Abstract:
A method and apparatus for stabilizing the wavelength of a laser are disclosed. The invention provides a way to stabilize a laser for applications in dense wavelength division multiplexing (DWDM) systems where frequency spacing is crucial. The invention accomplishes laser stabilization by generating an optical path which is passed through a filter to obtain a signal which is a function of frequency. A second optical path which does not contain a filter is generated to obtain a signal which is a function of power. The signals are then converted from optical to electrical and from analog to digital, and a microcontroller is used to normalize the frequency path with respect to the optical power path, process the signals via software code, and generate a signal which provides feedback to the laser for stabilization. By using a microcontroller; elements that lead to wavelength or frequency drift, or manufacturing component variations can be taken into account and the input signal to the laser can be adjusted accordingly.

Description:
FIELD OF THE INVENTION 
     The present invention relates to a novel and useful method for stabilizing the wavelength of a laser source. 
     BACKGROUND OF THE INVENTION 
     Laser sources are widely used in wavelength division multiplexed systems. In wavelength division multiplexed systems, it is important that the wavelength used is very stable. Although lasers are inherently very stable, increased stabilization of a laser&#39;s wavelength becomes crucial as systems migrate to dense wavelength division multiplexing (DWDM) types. In DWDM systems, many wavelengths are placed on a single fiber to increase system capacity. Currently the spacing in DWDM systems between frequencies is around 100 GHz and can be handled by traditional laser stabilization methods. However, as technology moves toward frequency spacings of 25-50 GHz or less, increased stabilization will be required to prevent interference between wavelengths as the spacings become closer and closer. 
     Presently, to wavelength stabilize lasers, the wavelength or equivalently the optical frequency of a laser is compared to a stable reference element. One method is to use an optical filter as a reference element. The output of the laser is split and part of the beam is passed through an optical filter to create an optical signal which is a function of wavelength or frequency and optical power (hereinafter “the optical filtered path”). The optical filtered path is then processed, assuming that a change in signal amplitude corresponds to a change in frequency, and a signal is generated which is fed back to the laser to stabilize the laser&#39;s wavelength. However, a change in signal amplitude at the output of the filter could be the result of a change in the power output of the laser rather than a change in the laser&#39;s frequency. 
     Another method of stabilizing a laser is to pass a slightly diverging beam of light, obtained by splitting the output of the laser source, through a filter at different angles of inclination as shown in FIG.  1 . The two photo-detectors, P 1  and P 2 , act as apertures and capture a different portion of the light emitted by the divergent source. This produces two different spectral responses, offset in wavelength according to their angular difference with respect to the filter. Since P 1  captures a portion of the emitted light which passed through the filter at a higher tilt angle than that captured by P 2 , it&#39;s response will peak at a slightly lower wavelength than P 2  as depicted in FIG.  2 . The filter and alignment parameter are chosen so that the wavelength offset between the two responses is roughly equal to their effective bandwidths. The signals are then compared differentially to generate a signal which can be used to stabilize the wavelength of the laser by maintaining λ=λ 0 , as further depicted in FIG.  2 . 
     In a stabilized system, wavelength or frequency drift can be introduced by the aging or temperature dependence of the laser itself, or by the aging or temperature dependence of the optical reference filter, the optical detectors, or the stabilization electronics. In addition, manufacturing variations of system components can result in varying wavelengths from system to system. Existing systems are unable to adequately compensate for the multitude of variables that can arise in a stabilization system when a very high level of stabilization is needed. 
     SUMMARY OF THE INVENTION 
     The present invention provides an improved method for stabilizing the wavelength of a laser source. The invention accomplishes this objective by using an optical filter, dual optical paths, analog and digital conversion, and a microcontroller. 
     In a preferred embodiment of the present invention, wavelength stabilization of a laser is accomplished via a laser, optical couplers, an optical filter, optical detectors, current-to-voltage converters, amplifiers, analog-to-digital converters, a microcontroller, and a digital-to-analog converter. 
     In the present invention, a laser generates a signal which is carried by a fiber optic cable. Two separate paths are created from the fiber optic cable via photo-couplers. The first path is an optical filtered path which passes through an optical filter. The second path is a power reference path used for normalization. Since the optical filtered path contains an optical filter, it provides a signal the power of which is a function of wavelength as well as the optical power output of the laser. The power reference path is unfiltered so as to provide a signal the power of which is a function only of the optical power output of the laser. A change in the output power of the optical filtered path should primarily indicate a frequency change of the laser. However, the change may be due to a change in the optical power of the laser. By normalizing the optical filtered path to the power reference path, the change in power in the optical filtered path that is due to frequency change rather than laser output power change can be isolated and used to stabilize the frequency of the laser source. 
     The other components are used to provide electrical signals, convert the signals into a usable form, and manipulate the signals. Optical detectors are used to convert the optical signals from the optical filtered path and the power reference path to electrical signals. The electrical signals produced by the detectors are then converted from current to voltage, via current-to-voltage converters. The current-to-voltage converters may provide some pre-amplification to the signal or pre-amplification may be provided by other means. Next, the signals from the converters are amplified, via amplifiers, to provide gain and prepare them for analog to digital conversion. The amplified signals are then converted from analog to digital by analog-to-digital converters to prepare them for processing by a microcontroller. The microcontroller then processes the signals in any manner desired using software code and generates an appropriate signal which is converted from digital to analog by a digital-to-analog converter for use in adjusting the laser&#39;s frequency. The microcontroller&#39;s processing can be accomplished by any of the following types of apparatus: microprocessor, processor, digital signal processor, computer, state machine, or essentially any digital processing circuit. 
