Frequency-modulated continuous wave (FMCW) based system for estimating and compensating for nonlinearities in linear swept sources - Patents.com

Abstract

The frequency-modulated continuous wave (FMCW)-based system is configured to convert measurements of a linearly modulated wave from the time domain to a frequency domain to generate a nonlinear frequency signal, the nonlinear frequency signal including a known linear component representing a desired linear modulation and an unknown nonlinear component representing the nonlinearity of the modulation. The FMCW-based system is further configured to determine coefficients of a basis function that approximates the difference between the nonlinear frequency signal and the linear frequency component in the frequency domain. The FMCW-based system is further configured to detect one or more spectral peaks of a distorted beat signal, the distortion of which has been compensated according to the basis function using the determined coefficients, to determine one or more distances to one or more objects in the scene.

Description

[Technical field]

[0001] The present disclosure relates generally to frequency modulated continuous wave (FMCW) based systems, and more particularly to FMCW based systems for estimation and compensation of nonlinearities in linear swept sources. [Background technology]

[0002] Linear swept sources in the audio, radio, and optical frequency ranges have been used to estimate the range (e.g., distance) of reflectors with high resolution, low hardware cost, and lightweight signal processing. Frequency-modulated continuous wave (FMCW) radar, optical frequency-domain reflectometry (OFDR), and swept-wavelength optical coherence tomography (SS-OCT) are typical applications of linear swept sources. Combined with multiple sweeps, FMCW-based sensing systems can simultaneously estimate the range and (line-of-sight) velocity of a reflector. In addition to range and velocity estimation, an array of FMCW-based sensors can be used to estimate the azimuth direction of a reflector.

[0003] For example, FMCW radar transmits a linearly frequency modulated continuous wave whose frequency pattern follows a sawtooth or triangular pattern over time. The reflected signals from various targets are mixed with a local oscillator signal to generate the transmitted signal, generate an analog beat signal, and output a digital beat signal via an analog-to-digital converter (ADC). Since the frequency of the beat signal is proportional to the distance of the object, a standard fast Fourier transform (FFT) of the beat signal can be used to identify the peaks and estimate the distance. For moving objects, the frequency of the beat signal also depends on the line-of-sight velocity between the FMCW radar and the object. This velocity can be estimated by a second FFT over multiple linear FM scans.

[0004] OFDR interferometers similarly provide a beat signal generated by optical interference between two optical signals. One reference signal comes from a linearly chirped highly coherent light source, and the other is obtained from reflected or backscattered light from the optical path of the fiber under test. The resulting interference signal is collected as a function of the optical frequency of a tunable laser source (TLS). Using an FFT, this frequency domain information is then converted into spatial information.

[0005] Similarly, SS-OCT uses a linear frequency-swept laser to provide high-precision range-resolved measurements for imaging applications. With a tunable laser source that scans a wide frequency range with a fast sweep rate and narrow instantaneous linewidth, SS-OCT obtains all range information in a single axial scan from the frequency spectrum of the interference signal between the reflected optical signal and a stationary reference signal.

[0006] One common challenge related to all three applications is that the range resolution is degraded if the swept source is not perfectly linearly modulated. Source nonlinearity can be due to the nonlinear tuning and phase noise of the laser source, impairments of low-cost voltage-controlled oscillators (VCOs), and temperature sensitivity of the laser source. Nonlinearity broadens the spectrum of the beat signal, thus degrading the spatial resolution and sensitivity. Also, the nonlinearity effect is range-dependent, i.e., it is smaller at shorter measurement distances and larger at longer measurement distances.

[0007] Current state-of-the-art computational methods use a known reference branch to achieve nonlinearity correction. Specifically, unknown nonlinearities in the modulated light source cause unknown shifts in the range estimate, which causes the entire estimation system to be underestimated. To that end, some systems use a dedicated path of known distance to remove at least one unknown from the range estimate and estimate the modulation nonlinearity. However, using a dedicated path requires additional hardware resources, which is undesirable for some applications and increases the overall system cost. Summary of the Invention

[0008] It is therefore an object of the present disclosure to provide a cost-effective FMCW-based system configured to estimate and overcome nonlinearities in linear swept sources.

[0009] Some embodiments are based on the recognition that one of the reasons for the need for a reference arm is due to the sampling of high frequency signals. FMCW-based systems explore frequency modulation and spectrum measurement at high frequencies. However, sampling signals at such high frequencies is very costly.

[0010] To this end, various FMCW-based systems use a lower frequency beat signal for measurement. For example, the measurement arm of an FMCW-based system mixes the transmitted signal with a reflection to generate a beat signal. Similarly, the reference arm mixes a delayed copy of it with a known delay to generate another beat signal for nonlinearity compensation. The hardware components for generating the beat signal require precision manufacturing and assembly, and are therefore relatively expensive.

[0011] Some embodiments are based on the realization that to compensate for the nonlinearity of a light source modulated signal, it is desirable to measure the modulated signal itself, rather than the beat signal after mixing the modulated signal with a known delayed copy. Such a measurement would not require building a dedicated reference arm, but would only require placing a sensor in the path of the modulated signal. However, the cost of building a dedicated path with known delay, a mixer, and sampling the high frequency modulated signal makes this approach impractical.

[0012] Some embodiments are based on the recognition that due to the modulation of the transmitted signal in FMCW-based systems, the modulated signal has different frequencies at different instants of time. Therefore, if a frequency filter that passes only certain frequencies is placed on the path of the modulated signal, the output of this frequency filter can be considered to be similar to a sampling. However, these outputs are very sparse and generally not suitable for nonlinearity compensation.

[0013] For example, an etalon is a device with two reflective glass plates, and is typically used to measure slight wavelength differences in light using the interference it creates. However, an etalon can function as a frequency filter, where the refractive index of the etalon and the distance between the plates govern the pass wavelength. Advantageously, an etalon is low cost, i.e., less expensive to manufacture than a reference arm. However, the sampling characteristic of a frequency filter such as an etalon is sparse. As used herein, sparse sampling refers to sampling at a sampling frequency that is at least 1 / 1000th of the modulation frequency of the transmitted wave in the frequency domain. For example, if the sampling frequency of the reference arm is 900MHz, the etalon peak of the pass wavelength is reported every 12.5us, which corresponds to a sampling frequency of only 80kHz.

[0014] Therefore, a system and method using a sparsely sampled linear modulation signal for nonlinearity compensation is required. Some embodiments are based on the recognition that when a sparsely sampled signal in the time domain is transformed into the frequency domain, the transformed nonlinear frequency signal has a known linear component representing the desired linear modulation and an unknown nonlinear component representing the nonlinearity of the undesired modulation. Therefore, the nonlinearity of the undesired modulation can be restored based on the difference between the nonlinear frequency signal in the frequency domain and the linear frequency signal corresponding to the linear modulation.

[0015] Such recovery is a computationally expensive ill-posed problem. However, some embodiments are based on the recognition that the recovery can be simplified if the unknown nonlinear frequency signal is approximated by unknown coefficients of known basis functions. In such a formulation, the nonlinearity of the modulation is defined by the coefficients of the basis functions that approximate the difference between the nonlinear frequency signal in the frequency domain and the linear frequency signal corresponding to the linear modulation. For example, the coefficients of the basis functions can be found by solving a least-squares problem that minimizes this difference.

