Method and system for target image reconstruction

Abstract

A method for target image reconstruction is provided. The method includes the steps of: transmitting step frequency waveforms having different constant frequencies at different time periods; modulating the step frequency waveforms into a frequency range each having a first frequency and a second frequency, wherein each step frequency waveform increases from the first frequency to the second frequency based on a range function, wherein the modulated step frequency waveforms are arranged with a certain sparsity factor. The method further includes: sending the modulated step frequency waveforms to a target and accepting reflections of the modulated step frequency waveforms reflected from the target; interfering the modulated step frequency waveforms with the reflections of the modulated step frequency waveforms to generate a beat signal of the interference between the modulated step frequency waveforms and the reflections of the modulated step frequency waveforms; and reconstructing an image of the target from the beat signal.

Description

TECHNICAL FIELD

[0001] The present invention relates generally to coherent optical sensors, and more particularly to a coherent optical sensor with sparse illumination. BACKGROUND

[0002] Coherent optical sensors are used to construct 3-D images of objects for applications such as medical imaging, industrial imaging, etc. A limitation of these sensors is that their resolution is limited by the bandwidth of the source used to illuminate the object. Conventional sensors use either a randomly varying high-bandwidth source combined with multiple detectors or a time-varying high-bandwidth optical source swept in the frequency domain combined with a single receiver. Both of these solutions result in high resolution, but are extremely costly due to the complexity of manufacturing the detectors in the former case and the source in the latter case. Problem: reduce the cost of coherent optical sensors.

[0003] Optical coherence tomography (OCT) is typically implemented with a swept source laser for high resolution. Unfortunately this laser is an extremely expensive component, making OCT an expensive to prohibitive technology for many applications. There is therefore a need to develop a coherent sensing system that enables the use of cheaper optical sources. SUMMARY

[0004] Some embodiments of the present disclosure are based on the recognition that the combination of multiple low-bandwidth sources chirped can achieve high bandwidth. By coherently combining low-bandwidth chirps, we can achieve performance equivalent to a high-bandwidth system for sparse targets.

[0005] Some embodiments of the present disclosure are based on the recognition that by using a single frequency optical source (e.g., a diode laser) combined with phase modulation, a significant fraction of the desired illumination bandwidth can be covered, allowing for sparse recovery of certain targets. Furthermore, in some cases, the number of optical frequencies required for such a system can be small enough that all of the lasers and modulation devices can be integrated into a single photonic integrated circuit (PIC). Avoiding nonlinear devices, mechanical swept components, and other common features of conventional swept sources will be a key factor in avoiding the high cost of these swept sources.

[0006] According to some embodiments of the present disclosure, a coherent optical sensing system is implemented with sparse illumination suitable for spatially sparse targets. It was found that performance equivalent to conventional Optical Coherence Tomography (OCT) is achieved while constraints on optical source performance can be greatly reduced. Since the bandwidth occupancy of the source can be reduced compared to previously proposed step frequency modulated coherent sensors (e.g., U.S. Patent Application No. 16 / 226,723), equivalent performance can be achieved with a significantly reduced number of unmodulated carriers, thus reducing source cost. Alternatively, the total bandwidth can be significantly expanded without increasing the number of unmodulated carriers, thus significantly improving on-axis resolution without increasing cost. As a result, an improved sensor for industrial applications with sparse targets can be implemented with greatly reduced cost.

[0007] It is an object of some embodiments to provide a sensor configured to reconstruct an image of a scene from frequency modulated signals reflected from targets in the scene. Such an image is referred to herein as a target image. It is an object of some embodiments to provide such a sensor that uses the functionality of a linear sweep source that emits a linear sweep waveform in the frequency domain, without the cost of manufacturing an ideal linear sweep source and / or the imperfections caused by non-linearity in the practical implementation of current linear sweep sources. It is an object of some embodiments to increase the bandwidth of these sweep sources without a high increase in manufacturing cost typically associated with high bandwidth sweep sources.

[0008] On the one hand, these objectives seem overly optimistic. However, some embodiments aim to utilize a step frequency sweep source instead of a linear sweep source, since a step frequency sweep source can cover almost arbitrarily high bandwidths without any cost increase associated with the increase in bandwidth or with a modest cost increase. However, in order to use a step frequency sweep source in frequency modulated image reconstruction, some embodiments overcome a number of challenges.

[0009] Some embodiments are based on the understanding that a step frequency sweep source is not suitable as such for frequency modulated image reconstruction. A step frequency sweep source emits waveforms with different constant frequencies at different time periods, but only a single frequency per time period. In essence, the waveforms emitted by a step frequency sweep source are step frequency waveforms that can be represented by a step function that is a piecewise constant function with only a finite number of pieces. Due to these properties, only a small number of frequencies in the covered bandwidth are defined (have a value), which degrades image reconstruction.

