Abstract:
An imaging system uses a dynamically varying coded mask, such as a spatial light modulator (SLM), to time-encode multiple degrees of freedom of a light field in parallel and a detector and processor to decode the encoded information. The encoded information may be decoded at the pixel level (e.g., with independently modulated counters in each pixel), on a read-out integrated circuit coupled to the detector, or on a circuit external to the detector. For example, the SLM, detector, and processor may create modulation sequences representing a system of linear equations where the variables represent a degree of freedom of the light field that is being sensed. If the number of equations and variables form a fully determined or overdetermined system of linear equations, the system of linear equations&#39; solution can be determined through a matrix inverse. Otherwise, a solution can be determined with compressed sensing reconstruction techniques with the constraint that the signal is sparse in the frequency domain.

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
       [0001]    This application claims the priority benefit of U.S. Application No. 62/352,267, which was filed on Jun. 20, 2016, and is incorporated herein by reference in its entirety. 
     
    
     GOVERNMENT SUPPORT 
       [0002]    This invention was made with Government support under Contract No. FA8721-05-C-0002 awarded by the U.S. Air Force. The Government has certain rights in the invention. 
     
    
     BACKGROUND 
       [0003]    Wide-area motion imaging (WAMI) has received increased attention for defense and commercial applications due to the importance of wide-area persistent surveillance for homeland protection, battlefield situational awareness, environmental monitoring, and intelligence, surveillance, and reconnaissance of denied areas. Recently developed systems, such as Argus-IS, can surveil up to 100 km 2  at over a gigapixel resolution from an airborne platform. This huge amount of visual data requires algorithms for automated detection and tracking of targets of interest. However, traditional kinematic data based tracking algorithms have challenges in wide area motion imagery due to a relatively low sampling rate, low spatial resolution, occlusions, changes in lighting, and multiple confusers. Incorporating hyperspectral data can boost the probability of detection, reduce false alarms, and improve performance in vehicle tracking and dismount detection. 
         [0004]    Currently fielded imaging spectrometers use either dispersive or interferometric techniques. A dispersive spectrometer uses a grating or prism to disperse the spectrum along one axis of a focal plane array (FPA) while the other axis is used to measure a single spatial dimension. An interferometric spectrometer reconstructs the spectrum from an interferogram measured at the FPA by splitting the incident light into two optical paths and varying the optical path distance of one of the paths with a moveable mirror. 
         [0005]    Neither dispersive spectrometers nor interferometric spectrometers are suitable for motion imaging a large area on the ground. For example, to cover 64 km 2  at a ground sampling distance of 0.5 m, an update rate of 1 Hz, and up to 256 spectral bands, a dispersive grating spectrometer must sacrifice signal-to-noise ratio (SNR) (&lt;4 μs dwell time per pixel). An interferometric spectrometer is not even capable of imaging at a 1 Hz update rate as its mirror would have to move more than an order of magnitude faster (65,000 steps/sec) than what is typically available (2000 steps/sec). Given these constraints, it is not surprising that no military or commercial WAMI platform has a hyperspectral sensing capability. Therefore, today&#39;s systems can offer large area coverage or wide spectral bandwidth, but not both. 
       SUMMARY 
       [0006]    Time-encoded multiplexed imaging has the potential to enable wide area hyperspectral motion imaging as it has greater throughput than a dispersive imager and a faster scan rate than an interferometric imager. It can be implemented with an imaging system that includes a first lens, a spatial light modulator (SLM), a second lens, and a detector array. In operation, the first lens images a first point in an object plane to a first point in a first focal plane and images a second point in the object plane to a second point in the first plane. The SLM, which is disposed in the first plane, encodes the first point in the first plane with a first temporal modulation and encodes the second point in the first plane with a second temporal modulation different from the first temporal modulation. The second lens, which is in optical communication with the SLM, images the first point in the first plane to a first point in a second plane and the second point in the first plane to a second point in the second plane. And the detector array, which is disposed in the second plane, includes a first detector element positioned to sense both the first temporal modulation and the second temporal modulation. 
         [0007]    Another example imaging system includes an SLM, an optical element in optical communication with the SLM, a detector array, and a processor operably coupled to the detector array. The SLM temporally encodes different portions of a light field with respective temporal modulations that are based on a Hadamard matrix. The optical element spatially combines the different portions of the light field at a first plane, where the detector array detects the light field at a spatial resolution lower than a spatial resolution of the SLM. The processor samples an output of the detector array at a rate based on the respective temporal modulations. 
         [0008]    Yet another example imaging system includes an SLM, a focal plane array in optical communication with the SLM, and a processor operably coupled to the focal plane array. The SLM applies temporal encoding sequences to multiple image features in parallel. The focal plane array samples the temporal encoding sequences. And the processor produces, based on the temporal encoding sequences, a super-resolution image, a hyperspectral image, a polarimetric image, a plenoptic image, and/or a spatially multiplexed image. 
         [0009]    It should be appreciated that all combinations of the foregoing concepts and additional concepts discussed in greater detail below (provided such concepts are not mutually inconsistent) are contemplated as being part of the inventive subject matter disclosed herein. In particular, all combinations of claimed subject matter appearing at the end of this disclosure are contemplated as being part of the inventive subject matter disclosed herein. It should also be appreciated that terminology explicitly employed herein that also may appear in any disclosure incorporated by reference should be accorded a meaning most consistent with the particular concepts disclosed herein. 
     
    
     
       BRIEF DESCRIPTIONS OF THE DRAWINGS 
         [0010]    The skilled artisan will understand that the drawings primarily are for illustrative purposes and are not intended to limit the scope of the inventive subject matter described herein. The drawings are not necessarily to scale; in some instances, various aspects of the inventive subject matter disclosed herein may be shown exaggerated or enlarged in the drawings to facilitate an understanding of different features. In the drawings, like reference characters generally refer to like features (e.g., functionally similar and/or structurally similar elements). 