     The present invention adds greater flexibility to wavelength stabilization systems. For example, long integration times, which are impractical via traditional stabilization means because of unrealizable component values and physical size restrictions, level shifting or stabilization on either/or both positive and negative slopes, and accommodation of manufacturing variations in the optical filter, are all possible utilizing the present invention. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of a two-path wavelength stabilization system in accordance with the prior art; 
     FIG. 2 is a graph depicting signal amplitude vs. wavelength of the signals at the photo-detectors, P 1  and P 2 , in the circuit of FIG. 1; 
     FIG. 3 is a block diagram of a two-path wavelength stabilization system in accordance with the present invention; 
     FIG. 4 is a circuit diagram of an exemplary pre-amplifier and current-to-voltage converter for use in the circuit of FIG. 3; 
     FIG. 5 is a graph of the voltage level in the optical filtered path prior to analog to digital conversion in accordance with the present invention; 
     FIG. 6 is a graph of the voltage level in the power reference path prior to analog to digital conversion in accordance with the present invention; 
     FIG. 7 is a graph depicting optical filter slope vs. signal-to-noise ratio of the overall circuit of FIG. 3; and 
     FIG. 8 is a graph depicting optical filter slope vs. total drift of the overall circuit of FIG. 3, assuming the required optical stability is 5 ppm. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring more specifically to the drawings, in FIG. 3, a two path wavelength stabilization system  10  in accordance with the present invention is depicted. FIG. 3 illustrates the components of the present invention which include: a laser source  12 , an optical fiber  14 , photo couplers  16  and  18 , an optical filter  20 , photo detectors  22  and  24 , current-to-voltage converters  28  and  32 , amplifiers  34  and  36 , analog-to-digital converters  38  and  40 , microcontroller  50 , and digital-to-analog converter  49 . The components connected together, as depicted in FIG. 3, provide increased stabilization for a laser to be used in dense wavelength division multiplexing (DWDM) systems or similar systems where very stable laser frequencies are required. The output  13  from either the front face or the back face of the laser  12  produces a signal having a power P L  which is placed on the fiber optic cable  14 . The initial signal on the fiber optic cable is then used to create two independent paths, the optical filtered path  101  and the power reference path  102 . The optical filtered path  101  and the power reference path  102  are created by placing photo-couplers  16  and  18 , respectively, on the fiber optic cable  14  carrying the signal from the laser  12 . The optical filtered path  101  is passed through an optical filter  20  to obtain a signal which is, at least partially, a function of wavelength or frequency, and becomes a reference element for frequency stabilization. The power reference path  102  does not pass through the optical filter  20  and provides a signal which is a function solely of the laser&#39;s optical power P L , and is eventually used for normalizing the optical filtered path  101 . 
     The optical filtered path  101  and the power reference path  102  are then processed to provide suitable signals for the microcontroller  50 . Separately, each path passes through a photo-detector  22  or  24 , current-to-voltage converter  28  or  32 , amplifier  34  or  36 , and analog-to-digital converter  38  or  40 . 
     The photo-detectors  22  and  24 , transform the optical signal from each path into an electrical signal which is required as an input for electrical circuits. The photo-detectors  22  and  24  produce an electrical current which is a function of the optical signal strength. The conversion or responsivity of the photo-detectors  22  and  24  is, for example, roughly 1 ampere of electrical current for each watt of optical power. Assuming the optical power into the photo-detectors  22  and  24  is 1 μW, the initial electric current out of the photo-detectors  22  and  24  is in the neighborhood of 1 μA. 
     The current-to-voltage converters  28  and  32 , convert the output of the photo-detectors  22  and  24  from a signal represented by a current to one represented by a voltage and provide some pre-amplification. The conversion of the signal from current to voltage and the signal&#39;s pre-amplification is combined as depicted in FIG.  4 . In FIG. 4, a current signal, i in , is amplified and transformed into a voltage signal, v out . The amplification and current to voltage transformation is accomplished by a transimpedance amplifier  60  created by using an inverting amplifier  62  with resistor  64  in a feedback loop. If a 100 kΩ resistor is used for feedback resistor  64 , the output voltage v out  will be approximately the input current 10 −6  A times the feedback resistance 100 kΩ, or about 0.1 V. 
     The amplifiers  34  and  36 , provide additional gain to the signal to condition the signal for the analog-to-digital converters  38  and  40 . If the amplifiers  34  and  36  provide a gain of  10 , the signals will be approximately 1 V as they enter the analog-to-digital converters. FIGS. 5 and 6 depict the signals on the optical filtered path and the power reference path, respectively, prior to entering the analog-to-digital converters  38  and  40 . As can be seen in the figures, at this point, the signals are DC voltages carrying some noise with the voltage of the optically filtered path  101  slightly lower than the voltage of the unfiltered path  102 . This example assumes that the components in the two paths are matched (which, of course, is not a requirement). 
     The analog-to-digital converters  38  and  40  convert the input analog signals to digital signals. The resultant digital signals  42  and  44  are in a form which can be processed and manipulated by the microcontroller  50 . 
     The digital signals  42  and  44  are then processed by the microcontroller  50 , which produces the output signal  48 . The microcontroller  50  numerically divides the optical filtered path digital signal  42  by the power reference path digital signal  44  to normalize the optical filtered path digital signal  42 , whereby a digital value which is a function solely of the lasers wavelength is derived. The microcontroller can then use the digital value representing the laser&#39;s wavelength to generate signal  48 . Signal  48  is then converted from digital to analog by digital-to-analog converter  49  to produce a laser adjustment signal  51  which can be used for adjusting the wavelength of the laser  12 . The processing by microcontroller  50  can be accomplished by any of the following types of apparatus: microprocessor, processor, digital signal processor, computer, state machine, or essentially any digital processing circuit. 