[0010] Further, according to some embodiments of the present disclosure, a method of target image reconstruction is provided. The method can include the steps of: transmitting step-frequency waveforms having different constant frequencies at different time periods; modulating the step-frequency waveforms into a frequency range, each having a first frequency and a second frequency, wherein each step-frequency waveform increases from the first frequency to the second frequency based on a range function, wherein the modulated step-frequency waveforms are arranged with a certain sparsity factor; transmitting the modulated step-frequency waveforms to a target and accepting reflections of the modulated step-frequency waveforms reflected from the target; interfering the modulated step-frequency waveforms with the reflections of the modulated step-frequency waveforms to generate beat signals of the interference between the modulated step-frequency waveforms and the reflections of the modulated step-frequency waveforms; and reconstructing an image of the target from the beat signals.

[0011] Further, some embodiments of the present disclosure provide a system for target image reconstruction. In this case, the system can include: a step-frequency transmitter configured to transmit step-frequency waveforms having different constant frequencies at different time periods; a modulator configured to modulate the step-frequency waveforms into a frequency range, each having a first frequency and a second frequency, wherein each step-frequency waveform increases from the first frequency to the second frequency based on a range function, wherein the modulated step-frequency waveforms are arranged with a certain sparsity factor at different time periods; a transceiver configured to transmit the modulated step-frequency waveforms to a target and to accept reflections of the modulated step-frequency waveforms reflected from the target; a mixer configured to interfere the modulated step-frequency waveforms with the reflections of the modulated step-frequency waveforms to generate beat signals of the interference between the modulated step-frequency waveforms and the reflections of the modulated step-frequency waveforms; and a signal processor configured to reconstruct an image of the target from the beat signals. BRIEF DESCRIPTION OF DRAWINGS

[0012] Embodiments of the present disclosure will be further described with reference to the drawings. The drawings shown are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the embodiments of the present disclosure.

[0013] [ Figure 1A ] Figure 1A A schematic diagram of a spectrum sparsity coherent sensing system according to some embodiments of the present disclosure is shown.

[0014] [ Figure 1B ] Figure 1B A frequency versus time schematic diagram of a step-frequency source after modulation according to some embodiments of the present disclosure is shown.

[0015] [ Figure 1C ] Figure 1C A frequency versus time schematic diagram of a step-frequency source after modulation according to some embodiments of the present disclosure is shown.

[0016] [Figure 1D ] Figure 1D An exemplary schematic diagram of a sparse illumination coherent sensor according to some embodiments of the application is shown.

[0017] [ Figure 2A ] Figure 2A A schematic diagram of the process of reconstructing a high resolution image from a series of low resolution measurements is shown.

[0018] [ Figure 2B ] Figure 2B An exemplary signal flow of reconstructing a high resolution image from many low resolution measurements according to embodiments of the present disclosure is shown.

[0019] [ Figure 2C ] Figure 2C An exemplary set of low resolution measurements being processed to generate a high resolution image according to some embodiments of the application is shown.

[0020] [ Figure 3 ] Figure 3 A schematic diagram of a system according to embodiments of the present disclosure is shown, illustrating a reflected waveform being mixed in a mixer with an unmodulated step frequency source.

[0021] [ Figure 4A ] Figure 4A An exemplary system according to embodiments of the present disclosure is shown, in which a reference signal is generated by mixing a modulated waveform with an unmodulated step frequency source.

[0022] [ Figure 4B ] Figure 4B An exemplary system according to embodiments of the present disclosure is shown, in which a digital reference signal generator is used, for example by storing the reference signal in a memory.

[0023] [ Figure 5 ] Figure 5 A schematic diagram of reconstructing an image of a target from a set of reflected signals and reference signals according to embodiments of the present disclosure is shown.

[0024] [ Figure 6A ] Figure 6A An exemplary architecture of a step frequency source with modulation according to embodiments of the present disclosure is shown.

[0025] [ Figure 6B ] Figure 6B An example of the process of applying modulation to a step frequency unmodulated source according to embodiments of the present disclosure is shown.

[0026] [ Figure 7 ] Figure 7 is a block diagram of a system comprising a system according to embodiments of the present disclosure.

[0027] [Figure 8A ] Figure 8A is an example of a reconstructed result of a test metal sample according to an embodiment of the present disclosure.

[0028] [ Figure 8B ] Figure 8B shows a reconstructed result using Fourier transform based processing followed by basic peak detection according to an embodiment of the present disclosure.

[0029] While the above figures set forth embodiments of the presently disclosed subject matter, other embodiments can also be contemplated as discussed in the Discussion. The present disclosure presents illustrative embodiments as representative of the presently disclosed subject matter. Numerous other modifications and embodiments can be devised by those skilled in the art that fall within the scope and spirit of the presently disclosed subject matter. DETAILED DESCRIPTION

[0030] Various embodiments of the present disclosure are described below with reference to the drawings. It will be noted that the drawings are not drawn to scale, and that similar structures or functions throughout the drawings can be indicated by like reference numerals. It should also be noted that the drawings are merely intended to facilitate description of the particular embodiments of the present application. They are not intended as an exhaustive description of the present application or as a limitation on the scope of the present application. In addition, aspects described in connection with a particular embodiment of the present application can not necessarily be limited to such embodiment, and can be practiced in any other embodiment of the present application.

