Multiplex sensors and the constant radiance theorem

Space-time compressive imaging

Compressive imaging systems typically exploit the spatial correlation of the scene to facilitate a lower dimensional measurement relative to a conventional imaging system. In natural time-varying scenes there is a high degree of temporal correlation that may also be exploited to further reduce the number of measurements. In this work we analyze space-time compressive imaging using Karhunen-Loève (KL) projections for the read-noise-limited measurement case. Based on a comprehensive simulation study, we show that a KL-based space-time compressive imager offers higher compression relative to space-only compressive imaging. For a relative noise strength of 10% and reconstruction error of 10%, we find that space-time compressive imaging with 8×8×16 spatiotemporal blocks yields about 292× compression compared to a conventional imager, while space-only compressive imaging provides only 32× compression. Additionally, under high read-noise conditions, a space-time compressive imaging system yields lower reconstruction error than a conventional imaging system due to the multiplexing advantage. We also discuss three electro-optic space-time compressive imaging architecture classes, including charge-domain processing by a smart focal plane array (FPA). Space-time compressive imaging using a smart FPA provides an alternative method to capture the nonredundant portions of time-varying scenes.

Coding for compressive focal tomography

We consider the capabilities and limits of strategies for single-aperture three-dimensional and extended depth of field optical imaging. We show that reduced spatial resolution is implicit in forward models for light field sampling and that reduced modulation transfer efficiency is intrinsic to pupil coding. We propose a novel strategy based on image space modulation and show that this strategy can be sensitive to high-resolution spatial features across an extended focal volume.

Increased field of view through optical multiplexing

Traditional approaches to wide field of view (FoV) imager design usually lead to overly complex optics with high optical mass and/or pan-tilt mechanisms that incur significant mechanical/weight penalties, which limit their applications, especially on mobile platforms such as unmanned aerial vehicles (UAVs).We describe a compact wide FoV imager design based on superposition imaging that employs thin film shutters and multiple beamsplitters to reduce system weight and eliminate mechanical pointing. The performance of the superposition wide FoV imager is quantified using a simulation study and is experimentally demonstrated. Here, a threefold increase in the FoV relative to the narrow FoV imaging optics employed imager design is realized. The performance of a superposition wide FoV imager is analyzed relative to a traditional wide FoV imager and we find that it can offer comparable performance.

Radiometric and signal-to-noise ratio properties of multiplex dispersive spectrometry

Recent theoretical investigations have shown important radiometric disadvantages of interferential multiplexing in Fourier transform spectrometry that apparently can be applied even to coded aperture spectrometers. We have reexamined the methods of noninterferential multiplexing in order to assess their signal-to-noise ratio (SNR) performance, relying on a theoretical modeling of the multiplexed signals. We are able to show that quite similar SNR and radiometric disadvantages affect multiplex dispersive spectrometry. The effect of noise on spectral estimations is discussed.

Recognition using information-optimal adaptive feature-specific imaging

We present an information-theoretic adaptive feature-specific imaging (AFSI) system for a M-class recognition task. The proposed system utilizes the recently developed task-specific information (TSI) framework to incorporate the knowledge from previous measurements and adapt the projection matrix at each step. The decision-making framework is based on sequential hypothesis testing. We quantify the number of measurements required to achieve a specified probability of misclassification (P(e)), and we compare the performances of three approaches: the new TSI-based AFSI system, a previously reported statistical AFSI system, and static FSI (SFSI). The TSI-based AFSI system exhibits significant improvement compared with SFSI and statistical AFSI at low signal-to-noise ratio (SNR). It is shown that for M=4 hypotheses, SNR=-20 dB and desired P(e)=10(-2), TSI-based AFSI requires 3 times fewer measurements than statistical AFSI, and 16 times fewer measurements than SFSI. We also describe an extension of the proposed method that is suitable for recognition in the presence of nuisance parameters such as illumination conditions and target orientations.

Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link

A multichannel free-space optical (FSO) communication system based on orbital angular momentum (OAM)-carrying beams is studied. We numerically analyze the effects of atmospheric turbulence on the system and find that turbulence induces attenuation and crosstalk among channels. Based on a model in which the constituent channels are binary symmetric and crosstalk is a Gaussian noise source, we find optimal sets of OAM states at each turbulence condition studied and determine the aggregate capacity of the multichannel system at those conditions. OAM-multiplexed FSO systems that operate in the weak turbulence regime are found to offer good performance. We verify that the aggregate capacity decreases as the turbulence increases. A per-channel bit-error rate evaluation is presented to show the uneven effects of crosstalk on the constituent channels.

Adaptive feature-specific imaging: a face recognition example

We present an adaptive feature-specific imaging (AFSI) system and consider its application to a face recognition task. The proposed system makes use of previous measurements to adapt the projection basis at each step. Using sequential hypothesis testing, we compare AFSI with static-FSI (SFSI) and static or adaptive conventional imaging in terms of the number of measurements required to achieve a specified probability of misclassification (Pe). The AFSI system exhibits significant improvement compared to SFSI and conventional imaging at low signal-to-noise ratio (SNR). It is shown that for M=4 hypotheses and desired Pe=10(-2), AFSI requires 100 times fewer measurements than the adaptive conventional imager at SNR= -20 dB. We also show a trade-off, in terms of average detection time, between measurement SNR and adaptation advantage, resulting in an optimal value of integration time (equivalent to SNR) per measurement.