           [0011]      FIG. 1  shows a time-encoded, spectrally multiplexed system that performs image encoding with a spatial light modulator (top) and image decoding with a digital focal plane array (DFPA) (bottom). 
           [0012]      FIG. 2  shows an alternative system for time-encoded, spectrally multiplexed imaging. 
           [0013]      FIG. 3  shows a time-encoded super-resolved imaging system. 
           [0014]      FIG. 4  shows a dispersing and recombining time-encoded imaging system. 
           [0015]      FIG. 5A  shows a system with a time-encoded aperture mask proximate to a pupil plane. 
           [0016]      FIG. 5B  shows a system for multiplexed ray angle imaging. 
           [0017]      FIG. 5C  shows a system for spatially multiplexed imaging. 
           [0018]      FIG. 6  shows a system with multiple time-encoded aperture masks used in an imaging system with optically multiplexed fields of view. 
           [0019]      FIG. 7  shows a dispersing time-encoded imaging system. 
           [0020]      FIG. 8  shows a dispersing time-encoded imaging system for division of aperture optically multiplexed imaging. 
           [0021]      FIG. 9  shows a dispersing time-encoded imaging system with a two-dimensional dispersing element. 
           [0022]      FIG. 10A  shows a time-encoded, polarization-multiplexed imaging system. 
           [0023]      FIG. 10B  shows images at the spatial light modulator (SLM) and focal plane array (FPA) planes in the system of  FIG. 10A  for different input polarizations. 
           [0024]      FIG. 11A  shows an alternative time-encoded, polarization-multiplexed imaging system. 
           [0025]      FIG. 11B  shows images of the polarization-dependent point spread function (PSF) at the SLM plane in the system of  FIG. 11A  for different input polarizations. 
           [0026]      FIG. 12A  is a photograph of an experimental implementation of a time-encoded, spectrally multiplexed imaging system. 
           [0027]      FIG. 12B  is a plot of a 128-channel spectrum of two pixels from an image of two LEDs with center wavelengths of 1300 nm and 1450 nm (right) and FWHM of 100 nm collected by the system shown in  FIG. 12A . 
           [0028]      FIG. 13  shows experimental spectra and images of LEDs with center wavelengths of 1450 nm and 1600 nm and a table showing the relationship between number of codes, number of frames, frame rate, hypercube rate, and spectral resolution for a time-encoded, spectrally multiplexed imaging system. 
           [0029]      FIG. 14  is a plot of reconstructed and decoded spectra of LEDs with center wavelengths of 1450 nm and 1600 nm. 
           [0030]      FIG. 15A  is an experimentally acquired image of seven LEDs, each of which has a different center wavelength, showing different temporal modulation waveforms for each LED. 
           [0031]      FIG. 15B  shows a pixel with an up/down counter in a DFPA pixel used to sample the incident beams encoded with the temporal modulation of  FIG. 15A . 
           [0032]      FIG. 15C  illustrates images of the modulated LEDs in  FIG. 15A  sampled with a DFPA with up/down counters like the one shown in  FIG. 15A . 
       
    
    
     DETAILED DESCRIPTION 
       [0033]    Time-encoded multiplexing imaging systems map different spectral features, polarization features, fields of view, or ray angles in a scene to orthogonal temporal codes. This allows them to measure information from an observed scene more efficiently than other imaging technologies. Time-encoded multiplexing is useful in multi-dimensional imaging applications, including but not limited to hyperspectral imaging, imaging polarimetry, plenoptic imaging, three-dimensional (3D) imaging, and optically multiplexed imaging. 
         [0034]    In a conventional imaging system, a single pixel on the focal plane can measure only one degree of freedom of the multi-dimensional light field at any moment in time. For example, a conventional pixel measures only integrated light intensity. Conversely, a single pixel in a time-encoded multiplexing system can simultaneously capture multiple degrees of freedom in each measurement. As a result, a time-encoded multiplexing imaging system can operate more quickly and/or with higher image resolution than a conventional imaging system. Operating more quickly with little to no degradation of signal-to-noise ratio (SNR) or spatial resolution enables staring imaging systems that can capture fast temporal phenomena and scanning imaging systems that can scan over large areas. 
         [0035]    Conventional imaging systems typically scan consecutively through a number of measurements, which degrades either the temporal resolution or frame rate of the sensor. These conventional systems are challenged when observing moving scenes or when placed on moving platforms. Other conventional systems disperse the degrees of freedom of a light field across the detector array to simultaneously make multiple measurements. These systems suffer a loss of spatial resolution, producing an image with fewer pixels than the focal plane. 
         [0036]    Conversely, time-encoded multiplexed imaging systems can measure multiple degrees of freedom of a light field simultaneously without sacrificing spatial or temporal resolution. In other words, an example time-encoded multiplexing imaging system can acquire multidimensional data with both fine spatial and fine temporal resolution. The orthogonal parallelized measurement used in time-encoded multiplexed imaging offers many benefits, including: 1) rapid simultaneous measurements of every imaging channel (e.g., enabling higher video rates) and/or 2) higher SNR than conventional imaging systems. 
         [0037]    Multiple applications exist for time-encoded multiplexed imaging systems in industrial and defense settings. In the area of hyperspectral imaging, applications include but are not limited to: precision agriculture, biotechnology, environmental monitoring, food inspection, industrial material identification, pharmaceuticals, defense and security. Other applications include plenoptic cameras (e.g. 3D facial recognition), imaging polarimetry (e.g., remote sensing), and optically multiplexed imaging (e.g., extreme panoramic video). 
         [0038]    One particular example of this technology is hyperspectral imagers for drones. A low-flying or maneuvering drone observes a quickly moving scene. The ability to collect fast video-rate hyperspectral data increases the coverage rate of a drone used to identify materials in a scene. This could be used to speed up agricultural inspections or to quickly identify dangerous materials in an industrial or defense application. 