[0031] Some embodiments of the present disclosure are based on the recognition that a spectrally sparse coherent sensing system can be configured to perform a method comprising the steps of transmitting a stepped frequency waveform having different constant frequencies at different time periods, the stepped frequency waveform being modulated into a frequency range having a first frequency and a second frequency. In this case, each stepped frequency waveform increases from the first frequency to the second frequency based on a range function, wherein the modulated stepped frequency waveforms are arranged by a sparse factor at different time periods. The method further comprises the steps of sending the modulated stepped frequency waveform to a target and accepting a reflection of the modulated stepped frequency waveform reflected from the target; interfering the modulated stepped frequency waveform with the reflection of the modulated stepped frequency waveform to generate a beat signal of the interference between the modulated stepped frequency waveform and the reflection of the modulated stepped frequency waveform; and reconstructing an image of the target from the beat signal.

[0032] The range of the target can be estimated by linearly chirping the frequency of the light source and interfering the returned light from the target with itself. Due to the interference of the two beams, the distance of the target is proportional to the beat frequency. Typically, the linear chirp image domain is achieved by taking the fast Fourier transform of the time domain signal and taking the magnitude. The coverage B is inversely proportional to the achievable resolution Δz, and using the Abbe resolution criterion, this can be quantified as where c is the speed of light in air. To maintain spatial resolution while reducing the scan bandwidth, linear step chirps can be used, where a constant frequency difference is used between chirps and the individual low resolution images reconstructed by a FFT. The high resolution image is then obtained by summing each multiplied by the correct phase and then taking the magnitude. However, in this case the unambiguous imaging range R U is now limited by the spacing between chirps where Af is the linear spacing between chirps. Thus, to achieve high resolution while also keeping the bandwidth occupancy low, the unambiguous range needs to be small, making it unsuitable for many applications. Random spacing between chirps can also be used with the linear reconstruction described previously for linear step chirps. In this case, the reconstruction can benefit from the fast processing time of the FFT, while the unambiguous range R U is now limited only by the sampling rate of the detector, as where f s is the sampling rate of the detector and s is the chirp rate. The main limitation of this approach is the side lobes in the reconstructed image. The smaller the occupancy bandwidth, the larger the side lobes, thus providing noise and distortion in the image domain as the side lobes look like targets. It should be noted that although low BW chirps can be used for matched filter ranging, this does not allow two close targets to be imaged simultaneously.

[0033] To avoid the trade-off between the unambiguous range and the imaging resolution, randomly spaced step frequency chirps can be used. The randomness is pseudo-random and chosen before the imaging is performed. For linear chirps, the resolution is determined by and the unambiguous range is where Af is the frequency spacing between chirps. The individual received waveforms have a constant term and a single frequency AWGN. No assumptions are made about the prior information of the scene, and the reconstruction is performed by matched filtering. One metric used to assess the resolution accuracy can be the peak to maximum side lobe ratio. This metric is used because it has an easy to analyze form and is related to the probability of error (within a probabilistic framework). A basic threshold on the peak can be used to determine the number of targets present within the imaged area. A basic probabilistic framework to estimate the probability of error of a false alarm can give the following.

[0034] The reconstructed image of a single low bandwidth chirp of index i is given by

[0035]

[0036] Thus the reconstructed high resolution image is given by

[0037]

[0038] This gives a peak to maximum side lobe ratio of

[0039]

[0040] Figure 1A A schematic diagram of a spectrum-sparse coherent sensing system 100 is shown, in accordance with some embodiments of the present disclosure. The system 100 is configured to reconstruct an image of a scene from frequency modulated signals reflected from targets in the scene. The system 100 uses a stepped frequency source 110. Such an image is referred to herein as a target image.

[0041] The stepped frequency source 110 is configured to generate a stepped frequency waveform 115, which is then sent to a modulator 120. The modulator 120 is configured to generate a modulated stepped frequency waveform 125. The modulated stepped frequency waveform 125 is provided to a target 130 and a mixer 140, and a reflection of the modulated waveform 135 is generated from the target 130. This reflection is then mixed with the modulated stepped frequency waveform 125 in the mixer 140 to generate an interference 145, which is then processed in a signal processor 150. The signal processor 150 is configured to generate a target image 155.

[0042] Figure 1B A frequency versus time schematic diagram of a stepped frequency source 110 is shown, in accordance with some embodiments of the present disclosure. The stepped frequency source 110 is configured to generate / send individual frequencies 121, 122, 123, 124, and 125 in sequence. In this case, the frequencies do not include overlap. Some embodiments are based on the recognition that given proper image reconstruction techniques, a spatially sparse target can be completely and accurately sensed with only a sparse illumination spectrum. Furthermore, the emitted illumination stepped frequency waveforms 121, 122, 123, 124, and 125 are different constant frequencies for different time periods, and the stepped frequency waveforms 121, 122, 123, 124, and 125 are modulated over a range of frequencies. In this case, each frequency range has a first frequency and a second frequency, and each stepped frequency waveform increases from the first frequency to the second frequency based on a range function. In some cases, the range function can be a linear function of time (i.e., a chirp). Furthermore, the modulated stepped frequency waveforms 121, 122, 123, 124, and 125 are arranged with some sparse factor.