[0016] Furthermore, some embodiments are based on the experimentally proven realization that when the estimation of nonlinearity in the frequency domain is formulated as a computational estimation of a frequency signal converted from samples in the time domain, the reduction of the sampling rate in the time domain has little effect on the estimation accuracy of the nonlinearity. Such realization allows some embodiments to further simplify the hardware requirements for FMCW-based systems. For example, in some embodiments, the cost of the time domain sensor is reduced because the sampling in the time domain is sparse, e.g., 1 / 1000 of the modulation frequency of the transmitted wave in the frequency domain.

[0017] Some embodiments use an optical filter that can be placed directly on the path of the modulated signal. For example, in one embodiment, the optical filter includes an etalon that generates an etalon signal, and the samples in the time domain are peaks of the etalon signal at different instants, so that the samples in the time domain are sparse. Specifically, an etalon can be considered as an optical interferometer that includes two refracting plates or mirrors separated by a small fixed distance. The refractive index of the etalon and the distance between the plates govern the pass wavelength.

[0018] In an etalon, the refractive index of the medium between the two mirrors increases as the incident optical field increases in intensity, resulting in a shift of the transmission peak of the etalon to other wavelengths, thus resulting in a frequency sweep. Thus, by sampling the peaks of the etalon signal in the time domain, a sparse signal can be obtained that is sparsely sampled for different instants of time. However, even such a sparsely sampled signal is sufficient to compensate for the nonlinearity of the modulation according to the principles of some embodiments.

[0019] Accordingly, one embodiment discloses a frequency modulated continuous wave based system, the system including an emitter configured to transmit at least one radiation wave into a scene, the transmitted wave being linearly modulated in a frequency domain, the linear modulation being subject to impairments that cause nonlinearity of the transmitted wave in the frequency domain. The FMCW-based system further includes a receiver configured to receive reflections of the transmitted wave from one or more objects in the scene, and a mixer operatively connected to the emitter and the receiver and configured to interfere a copy of the wave transmitted by the emitter with the reflection of the transmitted wave received by the receiver to generate a beat signal having a spectral peak corresponding to the reflection from the one or more objects in the scene, the beat signal being distorted due to the nonlinearity of the modulation caused by the impairment, the FMCW-based system further includes an analog-to-digital converter (ADC) operatively connected to the mixer and configured to generate samples of the distorted beat signal, and a frequency filter configured to pass signals of a predetermined frequency, the frequency filter operatively connected to the emitter and passing a linearly modulated wave transmitted by the emitter at different instants at the predetermined frequency to generate a measurement of the modulated waveform in a time domain. The FMCW-based system further includes at least one processor configured to convert the measurements of the linearly modulated wave from the time domain into a frequency domain to generate a nonlinear frequency signal, the nonlinear frequency signal including a known linear component representing a desired linear modulation and an unknown nonlinear component representing the nonlinearity of the modulation, and the processor is further configured to determine coefficients of a basis function approximating a difference between the nonlinear frequency signal and the linear frequency component in the frequency domain, and to use the determined coefficients to detect one or more spectral peaks of the distorted beat signal, the distortion of which has been compensated according to the basis function, to determine one or more distances to the one or more objects in the scene.

[0020] Accordingly, another embodiment discloses a method, the method comprising: an emitter transmitting at least one radiation wave into a scene, the transmitted wave being linearly modulated in a frequency domain, the linear modulation being subject to impairments causing nonlinearity of the transmitted wave in the frequency domain, the method further comprising: a receiver receiving reflections of the transmitted wave from one or more objects in the scene, and a mixer interfering copies of the transmitted wave with the received reflections of the transmitted wave to generate a beat signal having a spectral peak corresponding to the reflections from the one or more objects in the scene, the beat signal being distorted due to the nonlinearity of the modulation caused by the impairments, the method further comprising: an analog-to-digital converter (ADC) generating samples of the distorted beat signal, and a frequency filter passing a signal of a predetermined frequency, the frequency filter operatively connected to the emitter, passing the linearly modulated wave transmitted by the emitter at different instants at the predetermined frequency to generate a measurement of the modulated wave in a time domain. The method further includes transforming the measurements of the linearly modulated wave from the time domain to a frequency domain to generate a nonlinear frequency signal, the nonlinear frequency signal including a known linear component representative of a desired linear modulation and an unknown nonlinear component representative of the nonlinearity of the modulation, and the method further includes determining coefficients of a basis function that approximate a difference between the nonlinear frequency signal and the linear frequency component in the frequency domain, and using the determined coefficients to detect one or more spectral peaks of the distorted beat signal, the distortion of which has been compensated according to the basis function, to determine one or more distances to the one or more objects in the scene. [Brief description of the drawings]

[0021] [Figure 1] FIG. 1 is a block diagram of a Frequency Modulated Continuous Wave (FMCW) based system according to an exemplary embodiment. [Diagram 2] FIG. 2 illustrates an optical etalon for an FMCW-based system according to an exemplary embodiment. [Figure 3A] FIG. 1 illustrates a method for compensating for nonlinearity in a linear swept source by an optical etalon in an FMCW-based system according to an exemplary embodiment. [Figure 3B] FIG. 1 illustrates a method for compensating for nonlinearity in a linear swept source by an optical etalon in an FMCW-based system according to an exemplary embodiment. [Figure 4] FIG. 1 is a schematic diagram of an FMCW-based system implemented as an FMCW-based swept-wavelength optical interferometric sensing (SS-OCT) system according to an exemplary embodiment. [Diagram 5] 1 is a schematic diagram of an FMCW-based system implemented as an FMCW-based ranging system according to an exemplary embodiment; [Figure 6] FIG. 2 is a schematic diagram illustrating an FMCW waveform used by an FMCW-based ranging system according to an exemplary embodiment. [Figure 7A] 1 is a block diagram illustrating a receiver for an FMCW-based system according to an exemplary embodiment. [Figure 7B] FIG. 2 is a schematic diagram illustrating a time-domain FMCW waveform according to an exemplary embodiment. [Figure 7C] FIG. 2 is a schematic diagram illustrating a time-frequency pattern of an FMCW waveform according to an exemplary embodiment. [Figure 7D] FIG. 2 is a schematic diagram illustrating a time-domain waveform of a beat signal according to an exemplary embodiment; [Figure 7E] FIG. 4 is a schematic diagram illustrating a time-frequency pattern of a beat signal according to an exemplary embodiment. [Figure 8A] 1 is a schematic diagram illustrating time-frequency patterns of transmitted and reflected FMCW waveforms in the presence of a nonlinear light source according to an exemplary embodiment. [Figure 8B] FIG. 1 is a schematic diagram illustrating time-frequency patterns of beat signals for two reflectors at two distances in the presence of a nonlinear light source according to an exemplary embodiment. [Figure 9A]FIG. 2 illustrates a method for estimating a nonlinear light source from an etalon signal generated by an optical etalon according to an exemplary embodiment. [Figure 9B] FIG. 13 illustrates a cost function for determining delay and distance by coherently accumulating a beat signal compensated using an estimated nonlinearity function from an etalon signal according to an exemplary embodiment. [Figure 10A] 4A-4C are diagrams illustrating exemplary etalon signals generated by an optical etalon, according to exemplary embodiments. [Figure 10B] FIG. 1 illustrates a nonlinear frequency sweep according to an exemplary embodiment. [Figure 10C] FIG. 1 illustrates a diagram showing linear components of a non-linear sweep frequency according to an exemplary embodiment. [Figure 10D] FIG. 13 illustrates a diagram of a nonlinear component of a nonlinear sweep frequency according to an exemplary embodiment. [Figure 11A] FIG. 1 illustrates an experimental setup of an SS-OCT system implemented to compare a reference arm-less approach with a k-sampling method using a reference arm, according to an exemplary embodiment. [Figure 11B] FIG. 2 illustrates a time domain beat signal from a measurement arm according to an exemplary embodiment. [Figure 11C] FIG. 4 illustrates a reference signal from a reference arm according to an exemplary embodiment. [Figure 12A] FIG. 4 illustrates a spectrum of a beat signal from a measurement arm before nonlinearity compensation according to an exemplary embodiment. [Figure 12B] FIG. 13 illustrates a spectrum of a beat signal from a measurement arm after nonlinearity compensation according to an exemplary embodiment. [Figure 13] FIG. 1 illustrates a measurement profile for an FMCW-based system without a reference arm according to an exemplary embodiment. [Figure 14] FIG. 13 is a block diagram illustrating a deskew filtering based step for compensating beat signals with an estimated nonlinearity function according to an exemplary embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0022] While the above drawings depict embodiments disclosed herein, other embodiments are contemplated as described herein. The present disclosure presents illustrative embodiments by way of representation and not by way of limitation. Those skilled in the art can envision numerous other modifications and embodiments that fall within the scope and spirit of the principles of the embodiments disclosed herein.