       A Time-Encoded, Spectrally Multiplexed Imaging System 
       [0039]      FIG. 1  illustrates an imaging system  100  that temporally encodes and decodes different spectral features in the light field. The imaging system  100  includes an optical train (top of  FIG. 1 ) that encodes the light field and images the encoded light field from a scene  101  onto a digital focal plane array (DFPA)  140 , which detects and decodes an encoded image  141  of the scene (bottom of  FIG. 1 ). 
         [0040]    The optical train of the imaging system  100  shown in  FIG. 1  includes a prism  101 , grating, or other dispersive element that spatially separates different spectral components of the light field. A spatial light modulator (SLM)  120  modulates the amplitudes of each spectral component of the light field with a predetermined sequence in time. The SLM  120  can be a liquid-crystal SLM that operates in a transmissive geometry (e.g., as shown in  FIG. 1 ) or reflective geometry, a digital micromirror device (DMD) or deformable mirror that operates in a reflective geometry, a metamaterial device, shutter or light-blocking element, or any other suitable device as known in the art. It can encode signals by redirecting, blocking, or transmitting light, e.g., to produce binary (100% or 0%) modulation or partial attenuation (grayscale) modulation. It may also modulate the phase of the incident light. Phase modulation may include a linear phase term or so-called tilt, a quadratic phase term or so-called defocus, or a higher order phase term. 
         [0041]    Different wavelengths of light illuminate different regions of the SLM  120 , which allows multiple wavelengths to be amplitude modulated in parallel with different sequences (e.g., code 1, code 2, and code 3 shown in  FIG. 1 ). (The SLM  120  can also phase-modulate the different wavelengths for coherent detection.) The light modulated by the SLM  120  is recombined with another dispersive element (here, another prism  130 ) to form a subsequent image  41  that has time-encoded wavelength information. 
         [0042]    In other examples, the dispersive element(s) and SLM may be selected and/or positioned to encode other types of components of the light field. For instance, the optical train may include birefringent optics to separate and encode polarization features. Or the optical train may include an SLM placed in a pupil plane to encode plenoptic or multiplexed field-of-view (FOV) information. 
         [0043]    An optical detector—here, a DFPA  140 —converts incoming photons in the image  141  into a digital signal. Each pixel in the DFPA  140  includes a photodetector  142  that generates an analog photocurrent  143  whose amplitude is proportional to the incident photon flux. A current-to-frequency converter  144  coupled to the photodetector  142  converts the analog photocurrent  143  in each pixel to a digital bit stream  145  (this analog-to-digital (A/D) conversion may also be performed in the readout electronics). For practical implementations, A/D conversion at the pixel level is faster because it happens on many pixels in parallel. This allows time-encoded signals to be sampled at kilohertz to megahertz frequencies, which enables high framerate multidimensional motion imagery without the loss of spatial resolution suffered by alternative methods. For more information on A/D conversion at the pixel level and DFPAs, please see U.S. Pat. No. 8,179,296, U.S. Pat. No. 8,692,176, U.S. Pat. No. 8,605,853, and U.S. Pat. No. 9,270,895, each of which is incorporated herein by reference in its entirety. 
         [0044]    One or more (up/down) counters  146  in each pixel record use time-modulated sampling schemes to decode and store information  147  in the digital bit stream  145 . For example, the counters  146  may sample the digital bit stream  145  in a pattern that is the mathematical inverse of the modulation applied by the SLM  120 . Each counter (in each pixel) may sample the bit stream  145  with a different modulation pattern, making it possible to sense different colors (with different modulations) in different sections of the DFPA  140 . A processing unit  150  coupled to the DFPA  140  calculates the product of the SLM and counter modulation steps to produce a direct measurement of the encoded degree of freedom of the light field. 
         [0045]    This processing can be performed in electronics at the pixel level (e.g., the counters  146 ), in the readout electronics, on a dedicated circuit (e.g., the processor  150 ) such as an application-specific integrated circuit (ASIC) or field-programmable gate array (FPGA), in post processing, or some combination thereof. In-pixel processing is a powerful and efficient way to parallelize the processing and is another capability of the DFPA  140 . For instance, the counters  146  in the DFPA pixels can be modulated independently to allow simultaneous measurement of multiple signals encoded by the SLM  120 . 
         [0046]    The DFPA  140 , processor  150 , and/or other electronics (not shown) may execute the encoding and decoding process. This involves selecting the modulation patterns used by the SLM  120 , DFPA  140 , and processor  150  along with the additional data processing steps used to recover the light field. An example of an encoding framework may be described by applying Hadamard or S-matrix codes in the SLM  120 , DFPA  140 , and processor  150 . 
       Operation of a Time-Encoded, Spectrally Multiplexed Imaging System 
       [0047]    To illustrate time-encoded multiplexed imaging, consider a single spatial pixel. Each pixel can operate independently, so this technique can scale to any size array of pixels. In  FIG. 1  (top), a single spatial pixel contains three spectral colors: red, green, and blue. These colors are assigned the orthogonal codes {0,1,1}, {1,0,1}, and {1,1,0}. The light is dispersed through the first prism  110  onto three pixels on the SLM  120 , then recombined and measured at a single pixel detector  142  in the DFPA 140. During the integration period, the three codes are sequenced and the detector  142  makes three measurements. During the first time sequence (t 1 ), the SLM  120  is set to the first code {0,1,1}, which blocks the red light so the measurement m 1  is a sum of green and blue. This is repeated for the subsequent codes for a total of three measurements. An estimate of the amount of red, green, and blue light within the pixel can be calculated by addition or subtraction of the measurements. For example, the blue channel is the addition of the first two measurements and subtraction of the third measurement. 
