Patent Publication Number: US-2023146826-A1

Title: Digital tone-based apparatus and method for measuring the frequency response of coherent optical transmitters

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional of U.S. Pat. Application No. 17/375,575, filed on Jul. 14, 2021, which claims the benefit under 35 U.S.C. § 119(e) to U.S. Provisional Pat. Application No. 63/051,815, filed Jul. 14, 2020, both of which are incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     Optical communication systems typically include a first node that supplies optical signals carrying user information or data to a second node that receives such optical signals via an optical communication path that connects the first node to the second node. In certain optical communication systems, the first node is a so-called hub node that communicates with a plurality of second nodes, also referred to as leaf nodes. The optical communication paths that connect the hub with multiple leaf nodes may include one or more segments of optical fiber connected to one another by various optical components or sub-systems, such as optical amplifiers, optical splitters and combiners, optical multiplexers and demultiplexers, and optical switches, for example, wavelength selective switches (WSS). The optical communication path and its associated components may be referred to as a line system. 
     In each node, the various electrical and optical components or sub-systems may introduce impairments in the transmitted optical signals, such as a linear time-invariant impairments, nonlinear impairments, etc. Generally, linear time-invariant impairments are the dominant impairment type. These impairments cause a magnitude response or a phase response, or both, in the transmitted optical signal, thereby degrading the optical signal and limiting the transmitter from using higher modulation schemes when modulating the optical signal, which may result in a lower quality transmission. 
     Thus, a need exists for a system and method to measure and mitigate the effects of impairments introduced to the optical signals. It is to such a system and method that the present disclosure is directed. 
     SUMMARY 
     The problem of mitigating the effects of impairments introduced to the optical signals is solved by introducing an AM tone and data to an optical modulator generating a modulated optical signal, measuring an amplitude response of the AM tone within the modulated optical signal, calculating a frequency response based on the amplitude response, and calibrating the optical modulator with the frequency response. 
     In some embodiments, the problem of mitigating the effects of impairments introduced to the optical signals is solved by a transmitter, comprising a laser operable to supply an optical signal; an AM signal generator operable to supply first electrical signals based on an AM tone having a first known carrier frequency component at a first period of time and a second known carrier frequency component at a second period of time, wherein the first known carrier frequency component is different from the second known carrier frequency component; digital-to-analog conversion circuitry operable to output second electrical signals based on the first electrical signals; modulator driver circuitry operable to output third electrical signals based on the second electrical signals; an optical modulator operable to modulate the optical signal based on the third electrical signals to supply a modulated optical signal, the modulated optical signal based on the AM tone; a photodetector operable to measure a power of the modulated optical signal; and a demodulation circuitry coupled to the photodiode and operable to determine an amplitude response using a first power of the modulated optical signal and the first known carrier frequency component at the first period of time and a second power of the modulated optical signal and the second known carrier frequency component at the second period of time, to calculate a frequency response based on the amplitude response, and to calibrate the optical modulator with the frequency response. 
     Other implementations are directed to systems, hub transceivers, devices, and non-transitory, computer-readable media having instructions stored thereon, that when executed by one or more processors, cause the one or more processors to perform operations described herein. 
     The details of one or more implementations of the subject matter described in this specification are set forth in the accompanying drawings and the description below. Other aspects, features and advantages of the subject matter will become apparent from the description, the drawings, and the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate one or more implementations described herein and, together with the description, explain these implementations. The drawings are not intended to be drawn to scale, and certain features and certain views of the figures may be shown exaggerated, to scale or in schematic in the interest of clarity and conciseness. Not every component may be labeled in every drawing. Like reference numerals in the figures may represent and refer to the same or similar element or function. In the drawings: 
         FIG.  1    is a block diagram of an exemplary embodiment of an optical communication system constructed in accordance with the present disclosure. 
         FIG.  2    is a block diagram of an exemplary embodiment of a primary node and a secondary node of  FIG.  1    constructed in accordance with the present disclosure. 
         FIG.  3 A  is a diagram of an exemplary embodiment of an optical signal having a single subcarrier in accordance with the present disclosure. 
         FIG.  3 B  is a diagram of an exemplary embodiment of an optical signal having multiple subcarriers in accordance with the present disclosure. 
         FIG.  4    is a block diagram of an exemplary embodiment a transmitter shown in  FIG.  2    and constructed in accordance with the present disclosure. 
         FIG.  5    is a diagram of an exemplary embodiment of an AM signal generator constructed in accordance with the present disclosure. 
         FIG.  6    is a block diagram of an exemplary embodiment of a DSP of the transmitter shown in  FIG.  2    and constructed in accordance with the present disclosure. 
         FIG.  7    is a diagram of an exemplary embodiment of the shaping filter and subcarrier multiplexing circuitry of the transmitter constructed in accordance with the present disclosure. 
         FIG.  8    is a diagram of an exemplary embodiment of a controls and monitoring circuit of  FIG.  1    and constructed in accordance with the present disclosure. 
         FIG.  9    is a diagram of an exemplary embodiment of a shared laser constructed in accordance with the present disclosure. 
         FIG.  10    is a diagram of an alternative embodiment of an AM signal generator constructed in accordance with the present disclosure. 
         FIG.  11 A  is an exemplary embodiment of a filter flow diagram constructed in accordance with the present disclosure. 
         FIG.  11 B  is an exemplary embodiment of a filter flow diagram constructed in accordance with the present disclosure. 
         FIG.  12    is a flow diagram of an exemplary embodiment of a demodulation circuitry constructed in accordance with the present disclosure. 
         FIG.  13    is a flow diagram of an exemplary embodiment of a demodulation circuitry constructed in accordance with the present disclosure. 
         FIG.  14    is a process flow diagram of an exemplary embodiment of a frequency response determination process in accordance with the present disclosure. 
         FIG.  15    is a graph of an exemplary embodiment of the frequency response of a transmitter over a band of interest; also showing the AM-modulated tone whose carrier frequency is being swept across the band of interest. 
         FIGS.  16 A-D  are graphs of exemplary embodiments of measurements of the amplitude response measured for each of paths TEI, TEQ, TMI, and TMQ. 
         FIGS.  17 A-D  are graphs of exemplary embodiments of a frequency response calibration based on the amplitude responses of  FIGS.  16 A-D . 
         FIGS.  18 A-D  are graphs of an exemplary embodiment of the phase response (in radians) for each amplitude response of  FIGS.  16 A-D . 
         FIG.  19 A  is a graph of an exemplary embodiment of an amplitude response with and without an echo causing a phase response. 
         FIG.  19 B  is a graph of an exemplary embodiment of time-domain waveforms of  FIG.  19 A . 
         FIGS.  20 A-D  are graphs of exemplary embodiments of each path I, Q of each component X, Y of a calibrated vs uncalibrated optical signal of one channel. 
         FIG.  21 A  is a graph of an exemplary embodiment of an optical signal pre-calibration of frequency response. 
         FIG.  21 B  is a graph of an exemplary embodiment of a calibrated optical signal, post-calibration of frequency response of the optical signal of  FIG.  21 A . 
     
    
    