[0023] In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present disclosure. However, it will be apparent to one skilled in the art that the present disclosure may be practiced without these specific details. In other instances, the devices and methods are shown in block diagram form solely to avoid obscuring the present disclosure.

[0024] As used in the specification and claims, the terms "for example," "for example," and "such as," as well as the verbs "comprise," "have," "include," and other verb forms thereof, when used in conjunction with a list of one or more components or other items, should be construed as open-ended, meaning that the list should not be considered to exclude further components or items. The term "based on" means based at least in part on. Furthermore, it should be understood that the style and terminology used herein are for purposes of illustration and should not be considered to be limiting. Any headings used herein are for convenience only and should not be considered to have any legal or limiting effect.

[0025] FIG. 1 illustrates a block diagram of a frequency modulated continuous wave (FMCW)-based system 100 according to an exemplary embodiment. The FMCW-based system 100 (hereinafter also referred to as "system 100") includes at least one emitter 110 configured to transmit at least one linearly modulated wave of radiation 115 (hereinafter also referred to as "modulated signal 115") to a scene. In various implementations, the emitter 110 includes a linear modulator that linearly modulates a waveform in the frequency domain. For example, the emitter 110 may include a light source component that generates an FMCW waveform, a power amplifier, and an antenna configured to transmit the FMCW waveform to a medium. The modulation of the FMCW waveform is subject to impairments that cause nonlinearity in the modulation of the transmitted FMCW wave in the frequency domain. For example, the nonlinearity in the modulation may be caused by hardware aging and / or ambient temperature that changes over time.

[0026] The system 100 further includes at least one receiver 120 that receives reflections of the transmitted wave from one or more objects / reflectors at different positions in the scene. The system 100 also includes a mixer 130 operatively connected to the emitter 110 and the receiver 120 to interfere (or beat) a copy of the linearly modulated wave 115 output by the emitter 110 with a reflection 125 of the transmitted wave received by the receiver 120 to generate a beat signal 135. For example, the receiver 120 may include a receiving antenna, a low noise amplifier (LNA), and the mixer 130 that multiplies the received waveform (i.e., the reflection 125 of the transmitted wave) with the source FMCW waveform (i.e., the linearly modulated wave 115).

[0027] The beating performed by the mixer 130 involves finding the difference between two frequencies, namely the frequency of the copy of the modulated wave 115 and the frequency of the reflection 125 of the transmitted wave. This produces a beat signal 135 that oscillates at a beat frequency, which corresponds to the difference between these two frequencies. The beat signal 135 is therefore much lower in frequency than the linearly modulated wave 115 and the reflection 125 of the transmitted wave. By beating the copy of the linearly modulated wave 115 with the reflection 125 of the transmitted wave, the beat signal 135 includes spectral peaks that correspond to reflections from different positions in the scene. However, the beat signal 135 is distorted due to the nonlinearity of the modulation. This distortion may include or cause one or a combination of broadening and shifting of the spectral peaks of the beat signal 135, which reduces the accuracy of the range estimation.

[0028] To analyze the beat signal 135, the system 100 uses the processor 140. To do so, the beat signal 135 is sampled by an analog-to-digital converter (ADC) 160. The ADC 160 is operatively connected to the mixer 130. Because the beat signal 135 has a low frequency, the ADC 160 can easily sample the beat signal 135. However, the sampled beat signal 135 is distorted due to nonlinearities.

[0029] Some embodiments are based on the recognition that the distortion of the beat signal 135 depends not only on the type of nonlinearity but also on the distance to the object reflecting the linear modulated signal 115. Thus, the distorted beat signal depends on two types of unknowns, such as the modulation nonlinearity and the distance to the reflecting object. For example, different modulation nonlinearities may cause different broadening and shifting of the peaks of the beat signal 135, where the peaks of the beat signal 135 may be caused by reflections of the linear modulated signal 115 from the same object. However, different modulation nonlinearities may cause the same broadening and shifting of the peaks of the beat signal 135, where the peaks of the beat signal 135 may be caused by reflections of the modulated signal 115 from objects at different distances from the source of the nonlinearity. Thus, the representation of the distorted beat signal 135 is ill-posed, i.e., underestimated, since different combinations of nonlinearity values ​​and distance-to-object values ​​may result in the same distorted beat signal 135.

[0030] However, some embodiments are based on the realization that since there is only one nonlinear function that can cause a particular multi-peak distortion, the representation of the distorted beat signal 135 with multiple peaks corresponding to multiple reflections of the linearly modulated signal 115 transforms an ill-posed problem into a well-posed problem, i.e., a problem to be determined. Specifically, this realization is based on the understanding that a reflection of the linearly modulated signal 115 from a position in the scene carries information about both the modulation nonlinearity and a reflector-dependent range / delay parameter that indicates the distance to that position. If there are multiple reflections M, then the beat signal 135 is the sum of M responses characterized by M delay parameters and a common source of modulation nonlinearity.

[0031] Some embodiments are based on the realization that the linearly modulated signal 115 sampled at a particular frequency can be used to estimate the light source causing the nonlinearity in the modulation of the linearly modulated signal 115, which causes the distortion of the beat signal 135 at the output of the mixer 130. However, the linearly modulated signal 115 is a high frequency signal (on the order of gigahertz (GHz)). Sampling such a high frequency signal, for example using an ADC 160, can be very costly depending on the application.

[0032] Some embodiments are based on the realization that a low-cost passive filter (or optical filter) can be used as the frequency filter 117 for sampling the high-frequency linearly modulated signal 115. Furthermore, the sampled signal can be used to obtain a measurement value 119 of the linearly modulated signal 115. However, the frequency filter 117 may sample the linearly modulated signal 115 at a very low frequency, approximately at least 1 / 1000 of the sampling frequency of the ADC 160. The sampled signal thus comprises samples in the time domain, which are peaks of the sampled signal at different instants, making the samples in the time domain sparse. Thus, the sampled signal at the output of the frequency filter 117 comprises few samples or is a sparsely sampled signal.