         [0048]    The image decoding can be performed independently of the measurement by reading out an image frame for each time sequence; however, the frame rate of the imager (DFPA  140 ) limits the image decoding rate, which in turn limits the hyperspectral data (hypercube) acquisition rate. For example, at 100 frames/sec and 200 spectral channels, the acquisition rate is 0.5 Hz. 
         [0049]    Implementing decoding with the DFPA  140  enables much faster hypercube acquisition rates because the decoding can be performed in parallel and at the same time as the measurement. In a digital focal plane array (bottom of  FIG. 1 ), each pixel has an analog-to-digital converter (ADC) in the form of a current-to-frequency converter  144 . The ADC converts the input photocurrent  143  into a digital pulse stream  145 , and one or more counters  146  count the number of pulses within a given integration period. The magnitude of the count is proportional to the incident photon flux. The counters  146  can be controlled individually to count up, down, or not at all such that a duobinary {−1,0,+1} modulation signal can be applied. 
         [0050]    To decode the three-channel example, each of the counters  146  is set to count up or down during the time sequences. For example, to implement the first code at t 1 , the first counter is set to count down, and the second and third counters are set to count up. At the end of the integration period, each counter  146  has an estimate of its corresponding color channel. In other words, the counters  146  store spectrally multiplexed images of the scene. This in-pixel decoding can occur at Megahertz rates. At a rate of 1 MHz, the system  100  can acquire 200 spectral channels at a rate of 5 kHz (10,000 times greater than a 100 frames/sec imager). 
         [0051]    Mathematically, the encoded light (g) can be represented as a product of an encoding matrix (W E ) and a feature vector (f): g=W E f, where f is an N×1 vector of the spectral channels, W E  is an N×N matrix with each row corresponding to an orthogonal code, and N is the number of spectral channels. In order to recover the original spectral information, g is multiplied by a decoding matrix (W D ): s {circumflex over (f)}=W D g such that sI=W E W D , where I is the identity matrix and s a scalar constant. For example, for a vector of length N, a Hadamard matrix of rank N can be used for both W E  and W D , and s=N. In practice, it may not be practical to use a Hadamard matrix for W E  since it can be difficult to apply a negative modulation to light. Instead the S-matrix is used, which contains only binary values (0,+1) and is rank N−1. To convert a Hadamard matrix to a S-matrix: W E =S=(1−H)/2. 
         [0052]    More specifically, a Hadamard matrix of rank n (H n ) can be used to represent the 2-dimensional wavelength and time binary encoding pattern applied by the SLM 120. A related matrix, which is also H n  in this example, represents the 2-dimensional parallelized time-encoded modulation of the pixel in the DFPA  140 . This +1,−1 modulation can be implemented with a counter that can count up and down as explained above. If the incoming wavelength intensity spectrum on each pixel in the DFPA  140 , is represented as a vector Ψ, then the estimate of the wavelength spectrum, {circumflex over (Ψ)}, can be written as: 
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         [0053]    Alternatively, an S matrix of rank n (S n ) is used to represent the 2-dimensional wavelength and time binary encoding pattern applied by the spatial light modulator. A related matrix, which is also S n  in this example, represents the 2-dimensional parallelized time encoded sampling of the pixel. Again, Ψ represents the raw system measurement (i.e., the signal measured on each digital register in the DFPA). The measurement in each counter is scaled by a term related to the rank of the S matrix, and then offset by a term related to an non-encoded measurement to yield an estimate of the wavelength spectrum, {circumflex over (Ψ)}. A J matrix (matrix of ones) is used to represent the non-encoded term which may be measured directly or approximated from the encoded data. 
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       Time-Encoded Super-Resolved Imaging Systems 
       [0054]    Temporal encoding can also be used in super-resolution imaging. As understood by those of skill in the art, super-resolution imaging refers to enhancing the (spatial) resolution of an imaging system. A super-resolution imager can resolve spots that are tinier than the system&#39;s diffraction limit, can resolve more spots than there are pixels in the image sensor, or both. 
         [0055]      FIG. 2  shows a time-encoded super-resolved imager  200 . It includes a lens  202  and a time-encoded aperture mask  220 , which can be implemented with an SLM, placed proximate to an intermediate focal plane of the lens  202 . Time signatures are embedded into light passing through different regions of the time-encoded aperture mask  220 . A detector  240 , such as a DFPA, in the focal plane of the lens  202  detects the time signatures. The detector  240  and a processing unit  250  process the time signatures to produce a super-resolved image of the scene observed by the imager  200 . 
         [0056]      FIG. 3  shows a time-encoded imaging system  300  that encodes different positions in a scene with different temporal codes. In this example, the system  300  observes objects at positions A and B. An objective element  302  forms intermediate images A′ and B′ on a time-encoded aperture mask  320 , such as an SLM. The spatial resolution of the time-encoded aperture mask  320  is sufficient to uniquely encode time signatures into images A′ and B′. A relay element  322  reimages A′ and B′ to form the final images A″ and B″ on a detector  340 , such as a DFPA. The spatial resolution of the detector  340  is insufficient to spatially resolve A″ and B″ because both spots fall within a given pixel P. Time-modulated signals of objects A and B are measured by pixel P (e.g., as explained above with respect to  FIG. 1 ). The detector  340  and a processing unit  350  separate the time-modulated signals and use knowledge of the spatial mapping between the time-encoded aperture mask  320  and the detector  340  to produce a super-resolved image. In other words, the detector  340  and/or processor  350  recover multiple points of spatial information from each pixel on the detector  340  using the temporal codes. The processor  350  may synthesize one or more images from this spatial information. 
       Dispersing and Recombining Time-Encoded Imager 
       [0057]      FIG. 4  shows a dispersing and recombining time-encoded imager  400  like the imaging system  100  shown in  FIG. 1 . The imager  400  spatially disperses degrees of freedom of the light field prior to a coded mask (SLM  420 ) and then spatially recombines those degrees of freedom after the coded mask such that the image reaching the detector is spatially congruent with the observed scene. In this case information, at each detector pixel represents different components of the light field that are temporally encoded with different modulation sequences. 