     Like reference numbers and designations in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
     The following detailed description refers to the accompanying drawings. The same reference numbers in different drawings may identify the same or similar elements. 
     Before explaining at least one embodiment of the disclosure in detail, it is to be understood that the disclosure is not limited in its application to the details of construction, experiments, exemplary data, and/or the arrangement of the components set forth in the following description or illustrated in the drawings unless otherwise noted. 
     The disclosure is capable of other embodiments or of being practiced or carried out in various ways. Also, it is to be understood that the phraseology and terminology employed herein is for purposes of description and should not be regarded as limiting. 
     As used in the description herein, the terms “comprises,” “comprising,” “includes,” “including,” “has,” “having,” or any other variations thereof, are intended to cover a non-exclusive inclusion. For example, unless otherwise noted, a process, method, article, or apparatus that comprises a list of elements is not necessarily limited to only those elements but may also include other elements not expressly listed or inherent to such process, method, article, or apparatus. 
     Further, unless expressly stated to the contrary, “or” refers to an inclusive and not to an exclusive “or”. For example, a condition A or B is satisfied by one of the following: A is true (or present) and B is false (or not present), A is false (or not present) and B is true (or present), and both A and B are true (or present). 
     In addition, use of the “a” or “an” are employed to describe elements and components of the embodiments herein. This is done merely for convenience and to give a general sense of the inventive concept. This description should be read to include one or more, and the singular also includes the plural unless it is obvious that it is meant otherwise. Further, use of the term “plurality” is meant to convey “more than one” unless expressly stated to the contrary. 
     As used herein, qualifiers like “substantially,” “about,” “approximately,” and combinations and variations thereof, are intended to include not only the exact amount or value that they qualify, but also some slight deviations therefrom, which may be due to computing tolerances, computing error, manufacturing tolerances, measurement error, wear and tear, stresses exerted on various parts, and combinations thereof, for example. 
     As used herein, any reference to “one embodiment,” “an embodiment,” “some embodiments,” “one example,” “for example,” or “an example” means that a particular element, feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment and may be used in conjunction with other embodiments. The appearance of the phrase “in some embodiments” or “one example” in various places in the specification is not necessarily all referring to the same embodiment, for example. 
     The use of ordinal number terminology (i.e., “first”, “second”, “third”, “fourth”, etc.) is solely for the purpose of differentiating between two or more items and, unless explicitly stated otherwise, is not meant to imply any sequence or order of importance to one item over another. 
     The use of the term “at least one” or “one or more” will be understood to include one as well as any quantity more than one. In addition, the use of the phrase “at least one of X, Y, and Z” will be understood to include X alone, Y alone, and Z alone, as well as any combination of X, Y, and Z. 
     Where a range of numerical values is recited or established herein, the range includes the endpoints thereof and all the individual integers and fractions within the range, and also includes each of the narrower ranges therein formed by all the various possible combinations of those endpoints and internal integers and fractions to form subgroups of the larger group of values within the stated range to the same extent as if each of those narrower ranges was explicitly recited. Where a range of numerical values is stated herein as being greater than a stated value, the range is nevertheless finite and is bounded on its upper end by a value that is operable within the context of the invention as described herein. Where a range of numerical values is stated herein as being less than a stated value, the range is nevertheless bounded on its lower end by a non-zero value. It is not intended that the scope of the invention be limited to the specific values recited when defining a range. All ranges are inclusive and combinable. 
     When values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another embodiment. Reference to a particular numerical value includes at least that particular value, unless the context clearly dictates otherwise. The term “about” when used in reference to numerical ranges, cutoffs, or specific values is used to indicate that the recited values may vary by up to as much as 10% from the listed value. Thus, the term “about” is used to encompass variations of ± 10% or less, variations of ± 5% or less, variations of ± 1% or less, variations of ± 0.5% or less, or variations of ± 0.1% or less from the specified value. 
     Circuitry, as used herein, may be analog and/or digital components, or one or more suitably programmed processors (e.g., microprocessors) and associated hardware and software, or hardwired logic. Also, “components” may perform one or more functions. The term “component,” may include hardware, such as a processor (e.g., microprocessor), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a combination of hardware and software, and/or the like. The term “processor” as used herein means a single processor or multiple processors working independently or together to collectively perform a task. 
     Software may include one or more computer readable instructions that when executed by one or more components cause the component to perform a specified function. It should be understood that the algorithms described herein may be stored on one or more non-transitory computer readable medium. Exemplary non-transitory computer readable mediums may include random access memory, read only memory, flash memory, and/or the like. Such non-transitory computer readable mediums may be electrically based, optically based, magnetically based, and/or the like. Further, the messages described herein may be generated by the components and result in various physical transformations. 
     The generation of laser beams for use as optical data carrier signals is explained, for example, in U.S. Pat. No. 8,155,531, entitled “Tunable Photonic Integrated Circuits”, issued Apr. 10, 2012, and U.S. Pat. No. 8,639,118, entitled “Wavelength division multiplexed optical communication system having variable channel spacings and different modulation formats,” issued Jan. 28, 2014, which are hereby fully incorporated in their entirety herein by reference. 
     Referring now to the drawings, and in particular to  FIG.  1   , shown therein is a diagram of an exemplary embodiment of an optical communication system  10  constructed in accordance with the present disclosure. The optical communication system  10  generally includes a primary node  14 , such as a router, and one or more secondary node  18  shown as secondary nodes  18   a - 18   n . 
     In one embodiment, the primary node  14  includes a primary transceiver  22  (or transceiver module) that is operable to supply a downstream optical signal (DS), including optical subcarriers, to an optical fiber link  26 - 1  (e.g., part of a first or downstream optical communication path), and receives an upstream signal (US) from an optical fiber link  26 - 2  (e.g., part of a second or upstream optical communication path). In one embodiment, the primary transceiver or primary transceiver  22  may be referred to as a hub transceiver or hub transceiver module. The downstream optical signal DS is fed by the optical fiber link  26 - 1  to one or more optical line system component, such as an optical amplifier, an erbium-doped fiber amplifier, an add-drop module, an optical gateway, a ROADM, and/or the like. As discussed in greater detail below with reference to  FIG.  2   , the optical signals DS and US may each include one or more optical subcarrier, such as a Nyquist optical subcarrier. 
     In one embodiment, the secondary node  18  includes a secondary transceiver  34  that is operable to transmit optical signals to the primary node  14  and to receive optical signals from the primary node  14 . In one embodiment, the optical communication system  10  includes more than one primary node  14 , each of which communicates with one or more secondary node  18 . 
     In one embodiment, the primary transceiver  22  includes a transmitter, described below and shown in  FIG.  4   , that receives data and outputs an optical signal including one or more optical subcarrier. Each optical subcarrier is indicative of the transmitted data. In one embodiment, the primary node  14  includes more than one primary transceiver  22 . In this embodiment, the transmitter  70  of each primary transceiver  22  supplies a corresponding optical signal with an associated group of subcarriers. 
     In one embodiment, each secondary node  18  may have a structure similar to the primary node  14  and may operate in a manner similar to that described above with respect to the primary node  14 . 
     As further shown in  FIG.  1   , each secondary transceiver  34  may have a structure similar to and operate in manner similar to that described above with respect to the primary transceiver  22 . In one example, however, each of the secondary transceivers  34  may supply a modulated optical signal US′-1 to US′-n in an upstream direction. Each such optical signal may include one or more optical subcarriers. Collectively, a number the optical subcarriers output from the secondary transceivers  34  may be equal to, less than, or greater than the number of optical subcarriers output from the primary transceiver  22 . 
     The optical signals US′-1 to US′-n may be combined by a combiner in optical line system  50  and output towards the primary node  14  in combined form as the upstream optical signal US. The optical signal US may then be provided to the primary transceiver  22  via the optical fiber link  26 - 2 . 
     Referring now to  FIG.  2   , shown therein is a block diagram of an exemplary embodiment of the primary node  14  constructed in accordance with the present disclosure. The primary node  14  may include a transmitter  70  that supplies a downstream modulated optical signal including subcarriers, and a receiver that  74  that may receive upstream subcarriers carrying data originating from the secondary nodes  18 , such as from secondary transceivers 34a-n. The transmitter  70  and the receiver  74 , in one example, collectively constitute a primary node  14  or primary transceiver  22 . 
       FIG.  2    further shows a block diagram of an exemplary embodiment of one of the secondary node 18a-n, which may include a receiver  78  that receives one or more downstream transmitted subcarriers, and a transmitter  82  that transmits one or more subcarriers in the upstream direction. Collectively, receiver  78  and transmitter  82  constitute a secondary node  18  or edge node transceiver. 
     Details of the transmitters  70 ,  82  and the receivers  74 ,  78  of the primary node  14  and the secondary node  18 , respectively, are described in more detail below. It is understood that the transmitters  70 ,  82  have a similar structure and operate in a similar manner. Additionally, it is understood that the receivers  74 ,  78  have a similar structure and operate in a similar manner. 
     Referring now to  FIG.  3 A , shown therein is a diagram of an exemplary embodiment of a single-carrier optical signal  84  constructed in accordance with the present disclosure. The single carrier optical signal  84  includes a single carrier, or a single subcarrier, that may be output be the transmitter  70  of the primary transceiver  22 . The single carrier may be a Nyquist carrier and may have an optical spectral bandwidth that is at least equal to the Nyquist frequency, as determined by the baud rate of the single carrier. The single carrier may be centered around a frequency, fo. 
     Referring now to  FIG.  3 B , shown therein is a diagram of an exemplary embodiment of an optical signal in accordance with the present disclosure. The optical signal includes a plurality of subcarriers, SC1 to SC8 that may be output by the transmitter  70  of the primary transceiver  22 . Each of the subcarriers SC1 to SC8 may have a corresponding one of a plurality of frequencies f1 to f8. In addition, each of the subcarriers SC1 to SC8 may be a Nyquist subcarrier. In general, each subcarrier may have an optical spectral bandwidth that is at least equal to the Nyquist frequency, as determined by the baud rate of such subcarrier. 
     A Nyquist subcarrier is a group of optical signals, each carrying data, where (i) the spectrum of each such optical signal within the group is sufficiently non-overlapping such that the optical signals remain distinguishable from each other in the frequency domain, and (ii) such group of optical signals is generated by modulation of light from a single laser. 
     As discussed in greater detail below, the optical subcarriers SC1 to SC8 are generated by modulating light output from a laser. The frequency of such laser output light is f 0  and is typically a center frequency such that half the subcarrier subcarriers (e.g., f5 to f8) are above f 0 , e.g., have a greater frequency than f0, and half the subcarrier frequencies (e.g., f1 to f4) are below fo, e.g., have a lesser frequency than fo. 
     As further shown in  FIG.  3 B , the amplitudes of the subcarriers SC1 to SC8 may be collectively or independently modulated together to vary the amplitude of each subcarrier between a first amplitude A1 and a second lower amplitude A0. When the subcarriers SC1 to SC8 each have an amplitude A1, a ‘1’ bit, for example, is transmitted for line system management. On the other hand, when the subcarriers SC1 to SC8 each have an amplitude A0, a ‘0’ bit, for example, is transmitted for line system management. In this manner, subcarrier modulation may be employed to transmit control information from the primary node transceiver  106 , for example, to a line system component, as well as from the line system component to the primary transceiver  22 . Communication from a line system component to a secondary transceiver  34  may be carried out by amplitude modulating an upstream optical signal (including subcarriers) at a line system component in accordance with certain control information followed by transmitting a polarization modulated signal carrying such control information from the primary transceiver  22  to the secondary transceiver  34 . 
     Referring now to  FIG.  4   , shown therein is a diagram of an exemplary embodiment of the transmitter  70  constructed in accordance with the present disclosure. The transmitter  70  includes a digital signal processor (DSP  100 ) including circuit blocks  104 - 1 ,  104 - 2 , and  104 - 3 . In this example, the circuit block  104 - 1  receives data including one or more of eight data streams D1 to D8, each carrying user data or information. Such data is processed (e.g., as discussed in greater detail with respect to  FIG.  6   ), and the processed data is provided to the circuit block  104 - 3 . Second data, including, for example, control information, CDPS, destined for a downstream transceiver (e.g., the secondary transceivers  34 ) may be input to the circuit block  104 - 2 , which processes such control information and supplies the control information to the circuit block  104 - 3 . 
     As further shown in  FIG.  4   , the circuit block  104 - 3  supplies digital signals to DACs  108 - 1  to  108 - 4  of a D/A and Optics block  112 . Each of the DACs  108  is a digital-to-analog conversion circuit and is operable to output first electrical signals based on the digital signals supplied by the DSP  100 . The D/A and optics block  112  also includes modulator driver circuitry (MZMD  116 - 1  to  116 - 4 ). Each MZMD  116  is operable to output second electrical signals based on the first electrical signals received from a particular DAC  108 . 
     The D/A and optics block  112  further includes optical modulator circuitry (MZM  120 - 1  to  120 - 4 ). Each MZM  120  is operable to output a first modulated optical signal or a second modulated optical signal based on the second electrical signals. The first modulated optical signal includes multiple optical subcarriers (e.g., the optical subcarriers SC1 to SC8) carrying user data to be transmitted between nodes of the optical communication system  10 , and the second modulated optical signal is, for example, applying data to the orthogonal polarization, such as polarization multiplexing. 
     Each of the MZMs  120 - 1  to  120 - 4  of the D/A and optics block  112  may be a Mach-Zehnder Modulator (MZM) that modulates the phase and/or amplitude of the light output from a laser  124 . As further shown in  FIG.  4   , a light beam output from the laser  124  (also included in the optics block  112 ) is split such that a first portion of the light is supplied to a first MZM pairing including the MZMs  120 - 1  and  120 - 2  and a second portion of the light is supplied to a second MZM pairing including the MZMs  120 - 3  and  120 - 4 . The laser  124  can be a shared laser (as shown in  FIG.  9   ), or an unshared laser where the transmitter  70  and the receiver  74  include separate lasers  124 . 
     The first portion of the light is further split into third and fourth portions, such that the third portion is modulated by the MZM  120 - 1  to provide an in-phase (I) component of an X (or TE) polarization component of a modulated optical signal, and the fourth portion is modulated by the MZM  120 - 2  and fed to a phase shifter  128 - 1  to shift the phase of such light by 90 degrees in order to provide a quadrature (Q) component of the X polarization component of the modulated optical signal. 
