes only. Similarly, the selected output signal strength is arbitrary and will be chosen depending on the desired application of the present invention. This configuration of  FIG. 2(   a ) can also include pre-adjustment, where the output power is adjusted for loss expected in subsequent stages. 
     FIG. 2(   b ) illustrates a variation of the application shown and described in  FIG. 2(   a ). In  FIG. 2(   b ), a constant loss value is introduced to each wavelength (individual optical fiber) such that the optical signal strength of each optical signal exiting switch  103  is below a certain selected value. In the example, all connections have the same loss, 3 dB. Of course, as above, the signal strength on the input fibers and the loss and output signal strength in the example of  FIG. 2(   b ) is arbitrary, and selected for illustrative purposes only. The configuration of  FIG. 2(   b ) may also include pre-adjustment, where the output power is adjusted for loss expected in subsequent stages. 
   Array technology is important for producing large optical switches in volume. An expanded three-dimensional view of the core switch  103  based on array technology is shown in  FIG. 3 . In one embodiment of a switch implementation, free-space collimated beams are produced by positioning input fibers (not shown) in a fiber block  21   a  consisting of a two-dimensional array of fibers with a polished end-face and an input lens array  22   a.  The collimated input beams (e.g., beam A) are directed to input mirror array  23   a  then output mirror array  23   b , where the angle of each mirror in input array  23   a  and output array  23   b  can be moved in two axes. While referring to  23   a  and  23   b  as input and output mirror arrays, it will be appreciated that switches of the type shown are commonly bi-directional. This allows any optical beam input to be steered to any output lens in array  22   b,  which focuses the free space beams back into output fiber array  21   b  where fibers (not shown) carry the optical beam onward. 
   Lens arrays are available from MEMS Optical (Huntsville, Ala.). Arrays of mirrors that rotate in two axes are available from OpticNet (Campbell, Calif.) and from other vendors, selected depending upon application, requirements, etc. The preferred method of fabricating these mirror arrays will be described subsequently. 
   Mirror arrays of the type shown in  FIG. 3  are generally comprised of mirror assemblies of the type shown in the exploded portion of  FIG. 3 . As shown therein, each mirror assembly  27  comprises a centrally located mirror structure  24 , suspended by torsion members  25   a.  Mirror structure  24  rotates around the long axis of the torsion members  25   a,  which act as torsional springs which tend to oppose mirror structure rotation. Mirror structure  24  and torsion members  25   a  are carried by a frame  26  to which the torsion members  25   a  are attached. Frame  26  is itself carried by torsion members  25   b.  Frame  26  rotates around the long axis of the torsion members  25   b,  which act as torsional springs which tend to oppose rotation of frame  26 . Frame  26  and torsion members  25   b  are carried by an array framework (not shown) which itself does not move significantly relative to the frame/mirror system. As will be discussed further below, mirror  24  and frame  26  may be moved independently of one another. By constructing the assembly with torsion members  25   a  and  25   b  perpendicular to one another, a gimbaled mirror assembly may be provided with two full degrees of freedom of motion. 
   The optical switch configuration shown in  FIG. 3  has a loss in decibels that increases as approximately the square of the error in each mirror angle from the optimum alignment. This quadratic loss relationship holds for either axis of input mirror angle and either axis of output mirror angle, where the total loss is approximately the sum in decibels of the loss contribution from each mirror angle error. An example of loss as a function of mirror angle offset is shown in  FIG. 4(   a ), where switch loss is varied by rotating the output mirror. 
   Continuing with reference to  FIG. 4(   a ), near the point of optimum alignment  41 , the loss does not change substantially for small angle variations of the input mirror. However, as the mirror is detuned, for example at point  42 , to increase the optical loss, the slope of this curve increases, indicating that the sensitivity of the loss to mirror angle is much higher. 
   Referring now to  FIG. 4(   b ), the same loss function as in  FIG. 4(   a ) is shown, but the nominal alignment has been shifted to point  42  to give 2 dB of loss. That is, this is the state of the system if one should simply increase the loss to cause the optical signals through switch  103  to have either more uniform optical power or optical power that does not exceed a desired threshold. This increased mirror angle sensitivity creates several problems. One potential problem is sensitivity to control noise on the electrode controlling the mirror angle. A more fundamental problem is greatly increased sensitivity to mechanical vibration. 
