Linearization of Multi-Chirp Predistorted Laser for FMCW Lidar

Abstract

The present invention discloses a system and method for the measurement, predistortion and linearization of an FMCW (frequency modulated continuous wave) lidar chirped laser signal, wherein an I / Q channel of an IF optical signal combining delayed and undelayed versions of the laser signal is generated and used in the process of predistorting the waveform data for linearization.

Description

Technical Field

[0001] The present disclosure relates to LiDAR (Light Detection and Ranging) instrumentation and calibration, in particular to linearization of FMCW (Frequency Modulated Continuous Wave) LiDAR system emissions. Summary of the invention

[0002] According to a first aspect, a system for linearization of a lidar (light detection and ranging) chirped signal is provided, comprising: a first splitter for separating a chirped laser signal from a laser into two optical signals; a delay element for delaying one of the two optical signals to produce a delayed optical signal, the other of the two optical signals being an undelayed optical signal; and an optical 90° hybrid unit for receiving the undelayed and delayed optical signals, and generating a first IF optical signal output and a second IF optical signal output from the undelayed and delayed optical signals, wherein such generation imparts a relative IF phase shift of 90° between the first and second IF optical signal outputs, the first and second IF optical signal outputs corresponding to the I / Q channels of the IF optical signal of the combination of the undelayed and delayed optical signals.

[0003] According to a second aspect, a method for linearizing a lidar (light detection and ranging) chirped signal is provided, the method comprising: separating a chirped laser signal from a laser into two optical signals; delaying one of the two optical signals to produce a delayed optical signal, the other of the two optical signals being an undelayed optical signal; and generating a first IF optical signal output and a second IF optical signal output from the undelayed and delayed optical signals, wherein such generation imparts a relative IF phase shift of 90° between the first and second IF optical signal outputs, the first and second IF optical signal outputs corresponding to the I / Q channels of an IF optical signal that is a combination of the undelayed and delayed optical signals.

[0004] Some embodiments also provide an I channel receiver and a Q channel receiver pair for receiving the first and second IF optical signal outputs and generating I channel and Q channel digital data.

[0005] Some embodiments also provide a processing and driving circuit for receiving the I channel and Q channel digital data, determining the instantaneous phase of the IF optical signal from the I channel and Q channel digital data, pre-distorting the digital chirp waveform data using the instantaneous phase of the IF optical signal, generating new pre-distorted digital chirp waveform data for driving the laser to generate a chirped laser signal with improved linearity, and driving the laser with the new pre-distorted digital chirp waveform.

[0006] In some embodiments, the processing and driving circuit's pre-distortion of the digital chirp waveform data also includes: determining the edge of the chirp segment; determining whether the phase error of the chirp segment is acceptable; and for the chirp segment with unacceptable phase error, generating the new pre-distorted digital chirp waveform data for each data point of the chirp segment.

[0007] In some embodiments, determining the edge of the chirped segment includes: smoothing a copy of the instantaneous phase of the IF optical signal; determining a gradient of the smoothed copy of the instantaneous phase of the IF optical signal; and determining the edge of the chirped segment from a zero point of the gradient.

[0008] In some embodiments, determining whether the phase error of the chirped segment is acceptable includes: smoothing the instantaneous phase of the IF optical signal of the chirped segment to generate a smoothed instantaneous phase of the IF optical signal for each data point of the chirped segment; determining a nominal phase for each data point of the chirped segment; using the nominal phase and the smoothed instantaneous phase of the IF optical signal to determine the phase error for each data point of the chirped segment; using a metric to assign a single value that characterizes the phase error of at least a portion of the chirped segment; and comparing the single value to an acceptable threshold, and wherein generating the new pre-distorted digital chirped waveform data for the chirped segment includes: determining a correction factor for each data point of the chirped segment using the phase error; and determining new pre-distorted chirped waveform data using current chirp waveform data and the correction factor.

[0009] In some embodiments, smoothing the replica of the instantaneous phase of the IF optical signal comprises heavy Savitzky-Golay filtering, wherein smoothing the instantaneous phase of the IF optical signal of the chirped segment comprises Savitzky-Golay filtering using no expansion and a third-order polynomial, wherein the metric is a standard deviation of a weighted phase error of at least a portion of the chirped segment, wherein the correction factor is proportional to the phase error, and wherein determining new pre-distorted chirp waveform data comprises adding the current chirp waveform data to the correction factor.

[0010] In some embodiments, the optical 90° hybrid unit includes: second and third splitters, which are used to separate each of the undelayed and delayed optical signals into corresponding first and second undelayed optical signals and first and second delayed optical signals; first and second combiners, which are used to combine the first undelayed and delayed optical signals to generate a first IF optical signal output and combine the second undelayed and delayed optical signals to generate a second IF optical signal output; and at least one phase shifter, which is used to phase shift one or more of the first delayed optical signal, the second delayed optical signal, the first undelayed optical signal and the second undelayed optical signal.

[0011] In some embodiments, the at least one phase shifter includes: a first phase shifter for imparting a first optical phase shift to a first undelayed optical signal; and a second phase shifter for imparting a second optical phase shift to the first delayed optical signal, wherein the first optical phase shift and the second optical phase shift differ by an equivalent value of a relative optical phase difference of 90°.

[0012] In some embodiments, determining whether the phase error of the chirp segment is acceptable includes evaluating convergence of each iteration of the phase error of the chirp segment using a metric characterizing the phase error of at least a portion of the chirp segment.

[0013] Some embodiments also provide for receiving the first and second IF signal outputs and generating I channel and Q channel digital data.

[0014] Some embodiments also provide receiving the I channel and Q channel digital data, determining the instantaneous phase of the IF optical signal from the I channel and Q channel digital data, pre-distorting digital chirp waveform data using the instantaneous phase of the IF optical signal, generating new pre-distorted digital chirp waveform data for driving the laser to generate a chirped laser signal with improved linearity, and driving the laser with the new pre-distorted digital chirp waveform.

[0015] In some embodiments, generating a first IF optical signal output and a second IF optical signal output from the undelayed and delayed optical signals includes: receiving the undelayed and delayed optical signals, separating each of the undelayed and delayed optical signals into corresponding first and second undelayed optical signals and first and second delayed optical signals, phase shifting one or more of the first delayed optical signal, the second delayed optical signal, the first undelayed optical signal, and the second undelayed optical signal, combining the first undelayed and delayed optical signals to generate a first IF optical signal output, and combining the second undelayed and delayed optical signals to generate a second IF optical signal output.