Dispersion multiplexing with broadband filtering for miniature spectrometers

We replace the traditional grating used in a dispersive spectrometer with a multiplex holographic grating to increase the spectral range sensed by the instrument. The multiplexed grating allows us to measure three different, overlapping spectral bands on a color digital focal plane. The detector's broadband color filters, along with a computational inversion algorithm, let us disambiguate measurements made from the three bands. The overlapping spectral bands allow us to measure a greater spectral bandwidth than a traditional spectrometer with the same sized detector. Additionally, our spectrometer uses a static coded aperture mask in the place of a slit. The aperture mask allows increased light throughput, offsetting the photon loss at the broadband filters. We present our proof-of-concept dispersion multiplexing spectrometer design with experimental measurements to verify its operation.

Feature-specific structured imaging

We present a feature-specific imaging system based on the use of structured light. Feature measurements are obtained by projecting spatially structured illumination onto an object and collecting all the reflected light onto a single photodetector. Principal component features are used to define the illumination patterns. The optimal linear minimum mean-square error (LMMSE) operator is used to generate object estimates from the measured features. We study the optimal allocation of illumination energy into each feature measurement in the presence of additive white Gaussian detector noise and optical blur. We demonstrate that this new imaging approach reduces imager complexity and provides improved image quality in high noise environments. Compared to the optimal LMMSE postprocessing of a conventional image, feature-specific structured imaging provides a 38% rms error reduction and requires 400 times fewer measurements for a noise standard deviation of sigma = 2 x 10(-3). Experimental results validate these theoretical predictions.

Coded aperture Raman spectroscopy for quantitative measurements of ethanol in a tissue phantom

Coded aperture spectroscopy allows for sources of large étendue to be efficiently coupled into dispersive spectrometers by replacing the traditional input slit with a patterned mask. We describe a coded aperture spectrometer optimized for Raman spectroscopy of diffuse sources, (e.g., tissue). We provide design details of the Raman system, along with quantitative estimation results for ethanol at non-toxic levels in a lipid tissue phantom. With 60 mW of excitation power at 808 nm, leave-one-out and blind cross-validation of partial least squares (PLS) regression models achieve r(2) > 0.98. Leave-one-out cross-validation demonstrates prediction errors of <15% at the common legal limit for intoxication (17.4 mmol/L = 0.08% by vol) and the best blind cross-validation achieves <12% error at this concentration.

Static two-dimensional aperture coding for multimodal, multiplex spectroscopy

We propose a new class of aperture-coded spectrometer that is optimized for the spectral characterization of diffuse sources. The instrument achieves high throughput and high spectral resolution by replacing the slit of conventional dispersive spectrometers with a more complicated spatial filter. We develop a general mathematical framework for deriving the required aperture codes and discuss several appealing code families. Experimental results validate the performance of the instrument.

Signal-to-noise analysis of task-based imaging systems with defocus

We analyze the signal-to-noise ratio (SNR) of arbitrary imaging systems in the presence of defocus. The modulation transfer function (MTF) and the mean SNR are combined to calculate the spatial-frequency spectrum of the SNR (the spectral SNR). Computational imaging methods are used for extending the depth of field (DOF) of the system. The DOF of a task-specific imaging system is defined as the range of defocus that causes the spectral SNR to drop below a minimum value within a band of spatial frequencies of interest. We introduce the polar-SNR plot as a tool for visualizing the spectral SNR of defocused imaging systems with asymmetric pupil functions. As an example, we perform the analysis of an imaging system used for biometric iris recognition.

Analysis of slitless holographic spectrometers implemented by spherical beam volume holograms

The analysis of a slitless volume holographic spectrometer is presented in detail. The spectrometer is based on a spherical beam volume hologram followed by a Fourier-transforming lens and a CCD. It is shown that the spectrometer is not sensitive to the incident angle of the input beam for the practical range of applications. A holographic spectrometer based on the conventional implementation is also analyzed, and the results are used to compare the performance of the proposed method with the conventional one. The experimental results are consistent with the theoretical study. It is also shown that the slitless volume holographic spectrometer lumps three elements (the entrance slit, the collimator, and the diffractive element) of the conventional spectrometer into one spherical beam volume hologram. Based on the unique features of the slitless volume holographic spectrometer, we believe it is a good candidate for portable spectroscopy for environmental and biological applications.

Spherical beam volume holograms for spectroscopic applications: modeling and implementation

The spherical beam volume hologram, recorded by a plane wave and a spherical beam, is investigated for spectroscopic applications in detail. It is shown that both the diffracted and the transmitted beam can be used for spectroscopy when the hologram is read with a collimated beam. A new method is introduced and used for analysis of the spherical beam volume hologram that can be extended for analysis of arbitrary holograms. Experimental results are consistent with the theoretical study. It is shown that the spherical beam volume hologram can be used in a compact spectroscopic configuration when the transmitted beam is monitored. Also, on the basis of the properties of the spherical beam hologram, the response of a hologram recorded by a plane wave and an arbitrary pattern is predicted. The information can be used to optimize holographic spectrometer design.

Qualitative demonstration of spectral diversity filtering using spherical beam volume holograms

We investigate the feasibility of designing spectral diversity filters using spherical beam volume holograms. Our experimental results qualitatively show the separation of the information of different incident wavelength channels using spherical beam volume holograms. The major trade-off in using these holograms is between the degree of spatial spectral diversity and the number of allowed spatial modes (or the divergence angle) of the incident beam.