   As previously stated, in typical optical cross-connect switches, switching of an optical input beam between selected optical outputs is accomplished by reflecting the optical beam from an input fiber off of one or more mirrors which, based on the angle of their mirror surfaces to the optical beam, direct the optical beam to the desired output fiber. In such switches, different mechanisms can be used to control the switch mirror angles. According to one technique, magnetic actuation is used by passing current through loops to generate a magnetic field. According to another technique, a voltage is used to rotate the switch mirrors using electrostatic attraction. This voltage is generated by a microprocessor and a digital-to-analog converter, followed by a high-voltage amplifier to generate the voltages needed to drive the mirrors (typically 100–300V). The digital-to-analog converter generates quantization noise because it has a discrete number of possible output voltages. The high-voltage amplifier also generates noise. 
   As mentioned, it is possible to adjust the “tuning” (i.e., position) of the mirrors, for example to make the output optical power more uniform. Without careful design, however, these noise components can cause excessive amplitude modulation of the light signal as a mirror of the optical switch is detuned to increase the optical loss. Generally the electrical noise can be kept sufficiently small by using a D-A converter with enough resolution to minimize quantization noise. 
   MEMS mirrors are mechanical structures that tend to respond to mechanical vibration, which can cause undesirable rotation. As illustrated in the graph of  FIG. 4(   a ), for optimum mirror alignment, a small amount of rotation does not cause substantial amplitude modulation. As the mirror is detuned to increase optical loss, however, the vibration-induced rotation of only a few hundredths of a degree can cause excessive amplitude modulation of the optical signal. 
   The effect of high-frequency vibration can be suppressed by suspending the switch on springs, for example, as disclosed in, U.S. patent application Ser. No. 10/078,057, filed Oct. 25, 2001, titled “Low frequency vibration isolation and damping system,” now abandoned, incorporated by reference herein. However, the Telcordia Office Vibration procedure required for optical networking equipment calls for vibration testing at 5 Hz, which is too low a vibration frequency to easily suppress with a passive vibration system. In addition, a resonance in the test rack can amplify the required 0.1G (that is, 0.1 times the force of gravity) acceleration that is applied to the rack up to 1.5G acceleration at the location where the switch is mounted. Accommodation of vibration at these low frequencies require that the mirrors not be sensitive to low-frequency acceleration of the switch on the order of 1.5G. What is needed is a method to increase the loss of the optical switch for optical power balancing in the network, without increasing the vibration sensitivity. 
   The present invention includes a mirror embodiment in which rotation in two axes is obtained by a gimbal mirror, one embodiment of which is shown in  FIG. 5 . This invention may also be applied to mirrors with zero first-order moment of inertia for small acceleration, but some higher-order deflection caused by large acceleration. The mirrors and frames are actuated electrostatically by blades that hang down from the mirror. A cross-section of a mirror is shown in  FIG. 5 . Blade  57  is electrostatically attracted to blade  58  by applying a voltage difference between the blades produced by voltage source  59 . The attraction between blade  57  and blade  58  cause mirror  53  to rotate around torsional spring bars  55  that support the mirror and act as a pivot point. Because the electrostatic force causing rotation is strong, the hinges can be strong, making this blade actuator design well suited for building large optical switches. These strong hinges create a robust mirror array capable of withstanding significant shock. MEMS of this design have survived shock testing up to 1000G. 
   The disadvantage of the blade actuator geometry is that the center of mass of the mirrors is offset from the hinge pivot axis, resulting in a torque on the mirrors when accelerated due to vibration. Mechanical objects are commonly characterized by a center of mass and a moment of inertia. Acceleration of an object can be calculated based on the force applied to a location represented by the center of mass. The rotation of an object can be calculated by knowing the force applied perpendicular to the center of mass and the moment of inertia. The moment of inertia depends on the mass of the mirror and the distance of the center of mass from the pivot point, which in this case is the mirror hinge. The blade actuator design of  FIG. 5  has a relatively large moment of inertia, resulting in significant mirror rotation under acceleration. 
   A cross-section of the switch illustrating the effect of acceleration is shown in  FIG. 6 , with an input fiber  61  a and input collimating lens  62   a  directing the optical beam B onto input mirror  63   a.  Mirror  63   a  is suspended by torsional bars that act as a pivot point  65   a,  and also provide a restoring force for the mirror. Mirror  63   a  rotates to direct the optical beam onto output mirror  63   b,  which also has torsional bars that act as a pivot point  65   b.  Mirror  63   b  rotates to couple to optical beam B through focusing lens  62   b  to output fiber  61   b.    