[0016] In some embodiments, the phase shifting further comprises: imparting a first optical phase shift to the first undelayed optical signal and imparting a second optical phase shift to the first delayed optical signal, wherein the first optical phase shift and the second optical phase shift differ by an equivalent value of a relative optical phase difference of 90°.

[0017] The above and additional aspects and embodiments of the present disclosure will be apparent to those skilled in the art through detailed description of various embodiments and / or aspects in conjunction with the accompanying drawings, a brief description of which will be provided below. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The above and other advantages of the present disclosure will become apparent by reading the following detailed description and referring to the accompanying drawings.

[0019] Figure 1 is a schematic block diagram of a system employing predistortion laser linearization according to an embodiment;

[0020] Figure 2 According to the embodiment, such as Figure 1 The implementation of the optical 90° hybrid unit shown;

[0021] Figure 3 is a block diagram of a process for implementing predistortion laser linearization in a lidar system according to an embodiment; and

[0022] Figure 4 An exemplary desired repeating multi-chirp distribution for a laser signal emitted from a lidar system is shown.

[0023] Although the present disclosure is susceptible to various modifications and alternative forms, specific embodiments or implementations have been shown in the accompanying drawings by way of example and will be described in detail herein. However, it should be understood that the present disclosure is not intended to be limited to the specific forms disclosed. On the contrary, the present disclosure encompasses all modifications, equivalents, and alternatives that fall within the scope of the invention defined by the appended claims. DETAILED DESCRIPTION

[0024] Conventional frequency modulated continuous wave (FMCW) lidars utilize a series of laser frequency sweeps with a constant slope, known as a chirped laser signal and consisting of linear chirped segments, to achieve a high signal-to-noise ratio (SNR) signal in their detection and ranging operations. As the name implies, FMCW lidars utilize frequency modulation of a tunable continuous wave laser to generate a sequence of laser chirped segments for transmission and eventual reception. Although simple in theory, achieving an ideal chirped laser signal in practice is not simple. Even if the data representing the analog waveform used to drive the tunable laser is linear (hereafter referred to as a "digital chirped waveform"), the modulation behavior has associated heating and carrier injection / extraction effects that often result in nonlinear chirped behavior in the actual laser output signal. This affects the SNR and, therefore, the accuracy of the readings generated by the FMCW lidar system.

[0025] An idealized repetitive chirped laser signal is shown in Figure 4 In. Figure 4 As shown, a predetermined sequence of chirp segments, such as chirp segments 1, 2, 3, and 4, constitutes a specific finite chirp distribution with a duration called a chirp period. This chirp distribution is typically composed of alternating "down chirp" and "up chirp" segments of optionally different slopes, which are repeated continuously when the lidar system is in operation. The lidar system drives the laser in a manner that causes the laser to emit an optical frequency that ideally varies according to a repeating linear chirp sequence. The output chirped laser signal is reflected from an external object within a certain range, and the reflected signal is received and processed to generate information about the object, for example, information about the object's position, shape, distance, and / or speed. Because the accuracy and SNR of the process generally depends on the linearity of each chirp segment of the chirped laser signal, and because of nonlinearities caused by the laser not linearly following the drive signal due to electrical carriers or thermal effects, some methods of improving accuracy include determining and storing a "pre-distorted" digital chirp waveform that is specifically constructed to produce a laser chirp signal with less nonlinearity when used to control the drive of the laser.

[0026] For the sake of clarity, the data used to modulate the laser, including the chirp segments that make up the chirp profile used to repeatedly drive the laser, will be referred to hereinafter as a digital chirp waveform, sometimes also referred to as a function generator waveform. It should be noted that because the function generator 1300, the laser driver 1400, and the laser 1100 may all or each operate according to proprietary signaling, data formats, and / or voltage or current levels, the units, size, and format of the digital chirp waveform values ​​within the function generator 1300 and the laser driver 1400 may likewise be proprietary. It should be understood that references to a "digital chirp waveform," as it exists in any of these components, have been appropriately formatted and / or converted, and in particular, it should be understood that any necessary formatting and conversion required to transfer the digital chirp waveform from the microprocessor / FPGA 1200 (in IF phase units, as described below) to the function generator 1300 has been performed accordingly. Furthermore, as will become apparent below, once a digital chirp waveform has been pre-distorted, each chirp segment thereof, while still identifiable as a chirp segment, will no longer be technically linear.

[0027] Some methods that attempt to pre-adjust the modulation to correct for nonlinear chirp in the laser output rely on accurate measurements of the instantaneous laser frequency to determine the nature and magnitude of the nonlinearity that needs to be corrected. However, estimates of the known laser frequency based on the Hilbert transform are slow and inaccurate, especially near the edges where the chirp segments intersect, which is also the critical area that often exhibits the most nonlinearity and therefore determines the overall performance, especially the accuracy, of the lidar system. In addition, in these methods, measurement noise from the receiver, phase noise of the laser, and modulation signal noise all contribute to the apparent nonlinearity of the measurement, which is difficult to distinguish from the actual nonlinearity of the chirp segment of the laser signal that needs to be corrected, which often leads to undesirable linearization results.

[0028] The known methods are generally unable to accurately measure the instantaneous laser frequency, which also hinders the linearization of complex chirped segment sequences. For example, the thermal effect on multiple up-chirp and down-chirp segments with very different chirp segment bandwidths will produce an asymmetric nonlinear chirp segment behavior that is only apparent near the transition edges of the chirp segments of the chirped laser signal, which, as mentioned before, is difficult to accurately determine using known techniques.

[0029] In one known chirp-segment linearization approach, a predistorted modulated digital chirp waveform derived from the shift between a predetermined nominal laser frequency and the instantaneous laser frequency estimated using the Hilbert transform is implemented on individual up-and-down chirp segments. However, the resulting residual nonlinear noise remains high and impractical for long-range lidar systems.