[0033] Some embodiments are based on the recognition that the sparsely sampled signal can be used to estimate the light source nonlinearity. In the present disclosure, the estimation of the light source nonlinearity is solved as an optimization problem, and the difference between the sampled modulation signal obtained from the frequency filter 117 and the sum of an ideal linear modulation signal and a light source nonlinearity function is minimized to accurately estimate the light source nonlinearity. Furthermore, based on the estimated light source nonlinearity, the corresponding nonlinearity can be compensated in the beat signal 135. The compensated beat signal 135 can then be used to correctly determine the distance to multiple objects in the scene.

[0034] To that end, the processor 140 may resolve 150 the nonlinear light source to determine distances to multiple objects in the scene. The processor 140 is coupled to a memory 170, which is configured to store data for estimating range information of multiple reflectors (or objects) in the scene. The processor 140 may digitally sample and process the data to estimate range information of multiple reflectors in the scene. Furthermore, an output interface may be used to render the positions of multiple reflectors. In some embodiments, the processor 140 may further estimate velocity information of multiple reflectors in the scene.

[0035] Specifically, the processor 140 may be configured to convert the linearly modulated signal 115 (or sparsely sampled signal) measurements 119 from the time domain into the frequency domain to generate a nonlinear frequency signal (151). The converted nonlinear frequency signal includes a known linear component representing the desired linear modulation and an unknown nonlinear component representing the nonlinearity of the undesired modulation or a source of the nonlinearity. The nonlinearity of the undesired modulation may be recovered based on the difference between the nonlinear frequency signal in the frequency domain and the linear frequency signal (or linear frequency component) corresponding to the linear modulation.

[0036] To reduce the complexity of calculating the source of the nonlinearity, the processor 140 may be further configured to determine coefficients of a basis function that approximates the difference between the nonlinear frequency signal in the frequency domain and a linear frequency signal corresponding to the linear modulation (152). In this manner, the source of the nonlinearity may be estimated. Furthermore, the estimated nonlinearity may be used to compensate the distorted beat signal. The processor 140 may be further configured to detect one or more spectral peaks of the distorted beat signal, the distortion of which has been compensated according to the basis function using the determined coefficients, to determine one or more distances to one or more objects in the scene (153).

[0037] In some embodiments, the frequency filter 117 may include an optical etalon, which is a monolithic interference device that includes two parallel reflective surfaces. An optical etalon (also called a Fabry-Perot etalon) includes two mirrors with an air gap between them (air-gap etalon). When the optical etalon is inserted into the laser beam, it acts as an optical resonator (or cavity). In an optical resonator, the transmittance varies approximately periodically with the optical frequency. At resonance, the reflections from the two surfaces cancel each other by destructive interference. At anti-resonance, the reflection losses are highest and therefore the transmittance is lowest. The reflectance of each surface of the optical etalon may simply be due to a discontinuity in the refractive index between the material of the optical etalon and the air (Fresnel reflection) or may be modified using a dielectric coating. By increasing the reflectance, it is possible to sharpen the resonance without reducing the free spectral range. Thus, an optical etalon is a tunable optical filter that can be tuned to pass certain frequencies (on resonance) and reflect (or reject) other frequencies (on anti-resonance). An example of an optical etalon (Fabry-Perot etalon) for FMCW-based system 100 is described below with respect to FIG.

[0038] FIG. 2 illustrates a Fabry-Perot etalon 200 of the FMCW-based system 100 according to an exemplary embodiment. The Fabry-Perot etalon 200 includes a diffuse light source 210, a collimating lens 220, and a cavity 230, which includes a pair of partially reflecting, slightly wedge-shaped optical flats 230a and 230b. The Fabry-Perot etalon 200 further includes a focusing lens 240 and a screen 250. The main components of the Fabry-Perot etalon 200 are the cavity 230, which includes a pair of partially reflecting glass optical flats 230a, 230b (also called a pair of flats), which are spaced apart by micrometers to centimeters, with their reflective surfaces facing each other. Alternatively, the Fabry-Perot etalon 200 may use a single plate with two parallel reflective surfaces. The pair of flats 230a, 230b form a reflective cavity. The interferometer flats 230a, 230b are often wedged so that the back surface does not produce interference fringes, and the back surface often has an anti-reflective coating.

[0039] The Fabry-Perot etalon 200 exploits the phenomenon of multiple beam interference, which occurs when light from a diffuse light source 210 is emitted through a cavity 230 bounded by two reflective parallel surfaces (i.e., a pair of flats 230a, 230b). Each time the light hits any of these surfaces, a portion of the light is transmitted and the remaining portion is reflected. The net effect is that a single light beam is split into multiple light beams that interfere with each other. If the additional optical path length of the reflected beams (due to multiple reflections) is an integer multiple of the wavelength of the light, the reflected beams will constructively interfere. In other words, the more reflections there are inside the cavity 230, the sharper the interference maximum will be.

[0040] Furthermore, the diffuse light source 210 is set at the focal plane of the collimating lens 220. The diffuse light source 210 is used to provide illumination. Light emitted from a point (point A) on the light source is focused to a point in the image plane. In FIG. 2, only one light ray emitted from point A on the light source is traced for ease of explanation. When the light ray passes through the pair of flats 230a, 230b, it is reflected multiple times to generate multiple transmitted light rays, which may be focused by the focusing lens 240 to reach point A′ on the screen 250. If the pair of flats 230a, 230b does not exist, the focusing lens 240 may generate an inverted image of the light source. The complete interference pattern may look like a set of concentric circles, and the sharpness of these circles depends on the reflectivity of the pair of flats 230a, 230b.

[0041] In the Fabry-Perot etalon 200, the refractive index of the medium (air in this case) between the flats 230a, 230b increases as the incident optical field (i.e. light) increases in intensity. This results in an etalon signal whose transmission peak shifts to other wavelengths. The shift in the transmission peak of the etalon signal results in a frequency sweep. Thus, the peaks of the etalon signal can be sampled in the time domain to obtain a sparse signal that is sparsely sampled for different instants of time. An optical filter such as the Fabry-Perot etalon 200 described above can be used as a frequency filter 117 to sample the high frequency modulated signal 115.

[0042] In an exemplary embodiment, the frequency filter 117 may be replaced with at least one of a Michelson interferometer, a Twyman-Green interferometer, an unequal path laser interferometer (LUPI), or a step-phase interferometer to sample the high frequency modulated signal 115.

[0043] Further, a method for estimating the light source nonlinearity and compensating the beat signal 135 based on the estimated light source nonlinearity is described below with reference to FIG.

[0044] 3A and 3B generally illustrate a method 300 for compensating for nonlinearities in a linear swept source with an optical etalon (Fabry-Perot etalon 200) in an FMCW-based system 100, according to an example embodiment. Figures 3A and 3B are described in conjunction with Figures 1 and 2.

[0045] In step 310, at least one linearly modulated wave of radiation 115 (or modulated wave) may be transmitted into the scene by using an emitter 110, the linear modulation being subject to impairments that cause nonlinearities of the transmitted wave in the frequency domain.

[0046] In step 320, reflections of the transmitted wave from one or more objects in the scene may be received by receiver 120.

[0047] In step 330, a copy of the transmitted wave may be interfered (or beat) with reflections of the received transmitted wave by mixer 130 to generate beat signal 135. The spectrum of beat signal 135 includes spectral peaks corresponding to reflections from one or more objects in the scene. Additionally, beat signal 135 is distorted due to nonlinearities in the modulation.