   Each mirror is represented by a heavy mass  64   a  and  64   b  located at the actual center of mass of the mirror; the actual reflective surfaces  63   a  and  63   b  are of a less significant mass compared to the blade structure. Acceleration of the switch in the vertical direction with respect to the illustration of  FIG. 6  (labeled ‘perpendicular acceleration’) does not induce significant mirror rotation. In this acceleration direction, the hinge is approximately in line with the center of mass of the mirror. 
   Acceleration of the switch in the horizontal direction (labeled ‘mirror acceleration’) will cause force in a direction opposite the acceleration. The inertial force  66   a  will produce counterclockwise rotation of input mirror  63   a,  and the force  66   b  will cause clockwise rotation of output mirror  63   b.  For the purposes of this discussion, mirror angles are measured as positive for counter-clockwise rotation, so acceleration in the ‘mirror acceleration’ direction causes the angle of input mirror  63   a  to increase and output mirror  63   b  to decrease. 
   Motion in the switch in the ‘frame acceleration’ direction is indicated by a circle with a dot in the center in  FIG. 6 . This notation uses the point of an arrow moving out of the page to show the direction of motion. Acceleration of the switch in this ‘frame acceleration’ direction out of the plane of the illustration will produce the same direction of rotation in both frame angles. The frame angles for both input and output mirrors are measured positive when vectors drawn normal from the mirror to the other mirror direction rotate out of the page. 
   Optical signal strength may be measured, for example, by optical taps located in the optical path. For example, free-space beam splitter  67   a  may be introduced to direct a focused portion of beam B though lens  69  to an optical power detector  68   a.  Likewise, fiber-optic power splitter  67   b  may be introduced to direct a portion of beam B to an optical power detector  68   b,  after beam B has been coupled into optical fiber  61   b  by lens  62   b.    
   A contour plot of the loss of a switch that is otherwise optimally aligned is shown in  FIG. 7(   a ) as a function of misalignment of the input mirror angle and output mirror angle. A contour plot of the loss of the switch is shown in  FIG. 7(   b ) as a function of misalignment of the input frame and output frame angle relative to optimum alignment. The contour lines are widely spaced near optimum alignment point  701 , indicating that the loss is not changing for small angular variations due to ‘mirror acceleration’ or ‘frame acceleration’. 
   Vibration at frequencies well under the MEMS resonance (&lt;&lt;600 Hz) induces correlated motion between both mirrors or both frames. Vibration in the ‘mirror acceleration’ direction of  FIG. 6  causes one mirror angle to increase and one mirror angle to decrease, resulting in motion along the control plot of  FIG. 7(   a ) labeled ‘mirror acceleration.’ The loss function resulting from moving along this line of the contour plot produces the graph of loss of  FIG. 8(   a ) showing loss as a function of coupled mirror motion. Vibration in the ‘frame acceleration’ direction of  FIG. 6  causes both frame angles to increase or decrease, resulting in motion along the control plot of  FIG. 7(   b ) labeled ‘frame acceleration.’ The loss function resulting from moving along this frame motion line of the contour plot produces the graph of loss of  FIG. 8(   b ) showing loss as a function of coupled frame motion. 
   Detuning an input mirror to generate a loss of 2 dB produces the contour plot shown in  FIG. 9(   a ) for offsets in input and output mirror angle. Near the center of the graph corresponding to the 2 dB loss point, the contour lines are more closely spaced than the case in  FIG. 7(   a ) without loss detuning. Input mirror angle changes represented by horizontal motion on the contour plot cause more rapid loss variation than for an optimally aligned switch. Output mirror angle changes represented by vertical motion on the contour are parallel to contours of constant loss, so small changes in the output mirror angle do not significantly change loss. 
   Vibration causes motion in both the input mirror and output mirror, resulting in loss due to coupled input and output mirror motion as shown in  FIG. 9(   b ). The slope of this line is much higher than for the example of  FIG. 8(   a ) tuned for minimum loss, resulting in more amplitude variation from small mirror motion with mirror detuning as was predicted by the graph of  FIG. 4 . 
   Detuning both mirrors equally in the same direction to produce 2 dB of loss gives the contour plot for mirror angle offset as shown in  FIG. 10(   a ). Here acceleration of the switch in the ‘mirror acceleration’ direction produces an increase in loss from the input mirror and a decrease in loss from rotation of the output mirror, resulting in fairly constant optical loss if the magnitude of these input mirror angle and output mirror angle variations are approximately equal. This acceleration in the ‘mirror acceleration’ direction causes motion parallel to the loss contours resulting in low amplitude modulation, which can also be seen in  FIG. 10(   b ). 