     Similarly, the second portion of the light is further split into fifth and sixth portions, such that the fifth portion is modulated by the MZM  120 - 3  to provide an I component of a Y (or TM) polarization component of the modulated optical signal, and the sixth portion is modulated by the MZM  120 - 4  and fed to a phase shifter  128 - 2  to shift the phase of such light by 90 degrees to provide a Q component of the Y polarization component of the modulated optical signal. 
     The optical outputs of the MZMs  120 - 1  and  120 - 2  are combined to provide an X polarized optical signal including I and Q components and fed to a polarization beam combiner (PBC  132 ) provided in the optics block  112 . In addition, the outputs of the MZMs  120 - 3  and  120 - 4  are combined to provide an optical signal that is fed to a polarization rotator  136 , further provided in the optics block  112 , that rotates the polarization of such optical signal to provide a modulated optical signal having a Y (or TM) polarization. The Y polarized modulated optical signal is also provided to a PBC  132 , which combines the X and Y polarized modulated optical signals to provide a polarization multiplexed (“dual-pol”) modulated optical signal onto an optical fiber  140 . In some examples, the optical fiber  140  may be included as a segment of optical fiber in an example optical communication path of the optical communication system  10 . 
     In some implementations, the polarization multiplexed optical signal output from the D/A and optics block  112  includes the optical subcarriers SC1-SC8 (e.g., of  FIG.  3 B ), for example, such that each data subcarrier has X and Y polarization components and I and Q components. 
     In one embodiment, as shown in  FIG.  4   , each of the control signals CDXI, CDXQ, CDYI, and CDYQmay be supplied to respective one of the MZMD  116 - 1  to  116 - 4 . These control signals are indicative of an amplitude modulation scalar, and, based on these control signals, the MZMD  116  may further adjust the analog signals received from the DACs  108  in accordance with the amplitude modulation scalar, such that the MZM  120  are driven in such a manner as to collectively amplitude modulate the subcarriers SC1 to SC8. 
     In another example, a plurality of optical components  144  may be provided to receive an optical signal including the optical subcarriers SC1 to SC8 output from the PBC  132 . The optical components  144  may be any combination of a variable optical attenuator, an amplifier, an optical filter, such as a tunable filter, and/or the like. The optical component  144  may be operable to modify the optical signal output from the PBC  132 . For example, if the optical component is a VOA, the VOA may be operable to adjust or vary the attenuation of the optical signal. By varying the attenuation experienced by the optical subcarriers SC1 to SC8, the amplitude or intensity of such subcarriers may be adjusted or controlled, such that the subcarriers SC1 to SC8 are amplitude modulated. 
     The transmitter  70  may be provided in the module  148 , which may also house a receiver  74  of the primary transceiver  22  of the primary node  14 . Although the optical components block  144  is shown inside the module  148 , it is understood that the optical components  144  may be provided outside the module  148 . 
     In one embodiment, the transmitter  70  includes one or more optical tap  150  disposed between the PBC  132  and the optical fiber  140  and in optical communication to receive a portion of the optical signal from the PBC  132 . In the embodiment where the optical components  144  is included in the transmitter  70 , the optical tap  150  may be disposed between the optical components  144  and the PBC  132  and/or disposed between the optical components  144  and the output optical fiber  140 . As shown in greater detail below in reference to  FIG.  8   , the optical tap  150  may be used to direct a portion of the optical signal to a photodetector  332  and a demodulation circuitry  324  of a controls and monitoring circuit  300 . 
     In one embodiment, amplitude-modulated (AM) tones maybe added to the data coming from the DSP  104 - 3  by providing an AM signal generator  152  which provides each of outputs AMO-1 to AMO-4 to a respective input of the DACs  108 - 1  to  108 - 4 . These signals are generated in such a way that the DACs  108  output analog signals that include the AM tone overlaying or superimposed on the data carrying DAC outputs. Based on such DAC outputs, the MZMDs  116 , in turn, output drive signal to the MZMs  120 , as noted above. Accordingly, the combined MZM outputs supply optical subcarriers are superimposed with the AM tone based on the outputs AMO-1 to AMO-4 of the AM signal generator  152 . Both X and Y polarization components and both components I and Q of each polarization are capable of such AM tones being added to the high-speed data. In one embodiment, both X and Y polarization components and both I and Q components include a single AM tone, whereas in other embodiments, both X and Y polarization components and both I and Q components include a plurality of AM tones. 
     While the AM signal generator  152  is shown in  FIG.  4    as a single device, in one embodiment, the AM signal generator  152  could be more than one device. For example, a first AM signal generator could be implemented, similar in construction to the AM signal generator  152  to supply the output AMO-1 and the output AMO-2, while a second AM signal generator could be implemented, similar in construction to the AM signal generator  152  to supply the output AMO-3 and the output AMO-4. In another embodiment, a first AM signal generator could be implemented, similar in construction to the AM signal generator  152  to supply a first output while a second AM signal generator could be implemented to supply a second output, the first output and the second output are combined to form the AMO, such as the AMO-1 input to the DAC  108 - 1 . In yet another embodiment, a plurality of AM signal generators may be implemented to supply an output, the output of each of the plurality of AM signal generators may be combined to form the AM, such as the AMO-1 input to the DAC  108 - 1 . 
     In other embodiments, each DAC  108  is associated with a different AM signal generator  152  to provide an output AMO to the particular DAC  108 . In one embodiment, the primary transceiver  22  may share a single AM signal generator between multiple transmitters  70 . Similarly, in some embodiments, the primary node  14  may share a single AM signal generator between multiple primary transceivers  22 . 
     The controls and monitoring circuit  300  is in communication with the one or more optical tap  150  to receive the portion of the optical signal from the PBC  132  to monitor the optical signal. In one embodiment, the controls and monitoring circuit  300  may also be in communication with one or more of the optical components  144 , the D/A and Optics Block  112 , the AM signal generator  152 , and the DSP  100 . In one embodiment, the controls and monitoring circuit  300  outputs the CDPS signal as received by the block  104 - 2 . In one embodiment, the controls and monitoring circuit  300  communicates with the DSP  100  and optical component  144  to control various settings, such as, VOA setting, amplifier setting, MZM bias, AM signal generator, CDPS data, laser control, and the like, or some combination thereof. 
     Referring now to  FIG.  5   , shown therein is a diagram of an exemplary embodiment of an AM signal generator  152 - 1  similar to the AM signal generator  152  of  FIG.  4   , constructed in accordance with the present disclosure. In this embodiment, the AM signal generator  152 - 1  receives an AM amplitude setting AS1, i.e., a scalar value between 0 and 1, which may be multiplied, with a multiplier  156 - 1 , by a cosine function, cos(ω AM t), where ω AM  is indicative of a frequency of the amplitude modulation (in rad/s) and is selectable by the user or selected by the controls and monitoring circuit  300  and where t is a sampling time dependent on a sampling rate of the DSP  100  or the DAC resulting in discrete steps of, for example only, 10ps. The resulting product is output from the multiplier  156 - 1  and provided to an adder circuit  160 , which adds one to the product output from the multiplier  156 - 1 . The output or sum of the adder circuit  160  is next provided to a multiplier circuit  156 - 2 , which multiplies such sum by another cosine function, cos(ω Carrier t), where ω Carrier  is a carrier frequency (in rad/s) and t is a sampling time as described above. In one example, ω Carrier  is equal to zero. In other examples, ω Carrier  is selected from a frequency in the range of about 0.5 GHz to about 50 GHz; however, the frequency may be selected or provided by a user or controls and monitoring circuit  300 . The resulting product (AMO-1) is added or combined with a corresponding output of the DSP  100  and input to the DAC  108 - 1 . In one embodiment, the sampling time, t, is dependent on the sampling rate, for example, if the sampling rate is  100  giga-samples per second, then t includes every step of time, starting at 0, until termination of sampling, e.g., 0 s, 10 ps, 20 ps, 30 ps, etc. 
     In one embodiment, ω AM  is much smaller than ω Carrier , such as a frequency selected from the range of about 0 MHz to about 50 MHz. In one embodiment, ω AM  = 2πƒ AM . Where ƒ AM  is the AM frequency of the tone in Hz. 
     It is understood that the AM signal generator  152  may include circuitry similar to the AM signal generator  152 - 1  shown in  FIG.  5    to provide similar signals (AMO-2 to AMO-3) to the inputs of remaining the DACs  108 - 2  to  108 - 4 . 
     In one embodiment, the AM signal generator  152  may supply a first AM tone for a first period of time and a second AM tone for the second period of time. For example, the first AM tone may have a first ω AM-I  and a first ω Carrier-1 , at the first period of time and the AM tone may have a second ω AM-2  and a second ω Carrier-2  at the second period of time. In some embodiments, the first period of time and the second period of time are the same amount of time. In some embodiments, the first ω AM  and the second ω AM  are the same, however in other embodiments the first ω AM  and the second ω AM  are different. In some embodiments, the first ω Carrier  and the second ω Carrier  are the same, however in other embodiments, the second ω Carrier  and the second ω Carrier  are the same. In one embodiment, the controls and monitoring circuit  300  controls the AM signal generator  152  as part of a frequency response determination process  600  as shown in  FIG.  14   . 
     Referring now to  FIG.  6   , shown therein is a block diagram of an exemplary embodiment of the DSP  100  of  FIG.  4   , including circuit blocks  104 - 1  and circuit blocks  104 - 3 , in greater detail. As noted above, the circuit block  104 - 1  receives user data streams or inputs D1 to D8. A shown in  FIG.  5   , each such data stream is supplied to a respective one of the forward error correction encoders (FEC encoders  200 - 1  to  200 - 8 ). The FEC encoders  200 - 1  to  200 - 8  carry out forward error correction coding on a corresponding one of the switch outputs, such as, by adding parity bits to the received data. The FEC encoders  200 - 1  to  200 - 8  may also provide timing skew between the subcarriers to correct for skew introduced during transmission over one or more optical fibers. In addition, the FEC encoders  200 - 1  to  200 - 8  may interleave the received data. 
     Each of the FEC encoders  200 - 1  to  200 - 8  provides an output to a corresponding one of multiple bits to symbol circuits,  204 - 1  to  204 - 8  (collectively referred to herein as “204”). Each of the bits to symbol circuits  204  may map the encoded bits to symbols on a complex plane. For example, the bits to symbol circuits  204  may map four bits to a symbol in a dual-polarization Quadrature Phase Shift Keying (QPSK) or an m-quadrature amplitude modulation (m-QAM, m being a positive integer) constellation, such as 8-QAM, 16-QAM, 32-QAM, 64-QAM, and 128-QAM or a greater m-quadrature amplitude modulation. Each of the bits to symbol circuits  204  provides first symbols, having the complex representation XI + j*XQ, associated with a respective one of the data input, such as D1. Data indicative of such first symbols may be carried by the X polarization component of each subcarrier SC1-SC8. 
     Each of the bits to symbol circuits  204  may further provide second symbols having the complex representation YI + j*YQ, also associated with a corresponding one of the data inputs D1 to D8. Data indicative of such second symbols, however, is carried by the Y polarization component of each of the subcarriers SC1-SC8. 
     As further shown in  FIG.  6   , each of the first symbols output from each of the bits to symbol circuits  204  is supplied to a respective one of first overlap and save buffers  208 - 1  to  208 - 8  (collectively referred to herein as overlap and save buffers  208 ) that may buffer  256  symbols, for example, however, in other embodiments, a greater or fewer number of symbols may be buffered. Each of the overlap and save buffers  208  may receive  128  of the first symbols or another number of such symbols at a time from a corresponding one of bits to symbol circuits  204 . Thus, the overlap and save buffers  208  may combine  128  new symbols from the bits to symbol circuits  204 , with the previous  128  symbols received from the bits-to-symbol circuits  204 . 
     Each overlap and save buffer  208  supplies an output, which is in the time domain, to a corresponding one of the fast Fourier Transform (FFT) circuits  212 - 1  to  212 - 8  (collectively referred to as “FFTs 212”). In one example, the output includes  256  symbols or another number of symbols. Each of the FFTs  212  converts the received symbols to the frequency domain using or based on, for example, a fast Fourier transform. Each of the FFTs  212  may include  256 , for example, memories or registers, also referred to as frequency bins or points, that store frequency components associated with the input symbols. 
     Each of the replicator components  216 - 1  to  216 - 8  may replicate the  256  frequency components associated with of the FFTs  212  and store such components in  512  or another number of frequency bins (e.g., for T/2 based filtering of the subcarrier) in a respective one of the plurality of replicator components. Such replication may increase the sample rate. In addition, replicator components  216 - 1  to  216 - 8 , or circuits, may arrange or align the contents of the frequency bins to fall within the bandwidths associated with shape filter circuits  220 - 1  to  220 - 8  described below. 
     In one embodiment, each of the shape filter circuits  220 - 1  to  220 - 8  may apply a pulse shaping filter to the data stored in the  512  frequency bins of a respective one of the plurality of replicator components  216 - 1  to  216 - 8  to thereby provide a respective one of multiple filtered outputs, which are multiplexed and subject to an inverse FFT, as described below. The shape filter circuits  220 - 1  to  220 - 8  calculate the transitions between the symbols and the desired subcarrier spectrum so that the subcarriers can be spectrally packed together for transmission (e.g., with a close frequency separation). The shape filter circuits  220 - 1  to  220 - 8  may also be used to introduce timing skew between the subcarriers to correct for timing skew induced by links between nodes shown in  FIG.  1   , for example. 
     In one embodiment, the shape filter circuits  220 - 1  to  220 - 8  may further include a frequency domain equalizer filter, pre-compensation filter, and/or a CD filter, discussed in more detail below in reference to  FIGS.  13 - 15   . The shape filter circuits  220 - 1  to  220 - 8  having a frequency domain equalizer filter, pre-compensation filter, or a CD filter may be referred to as an FDEQ filter. The FDEQ filter may be used to apply a frequency response (discussed in more detail below) to the shape the subcarriers or the subcarrier spectrum. 
     In one embodiment, the shape filter circuits  220 - 1  to  220 - 8  may further receive an array of amplitude and/or phase values, such as from the amplitude response and/or phase response derived below) and apply the amplitude and/or phase values to the spectrum of each subcarrier of the optical signal. 
     In one embodiment, a memory component  224 , which may include a multiplexer circuit or memory, may receive the filtered outputs from the shape filter circuits  220 - 1  to  220 - 8 , and multiplex or combine such outputs together to form an element vector. 
     The output of the memory component  224  is fed to the circuit block  104 - 3 , which includes, in this example, an IFFT circuit  228 - 1 . The IFFT circuit  228 - 1  may receive the element vector and provide a corresponding time domain signal or data based on an inverse fast Fourier transform (IFFT). In one example, the time domain signal may have a rate of  64  G Sample/s. A take last buffer or memory circuit  232 - 1  may select the last 1024 or another number of samples from an output of the IFFT circuit  228 - 1  and supply the samples to a downstream node at  64  G Sample/s, for example. 
