Abstract:
Methods and apparatus are provided for detection and control of multiple-axis active alignment for a free-space-coupled single-mode fiber-optic transmission system that automatically optimizes the coupling through the system. In a specific embodiment, a measurement of coupled power is made and error signals are used to control actuation via four axes of beam steering elements to null four generally orthogonal alignment errors (combinations of two lateral errors and two angular errors) of the beam between the input and output fibers. The four alignment errors are detected using a synchronous-detection approach. A feedback control system nulls the four errors.

Description:
BACKGROUND OF THE INVENTION 
     The invention relates to optical switching and free-space coupling of fiber optic waveguides in a single-mode fiber-optic transmission system. The invention finds application to micro-electromechanical systems (MEMS), but it is not so limited. 
     Four-axis detection schemes in fiber optic switch fabrics are known which use complex metrology systems to indirectly infer positioning of a laser beam of interest. One such technique, which is representative of the prior art, is described in U.S. Pat. No. 6,097,858, assigned to Astarte Fiber Networks of Boulder, Colorado. It uses forward- and reverse-facing metrology lasers (i.e., lasers located at input fibers and output fibers, respectively) and two-axis photoconductive sensors surrounding the input and output fibers to detect the beam alignment as measured by the metrology system. Since these augmented-metrology systems do not make direct use of the power signal they are attempting to maximize, their performance (ability to maximize the coupled power) is degraded by the unavoidable time-varying misalignment between the metrology system and the actual beam. 
     A Melles Griot active alignment system for fiber-optic coupling known as the NanoTrak Autoalignment system uses the measured output power and a synchronous-detection approach to null the errors in two angles using a coning motion in the two controlled axes of an optical mount. Conical scanning, while appropriate for detecting errors in two axes, is not well suited to a four-axis system addressed by the present invention or to systems with even greater degrees of freedom. The key limitation is that coning the first mirror at one frequency and the second mirror at a second frequency yields a coupled power response that contains oscillatory components at frequencies equal to the sums, differences, and first harmonics of the two frequencies, even when the alignment errors (ignoring coning angles) are zero. Thus, the double-coning approach cannot be used in a system requiring a constant output power. 
     What is needed is a technique for active alignment that overcomes the above limitations. 
     SUMMARY OF THE INVENTION 
     According to the invention, methods and apparatus are provided for detection and control of multiple-axis active alignment for a free-space-coupled single-mode fiber-optic transmission system that automatically optimizes the power coupled through the system. In a specific embodiment, a measurement of coupled power is made and detected error signals are used to control actuation via four axes of beam steering elements to null four generally orthogonal alignment errors (combinations of two lateral errors and two angular errors) of the beam between the input and output fibers. The four alignment errors are detected using a synchronous-detection approach. A feedback control system nulls the four errors.The theoretical basis as presented here for four-axis detection and control is sufficient for the general case. Therefore, the disclosure is to be understood to address the cases for applications of more or fewer axes than four. 
     The present invention related to alignment has application to synchronous detection. In the case of four-axis synchronous detection, a control system superimposes four distinct modes of oscillatory commands (dithers) as excitation signals on four nominal steering commands. These dithers, which themselves must be orthogonal, are specifically chosen to produce four corresponding time-orthogonal variations in measured coupled power at the dither frequencies that are proportional to the respective alignment errors. Specific examples of orthogonal mode variable signals for detection as disclosed herein are two sets of sine and cosine signals at two different frequencies. The invention will be better understood by reference to the following detailed description in connection with the accompanying embodiments. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of a four-port MEMS mirror array fiber optic switch in which the present invention may be implemented. 
     FIG. 2 is a diagram to illustrate beam alignment errors at the output lens as used in the present invention. 
     FIG. 3 is a three dimensional graph to illustrate constant-power dithering. 
     FIG. 4 is an illustrated flow chart to show steps in the synchronous detection method according to the invention. 
     FIG. 5 is a schematic diagram of a control system according to the invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Free-Space-Coupled Fiber Optic Switch Using MEMS 
     Referring to FIG. 1 there is shown an example of a four-port MEMS mirror array fiber-optic switch  10  in which the present invention may be implemented. The function of the fiber-optic switch  10  is to produce desired free-space couplings between the input fibers (in a first fiber array  12 ) and output fibers (in a second fiber array  14 ) via two-axis steering mirrors on a first mirror array  16  and a second mirror array  18 . In the embodiment illustrating the invention, the optical path is unidirectional between input fibers and output fibers, although the invention is not so limited. Expanding laser beams emanating from the input fiber array  12  are substantially collimated using a first lens array  20  confronting the first fiber array  12 . Mirrors on the first or input mirror array  16  steer the collimated beams  23 - 26  from the first lens array  20  toward the appropriate mirrors on the second or output mirror array  18 . The mirrors on the output mirror array  18  steer their incident beams  23 ′- 26 ′ into the corresponding lenses on a second or output lens array  30 . The output lenses of the second lens array  30  produce converging beams necessary for coupling power into the output fibers  23 ″- 26 ″ of the second fiber array  14 . 
     Output Beam Alignment Geometry 
     Referring to FIG. 2, there is shown a diagram defining the alignment of an output beam relative to its output lens/fiber port in accordance with the invention. This technique may be applied in a variety of geometries, only one of which is that of FIG.  1 . The axes “x”, “y”, and “z” define an “output” frame. The axis z is defined as the optical axis of the particular lens/fiber port (which may vary across the array of lens/fiber ports), and the perpendicular axes x and y are in the plane perpendicular to z. The beam intersects the output x-y plane at the linear displacements P x  and P y  in x and y, respectively. The two angles θ x  and θ y  define the orientation of the beam in the output x-y-z frame. With θ x  and θ y  equal to zero, the beam is parallel to the z axis. θ x  and θ y  are the rotations of the beam in the x and y directions, respectively, where a small-angle approximation (valid for the purpose of analyzing optical coupling) eliminates the need to define the order of the rotations. To clarify the sense of the rotations, the small-angle approximation for the unit vector in the direction of the beam expressed in the output frame is given by: 
     