         [0058]    The imager  400  observes an object at position A. Together, an objective element  402  and a dispersing element  410  form an intermediate image of the object in which different light field components (e.g., different wavelengths or polarizations) are spatially separated on a time-encoded aperture mask  420 , such as an SLM. The time-encoded aperture mask  420  encodes time signatures into the dispersed image features A 1 ′, A 2 ′, and A 3 ′. Light then passes through a recombining element  430  that reverses the dispersion from the dispersing element 410. A relay element  432  then forms an image A″ on pixel P of a detector  440  (e.g., a DFPA) that is spatially congruent with the object at position A. Time-modulated signals of the light field components are measured by pixel P. A processing unit  450  separates the time-modulated signals. 
         [0059]    Knowledge of the spatial dispersion at the time-encoded aperture mask  420  allows the signals to be attributed to known fight field components. For example, if a wavelength spectrum is dispersed via a prism or diffraction grating the signals associated with modulation of A 1 ′, A 2 ′, and A 3 ′ will represent different known wavelength regions of the multi-spectral image A″. Alternatively a polarization dispersing element such as a birefringent prism may be used to disperse polarization states of the light field and form an image of multiple polarization states of the object A. 
         [0060]    In the example shown in  FIG. 4 , a single point object is depicted. An extended object produces a dispersed intermediate image in which a light field component from one object point may be superimposed with a different light field component from another object point. In this case, knowledge of the spatial dispersion pattern at the time-encoded aperture mask  420  allows for encoded signals to be attributed with the proper light field component. 
       Plenoptic/Optically Multiplexed Time-Encoded Imaging Systems 
       [0061]      FIG. 5A  shows a plenoptic/optically multiplexed time-encoded imaging system  500 . In this system  500 , a time-encoded aperture mask  520 , such as an SLM, is placed proximate to the aperture stop or proximate to a conjugate pupil image to encode passing light with a single that may be correlated to the pupil region from which it entered. The time-encoded aperture mask  520  encodes time signatures into light passing through different aperture regions (a.k.a. pupil regions). A lens  530  focuses light entering pupil regions E, F, and G onto a pixel P of a detector  540 , such as a DFPA. A processing unit  550  coupled to the detector  540  associates the signals entering pixel P with the pupil region from which they entered. 
         [0062]    In plenoptic imaging, the processor  550  correlates the pupil positions (E, F, and G) and image position (P) to determine ray angles. In optically multiplexed imaging, the processor  550  uses the division of aperture optical architecture pupil region information to de-multiplex different imaging channels (E, F, and G). 
         [0063]      FIG. 5B  shows a system  501  for multiplexed ray angle imaging. The objects&#39; ray angles, R 1 , R 2 , R 3  are focused with an objective lens  501  onto a microlens array  511  with a time-encoded mask  521  placed behind the microlens array  511 . The time-encoded mask  521  modulates the amplitudes of R 1 , R 2 , and R 3  at positions E, F, and G, respectively. A second lens  531  relays the resulting modulated image to a detector  541  where it is sampled at a single pixel P. A processing unit  551  coupled to the detector  541  decodes the measurement at pixel P to recover the ray information of R 1 , R 2 , and R 3 . 
       Spatially Multiplexed Time-Encoded Imaging Systems 
       [0064]      FIG. 5C  shows a system  502  for spatially multiplexed time-encoded imaging. A first lens  512  images an object onto a time-encoded mask  522 . The time-encoded mask  522  modulates the amplitudes of the image at different positions, temporally encoded each object position resolvable with the first lens  512  and mask  522 . A second lens  532  relays the resulting modulated image to a detector  542 , which has fewer sensing elements (detector pixels) than the time-encoded mask  522  has modulating elements (modulator pixels). In other words, multiple modulator pixels on the time-encoded mask  522  are imaged onto each detector pixel in the detector  542 . A processing unit  552  coupled to the detector  542  decodes the detector measurements to distinguish the different object features imaged onto each detector pixel based on the different temporal modulations applied by the time-encoded mask  522 . 
       Multiple Time-Encoded Aperture Masks for Optically Multiplexed Imaging 
       [0065]      FIG. 6  shows a system  660  with multiple time-encoded aperture masks  620   a  and  620   b  (collectively, time-encoded aperture masks  620 ) for optically multiplexed imaging. Each time-encoded aperture mask  620  is placed in an imaging channel of the optically multiplexed imaging system  600 , which uses a division of aperture architecture to divide the entrance pupil of the system  600  into regions E and F. (Alternatively, a division of amplitude architecture could also be used (i.e., dividing the transmission of the pupil rather than the area).) Prisms  630   a  and  630   b  bend the temporally modulated beams emitted by the time-encoded aperture masks  620 , e.g., as disclosed in R. H. Shepard et al., “Design architectures for optically multiplexed imaging,” Optics Express 23:31419-36 (23 Nov. 2015), which is incorporated herein by reference in its entirety. A lens  632  images the temporally modulated beams onto a detector array  640 , which is coupled to a processing unit  650  that separates the modulated signals into the separate imaging channels. 
         [0066]    Temporally modulating each imaging channel embeds a true signature into each imaging channel such that signals in a pixel P of the detector array  640  can be associated with the correct imaging channel. Each time-encoded aperture mask  620  may be a single spatial element per channel (such as a shutter) to encode the entire channel uniformly. Or each aperture mask  620  may have finer spatial resolution to encode spatial information within each channel. 