     As further shown in  FIG.  6   , each of the bits to symbol circuits  204 - 1  to  204 - 8  outputs a corresponding one of symbols indicative of data carried by the Y polarization component of the polarization multiplexed modulated optical signal output on the optical communication path or optical fiber  140 . As further noted above, these symbols may have the complex representation YI+j*YQ. Each such symbol may be processed by a respective one of the overlap and save buffers  240 - 1  to  240 - 8 , a respective one of the FFT circuits  244 - 1  to  244 - 8 , a respective one of the replicator components or circuits  248 - 1  to  248 - 8 , the shape filter circuits  252 - 1  to  252 - 8 , and the multiplexer or memory  256  of block the  104 - 1 . Moreover, the output of the multiplexer or memory  256  may be fed to the circuit block  104 - 3 , which further includes a IFFT  228 - 2 , and a take last buffer or memory circuit  232 - 2 , to provide processed symbols having the representation YI+j*YQ in a manner similar to or the same as that discussed above in generating processed symbols XI+j*XQ output from the memory circuit  232 - 1 . In addition, symbol components YI and YQ are provided to the downstream node. 
     While  FIG.  6    shows the Tx DSP  100  as including a particular quantity and arrangement of functional components, in some implementations, the DSP  100  may include additional functional components, fewer functional components, different functional components, or differently arranged functional components. In addition, typically the number of overlap and save buffers, FFTs, replicator circuits, and pulse shape filters associated with the X component may be equal to the number of data inputs, and the number of such circuits associated with the Y component and may also be equal to the number of switch outputs. However, in other examples, the number of data inputs may be different than the number of these circuits. As noted above, based on the outputs of the MZMDs  116 - 1  to  116 - 4 , multiple optical subcarriers SC1 to SC8 may be output onto the optical fiber  140 . 
     Referring now to  FIG.  7   , shown therein is a plurality of multiplier circuits  260 - 1  to  260 - 8 , which may be complex multiplier circuits, are provided within the DSP  100 , to receive a respective one of outputs O1 to O8 from a corresponding one of the shape filter circuits  220 - 1  to  220 - 8 . Each of the multiplier circuits  260 - 1  to  260 - 8  receives a corresponding one of gain parameters G1 to G8 (i.e., a scalar), such that, in this example, each of the outputs O1 to O8 is multiplied by a corresponding one of the gain parameters G1 to G8. Each output O1 to O8 is associated with a respective one of the subcarriers SC1 to SC8. Moreover, each is associated with a gain or amplitude of a respective one of the subcarriers. That is, the amplitude of each of the optical subcarriers SC1 to SC8 output from the MZM  120  may be based on the gain parameters G1 to G8. Thus, by varying the gain parameters G1 to G8, the amplitude of the optical subcarriers SC1 to SC8 may also be varied or modulated. The gain parameters G1 to G8, may therefore be adjusted or controlled to adjust the power of the subcarriers SC1 to SC8. 
     In some implementations, the gain of each multiplier  260  is software programmable (or may be implemented in firmware) along with a frequency shaping function in the filter circuit  220  preceding the multiplexing performed by the multiplexer or memory component  224 . 
     In one embodiment, in the example shown in  FIG.  7   , the gain parameter changes or variations are synchronized to occur at the same time or substantially the same time so that the amplitudes of the subcarriers SC1 to SC8 vary at the same time or substantially the same time. Moreover, the above-described multiplier circuits  260  may be included in the DSP  100  to adjust the power of the X polarization component of each of the subcarriers SC1 to SC8. It is understood that similar multiplier circuits may be provided between the shape filters  252  and the memory  256  to provide corresponding power adjustment of the Y polarization component of each subcarrier SC1 to SC8. 
     In one embodiment, the gain parameters may be used as limited pre-compensation filter parameters for each subcarrier SC1 to SC8. In other words, adjusting the gain parameters may adjust an average power of a subcarrier. This embodiment, however, cannot mitigate power variance within any particular subcarrier. 
     As discussed in greater detail below, optical subcarriers may be selectively output by primary transceivers  22  and/or secondary transceivers  34 . The number of optical subcarriers that may be output, however, can vary over time in accordance with bandwidth of data capacity requirements of the transceiver. For example, if at one point in time, network bandwidth requirements are such that transceiver  34   a  transmits  200  Gbit/s to primary transceiver  22 , and, each subcarrier carries data associated with  100  Gbit/s transmission, transceiver  34   a  outputs two optical subcarriers (2 subcarriers X  100  Gbit/s). 
     As noted above, however, bandwidth requirements are often not static. Accordingly, in the current example, at another point in time, the network capacity requirements may be such that transceiver  34   a  transmits  100  Gbit/s to primary transceiver  22 . As a result, transceiver  34   a , turns off or cancels one of the subcarriers that previously had been transmitted. On the other hand, if, for example, additional bandwidth or capacity is required to be output from transceiver  34   a , instructions may be provided to increase the number of optical subcarriers output from transceiver  34   a . 
     Referring now to  FIG.  8   , shown therein is a diagram of an exemplary embodiment of the controls and monitoring circuit  300  constructed in accordance with the present disclosure. The controls and monitoring circuit  300  generally includes a demodulation circuitry  342 , which may be implemented on a microprocessor, FPGA, ASIC, circuitry, and/or the like. In some implementations, one or more of the components of the controls and monitoring circuit  300  can be placed at various locations within the primary node  14  or the secondary node  18  of the optical communication system  10 . 
     While  FIG.  8    shows the control and monitoring circuitry  300  as including a particular quantity and arrangement of functional components, in some implementations, the control and monitoring circuitry  300  may include additional functional components, fewer functional components, different functional components, or differently arranged functional components. For example, the controls circuit  300  may have one or more additional component providing additional functionality, such as power monitoring, power control, laser control, MZM control, alarm monitoring, and/or the like. 
     Detection of an AM tone applied from the AM signal generator  152  generated at the transmitter  148  of a near end transceiver, primary transceiver  22 , will next be described. The optical signal is input to an optical tap  150 , which may provide an optical power split portion of the optical signal (e.g., 1% to 10%) to a photodetector  332 , which may be a photodiode or other device operable to detect a power of the optical signal. A remaining portion of the optical signal continues to propagate along optical communication path  316  via the fiber optical  140 . A VOA  312 - 1  or other optical component  144  may optionally be provided for processing the output signal. For example, the VOA  312 - 1  can receive the signal output by the optical tap  150  via an optical input port  336 - 1 , and attenuate the signal according to an analog signal  340  received via the optical input port  336 - 2 . In one embodiment, as described above, the optical tap  150  may be placed after the VOA  312 - 1 . In one embodiment, the VOA  312 - 1  is set to a fixed gain. In this manner, the gain of the VOA  312 - 1  will not compromise detection of a frequency response. 
     As further shown in  FIG.  8   , the tapped portion of the optical signal is converted by the photodetector  332  to a corresponding analog electrical signal (e.g., a voltage or a current). The analog signal is fed to a demodulation circuitry  342  comprising an ADC  344 , which supplies digital signals based on the received analog electrical signal, a demodulator  348 , and a low pass filter  352 . Such digital signals are optionally provided to the demodulator  348  and then output to a low pass filter  352 , which outputs an amplitude response based on the AM tone. The amplitude response is a signal difference from the AM tone caused by impairments in transmitter side optical components before the optical signal proceeds down the optical fiber  140 . The ADC  344  converts the analog signal into the digital domain. 
     In one embodiment, the amplitude response is one component of the frequency response caused by impairments in components of the primary node  14 , primary transceiver  22 , and/or transmitter  70 . The amplitude response, in conjunction with a phase response, comprise the frequency response. The frequency response is a linear time-invariant impairment of the primary node  14 , primary transceiver  22 , and/or transmitter  70 . Linear time-invariant impairments may be caused by components such as the DAC  108 , traces and/or cables between components, the MZMD  116 , MZM frequency roll-off, echoes in the transmitter  70  (e.g., caused by impedance mismatch), ripple in the spectral response, skew, any non-linear phase response, MZMD  116  peaking, low latency attenuation, and the like. Additionally, the frequency response may be temperature dependent, that is, the frequency response may change based on a temperature of the transmitter  70  and/or other components of the primary transceiver  22 . The frequency response may also be age dependent, that is, the frequency response may change based on an age of the transmitter  70  and/or other components of the primary transceiver  22 . The frequency response may also be optical laser frequency dependent, that is, the frequency response may change based on the operational laser frequency of the transmitter  70  and/or other components of the primary transceiver  22 . 
     Referring now to  FIG.  9   , shown therein is a diagram of an exemplary embodiment of a shared laser constructed in accordance with the present disclosure. In this embodiment, the laser  124  is provided that is “shared” between the transmitter  70  and the receiver  74  in the primary transceivers  22  or between the receiver  78  and the transmitter  82  of the secondary transceiver  34 . For example, a splitter  380  can provide a first portion of light output from the laser  124  to the MZMs  120  in the transmitter portion of the transmitter  70 . Further, the splitter  380  can provide a second portion of such light acting as a local oscillator signal fed to 90-degree optical hybrids in the receiver  74  of the transmitter  70 , as shown in  FIG.  9   . 
     Generation of multiple amplitude modulated tones in the data paths will next be described. As noted above, the AM signal generator  152  can generate and transmit the AM tone super-imposed onto high-speed data supplied from the DSP  100 . Referring now to  FIG.  10   , shown therein is an alternative embodiment of an AM signal generator  152 - 2  constructed in accordance with the present disclosure. Here, the AM signal generator  152 - 2  is modified, from the AM signal generator  152 - 1  shown in  FIG.  5   , to include a plurality of AM tone generators  152 - 2   a  and  152 - 2   b  at different frequencies (differing carrier frequencies ω Carrier  and/or differing AM frequencies, ω B  and ω C  to carry a first AM signal AS1 and a second AM signal AS2 simultaneously, or nearly simultaneously, as opposed to only one frequency as noted above with respect to  FIG.  5   . As in the example noted above, the AM signal generator  152 - 2  provides each of the outputs AMO-1 to AMO-4 to a respective input of the DACs  108 - 1  to  108 - 4  (see  FIG.  4   ). These signals are generated in such a way that the DACs  108  output analog signals that include multiple amplitude modulated signals overlaying or superimposed on the data carrying DAC outputs. Based on the DAC outputs, the MZMDs  116 , in turn, output drive signal to the MZMs  120 , as noted above. Accordingly, the combined MZM outputs supply optical subcarriers superimposed with multiple amplitude modulated signals at different frequencies based on the outputs of the AM signal generator  152 , whereby both the X and Y polarization components are capable of such amplitude modulation. 
     Returning to  FIG.  10   , the AM signal generator  152 - 2  includes a multiplier circuit  424 - 1  that multiplies first AM signal amplitude AS1 by a cosine function, cos(ω B t), where ω B  is indicative of a frequency of the amplitude modulation (in rad/s) and t is time as discussed above. In a similar manner as that described above in regard to  FIG.  5   , the output of the multiplier circuit  424 - 1  is provided to the adder circuit  428 - 1  which adds one (1) to product supplied by the multiplier circuit  424 - 1 . The resulting sum output from the adder circuit  428 - 1  is provided to a multiplier circuit  432 - 1 , which multiplies the resulting sum by a carrier frequency ω Carrier  resulting in a first output. 
     The AM signal generator  152 - 2  also includes, for example, a multiplier circuit  424 - 2  that multiplies the second AM signal amplitude AS2 by a cosine function, cos(ω C t), where ω C  is indicative of a frequency of another amplitude modulation and t is time as discussed above. Adder circuit  428 - 2  and the multiplier circuit  432 - 2  operate in a similar manner as the adder circuit  428 - 1  and the multiplier circuit  432 - 1  (except that the multiplier circuit  432 - 1  multiplies the resulting sum of the adder circuit  428 - 2  by cos(ω’ Carrier t)) resulting in a second output. As further shown in  FIG.  10   , the second output of the multiplier circuit  432 - 2  and the first output of the multiplier circuit  432 - 1  are provided to an adder circuit  436 , which adds the first output and the second output and the resulting sum (AMO-1 in  FIG.  4   ) is combined with a corresponding output from the DSP  100  and input to the DAC  108 - 1 . Accordingly, amplitude modulation at different frequencies, a first amplitude modulation in band ω B  and a second amplitude modulation in band ωc, are fed to the DAC  108 - 1 . As a result, both X and Y polarization components of each optical subcarrier are modulated at multiple frequencies to carry the AM tone. 
     It is understood that additional circuitry similar to the AM signal generator  152 - 2  shown in  FIG.  10    is also included in the AM signal generator  152 , in this example, to provide similar signals (AMO-2 to AMO-4) to the inputs of remaining DACs  108 - 2  to  108 - 4 . As noted above, based on such inputs, the combined output of the MZMs  120  supplies optical subcarriers that are collectively amplitude modulated, such that both the first AM tones and second AM tones are superimposed onto the optical subcarriers to thereby carry first and second AM signals, for example. 
     Moreover, one or more of the secondary transceivers  34  may include transmitter  82 , or transmitter circuitry, similar to the transmitter  70  and may include any of the AM signal generator  152 ,  152 - 1 , and/or  152 - 2 , as described above. 
     Referring now to  FIG.  11 A , shown therein is a general schematic of an exemplary embodiment of a filter  500  constructed in accordance with the present disclosure. The filter  500  is an exemplary embodiment of the shape filter circuits  220 - 1  to  220 - 8  and/or shape filter circuits  252 - 1  to  252 - 8  shown in  FIG.  6    and  FIG.  7   . Generally, the filter  500  receives a first X component  502 - 1  (Xi) and a second X component  502 - 2  (Xq). In one embodiment the first X component  502 - 1  is an XI component and the second X component  502 - 2  is an XQ component. The first X component  502 - 1  is then split and filtered by Hii filter  504 - 1  and Hiq filter  504 - 2  and the second X component  502 - 2  is split and filtered by an Hqi filter  504 - 3  and an Hqq filter  504 - 4 . The Hii filtered signal  504 - 1  from the first X component  500 - 1  and the Hqi filtered signal  504 - 3  of the second X component  502 - 2  are summed in adder  508 - 1  resulting in a first X component output  512 - 1  equal to Hii*Xi+Hqi*Xq. The Hiq filtered signal  504 - 2  from the first X component  500 - 1  and the Hqq filtered signal  504 - 4  of the second X component  502 - 2  are summed in adder  508 - 2  resulting in a second X component output  512 - 2  equal to Hiq*Xi+Hqq*Xq. Note that all signals Xi, Xq and all filters Hii, Hiq, Hqi, Hqq are frequency domain vectors, hence filtering can be denoted as a multiplication. 
     In some embodiments, because the crosstalk between the first X component  502 - 1  and the second X component  502 - 2  is very small, minimal, or non-existent, the Hiq filter values  504 - 2  and the Hqi filter values  504 - 3  can be set to “0” resulting in the first X component output  512 - 1  being equal to Hii*Xi and the second X component output  512 - 2  being equal to Hqq*Xq. 
     The filter  500  shown in  FIG.  11 A  is directed to a single polarization, i.e., the X component; however, it is understood that similar circuitry as that shown in  FIG.  11 A  may be employed to determine the Y component as well. 
     Referring now to  FIG.  11 B , shown therein is a block diagram of an exemplary embodiment of a filter  500 - 1  constructed in accordance with the present disclosure. The filter  500 - 1  is an alternative embodiment of the filter  500  described above in reference to  FIG.  11 A . The filter  500 - 1  is shown as receiving an input  516  of X in  where X is a complex denotation of an X I  and X Q  stream data where X in  = X i_in  + jX q_in  and X out  = X i_out  + jXq_ out . The input  516  is split between two paths, where on the first path, the input  516  is filtered by a complex-valued H direct  filter  520  and on the second path, the input  516  passes through a conjugation block  524 , where the conjugation block  524  negates imaginary components of the input  516 , and a complex-valued H hermitian  filter  528 . The input  516  after passing through the first path and the input  516  after passing through the second path are combined by an adder  532  resulting in an output  536  of X out . The output  536 , therefore, can be represented by the equation  
     