[0043] Some embodiments of the present invention are based on the recognition that a stepped frequency source (or stepped chirp light source) 110 with a modulator 120 and modulated signal can have a significantly lower cost than an equal bandwidth continuous swept source, while providing equivalent performance for spatially sparse targets. An optical system containing multiple discrete lasers acting as the stepped frequency source 110 and a modulator 120 to provide some extension of the bandwidth can be implemented on a single photonic integrated circuit without any physical moving components. This in turn allows the use of modern semiconductor manufacturing, processing, and packaging techniques, and is significantly less costly than traditional devices that require extensive mechanical assembly, alignment, and calibration.

[0044] In some embodiments, the stepped frequency source 110 can be implemented by connecting multiple single frequency lasers and multiplexing with a phase modulator. The detector sampling rate can be between about 100 MHz and 1 GHz. For example, the sampling rate can be 400 MHz, and the chirp rate can be between about 10 16 Hz / s and about 10 17 Hz / s. The chirp bandwidth can be between about 10 GHz and 50 GHz. In some cases, the chirp bandwidth can be 15 GHz. Image reconstruction can be performed using the size of the Fourier transform of the received waveform.

[0045] Generally, the modulator 120 is a device configured to modulate an incoming signal. For example, some embodiments use a Mach-Zehnder modulator (MZM), which is an optical device that exhibits an electro-optic effect for signal control elements to modulate a light beam. In one embodiment, a modulation is applied to the phase and / or amplitude of the light beam. Modulation bandwidths of several tens of gigahertz can be achieved with Mach-Zehnder modulators.

[0046] In one embodiment, the stepped frequency waveform has a constant height for each step, such that the difference between any two adjacent frequencies is constant. In this embodiment, a single modulator configured to expand a constant frequency over the range defined by the steps of the stepped frequency waveform can modulate the entire stepped frequency waveform to occupy the entire bandwidth. In this way, a single stepped frequency sweep source (which can be implemented with multiple constant frequency sources) and a single modulator can generate a modulated signal covering a bandwidth 134 of almost any size.

[0047] Figure 1C A frequency versus time plot of the modulated stepped frequency source 135 is shown. Each frequency 131 is modulated to provide an expanded bandwidth 133. The modulation can optionally be performed such that the frequency increases constantly and linearly over time 132 to generate a linear chirp. The total measured bandwidth 134 is defined as the difference between the maximum and minimum frequencies over the entire modulated waveform 135. We can define a sparsity factor as the number of wavelengths multiplied by the bandwidth per wavelength, divided by the total measured bandwidth. For example, the sparsity factor can be determined such that the sum of the frequency ranges is less than the total bandwidth over the target measurement.

[0048] Figure 1DAn exemplary schematic diagram showing a sparse illumination coherent sensor (system) 100 according to some embodiments of the present application. The sparse illumination coherent sensor 100 can include a stepped frequency source 161, a modulator 110, a circulator 17, a lens or antenna 175, a digital signal processor 195, and a coherent sensor 190. The stepped frequency source 161 sends a waveform 165 to the modulator 110. The modulated waveform 111 is then sent to the circulator 170, which is then sent to the lens or antenna 175, which then sends the waveform 180 to the target 185. The reflection is then collected by the lens or antenna 175, which then passes through the circulator 170. The reflected signal 135 is then mixed with a portion of the modulated waveform 115 in the coherent sensor 190, which is then processed in the digital signal processor 195.

[0049] In some cases, the circulator 170 is a passive, non-reciprocal three or four port device in which a microwave or radio frequency signal entering any port is sent rotationally to the next port. In one implementation, the circulator 170 is a 3-port circulator designed such that a signal entering any port exits from the next port. This means that if a signal enters port 1, it is emitted from port 2, but if some of the emitted signal is reflected back into the circulator, it does not exit from port 1, but from port 3. In embodiments using optical signals (e.g., using a laser as the stepped frequency source 161), the circulator 170 is an optical circulator.

[0050] According to embodiments of the present disclosure, the modulated waveform emitted from the second port of the circulator 170 is sent to the lens or antenna 175. The imaging head is a device that provides for optical coupling into and out of the sensor and directs light onto the target. The modulated waveform is then sent to the target 185 via the free space channel 180. The reflection from the target is then collected by the lens or antenna 175, which is then sent between ports 2 and 3 of the circulator 170. The reflected signal 135 is then mixed with the unmodulated stepped frequency waveform 115 in the mixer 190, which is then processed by the signal processor 150. In some cases, the signal processor 150 can be a digital signal processor 195.

