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The spatial resolution of a conventional imaging lidar system is constrained by the diffraction limit of the telescope's aperture. The combination of the lidar and synthetic aperture (SA) processing techniques may overcome the diffraction limit and pave the way for a higher resolution air borne or space borne remote sensor. Regarding the lidar transmitting frequency modulation continuous-wave (FMCW) signal, the motion during the transmission of a sweep and the reception of the corresponding echo were expected to be one of the major problems. The given modified Omega-K algorithm takes the continuous motion into account, which can compensate for the Doppler shift induced by the continuous motion efficiently and azimuth ambiguity for the low pulse recurrence frequency limited by the tunable laser. And then, simulation of Phase Screen (PS) distorted by atmospheric turbulence following the von Karman spectrum by using Fourier Transform is implemented in order to simulate turbulence. Finally, the computer simulation shows the validity of the modified algorithm and if in the turbulence the synthetic aperture length does not exceed the similar coherence length of the atmosphere for SAIL, we can ignore the effect of the turbulence.

A conventional optical imager is limited in spatial resolution by the diffraction limit of the telescope aperture [

A number of fundamental but innovative synthetic-aperture experiments in the optical domain were performed [

Fortunately, we can learn experience from SAR, a mature field that was developed to construct microwave images of high resolution by use of antennas of reasonable size. The spotlight model SAR allows the generation of images with a high geometry resolution. If we make SAIL work in spotlight model, amazing resolution can be obtained. Since the SAIL system uses continuous wave (CW) form while pulses are used in the SAR system [

In this paper, the FM-CW SAIL signal processing will be addressed and the response to a point target will be developed first. Then, a modified Omega-K algorithm will be derived for the CW signal in the spotlight model. Finally, computer simulation will show the validity of the modified algorithm. Considering the effect of the atmosphere that certainly has potential to do harm to SAIL resolution, the wave distortions caused by atmospheric turbulence will be simulated by means of phase screens, and analysis in provided.

This section derives an analytical development of the dechirped signal [here by “dechirped” we mean heterodyning the return chirped signal with a similarly chirped local oscillator (LO)], which is the FMCW SAIL signal in the two-dimensional time domain without using the stop-and-go approximation that is assumed in a conventional pulsed SAR system.

_{p}_{p}_{p}_{c}

For typical pulsed SAR systems the pulse length _{p}

_{B}_{t}_{t}_{m}_{m}_{p}_{a}

_{x}_{y}_{0} is the similar coherence length of atmosphere defined by Karr [_{x}_{y}_{0} = 2_{0}, and _{0} is called the outer scale. Due to the fact that the phase error is a nonparametric error, it is hard for us to give the exact expression. In the simulation, we transform the phase error _{t}

So the received signal can be written as
_{ref}_{s}_{ref}

In the equation, the first exponential term is the Doppler modulation in azimuth and the second term represents the range signal, which is a sinusoidal signal with a constant frequency corresponding to the azimuth dependent distance to the point target _{t}

Starting from the square root expression for range _{a}_{d}

In a SAIL system, the effects induced by the continuous motion are very small in

The term

The fist exponential term is the Doppler shift induced by continuous motion. Here, we make use of the following several simplifying assumptions, all of which can be eliminated by suitable methods,

The laser is frequency chirped for range resolution.

The laser is modeled as a scalar wave field (no optical polarization).

The image effects of noise, laser speckle [

First of all, we take the azimuth ambiguity mentioned above into account. As we know, the ambiguity is induced by a smaller PRF than the azimuth bandwidth in the spotlight case. A way to overcome this limitation of PRF is based on the spectral analysis technique [_{m,center} is the center of _{a}

The key step of azimuth preprocessing is a convolution operation between the signal _{a}

This convolution operation can be represented by:

Let us now consider the discrete domain implementation of the azimuth preprocessing step, which is particularly due to the sampled characteristics of the raw signal, and rewrite the

We finally rewrite

Up to now, the azimuth ambiguity has been eliminated, but in the operation a convolution has been done. Now we must countervail the convolution by multiplying the following equation:
_{a}_{dc}_{a,ref}_{a,ref}_{a}_{ref}_{s}_{B}

The first operation of the algorithm is a Fourier transform in the along-track dimension [

Different from [

The second step in the Omega-K algorithm is application of a two-dimensional phase compensation to the azimuth-transformed signal using the following matched filter:

This operation perfectly corrects the range curvature of all scatterers at the same range as the scene center and removes the Doppler shift due to the long sweeps of the continuous wave successively.

Then, the received signal is obtained as:

The third step performed by the Omega-K algorithm is known as Stolt transformation [

With these definitions

At this point, _{X}_{R}_{B}_{B}_{X}_{R}_{B}

Application of this transformation yields the desired signal:

Finally, a two-dimensional inverse Fourier transform is computed to fully compress the scatterers in range and azimuth.

SAIL has a very different parametric dependence from real-aperture (active or passive) imaging on the usual optical parameters such as aperture

_{0} = 3.2_{SA}

_{0} = 1.6_{SA}_{0} = 1/2. The sidelobes become higher, and they come out pseudo-objects. But we can still recognize the point objects, and the resolution in range is unaffected.

_{0} = 0.1_{SA}_{0} = 8. We can see that image quality is severely degraded, but the resolution in range is also unaffected.

In summary, we have derived a modified frequency algorithm that is suitable for the SAIL in spotlight model using the heterodyne detection system and some results of a simulation of SAIL through the turbulence have been given. We know that SA processing is feasible at the optical wavelength, and that the given algorithm can process the data successfully. SAIL range resolution is unaffected by turbulence, while SAIL azimuth resolution is determined not only by the synthetic aperture length [

This work was supported by the National High Technology Research and Development Program of China (“863” Program) under grant No. 2006AA12Z144.

FMCW signal in frequency-time domain.

SAIL system geometry.

Sketch of azimuth preprocessing.

The data processing using the modified Omega-K algorithm.

Contour of the points.

Contour map of one point dimension

Profile of azimuth dimension.

ratio of synthetic aperture length to coherence length of atmosphere is 1/4.

ratio of synthetic aperture length to coherence length of atmosphere is 1/2.

ratio of synthetic aperture length to coherence length of atmosphere is 8/1.

SAIL and phase screen simulation parameters.

Wavelength |
1 |

Bandwidth B | 15_{Z} |

Pulse repetition interval |
200 |

Distance between platform and center of the imaging area _{s} |
4000 |

Velocity |
50 |

Sampling aperture in azimuth D | 2 |

Width of the area _{r} |
10 |

Sampling frequency _{s} |
300_{Z} |

Grid interval | 0.01 |

Grid point number | 512×512 |

Outer scale _{0} |
20 |