Proceedings Volume 7468

Adaptive Coded Aperture Imaging, Non-Imaging, and Unconventional Imaging Sensor Systems

David P. Casasent, Stanley Rogers, Jean J. Dolne, et al.
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Proceedings Volume 7468

Adaptive Coded Aperture Imaging, Non-Imaging, and Unconventional Imaging Sensor Systems

David P. Casasent, Stanley Rogers, Jean J. Dolne, et al.
View the digital version of this volume at SPIE Digital Libarary.

Volume Details

Date Published: 21 August 2009
Contents: 8 Sessions, 26 Papers, 0 Presentations
Conference: SPIE Optical Engineering + Applications 2009
Volume Number: 7468

Table of Contents

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Table of Contents

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  • Imaging and Non-Imaging Sensor Needs
  • Imaging and Non-Imaging Diffraction System Concepts
  • Imaging and Non-Imaging Algorithms
  • Diffraction Imaging Hardware I
  • Diffraction Imaging Hardware II
  • Wide Field-of-View and Turbid Media Imaging
  • Synthetic Aperture and Super-resolution
  • THz and Photon Counting Imaging
Imaging and Non-Imaging Sensor Needs
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Airborne infrared persistent imaging requirements
Michael Groenert, Daniel Bryski
The task of detecting, identifying, and engaging asymmetric threats operating amongst civilian populations is a significant challenge for modern armies. Enemy activities in urban areas can be very difficult to detect and monitor using traditional intelligence, surveillance, and reconnaissance (ISR) assets. The concept of Persistent Surveillance provides a new methodology for detecting and identifying hostile forces operating amongst civilians in urban battlefields. The sensors, platforms, and data architectures which compose a persistent surveillance system must be chosen to maximize coverage and minimize obscuration while providing timely and relevant data to friendly forces on the ground. An illustrative example considering the specific operational concepts and resulting system choices for optimizing an airborne infrared persistent imaging system will be discussed.
Hybrid computational imaging techniques
Significant advances are being made in exploiting the benefits of hybrid imaging techniques, partly as a result of the evolution in modern focal plane technologies and the ability to process the outputs of the detector array using fast algorithms on a real time basis. Such advances are appearing in areas as diverse as coded aperture imaging, pupil plane encoding and compressive sensing. In some cases it is also possible to address the challenges presented in discriminative imagery, with a goal of reducing the datasets associated with polarimetry or spectral hypercubes. This paper will present a review of advances in the field, with particular attention to the consideration of advanced adaptive coded aperture techniques.
Modified light field architecture for reconfigurable multimode imaging
Roarke Horstmeyer, Ravindra Athale, Gary Euliss
Light field cameras can simultaneously capture the spatial location and angular direction of light rays emanating from a scene. By placing a variable bandpass filter in the aperture of a light field camera, we demonstrate the ability to multiplex the visible spectrum over this captured angular dimension. The result is a novel design for a single-snapshot multispectral imager, with digitally reconstructed images exhibiting reduced spatial resolution proportional to the number of captured spectral channels. This paper explores the effect of this spatial-spectral resolution tradeoff on camera design. It also examines the concept of utilizing a non-uniform pinhole array to achieve varying spectral and spatial capture over the extent of the sensor. Images are presented from several different light field - variable bandpass filter designs, and limitations and sources of error are discussed.
Optical sensing data processing and management
The Defense Advanced Research Projects Agency (DARPA) is in a unique position to question traditional sensing architectures and concepts while possessing both the charter and funding to explore and develop the technologies necessary to accomplish both existing and desired applications. This paper describes the re-thinking of the Optical Processing system when applied to non-imaging sensors.
Imaging and Non-Imaging Diffraction System Concepts
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Sub-pixel super-resolution by decoding frames from a reconfigurable coded-aperture camera: theory and experimental verification
Geoffrey D. de Villiers, Neil T. Gordon, Douglas A. Payne, et al.
In a previous paper we presented initial results for sub-detector-pixel imaging in the mid-wave infra-red (MWIR) using an imager equipped with a coded-aperture based on a re-configurable MOEMS micro-shutter. It was shown in laboratory experiments that sub-pixel resolution is achievable via this route. The purpose of the current paper is to provide detail on the reconstruction method and to discuss some challenges which arise when imaging real-world scenes. The number of different mask patterns required to achieve a certain degree of super-resolution is also discussed. New results are presented to support the theory.