[0051] Figure 2A An exemplary schematic diagram showing the process of reconstructing a high resolution image from a series of low resolution measurements using the system 100, each low resolution measurement corresponding to a measurement over a single modulated stepped frequency with a bandwidth equal to the modulation. The low bandwidth measurements are upsampled 201 to provide a set of upsampled low resolution measurements 205. The measurements are then subjected to a frequency shift corresponding to the relative frequency of their respective stepped frequencies 202 to generate a set of frequency shifted measurements 206. The low resolution measurements are then summed 203 to generate a single high resolution measurement 207. This high resolution measurement 207 is then subjected to a Fourier transform 204 to generate a high resolution image 208.

[0052] Figure 2B An example signal flow is shown that reconstructs a high resolution image from a number of low resolution measurements according to some embodiments of the present disclosure. According to some embodiments of the present disclosure, the low resolution measurements correspond to spectra of low resolution images. The plurality of low resolution measurements 210, 211, 212 are upsampled and frequency translated 220, 221, 222 according to the relative frequencies of the corresponding step frequency source frequencies. These manipulated low resolution measurements are then summed 225 and then undergo a Fourier transform 226 to generate a high resolution image 227.

[0053] Figure 2C An example set of low resolution measurements being processed to generate a high resolution image according to some embodiments of the present disclosure is shown. In this case, the reconstructed image can be performed by including the following steps: generating a set of low bandwidth measurements using low bandwidth measurements from each step frequency of an unmodulated waveform; increasing the sampling rate of each of the set of low bandwidth measurements by zero padding in the frequency domain to generate a set of oversampled measurements; applying a frequency shift to each low bandwidth measurement corresponding to its relative optical frequency to generate a set of frequency shifted measurements; summing the frequency shifted measurements to generate a single high bandwidth measurement; and transforming the high bandwidth measurement with a Fourier transform to generate a target image. In this case, the resolution of the target image can be greater than the resolution of each of the low resolution images.

[0054] For example, a plurality of low resolution measurements 260, 270, 280 can be upsampled in the frequency domain and frequency translated 261, 271, 281 according to the relative frequencies of the corresponding step frequency source frequencies for a small portion or the entire axial measurement of the measurement. These manipulated low resolution measurements are then summed 290 and then undergo a Fourier transform to generate a high resolution image 295.

[0055] Some embodiments are based on the recognition that knowledge of the modulation parameters can be used for target image reconstruction. Examples of modulation parameters include the modulation signal, the system impulse response, and the modulation sequence timing representing the relative phase of the modulation sequence with respect to the measurement device. In particular, the waveform from the target reflection is affected by the number of processes including the process of interest and auxiliary processes. The process of interest is reflected from the target image. This process affects the waveform in a manner that allows for reconstruction of the target image. The auxiliary processes include the manner in which the waveform is generated and modulated. The effect of the generation is reduced by interfering the reflection of the modulated step frequency waveform with the original unmodulated step frequency waveform. However, the effect of the modulation during target image reconstruction also needs to be taken into account.

[0056] The modulation parameters have a different principle than the propagation principle of the processed waveforms. Thus, it would be difficult to directly consider these parameters in the target image reconstruction. However, some embodiments are based on the recognition that one way to consider the modulation in the target image reconstruction is to have a reference signal to indicate the interference of the unmodulated and modulated stepped frequency waveforms, allowing the modulation parameters to be received in a similar form as the processed waveforms. This reference signal can help to separate the effects of the modulation on the reflection of the modulated stepped frequency waveform.

[0057] Further, a system according to embodiments of the present disclosure can perform by including the steps of generating a reference signal indicating the interference of the unmodulated and modulated stepped frequency waveforms; and reconstructing the target image using the beat signal and the reference signal. In some cases, the reconstructing step can include the steps of cross-correlating the beat signal and the reference signal in the frequency domain for each constant frequency of the unmodulated stepped frequency waveform to generate a correlation signal, such that there is one correlation signal for each constant frequency; combining the correlation signals in the frequency domain in the order of their respective frequencies to generate a frequency image of the target in the frequency domain; and transforming the frequency image using a Fourier transform to generate the target image. Further, the interference is performed in the digital domain.

[0058] Figure 3 An example schematic illustrating a system according to some embodiments of the present disclosure is shown. In this case, the reflected waveform 302 is mixed with the unmodulated stepped frequency source 301 in a mixer 305. The resulting beat signal 315 is sent to a signal processor 330 along with a reference signal 320 generated in a reference signal generator 310.

[0059] Some embodiments of the present invention are based on the recognition that although the image reconstruction requires deconvolution of the transmitted modulated waveform and the received waveform, this can be done in the digital domain without penalty. Further, some embodiments of the present invention are based on the recognition that if the reflected waveform is mixed with a stepped frequency waveform to form a beat signal, and the modulated waveform is mixed with a stepped frequency source to form a reference signal, then the modulated signal can be any waveform with the required bandwidth and equal power in all frequency components.