       A Dispersing Time-Encoded Imager 
       [0067]      FIG. 7  shows a dispersing time-encoded imager  700  that observes objects at positions A and B. An objective element  702  produces intermediate images A′ and B′ on a time-encoded aperture mask  720 , such as an SLM, that is spatially congruent with the object. The elements of the time-encoded aperture mask  720  encode the intermediate image with time signatures that may be associated with the object&#39;s 2D spatial information. Light then passes through a dispersing element  730 , such as a prism or grating, and is focused by a relay lens  732  to a detector  740 . At the detector  740 , light field components from the objects at positions A and B (A 1 ″, A 2 ″, and A 3 ″, and B 1 ″, B 2 ″, and B3″) are spatially dispersed and superimposed on pixels P 1 , P 2 , P 3 , and P4. The pixels sample the encoded time patterns and a processing unit  750  coupled to the detector  740  separates the signals. 
         [0068]    In this case, the information for spatially reconstructing the dispersed image is encoded in the time signatures. Knowledge of the spatial dispersion pattern is used along with the observed pixel location to determine the light field components. For example, in a multi-spectral application, the dispersing element  30  may disperse the multi-spectral image A′ into the known narrow wavelength regions A 1 ″, A 2 ″, and A 3 ″. Wavelength information is obtained by observing the time-encoding pattern associated with object point A in three different pixels on the detector  740 . 
       Division of Aperture Optically Multiplexed Imaging 
       [0069]      FIG. 8  shows a dispersing time-encoded imager  800  for division of aperture optically multiplexed imaging. In this optical system, the degrees of freedom of the light field are dispersed after a time-encoded aperture mask  820  and are not spatially recombined such that the image reaching the detector  840  is spatially incongruent with the observed scene. In this case the temporally encoded information in each detector pixel is used in conjunction with the known spatial dispersion pattern to computationally reconstruct an image that is spatially congruent with the scene that contains additional light field information. 
         [0070]    Prisms  810   a  and  810   b  in the image  800  direct two fields of view (FOV  1  and FOV  2 ) into the system  800 . FOV  1  contains two objects A 1  and A 2 , and FOV  2  contains two objects B 1  and B 2 . An objective lens  802  forms intermediate overlapping images of FOV  1  and FOV  2  on a time-encoded aperture mask  820 , such as an SLM, in which the images A 1 ′ and A 2 ′ are superimposed with B 1 ′ and B 2 ′, respectively. The elements of the time-encoded aperture mask  820  encode the multiplexed intermediate images with time signatures that are associated with the multiplexed intermediate images&#39; 2D spatial information. The encoded light passes through a relay lens  822  and a dispersing element array  830  that is spatially matched to the divided pupil regions so as to disperse each channel differently. The relay lens  822  produces final images A 1 ″, A 2 ″, B 1 ″, and B 2 ″ on pixels P 1 , P 2 , P 3  of a detector array  840 . The pixels sample the time-encoded patterns, and a processing unit  850  coupled to the detector array  840  separates the signals. The processing unit  850  de-multiplexes the final image by observing multiple signals in each pixel and correlating this information with the known dispersion pattern. In this example, pixel P 2  measures a superposition of information from FOV  1  and FOV  2 , but this information can be disambiguated because the signals from object A 2  and object B 1  are encoded differently by the aperture mask  820 . 
       1-Dimensional and 2-Dimensional Dispersing Elements 
       [0071]    The dispersing elements shown in  FIGS. 1, 4, 7, and 8  may disperse the light field in one or two dimensions. This may be done as part of a dispersing and recombining arrangement ( FIGS. 1 and 4 ) or in a dispersing arrangement ( FIGS. 7 and 8 ). 
         [0072]      FIG. 9  shows a two-dimensionally dispersing time-encoded imager  900 . It can encode multiple degrees of freedom simultaneously through the use a of a dispersing element that produces a 2-dimensional dispersion pattern on an SLM  910 . For example, wavelength information might be dispersed horizontally on the spatial light modulator and polarization information might be dispersed vertically. Other combinations of light field components in other 2-dimensional dispersion patterns can be implemented as well. 
         [0073]    The image  900  includes a dispersing element  910 , such as a diffractive or holographic element, that disperses light from a single point A in an object plane  901  in two transverse dimensions (e.g., x and y, where z is the direction of propagation). A lens  902  images the dispersed light to different positions A 1 ′, A 2 ′, A 3 ′, A 1   * , A 2   * , and A 3   *  in an image plane  911 . Dispersing light in two dimensions allows for multiple components of the light field to be encoded simultaneously. For example, the dispersing element  910  may disperse light by wavelength coarsely in one dimension and finely in an orthogonal dimensions, e.g., as with a virtual image phased array (VIPA) device. Or a wavelength dispersing prism can be used to disperse the light horizontally and a polarization-dividing prism can be used to disperse the light vertically to produce a spectral-polarimetric imager. Other combinations of light field components can also be dispersed; for instance, a dispersing element array can be used to disperse channels in an optically multiplexed imaging application ( FIG. 8 ) along with a wavelength or polarization dispersing element in the orthogonal direction. 
       Time Encoding for Different Polarizations 
       [0074]      FIGS. 10A and 10B  illustrate a system  1000  that time encodes different polarizations of an incident light field  1001 . It makes measurements that yield the first two components of the Stokes parameters, which describe the polarization state of light. 
         [0075]      FIG. 10A  shows the system&#39;s components, which include a first Wollaston prism  1008 , a first dispersing element (prism)  1010 , a first lens  1012 , an SLM  1020 , a second lens  1028 , a second dispersing element (prism)  1030 , a second Wollaston prism  1032 , a third lens  1034 , and an FPA  1040  in optical series with each other. The first Wollaston prism  1008  separates the incident light field  1001  according to its polarization, with vertically polarized light propagating at angle out of the page and horizontally polarized light propagating at an angle into the page. The first dispersing element  1010  vertically separates the different spectral components of the vertically and horizontally polarized beams, producing spots in the plane of the SLM  1020  that are separated by polarization state and wavelength. The SLM  1020  modulates the phase and/or amplitude of each spot (light field component) as a function of time using, e.g., Hadamard encoding. The second dispersing element  1030  and second Wollaston prism  1032  recombine the modulated light field components. And the FPA  1040  senses the combined intensities of recombined light field components. 