     The signal  51  can be in any form desired for controlling the frequency of the laser  12  and can be modified by changes in the microcontroller&#39;s software code via remote input  46 . The signal  51  generated through the digital-to-analog converter  49  by the microcontroller  50  may be a current for adjusting the temperature of a thermoelectric cooler on which the laser  12  is mounted, or the microcontroller  50  may generate other appropriate signals either with or without digital to analog conversion depending on the method used to modify the frequency of the laser  12 . 
     The present invention can use this two path digital wavelength stabilization method to achieve a level of wavelength stabilization that is impractical or impossible via analog means. For example, improved stabilization can be achieved by identifying small variations in the laser&#39;s wavelength. Small wavelength variations can be masked by noise in the laser  12  and stabilization circuitry  10 . In order to increase the signal to noise ratio, the normalized signal can be integrated over a period of time, with improved signal to noise ratios resulting from longer integration periods. Traditional analog systems are constrained by an RC (resistance and capacitance) time constant. In order to obtain long integration times, such as a month, a capacitor the size of a trash can would be required. By using microcontroller  50 , the signals can be sampled over a period of minutes, days, months, or even years, depending on the amount of time required to obtain a desirable signal to noise ratio. The microcontroller can accomplish long integration times by storing signal values in memory or keeping a running total of averages digitally. 
     Additionally, the digital approach to wavelength stabilization allows for flexibility in choosing system components. Different types of filters with varying characteristics can be used for optical filter  20  by modifying software in the microcontroller  50 , without changing other system components. This allows for using inexpensive filters or incorporating new filter designs into stabilization circuit  10 . Also, photo-detectors  22  and  24 , current-to-voltage converters  28  and  32 , and amplifiers  34  and  35  can be chosen based on availability or cost with variations in their respective signal levels accommodated by software in the microcontroller  50 . For example, if the optical filtered path digital signal  42  was twice as big as the power reference path digital signal  44 , due to mismatched components, the microcontroller  50  could divide the optical filtered path  42  by two or multiply the power reference path  44  by two. Attempting system modifications such as this, although readily achievable with a microcontroller, would require almost completely redesigning a circuit to accomplish in an analog system. 
     Further, this method of wavelength stabilization allows for the use of components with high levels of manufacturing variations, permitting the use of less expensive components. Variations in system components can be accommodated by changing software code in the microcontroller  50 , either at the factory when the laser&#39;s frequency is originally set, or via remote input  46  at a later date. The microcontroller  50  software can numerically account for amplifier component variations resulting in digital signal levels that are too high or too low, filters with varying wavelength characteristics, and other types of system variations. Attempting similar flexibility in an analog system would require exhaustive design considerations. 
     The wavelength stabilization system  10  according to the present invention offers vast improvements over traditional stabilization systems. As stated above, long integration times, which were previously impractical because of unrealizable component values, flexibility in choosing system components, and accommodation of manufacturing variations in the optical filter  20  and other components in the circuit  10 , are all easily achievable utilizing the digital stabilization system  10 . The flexibility gained by using the new stabilization system  10  is due to the ability to program the microcontroller  50  to perform many different functions on the digital inputs  42  and  44  with software using mathematical equations, versus attempting to use analog circuit components to accomplish the same type of functions in an analog system. In addition, the remote input  46  can be used to modify software code in the microcontroller  50 . For example, various control algorithms or normalization methods can be used or changed at will via code changes in the microcontroller  50  via remote input  46 . 
     Support for Digital Stabilization and Optical Filter Selection 
     The invention relates to a two path digital optical wavelength stabilization method which uses a microcontroller. The required optical filter selectivity which depends on the signal to noise ratio and unwanted amplitude drift is considered. This digital method where the wavelength set points are set numerically has many advantages, including: 
     manufacturing variations in the optical filter are easily accommodated; 
     remote accessibility and field reprogrammability; 
     highly flexible functional approach; 
     accommodation of various frequency grids via software; 
     quick response to customer changes via software; 
     easy interface with other digital components; and 
     performance not limited by practical analog component values, e.g. digital integration. 
     In the following sections, the required optical frequency stability is given as Δf s . For any optical channel i, the overall noise is assumed to have a Gaussian distribution with an equivalent standard deviation σ f  (rms noise) and a mean value, Δf=f−f chi . If σ f &lt;&lt;Δf s , the entire Δf s  can be assigned to aging, defined as Δf. Otherwise, Δf s , must be divided between noise and aging. 
     I. Calculation Of Signal To Noise Ratio 
     i. Noise Current from Noise Voltage 
     Before the overall signal to noise ratio can be calculated, several intermediate terms are calculated. The series input noise current as a function of the shunt noise voltage of the pre-amplifier  60  is calculated here in order to place all values in the form of an equivalent noise current. The input noise voltage is usually found in the product data sheet for the particular pre-amplifier chosen. An exemplary pre-amplifier  60  circuit is shown in FIG.  4 . 
     The rms input noise current squared is given by                i   in   2     =       ∫   0   ∞            v   in   2                 Y   in          2             f                 (   1   )                                
     where v in  is the input noise voltage and Y in  is the admittance at the input node. At the input node                  i   in     +         v   o     -     v   in         R   F       -     j                 ω                   CV   in       -       v   in       R   in         =   0           (   2   )                                
     And using 
     