[0060] Figure 4A An example system generating a reference signal by mixing a modulated waveform with an unmodulated stepped frequency source is shown. The reflected waveform 302 is mixed with the unmodulated stepped frequency source 301 in a mixer 305. The resulting beat signal 315 is then digitized in a digitizer 415 and then sent to a digital signal processor 430. At the same time, the modulated waveform 401 is mixed with the unmodulated stepped frequency source 301 in a mixer 402. The resulting reference signal 320 is then digitized in a digitizer 425 and then sent to the digital signal processor 430.

[0061] Figure 4B Another example system is shown that uses a digital reference signal generator, for example, by storing the reference signal in memory. The reflected waveform 302 is mixed in a mixer 305 with an unmodulated stepped frequency source 301. The resulting beat signal 315 is then digitized in a digitizer 415 and then sent to a digital signal processor 430. At the same time, a digital reference signal 435 is sent to the digital signal processor 430.

[0062] Figure 5 An example is shown of reconstructing a high resolution target image from a set of low resolution beat signals with a corresponding reference signal. The beat signal 505 and the reference signal 500 are used to compute a cross correlation 510, resulting in a low resolution image 515. A Fourier transform such as a fast Fourier transform (FFT) 520 is then used to generate a low bandwidth spectrum of the target image. The image spectrum is then upsampled and frequency translated to create single stepped frequency components of a total spectrum 527. The component spectra 527 are then summed 530 to generate a high bandwidth spectrum 535, which is then used to create a high resolution image 550 using an inverse Fourier transform 540.

[0063] Figure 6A An example architecture is shown with a modulated stepped frequency source. A set of N single frequency carriers 601, 602, and 603 are switched with a lxN switch 610 configured to generate an output 615 with a stepped frequency. The switch is controlled by a switch controller 611 that uses a switch timing provided by a timing signal 612. The stepped frequency source 615 is modulated by a modulator 620 that modulates according to a modulation signal 621 to generate a modulated waveform 625. The modulation signal 621 has a timing that is also synchronized to the timing signal 612.

[0064] Figure 6B An example is shown of the process of applying modulation to a stepped frequency unmodulated source. An initial stepped frequency source is shown in 640. Using a set of single frequency sources, the instantaneous frequency is constant for some period of time 645. In this case, the effective occupation of the total bandwidth 647 is close to zero. 650 shows a modulation signal to be applied to the stepped frequency. The modulation signal covers a fixed bandwidth 655, repeating with the same period as the frequency shift 645 of the stepped source. In this case, the bandwidth is completely occupied, but only limited to the modulation bandwidth. In 650, the instantaneous frequency is constantly changing. 660 shows a schematic of the modulated stepped frequency waveform. The individual components of the stepped frequency source are modulated to achieve an increased bandwidth 645, while the total bandwidth of the modulated stepped frequency source is partially occupied with some non-zero sparsity.

[0065] Figure 7 A computer program product 1000 comprising a computer readable medium 1002 is in accordance with embodiments of the present disclosure. The computer readable medium 1002 stores instructions 1004 which, when executed by a computer processor 1006, cause the computer processor 1006 to perform operations in accordance with embodiments of the present disclosure. Figure 1Da block diagram of the system of the digital signal processor (system) 195, which can be implemented using an alternative computer or hardware processor. The computer 1111 includes a hardware processor 1140, a computer readable memory 1112, a storage 1158, and a user interface 1149 having a display 1152 and a keyboard 1151, connected by a bus 1156. The computer readable memory 1112 stores an image reconstruction algorithm for generating the target image 155. The processor 1140 is configured to generate the target image in conjunction with the computer readable memory 1112 using signals provided via the interface. When referring to Figure 1A the interference 145 has received the signal from the mixer 140, where the reflected signal 135 and the modulated step frequency waveform 125 are mixed.

[0066] For example, upon receiving input from a user from the surface of the user interface 1149 (the keyboard surface 1151), the user interface 1149, in communication with the hardware processor 1140 and the computer readable memory 1112, acquires the signal data example and stores it in the computer readable memory 1112.

[0067] Depending on the application, the computer 1111 can include a power supply 1254, which can optionally be external to the computer 1111. A user input interface 1157 adapted to connect to a display device 1148, which can include a computer monitor, a camera, a television, a projector, or a mobile device, among others, can be linked through the bus 1156. A printer interface 1159 can also be connected through the bus 1156 and adapted to connect to a printing device 1132, which can include a liquid inkjet printer, a solid ink printer, a large-format commercial printer, a thermal printer, a UV printer, or a dye-sublimation printer, among others. A network interface controller (NIC) 1154 is adapted to connect to a network 1136 through the bus 1156, where time series data or other data, among others, can be presented on third-party display devices, third-party imaging devices, and / or third-party printing devices external to the computer 1111.

[0068] Still referring to Figure 7signal data or other data, etc. can be transmitted via the communication channels of network 1136 and / or stored within storage system 1158 for storage and / or further processing. It is contemplated that signal data can be initially stored in external memory and later retrieved by the hardware processor for processing, or stored in the hardware processor's memory for processing at a later time. The hardware processor memory includes stored executable programs executable by the hardware processor or computer for performing the resilient restoration system / method, power distribution system operational data, and historical power distribution system data of the same type as the power distribution system and other data related to the resilient restoration of the power distribution system or a power distribution system of the same type as the power distribution system.