[0048] In step 340 , samples of the distorted beat signal 135 may be generated using the ADC 160 .

[0049] In step 350, a signal of a predetermined frequency can be passed by the frequency filter 117. The frequency filter 117 is operatively connected to the emitter 110 to pass the linearly modulated wave 115 transmitted by the emitter 110 at a predetermined frequency at different instants to generate measurements of the linearly modulated wave 115 in the time domain. In particular, the Fabry-Perot etalon 200 generates an etalon signal such that the transmission peak of the etalon signal is shifted to other wavelengths. The shift of the transmission peak of the etalon signal results in a frequency sweep. Thus, the peak of the etalon signal can be sampled in the time domain to obtain a sparse signal that is sparsely sampled for different instants.

[0050] In step 360, the measurements of the linearly modulated wave 115 may be transformed from the time domain to the frequency domain to generate a nonlinear frequency signal that includes a known linear component that represents the desired linear modulation and an unknown nonlinear component that represents the nonlinearity of the modulation.

[0051] In step 370, coefficients of basis functions that approximate the difference between the nonlinear frequency signal and the linear frequency components may be determined in the frequency domain. To that end, the processor 140 may be configured to estimate the coefficients of the basis functions by solving a least-squares problem that minimizes this difference. The estimated coefficients of the basis functions may be functions of the polynomial components and the peak instants.

[0052] In step 380, the distortion of the spectral peaks of the distorted beat signal 135 is compensated based on the coefficients of the basis functions. The compensated beat signal may be further used to determine the distance of one or more objects from the emitter 110. The distance of the one or more objects may be determined based on the phase information comprised in the compensated beat signal 135.

[0053] The FMCW-based system 100 may be implemented in a variety of embodiments, examples of which are described below with reference to Figures 4 and 5.

[0054] FIG. 4 shows a schematic diagram of the FMCW-based system 100 implemented as an FMCW-based swept-wavelength optical interferometric sensing (SS-OCT) system 400 according to an exemplary embodiment. In some implementations, the swept-wavelength OCT system includes a reference arm, a sample arm, and a photodetector. Light is generated from a frequency-swept (or wavelength-swept) laser source 410 having a time-frequency pattern such as pattern 411 and is split by a beam splitter 420 to both a reference mirror 430 and a sample of interest 440 (hereinafter also referred to as "sample 440"). Backscattered and reflected light from the sample 440 is interfered (or beat) with a reflection from the reference mirror 430 having a time-frequency pattern such as pattern 412. Furthermore, a beat signal 451 is detected by a detector 450. For a fixed sweep rate, different beat frequencies correspond to different delays or reflections from different depths in the sample 440. Thus, by applying a Fourier transform, the beat signal 451 can generate a beat frequency spectrum 460, where the spectral peak frequency corresponds to distance. In some embodiments, an axial profile of the reflection magnitude versus depth is obtained based on the interference signal 460. Multiple axial scans, in conjunction with xy scans, can be used to create comprehensive 2D and 3D volumetric data sets that can be used to construct any cross-sectional image, projections along any axis, or renderings similar to magnetic resonance imaging (MRI) or computed tomography (CT).

[0055] 5 shows a schematic diagram of the FMCW-based system 100 implemented as an FMCW-based ranging system 500 according to an exemplary embodiment. The FMCW-based ranging system 500 outputs a waveform to at least one reflector 540, receives a reflected waveform, mixes the reflected waveform with a transmitted waveform, and generates a beat signal according to a different embodiment. The beat signal has a lower frequency than the transmitted modulated wave. Therefore, the beat signal is sampled using an analog-to-digital converter. Furthermore, based on the estimation, the nonlinearity of the sampled beat signal is compensated.

[0056] The FMCW-based ranging system 500 includes an FMCW light source 510 that sweeps the frequency (e.g., [77, 81] GHz for automotive radar) over a short period of time. The light source FMCW waveform may be generated by a baseband FMCW waveform (e.g., [-2, 2] GHz) and an upconverter that modulates the baseband FMCW waveform to a carrier frequency (e.g., 79 GHz). The light source FMCW waveform may be further amplified by a power amplifier 520 before being fed to a transmit antenna 530. The transmit antenna 530 transmits the light source FMCW waveform toward a scene to detect at least one potential reflector 540. The reflected waveform from the at least one reflector 540 is captured by a receive antenna 550. The received waveform may further pass through an LNA 560 to increase the signal-to-noise ratio (SNR). The received waveform is further mixed with the light source FMCW waveform by a mixer 570. As a result, a beat signal 571 is generated, which may be further processed to estimate the nonlinearity in the beat signal and compensate for the estimated nonlinearity, thereby improving the sensitivity of the FMCW-based electromagnetic sensing system 500.

[0057] 6 is a schematic diagram illustrating an FMCW waveform used by an FMCW-based ranging system 600 according to an exemplary embodiment. For scanning, the FMCW (transmit) waveform has a linear frequency pattern 610 over a period T and a time domain waveform similar to 620. Furthermore, the transmit frequency f of the FMCW waveform sweeps across a bandwidth B. For scanning, the FMCW-based ranging 600 system can detect the distances of multiple reflectors, which may be stationary.

[0058] In an exemplary embodiment, receiver 120 itself includes mixer 130 and ADC 170. Thus, upon receiving a reflection of transmitted wave 125, receiver 120 may use mixer 130 to generate beat signal 135 and ADC 170 to sample beat signal 135 and convert beat signal 135 from the analog domain to the digital domain for further analysis by processor 140. An exemplary receiver configured to analyze beat signal 135 is described below with reference to FIG. 7A.

[0059] FIG. 7A is a block diagram illustrating the receiver 120 of the FMCW-based system 100 according to an exemplary embodiment. In this embodiment, an analog-to-digital converter (ADC) 710 samples the analog beat signal 135 into a digital beat signal. The digital beat signal is further converted to the frequency domain by a Fourier transformer (FFT) 720. As a result, a spectrum 730 of the beat signal 135 over frequency is obtained, which describes the reflected energy distribution over the range domain. To determine the range information of some strong reflectors, their corresponding peak frequencies can be identified. The peaks may be distorted due to impairments of the transmitted wave (or modulated wave 115) that cause nonlinearity in the beat signal 135. The source of the nonlinearity is estimated, and the beat signal 135 is compensated based on the estimated source of the nonlinearity. The compensated beat signal is further used to determine the distance information 740 associated with the reflectors.

[0060] Further, the time-domain waveforms and time-frequency patterns of the linearly modulated wave 115 (or FMCW wave) and the beat signal 135 are analyzed below with reference to FIGS. 7B, 7C, 7D, and 7E.

[0061] FIG. 7B is a schematic diagram illustrating a time-domain FMCW waveform 620 according to an exemplary embodiment. FIG. 7C is a schematic diagram illustrating a time-frequency pattern 610 of an FMCW waveform according to an exemplary embodiment. FIG. 7D is a schematic diagram illustrating a time-domain waveform of a beat signal 760 according to an exemplary embodiment. The time-domain waveform of the beat signal 760 is obtained by mixing the transmitted waveform and the reflected waveform. In FIG. 7D, the transmitted waveform corresponds to the modulated signal 115, and the reflected waveform corresponds to the reflection 125 of the transmitted wave (i.e., the modulated signal 115). FIG. 7E is a schematic diagram illustrating a time-frequency pattern of a beat signal according to an exemplary embodiment. Due to the round-trip delay from the transmitter to one reflector, the time-frequency pattern 750 of the reflected FMCW waveform is shifted to the right as shown in FIG. 7C. The mixer 130 generates the beat signal 760 as shown in FIG. 7D. In the case of one reflector, the beat signal is dominant at one frequency corresponding to the distance of this reflector to the transmitter. In other words, the time-frequency pattern 761 of the beat signal (in FIG. 7E) is parallel to the time axis.