         [0076]      FIG. 10B  illustrates the light field for different input polarizations at different planes within the system  1000  shown in  FIG. 10A . (The planes in  FIG. 10B  are rotated about the z axis by 90 degrees with respect to the view shown in  FIG. 10A .) The top row shows the input polarization, the middle row shows the intensity in the plane of the SLM  1020 , and the bottom row shows the intensity in the plane of the FPA  1040 . For vertical and horizontal input polarization, a single band of color appears in the plane of the SLM  1020  and a single spot appears in the plane of the FPA  1040 . But for diagonal input polarization, the first Wollaston prims  1008  resolves two different polarization components, which yields two bands of color in the plane of the SLM  1020 , with the upper band corresponding to the vertical polarization component and the lower and corresponding to the horizontal polarization component. The second dispersing element  1030  and second Wollaston prism  1032  recombine these components after they have been encoded by the SLM  120  to produce a single spot in the plane of the FPA  1040 . 
         [0077]      FIGS. 11A and 11B  show how the system  1000  of  FIGS. 10A and 10B  can be extended to measure all four Stokes parameters. More specifically,  FIG. 11A  shows the front end of a time-encoding imaging system  1100  like the one in  FIG. 10A . In this case, however, the system includes four Wollaston prisms  1108   a - 1108   d.  Prisms  1108   b  and  1108   d  are rotated by 45 degrees about the optic axis. Quarter-wave plates  1106   a  and  1106   b  are disposed in front of and aligned to the optical axes of Wollaston prisms  1108   a  and  1108   d,  respectively. Together, the Wollaston prisms and quarter-wave plates resolve an incident light field  1101  into a polarization-dependent point-spread function (PSF) in the plane of the SLM  1120 . When the light field contains unpolarized light, this polarization-dependent PSF includes eight spots—one pair of spots for each Wollaston prism  1108 —with each spot illuminating a different pixel on the SLM  1120 . Thus, the SLM  1120  can modulate (and the system  1100  can measure) each Stokes parameter of the incident light field  1101 . The back end (not shown) of the system  1100  includes a complementary arrangement of Wollaston prisms and quarter-wave plates that recombine the modulated beams for detection by an FPA (not shown). 
         [0078]      FIG. 11B  shows the polarization-dependent PSF at the plane of the SLM  1120  in the system  1100  in for different input polarization states. Vertically (0° polarized light produces seven spots arranged in a horseshoe-like shape with the opening pointed downwards. Rotating the polarization of linearly polarized light changes the orientation of this horseshoe-like shape as shown for horizontally (180° and diagonally (45° and 135°) polarized light. For left-hand circular (LHC) polarized light and right-hand circular (RHC) polarized light, only six spots appear in the SLM plane. And for arbitrarily polarized light, eight spots of varying intensity appear in the SLM plane. The intensities of these eight spots can be decomposed using the other six patterns of spots shown in  FIG. 11B  as a basis set to determine the Stokes parameters characterizing the arbitrarily polarized light. 
         [0079]    As readily appreciated by those of skill in the art, the Wollaston prisms in  FIGS. 10A  and 11A can be replaced by other polarization dispersing elements, including but not limited to thin-film devices, crystal optic devices, polarization gratings, and metasurfaces. Some of these devices, including polarization gratings and metasurfaces, may be integrated with wavelength-dispersing elements, such as prisms, gratings, and holographic optical elements. 
       Experimental Demonstration of a Programmable Hyperspectral Imaging 
       [0080]    The time-encoded multiplexed approach enables flexible encoding and decoding. At the spatial light modulator, panchromatic operation can be enabled by fixing the mirrors, and hyperspectral resolution can be decreased to increase hypercube acquisition. At the DFPA, selected codes or linear combinations of codes can be decoded. This capability can be useful for decoding only spectral bands of interest or combinations of spectral bands for spectral matched filtering. For example, for 256 spectral bands approximately half are ignored due to overlap with atmospheric water absorption bands. The DFPA can selectively decode the good bands, whereas both the dispersive and interferometric methods need to measure the entire spectrum. 
         [0081]      FIG. 12A  is a photograph of a laboratory system that demonstrates flexible encoding and decoding. The laboratory system included commercial of the shelf (COTS) optical elements, a digital micromirror device (DMD) spatial light modulator (SLM) from Texas Instruments, and a custom MIT Lincoln Laboratory 32×32 8-channel digital focal plane array. It was used to image a 1300 nm light-emitting diode (LED) and a 1450 nm LED, each having a spectral width of 100 nm. 
         [0082]      FIG. 12B  is a plot of data collected from the LEDs by the system shown in  FIG. 12A . (The inset of  FIG. 12B  shows the LEDs that were imaged.) It shows the entire decoded spectrum of two pixels of the image with 10 nm spectral resolution; 128 codes are used which involved acquiring 16 frames, 8 codes at a time. The SLM operated at a 10 kHz modulation frequency. 
         [0083]      FIG. 13  shows the capability of flexible encoding and the tradeoff between hypercube acquisition rate and spectral resolution in the system of  FIG. 12A . In this experiment, each frame read out from the DFPA contained eight spectral channels. Since the SLM was operating at 10 kHz, the total integration time was N×100 μs, where N is the number of spectral channels or codes. The hypercube acquisition rate was the frame rate divided by the number of frames needed to acquire the full hypercube. For example, to acquire 128 spectral channels, sixteen frames were used where eight spectral channels are acquired per frame. Decreasing the number of spectral channels decoded increased the overall hypercube rate. 
         [0084]      FIG. 14  shows an example of the flexible decoding enabled with a suitable DFPA. In this simulation, the DFPA decoded the top eight principal components. This data was read out in a single frame. The reconstructed spectrum shows good agreement with data acquired through fully decoding the spectrum ( FIG. 13 ). By decoding the principal components, the hypercube acquisition rate can be increased to the frame rate. For example, 64 spectral channels can be acquired at 156 Hz instead of 19.5 Hz. Furthermore, this method can be used to implement spectral matched filtering. 