[0030] Reference Figure 1, an exemplary lidar chirp linearization system 1000 utilizing optical processing equivalent to instantaneous laser frequency measurement according to an embodiment will be discussed below. For ease of illustration and understanding, Figure 1 Most of the remaining structure and functionality of the lidar system of the illustrated lidar chirp linearization system 1000 is not shown or described in detail. In this regard, it should be understood that the optical tap between the laser 1100 and the first beam splitter 1110 is used to reserve a relatively small but sufficient amount of optical power for linearization, which is transmitted to the beam splitter 1110 of the linearization system 1000, while the majority of the optical power is used as a laser output signal from the lidar system (not shown) that is actually used in detection and ranging. Therefore, the laser 1100 should be understood to be the main ranging laser used in the lidar system for detection and ranging, and any one or more of the laser driver 1400, the function generator 1300, and the microprocessor / FPGA 1200 can be the same components commonly found in lidar systems, constructed and adapted according to the following, or can be additional components used only for linearization purposes.

[0031] The tunable laser 1100 of the laser radar system and the laser radar chirp linearization system 1000, for example, a distributed Bragg reflector (DBR) laser, a distributed feedback (DFB) laser, a step grating laser, and a laser using an AWG for wavelength selection, which is usually integrated on a PIC (photonic IC), is optically connected to a first optical splitter 1110 (1x2, 2x2 optical coupler, etc.) via a waveguide and a tap (not shown), and the first optical splitter has a delay element 1120 (in Figure 1 and connected via waveguide optics to polarization controller 1130 (on the waveguide arm labeled “SIGNAL” in FIG. Figure 2 The delay element 1120 may be any delay element having a free-space group delay suitable for generating an IF (intermediate frequency) signal (as described below), and may be a delay line, such as, but not limited to, a winding integrated waveguide of constant width or a winding wide multimode waveguide that tapers (widens) to a narrower single-mode waveguide before (after) its turn. In some implementations, such as on-chip implementations using polarization-maintaining waveguides, the polarization controller 1130 is not required. The optical outputs from the delay element 1120 and the polarization controller 1130 are optically combined in the optical 90° hybrid unit 2000, as shown below in combination with Figure 2As shown and described. Four signals are output from the optical 90° hybrid unit 2000 through corresponding waveguides, namely, a pair of I channel signals I+, I- and a pair of Q channel signals Q+, Q-, the I+ / I- pair is connected to the I channel receiver 1140 via a corresponding pair of waveguides, and the Q+ / Q- pair is connected to the Q channel receiver 1150 via a corresponding pair of waveguides. The I channel receiver 1140 and the Q channel receiver 1150 may include, for example, a photodetector, a TIA, and a high-speed ADC (analog-to-digital converter). The electrical outputs and usually digital outputs of the I channel and Q channel receivers are connected to the microprocessor / FPGA 1200. The microprocessor / FPGA 1200 is electrically connected to a function generator 1300, which is connected to a laser driver 1400, which is in turn connected to the laser 1100. It should be noted that the optical portion of the lidar chirp linearization system 1000 can be built entirely on an integrated photonics chip, or entirely using free space optical components (e.g., using a free space beam splitter), or any combination of these two components. In this regard, in some embodiments, waveguides between elements may or may not be present. It should also be noted that in some embodiments, the optical portion of the LiDAR chirp linearization system 1000 can be implemented entirely on an integrated photonic chip by using directional couplers, tapered couplers, MMIs as splitters and combiners, microheaters as phase shifters, and long winding spiral waveguides for delay elements.

[0032] The function of the lidar chirp linearization system 1000 is to form a laser linearization loop, which measures the instantaneous frequency of the chirped laser signal of the laser 1100, determines what kind of nonlinearity the chirped laser signal exhibits, and corrects its chirp linearity by updating the chirp distribution of the digital chirp waveform used to drive the laser 1100.

[0033] The laser 1100 outputs a chirped laser signal driven by a digital chirp waveform used by a laser driver 1400 to drive or modulate the laser 1100. A first optical splitter 1110 receives the chirped laser signal from the laser 1100 via a tap (not shown) and splits the input laser power into a "LO" (local oscillator) signal and a "SIGNAL" signal through respective paths. If desired, a polarization controller 1130 is configured to ensure that the polarizations on the LO and SIGNAL paths are the same at the I channel receiver 1140 and the Q channel receiver 1150. The optical signal passing through the SIGNAL path is delayed by a delay element 1120, which may be a delay line having an equivalent free space group delay of 0.1 to 5 meters, or any other delay value large enough to delay the optical signal to allow accurate I and Q channel detection of the IF signal discussed below and small enough to reduce optical losses in the delay element. It should be noted that the delay element 1120 and the polarization controller can be interchanged on the LO and SIGNAL paths, or both can be present on a single LO or SIGNAL path, as long as there is an appropriate delay difference between the two optical inputs to the optical 90° hybrid unit 2000 and the polarizations of the two optical inputs are matched in the sense described above. The optical SIGNAL and LO signals (in which delays have been incorporated and whose polarizations have been controlled or maintained) are input to the two inputs of the optical 90° hybrid unit 2000.

[0034] Reference Figure 2 , the structure and function of an exemplary optical 90° hybrid unit 2000 according to an embodiment will be discussed below.

[0035] The LO input of the optical 90° hybrid unit 2000 connected to the LO signal path is optically connected to the second optical splitter 2100 (1x2, 2x2 optical coupler, etc.) via a waveguide, and the signal input of the optical 90° hybrid unit 2000 connected to the SIGNAL signal path is optically connected to the third optical splitter 2200 (1x2, 2x2 optical coupler, etc.) via a waveguide. The first output of the second optical splitter is optically connected to the first phase shifter 2300 via a waveguide, and the first output of the third optical splitter 2200 is optically connected to the second phase shifter 2400 via a waveguide. The second output of each of the second optical splitter 2100 and the third optical splitter 2200 is connected to the first combiner 2500 (e.g., 2x2 MMI or 50 / 50 directional coupler) via a waveguide. The output of each of the first phase shifter 2300 and the second phase shifter 2400 is connected to the second combiner 2600 (e.g., 2x2 MMI or 50 / 50 directional coupler) via a waveguide. Each of the first combiner 2500 and the second combiner 2600 outputs a pair of optical signals, the first combiner 2500 outputs a pair of I channel signals I+, I−, and the second combiner 2600 outputs a pair of Q channel signals Q+, Q−.

[0036] The function of the optical 90° hybrid unit 2000 is to generate two combinations of an optical signal (LO) and a delayed version of the optical signal (SIGNAL). Due to the delay between the LO and SIGNAL signals, when combined in the optical 90° hybrid unit 2000, they have slightly different frequencies, thereby producing a combination that presents an IF (intermediate frequency) signal. The optical 90° hybrid unit 2000 applies a relative optical phase shift to one of the combinations for producing an I / Q signal pair with a relative IF signal phase shift of 90°. The phase of the IF signal, which is directly associated with the instantaneous frequency of the optical signal of the laser, is measured. It should be noted that although the instantaneous frequency of the laser can be determined digitally from the phase of the IF signal, since the phase of the IF signal is proportional to the instantaneous frequency, linearization can be performed with reference only to the phase of the IF signal without any additional calculation of the actual frequency, as described below.