   The mirror misalignment illustrated in  FIG. 10  produces a frame motion loss control plot shown in  FIG. 11(   a ). The best frame alignment produces a loss of 2 dB, because frame alignment cannot make up for the 2 dB loss attributable to misalignment of the mirrors. When the frames are aligned for minimum optical loss, small variations of either input or output frame angle do not significantly change the optical loss as shown in  FIG. 11(   b ). As  FIG. 11  demonstrates, mirror misalignment does not qualitatively change the frame misalignment curve, and frame misalignment does not qualitatively change the mirror misalignment curve. Consequently the remaining curves will show only mirror misalignment or frame misalignment. 
   Detuning both mirrors equally in the opposite direction to produce 2 dB of loss gives the contour plot shown in  FIG. 12(   a ). Here acceleration of the switch in the ‘mirror acceleration’ direction is perpendicular to the mirror loss contours, so acceleration produces both an increase in loss from the input mirror and an increase in loss from rotation of the output mirror. These loss terms add to enhance sensitivity to vibration as shown in  FIG. 12(   b ). 
   The input and output frame angles can be detuned from the minimum loss condition, instead of detuning the input and output mirror angles. Detuning both frames simultaneously in opposite directions to produce 2 dB of loss gives the contour plot for frame misalignment shown in  FIG. 13(   a ). Although the frame angles are detuned in opposite directions, each frame angle is measured with respect to its mirror array, so for this detuning condition vectors drawn normal to the input and output mirror in the illustration of  FIG. 6  rotate out of and into the page for the input and output mirror, respectively. Here, acceleration of the switch in the ‘frame acceleration’ direction produces an increase in loss from rotation of the input frame and a decrease in loss from rotation of the output frame, resulting in fairly constant optical loss if these input frame angle and output frame angle variations are matched. 
   Just as mirror angle detuning does not enhance vibration sensitivity of the frame angles, as demonstrated in  FIG. 11 , so frame angle detuning does not enhance vibration sensitivity of the mirror angles. Thus, the switch is relatively insensitive in the ‘mirror acceleration’ direction as well as the ‘frame acceleration’ direction when loss detuning using frame angles, as it was for loss detuning using mirror angles. 
   The previous examples assumed that acceleration produced the same magnitude of rotation in both mirrors, or in both frames. The amount of mirror rotation induced by acceleration is determined by the mirror or frame moment of inertia, which determines the rotational force under acceleration, and by the mirror or frame hinge stiffness, which determines the resistance to rotation. 
   The mass of each mirror is determined by photolithography, so the moment of inertia in general is well matched between mirrors. The hinge stiffness varies as the third power of the hinge width, so the hinge stiffness is much more difficult to control, and precise matching of vibration sensitivity between mirrors is difficult. 
   This technique of loss detuning by rotating both mirrors or both frames to suppress vibration dependence can be implemented even if vibration induces a different amount of input and output mirror rotation, or induces a different amount of input and output frame rotation. By detuning input and output mirrors different amounts from the condition of minimum loss, the resulting mirror motion labeled ‘mirror acceleration’ can still be made parallel to the constant loss contours, giving similar vibration insensitivity to that shown in  FIG. 12(   b ). Detuning both mirrors simultaneously in the same direction by different amounts produces contour plots as shown in  FIG. 14(   a ), where the input mirror is assumed to be twice as sensitive to vibration as the output mirror. A linear plot as a function of rotation of the more sensitive mirror is shown in  FIG. 14(   b ). 
   Experimental results are shown  FIG. 15(   a ) with a switch under vibration at 8 Hz. The rack was shaken at an amplitude of 0.1G. The switch was mounted in a mechanical system with a net vibration transmissibility of about 1 at 8 Hz, so the switch itself also experienced a vibration level of about 0.1G. First the switch was set for minimum loss, giving the relatively small vibration response  1510 . The loss was increased to 2 dB by detuning a single mirror, resulting in the large amplitude vibration of  1512 . Detuning both mirrors to give a total of 2 dB loss with the mirrors oriented in the opposite direction such that the vibration response of each mirror adds gave a similar large amplitude variation  1514 . 