         [0085]      FIGS. 15A-15C  illustrate flexible decoding for multiple LEDs, each of which emits light at a different central wavelength. The system (see, e.g.,  FIG. 12A ) disperse and modulates the beam from each LED with a different binary modulation as shown in  FIG. 15A . Each DFPA pixel includes an up/down counter, shown in  FIG. 15B , that can be toggled to sample the recombined, modulated light field. When toggled appropriately, the up/down counter in a given pixel can be used to filter the incident light in a way that makes it possible same a subset of the LEDs at a given time. 
         [0086]      FIG. 15C  shows how the duty cycle of the modulation waveform at the DFPA can be varied. For example, in the LED experiment described above, the LED is pulsed on for 1 μs whereas the pixel modulation pulse is 200 ns. Controlling the width of the modulating pulse at the DFPA enables decoding of linear combinations of codes. For example, in  FIG. 15C , the two LEDs at upper left are decoded in a single channel by adding the Hadamard codes. The first LED has a code of {+1,−1,+1,−1,+1,−1,+1,−1} and the second LED has a code of {+1,+1,−1,−1,+1,+1,−1,−1}. When added together, this creates a new code {+2, 0, 0, −2, +2, 0, 0, −2}. This can be implemented at the DFPA by increasing the width of the pulse from 200 ns to 400 ns. 
       Conclusion 
       [0087]    While various inventive embodiments have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other means and/or structures for performing the function and/or obtaining the results and/or one or more of the advantages described herein, and each of such variations and/or modifications is deemed to be within the scope of the inventive embodiments described herein. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and/or configurations will depend upon the specific application or applications for which the inventive teachings is/are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific inventive embodiments described herein. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, inventive embodiments may be practiced otherwise than as specifically described and claimed. Inventive embodiments of the present disclosure are directed to each individual feature, system, article, material, kit, and/or method described herein. In addition, any combination of two or more such features, systems, articles, materials, kits, and/or methods, if such features, systems, articles, materials, kits, and/or methods are not mutually inconsistent, is included within the inventive scope of the present disclosure. 
         [0088]    The above-described embodiments can be implemented in any of numerous ways. For example, embodiments of designing and making the technology disclosed herein may 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. 
         [0089]    The various methods or processes (e.g., of designing and making the technology disclosed above) outlined herein may be coded as software that is executable on one or more processors that employ any one of a variety of operating systems or platforms. Additionally, such software may be written using any of a number of suitable programming languages and/or programming or scripting tools, and also may be compiled as executable machine language code or intermediate code that is executed on a framework or virtual machine. 
         [0090]    In this respect, various inventive concepts may be embodied as a computer readable storage medium (or multiple computer readable storage media) (e.g., a computer memory, one or more floppy discs, compact discs, optical discs, magnetic tapes, flash memories, circuit configurations in Field Programmable Gate Arrays or other semiconductor devices, or other non-transitory medium or tangible computer storage medium) encoded with one or more programs that, when executed on one or more computers or other processors, perform methods that implement the various embodiments of the invention discussed above. The computer readable medium or media can be transportable, such that the program or programs stored thereon can be loaded onto one or more different computers or other processors to implement various aspects of the present invention as discussed above. 
         [0091]    The terms “program” or “software” are used herein in a generic sense to refer to any type of computer code or set of computer-executable instructions that can be employed to program a computer or other processor to implement various aspects of embodiments as discussed above. Additionally, it should be appreciated that according to one aspect, one or more computer programs that when executed perform methods of the present invention need not reside on a single computer or processor, but may be distributed in a modular fashion amongst a number of different computers or processors to implement various aspects of the present invention. 
         [0092]    Computer-executable instructions may be in many forms, such as program modules, executed by one or more computers or other devices. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Typically, the functionality of the program modules may be combined or distributed as desired in various embodiments. 
         [0093]    Also, various inventive concepts may be embodied as one or more methods, of which an example has been provided. The acts performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments. 
         [0094]    All definitions, as defined and used herein, should be understood to control over dictionary definitions, definitions in documents incorporated by reference, and/or ordinary meanings of the defined terms. 
         [0095]    The indefinite articles “a” and “an,” as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean “at least one.” 
         [0096]    The phrase “and/or,” as used herein in the specification and in the claims, should be understood to mean “either or both” of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Multiple elements listed with “and/or” should be construed in the same fashion, i.e., “one or more” of the elements so conjoined. Other elements may optionally be present other than the elements specifically identified by the “and/or” clause, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, a reference to “A and/or B”, when used in conjunction with open-ended language such as “comprising” can refer, in one embodiment, to A only (optionally including elements other than B); in another embodiment, to B only (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc. 
         [0097]    As used herein in the specification and in the claims, “or” should be understood to have the same meaning as “and/or” as defined above. For example, when separating items in a list, “or” or “and/or” shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as “only one of” or “exactly one of,” or, when used in the claims, “consisting of,” will refer to the inclusion of exactly one element of a number or list of elements. In general, the term “or” as used herein shall only be interpreted as indicating exclusive alternatives (i.e. “one or the other but not both”) when preceded by terms of exclusivity, such as “either,” “one of,” “only one of,” or “exactly one of” “Consisting essentially of,” when used in the claims, shall have its ordinary meaning as used in the field of patent law. 
         [0098]    As used herein in the specification and in the claims, the phrase “at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase “at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently “at least one of A and/or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc. 
         [0099]    In the claims, as well as in the specification above, all transitional phrases such as “comprising,” “including,” “carrying,” “having,” “containing,” “involving,” “holding,” “composed of,” and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of” and “consisting essentially of” shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03.