       
           u   beam   out =[θ y −θ x 1]. 
       
     
     Gaussian Power Coupling 
     Assuming that longitudinal misalignments are zero and that the beam is matched to the mode field radius of the output fiber, the total coupled power P out  (a scalar quantity measured at the output fiber) can be approximated in a Gaussian form in terms of an input power P in  and four normalized beam alignment errors: 
     
       
           P   out   =P   in   e −(α 2 +β 2 +ρ 2 +σ 2 ),  (1) 
       
     
     where P in  is the optical power before loss due to alignment errors, and the four normalized errors α, β, ρ, and σ are given by:          α   =       f     ω   0            θ   x         ,     
          β   =       f     ω   0            θ   y         ,     
          ρ   =           n   gap        π                   ω   0         λ                 f                       (       P   x     -     f                   θ   y         )         ,              and             σ   =           n   gap        π                   ω   0         λ                 f                       (       P   y     +     f                   θ   x         )         ,                          
     where: 
     f is the lens focal length, 
     w 0  is the beam radius at 1/e 2  power density, 
     λ is the laser wavelength, and 
     n gap  is the index of refraction of the medium in the lens/fiber gap. 
     Constant-Power Dithering 
     In the case of a MEMS fiber-optic switch for which the coupled power is Gaussian in the four normalized alignment errors, quadrature (sine and cosine signals at a given frequency) dithering of the beam alignments produces a constant coupled power when the alignment errors (ignoring the dither component) are zero and the model parameters of the system are properly tuned. FIG. 3 illustrates for two of the four axes the concept of using quadrature dithering to provide a constant output power when the coupled power is Gaussian in the two alignment errors shown. When the alignment errors (ignoring the dither component) are zero as in FIG. 3, the sine and cosine dithers at any given frequency, whether above or below the natural resonance of the device, produce a circular trajectory in the two alignment errors. Since the sum of the squares of these two alignment errors is constant (due to the sine and cosine dithering), the result, as dictated by Equation 1, is a constant attenuated coupled power even though the individual errors are changing. If the other two dithers are also in quadrature form, these dithers will contribute a second constant loss term, such that the overall attenuation level due to the four dithers is constant. 
     Synchronous Alignment-Error Detection Technique for Gaussian Coupling 
     As discussed previously, the four normalized coordinate errors in angles α and β, and positions P and O are detected using synchronous detection. The detection process is explained as follows for the simplified case of a scalar normalized error x. The coupled output power is given in Gaussian form by 
     
       
           P   out   =P   in   e   −x     2   , 
       
     
     where x(t) at time t is the sum of the unknown error x u  and the known sinusoidal dither component x d (t) at frequency f d : 
     
       
           x=x   u   +x   d . 
       
     
     The logarithm of the power P out  is given by: 
     
       
         log( P   out )=log( P   in )− x   2 . 
       
     
     Since the quantity x 2  is given by:                x   2     =                  (       x   u     +     x   d       )     2                   =                  x   u   2     +     2        x   u          x   d       +     x   d   2         ,                                
     the log of the power is given by: 
     
       
         log( P   out )=log( P   in )−( x   u   2 +2 x   u   x   d   +x   d   2 ). 
       