   Detuning both mirrors to give a loss of 2 dB with the mirrors oriented in the same direction to cancel vibration sensitivity produces a small amplitude variation  1516 , as shown in  FIG. 15(   a ). Detuning both frames to give a loss of 2 dB with the frames oriented in the opposite direction to cancel vibration sensitivity also gave a small amplitude variation  1518 . 
   Very precise mirror angle control is needed for large optical switches. Consequently, one method of mirror control is to measure the optical power coupled into the output fiber, and use feedback to stabilize the optical loss as disclosed in U.S. patent application Ser. No. 09/548,587, titled, “Feedback stabilization of a loss optimized switch,” has issued as U.S. Pat. No. 6,456,751 B1. The first step in using feedback stabilization algorithm is to characterize the present switch alignment in order to know what correction to make to the alignment of the mirrors. 
   One method to characterize switch alignment is to measure the loss of the switch, then adjust each one of the mirror or frame angles, one at a time, away from optimum alignment and again measure the loss of the switch. For better measurement accuracy, switch loss may be measured for both a positive and negative offset of each mirror angle, which uniquely determines the switch alignment. The magnitude of the mirror angle offset to use in this technique is a tradeoff between achieving good signal to noise ratio with a large offset, and achieving minimum amplitude modulation using a small offset. An acceptable compromise is to use a mirror angle offset that results in a 0.1 dB power loss when moving away from optimum alignment. 
   A simple procedure for measuring the mirror slopes used to determine the alignment of the input mirror angle and output mirror angle is illustrated in  FIG. 16 . First, the loss of the switch is measured with the present switch alignment  1610 . Then, the input mirror is increased by the predetermined angle offset to position +M 1 , and power measurement  1611  is made. Next, the input mirror is returned it nominal position and the output mirror angle is increased by the predetermined offset to position +M 2 , and power measurement  1612  is made. Next, the output mirror is returned to its nominal position and the input mirror angle is decreased by a predetermined offset to position −M 1 , and power measurement  1613  is made. Next, the input mirror is returned to its nominal position and the output mirror is decreased by the predetermined offset to position −M 2 , and power measurement  1614  is made. Next, the output mirror is returned to its nominal position, and the sequence of  FIG. 16  is repeated for the input frame angle and output frame angle. 
   In many switch applications it is desired to minimize the optical loss. In this case the switch loss in decibels is approximately the sum of quadratic functions of each mirror angle and each frame angle as shown in the contour plots of  FIG. 7 . Switch optimization for minimum loss can be performed by optimizing each mirror angle separately. 
   Loss measurements are taken at the nominal mirror alignment  1710 , for a positive mirror offset  1712 , and a negative mirror offset  1714  as shown in  FIG. 17 . For each mirror angle, the three measurements are curvefit to a quadratic function  1716 . For minimizing loss, the angle is changed to the angle  1718  corresponding to the maximum of the curvefit  1716 . 
   The procedure of stabilizing the switch alignment at a value other than that of minimum loss is very similar to the process of minimizing switch loss. To increase the loss of the switch, the alignment of the input and output mirrors or input and output frames is changed to move the switch alignment to the point  1720  matching the appropriate slope  1722  needed to provide the correct loss as shown in  FIG. 17 . 
   For a switch with the mirror angles detuned to induce loss, the input and output mirror are aligned away from the minimum loss condition as shown, while the input and output frame angles are aligned to minimize loss. For a switch with the frame angles detuned to induce loss, the input and output frames are aligned away from the minimum loss position, while the input and output mirror angles are aligned to minimize loss. 
   The process of optimizing the switch for a given loss is shown in  FIG. 18 . The first step  1801  is propagating a group of optical switches  1801 , and inputting the signals to an optical switch  1803 . The next step is calculating the desired slope for each mirror and frame angle to give the desired attenuation  1805 , then moving each beam through a dither pattern  1807 . The next step is detecting the beam and measuring optical power at point in the dither pattern  1809 , then determining if the alignment is correct  1811 . If the alignment is not correct, the next step is calculating the correction to the alignment  1813 , then applying that correction  1815 . The process is repeated to maintain optical alignment, starting by dithering each beam  1807 . 
   Although several embodiments of this invention have been described in detail herein with reference to the accompanying drawings, it is to be understood that the present invention is not limited to these precise embodiments, and that various changes and modifications may be effected thereto by one skilled in the art without departing from the spirit and scope of the present invention as defined in the appended claims.