       
         
           
             
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     . It should be noted that the conjugation block  524  may be denoted in the equation for X out  as an asterisk (*), such that if the conjugation block  524  receives an input of X = XI + jXQ, then the conjugation block  524  may have an output of X* = XI - jXQ. 
     Referring now to  FIG.  12   , shown therein is a flow diagram of an exemplary embodiment of a demodulation circuitry  342 - 1  constructed in accordance with the present disclosure. The demodulation circuitry  342 - 1  is similar in function to the demodulation circuitry  342  shown in  FIG.  8    and is a particular embodiment of the demodulation circuitry  342 . As shown above in  FIG.  8   , a portion of the optical signal is measured by the photodetector  332 , creating an analog signal (e.g., voltage or current) that is then received by the ADC  344 . The analog signal is amplified and sampled by the ADC  344  resulting in a digital signal that first passes through an auto gain offset module  350  before passing to the demodulator  348 . The demodulator  348  may include one or more correlator to demodulate the digital signal. In one embodiment, the demodulator  348  and/or the one or more correlator is implemented in an FPGA or an ASIC, whereas in other embodiments, another processor is used such as the microprocessor  300  or the DSP  100 , for example. In one embodiment, each correlator has about 30 MHz bandwidth. In another embodiment, a particular correlator of the one or more correlator is used for all measurements, e.g., for consistency to reduce differences between each correlator. 
     In one embodiment, the photodetector  332  may be implemented as a simple photodiode with narrow bandwidth, e.g., a bandwidth of about 100 KHz to 100 MHz, or some range there-between. 
     Referring now to  FIG.  13   , shown therein is a flow diagram of an exemplary embodiment of a demodulation circuitry  342 - 2  constructed in accordance with the present disclosure. In one embodiment, the demodulation circuitry  342 - 2  is implemented in an FPGA or an ASIC processor and is a photodetector current demodulator. The demodulation circuitry  342  correlates to a desired frequency and extracts the power at that frequency. As shown above in  FIG.  8   , a portion of the optical signal is measured by the photodetector  332 , creating an analog signal (e.g., voltage or current) that is then received by the ADC  344 . The analog signal is amplified and sampled by the ADC  344  resulting in a digital signal that is processed by a filter component  550  such as a high-pass filter or a DC Block. Once the digital signal is processed by the filter component  550  the signal is split onto two paths. 
     On the first path, the digital signal is multiplied by sin(ω AM t) by multiplier  554 - 1 . The sine-multiplied signal, then passes through a low-pass filter  558 - 1 , is amplified by amplifier  562 - 1  and enters a summation block  566 . On the second path, the digital signal is multiplied by cos(ω AM t) by multiplier  554 - 2 . The cosine-multiplied signal, then passes through a low-pass filter  558 - 2 , is amplified by amplifier  562 - 2  and enters the summation block  566 . At the summation block  566 , the sine-multiplied signal and the cosine-multiplied signal are combined into a tone amplitude response at frequency ω AM . 
     In one embodiment, the AM tone is the same as the one generated by the AM signal generator  152 . In one embodiment, the low-pass filter  558 - 1  and/or the low-pass filter  558 - 2  is a low bandwidth filter. In one embodiment, the photodetector  332  is a low bandwidth photodetector that detects a power of the AM tone but is insensitive to frequencies of the optical signal at which data is being transmitted. It is important that the bandwidth of the photodetector  332  and the demodulation circuitry  342  are above the frequency of the AM tone (ω AM ). Note that the bandwidth of the photodetector  332  and the demodulation circuitry  342   may be less than the bandwidth of the optical signal carrying data. In this manner, the AM tone is not affected, or is minimally affected, by the data transmitted on the optical signal, and, similarly, the data transmitted on the optical signal is not affected, or is minimally affected, by the AM tone. 
     Referring now to  FIG.  14   , shown therein is a process flow diagram of an exemplary embodiment of a frequency response determination process  600  in accordance with the present disclosure. The frequency response determination process  600  generally includes the steps of: setting up the AM signal generator (step  604 ); sweeping the carrier frequency of the AM tone across the band of interest (step  608 ); measuring the power at a tone detector at multiple instants of time during the sweep (step  612 ); obtaining the amplitude response at each instant of time (step  616 ); calculating the phase response (step  620 ); determining the frequency response (step  624 ); calculating pre-compensation filter parameters (step  628 ); and implementing the pre-compensation filter parameters (step  632 ). In some embodiments, the frequency response determination process  600  is performed for one or more channel or subcarrier in the optical signal. In one embodiment, the frequency response determination process is performed for each data path (XI/TEI, XQ/TEQ, YI/TMI, YQ/TMQ). 
     In one embodiment, setting up the AM signal generator (step  604 ) includes, for each channel or subcarrier, for each polarization X and Y and for each path I and Q, setting up the AM signal generator  152  with an AM signal resulting in an AM tone having a known carrier frequency and a known AM frequency. In one embodiment, the AM tone has a component at the carrier frequency, a component at the carrier frequency less the AM frequency, and a component at the carrier frequency plus the AM frequency, as described in more detail below with respect to  FIG.  15   . 
     In one embodiment, sweeping the AM tone across the band of interest (step  608 ) includes causing the AM signal generator  152  to transmit a plurality of AM tones  658  across a band of interest, such as a subcarrier or an optical signal. In one embodiment, sweeping the AM tone across the band of interest (step  608 ) includes sweeping the AM tone across only a portion of the band of interest. In one embodiment, sweeping the AM tone’s carrier frequency across the band of interest (step  608 ) includes sweeping the AM tone’s carrier frequency (ω carrier ) from a frequency of about 0.5 GHz to a frequency of about 50 GHz with steps of about 0.1 GHz. In other words, the AM tone is first centered on a 0.5 GHz carrier frequency, then centered on a 0.6 GHz frequency, then centered on a 0.7 GHz frequency, etc., until, lastly, the AM tone is centered on a 50 GHz carrier frequency. In one embodiment, the AM tone is centered on each frequency in order from lowest frequency to highest frequency, the AM tone is centered on each frequency in order from highest frequency to lowest frequency, or the AM tone is centered on one or more test frequency between the lowest frequency and the highest frequency, inclusive, where the test frequency is the lowest frequency plus a multiplier of the step frequency in any order not ascending or descending. 
     In one embodiment, the tone detector is a photodetector, such as the photodetector  332 , a SOA in reverse bias, or any other device operable to detect and/or measure a power of the optical signal. In one embodiment, measuring the power at the tone detector (step  612 ) includes measuring an output of the photodetector  332 , such as by the ADC  344  of the demodulation circuitry  342 , which corresponds to the square of the amplitude response of the transmitter path. In one embodiment, measuring the power at the tone detector (step  612 ) is performed while the AM tone  658  is being swept across the band of interest. For example, as shown in  FIG.  15    below, measuring the power at the tone detector (step  612 ) may include measuring the power of the photodetector  332  for a first period of time when the AM tone  658 - 1  is supplied, e.g., to the DAC  108  and measuring the power of the photodetector  332  for a second period of time when the AM tone  658 - 2  is supplied, e.g., to the DAC  108 . 
     In one embodiment, measuring the power at the tone detector (step  612 ) includes measuring the power of the photodetector  332  multiple times and calculating an average of the measured power. In one embodiment, measuring the power at the tone detector (step  612 ) further includes determining a measured power of the photodetector  332  by passing the voltage of the photodetector through the ADC  344 . In one embodiment, measuring the power at the tone detector (step  612 ) is performed by an FPGA, ASIC, or microprocessor  300 , the DSP  100 , or the like, implementing the ADC  344 . 
     In one embodiment, obtaining the amplitude response (step  616 ) includes interpolating and normalizing the measured power at the tone demodulator from step  612 . Obtaining the amplitude response (step  616 ) may be performed by the demodulation circuitry  342 . As discussed above, the measured power may be analyzed by the demodulation circuitry  342 , e.g., the demodulation circuitry  342 - 2 , to determine the amplitude response. The amplitude response is the square root of the measured tone strength as the AM tone is swept across the band. 
     In one embodiment, calculating the phase response (step  620 ) includes calculating the phase response using Kramers-Kronig relation: 
     