     
     Defining λ as the negative of the log of the power: 
     
       
         λ=−log( P   out ), 
       
     
     λ is given by: 
     
       
         λ=( x   u   2 −log( P   in ))+2 x   u   x   d   +x   d   2 . 
       
     
     The expression λ can be decomposed into three components as follows: 
     1. (x u   2 −log(P in )) is a near-dc term (assuming a constant P in  and that the signal content of x u  is at low frequencies relative to f d ); 
     2. 2 x u  x d , a modulation of the unknown error and the dither, has a term at f d ; 
     3. x d   2  has a DC term and a 2f d  term. 
     The squaring effect of the coupling thus produces a component in the logarithm of the power (component #2 of λ) proportional to the dither signal x d  modulated by the unknown alignment error x u . The unknown error x u  can be extracted from λ(t) using a demodulation process by multiplying λ(t) by the dither signal x d (t) and filtering the resulting product to remove the residual terms at the dither frequency and its harmonics. The multiplication step produces the product signal Λ(t) given by: 
     
       
         Λ( t )=λ( t ) x   d ( t).   
       
     
     The product of λ(t) and the sinusoidal dither x d (t) yields various powers of x d (t) in Λ(t). The DC terms of λ yield a term in Λ proportional to x d  with signal content at the dither frequency f d . The 2f d  term of the x d   2  component of λ produces signals in Λ at f d  and 3f d . The    2   x u  x d  component yields a DC term in Λ (the detected error x det ) proportional to x u  and the amplitude of x d , and also yields a signal in Λ at 2f d  with an amplitude proportional to the square of the amplitude of x d . The detected error x det  is the sole term of Λ at DC and can be separated using a moving average filter spanning a time period T avg  equal to one or more periods T d  of the dither signal (T d =1/f d ). Such a filter preserves the low-frequency band of its input signal, while squelching signals at the averaging frequency f avg =1/T avg  and its harmonics. Filtering Λ with this filter thus extracts the detected error x det  while squelching the signal content at f d  and its harmonics: 
     
       
           x   det =Move Avg Filt(Λ( t )). 
       
     
     FIG. 4 illustrates the method of synchronous detection with Gaussian coupled power according to the invention. Referring to FIG. 4, the unknown beam alignment error A and mechanically injected dither B (altered by the prewarp function I) combine to produce a total alignment error x (as shown in C) at the output lens. The fraction of power in beam  23 ′ coupled into fiber  23 ″ (as shown in FIG. 1) is given by the Gaussian function of the alignment errors e −x     2    as shown in D, which produces an optical output power P out =P in  e −x     2    having a characteristic E as illustrated. The logarithm function F of the output power extracts the quantity x 2 . This quantity, which contains a modulation of the unknown error and the dither, is demodulated by multiplication G by the dither B. Filtering the demodulated signal with a moving average filter H with the appropriate frequency response tailored to the dither yields the detected error signal J. The prewarp I modifies the gain and phase of the dithers as a preemptive counterbalance to effects of the plant and control system on measured coupled power gain and phase. Increasing the frequency of the dithering allows for a higher detection bandwidth without departing from the desirable constant power characteristic. If the frequency of the dithers is sufficiently above the resonant frequency of the MEMS device, the detection bandwidth may also be sufficient to allow attenuation of resonant responses. 
     Extending the Detection Technique to Four Axes 
     According to the invention, the synchronous detection technique described in the previous section can be extended to simultaneously detect errors in the four alignments associated with the MEMS fiber-optic switch (as shown in FIG.  2 ). In this case, four time-orthogonal mode dither signals are used in conjunction with the four beam alignment coordinates. The approach is to excite the four beam-alignment coordinates with the four orthogonal dithers in a one-to-one manner to ensure a decoupled detection of the alignment errors. 
     As an example, the invention may be implemented using sine and cosine signals at two disparate frequencies for the four dithers, with the averaging frequency f avg  and two dither frequencies f 1  and f 2  having the ratio 1:2:3, respectively: 
     
       
           f   1 =2 f   avg , 
       
     
     
       
           f   2 =3 f   avg . 
       
