Characterization Performance of a Laser Imaging System through Atmosphere By

Mazen S. Nairat Principle of Laser Imaging System The two primary factors of the atmosphere are:

the turbulence and the extinction Atmosphere Characteristics The problem of scanning a two dimension target within Fresnel zone distance is examined for a long and short exposures . Modeling and Simulation of a Long Range Laser Scanning through Atmospheric Turbulence Laser Detection and Ranging is an effective technique to navigate and map the objects.

It employes discrete pulses of visible light or IR beam and scan the desired scene and detect the back scattering signal.

It is effective and accurate but sensitive to the atmosphere presence. LADAR Over view The detected intensity is given by: LADAR Principle Imaging System sees the objects as either targets or background depends on the reflectivity Level (contrast) Navigation system technically concerns about resolving power of the closing points Rayleigh criterion Atmospheric Turbulence Generated due to refractive index fluctuations.

Modeled as vortices of various sizes

Structure parameter of the refractive index fluctuations Structure Function Spatial Power Spectrum 3-D Fourier Trans. of covariance function Kolomogorov Spectrum Power spectral density for refractive index fluctuations over the inertial sub range is given by Integral evaluation will be Propagation through

the Atmosphere Free Propagation The propagation can be described by the Huygens-Fresnel integral Main Atmospheric Effect on the Imaging Irradiance Fluctuation Called Scintillation Index For asymptotic wave cases, defined by Rytov Variance Image Blurring Image blurring due to the atmospheric turbulence is examined through the associated optical transfer function (OTF)

OTF does like spatial frequency filter

Image blurring can be indicated by cutoff frequency Image Dancing Generated due to fluctuation in the angle of arrival Beam Wander Propagation through atmospheric turbulence causes additional beam widening Beam wander component at Kolomogrove spectrum given by Atmospheric Coherence Length Characteristic measure for the correlation length of atmospheric turbulence.

Denoted by D.Fried 1965

Calculated by In case of isoplanic plane waves and Kolomogrove spectrum, It is given by Wave Optics Simulation Numerical tool to solve the problems

Our simulation approach based on the Fast Fourier Transform.

Matlab software is used. Discrete Representation and Sampling Theory Sampling function in discrete representation Sampling Rate Uniform Sampling Discrete Fourier Transform Wave Propagation Simulation Huygens-Fresnel Principle Impluse Response Function Imaging System Simulation Imaging of coherent source Imaging incoherent Source It should be mentioned here that for the same imaging system, the cutoff frequency value for an incoherent system is twice that of a coherent system Simulation of Atmospheric turbulence Atmospheric turbulence is modeled as a transmittance through a sequence of independent random phase screens. The transmittance function of each phase screen can be given as For a Gaussian random process Incorporating Aerosol Scattering in Wave Optics Propagation Simulation The aerosol medium is also modeled as a sequence of phase screens placed along the propagation path

The key to the approach is to translate the aerosol scattering PSF into a collection of phase screens realizations

A random wave front tilt is applied at each single scatter screen to simulate the amount of scattered power. The procedure is based on generating a Gaussian phase function that represents forward scattering and causes an angular distribution of the transmitted power. Atmospheric Turbulence Atmospheric Extinction Optical beam extinction described by Beer-Lambert law We concern about scattering and absorption due to the Aerosol. We adopt Mie Theory to describe the forward scattering Back Ground The fraction of the scattered power at certain direction represented by the phase function