Adaptive feature-specific imaging
Feature-specific imaging (FSI) is a method by which non-traditional projections of object space may be computed directly in the optical domain. The resulting feature-specific measurements provide the advantages of reduced hardware complexity and improved measurement SNR. This SNR advantage translates into improved task (e.g., target recognition and/or tracking) performance. Adaptive FSI refers to any FSI system for which the results of previous measurements are used to determine future measurement basis vectors. This paper will describe an adaptive FSI system based on the sequential hypothesis testing approach. We will quantify the benefits of adaptation for a M-class recognition task, and present an extension of the AFSI system to incorporate null hypothesis.
Compressive measurement for target tracking in persistent, pervasive surveillance applications
Motion tracking in persistent surveillance applications enters an interesting regime when the movers are of a size on the order of the image resolution elements or smaller. In this case, for reasonable scenes, information about the movers is a natively sparse signal - in an observation of a scene at two closely separated time-steps, only a small number of locations (those associated with the movers) will have changed dramatically. Thus, this particular application is well-suited for compressive sensing techniques that attempt to efficiently measure sparse signals. Recently, we have been investigating two different approaches to compressive measurement for this application. The first, differential Combinatorial Group Testing (dCGT), is a natural extension of group testing ideas to situations where signal differences are sparse. The second methodology is an ℓ-1-minimization based recovery approach centered on recent work in random (and designed) multiplex sensing. In this manuscript we will discuss these methods as they apply to the motion tracking problem, discuss various performance limits, present early simulation results, and discuss notional optical architectures for implementing a compressive measurement scheme.
Visible band lens-free imaging using coded aperture techniques
Kevin D. Ridley, Geoffrey D. de Villiers, Douglas A. Payne, et al.
Traditionally, coded aperture techniques have been applied to short-wavelength imaging: X-rays and γ-rays. For these wavelengths, it is valid to neglect diffraction and describe the operation of the imager in purely geometric-optics terms. We have investigated coded aperture imaging in the visible band. The much longer wavelengths in this region of the spectrum mean that diffraction effects cannot be neglected. We describe the effects of diffraction and the implications for image resolution. We present experimental results from a lens-free coded-aperture imager operating in the visible band and describe the techniques used to obtain good quality images of complex greyscale scenes.
Imaging and Non-Imaging Algorithms
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Tracking targets in multiplexed imagery
We consider the application of compressive imaging theory to the problem of persistent surveillance. As the compressive sensing theory enjoys significant research attention, the application areas for compressive imaging have not kept pace without an optical architecture which could directly improve current sensing capabilities. This paper overviews two methodologies for image multiplexing; each showing a dramatic (2 orders of magnitude) increase in performance for the persistent surveillance application. Field-of-View Multiplexing and time domain multiplexing are discussed and a simulated example is given which shows an increase in performance over current capabilities.
Coded aperture computed tomography
Diverse physical measurements can be modeled by X-ray transforms. While X-ray tomography is the canonical example, reference structure tomography (RST) and coded aperture snapshot spectral imaging (CASSI) are examples of physically unrelated but mathematically equivalent sensor systems. Historically, most x-ray transform based systems sample continuous distributions and apply analytical inversion processes. On the other hand, RST and CASSI generate discrete multiplexed measurements implemented with coded apertures. This multiplexing of coded measurements allows for compression of measurements from a compressed sensing perspective. Compressed sensing (CS) is a revelation that if the object has a sparse representation in some basis, then a certain number, but typically much less than what is prescribed by Shannon's sampling rate, of random projections captures enough information for a highly accurate reconstruction of the object. This paper investigates the role of coded apertures in x-ray transform measurement systems (XTMs) in terms of data efficiency and reconstruction fidelity from a CS perspective. To conduct this, we construct a unified analysis using RST and CASSI measurement models. Also, we propose a novel compressive x-ray tomography measurement scheme which also exploits coding and multiplexing, and hence shares the analysis of the other two XTMs. Using this analysis, we perform a qualitative study on how coded apertures can be exploited to implement physical random projections by "regularizing" the measurement systems. Numerical studies and simulation results demonstrate several examples of the impact of coding.
