If these were echoes from multiple targets, it would be possible to get a general idea of the targets' locations because the echoes are spread far enough apart. However, if the targets are closer together, their responses mix.
To improve range resolution , or the ability to detect closely-spaced targets, use a linear frequency modulated pulse for cross-correlation. Complete the same procedure but with a complex chirp with a frequency that starts at 0 Hz and linearly increases to 10 Hz. Real-world radar systems often use complex-valued linear FM signals to improve range resolution because the matched filter response is larger and narrower.
Since there is an imaginary component to the chirp and matched filter, all plots must be made using the real part of the waveform. The cross-correlation with a linear FM chirp provides much finer resolution for target noise despite the target echoes being closer together. The sidelobes of the echoes are also greatly reduced compared to the rectangular chirp, allowing for more accurate target detection. While cross-correlation does improve the range resolution, the algorithm lends itself better to analog hardware implementation.
More commonly, radar systems employ a similar process in the digital domain called matched filtering , where the received signal is convolved with a time-reversed version of the transmitted pulse. Matched filtering is often done in the frequency domain because convolution in the time domain is equivalent to multiplication in the frequency domain, making the process faster.
Because the initial pulse is time-reversed, the filtered output is delayed by the pulse width T , which is 1 second. To show this, time-reverse the original linear FM pulse and pad the pulse with zeros to make the pulse and transmitted waveform the same length. Calculate and plot the Fourier transform of the complex conjugate of the time-reversed pulse and the noisy signal.
Laser optimization data. The measured laser shows a Pi phase jump around nm, resulting in a dramatic loss of contrast and peak energy of the ultrafast pulse. Phase stabilization software. Moulet et al: « Single-shot, high-dynamic-range measurement of sub fs pulses by self-referenced spectral interferometry » Opt. Most of CPA systems operate in the saturation regime to extract more energy with a better stability. To improve the range resolution for a relatively long transmission pulse duration, the transmission pulse is modulated internally.
Now a frequency comparison can be made in the received echo, for example, which makes it possible to localize the reflecting object within the pulse.
The Pulse Compression Ratio PCR is the ratio of the time length of the uncompressed transmitted pulse to the length of the compressed pulse. The noise is always broadband and the noise pulses have a statistical distribution. The frequency-synchronous part of the noise i. Therefore, the non-frequency synchronous part of the input noise is reduced by the filters. This way an output signal is still obtained even if the input signal has long since been lost in the noise and would thus be lost for simple demodulation.
Compared to the non-modulated pulse, an additional gain is thus obtained, the pulse compression gain or pulse compression factor, which is approximately equal to the Pulse Compression Ratio PCR. For a linear i. For further calculations, the time-bandwidth product is introduced, the derivation of which results from the ratio of the different range resolutions :. The range resolution of a pulse modulated radar is therefore a multiple by a factor of the Pulse Compression Rate PCR of the range resolution of an intra-pulse modulated radar:.
With the help of pulse compression, a relatively long transmission pulse with comparatively low peak power can achieve a better, longer range than the basic radar equation would suggest. This is because pulse compression can still detect echo signals that have already disappeared in the noise before pulse compression.
The probability is very low that a noise pattern similar to the intra-pulse modulation will occur in such a way that this noise also forms an output signal during pulse compression. In the radar equation, the advantage of intrapulse modulation and pulse compression must be seen as an increase in range. In the equation the pulse compression ratio PCR or N is often entered directly, i.
This then results in a pulse power multiplied by the transmission pulse duration, i. This is divided by the minimum possible received power P E min multiplied by the duration of the compressed pulse, together also an energy. The pulse compression ratio is sometimes also called Pulse Compression Factor K , because it is entered directly as a factor in the radar equation under the fourth root:.
However, this requires a largely lossless pulse compression, which can never be achieved in practice. Originally unchirped pulses can be spectrally broadened by propagation in a normally dispersive optical fiber and then dispersively compressed as discussed above in the context of linear pulse compression [8].
The fibers used for spectral broadening may be standard optical fibers, photonic crystal fibers , hollow-core fibers , or hollow capillary fibers for extremely intense pulses, see below.
It is possible e. Note that the pulse energy can in principle be fully preserved, although substantial parasitic losses are often encountered in practice. For high-intensity femtosecond pulses, the spectral broadening can be performed in a gas-filled hollow fiber or capillary [17]. Most of the optical power propagates in the gas, where self-phase modulation occurs. The regime with ionization of the gas is avoided by staying at sufficiently low intensities.
Subsequent dispersive compression can be done, e. This method is suitable e. After spectral broadening with a nonlinearity as described above, pulses can also be shorted by sending them through a suitable bandpass filter and no dispersive element , if the filter bandwidth is well below the pulse bandwidth [44].
That kind of compression is of course associated with a substantial loss of pulse energy. Figure 2: Setup for pulse compression with a fiber only. The compression mechanism could be higher-order soliton compression or adiabatic soliton compression. After a certain propagation distance, a strongly compressed pulse can be obtained, but the choice of propagation distance can be critical. The pulse energy can be roughly one to two orders of magnitude above that of a fundamental soliton.
Alternatively, the pulse energy can be increased by amplification in a doped fiber with constant dispersion properties. The pulse energy is fairly limited due to the small soliton pulse energies of typical fibers.
Figure 3: Setup for pulse compression with similariton pulse propagation. While the pulse is amplified in a rare-earth-doped fiber , its duration and spectral width both increase. A dispersive compressor can subsequently reduce the pulse duration strongly. In a fiber amplifier with normal dispersion, self-similar parabolic pulses experience spectral broadening while a high pulse quality is preserved [16].
The parameters of the input signal pulses are fairly uncritical, and high pulse energies are possible. The resulting linear chirp makes it relatively easy to obtain strong temporal compression in a subsequent dispersive optical element.
Under certain circumstances, frequency doublers or optical parametric oscillators can emit pulses which are much shorter than the pump pulses. The underlying physical mechanism is completely different to that of other methods of pulse compression. Figure 4: Simulation widget from 3DOptix , demonstrating a prism compressor.
Click on the preview image to load the simulation. Questions and Comments from Users Here you can submit questions and comments. Bibliography [1] E. Quantum Electron.
0コメント