       
         v o =−A(f)v in ≅−Av in   (3) 
       
     
     where                A        (   f   )       =         A                          -   j                     (       ω                 t     -   χ     )             i   +       j                 f       f   ref           ≃   A             (   4   )                                
     gives                i   in     =             A   +   1       R   f            v   in       -     j                 ω                   cv   in       -       v   in       R   in         =   0             (   5   )                                
     Therefore                  Y   in     =         A   +   1       R   F       +     j                 ω                 C     +     1     R   in                
        and           (   6   )                        Y   in          2     =         (       A     R   F       +     1     R   F       +     1     R   in         )     2     +       (                ω                   C   in       )     2               (   7   )                                
     This gives                i   in   2     =       ∫   0   ∞            v   in   2          {         (       A     R   F       +     1     R   F       +     1     R   in         )     2     +       (                ω                 C     )     2       }             f                 (   8   )                                
     Since the noise bandwidth (hereinafter BW) is limited, we can integrate over zero to BW rather than 0 to ∞. Also, a graph Of v in   2  is given in a typical pre-amplifier data sheet. One potential pre-amplifier that can be used in accordance with the present invention is the LMC 660 manufactured by the National Semiconductor Corp. of Santa Clara, Calif., USA. For the frequency range of interest here, the noise voltage curve shown in the data sheets for the LMC 660 is found to be approximated by 
     