An analysis of coded aperture acquisition and reconstruction using multi-frame code sequences for relaxed optical design constraints
We present an investigation of the performance of coded aperture optical systems where the elements of a set of binary coded aperture masks are applied over a sequence of acquired images. In particular, we are interested in investigating code sequences and image reconstruction algorithms that reduce the optical fidelity and hardware requirements for the system. Performance is jointly tied to the mask design, the image estimation algorithm, and the inherent optical response of the system. As such, we adopt a simplified reconstruction model and consider generalized optical system aberrations in designing masks used for multi-frame reconstruction of the imagery. We also consider the case of non-Nyquist sampled (aliased) imagery. These investigations have focused on using a regularized least-squares reconstruction model and mean squared error as a performance metric. Masks are found by attempting to minimize a closed form objective that predicts the mean squared error for the reconstruction algorithm. We find that even with suboptimal solutions that binary masks can be used to improve imagery over the case of an uncoded aperture with the same aberration.
Diffraction Imaging Hardware I
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A scalable multi-chip architecture to realise large-format microshutter arrays for coded aperture applications
Mark E. McNie, David O. King, Gilbert W. Smith, et al.
Coded aperture imaging has been used for astronomical applications for several years. Typical implementations used a fixed mask pattern and are designed to operate in the X-Ray or gamma ray bands. Recently applications have emerged in the visible and infra red bands for low cost lens-less imaging systems and system studies have shown that considerable advantages in image resolution may accrue from the use of multiple different images of the same scene - requiring a reconfigurable mask. Previously we reported on the realization of a 2x2cm single chip mask in the mid-IR based on polysilicon micro-opto-electro-mechanical systems (MOEMS) technology and its integration with ASIC drive electronics using conventional wire bonding. The MOEMS architecture employs interference effects to modulate incident light - achieved by tuning a large array of asymmetric Fabry-Perot optical cavities via an applied voltage and uses a hysteretic row/column scheme for addressing. In this paper we present the latest transmission results in the mid-IR band (3-5μm) and report on progress in developing a scalable architecture based on a tiled approach using multiple 2 x 2cm MOEMS chips with associated control ASICs integrated using flip chip technology. Initial work has focused on a 2 x 2 tiled array as a stepping stone towards an 8 x 8 array.
Microelectromechanical (MEMS) optical beam control
This experiment explores the manufacturability of controllable Micro-electromechanical (MEMS) mirrors to direct optical signals. Design includes four separate mirrors which independently control vertical displacement, horizontal displacement, vertical pitch and horizontal pitch. Such devices could be used for a variety of applications but were specifically intended for future use in communications between optical based circuits residing on separate chips. Prototype devices were built in PolyMUMPs to test the feasibility of this process for applications such as this, including a full outgoing beam path with mirror orientations and actuation designs to accomplish this. Several elements of this outgoing beam path were successful and those which needed improvement indicate a high probability of success with limited trials needed. Improvement recommendations on currently successful design elements which could still be improved within the scope of PolyMUMPs have been identified. Originally intended only to direct the outgoing beam, this design could be used on the incoming path as well. Such a design would ensure that the receiving device only requires a target location and not that a specific incoming vector be obtained. This would thus comprise all the elements needed for a prototype proof of concept device to be built. More sophisticated fabrication processes could provide drastic improvements to both transmission and reception beam paths and potentially allow for a variety of more sophisticated designs to improve compactness, controllability, tighten tolerances on moving parts, increase mirror quality, and improved productivity of large quantities of devices.
Utilizing micro-electro-mechanical systems (MEMS) micro-shutter designs for adaptive coded aperture imaging (ACAI) technologies
Coded aperture imaging (CAI) has been used in both the astronomical and medical communities for years due to its ability to image light at short wavelengths and thus replacing conventional lenses. Where CAI is limited, adaptive coded aperture imaging (ACAI) can recover what is lost. The use of photonic micro-electro-mechanical-systems (MEMS) for creating adaptive coded apertures has been gaining momentum since 2007. Successful implementation of micro-shutter technologies would potentially enable the use of adaptive coded aperture imaging and non-imaging systems in current and future military surveillance and intelligence programs. In this effort, a prototype of MEMS microshutters has been designed and fabricated onto a 3 mm x 3 mm square of silicon substrate using the PolyMUMPSTM process. This prototype is a line-drivable array using thin flaps of polysilicon to cover and uncover an 8 x 8 array of 20 μm apertures. A characterization of the micro-shutters to include mechanical, electrical and optical properties is provided. This prototype, its actuation scheme, and other designs for individual microshutters have been modeled and studied for feasibility purposes. In addition, microshutters fabricated from an Al-Au alloy on a quartz wafer were optically tested and characterized with a 632 nm HeNe laser.