[0069] Further, signal data or other data can be received wirelessly or hardwired from receiver 1146 (or external receiver 1138) or transmitted wirelessly or hardwired via transmitter 1147 (or external transmitter 1139), both of which are connected by bus 1156. Computer 1111 can be connected to external sensing devices 1144 and external input / output devices 1141 via input interface 1108. For example, external sensing devices 1144 can include sensors that collect data before, during, and after the collection of signal data of the power distribution system. For example, disaster-inducing fault line segments and fault types and fault impact customers. Computer 1111 can be connected to other external computers 1142. Output interface 1109 can be used to output processed data from hardware processor 1140. It is noted that upon receiving input from a user from surface 1152 of user interface 1149, user interface 1149, in communication with hardware processor 1140 and non-transitory computer readable storage medium 1112, acquires the area data and stores it in non-transitory computer readable storage medium 1112.

[0070] Figure 8A is an example of experimental reconstruction results for a test metal sample using Fourier transform based processing followed by basic peak detection using a 3dB threshold (based on the maximum peak) for full chirp (i.e., traditional FMCW), step-chirp (i.e., spectrally sparse FMCW), and multi-peak cases. The cross-hair indicates the detected peak(s) of the test metal sample and their corresponding locations (test pattern / morphology pattern). The standard deviation is 1.3 pm, the imaging parameters are 400 MHz sampling rate, scanned roughly from 1580 nm to 1610 nm, chirp rate is 8.398e16 Hz / s, chirp bandwidth is 15 GHz, reconstruction resolution is 1.8 um, 64 frequencies. This figure clearly indicates that for spatially sparse targets (such as the one measured), spectrally sparse illumination can achieve the same performance as traditional FMCW based OCT. Good precision is obtained while the system shows the ability to simultaneously detect multiple peaks at wide (roughly 1 mm) spacing.

[0071] Figure 8B The reconstruction results using Fourier transform based processing followed by basic peak detection using a 3 dB threshold (based on the maximum peak) are shown, with parameters identical to those described for Figure 8A The proposed spectrally sparse illumination system is shown to achieve equal on-axis resolution to conventional FMCW OCT for spatially sparse targets, such as the one shown here. Multiple reflections are clearly detected with approximately 40 micron spacing, and the spectrally sparse OCT shows negligible performance penalty compared to FMCW OCT.

[0072] As shown, a coherent optical sensing system with sparse illumination is suitable for spatially sparse targets. This demonstrates performance comparable to conventional Optical Coherence Tomography (OCT), while the constraints on optical source performance, and thus source cost, can be greatly reduced.

[0073] The above-described embodiments of the present disclosure can be implemented in any of numerous ways. For example, the embodiments can be implemented using hardware, software or a combination thereof. When implemented in software, the software code can be executed on any suitable processor or collection of processors, whether provided in a single computer or distributed among multiple computers. These processors can be implemented as integrated circuits, with one or more processors in a single integrated circuit component. However, a processor can be implemented using circuitry in any suitable format.

[0074] Additionally, embodiments of the invention can be embodied as a method, of which an example has been provided. The acts performed as part of the method can be ordered in any suitable way. Accordingly, embodiments can be constructed in which acts are performed in an order different than illustrated, which can include performing some acts simultaneously, even though shown as being performed sequentially in illustrative embodiments.

[0075] The use of ordinal terms such as "first", "second", "third" etc. in the claims to modify a claim element does not imply any priority or order of one claim element over another or the temporal order in which acts are performed, but merely makes for a conciser reference only for those claim elements so designated. Thus in this document, the ordinal terms are used as labels to distinguish between claim elements having the same name (but for use of the ordinal term) to distinguish the claim elements.

[0076] While the present invention has been described as a preferred embodiment, it is understood that various other modifications and changes can be made without departing from the true spirit and scope of the present invention.

[0077] Accordingly, it is intended that all such alterations and modifications be considered as falling within the true spirit and scope of the present invention.

Claims

1. A method for target image reconstruction, the method comprising the steps of: emitting step frequency waveforms having different constant frequencies at different time periods; modulating the step frequency waveforms into frequency ranges each having a first frequency and a second frequency, wherein each of the step frequency waveforms increases from the first frequency to the second frequency based on a range function, wherein the modulated step frequency waveforms are arranged with a sparsity factor determined such that a sum of the frequency ranges is less than a total bandwidth on a measurement of a target; sending the modulated step frequency waveforms to the target and accepting reflections of the modulated step frequency waveforms reflected from the target; interfering the modulated step frequency waveforms with the reflections of the modulated step frequency waveforms to generate beat signals of the interference between the modulated step frequency waveforms and the reflections of the modulated step frequency waveforms; and reconstructing an image of the target from the beat signals.