[0037] The optical signal (LO) passing through the LO input of the optical 90° hybrid unit 2000 is separated into two signals by the second optical splitter 2100, and the delayed version of the optical signal (SIGNAL) passing through the signal input of the optical 90° hybrid unit 2000 is also separated into two signals by the third optical splitter 2200. The first version of the delayed (SIGNAL) optical signal and the undelayed (LO) optical signal are combined in the first combiner 2500 without applying any phase shift thereto, while the second version of the delayed (SIGNAL) optical signal and the undelayed (LO) optical signal each pass through a phase shifter before being combined. The unphase-shifted combination of the optical signals emerges from the first combiner 2500 and the optical 90° hybrid unit 2000 as an I+ / I- pair, while the phase-shifted combination of the optical signals emerges from the second combiner 2600 and the optical 90° hybrid unit 2000 as a Q+ / Q- pair.

[0038] The purpose of the phase shifters 2300 and 2400 is to provide a 90° IF signal phase shift between the I+ / I- channel and the Q+ / Q- channel. In order to make the IF signal of the Q+ / Q- pair have a relative IF signal phase shift of 90° relative to the I+ / I- pair, the optical phase shift provided by the first phase shifter 2300 and the second phase shifter 2400 are arranged so that the difference between the optical phase shifts they each impart is equal to an optical phase shift of 90°. It should be understood that in the context here, a relative phase difference of 90° is equal to any relative phase difference of 90°+n*360° (where n is an integer). For example, the first phase shifter 2300 can be set to shift the first output of the second beam splitter 2100 by an optical phase shift of 180°, while the second phase shifter 2400 can be set to shift the first output of the third beam splitter 2200 by an optical phase shift of 90°. Thus, the resulting IF signal of the Q+ / Q- pair will be phase shifted 90° relative to the IF frequency of the I+ / I- pair. Since only the IF signal phase shift relative to 90° between the Q+ / Q- and I+ / I- pairs is important, any combination of first phase shifter 2300 and second phase shifter 2400 that impart optical phase shifts 90° apart in the optical phase shift may be used. In some embodiments, only a single phase shifter with a 90° optical phase shift is used (in Figure 2LO or lower SIGNAL path in such an embodiment). However, in such an embodiment, the absence of a phase shifter on the other of the upper or lower paths would introduce an amplitude imbalance, so in some embodiments there are two phase shifters 2300, 2400, even if one of the phase shifters is only a "pseudo phase shifter" (set to 0°) that does not change the phase but still introduces a loss of balance. In order to obtain a perfect I / Q signal, the phase shifters need to provide an exact 90° IF phase offset from the I+ / I- channels to the Q+ / Q- channels. In practice, this is fine-tuned after the device is manufactured. It should also be noted that since the Q+ / Q- signals differ from the I- / I+ signals only in their relative IF phase, Figure 2 The signs in the can be reversed and the phase shift is inverted, or the position of the phase shifters 2300, 2400 is moved to the waveguide leading to the first combiner 2500, and the phase shift is inverted, and other similar arrangements that will be understood by those skilled in the art. In general, any one or more of all four optical signals leaving the second optical splitter 2100 and the third optical splitter 2200 can be appropriately phase shifted to produce I+ / I- and Q+ / Q- signals.

[0039] Since the 90° relative phase of the combined optical signal induced by the phase shifter results in a 90° relative shift of the resulting IF signal at the output of the combiner, a usable I / Q signal pair of the IF signal is produced, independent of the actual frequency difference, which may vary as a result of any non-linearity in the actual chirped segment. This is particularly useful when the chirped segment produced in the output signal deviates significantly from the desired chirped signal, especially near the chirped segment edges, as it allows the actual instantaneous IF phase corresponding to the actual instantaneous optical frequency to be measured.

[0040] As will be apparent from the foregoing, the function of the optical 90° hybrid unit 2000 is to generate I and Q channel versions of the IF signal resulting from a combination of the undelayed and delayed signals.

[0041] The I+ / I and Q+ / Q signal pairs output from the optical 90° hybrid unit 2000 are measured by I-channel and Q-channel receivers (1140 and 1150), which convert the optical I and Q signals into digital electrical signals, which are then forwarded to the microprocessor / FPGA 1200. In some embodiments, the I-channel receiver 1140 and the Q-channel receiver 1150 include photodetectors for converting optical power into current, transimpedance amplifiers (TIAs) for converting current into voltage, and analog-to-digital converters (ADCs) for generating digital data from the voltage. I / Q detection, and in particular analysis of the instantaneous phase of the IF signal, provides a very accurate measurement that corresponds directly to the instantaneous frequency, which forms the basis of the linearization process. The microprocessor / FPGA 1200 determines a new pre-distorted digital chirp waveform that results in improved linearization of the optical output of the laser 1100, as described below in conjunction with Figure 3 In some embodiments, the microprocessor / FPGA 1200 feeds the new digital chirp waveform (formatted and / or converted as needed) to the function generator 1300 and cooperates with it to control the laser driver 1400 to modulate the laser 1100 according to the new pre-distorted digital chirp waveform. The function generator 1300 stores a buffered waveform to be provided to the laser driver 1400, which generates an instantaneously changing analog drive current (or voltage) to modulate the frequency of the laser 1100.

[0042] Function generator 1300 stores the entire periodic chip distribution as a digital chirp waveform, for example, with Figure 4 1, 2, 3, and 4 in the laser radar system and is used to generate a digital chirp waveform of the chirp segment, and outputs the buffered (and replayed) waveform to the laser driver 1400 for modulating the laser 1100 during active operation of the laser radar system. In some embodiments, the function generator 1300 is part of and / or integrated with the microprocessor / FPGA 1200, while in other embodiments the function generator 1300 is part of and / or integrated with the laser driver 1400.