[0062] FIG. 8A is a schematic diagram 810 illustrating the time-frequency patterns of transmitted and reflected FMCW waveforms in the presence of a nonlinear light source, according to an exemplary embodiment. FIG. 8B is a schematic diagram 820 illustrating the time-frequency patterns of beat signals for two reflectors at two distances in the presence of a nonlinear light source, according to an exemplary embodiment. An FMCW-based sensing system requires an ideal linear frequency pattern to determine the reflector distance from the beat signal (e.g., beat signal 135). In the presence of light source nonlinearities caused by hardware impairments, low-cost components, and open-loop VCOs, the time-frequency pattern 811 is not perfectly linear. For two reflectors at different distances to the transmitter, the time-frequency pattern of the reflected signal is then shifted according to the corresponding round-trip delay. For example, the time-frequency pattern of the closer reflector is shown by dashed line 812, and the farther reflector has a time-frequency pattern shown by dashed line 813. When both reflected signals from two different reflectors are mixed with the light source signal, the beat signal contains two components, which show different distortions due to the light source nonlinearities. In particular, the near reflector provides a beat signal with a time frequency pattern 821, while the far reflector provides a beat signal with a time frequency pattern 822. Even with the same light source nonlinearity, the effect on the spectrum of the beat signal is range dependent. It is difficult to mitigate the distortion of the beat signal when both the light source nonlinearity function and the range information of the reflectors are unknown.

[0063] Furthermore, a detailed (mathematical) analysis is performed to estimate the source of nonlinearity in the modulated signal 115 and to compensate for the nonlinearity in the beat signal 115. To this end, a comparative analysis is performed between an FMCW-based system with a reference arm (the conventional method of estimating nonlinearity) and an FMCW-based system without a reference arm (i.e., the proposed method of estimating nonlinearity using a frequency filter 117). For ease of understanding, an SS-OCT system (described with reference to FIG. 4), which is one of the FMCW-based systems, is used in the analysis. Exemplary Formulation

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[0079] The etalon signal tracks the source laser wavelength at the coarsely sampled instants. In an etalon, the refractive index of the medium between the two mirrors increases as the incident optical field increases in intensity, resulting in a shift of the etalon's transmission peaks to other wavelengths. The shift of the etalon's transmission peaks to other wavelengths is achieved by a frequency sweep. The transmission peaks can be traced by the time-domain output etalon signal as shown in Figure 10A. In particular, the etalon signal always outputs a constant number of peaks at a given wavelength.

[0080] FIG. 9A illustrates a method 900 for estimating a nonlinear light source from an etalon signal generated by an optical etalon, according to an exemplary embodiment. FIG. 9A is described below with reference to FIG. 9B and FIG. 10A. FIG. 10A illustrates an etalon signal and a nonlinearity function estimation from the etalon signal. FIG. 9B illustrates a cost function for determining delay and distance by coherently accumulating a beat signal compensated using an estimated nonlinearity function from the etalon signal, according to an exemplary embodiment. FIG. 10A illustrates an exemplary etalon signal generated by an optical etalon (such as a Fabry-Perot etalon 200), according to an exemplary embodiment. FIG. 10B illustrates a nonlinear frequency sweep, according to an exemplary embodiment. FIG. 10C illustrates a linear component of a nonlinear swept frequency, according to an exemplary embodiment. FIG. 10D illustrates a nonlinear component of a nonlinear swept frequency, according to an exemplary embodiment.

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[0083] For the etalon signal in FIG. 10A, the frequency converted from the wavelength corresponding to the peak is shown as a red dot in FIG. 10B.

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[0085] In step 940, the chirp rate α is determined by the relative frequency change from the center frequency to the next frequency point over the time interval between the two peaks. As shown in FIG 10C, the red dot indicates the determined center frequency and the blue line indicates the chirp rate.

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[0090] In this way, the optimally compensated beat signal can correct the spectral broadening of the originally measured beat signal (e.g., beat signal 135) and form a sharp peak around the correct beat frequency, as will be further illustrated below with numerical results. To that end, a comparative analysis between the proposed approach without a reference arm and the k-sampling method with a reference arm is provided below with reference to FIG. 11A.

[0091] FIG. 11A shows an experimental setup of an SS-OCT system 1100 implemented to compare a no-reference-arm approach with a k-sampling method using a reference arm, according to an exemplary embodiment. FIG. 11A is described below in conjunction with FIG. 11B and FIG. 11C. FIG. 11B shows a time-domain beat signal from a measurement arm 950 (ch1), according to an exemplary embodiment. FIG. 11C shows a reference signal from a reference arm 940 (ch2), according to an exemplary embodiment.

[0092] In FIG. 11A, the SS-OCT system 1100 (also referred to as "system 1100") includes a swept-source laser 1110 and a frequency filter 1120, which corresponds to the frequency filter 117. The SS-OCT system 1100 further includes a reference arm 1140, a measurement arm 1150, a coupler 1130, and a target (i.e., an object or reflector) 1160. The reference arm 1140 includes a first coupler 1141 and a second coupler 1143, a first optical delay line 1142a and a second optical delay line 1142b, and a balanced photodetector (BPD) 1144. Similarly, the measurement arm 1150 includes a coupler 1151, an optical delay line 1152, a lens 1153, an integrated coherent receiver (ICR) 1154, and a circulator 1155.

[0093] For example, the swept-source laser 1110 emits a laser light with a wavelength of 1.55 μm at a repetition rate of x kHz. The laser light is then split into a reference arm 1140 (denoted as Ch2 or channel 2) and a measurement arm 1150 (denoted as Ch1 or channel 1). For the reference arm 1140, a k-sampling clock is generated. To this end, the reference arm 1140 includes a clock generator (not shown in FIG. 11A). Meanwhile, the measurement arm 1150 further splits the laser light into two paths. One path passes through a circulator 1155 and a lens 1153 toward a target 1160. The laser light is then reflected by the target 1160, and the reflected laser light is interfered in the other path to generate a beat signal.

[0094] Meanwhile, the etalon signal is generated by the frequency filter 1120 and generated from channel 3 (or ch3) together with the trigger signal 1170. In the case of the k-sampling based method (i.e., while using the reference arm 1140), the SS-OCT system 1100 uses signals from ch1 and ch2 for nonlinearity compensation. On the other hand, in the method without the reference arm, the SS-OCT system 1100 uses the measurement arm 1150 in ch1 and the etalon signal in ch3. From FIG. 11A and FIG. 11B, it can be observed that both time domain signals are amplitude modulated.

[0095] Furthermore, the spectra of the beat signal before and after nonlinearity compensation from measurement arm 1150 are compared in Figures 12A and 12B.