       
         v in (f)≅V A /f 0.35   (9) 
       
     
     where the noise voltage at 1 Hz is V A =200 nV/{square root over (Hz)}, f is dimensionless, i.e. f/f 0 , where f 0 =1 Hz, and the preamplifier gain is A≅10 4  for R L =2 kΩ. 
     This gives                i   in   2     ≃       V   2          {           (       A     R   F       +     1     R   F       +     1     R   in         )     2            BW   0.3     0.3       +         (     2        ∏                C   in         )     2            BW   2.3     2.3         }               (   10   )                                
     Only the last term, the capacitance term, is usually shown in a typical receiver noise analysis, but for the condition of long integration times or low noise bandwidth, the first term, the A/R F  term, dominates. 
     ii. Quantization Noise of Analog-to-Digital Converter 
     The analog-to-digital (A/D) converter quantization noise is addressed here following the analysis of J. G. Proakis and D. G. Manolakis, Digital Signal Processing pg 412, Macmillan Publishing Company ISBN 0-02-396815-X, incorporated herein by reference. A number of assumptions regarding the nature of the quantization noise are made, i.e. uncorrelated, uniformly distributed, stationary white noise, etc. The signal to quantization noise ratio is given as                S   N     =       10                 log                   Psig   Pnoise       =       6.02      b     +   16.81   -     20                 log                   R     σ   sig                       (   dB   )                   (   11   )                                
     where Psig is the signal power, Pnoise is the noise power, b is the number of bits, R is the range setting, and σ sig  is the rms signal amplitude. The overload noise or clipping is set to be negligible by way of the chosen range value and is ignored. An analog-to-digital converter is selected with an adequate number of bits sufficient to make the quantization noise trivial. This is verified in the spreadsheet described in the following section. 
     iii. Overall Signal to Noise Ratio 
     The overall signal to noise ratio seen by the microcontroller is calculated in this section. The remaining terms beyond those discussed above are well known. Table 1 describes the various noise terms referenced to the equivalent noise current at the detector output. 
     
       
         
               
             
               
               
             
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Noise Terms 
               
             
          
           
               
                 Term 
                 Units 
               
               
                   
               
             
          
           
               
                 BW 
                 Hz 
                 Noise Band Width 
               
               
                 R f   
                 Ohms 
                 Feedback Resistance 
               
               
                 R IN   
                 Ohms 
                 Resistance at Input Node 
               
               
                 C IN   
                 F 
                 Capacitance at Input Node 
               
               
                 b 
                   
                 Number of Effective Bits in A/D Converter 
               
               
                 R 
                 V 
                 Range Setting of A/D Converter 
               
               
                 R/σ 
                   
                 Range to Noise Ratio at A/D Converter Input 
               
               
                 IC Noise 
                 pA/✓Hz 
                 LMC 660 Data Sheet ˜2E-4 
               
               
                 Current 
               
               
                 Noise Voltage 
                 V/✓Hz 
                 LMC 660 Data Sheet, Obtain ˜2E-7/f{circumflex over ( )}0.35 
               
               
                 Noise Current 
                 A 2   
                 (2E-7){(A/Rf + l/Rf + l/Ri) 2 *BW{circumflex over ( )}0.3/0.3 + 
               
               
                 From Noise 
                   
                 (2*II*C) 2 *BW{circumflex over ( )}2.3/2.3} 
               
               
                 Voltage 
               
               
                 Thermal Noise 
                 A2 
                 4*k*T*BW/Rf 
               
               
                 Current 
               
               
                 Shot Noise 
                 A2 
                 4*e*l*BW 
               
               
                 Current 
               
               
                 Laser RIN 
                 A2 
                 BW*l{circumflex over ( )}2*RIN 
               
               
                 Quantization 
                 dB 
                 6.02*b + 16.81 − 20*LOG(R/σ) 
               
               
                 S/N 
               
               
                   
               
             
          
         
       
     
     Table 2 is a spreadsheet for calculating the overall signal to noise ratio seen by the microcontroller  50 . 
     
