Comparison with time lens imaging

Another technique, that involves a time lens, can also be used to slow down (mostly optical) signals in time. The time-lens concept relies on the mathematical equivalence between spatial diffraction and temporal dispersion, the so called space-time duality. A lens held at fixed distance from an object produces a magnified image visible to the eye. The lens imparts a quadratic phase shift to the spatial frequency components of the optical waves; in conjunction with the free space propagation (object to lens, lens to eye), this generates a magnified image. Owing to the mathematical equivalence between paraxial diffraction and temporal dispersion, an optical waveform can be temporally imaged by a three-step process of dispersing it in time, subjecting it to a phase shift that is quadratic in time (the time lens itself), and dispersing it again. Theoretically, a focused aberration-free image is obtained under a specific condition when the two dispersive elements and the phase shift satisfy the temporal equivalent of the classic lens equation. Alternatively, the time lens can be used without the second dispersive element to transfer the waveform’s temporal profile to the spectral domain, analogous to the property that an ordinary lens produces the spatial Fourier transform of an object at its focal points.

In contrast to the time-lens approach, PTS is not based on the space-time duality – there is no lens equation that needs to be satisfied in order to obtain an error-free slowed-down version of the input waveform. Time-stretch technique also offers continuous-time acquisition performance, a feature needed for mainstream applications of oscilloscopes.

Another important difference between the two techniques is that the time lens requires the input signal to be subjected to high amount of dispersion before further processing. For electrical waveforms, the electronic devices that have the required characteristics: high dispersion to loss ratio, uniform dispersion, and broad bandwidths, do not exist. This renders time lens not suitable for slowing down wideband electrical waveforms. In contrast, PTS does not have such a requirement. It was developed specifically for slowing down electrical waveforms and enable high speed digitizers.

September 27, 2011

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