[0096] FIG. 12A illustrates the spectrum of the beat signal from the measurement arm 1150 before nonlinearity compensation, according to an exemplary embodiment. FIG. 12B illustrates the spectrum of the beat signal from the measurement arm 1150 after nonlinearity compensation, according to an exemplary embodiment. In FIG. 12A, the spectrum of the beat signal from the measurement arm 1150 is broadened to a peak corresponding to the target distance. In fact, the effect of the nonlinearity of the light source causes not only the broadening of the peak, but also a shift of the spectral peak. In contrast, FIG. 12B clearly shows that the peak-to-sidelobe level is significantly improved, and the broadened peak in FIG. 12B is more concentrated around the beat frequency, and the spectral power is even higher at 60 dB.

[0097] Furthermore, the range estimation performance of the proposed approach without a reference arm is evaluated and the results are shown in FIG. 13. To do so, a mirror is placed as an object at 11 distances with a step size of 100 μm. For each distance, the measurement is repeated 10 times to calculate the range estimation statistics, e.g., bias and standard deviation. FIG. 13 shows a measurement profile for an FMCW-based system without a reference arm according to an exemplary embodiment. The measurement profile corresponds to a set of 11 distances against the ground truth on the horizontal axis. The results are overlaid with a 45° diagonal line for comparison. For each distance, the average value of these 10 distance estimates from the compensated peak frequency of FIG. 12B and the standard deviation around the average value are plotted. Overall, the results show a small estimation bias (up to 8 μm) and a standard deviation of up to 4 μm. Furthermore, it is observed that unaccounted amplitude modulation may contribute to the estimation bias.

[0098] In some embodiments, a deskew filtering approach is used to compensate the beat signal based on the estimated light source nonlinearity.

[0099] 14 is a block diagram 1400 illustrating a deskew filtering process for compensating a beat signal with an estimated nonlinearity function according to an exemplary embodiment. FIG 14 illustrates a different nonlinearity compensation approach based on a beat signal from an unknown reflector (e.g., target 1160 in FIG 11A) and an estimated nonlinearity function (as described with respect to Equation 17) from a reference beat signal.

[0100] In step 1401, the nonlinearity due to the transmitter side in the beat signal 1408 is first removed using the estimated nonlinearity function 1407. In step 1402, a deskew filter is applied to the first compensated beat signal. The deskew filter applies a range-dependent / frequency-dependent time shift to the input signal. In other words, the amount of time shift varies depending on the frequency component. Since the frequency is directly related to the range of the beat signal, the deskew filter aims to compensate the range-dependent distortion for different reflectors such that the remaining distortion is range-independent. In step 1403, the remaining range-independent distortion for all frequencies / ranges is removed utilizing the estimated nonlinearity function 1407. Then, the fully compensated beat signal is transformed into the frequency domain by application of an FFT 1404. The range information 1406 of the unknown reflectors can be determined by the spectrum 1405 of the beat signal. Thus, the effect of the nonlinear components is suppressed. Embodiment

[0101] The description provides only exemplary embodiments and is not intended to limit the scope, applicability, or configuration of the disclosure. Rather, the following description of exemplary embodiments will provide those skilled in the art with an enabling description for implementing one or more exemplary embodiments. It is contemplated that various changes may be made to the function and configuration of elements without departing from the spirit and scope of the disclosed subject matter as set forth in the appended claims. Specific details are given in the above description to provide a thorough understanding of the embodiments. However, those skilled in the art will understand that the embodiments may be practiced without these specific details. For example, systems, processes, and other elements in the disclosed subject matter may be shown as components in block diagram form so as not to obscure the embodiments in unnecessary detail. In other examples, well-known processes, structures, and techniques may be shown without unnecessary detail so as not to obscure the embodiments. Additionally, like reference numbers and names in the various drawings refer to like elements.

[0102] Also, individual embodiments may be described as a process that is depicted as a flowchart, a flow diagram, a data flow diagram, a structure diagram, or a block diagram. Although a flowchart may describe operations as a sequential process, many of the operations may be performed in parallel or simultaneously. In addition, the order of operations may be rearranged. A process may be terminated when its operations are completed, but may have additional steps not discussed or included in the diagram. Moreover, not all operations in any process specifically described may occur in all embodiments. A process may correspond to a method, a function, a procedure, a subroutine, a subprogram, or the like. When a process corresponds to a function, the end of the function may correspond to a return of the function to the calling function or to the main function.

[0103] Additionally, embodiments of the disclosed subject matter may be implemented, at least in part, either manually or automatically. The manual or automated implementation may be performed, or at least assisted, through the use of machines, hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof. When implemented in software, firmware, middleware, or microcode, the program code or code segments to perform the necessary tasks may be stored on a machine-readable medium. A processor(s) may perform the necessary tasks.

[0104] Furthermore, the embodiments of the present disclosure and the functional operations described herein can be implemented in digital electronic circuitry, tangibly embodied computer software or firmware, computer hardware including the structures disclosed herein and their structural equivalents, or one or more combinations thereof. Furthermore, some embodiments of the present disclosure can be implemented as one or more computer programs, i.e., as one or more modules of computer program instructions encoded on a tangible, non-transitory program carrier for execution by or to control the operation of a data processing apparatus. Furthermore, the program instructions can be encoded on an artificially generated propagated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, generated to encode information to be transmitted to a suitable receiving device for execution by the data processing apparatus. The computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or one or more combinations thereof.

[0105] A computer program (which may also be referred to or described as a program, software, software application, module, software module, script, or code) can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and can be deployed in any form, such as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program may correspond to a file in a file system, but does not have to. A program can be stored in part of a file that holds other programs or data, for example in one or more scripts stored in a markup language document, in a single file dedicated to the program, or in multiple coordinated files, for example in a file that stores one or more modules, subprograms, or portions of code. A computer program can be deployed to be executed on one computer or on multiple computers located at one location or distributed across multiple locations and interconnected by a communications network.

[0106] A computer suitable for executing a computer program may be based, by way of example, on a general-purpose or dedicated microprocessor or both, or on any other type of central processing unit. Typically, the central processing unit receives instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a central processing unit for implementing or executing instructions, and one or more memory devices for storing instructions and data. Typically, a computer also includes one or more mass storage devices, such as magnetic, magneto-optical, or optical disks, for storing data, or is operatively coupled to said disks to receive data therefrom or transfer data thereto, or both. However, a computer need not have such devices. Furthermore, a computer may be embedded in another device, such as a mobile phone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a global positioning system (GPS) receiver, or a portable storage device, such as a universal serial bus (USB) flash drive, to name a few.

[0107] To provide for user interaction, embodiments of the subject matter described herein may be implemented on a computer having a display device, e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor, for displaying information to the user, and a keyboard and pointing device, e.g., a mouse or trackball, for allowing the user to provide input to the computer. Other types of devices may be used to provide user interaction. For example, feedback provided to the user may be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback, and input from the user may be received in any form, including acoustic input, speech input, or tactile input. Additionally, the computer may provide for user interaction by sending documents to and receiving documents from a device used by the user, e.g., by sending a web page to a web browser on the user's client device in response to a request received from the web browser.

[0108] Embodiments of the subject matter described herein can be implemented in a computing system that includes a back-end component, e.g., as a data server, or includes a middleware component, e.g., an application server, or includes a front-end component, e.g., a client computer having a graphical user interface or web browser that allows a user to interact with an implementation of the subject matter described herein, or includes any combination of one or more of such back-end, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication, e.g., a communications network. Examples of communications networks include local area networks ("LANs") and wide area networks ("WANs"), e.g., the Internet.

