Miller

Multi-Aperture Coherent Imaging

Nicholas J. Millera, Joseph W. Haus

a,b, Paul F. McManamon

a and David Shemano

a

aLadar and Optical Communications Institute

bElectro-Optics Program

University of Dayton

300 College Park

Dayton, OH 45469-2950 USA

millernj@notes.udayton.edu, joseph.haus@notes.udayton.edu, paul@excitingtechnology.com,

Introduction

The resolution of a diffraction-limited imaging system is proportional to its aperture diameter. However, using a large aperture to achieve fine target resolution is costly in weight, volume, and dollars. By flood illuminating a target with a laser, the reflected field can be coherently detected at multiple, spatially separated small apertures. Post-detection, the field measurements from each of these small apertures can be assembled into a synthetic array based on their physical locations. If the fields in the synthetic array are correctly phased, the resolution of the resulting image is now proportional to the array dimensions. Hence, we can attain high resolution imagery by synthesizing a large array from many smaller apertures.

The Innovative Multi-Aperture Gimbal-less Electro-optical, (IMAGE) testbed, is being developed by the University of Dayton Ladar and Optical Communications Institute (LOCI) as a research tool in support of multiple sub-aperture based EO systems. The IMAGE testbed will be used to test coherent imaging techniques and phasing algorithms that provide the full diffraction limited resolution associated with array dimensions. The testbed will provide a means of testing components and imaging through a turbulent atmospheric path. The IMAGE testbed is designed to image targets at a 7Km horizontal range. In this paper we describe a prototype testbed assembled from COTS components and tested in our indoor range hall. The prototype testbed consists of three sub-apertures operating at 532nm wavelength with inexpensive CMOS cameras. This paper reports experimental images of an ISO12233 resolution target at an apparent range of 330 meters using our indoor compact range.

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Description of the IMAGE system

Optical aperture synthesis creates a high resolution image from the complex-valued fields in each sub-aperture pupil. The fields in the spatially separated pupils are numerically propagated and superposed

in a common focal plane forming a synthetic image with resolution described by the spatial extent of the array

1. The complex-valued field is measured

by a holographic technique in which phase is encoded in an interference pattern detected by an inexpensive conventional two-dimensional detector array.

The prototype IMAGE testbed uses the spatial heterodyne method successfully employed by Marron

2. Coherent spatial heterodyne imaging

requires flood illuminating the target with a coherent laser source and mixing the target reflected wavefront with a reference beam derived from the same laser source, referred to as the local oscillator (LO). If an appropriate tilt is applied to the reference beam and the resulting interferogram is Fourier transformed, the desired complex field is spatially isolated

3. The prototype IMAGE testbed

spatial heterodyne system flood illuminating a diffuse target at a nominal 7Km range is shown in Figure 1. An 8X afocal telescope maps the 48mm entrance pupil to a 6.2mm exit pupil coincident with a two-dimensional CMOS sensor array. The LO is fiber delivered to each of three sub-apertures where a pupil plane interferogram is detected and post-processed to obtain the pupil plane complex field.

Figure 1: Prototype IMAGE testbed schematic

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Indoor compact range

In order to simulate the 7Km outdoor range over Dayton OH, an indoor compact range has been assembled. The compact range is a M=38X afocal telescope using of 61cm diameter objective mirror that scales longitudinal dimensions by M

2 and the

transverse dimensions by M. The 61cm diameter compact range objective can accommodate large arrays and image at distances greater than 40Km.

Experimental imaging results

A diffuse ISO12233 resolution target was imaged through the prototype IMAGE testbed at a scaled range of 330 meters using the compact range.

Figure 2: Experimental Schematic

Figure 3: Detected irradiance (following subtraction of a subsequent LO only frame). The LO irradiance

approximately 130X target return irradiance.

The circular shape of the 6.2mm diameter telescope exit pupil irradiance mixing with the LO on the CMOS camera array is plainly evident.

Figure 4: 16X magnification of previous figure

The diagonal fringes visible within the speckles result from mixing of the tilted LO with the diffuse resolution target return. The target return phase is encoded in these irradiance fringes.