       
         
           
             Re 
             
               
                 H 
                 
                   ω 
                 
               
             
             = 
             
               2 
               ω 
             
             ∗ 
             I 
             m 
             
               
                 H 
                 
                   ω 
                 
               
             
             = 
             
               
                 
                   ∫ 
                   
                     − 
                     ∞ 
                   
                   ∞ 
                 
                 
                   
                     2 
                     
                       ω 
                       − 
                       
                         ω 
                         
                             
                           &#39; 
                         
                       
                     
                   
                 
               
             
               
             I 
             m 
             
               
                 H 
                 
                   
                     ω 
                     ′ 
                   
                 
               
             
             d 
             
               ω 
               ′ 
             
             . 
           
         
       
     
      If the transmitter  70  has an impulse response that is well-behaved and matches Kramers-Kronig conditions, the phase response can be calculated from the amplitude response. The Kramers-Kronig conditions that should be matched include that h(t) is (1) a real value, (2) is causal, and (3) is analytic. If the conditions are matched, the following equation is true: 
     
       
         
           
             Re 
             
               
                 H 
                 
                   ω 
                 
               
             
             = 
             
               2 
               ω 
             
             ∗ 
             I 
             m 
             
               
                 H 
                 
                   ω 
                 
               
             
             = 
             
               
                 
                   ∫ 
                   
                     − 
                     ∞ 
                   
                   ∞ 
                 
                 
                   
                     2 
                     
                       ω 
                       − 
                       
                         ω 
                         ′ 
                       
                     
                   
                   I 
                   m 
                   
                     
                       H 
                       
                         
                           ω 
                           ′ 
                         
                       
                     
                   
                   d 
                   
                     ω 
                     ′ 
                   
                   . 
                 
               
             
           
         
       
     
      Further simplifications results in the equation 
     
       
         
           
             ∠ 
             H 
             
               ω 
             
             = 
             − 
             
               π 
               2 
             
             
               1 
               
                 2 
                 π 
               
             
             
               
                 
                   ∫ 
                   
                     − 
                     ∞ 
                   
                   ∞ 
                 
                 
                   
                     
                       d 
                       
                         
                           M 
                           
                             
                               ω 
                               , 
                               v 
                             
                           
                         
                       
                     
                     
                       d 
                       v 
                     
                   
                 
               
             
             f 
             
               v 
             
             d 
             v 
               
             where  
             M 
             
               
                 w 
                 , 
                 v 
               
             
             = 
             ln 
             
               
                 
                   
                     H 
                     
                       
                         ω 
                         
                           e 
                           v 
                         
                       
                     
                   
                 
               
             
           
         
       
     
      and 
     
       
         
           
             f 
             
               v 
             
             = 
             
               2 
               
                 
                   π 
                   2 
                 
               
             
             ln 
             
               
                 coth 
                 
                   
                     
                       
                         
                           v 
                         
                       
                       2 
                     
                   
                 
               
             
             . 
           