Diffraction Imaging Hardware II
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Optical metamaterials for photonics applications
This paper discusses our investigation into artificial structures called metamaterials. Metamaterials make it possible to achieve electromagnetic properties not existing in nature. The investigation focuses on the modeling, fabrication and testing of metamaterials at optical frequencies. The main purpose of this research is to identify a method to fabricate the artificial structures. We identify limitations in the fabrication process which are used to build the metamaterials. Measured reflectance data from fabricated devices is then compared with modeled data to identify limitations affecting the "as-built" figure of merit (FOM). Understanding the parameters which limit the FOM will lead to device fabrication improvements and ultimately to components suitable for optical applications such as optical surveillance systems.
Retroreflector for photonic Doppler velocimetry
In order to meet the goals of the Department of Defense (DoD) for smaller and more accurate weapons, numerous projects are currently investigating the miniaturization of weapons and munition fuze components. One of these efforts is to characterize the performance of small detonators. The velocity of the flyer, the key component needed to initiate a detonation sequence, can be measured using a photonic Doppler velocimeter (PDV). The purpose of this research was to develop a microelectromechanical system (MEMS) device that would act as an optimal retroreflective surface for the PDV. Two MEMS solutions were explored: one using the PolyMUMPsTM fabrication process and one in-house fabrication design using silicon on insulator (SOI) wafers. The in-house design consisted of an array of corner reflectors created using an SOI wafer. Each corner reflector consisted of three separate mirror plates which were self-assembled by photoresist pad hinges. When heated to a critical temperature (typically 140-160 °C), the photoresist pads melted and the resulting surface tension caused each mirror to rotate into place. The resulting array of corner reflectors was then coated with a thin layer of gold to increase reflectivity. Despite the successful assembly of a PolyMUMPsTM corner reflector, assembling an array of these reflectors was found to be unfeasible. Although the SOI corner reflector design was completed, these devices were not fabricated in time for testing during this research. However, the bidirectional reflectance distribution function (BRDF) and optical cross section (OCS) of commercially available retroreflective tapes were measured. These results can be used as a baseline comparison for future testing of a fabricated SOI corner reflector array.
Alternative imaging to conventional lens
In designing optical systems in the EO/IR wavelength region for conventional lens are most common and efficient when low F# and large field of view is desired. Conventional lenses are efficient in meeting optical response but come at a cost in size and weight and often are complex in nature (aberrations). In this paper we discuss alternatives to conventional lenses. We examine diffractive optics (DO), and explore resonating and diffractive periodic metalo-dielectric structures as an alternative lensing. An oscillator model is employed to interpret these structures, wavefront bending and a design approach is provided.
Wide Field-of-View and Turbid Media Imaging
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Observations of a geosynchronous satellite with optical interferometry
We report an interferometric detection of an earth-orbiting artificial satellite using optical interferometry. We targeted four geosynchronous communications satellites with the Navy Prototype Optical Interferometer (NPOI) near Flagstaff, AZ, and obtained interferometric fringes on one of them, DIRECTV-9S. We used an east-west 15.9-meter baseline of the NPOI and took data in 16 spectral channels covering the 500-850 nm wavelength range. Observations took place during the "glint season" of 28 February to 3 March 2008, and then again in February - March 2009, when the geometry of the solar panel arrays and the Sun's position creates glints as bright as 2nd magnitude of a few minutes' duration each night. We detected fringes on the satellite at approximately the 2 sigma level on 1 March at magnitude 4.5. Subsequent analysis shows that the fringe amplitudes are consistent with a size scale of 2 meters (50 nanoradians at GEO) in an east-west direction. This detection shows that interferometric detection of satellites at visual wavelengths is possible, and suggests that a multi-baseline interferometer array tailored to the angular size and brightness of geosynchronous satellites could lead to images of these satellites.