[0043] In some embodiments, unbalanced I channel receivers 1140 and Q channel receivers 1150 are used instead of balanced I channel receivers 1140 and Q channel receivers 1150, each of which accepts only a single unbalanced input. In those embodiments, only a single output of each of the first combiner 2500 and the second combiner 2600 is output from the optical 90° hybrid unit 2000 as a respective single unbalanced I+ and Q+ signal (or unbalanced I- and Q- signal) for detection by the respective unbalanced I channel receivers 1140 and Q channel receivers 1150. It should be understood that even in the case of balanced I channel receivers 1140 and Q channel receivers 1150, there may be an imbalance between I- and I+ or Q- and Q+ in the optical path leading to the receivers 1140, 1150, or the imbalance may be caused by the receivers 1140, 1150 themselves. In most cases, any unwanted imbalance can be mitigated by processing in the microprocessor / FPGA (1200).

[0044] Reference Figure 3 , an exemplary process 3000 of pre-distortion according to an embodiment to improve the linearization of a chirped optical signal output from the laser 1100 will be discussed below.

[0045] Figure 3 The process 3000 shown in can be run in parallel with the normal operation of the lidar system, that is, all structures and functions of the lidar system (not shown) performing detection and ranging are online at the same time. Figure 3 A process of 3000 cycles is used to analyze and linearize the entire chirp distribution, e.g. Figure 4 The chirp segments 1 to 4 can be repeated as described below. It should be noted that due to Figure 3 The data blocks read from the I and Q channel receivers should include an amount sufficient to ensure that the entire chirp distribution is captured, plus an amount sufficient to smooth and determine the edges of the chirp segments, as described below. In some embodiments, the amount of data received from the I channel receiver 1140 and the Q channel receiver 1150 corresponds to an amount of data within a duration of 1.5 to 3 times the entire chirp period of the chirp distribution.

[0046] In some embodiments, such as Figure 1 The microprocessor / FPGA implementation shown Figure 3 All steps of the linearization process 3000 are repeated. Because of the nonlinearity in the relationship between the chirp waveform produced by the laser 1100 and the resulting chirp distribution, which is why correction is required, the exact effect of any adjustment of the digital chirp waveform is generally unknown, and therefore linearization often involves multiple iterations of the entire process 3000.

[0047] The linearization process 3000 can be performed as a calibration, and the predistorted digital chirp waveform stored in the persistent memory is stored, for example, in the function generator 1300 or elsewhere (the storage step is not explicitly shown). For example, such calibration can be performed periodically or continuously when the laser radar system is manufactured, during periodic and / or regular intervals during the operating life of the laser radar system, or at system startup just before active use of the laser radar system, and / or during a session of using the laser radar system in the field. Values ​​that exhibit improved linearization can also be calibrated and stored in a lookup table (LUT) provided with the laser radar system, the LUT containing separate predistorted chirp distributions customized for different possible external conditions (e.g., for different temperature ranges or for specific temperatures). When the laser radar system is operated under specific external conditions, the predistorted digital chirp distribution corresponding to the specific external condition is found and obtained using the range in the LUT that the specific condition falls into or the specific value in the LUT that the condition is closest to. In some embodiments, these distributions can be updated during the service life of the laser radar system, or custom distributions can be added to the LUT by the user or the laser radar system. In some embodiments, the linearization process can be performed in real time, where I / Q data is collected in real time while the lidar system is actively operating to perform detection and ranging. In such an embodiment, once linearization of all chirp segments is complete (or acceptable), the digital chirp waveform is updated and thereafter can be repeated indefinitely while the lidar system is in operation to maintain and / or continuously improve the linearization.

[0048] First, at 3010, digital I / Q data is read from the I channel receiver 1140 and the Q channel receiver 1150 until a data block of sufficient duration has been read and stored, e.g., as a series of data points stored in an array or memory. At 3020, the instantaneous phase of the I / Q signal (intermediate frequency (IF) signal) representing the instantaneous laser frequency is determined from the data points, e.g., by calculating instantaneous IF phase = Arctan (Q / I). This is performed for all data points of all chirp segments of the block. At this point, it should be emphasized that the phase of the IF signal corresponds to the instantaneous optical frequency, as follows:

[0049]

[0050] in is the instantaneous phase of the IF signal, τ is the group delay time of the delay element, and f laser is the instantaneous frequency of the laser 1100. Since the IF phase corresponds directly to the instantaneous optical frequency, so when the chirp direction changes, that is, when the slope of the optical frequency with respect to time changes sign, the sign of the slope of the IF phase with respect to time also changes sign and thus instantaneously becomes zero.

[0051] Then, at 3030 (see Figure 4 , which shows multiple chirp segments for various bandwidths and chirp segment durations), the chirp segment edges or endpoints within the block are determined by finding the zero crossings of the gradient (slope) of a smoothed version of the IF phase. Because there may be significant noise in the data due to noise sources unrelated to the chirp nonlinearity (e.g., laser phase noise, receiver noise, and function generator noise), in some embodiments, heavy smoothing is applied to the temporary copy of the IF phase to remove them in the process of determining the chirp segment edges. The smoothing algorithm can be any type of digital low-pass filter such as a moving average or a low-order polynomial (e.g., n=1~5) Savitzky-Golay filter, whose window size is defined by the user to optimize efficiency and accuracy, etc. In a typical chirped lidar signal, there will be multiple zero crossings in the slope of the IF phase, which correspond to different turning points at the edge of each chirp segment. In some embodiments, one of the zero crossings is arbitrarily assigned as the starting point of the repeating chirp distribution (typically, corresponding to the starting point of the first chirp segment in the buffer of the function generator 1300), for example, the first zero point at the beginning of the chirp distribution includes segments 1, 2, 3, and 4, together with Figure 4 The chirp period is shown. In some embodiments, the gradient (slope) of the smoothed version of the IF phase is itself smoothed before finding the zero point.

[0052] In some implementations using floating nominal values ​​(see below), starting from this starting point and proceeding through the block, each chirp segment of the chirp distribution of the block is isolated into separate IF phase segments based on the zero crossings found.

[0053] In some embodiments using fixed nominal values ​​(see below), starting from the starting point, the remaining edges of the chirp distribution are determined from a set of user-defined data that fixes them relative to the starting point. In some embodiments, in addition to the starting point, an ending point is determined, and the remaining edges of the chirp distribution are determined from a set of user-defined data that fixes the edges based on both the starting point and the ending point. For example, if a block includes four chirp segments of equal length, the starting and ending edges of the group of four chirp segments will be determined to have the above-mentioned zero crossings, but the edges between the chirp segments can be calculated according to the user-defined data as being at one-quarter, one-half, and three-quarters points along the entire group of four chirp segments.

