Multi aperture coherent imaging IMAGE testbed

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1 Multi aperture coherent imaging IMAGE testbed Nick Miller, Joe Haus, Paul McManamon, and Dave Shemano University of Dayton LOCI Dayton OH 16 th CLRC Long Beach 20 June 2011

2 Aperture synthesis (part 1 of 2) The complex valued field reflected off a target is measured in multiple, spatially separated sub apertures. 1.22R Resolution spot size D CMOS CMOS CMOS

Aperture synthesis (part 2 of 2) Multiple measured sub aperture complex fields can

the correct phase relationship between the sub apertures an improved resolution

Single aperture Multiple apertures Sub aperture pupil field Digital array of sub

3 Aperture synthesis (part 2 of 2) Multiple measured sub aperture complex fields can be placed in a numerical array corresponding to their physical locations and with the correct phase relationship between the sub apertures an improved resolution synthetic image is obtained. Single aperture Multiple apertures Sub aperture pupil field Digital array of sub aperture pupil fields Numerically propagate the pupil field to the image plane Sub aperture focal image Phased array synthetic focal image

4 Coherent detection method Spatial heterodyne Measures complex field (amplitude and phase) in each sub aperture entrance pupil A collimated LO at the same temporal frequency as the target return, but tilted with respect to the target return beam mixes in the CMOS plane (aka spatial heterodyne detection). CMOS CMOS detected irradiance (Note spatial carrier fringes)

5 Sub aperture array geometry and theoretical MTF Ø48.3[mm] 70.5[mm] Autocorrelate the pupil array to obtain the MTF

6 Aperture synthesis (Experiment schematic) 350[mW] CW laser at = 532[nm] ISO12233 resolution target Apparent range, R = 330[m] Apparent size = 76x44[cm] CMOS CMOS CMOS

7 Compact range Simulates ranges up to ~40[Km] within LOCI s 30[m] range hall. Compact range is an afocal telescope with M=38X magnification which scales targets by M transversally and by M 2 longitudinally. 608[mm] dia. objective filled by Hex 61 array of 48mm dia. apertures.

8 Spatial heterodyne (Experimental results 1 of 3) Irradiance after LO frame subtraction 16X zoom

9 Spatial heterodyne (Experimental results 2 of 3) DFT of the CMOS irradiance (log scaled) Quadratic phase curvature focuses to 330[m] range Resolution target ROI R FOV M pixel pitch Ground Sample Distance, (GSD) = 1.64mm m

10 Spatial heterodyne (Experimental results 3of 3) Coherent focal plane irradiance image Speckle averaged focal plane image using 256 speckle realizations

11 Spatial heterodyne (coherent speckle noise) High contrast speckle noise plagues coherent images of optically diffuse targets. Speckle noise can be mitigated by summing multiple coherent irradiance images of a target with independent speckle realizations. Averaging N coherent images with independent speckle realizations improves by, SNR Simulated speckle averaged images consisting of N independent realizations N N = 1 N = 4 N = 16 N = 64

12 Sub aperture phasing (Aberrations) Optical aberrations consist of Static aberrations which are fixed between exposures. Temporal aberrations which vary between exposures. Both static & temporal aberrations can be further subdivided into, Intra aperture aberrations corrupt sub aperture images and include defocus, astigmatism, coma, spherical, and higher order aberrations. Inter aperture aberrations only corrupt synthetic images and include piston, tip, and tilt.

13 Image sharpness metric (Incoherent images) Iterative optimization algorithm maximizes the image statistics metric: S I p, q p, q where p and q are pixel indices of the intensity image, I Minimizing the metric makes dark features darker. Defocused Focused S 0.5 = 1.51x10 4 S 0.5 = 1.45x10 4

The sharpness metric can be modified to operate on an image averaged over N coherent images with independent

14 Image sharpness metric (coherent speckled images) The sharpness metric of a speckly coherent image is a Gaussian random variable with mean proportional to the incoherent metric. The sharpness metric can be modified to operate on an image averaged over N coherent images with independent speckle realizations: S 1 N N Inp, q p, q n1 Defocused <1: Minimizing metric makes dark features darker. Focused S 0.5 = 1.07x10 3 S 0.5 = 1.01x10 3

15 Static intra aperture aberration correction Apply same phase correction to all N exposures. Compute sharpness metric on the speckleaveraged sub aperture image. Speckle realization index n = 1 B images Example phase correction (waves) n = 2 n = N Speckle averaged sub aperture image

16 n = 1 Static inter aperture aberration correction Apply the same tip, tilt, and piston correction to all N exposures. Compute sharpness metric on the speckle averaged synthetic image. Speckle realization index A images B images C images * Synthetic images n = 2 * n = N * * Indicates corrected image Speckle averaged synthetic image