     
     In the time period of one averaging cycle given by T avg =1/f avg , the 2× dithers repeat twice and the 3× dithers repeat three times, at which time the four dithers complete one full cycle of relative phasing. The time period T avg  for this full cycle of relative phasing is the defining time period for the notion of time-orthogonal bases. In one averaging period, the mean value of the products of the four dither signals is zero. Averaging over the full cycle of relative phasing thus prevents cross-dither-frequency interference in the demodulation phase. The sine and cosine dither signals at each dither frequency are inherently time-orthogonal with each other over a single cycle of their respective periods, so they are naturally time-orthogonal over T avg  equal to 2× or 3× of their cycles times. 
     Control System 
     FIG. 5 is a schematic diagram of a control system  100  according to the invention illustrated in interaction with elements of a fiber optic switch of FIG.  1 . The control system  100  provides detection and servo control of alignment errors. The control system  100  supplies the actuation voltages for a pair of MEMS mirrors on mirror arrays  16  and  18 . The MEMS mirrors produce the four mirror angles as a function of the actuation voltages. Reflection kinematics  109  specific to the optical design define the mapping of the four mirror angles to the four beam alignment errors at the output lens of lens array  30  (as shown in FIG.  2 ). As defined in Equation 1, the coupling of power into the output fiber of output fiber array  14  is Gaussian in the four beam alignment errors. FIG. 5 schematically illustrates the transformation shown in FIG. 1 in which beam  23  is steered by mirrors  16  and  18  to yield beam  23 ′ incident at a lens in the output lens array  30 , and the coupling of incident beam  23 ′ through the lens into the associated fiber  23 ″ of the output fiber array  14 . A power tap  108  at the optical output supplies the feedback signal, which is converted to an electrical signal by a photodetector  110 . Within the control system  100 , the feedback power signal is converted to a log signal by log function  112 , which in turn supplies the input to a multiplier  114 . The dither reference signals  120  are fed to the multiplier  114  and the prewarp stage  121 . The prewarp stage modifies the gain and phase of the dithers as a preemptive as counterbalance to the effects of the plant and control system on the gain and phase of the measured coupled power. 
     Referring again to FIG. 5, the output of the multiplier  114 , which is the product of the dither references  120  and the logarithm of the measured power  112 , is supplied to a filter  124 . The filter  124  may be a moving average filter of a pre-selected cycle length for extracting the error signal (near DC) components while squelching the artifacts of the dithering references, as explained previously. The error signal e is supplied to the servo control law element  102 , which produces a set of feedback control signals. 
     The summer  104  combines the feedback control signals from servo element  102  and the prewarped dithers from prewarp stage  121 , both of which are vectors in the output-space components α, β, ρ, and σ. The inverse kinematics and actuation element  107  converts the output-space commands into voltage feedback commands. The nominal connection bias voltages  126  are added to the feedback voltage commands at summer  105  to produce the actuator voltage commands. 
     Novel Features 
     Several aspects of this four-axis detection approach are novel. First, the present invention makes direct use of the measured coupled power signal rather than an in-parallel metrology system (with associated tolerance and drift errors) to detect the four controllable errors in the system, thereby guaranteeing an unbiased error estimate for use by the controller and thus maximum output. Second, the invention is the first use of synchronous detection as a means of detecting the four beam alignment errors. Third, the dither modes (static combinations of steering commands) are chosen to minimize coupling in the error detection (such that individual errors do not influence the values detected for the other errors). Decoupled detection enables faster servo response. Fourth, the modulation and demodulation dither signals are amplified and time-phased in a prewarp stage to accommodate gain and phase in the system, which prevents an additional frequency-dependent coupling in the error detection. Fifth, the modulation/demodulation technique specifies how to choose two dither frequencies and a third averaging frequency to prevent cross-frequency interference, another source of coupling in the detection. Sixth, the relative amplitudes of the dithers are scaled to yield a constant output power when the alignment errors are zero. 
     The invention has numerous advantages. If the beam alignment error is zero, then the response in power coupled through the system is flat, and there will be no power variation it the frequency of the applied dithering signals, even though dithering may lower the DC power level of the output signal. Moreover, no harmonics of the dither frequencies will be evident in the power of the output signal, since the two dithers at a given frequency are in two orthogonal axes in phase quadrature with each other. This is evident from an examination of FIG.  3 . 
     Alternate Implementations 
     Choices other than sine and cosine waves at two frequencies are possible for the dither mode variables. Sinusoids at four frequencies can be used, but the output power cannot be made constant and the averaging scheme used to minimize cross-frequency interference becomes more difficult. Spread-spectrum dithers are also possible, but suffer from the same issues. 
     Rather than using spatially decoupled dither modes as previously described, spatially coupled modes can be used. In this case, an extra step of decoupling the demodulated error signals is necessary. 
     Other choices of averaging and dither frequencies are possible. For example, a 1:1:2 combination of average and dither frequencies provides a time-orthogonal set, but residual harmonics of the 1× dither will corrupt the detection at the 2× frequency. Other multiples are also possible, but each case needs to be evaluated with respect to properties of the system. 
     The invention has been explained with reference to specific embodiments. Other embodiments will be evident to those of ordinary skill in the art. For example, this beam alignment system may be applied to beam tracking and the like. It is therefore not intended that this invention be limited, except as indicated by the appended claims.