         
       
     
      With an additional condition that h(t) is a minimum phase, e.g., mod 2n, the above equation can be simplified to 
     
       
         
           
             ∠ 
             H 
             
               ω 
             
             = 
             − 
             h 
             i 
             l 
             b 
             e 
             r 
             t 
             
               
                 ln 
                 
                   
                     
                       
                         H 
                         
                           ω 
                         
                       
                     
                   
                 
               
             
           
         
       
     
      (equation 1) where 
     
       
         
           
             h 
             i 
             l 
             b 
             e 
             r 
             t 
             
               
                 x 
                 
                   t 
                 
               
             
             = 
             
               1 
               π 
             
             
               
                 
                   ∫ 
                   ∞ 
                   
                     − 
                     ∞ 
                   
                 
                 
                   
                     
                       x 
                       
                         τ 
                       
                     
                     
                       t 
                       − 
                       τ 
                     
                   
                   d 
                   τ 
                   . 
                 
               
             
           
         
       
     
      By using Equation 1, the phase response can be calculated for the amplitude response for each path I, Q, of each component X, Y as shown in  FIGS.  18 A-D . In one embodiment, calculating the phase response (step  620 ) is performed by an FPGA, ASIC, microprocessor  300 , the DSP  100 , the central software  38 , or the like. 
     In one embodiment, determining the frequency response (step  624 ) includes combining the amplitude response and the phase response into the frequency response. In some embodiments, this is performed by the DSP  100 , the microprocessor  300 , e.g., within the demodulation circuitry  342 , within an FPGA, within an ASIC, the central software  38 , or the like. In one embodiment, determining the frequency response (step  624 ) includes averaging the amplitude response, the phase response, and/or the frequency response over multiple sweeps of the AM tone across the bands of interest. 
     In some embodiments, determining the frequency response (step  624 ) is performed without first calculating the phase response. In these embodiments, the frequency response includes only the amplitude response and not the phase response. 
     In one embodiment, determining the frequency response (step  624 ) includes combining the amplitude response with the phase response for each path I, Q, of each component X, Y to determine a frequency response for each channel of the optical signal. In one embodiment, determining the frequency response (step  624 ) includes combining the amplitude response with the phase response for each path I, Q, of each component X, Y for each channel to determine a frequency response of the optical signal. 
     In one embodiment, calculating pre-compensation filter parameters (step  628 ) includes taking an inverse of the frequency response determined in step  624 . In one embodiment, calculating pre-compensation filter parameters (step  628 ) includes taking an inverse of the amplitude response for each path I, Q, of each component X, Y, as shown in  FIGS.  17 A-D  below. 
     In one embodiment, calculating pre-compensation filter parameters (step  628 ) includes taking an inverse of the frequency response for each path I, Q, of each component X, Y, as shown in  FIGS.  17 A-D  below. In one embodiment, calculating pre-compensation filter parameters (step  628 ) is performed by an FPGA, ASIC, the DSP  100 , the microprocessor  300 , the central software  38 , or the like. 
     In one embodiment, implementing the pre-compensation filter parameters (step  632 ) includes applying one or more of the pre-compensation filter parameters for the frequency response on one or more of the shape filter circuits  220 - 1  to  220 - 8  or  252 - 1  to  252 - 8 . The pre-compensation filter parameters may include an amplitude and/or phase filter to be performed on the optical signal at a particular frequency or on a particular range of frequencies. The amplitude filtering may correspond to the amplitude, in dB, of the inverse of the frequency response as shown in  FIGS.  17 A-D . In one embodiment, implementing the pre-compensation filter parameters (step  632 ) is performed by the DSP  100 , the shape filter circuits  220 - 1  to  220 - 8 ,  252 - 1  to  252 - 8 , a CD filter, an FDEQ, or any other frequency domain filter or amplifier in the transmitter  70  able to affect the amplitude and/or phase of the optical signal. 
     In one embodiment, implementing the pre-compensation filter parameters (step  632 ) includes applying one or more of the pre-compensation filter parameters for the frequency response against the optical signal. In embodiments where the optical signal does not include multiple subcarriers, implementing the pre-compensation filter parameters (step  632 ) includes applying one or more of the pre-compensation filter parameters for the frequency response on the bandwidth of the optical signal on which data is being transmitted. For example, if data is being transmitted on an optical signal from a first frequency to a second frequency, implementing the pre-compensation filter parameters may include applying the pre-compensation parameters on the optical signal from the first frequency to the second frequency, e.g., by using a frequency domain equalizer or a CD filter. 
     In one embodiment, implementing the pre-compensation filter parameters (step  632 ) includes storing the pre-compensation filter parameters in a memory associated with the DSP  100  or otherwise associated with the primary node  14 . In one embodiment, the pre-compensation filter parameters are stored in the memory component  224  or  256 . In another embodiment, the pre-compensation filter parameters are stored in the central software  38 . 
     In one embodiment, the frequency response determination process  600  is performed while the primary node  14 , the primary transceiver  22 , and/or the transmitter  70  is in operation, that is, while the primary node  14 , the primary transceiver  22 , and/or the transmitter  70  is transmitting data to the secondary node  18 . In other embodiments, one or more of the steps  604 - 632  of the frequency response determination process  600  is performed while the primary node  14 , the primary transceiver  22 , and/or the transmitter  70  is in use or operation, is in a maintenance window, is being manufactured, and/or when the frequency response determination process  600  is triggered, or some combination thereof. 
     In one embodiment, the frequency response determination process  600  is triggered by the central software  38 , by a user in communication with the primary node  14  or some component of the primary node  14  such as the primary transceiver  22  or the transmitter  70 , after a predetermined period of time has elapsed since the frequency response determination process  600  was previously executed, when a temperature of one or more of the primary node  14 , the primary transceiver  22 , and/or the transmitter  70  exceeds a predetermined temperature threshold, when a temperature of one or more of the primary node  14 , the primary transceiver  22 , and/or the transmitter  70  exceeds a predetermined temperature threshold for a specified period of time, when one or more of the primary node  14 , the primary transceiver  22 , and/or the transmitter  70  has been in service for a specified period of time, e.g., since the primary node  14 , the primary transceiver  22 , and/or the transmitter  70  was installed in the optical communication system  10 , when one or more of the primary node  14 , the primary transceiver  22 , and/or the transmitter  70  has transmitted a quantity of data beyond a data transfer threshold, or some combination thereof, or the like. 
     Referring now to  FIG.  15   , shown therein is a graph of an exemplary embodiment of a band of interest  650  and an AM tone in the optical domain. As shown, the band of interest  650  is centered around an optical frequency  654  of ƒ λ  Also shown is an AM tone 658-1-1 and an AM tone 658-2-1. Both the AM tone 658-1-1 and the AM tone 658-2-1 are amplitude modulated tones centered at ƒ λ  and offset from ƒ λ  by a carrier frequency  662  (carrier frequency  662 - 1  and carrier frequency  662 - 2 , respectively). For example, the AM tone 658-1-1 is offset from ƒ λ  by the carrier frequency  662 - 1  of nƒ c , thereby centering the AM tone 658-1-1 at ƒ λ  + nƒ c  and a conjugate tone 658-1-2 at ƒ λ  - nƒ c . The AM tone 658-1-1 is further comprised of a first component  666 - 1  offset from the AM tone center by +ƒ AM , and is thereby located at ƒ λ  + nƒ c  + ƒ AM  and a second component  670 - 1  offset from the AM tone center by —ƒ AM , thereby located at ƒ λ  + nƒ c  - ƒ AM . The conjugate tone 658-1-2, being a replica of the AM tone 658-1-1, is similarly constructed wherein the conjugate tone 658-1-2 comprises a first component offset from the AM tone center by +ƒ AM , and is thereby located at ƒ λ  - nƒ c  + ƒ AM  and a second component offset from the AM tone center by -ƒ AM , thereby located at ƒ λ  - nƒ c  - ƒ Am . 
     Similarly, the AM tone 658-2-1 is offset from ƒ λ  by the carrier frequency  662 - 2  of +mƒ c , thereby centering the AM tone 658-2-1 at ƒ λ  + mƒ c  and a conjugate 658-2-2 at ƒ λ  - mƒ c . The AM tone 658-2-1 is further comprised of a first component  666 - 2  offset from the AM tone center by +ƒ AM , thereby located at ƒ λ  + mƒ c  + ƒ AM  and a second component  670 - 2  offset from the AM tone center by -ƒ AM , thereby located at ƒ λ  + mƒ c  - ƒ AM . The conjugate tone 658-2-2, being a replica of the AM tone 658-2-1, is similarly constructed wherein the conjugate tone 658-2-2 comprises a first component offset from the AM tone center by +ƒ AM , and is thereby located at ƒ λ  - mƒ c  + ƒ AM  and a second component offset from the AM tone center by -ƒ AM . thereby located at ƒ λ  - mƒ c  - ƒ AM . 
     In one embodiment, the AM tone  658 - 1  and  658 - 2 , after passing through various optical component, thereby experiencing different transmitter impairments, includes an amplitude response  674 , i.e., amplitude response  674 - 1  and amplitude response  674 - 2 , respectively. Note that due to the nature of MZM modulation, the AM tone 658-1-1 and 658-2-1, as well as conjugate tone 658-1-2 and 658-2-2, will be sampled simultaneously. 
     In one embodiment, the AM tone  658 - 1  is an AM tone transmitted at a first period of time and the AM tone  658 - 2  is an AM tone transmitted at a second period of time where the first period of time and the second period of time are different. In one embodiment, additional carrier frequencies  662  may be centered at a frequency offset by a multiple (n or m) of ±ƒ c , e.g., ±2ƒ c , ±3ƒ c , ±4ƒ c , etc. 
     In one embodiment, the carrier frequency  662  may have a step size, i.e., ƒ c , of 100 MHz. In other embodiments, the carrier frequency  662  may have a step size ƒ c  of between about 10 MHz and about 10 GHz. The carrier frequency  662  step size, ƒ c , may be selected based on a desired amplitude response, or frequency response, resolution where a smaller step size, ƒ c , results in a higher resolution and a larger step size, ƒ c,  results in a lower resolution. 
     In one embodiment, the carrier frequency  662  may have a frequency range, that is, has a maximum frequency offset of mƒ c  and a minimum frequency offset of nƒ c . In one embodiment, the frequency range is 18 GHz, whereas in other embodiments the frequency range is a range selected from within a frequency of about 0.5 GHz to about 100 GHz. It is conceivable that the frequency range has an upper bound greater than 100 GHz and that the upper bound is limited by capabilities of the transmitter  70  such that the frequency range is selected from a range based on the frequencies the transmitter  70  is capable of processing. In one embodiment, the frequency range is the bandwidth of an optical signal, or the bandwidth of an optical subcarrier. 
     In one embodiment, the AM signal generator  152  may supply the AM tone  658 - 1  at the first period of time and the AM tone  658 - 2  at the second period of time. The AM signal generator  152  may then change a multiplier (n, m) and supply the AM tone  658  centered at a different frequency with the frequency range. The AM signal generator  152  adjusting the step multiplier (n, m) resulting in multiple AM tones  658  within the frequency range may be referred to as frequency sweeping, e.g., sweeping the AM tone  658  across the band of interest. 
     Referring now to  FIGS.  16 A-D , shown there are graphs of exemplary embodiments of real-world measurements of the amplitude response measured by the ADC  344  and analyzed by the demodulation circuitry  342 . Shown in  FIG.  16 A  is an TEI amplitude response  678 - 1 , shown in  FIG.  16 B  is an TEQ amplitude response  678 - 2 , shown in  FIG.  16 C  is a TMI amplitude response  678 - 3 , and shown in  FIG.  16 D  is a TMQ amplitude response  678 - 4 . As shown in  FIGS.  16 A-D , the frequency step is 0.5 GHz with a frequency range of about 0 GHz to about 60 GHz. 
     Referring now to  FIGS.  17 A-D , shown therein are graphs of exemplary embodiments of an amplitude response calibration  686  based on the amplitude response  678  of  FIGS.  16 A-D , respectively. Shown in  FIG.  17 A  is a TEI amplitude response calibration  686 - 1  based on an inverse of the TEI amplitude response  678 - 1  of  FIG.  16 A , shown in  FIG.  17 B  is a TEQ amplitude response calibration  686 - 2  based on an inverse of the TEQ amplitude response  678 - 2  of  FIG.  16 B , shown in  FIG.  17 C  is a TMI amplitude response calibration  686 - 3  based on an inverse of the TMI amplitude response  678 - 3  of  FIG.  16 C , and shown in  FIG.  17 D  is a TMQ amplitude response calibration  686 - 4  based on an inverse of the TMQ amplitude response  678 - 4  of  FIG.  16 D . 
     In one embodiment, when the amplitude response calibration  686  is not associated with a phase response, the amplitude response calibration  686  for any of TEI, TMI, TEQ, orTMQ shown in  FIGS.  17 A-D  may be used in the shape filter circuits  220 - 1  to  220 - 8  or  252 - 1  to  252 - 8  as pre-compensation for only the amplitude responses. 
     In some embodiments, when the amplitude response calibration  686  has a bandwidth greater than the amplitude responses  678 , for any frequency outside the frequency range of the amplitude responses  678 , the amplitude response calibration  686  will include a frequency cutoff where the amplitude response calibration is set to zero (0). 
     In one embodiment, the amplitude response calibration for each of the TEI amplitude response calibration  686 - 1 , the TEQ amplitude response calibration  686 - 2 , the TMI amplitude response calibration  686 - 3 , and the TMQ amplitude response calibration  686 - 4  also includes a maximum filter attenuation, as set in the demodulation circuitry  342 . The maximum filter attenuation may be a power, in dB, set as a limit for the amplitude response calibration. For example, the maximum filter attenuation may be set to about 8 dB. In one embodiment, the maximum filter attenuation may be set to a power in the range of about 1 dB to about  40  dB. As shown in  FIG.  17   , the maximum filter attenuation is set to 20 dB. In some embodiments, the maximum filter attenuation may be in a range from about 20 dB to 40 dB. In one embodiment, the maximum filter attenuation may be dependent on compensation capability of the shaping filters  220 - 1  to  220 - 8  and the shaping filters  252 - 1  to  252 - 8 . 
     In some embodiments, the amplitude response calibration  686  for each of TEI, TMI, TEQ, and TMQ is a frequency response calibration when the amplitude response calibration  686  is combined with a phase response for each of the TEI, TMI, TEQ, and TMQ optical signals. The frequency response calibration may be referred to as a full frequency response calibration when the amplitude response calibration  686  is combined with the phase response for each of the TEI, TMI, TEQ, and TMQ optical signals. 
     Referring now to  FIGS.  18 A-D , shown therein are graphs of an exemplary embodiment of the retrieved phase response (unwrapped and in radians) derived from each of the measured TEI amplitude response  678 - 1 , TEQ amplitude response  678 - 2 , TMI amplitude response  678 - 3 , and TMQ amplitude response  678 - 4 , respectively. The phase response for each of TEI  720 - 1 , TEQ  720 - 2 , TMI  720 - 3 , and TMQ  720 - 4  is calculated by applying the equations 
     