       
         
               
             
               
               
             
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Noise Analysis 
               
             
          
           
               
                 NOISE ANALYSIS 
                 Units 
               
               
                   
               
             
          
           
               
                 Preamp Shunt Noise Voltage Calculated from 
                 V/✓Hz 
                 2.000E−07 
               
               
                 Data Sheet of Assumed Device 
               
               
                 Preamp Feedback Rx Value 
                 Ohms 
                 1.000E+05 
               
               
                 Effective Post Amp Gain Front End Output to 
                 Linear 
                 10 
               
               
                 A/D Input 
               
               
                 Effective Electronic BW 
                 Hz 
                 1.000E+02 
               
               
                 Numerical Sampling Frequency = 
                 Sec 
                 2.000E+02 
               
               
                 2*electronic BW 
               
               
                 Numerical Averaging Time 
                 Sec 
                 1.2000E+02 
               
               
                 Effective Numerical Noise BW (BW ˜1/T) 
                 Hz 
                 8.333E−03 
               
               
                 Effective Overall Noise BW, 
                 Hz 
                 8.333E−03 
               
               
                 Electronic &amp; Numerical 
               
               
                 Temp 
                 ° C. 
                 25 
               
               
                 Temp 
                 ° K. 
                 2.980E+02 
               
               
                 Total Capacitance at Input Node 
                 F 
                 1.000E−11 
               
               
                 Assumed Optical Path Conditions 
               
               
                 Assumed CW Laser Power at Optical Feedback 
                 dBm 
                 −16.0 
               
               
                 Circuit 
               
               
                 Assumed Optical Path (Loss), 
                 dB 
                 −13.0 
               
               
                 Fiber/Coupler/Filter 
               
               
                 Received Average Optical Power 
                 dBm 
                 −29.0 
               
               
                 Equivalent Signal Current 
                 A 
                 1.257E−06 
               
               
                 Assuming ETTA = 0.8 
               
               
                 Equivalent Signal Current Squared 
                 A 2   
                 1.581E−12 
               
               
                 Calculate Total Elect Noise at Elect BW 
               
               
                 Assumed Laser RIN Value 
                 /Hz 
                 1.000E−14 
               
               
                 Post Amp Noise Figure Etc., Ignore 
                 dB 
                 0.000E+00 
               
               
                 Post Amp Noise Figure Etc., Ignore 
                 Linear 
                 1.000E+00 
               
               
                 Equivalent Preamp IC Noise Current Sq. at Input 
                 A 2   
                 4.000E−30 
               
               
                 Equivalent Preamp Noise Current Sq. 
                 A 2   
                 5.309E−15 
               
               
                 from Noise Voltage 
               
               
                 TH. RMS Noise Current Sq. at Detector 
                 A 2   
                 1.645E−23 
               
               
                 Shot Noise Current Sq. in Received 
                 A 2   
                 4.028E−23 
               
               
                 Optical Signal 
               
               
                 Laser Mean Sq. RIN Noise Current 
                 A 2   
                 1.581E−24 
               
               
                 Total Electronic Noise Current Sq. 
                 A 2   
                 5.309E−15 
               
               
                 S/N Power Ratio at Electrical BW, 
                 dB 
                 25 
               
               
                 Signal Path Only 
               
               
                 Calculate A/D Overload 
               
               
                 (Verifies Proper A/D Range) 
               
               
                 Set Value for A/D Range 
                 V 
                 1.500E+00 
               
               
                 Electronic RMS Noise Voltage at A/D Input 
                 V 
                 0.0729 
               
               
                 Electronic Signal Voltage/Noise Voltage 
                   
                 17.2558 
               
               
                 at A/D Input 
               
               
                 Ratio of A/D Range to Noise Sigma 
                   
                 20.5863 
               
               
                 (Ignore Aging and Drift) 
               
               
                 A/D Overload (# overload samples per # samples) 
                   
                 3.65E−94 
               
               
                 Total Noise Current at PIN at 
               
               
                 Total BW, Excluding A/D Quant Noise 
               
               
                 Assumed Laser RIN Value 
                 /Hz 
                 1.000E−14 
               
               
                 Ignore other Noise, Post Amp Noise Figure Etc. 
                 dB 
                 0.000E+00 
               
               
                 Ignore other Noise, Post Amp Noise Figure Etc. 
                 Linear 
                 1.000E+00 
               
               
                 Equivalent Preamp IC Noise Current Sq. at Input 
                 A 2   
                 3.333E−34 
               