For the atmospheric medium, it is popular to use Gaussian formula The Phase Function Beam Angular Divergence Additional beam widening rises due to propagation through aerosol medium An OTF for wave front tilt is introduced to describe the specific effect of beam wander Wave optics simulations are performed to visualize the performance of the scanning system * PhD candidate at Physics Department at New Mexico State University wander Effect Short Exposure Long Exposure Figure 2 : Simulated images using the concept of MTFs D/r0=9.6 D/r0=0.8 D/r0=2.4 A numerical simulation is performed to illustrate image results for long-time and short-time exposures, as well as for the effect of beam wander only. The simulation involves a three-bar target and filtering is applied in the frequency domain based on the MTF functions. Image resolution can be defined mathematically as the integration of the MTF over the full spatial frequency range and the resolution is found to be a function of D/r0 . Figure 2 shows how image resolution depends on the ratio D/r0 for the different types of exposures given the same link parameters . Optics Simulation where r0 is the atmospheric coherence parameter The normalized MTF for this system is related to the beam spot size and shape at the target. In free space the MTF is given by The beam wander (wave front tilt ) effect can be expressed in terms of the MTF as follow: Figure 1 : Scanning laser imaging system model. where λ Detector Target L Cn2 Random media D This study is supported by the Air Force office of Scientific Research (AFOSR) where is spatial frequency and D is the practical diameter of the beam at the transmitter plane. Fried (JOSA v. 56, 1966) derived the statistical average of the MTF due to atmospheric turbulence. He defined two types of exposure: long-time and short-time. The exposures differ due to a random factor related to wave front tilt that is part of the long-time exposure. For propagation through weak turbulence and based on the Kolomogrov spectrum, the MTFs for both long-time and short-time exposures can be written as A focused Gaussian beam of wavelength λ illuminates a 2-D target at a distance L as shown in Figure 1. The laser spot is scanned over the target area and the backscattered flux measured by the detector represents a record of the target reflectance function. The imaging performance of a long range laser scanning system through atmospheric turbulence is examined using the concept of the modulus transfer function (MTF). The target is assumed to be within the Fresnel zone and long-time and short-time average exposures are considered. The effect of beam wander is described in terms of the MTF. Our analysis indicates that wave front tilt is a dominant factor that limits the recovery of high spatial frequencies. A numerical simulation is employed to demonstrate the utility of MTF approach and illustrate the effects of turbulence on the resulting images. Theoretical Model Abstract Mazen Nairat* and David Voelz

Klipsch School of ECE

New Mexico State University Performance of Scanning Ladar Imaging through Atmospheric Turbulence Our analysis shows that the wave front tilt has more significant limitation than short exposure The simulation and analytic results were consistent for the operational parameter Performance Characteristics of a Scanning Laser Imaging System through Atmospheric turbulence The scanning Procedure The pixilated receiver yields 2-D transverse spatial information.

The depth profile is determined using time of flight measurement.

The generated point cloud data provides 3-D coordinates of the reflectance value of the scene.

The sequential spacing laser spots at the scene determines the spatial sampling way. Over Scanning Full Scanning Under Scanning Angular divergence of the scanning beam Image Sampling Nyquist Frequency Transverse Spatial Resolution is a function of sampling mode with Nyquist freq = 2 (char. freq)

best resolution is achieved In terms of angular spacing : Atmospheric Turbulence Consistent with conventional imaging features Beam Truncation Effect Approach for incorporating Aerosol Scattering in Wave Optics simulation The angular irradiance profile of the Gaussian beam at propagation distance L is given by : In the presence of the aerosol, PSF is calculated as follow Aerosol Scattering in Wave Optics Simulation A simulation procedure is proposed to simulate the angular irradiance profile through aerosol

A collimated Gaussian beam propagation is examined at two different media

- light aerosol media with and - wide scattering media Publication - M. Nairat and D. Voelz, “Performance Characteristics of a Scanning Laser Imaging System through Atmospheric Turbulence," Opt. Eng., 15(10), 101708, (2012). -M. Nairat and D. Voelz, “Approach for incorporating aerosol scattering in wave optics propagation simulation,” IEEE Aerospace conf. 2013, Big Sky, MT, mar. (2013). - M. Nairat and D. Voelz, "Imaging performance of long range laser scanning through atmospheric turbulence, "Proc. SPIE 8165, 81650I (2011). Ph.D Dissertation Defense Chair

Dr.David Voelz Summary and Conclusion The PSF and OTF of a Laser scanning system through atmosphere are characterized.

Long and short exposures through atmospheric turbulence are analytically analyzed.

Random wave front tilt due to the turbulence is described through the associated OTF.

Beam wander has most significant influence on the imaging performance.

Spatial sampling procedure is analyzed.

This study emphasis the over scanning procedure with spots separated by beam radius provides best resolution. Summary and Conclusion The resolution metric is calculated and Strehl Ratio is determined.

Our results state that the spatial resolution will be reduced by more than 90% in a homogenous turbulence when the beam waist size on the order of

Beam truncation by the exiting aperture has no significant influence in the turbulence.

Wave optics propagation simulation is introduced.

Our results provide good agreement with the simulation results. Summary and Conclusion We proposed a simulation procedure to describe the aerosol influence on the laser imaging.

The developed approach is applicable in inhomogeneous medium with varying scatter function.

The proposed simulation can be applied simultaneously with propagation through turbulent media There is a good agreement between the achieved simulated results and the analytical results Good Results

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