Wide field astronomical image compensation with multiple laser-guided adaptive optics
We report closed-loop results obtained from the first adaptive optics system to deploy multiple laser guide beacons. The system is mounted on the 6.5 m MMT telescope in Arizona, and is designed to explore advanced altitude-conjugated techniques for wide-field image compensation. Five beacons are made by Rayleigh scattering of laser beams at 532 nm integrated over a range from 20 to 29 km by dynamic refocus of the telescope optics. The return light is analyzed by a unique Shack-Hartmann sensor that places all five beacons on a single detector, with electronic shuttering to implement the beacon range gate. Wavefront correction is applied with the telescope's unique deformable secondary mirror. The system has now begun operations as a tool for astronomical science, in a mode in which the boundary-layer turbulence, close to the telescope, is compensated. Image quality of 0.2-0.3 arc sec is routinely delivered in the near infrared bands from 1.2-2.5 μm over a field of view of 2 arc min. Although it does not reach the diffraction limit, this represents a 3 to 4-fold improvement in resolution over the natural seeing, and a field of view an order of magnitude larger than conventional adaptive optics systems deliver. We present performance metrics including images of the core of the globular cluster M3 where correction is almost uniform across the full field. We describe plans underway to develop the technology further on the twin 8.4 m Large Binocular Telescope and the future 25 m Giant Magellan Telescope.
Analytic versus adaptive image formation using optical phased arrays
Rick Kendrick, Joseph C. Marron
Current optical phased arrays produce images by adaptively phasing the output of several telescopes on a common focal plane. Image based phasing techniques such as Phase Diversity, are used to maintain the phasing in real time. This requires both a computationally intensive algorithm for estimating the phasing errors as well as a means for rapidly adjusting the optical path length through each telescope. In this paper we will compare the adaptive technique of phasing multiple telescopes with the analytic technique of digital holography. Digital holography provides a means of digitally estimating and correcting the phasing errors between the multiple telescopes. The process can occur long after the data has been acquired which relaxes the requirements on the stability of the phased array as well as the mechanical complexity. Experimental results will be shown for adaptive and analytical image formation in remote sensing applications.
Wavefront correction using a Fourier-based image sharpness metric
Conventional wavefront correction uses direct wavefront sensing methods such as the Shack-Hartmann sensor to measure the wavefront at the pupil of the system. Image sharpening is an indirect wavefront sensing method where the wavefront correction is performed using measurements from the image plane. Wavefront correction using image sharpening is advantageous in systems where a point source isn't available or where the number of optical components needs to be reduced by using the scientific camera that is already in place. Correction is performed by measuring the sharpness value as the correction device, such as a deformable mirror, cycles through until the sharpness value is maximized and continues to adapt as the aberrations change. A sharpness metric, or definition, is needed to measure the sharpness value such that it reaches a maximum when aberrations are minimized. This work investigates the use of the Fourier transform of the image, the image spatial frequency spectra, as a Fourier-based sharpness metric. The image spatial frequency spectra is obtained two ways, digitally by computing the Fourier transform of the image plane and optically with a coherent source by using the Fourier transform properties of a convex lens. Affects of aberrations on the intensity at various spatial frequencies are investigated to obtain a sharpness metric that reaches a maximum and aberration strengths decrease. Results from experimentation of various optical configurations are presented to evaluate the performance of these Fourier-based metrics.
Spatially multiplexed optical MIMO imaging system in cloudy turbulent atmosphere
M. Kavehrad, Z. Hajjarian, J. Fadlullah
Active optical imaging is preferred over Radio Frequency (RF) counterparts due to its higher resolution, faster area search rate, and relatively easier interpretation by a human observer. However, in imaging through atmosphere one should consider dispersive effects of multiple scatterings and turbulence-induced wave perturbations, which give rise to intensity fluctuations, and wave-front distortions. All these phenomena broaden and distort the spatial impulse response known as the Point Spread Function (PSF). In this paper, a multiplexed Multi-Input Multi-Output (MIMO) imaging system design is introduced. At the transmitter, a computer generated holographic beam-splitter is used to generate arrays of beamlets, providing faster area search rate and a uniformly distributed illumination all over the target. Then at the receiver, an array of photo-detectors is used to collect the reflected rays. While a Monte-Carlo Ray Tracing (MCRT) algorithm, developed at Pennsylvania State University, Center for Information and Communications Research (CICTR), is used to model imaging in multiple scattering turbid media, phase-screens are employed to simulate turbulence-induced wave-front distortions. Hence, a comprehensive frame work is exploited that takes into account possible sources of degradation. Using this frame of work, system performance is analyzed under different meteorological conditions and restoration techniques such as Blind Deconvolution (BD) are used to retrieve the original image by deconvolving PSF and observed image.