               
                 Equivalent Preamp Noise Current Sq. from 
                 A 2   
                 3.172E−16 
               
               
                 Noise Voltage 
               
               
                 TH. RMS Noise Current Sq. at Detector 
                 A 2   
                 1.371E−27 
               
               
                 Shot Noise Current Sq. in Received 
                 A 2   
                 3.357E−27 
               
               
                 Optical Signal 
               
               
                 Laser Mean Sq. RIN Noise Current 
                 A 2   
                 1.317E−28 
               
               
                 Total Noise Current Sq. 
                 A 2   
                 3.172E−16 
               
               
                 S/N Power Ratio at Total BW 
                 Linear 
                 4.985E+03 
               
               
                 S/N Power Ratio at Total BW 
                 dB 
                 37 
               
               
                 A/D Effects Included Below 
               
               
                 Chosen Number of Bits of A/D Converter 
                   
                 10 
               
               
                 S/N of A/D Converter (Power Ratio) 
                 dB 
                 75 
               
               
                 S/N of A/D Converter (Power Ratio) 
                 Linear 
                 118534 
               
               
                 S/N Current Ratio Sq. after Digitization, 
                 A 2   
                 4783 
               
               
                 Including A/D Converter 
               
               
                 S/N Ratio After Digitization, 
                 dB 
                 37 
               
               
                 Including A/D Converter 
               
               
                   
               
             
          
         
       
     
     In practice only one or a few noise terms above dominate, but the various terms are included for completeness. They also serve as place holders to allow calculations over a wide range of future conditions. At present, the noise voltage dominates the other noise terms by a wide margin and is the place to focus attention should a reduction in noise be required beyond what can be achieved through averaging. 
     In Table 2, the received optical power available to the stabilization circuit at photodetectors  22  or  24  is (initially) assumed to be −29 dBm. Different time constants or noise bandwidths exist for the analog and digital signals. The time constant in the analog portion of the circuit is determined by component selection, and is limited by component availability. The digital time constant is bound by the available memory and the software code in the microcontroller  50 . The analog and digital time constants are combined on a sum of squares basis to get an overall time constant, although in practice the digital bandwidth will be set to dominate the analog bandwidth by a wide margin. 
     To verify that a proper range setting of the analog signal was chosen to avoid overload or clipping in the analog-to-digital converter, the total analog noise current of the analog signal at the electronic noise bandwidth is first calculated. The total noise except for the quantization noise can then be calculated at the overall noise bandwidth. Next, the quantization noise of the analog-to-digital converter  38  or  40  can be included to obtain the total noise, both analog and digital. The overall signal to noise ratio is then calculated using the signal current determined from the optical power. 
     II. Filter Slope Versus Noise and Aging 
     i. Introduction 
     Given a certain stability requirement and the optical filter selectivity, a signal to noise ratio can be determined to meet the stability specification. At the optical detector  22 , the electrical signal current is given in the usual manner for the optical filtered path  101  by 
     
       
         i 1 =P L C 1 C(f)R  (12) 
       
     
     and at the analog-to-digital converter  38 , the input signal voltage is given by 
     
       
         V A/D     1   =P L C 1 C(f)RR T G  (13) 
       
     
     where P L  is the optical output power  13  of the laser  12  into the control system, C 1  is the optical path loss which includes the optical coupler  16 , C(f) is the optical filter  20  insertion loss, R is the detector  22  responsivity, R T  is the feedback resistance  26  across the preamplifier  60 , and G is the postamplifier  34  gain which includes all electrical path losses. For convenience, either C(λ) or C(f) can be used. Assume that the optical filter  20  response is given by                C        (   f   )       ≅              C          f          Δ                 f     +     C   chi               (   14   )                                
     where C(f) is the optical filter transmission response, dC/df is the filter  20  slope objective, Δf is the frequency difference from the desired value at channel i, and C chi  is the filter  20  insertion loss for channel i. 
     The signal current or voltage is normalized with respect to optical power such that only C(f) is obtained, and not C(f, P L ). If the two paths are considered identical except for the optical filter, the signal current after normalization is given as                  i   1       i   2       =     {              C          f          Δ                 f     +     C   chi       }             (   15   )                                
     For simplicity in the following analysis, path  102 , the normalization path, will not be included and the noise is understood to be the noise after normalization. 
     ii. Required Signal to Noise Ratio 
     In this section, the maximum overall noise is determined assuming that the mean value of the optical frequency is constant (no aging) and the entire frequency stability specification can be allocated to the noise. As described earlier, the noise is assumed to be Gaussian with an equivalent optical standard deviation σ f  and a mean value Δf. Thus, Δf is assumed to be zero (no aging) and the entire optical frequency specification is allocated to the standard deviation. Therefore,                  Δ                   f   s         σ   f       ≥   ɛ           (   16   )                                
     where Δf, is the optical frequency stability specification and ε is the specification that defines the number of standard deviations to which the frequency specification, Δf s , applies, or equivalently the fraction of time that Δf s  can be exceeded. For example, if ε=1, Δf s , will be exceeded 32% of the time. Typically, ε is expected to range from 1 to 3. 
     This gives 
     