[0054] In some embodiments, rather than determining the chirp segment edges from the IF phase data, the determine chirp segment edges step 3030 uses external data (eg, an external clock) to correlate points in the stored IF phase data to known edges of the chirp segment.

[0055] Each chirp segment is then individually smoothed at 3040 using a digital low pass filter, which may be the same or different than the filter used to determine the chirp edges at 3030, but is performed treating the ends of the chirp segments as fixed limits. In some embodiments, a Savitzky-Golay filter with no expansion and a third order polynomial may be used to better match the edge behavior of the thermally induced delay response.

[0056] Once the edges of the chirp segments of the chirp distribution within the block are determined and the chirp segments are smoothed, the nominal phase of each data point of each chirp segment is determined at 3050. The nominal phase represents the expected chirp waveform to which the measured value is compared.

[0057] In some embodiments, a fixed nominal value is determined. The starting nominal value of a chirped segment is taken from the first value of the smoothed IF phase of the chirped segment. The ending nominal value of the chirped segment is then determined from the expected IF phase shift of the chirped segment, which is added to the starting nominal value of the IF phase of the chirped segment. For an upward-tilted chirped segment, the expected phase shift is positive, while for a downward-tilted chirped segment, the expected phase shift is negative. The expected IF phase shift can be calculated from the expected frequency shift of the chirped segment and equation (1). The nominal phase of the next chirped segment and subsequent segments is calculated based on the last point of the nominal phase of the previous segment plus the expected IF phase. Therefore, an implementation scheme utilizing a fixed nominal value method optimizes chirp linearity based on a fixed chirp segment bandwidth using a fixed array of all nominal chirp values.

[0058] In some embodiments, a floating nominal method is used. In these embodiments, the starting and ending nominal values ​​of a chirp segment are taken from the smoothed IF phase of the chirp segment endpoints, and the nominal values ​​between these endpoints are linearly interpolated. It should be noted that since the endpoints of each chirp segment are defined by the zero point of the smoothed IF phase, these starting and ending nominal values ​​of the chirp segment correspond to the maximum and minimum values ​​of the smoothed IF phase of the chirp segment (and vice versa). Therefore, embodiments utilizing the floating nominal method optimize linearity, but do not fix the chirp waveform to a specific absolute phase point, nor to any fixed chirp segment bandwidth. In some embodiments involving multiple iterations, the starting and ending nominal values ​​of the chirp segment are determined from the weighted average of the smoothed IF phases of the chirp segment endpoints of the current iteration and the previous iteration.

[0059] Once the nominal phase for each data point of each chirp segment is determined or retrieved at 3050, the phase error distribution for each data point of each chirp segment is calculated at 3060. For each data point of each chirp segment, the phase error is determined as:

[0060] Phase error = nominal phase – smoothed IF phase (2)

[0061] The standard deviation of this phase error for each chirp segment (or a portion thereof) can then be used as a metric to determine whether the chirp segment is sufficiently linear at the branch point 3070, where each chirp segment is processed separately and can proceed along a different branch. If the standard deviation of the phase error for a particular chirp segment (or a portion thereof) is below a specific threshold defined by the user, the process determines that the chirp segment is acceptable and no correction is performed on the chirp segment. In some embodiments, only the standard deviation of the phase error for a portion of each chirp segment (e.g., the middle portion of each chirp segment) is used as a metric. In some embodiments, the standard deviation of the weighted phase error is used as a metric, where the phase error at each point along at least a portion of the chirp segment is weighted by a weighting function. In some embodiments, instead of calculating the phase error from the difference between the nominal phase and the smoothed IF phase, the phase error is determined as the ratio of the nominal phase to the smoothed IF phase.

[0062] If the standard deviation of the phase error for a particular chirp segment is above a user defined threshold, then branch point 3070 determines that the phase error is unacceptable and the linearization process continues to calculate new data for the chirp segment of the digital chirp waveform to replace the data currently used by the function generator. First, a correction factor is determined at 3080 for each data point in the chirp segment, which is determined as:

[0063] Correction factor = phase error * sensitivity (3)

[0064] In some embodiments, the sensitivity is a user-defined constant, similar to the gain of a feedback loop. This is particularly applicable when the entire linearization process 3000 is iteratively repeated to optimize linearity. In some embodiments, the constant is different for different chirp segments of the chirp distribution. For example, a chirp with a higher bandwidth may have a lower sensitivity. In embodiments with multiple iterations, the sensitivity can also be set and adjusted to control the convergence speed. In some embodiments, the sensitivity can vary as a function of the slope of the IF phase, the proximity to the initial or trailing edge of the chirp, the sign of the gradient, etc., rather than a constant. In other embodiments, the correction factor is a function of the phase error that has been determined to converge to an ideal value in fewer iterations. In some embodiments, such as those with a phase error determined by a ratio, a dimensionless and / or multiplicative correction factor is determined.

[0065] Once the correction factor for each data point of the chirp segment is determined, a new digital chirp waveform is determined from the correction factor at 3090 for each chirp segment:

[0066] New waveform = old waveform + correction factor (4)

[0067] Here, the new digital chirp waveform data is stored in units associated with the IF phase, but must be converted to waveform data suitable for use in the function generator 1300 before transmission. In some embodiments that utilize a phase error in the form of a ratio and utilize a dimensionless multiplication correction factor, the old waveform is multiplied by the correction factor and replaced with the result. In some embodiments, the value selected for sensitivity or generally for the correction factor is determined taking into account the unit and / or format (e.g., various bit formats) so that the correction factor can be added directly to the waveform data in the function generator 1300 rather than replacing it. In some embodiments, values ​​that fall outside the acceptable range of the function generator 1300 are fixed at the minimum or maximum acceptable value.

[0068] Therefore, at 3100, new digital chirp waveform data for each chirp segment having unacceptable phase error is corrected, converted, and updated in the function generator, while digital chirp waveform data associated with any chirp segment of the chirp distribution having acceptable error remains unchanged in the function generator.