Synthetic Aperture and Super-resolution
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Optical synthetic aperture imaging with spatial heterodyne interferometry
Experimental demonstrations of optical synthetic aperture imaging using spatial heterodyne interferometry have been achieved at the Lockheed Martin Advanced Technology Center in Palo Alto, CA. In laboratory experiments, a reflective binary star scene and an Air Force resolution bar target were illuminated and imaged by a 532 nm laser and an afocal telescope. The real aperture diffraction limit in the horizontal direction was 65 microRadians. Complex pupil information was obtained by mixing the scattered return light from the target with light from an off-axis local oscillator, thus forming a linear fringe pattern on a CCD array placed at the pupil plane. Fourier transform methods were used to extract pupil amplitude and phase. By translating the real aperture pupil, collecting data at different locations, and extracting and combining the pupil data, a synthetic aperture twice the real aperture size was created. In the reconstructed image resulting from the synthetic aperture pupil data, features down to 32 microRadians were clearly resolved.
Antenna aperture and imaging resolution of synthetic aperture imaging ladar
Liren Liu
In this paper, the azimuth imaging resolutions of synthetic aperture imaging ladar (SAIL) using the antenna telescopes with a circular aperture for reception and a circular plan or a Gaussian beam for transmitting and with a rectangular aperture for reception and a rectangular plane or an elliptic Gaussian beam for transmitting are investigated. The analytic expressions of impulse response for imaging are achieved. The ideal azimuth spot of resolution and its degradation due to the target deviation from the footprint center, the mismatch from the quadratic phase matched filtering, the finite sampling rate and width are discussed. And the range resolution is also studied. Mathematical criteria are all given. As a conclusion, the telescope of rectangular aperture can provide a rectangular footprint more suitable for the SAIL scanning format, and an optimal design of aperture is thus possible for both a high resolution and a wide scan strip. Moreover, an explanation to the resulted azimuth resolution from our laboratory-scaled SAIL is given to verify the developed theory.
A multi-purpose SAIL demonstrator design and its principle experimental verification
A fully 2-D synthetic aperture imaging ladar (SAIL) demonstrator is designed and being fabricated to experimentally investigate and theoretically analyze the beam diffraction properties, antenna function, imaging resolution and signal processing algorithm of SAIL. The design details of the multi-purpose SAIL demonstrator are given and, as the first phase, a laboratory-scaled SAIL system based on bulk optical elements has been built to verify the principle of design, which is similar in construction to the demonstrator but without the major antenna telescope. The system has the aperture diameter of about 1mm and the target distance of 3.2m.
THz and Photon Counting Imaging
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Active terahertz imaging with Ne indicator lamp detector arrays
The advantages of terahertz (THz) imaging are well known. They penetrate well most non-conducting media and there are no known biological hazards, This makes such imaging systems important for homeland security, as they can be used to image concealed objects and often into rooms or buildings from the outside. There are also biomedical applications that are arising. Unfortunately, THz imaging is quite expensive, especially for real time systems, largely because of the price of the detector. Bolometers and pyroelectric detectors can each easily cost at least hundreds of dollars if not more, thus making focal plane arrays of them quite expensive. We have found that common miniature commercial neon indicator lamps costing typically about 30 cents each exhibit high sensitivity to THz radiation [1-3], with microsecond order rise times, thus making them excellent candidates for such focal plane arrays. NEP is on the order of 10-10 W/Hz1/2. Significant improvement of detection performance is expected when heterodyne detection is used Efforts are being made to develop focal plane array imagers using such devices at 300 GHz. Indeed, preliminary images using 4x4 arrays have already been obtained. An 8x8 VLSI board has been developed and is presently being tested. Since no similar imaging systems have been developed previously, there are many new problems to be solved with such a novel and unconventional imaging system. These devices act as square law detectors, with detected signal proportional to THz power. This allows them to act as mixers in heterodyne detection, thus allowing NEP to be reduced further by almost two orders of magnitude. Plans are to expand the arrays to larger sizes, and to employ super resolution techniques to improve image quality beyond that ordinarily obtainable at THz frequencies.