17 n = 1 Temporal inter aperture piston, tip, tilt correction Apply unique piston, tip, and tilt corrections to a each exposure Compute sharpness metric on the running speckle averaged synthetic image. A images B images C images * Synthetic images n = 2 n = N Step 1 * Indicates corrected image Speckle averaged synthetic image

18 Temporal inter aperture piston, tip, tilt correction Apply unique piston, tip, and tilt corrections to a each exposure Compute sharpness metric on the running speckle averaged synthetic image. n = 1 A images B images C images * Synthetic images n = 2 * n = N Step 2 * Indicates corrected image Speckle averaged synthetic image

Temporal inter aperture piston, tip, tilt correction Apply unique piston, tip, and tilt corrections to a each exposure Compute sharpness metric on the running

19 Temporal inter aperture piston, tip, tilt correction Apply unique piston, tip, and tilt corrections to a each exposure Compute sharpness metric on the running speckle averaged synthetic image. n = 1 A images B images C images * Synthetic images n = 2 * n = N * Step N * Indicates corrected image Speckle averaged synthetic image

20 The ISO resolution target (for reference) Phasing algorithm minimized the sharpness metric, N S Inp, q p, q N n1 which strives to make the dark features darker.

Total peak to valley phase correction < /5 with appreciable power only in defocus,

21 Sub aperture phasing (Experimental results 1 of 4) Zernike polynomials (up to 6 th order) formed the basis for the static intra aperture phase corrections. Total peak to valley phase correction < /5 with appreciable power only in defocus, astigmatism, and spherical aberration terms. Static sub aperture phase correction solutions (waves) Left Center Right

22 Sub aperture phasing (Experimental results 2 of 4) Sub aperture image corrected for static intra aperture aberrations

23 Sub aperture phasing (Experimental results 3 of 4) Synthetic image corrected for static inter aperture aberrations

24 Sub aperture phasing (Experimental results 4 of 4) Synthetic image corrected for temporal piston, tip, and tilt

25 Aperture Synthesis (Current work) Place turbulence phase screens in the compact range s small beam propagation path to model distributed turbulence. Construct arrays with larger numbers of sub apertures. Illumination beam GREEN Target reflected beam RED

26 Imaging over 7Km outdoor range (Future work) Veterans Administration Hospital Shed on roof + resolution target

27 Summary Spatial heterodyne technique measures complex valued fields. Complex valued fields measured in spatially separated locations can be properly phased and numerically propagated to a focal plane forming a high resolution synthetic image. Sub apertures can be phased with an optimization algorithm using an image sharpness metric on focal plane synthetic images. We demonstrated near diffraction limited image resolution in the laboratory with 3 apertures imaging a resolution target at a virtual range of 330m using LOCI s compact range.

28 Acknowledgements This effort was supported in part by the U.S. Air Force through contract #FA , and by the Ladar and Optical Communications Institute (LOCI) 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.

$16 images of a point recorded over a period of ~60 seconds Point images maintain constant, nearly diffraction limited shapes but the image centroids wandered from$

30 What aberrations are present in the experimental range? 16 images of a point recorded over a period of ~60 seconds Point images maintain constant, nearly diffraction limited shapes but the image centroids wandered from exposure to exposure. Indicative of weak, static, intra aperture aberrations and temporal tip and tilt aberrations.

I Spatial heterodyne processing Extracts the complex valued focal plane field from the CMOS irradiance CMOS u tar u LO 2 (CMOS irradiance) I CMOS u tar 2 u LO 2 u tar u * LO u * tar u LO (Expand the

31 I Spatial heterodyne processing Extracts the complex valued focal plane field from the CMOS irradiance CMOS u tar u LO 2 (CMOS irradiance) I CMOS u tar 2 u LO 2 u tar u * LO u * tar u LO (Expand the CMOS irradiance) FT 2 2 * * I DFT u u DFTu u DFTu u CMOS tar LO tar LO tar LO (DFT of CMOS irradiance) DFT I AutocorrelationDFTu Autocorrelation DFTu CMOS tar * LO DFTu tar DFTu x, y tar x, y Complexvalued image Pupil plane fields map to focal plane via DFT. A digital, quadratic phase curvature applied to the CMOS irradiance focuses the complex Centered autocorrelations Conjugate image

SIGNAL TO NOISE RATIO EFFECTS ON APERTURE SYNTHESIS FOR DIGITAL HOLOGRAPHIC LADAR

SIGNAL TO NOISE RATIO EFFECTS ON APERTURE SYNTHESIS FOR DIGITAL HOLOGRAPHIC LADAR Thesis Submitted to The School of Engineering of the UNIVERSITY OF DAYTON In Partial Fulfillment of the Requirements for