[0069] Once all chirp segments of the chirp profile have passed through the process of branch point 3070, the process checks at 3110 whether to subject the chirp profile to another iteration of the entire process 3000: if "yes", the process 3000 returns to 3010 to read digital I / Q data from the I channel receiver 1140 and the Q channel receiver 1150; if "no", the process 3000 ends. In some embodiments, the process always answers 3110 affirmatively, repeating the process 3000 loop indefinitely until the user overrules and ends the process 3000. In some embodiments, a counter is used to count a predetermined fixed number of cycles that the process 3000 will go through. In other embodiments, the linearization process 3000 is iteratively performed to continuously improve the linearity of the predistorted digital chirp waveform, and is repeated until: 1) the standard deviation of the phase error of each chirp segment has converged and fluctuates to a very small value defined by the user, or 2) the standard deviation reaches a satisfactory lower threshold also defined by the user, or it may be repeated until any other criteria regarding the phase error and its level or convergence are met. In some embodiments, a combination of the above conditions is used in 3110 to determine whether to continue to another iteration or end the process.

[0070] although Figure 3The branch point 3070 process has been described as being based on the standard deviation of the phase error of the chirp segment, but other criteria may be used to determine whether a particular chirp segment is sufficiently linear to decide whether a correction is to be made. Where multiple iterations are performed, the convergence criteria may be determined individually and tracked for each chirp segment. In such an embodiment, for purposes of 3070, a chirp segment that has met the convergence criteria for each iteration (e.g., a very small fluctuation in a value defined by the user) is considered to have an acceptable phase error. In some embodiments, both the convergence criteria and the criteria are used by the branch point 3070 process.

[0071] although Figure 3 The process of branch point 3070 has been described as processing each chirp segment individually, but in some embodiments, the process of branch point 3070 evaluates whether the phase error of each chirp segment is acceptable, and if the phase error of any chirp segment is unacceptable, the linearization process continues to calculate new data for all chirp segments. In some embodiments, for example, when a predetermined fixed number of cycles or iterations of process 3000 are to be performed, the process of branch point 3070 can be completely eliminated, and process 3000 can proceed directly from the step of determining phase error 3060 to the step of determining correction factors 3080 for all chirp segments.

[0072] although Figure 3 The process of branch point 3070 has been described as processing each chirp segment according to a metric that characterizes the phase error of each individual chirp segment, but in some embodiments, the process of branch point 3070 evaluates a single metric that characterizes the phase errors of all chirp segments together, and determines whether the phase errors of all chirp segments as a whole are acceptable. In such an embodiment, all chirp segments either undergo linearization collectively or do not undergo linearization.

[0073] Although the linearization process 3000 described above includes heavy smoothing of the IF phase data in the step of determining chirp edges 3030, in some embodiments, some smoothing is applied separately to the I and Q data before calculating the IF phase according to the above equation when determining the IF phase 3020. In such embodiments, the amount of smoothing in the steps of determining chirp edges 3030 and smoothing chirp segments 3040 can be reduced or appropriately changed.

[0074] It should be understood that interpolation may be performed as necessary to account for the possibility of differences between the sampling rates of I channel receiver 1140 and Q channel receiver 1150 and the data update rate of function generator 1300.

[0075] It should be understood that the components of the lidar system and lidar linearization system 1000 in cooperation therewith may operate as part of a single instrument or device, or may operate as part of multiple interconnected devices working together either nearby or remotely, or any combination thereof.

[0076] The linearization process 3000 may be performed by a processing device, for example Figure 1 The microprocessor / FPGA 1200 or any other similar device(s), which may use one or more application specific integrated circuits (ASICs), microcontrollers, general purpose computer systems, digital signal processors, programmable logic devices (PLDs), field programmable logic devices (FPLDs), etc., as understood by technicians in the optical, networking, software, and computing fields, and programmed according to the teachings shown and described herein.

[0077] In addition, two or more computing systems or devices may replace any one of the processors or controllers described herein. Therefore, the principles and advantages of distributed processing, such as redundancy, replication, etc., may also be implemented as needed to improve the robustness and performance of the processors or controllers described herein.

[0078] The operations of the exemplary linearization method can be performed by machine-readable instructions. In these examples, the machine-readable instructions include an algorithm for execution by (a) a processor, (b) a controller, and / or (c) one or more other suitable processing devices. The algorithm can be embodied in software stored on a tangible medium, such as a flash memory, a CD-ROM, a floppy disk, a hard disk drive, a digital video (universal) disk (DVD), or other storage device, but a person of ordinary skill in the art will readily understand that the entire algorithm and / or portions thereof may be selectively executed by a device other than a processor and / or embodied in firmware or dedicated hardware in a well-known manner (e.g., it may be implemented by an application-specific integrated circuit (ASIC), a programmable logic device (PLD), a field programmable logic device (FPLD), discrete logic, etc.). For example, any or all of the component processes or steps of the linearization method may be implemented by software, hardware, and / or firmware. In addition, some or all of the represented machine-readable instructions may be implemented manually.

[0079] While particular implementations and applications of the present disclosure have been shown and described, it should be understood that the disclosure is not limited to the precise construction and composition disclosed herein and that various modifications, changes and variations may be apparent from the foregoing description without departing from the spirit and scope of the invention as defined in the appended claims.

Claims

1. A system for linearizing a laser radar chirp signal, comprising: a first optical splitter for separating a chirped laser signal from a laser into two optical signals; an optical delay element for imparting a known delay to one of the two optical signals to generate a delayed optical signal, the other of the two optical signals being an undelayed optical signal; and Optical 90° hybrid unit, which is used for receiving the undelayed and delayed optical signals, and generating a first IF optical signal output and a second IF optical signal output from the undelayed and delayed optical signals, Wherein such generation imparts a relative IF phase shift of 90° between first and second IF optical signal outputs corresponding to I / Q channels of a combined IF optical signal of said undelayed and delayed optical signals.

2. The system of claim 1 further comprising an I channel receiver and a Q channel receiver pair for receiving the first and second IF optical signal outputs and generating I channel and Q channel digital data.

3. The system according to claim 2, further comprising: Processing and drive circuits for receiving the I channel and Q channel digital data, determining the instantaneous phase of the IF optical signal from the I channel and Q channel digital data, pre-distorting the digital chirp waveform data using the instantaneous phase of the IF optical signal to generate new pre-distorted digital chirp waveform data for driving the laser to generate a chirped laser signal with improved linearity, and The laser is driven with the new pre-distorted digital chirp waveform.

4. The system of claim 3, wherein pre-distorting the digital chirp waveform data performed by the processing and driving circuit comprises: determining the edges of the chirp segment; determining whether a phase error of the chirp segment is acceptable; and For chirp segments where the phase error is unacceptable, The new pre-distorted digital chirp waveform data is generated for each data point of the chirp segment.