[0109] A computing system may include clients and servers. Clients and servers are generally remote from each other and typically interact through a communication network. The relationship of client and server arises from computer programs running on the respective computers and having a mutual relationship of client and server.

[0110] Although the present disclosure has been described with respect to certain preferred embodiments, it should be understood that various other adaptations and modifications can be made within the spirit and scope of the disclosure. It is therefore the object of the following claims to cover all such variations and modifications that fall within the true spirit and scope of the disclosure.

Claims

1. 1. A frequency modulated continuous wave (FMCW) based system, comprising: and an emitter configured to transmit at least one radiation wave into a scene, the transmitted wave being linearly modulated in a frequency domain, the linear modulation being impaired to cause nonlinearity of the transmitted wave in the frequency domain, the system further comprising: a receiver configured to receive reflections of the transmitted waves from one or more objects in the scene; a mixer operatively connected to the emitter and the receiver and configured to interfere a copy of the wave transmitted by the emitter with the reflection of the transmitted wave received by the receiver to generate a beat signal having spectral peaks corresponding to reflections from the one or more objects in the scene, the beat signal being distorted due to the nonlinearity of the modulation caused by the impairment, the system further comprising: an analog-to-digital converter (ADC) operatively connected to the mixer and configured to generate samples of the distorted beat signal; a frequency filter configured to pass signals of a predetermined frequency, the frequency filter operatively connected to the emitter and configured to pass a linear modulated wave transmitted by the emitter at the predetermined frequency at different instants to generate measurements of the modulated wave in the time domain, the system further comprising: at least one processor, the processor comprising: and configured to transform the measurements of the linearly modulated wave from the time domain into a frequency domain to generate a nonlinear frequency signal, the nonlinear frequency signal including a known linear component representing a desired linear modulation and an unknown nonlinear component representing the nonlinearity of the modulation, the processor further comprising: determining coefficients of basis functions that approximate the difference between the nonlinear frequency signal and the linear frequency components in the frequency domain; and detecting one or more spectral peaks in the distorted beat signal, the distortion of which has been compensated in accordance with the basis functions using the determined coefficients, to determine one or more distances to the one or more objects in the scene.

2. 2. The FMCW-based system of claim 1, wherein a sampling frequency of the measurements of the linearly modulated wave produced by the frequency filter is 1 / 1000 of a sampling frequency of the ADC.

3. 2. The FMCW-based system of claim 1, wherein the frequency filter includes an etalon that generates an etalon signal, and the samples in the time domain are peaks of the etalon signal at the different instants, such that the samples in the time domain are sparse.

4. The processor: converting the etalon peaks to wavelengths based on a function of the index of each of the etalon peaks; 4. The FMCW-based system of claim 3, configured to convert the wavelength to the nonlinear frequency signal based on a base wavelength of the etalon and an order of the etalon.

5. 5. The FMCW-based system of claim 4, wherein the linear frequency signal is a linear function of time having a constant term of a center frequency at an etalon peak having the largest frequency change among all said etalon peaks and a time coefficient of relative frequency change over a time interval between two adjacent etalon peaks measured at two adjacent instants.

6. To compensate for distortion of the distorted beat signal, the processor maximizing a cost function of an approximation coherent sum of compensated distorted beat signals using the determined parameters of the nonlinear frequency signal, including the coefficients of the basis functions, the center frequency, and the time coefficients, to generate a time delay estimate of the reflection of the transmitted wave; The FMCW-based system of claim 5 , configured to compensate for distorted beat signals based on the estimated time delay.

7. The FMCW-based system of claim 1 , wherein the processor is configured to estimate the coefficients of the basis functions by solving a least-squares problem that minimizes the difference.

8. The FMCW-based system of claim 7 , wherein the coefficients of the estimated basis functions are functions of polynomial components and peak instants.

9. To compensate for distortion of the distorted beat signal, the processor expressing the nonlinearity of the modulation caused by the impairment as a phase-domain nonlinearity function of the coefficients of the basis functions and an unknown phase; The FMCW-based system of claim 1 , configured to compensate for the distortion caused by the phase-domain nonlinearity function in the phase domain using a deskew filtering approach.

10. 1. A method comprising: and a method for detecting a nonlinearity of the transmitted wave in the frequency domain, the method further comprising: an emitter transmitting at least one radiation wave into a scene, the transmitted wave being linearly modulated in a frequency domain, the linear modulation being impaired to cause nonlinearity of the transmitted wave in the frequency domain; a receiver receiving reflections of the transmitted waves from one or more objects in the scene; a mixer interfering a copy of the transmitted wave with the received reflection of the transmitted wave to generate a beat signal having spectral peaks corresponding to reflections from the one or more objects in the scene, the beat signal being distorted due to the nonlinearity of the modulation caused by the impairment, the method further comprising: an analog-to-digital converter (ADC) generating samples of the distorted beat signal; a frequency filter passing a signal of a predetermined frequency, the frequency filter operatively connected to the emitter and passing a linear modulated wave transmitted by the emitter at the predetermined frequency at different instants to generate a measurement of the modulated wave in the time domain, the method further comprising: and transforming the measurements of the linearly modulated wave from the time domain into a frequency domain to generate a nonlinear frequency signal, the nonlinear frequency signal including a known linear component representing a desired linear modulation and an unknown nonlinear component representing the nonlinearity of the modulation, the method further comprising: determining coefficients of basis functions that approximate the difference between the nonlinear frequency signal and the linear frequency components in the frequency domain; and detecting one or more spectral peaks in the distorted beat signal, the distortion of which has been compensated in accordance with the basis functions using the determined coefficients, to determine one or more distances to the one or more objects in the scene.

11. The method of claim 10, wherein a sampling frequency of the measurements of the linearly modulated wave produced by the frequency filter is 1 / 1000th of a sampling frequency of the ADC.

12. 11. The method of claim 10, wherein the frequency filter includes an etalon that generates an etalon signal, and the samples in the time domain are peaks of the etalon signal at the different instants, such that the samples in the time domain are sparse.

13. The method further comprises: converting the etalon peaks to wavelengths based on a function of the index of each of the etalon peaks; and converting the wavelength to the nonlinear frequency signal based on a base wavelength of the etalon and an order of the etalon.

14. 14. The method of claim 13, wherein the linear frequency signal is a linear function of time with a constant term at a center frequency at an etalon peak having the largest frequency change among all the etalon peaks and a time coefficient of relative frequency change over a time interval between two adjacent etalon peaks measured at two adjacent instants.

15. To compensate for distortion of the distorted beat signal, the method further comprises: maximizing a cost function of an approximate coherent sum of compensated distorted beat signals using the determined parameters of the nonlinear frequency signal, including the coefficients of the basis functions, the center frequency, and the time coefficients, to generate a time delay estimate of the reflection of the transmitted wave; and compensating the distorted beat signal based on the estimated time delay.

16. The method of claim 10 , wherein the method further comprises estimating the coefficients of the basis functions by solving a least-squares problem that minimizes the difference.

17. The method of claim 16 , wherein the coefficients of the estimated basis functions are functions of polynomial components and peak instants.

18. To compensate for distortion of the distorted beat signal, the method further comprises: expressing the nonlinearity of the modulation caused by the impairment as a phase-domain nonlinearity function of the coefficients of the basis functions and an unknown phase; and compensating for the distortion caused by the phase-domain nonlinearity function in the phase domain using a deskew filtering approach.

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