       
         
           
             ∠ 
             H 
             
               ω 
             
             = 
             − 
             h 
             i 
             l 
             b 
             e 
             r 
             t 
             
               
                 ln 
                 
                   
                     
                       
                         H 
                         ω 
                       
                     
                   
                 
               
             
           
         
       
     
      where 
     
       
         
           
             h 
             i 
             l 
             b 
             e 
             r 
             t 
             
               
                 x 
                 
                   t 
                 
               
             
             = 
             
               1 
               π 
             
             
               
                 
                   ∫ 
                   ∞ 
                   
                     − 
                     ∞ 
                   
                 
                 
                   
                     
                       x 
                       
                         τ 
                       
                     
                     
                       t 
                       − 
                       τ 
                     
                   
                   d 
                   τ 
                 
               
             
           
         
       
     
      to the TEI amplitude response  678 - 1 , TEQ amplitude response  678 - 2 , TMI amplitude response  678 - 3 , and TMQ amplitude response  678 - 4 , respectively. 
     Referring now to  FIG.  19 A , in conjunction with  FIG.  19 B , shown therein is a graph an exemplary embodiment of one transmitter path, e.g., one of TEI, TMI, TEQ, and TMQ, having an amplitude response  740 , and having a simulated frequency-dependent echo response744 on top of the amplitude response  740 . The frequency-dependent echo response  744  may be caused by the nature of various optical components of the transmitter  70 , for example, and may, for example, be from impedance mismatch of the electronic cabling, etc., as previously discussed. 
     The frequency-dependent echo response  744  results in a phase response, which in turn creates ringing  746  vs frequency in the amplitude plot of  FIG.  19 A . It should be noted that the ringing  746 , as identified in  FIG.  19 A , only identifies larger-amplitude ringing in a range of about 5 GHz to about 18 GHz as an example; however, the ringing  746  may extend throughout the frequency range of the amplitude response  740  at greater or lesser amplitudes than the amplitude of the ringing  746  in the range identified. 
     The phase response can be calculated by plugging the amplitude response into Equation 1, and the result, in the time domain, is shown in  FIG.  19 B  overlaid on the original waveform in the time domain to show that Equation 1 can be used to retrieve the phase response. As shown in  FIG.  19 B , a retrieved time-domain response  752  has a short-delay main component  754 , e.g., due to the amplitude impairments of the path (one of TEI, TMI, TEQ, and TMQ), and a smaller echo component  756  at some offset delay  758  due to the phase response. 
     Referring now to  FIGS.  20 A-D , shown therein are graphs of exemplary embodiments of each path I, Q of each polarization X, Y of a calibrated optical signal  760  of the optical signal  764  having eight subcarriers  768  of a single channel. Shown in  FIG.  20 A  is a TEI calibrated optical signal  760 - 1  comprising eight subcarriers  768 - 1  compared to optical signal  764 - 1  without calibration. Shown in  FIG.  20 B  is a TEQ calibrated optical signal  760 - 2  comprising eight subcarriers  768 - 2  compared to optical signal  764 - 2  without calibration. Shown in  FIG.  20 C  is a TMI calibrated optical signal  760 - 3  comprising eight subcarriers  768 - 3  compared to optical signal  764 - 3  without calibration. Shown in  FIG.  20 D  is a TMQ calibrated optical signal  760 - 4  comprising eight subcarriers  768 - 4  compared to optical signal  764 - 4  without calibration. 
     Referring now to  FIG.  21 A , shown therein is a graph of an exemplary embodiment of a measured combined optical signal  800  pre-calibration of frequency response. The optical signal  800  is shown for the components with both paths I, Q and polarizations X and Y combined. As shown, the optical signal  800  includes eight subcarriers  804 . As shown in  FIG.  21 A , the optical signal  800  has a power that fluctuates across a frequency range of approximately 193.68 THz to 193.78 THz as shown by a max power difference  812 - 1  and a min power difference  812 - 2 . The power differences  812  may be effects of impairments introduced to the optical signals by various optical components within the transmitter  70  as described above. Because the power differences  812  are caused by one or more linear time-invariant impairment of the transmitter, the frequency response determination process  600  can be used to calibrate the transmitter and minimize the power differences  812  as shown in  FIG.  21 B . 
     Referring now to  FIG.  21 B , shown therein is a graph of an exemplary embodiment of a measured calibrated optical signal  820 , post-calibration of frequency response. The calibrated optical signal  820  is shown for the both paths I, Q and both polarizations X and Y combined. As shown, the calibrated optical signal  820  includes eight subcarriers  804 , as also shown in  FIG.  21 A . The calibrated optical signal  820 , however, has a power that fluctuates across a frequency range of approximately 193.68 THz to 193.78 THz as shown by a max power difference  824 - 1  and a min power difference  824 - 2 . The power differences  824  as shown in  FIG.  21 B  (post-calibration) are smaller than the power differences  812  as shown in  FIG.  21 A  (pre-calibration). The power differences  824 , compared to the power differences  812 , show a reduction in fluctuations and attenuation resulting in the calibrated optical signal  820  being substantially flat to a high resolution, i.e., closely following an average power  808 . As shown, the smaller power differences  824  result in a higher-quality optical signal being transmitted from the transmitter  70  to the secondary node  18 , thereby allowing the transmitter  70  to transmit data in the optical signal at a faster rate and over longer distances as compared to the pre-calibration optical signal of  FIG.  21 A .Particular embodiments of the subject matter have been described. Other embodiments are within the scope of the following claims. For example, the actions recited in the claims can be performed in a different order and still achieve desirable results. As one example, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some cases, multitasking and parallel processing may be advantageous.