2. The method of claim 1, wherein, The emitted step frequency waveforms have different constant frequencies at different time periods; The step frequency waveforms are modulated over frequency ranges each having a first frequency and a second frequency, wherein each of the step frequency waveforms increases from the first frequency to the second frequency based on a range function, wherein the modulated step frequency waveforms are arranged with the sparsity factor.

3. The method of claim 1, wherein, The step of reconstructing the image of the target comprises the steps of: generating a set of low bandwidth measurements using low bandwidth measurements from each step frequency of an unmodulated waveform; increasing a sampling rate of each of the set of low bandwidth measurements by zero padding in a frequency domain to generate a set of oversampled measurements; applying a frequency shift to each of the low bandwidth measurements corresponding to its relative optical frequency in the frequency domain to generate a set of frequency shifted measurements; summing the frequency shifted measurements to generate a single high bandwidth measurement; transforming the high bandwidth measurement with a Fourier transform to generate a target image, wherein a resolution of the target image is greater than a resolution of each low resolution image.

4. The method of claim 1, further comprising the steps of: generating a reference signal indicative of an interference of an unmodulated step frequency waveform and the modulated step frequency waveforms; and reconstructing a target image using the beat signals and the reference signal. The step of reconstructing the image of the target comprises the steps of:

5. The method of claim 4, wherein, cross correlating the beat signals and the reference signal in a frequency domain for each constant frequency of the unmodulated step frequency waveform to generate a correlation signal such that there is one correlation signal for each constant frequency; combining the correlation signals in the frequency domain in an order of their respective frequencies to generate a frequency image of the target in the frequency domain; and transforming the frequency image with a Fourier transform to generate the target image. The range function is a linear function as a function of time.

6. The method of claim 1, wherein, 7. A system for target image reconstruction, the system comprising: a step frequency transmitter configured to emit step frequency waveforms having different constant frequencies at different time periods; ​ a modulator configured to modulate the stepped frequency waveforms into a frequency range, each of the stepped frequency waveforms having a first frequency and a second frequency, wherein each of the stepped frequency waveforms increases from the first frequency to the second frequency based on a range function, wherein the modulated stepped frequency waveforms are arranged with a sparsity factor determined such that a sum of the frequency range is less than a total bandwidth on a measurement of a target; a transceiver configured to transmit the modulated stepped frequency waveforms to the target and to accept a reflection of the modulated stepped frequency waveforms reflected from the target; a mixer configured to interfere the modulated stepped frequency waveforms with the reflection of the modulated stepped frequency waveforms to generate a beat signal of the interference between the modulated stepped frequency waveforms and the reflection of the modulated stepped frequency waveforms; and a signal processor configured to reconstruct an image of the target from the beat signal.

8. The system of claim 7, wherein, The emitted stepped frequency waveforms have different constant frequencies at different time periods, wherein the stepped frequency waveforms are modulated over a frequency range, each of the stepped frequency waveforms having a first frequency and a second frequency, wherein each of the stepped frequency waveforms increases from the first frequency to the second frequency based on a range function, wherein an arrangement of the modulated stepped frequency waveforms has the sparsity factor.

9. The system of claim 7, wherein, The signal processor performs the following steps: generating a set of low bandwidth measurements using low bandwidth measurements from each of the stepped frequencies of the unmodulated waveforms; increasing a sampling rate of each of the set of low bandwidth measurements by zero padding in a frequency domain to generate a set of oversampled measurements; applying a frequency shift to each of the low bandwidth measurements corresponding to its relative optical frequency in the frequency domain to generate a set of frequency shifted measurements; summing the frequency shifted measurements to generate a single high bandwidth measurement; transforming the high bandwidth measurement with a Fourier transform to generate a target image, wherein a resolution of the target image is greater than a resolution of each of the low resolution images.

10. The system of claim 7, wherein, The signal processor further performs the following steps: generating a reference signal indicative of an interference of an unmodulated stepped frequency waveform and the modulated stepped frequency waveforms; and reconstructing a target image using the beat signal and the reference signal.

11. The system of claim 10, wherein, The step of reconstructing the target image includes the following steps: cross correlating the beat signal and the reference signal in a frequency domain for each constant frequency of the unmodulated stepped frequency waveform to generate a correlation signal such that there is one correlation signal for each constant frequency; combining the correlation signals in the frequency domain in an order of their respective frequencies to generate a frequency image of the target in the frequency domain; and transforming the frequency image with a Fourier transform to generate the target image.

12. The system of claim 7, wherein, The range function is a linear function as a function of time. The signal processor further performs the following steps: generating a reference signal indicative of an interference of an unmodulated stepped frequency waveform and the modulated stepped frequency waveforms; and reconstructing a target image using the beat signal and the reference signal. The step of reconstructing the target image includes the following steps: cross correlating the beat signal and the reference signal in a frequency domain for each constant frequency of the unmodulated stepped frequency waveform to generate a correlation signal such that there is one correlation signal for each constant frequency; combining the correlation signals in the frequency domain in an order of their respective frequencies to generate a frequency image of the target in the frequency domain; and transforming the frequency image with a Fourier transform to generate the target image. The range function is a linear function as a function of time.

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