       
         σ n0 =σ f |dC/df|  (17) 
       
     
     where σ n0  is the dimensionless allowable electrical standard deviation of the total noise distribution which in practice is dominated by the electrical noise (see Table 2). In (17), the allowable standard deviation as a function of frequency, σ f , was translated into a corresponding normalized amplitude distribution via the optical filter slope. It is assumed that either |dC/df| or |dC/dλ| provides a stable operating point. Combining (16) and (17) gives 
     
       
         σ n0 ≦(Δf s /ε)|dC/df|  (18) 
       
     
     Translating σ n0  from dimensionless units to equivalent units of current, referenced to the photo-detector output gives the rms electrical noise 
     
       
         σ n =σ n0 P L C 1 C chi R  (19) 
       
     
     The signal to noise power ratio at channel  1  is given by 
     
       
         S 1 /N 1 =i 1   2 /σ n   2 =1/σ n0   2   (20) 
       
     
     Combining (18) and (20) gives 
     
       
         |dC/df|≧ε/{f(Δf s /f)(S 1 /N 1 ) ½ }.  (21) 
       
     
     Or, in terms of the normalized optical wavelength 
     
       
         (1/C chi )|dC/dλ|≧ε/{C chi λ(Δf s /f) (S 1 /N 1 ) ½ }).  (22) 
       
     
     Equation (22) gives the required normalized optical filter slope in terms of the frequency stability specification, (Δf s /f), and the equivalent signal to noise ratio at the optical detector output under the assumption of zero drift. The signal to noise ratio may be the overall value which includes electronic noise. A plot of equation (22) is shown in FIG. 7 where ε is assumed to be 1. 
     iii. Aging 
     Aging, also called drift or amplitude change, is considered here. All aging is included as an equivalent optical filter change. The entire frequency stability specification is assigned to this effect and thus, noise is ignored. The optical filter transmission is given by                C        (   f   )       =                   C          f                                 Δ                 f            +     C   chi     -          Δ                 C                    (   23   )                                
     where ΔC is the total drift or amplitude aging effect from all causes at optical frequency f=f chi , i.e. 
     
       
         ΔC=C(f chi ) t     2   |−C(f chi ) t     1   |  (24) 
       
     
     If at time t=t 2 , the controller resets the control signal amplitude back to its original value then                {                   C          f                                 Δ                 f            +     C   chi     -          Δ                 C            }     =     {     C   chi     }             (   25   )                                
     And if Δf remains within the frequency stability specification, this gives                  1     C   chi                      C          λ              ≥       1     λ        (     Δ                     f   S     /   f       )                     Δ                 C            C   chi                 (   26   )                                
     Equation (26) is plotted in FIG. 8 where the required normalized optical filter selectivity is given in terms of the normalized total amplitude aging assuming the required frequency stability is 5 ppm and λ=1.55*10 −6  m. As stated earlier, noise was ignored and the entire frequency stability specification was assigned to aging which includes changes in the optical path, optical couplers, optical filters, optical detectors, and all electronics to the microcontroller. In practice the aging of components are unknown and will require measurement. 
     iv. RMS Method 
     Since the signal is digitized, various parameters associated with the signal can be calculated and although holding the DC amplitude constant has been implied, other control methods could be used such as calculating the RMS value and holding that constant. 
     Conclusion 
     Having thus described a few particular embodiments of the invention, various alterations, modifications, and improvements will readily occur to those skilled in the art. Such alterations, modifications and improvements as are made obvious by this disclosure are intended to be part of this description though not expressly stated herein, and are intended to be within the spirit and scope of the invention. Accordingly, the foregoing description is by way of example only, and not limiting. The invention is limited only as defined in the following claims and equivalents thereto.