Next, a discrete Fourier transform spatially separates the interferogram components as seen in Figure 5. The in focus image is located in the upper left quadrant, while the defocused conjugate image is located in the lower right quadrant. Defocused autocorrelations of the Fourier transforms of both the LO and target are located in the center.

Figure 5: Discrete Fourier transform of the interferogram shown (log-scaled) following

multiplication by quadratic phase factor corresponding to 330[m] range to target.

The high contrast speckle evident in Figure 5 can be reduced by summing multiple irradiance images of the target, each with independent speckle realizations

5. Independent speckle realizations

Miller

were generated by propagating the illumination beam through spatially independent sections of a diffuser so that the wavefront propagating off the diffuse resolution target is randomized in phase. Figure 6 is the sum of 256 irradiance images with I independent speckle realizations.

Figure 6: Sub-aperture irradiance image from 256 statistically independent speckle realizations.

The predicted diffraction-limited incoherent imaging performance of a single sub-aperture as well as the three sub-aperture horizontal array is described by the modulation transfer function (MTF) shown in Figure 7. The MTF’s abscissa is scaled to ISO12233 chart numerals, showing a resolution limit of about ‘2.3’ for a single sub-aperture. Figure 6, exhibits sub-aperture imaging performance just short of this diffraction limit.

Figure 7: Theoretical array performance

Next, the fields measured in each sub-aperture were phased by sequentially correcting two types of aberrations: 1. Static aberrations which are identical for each speckle realization exposure, and 2. temporal aberrations which vary between speckle realization exposures

4. Zernike polynomial

phase corrections (up to 6th order) are applied to

the sub-aperture pupils6. For both the static and

temporal corrections, a Matlab optimization algorithm converges on Zernike polynomials coefficients that maximize an image sharpness metric

7-10. When imaging the ISO12233 resolution

target consisting of dark features on a mainly white field, the algorithm reliably converged using

Muller/Buffington’s S5 metric with β=0.57.

Correcting for static aberrations requires a single, initial calibration. Temporal aberrations must be continually corrected. The experimental image data acquired in our indoor range hall exhibited only tip, tilt, and piston temporal aberrations. This would also be the case when imaging through a turbulent atmospheric path in which the sub-aperture diameter is substantially less than the atmospheric coherence diameter, r0. Tip, tilt, and piston corrections are applied to each sub-aperture and the optimization algorithm maximizes the sharpness of a running speckle-averaged composite image as described by Rabb et al

4.

Once tip, tilt, and piston are corrected for a single speckle realization exposure, an improved speckle-averaged synthetic image is computed. This tip, tilt, and piston correction process is repeated for each speckle realization exposure. Because the three sub-apertures are arranged horizontally, a resolution gain is only observed along that axis.

Figure 8: Synthetic irradiance image from 256 statistically independent speckle realizations.

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Future work

The present three-aperture prototype testbed will be used in imaging experiments through simulated atmospheric turbulence. We will investigate the imagery and develop algorithms to correct for distributed turbulence. As seen in the proposed configuration shown in Figure 9, two phase screens will be located at intermediate virtual ranges. By selecting appropriate ranges and turbulence strengths for the two phase screens, we model a distributed atmospheric path with a given atmospheric coherence diameter, r0, and

isoplanatic angle, θ0. Note, that both the transmit and receive beams pass through the turbulent atmospheric path.

Figure 9: Multi-aperture testbed incorporating atmospheric turbulence phase screens.

Additionally, we continue work on the IMAGE testbed. The IMAGE testbed will consist of seven or more sub-apertures placed into a hexagonal grid up to 61cm diameter.

Conclusions

We have described an experiment in which the field reflected off a coherently illuminated resolution chart placed at an apparent range of 330 meters is measured within each of three linearly aligned sub-apertures. A post-detection optimization algorithm correctly phased and propagated these independent, spatially separated complex fields to a common image plane synthesizing a higher resolution image. In fact, the resulting synthetic image nearly reaches the theoretical diffraction-limit of the array.

Acknowledgements

This effort was supported in part by the U.S. Air Force through contract number FA 8650-06-2-1081 and the Ladar and Optical Communication Institute at the University of Dayton. The views expressed in this article are those of the authors and do not reflect on the official policy of the Air Force, Department of Defense or the U.S. Government.

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