5. The system of claim 4, wherein determining an edge of a chirp segment comprises: smoothing a replica of the instantaneous phase of the IF optical signal; determining a gradient of a smoothed copy of the instantaneous phase of the IF optical signal; and The edges of the chirp segment are determined from the zero points of the gradient.

6. The system of claim 4, wherein determining whether the phase error of the chirp segment is acceptable comprises: smoothing the instantaneous phase of the IF optical signal of the chirped segment, generating a smoothed instantaneous phase of the IF optical signal for each data point of the chirped segment; determining a nominal phase for each data point of the chirp segment; determining a phase error for each data point of the chirp segment using the nominal phase and the smoothed instantaneous phase of the IF optical signal; using a metric, assigning a single value characterizing a phase error of at least a portion of the chirp segment; and comparing the single value to an acceptance threshold, and The step of generating the new pre-distorted digital chirp waveform data for the chirp segment includes: Determining a correction factor for each data point of the chirp segment using the phase error; and New pre-distorted chirp waveform data is determined using the current chirp waveform data and the correction factor.

7. The system of claim 6, wherein smoothing the instantaneous phase of the IF optical signal of the chirped segment comprises using Savitzky-Golay filtering without expansion and a third-order polynomial, wherein the metric is a standard deviation of a weighted phase error of at least a portion of the chirped segment, wherein the correction factor is proportional to the phase error, and wherein determining new pre-distorted chirped waveform data comprises adding the current chirped waveform data to the correction factor.

8. The system of claim 1, wherein the optical 90° hybrid unit comprises: second and third optical splitters for separating each of the undelayed and delayed optical signals into respective first and second undelayed optical signals and first and second delayed optical signals; first and second combiners for combining the first undelayed and delayed optical signals to generate a first IF optical signal output and combining the second undelayed and delayed optical signals to generate a second IF optical signal output; and At least one phase shifter is configured to phase shift one or more of the first delayed optical signal, the second delayed optical signal, the first undelayed optical signal, and the second undelayed optical signal.

9. The system of claim 8, wherein the at least one phase shifter comprises: a first phase shifter for imparting a first optical phase shift to the first undelayed optical signal; and a second phase shifter for imparting a second optical phase shift to the first delayed optical signal, An equivalent value of a relative optical phase difference in which the first optical phase shift and the second optical phase shift differ by 90°.

10. The system of claim 4, wherein determining whether the phase error of the chirp segment is acceptable comprises evaluating convergence of each iteration of the phase error of the chirp segment using a metric characterizing the phase error of at least a portion of the chirp segment.

11. A method for linearizing a laser radar chirp signal, the method comprising: separating a chirped laser signal from a laser into two optical signals; Using an optical delay element to impart a known delay to one of the two optical signals to produce a delayed optical signal, the other of the two optical signals being an undelayed optical signal; and generating a first IF optical signal output and a second IF optical signal output from the undelayed and delayed optical signals, Wherein such generation imparts a relative IF phase shift of 90° between first and second IF optical signal outputs corresponding to I / Q channels of a combined IF optical signal of said undelayed and delayed optical signals.

12. The method of claim 11 further comprising receiving the first and second IF optical signal outputs and generating I channel and Q channel digital data.

13. The method according to claim 12, further comprising: receiving the I channel and Q channel digital data, determining the instantaneous phase of the IF optical signal from the I channel and Q channel digital data, pre-distorting the digital chirp waveform data using the instantaneous phase of the IF optical signal to generate new pre-distorted digital chirp waveform data for driving the laser to generate a chirped laser signal with improved linearity, and The laser is driven with the new pre-distorted digital chirp waveform.

14. The method according to claim 13, wherein pre-distorting the digital chirp waveform data further comprises: determining the edges of the chirp segment; determining whether a phase error of the chirp segment is acceptable; and For chirp segments where the phase error is unacceptable, The new pre-distorted digital chirp waveform data is generated for each data point of the chirp segment.

15. The method of claim 14, wherein determining an edge of a chirp segment comprises: smoothing a replica of the instantaneous phase of the IF optical signal; determining a gradient of a smoothed copy of the instantaneous phase of the IF optical signal; and The edges of the chirp segment are determined from the zero points of the gradient.

16. The method of claim 14, wherein determining whether the phase error of the chirp segment is acceptable comprises: smoothing the instantaneous phase of the IF optical signal of the chirped segment, generating a smoothed instantaneous phase of the IF optical signal for each data point of the chirped segment; determining a nominal phase for each data point of the chirp segment; determining a phase error for each data point of the chirp segment using the nominal phase and the smoothed instantaneous phase of the IF optical signal; using a metric, assigning a single value characterizing a phase error of at least a portion of the chirp segment; and comparing the single value to an acceptance threshold, and The step of generating the new pre-distorted digital chirp waveform data for the chirp segment includes: Determining a correction factor for each data point of the chirp segment using the phase error; and New pre-distorted chirp waveform data is determined using the current chirp waveform data and the correction factor.

17. The method of claim 16, wherein smoothing the instantaneous phase of the IF optical signal of the chirped segment comprises using Savitzky-Golav filtering without expansion and a third-order polynomial, wherein the metric is a standard deviation of a weighted phase error of at least a portion of the chirped segment, wherein the correction factor is proportional to the phase error, and wherein determining new pre-distorted chirped waveform data comprises adding the current chirped waveform data to the correction factor.

18. The method of claim 11, wherein generating a first IF optical signal output and a second IF optical signal output from the undelayed and delayed optical signals comprises: receiving the undelayed and delayed optical signals, separating each of the undelayed and delayed optical signals into respective first and second undelayed optical signals and first and second delayed optical signals, phase shifting one or more of the first delayed optical signal, the second delayed optical signal, the first undelayed optical signal, and the second undelayed optical signal, combining the first undelayed and delayed optical signals to generate a first IF optical signal output, and The second undelayed and delayed optical signals are combined to generate a second IF optical signal output.

19. The method of claim 18, wherein the phase shifting further comprises: imparting a first optical phase shift to the first undelayed optical signal, imparting a second optical phase shift to the first delayed optical signal, An equivalent value of a relative optical phase difference in which the first optical phase shift and the second optical phase shift differ by 90°.

20. The method of claim 14, wherein determining whether the phase error of the chirped segment is acceptable comprises evaluating convergence of each iteration of the phase error of the chirped segment using a metric characterizing the phase error of at least a portion of the chirped segment.

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