The time-stretch analog-to-digital converter (TS-ADC), also known as the time-stretch enhanced recorder (TiSER), is an analog-to-digital converter (ADC) system that has the capability of digitizing very high bandwidth signals that cannot be captured by conventional electronic ADCs. Alternatively, it is also known as the photonic time-stretch (PTS) digitizer,J. Capmany and D. Novak, "Microwave photonics combines two worlds," ''Nature Photonics'' 1, 319-330 (2007)

/ref> since it uses an Optics, optical frontend. It relies on the process of time-stretch, which effectively slows down the

analog signal An analog signal or analogue signal (see spelling differences) is any continuous signal representing some other quantity, i.e., ''analogous'' to another quantity. For example, in an analog audio signal, the instantaneous signal voltage varies c ...

in time (or compresses its bandwidth) before it can be digitized by a standard electronic ADC.

Background

There is a huge demand for very high-speed analog-to-digital converters (ADCs), as they are needed for test and measurement equipment in laboratories and in high speed data communications systems. Most of the ADCs are based purely on electronic circuits, which have limited speeds and add a lot of impairments, limiting the bandwidth of the signals that can be digitized and the achievable

signal-to-noise ratio Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in deci ...

. In the TS-ADC, this limitation is overcome by time-stretching the analog signal, which effectively slows down the signal in time prior to digitization. By doing so, the bandwidth (and carrier frequency) of the signal is compressed. Electronic ADCs that would have been too slow to digitize the original signal can now be used to capture and process this slowed down signal.

Operation principle

The time-stretch processor, which is generally an Optics, optical frontend, stretches the signal in time. It also divides the signal into multiple segments using a filter, for example, a

wavelength division multiplex In fiber-optic communications, wavelength-division multiplexing (WDM) is a technology which multiplexes a number of optical carrier signals onto a single optical fiber by using different wavelengths (i.e., colors) of laser light. This techniq ...

ing (WDM) filter, to ensure that the stretched replica of the original analog signal segments do not overlap each other in time after stretching. The time-stretched and slowed down signal segments are then converted into

digital Digital usually refers to something using discrete digits, often binary digits. Technology and computing Hardware *Digital electronics, electronic circuits which operate using digital signals **Digital camera, which captures and stores digital i ...

samples by slow electronic ADCs. Finally, these samples are collected by a

digital signal processor A digital signal processor (DSP) is a specialized microprocessor chip, with its architecture optimized for the operational needs of digital signal processing. DSPs are fabricated on MOS integrated circuit chips. They are widely used in audio si ...

(DSP) and rearranged in a manner such that output data is the digital representation of the original analog signal. Any distortion added to the signal by the time-stretch preprocessor is also removed by the DSP. An optical front-end is commonly used to accomplish this process of time-stretching. An ultrashort optical pulse (typically 100 to 200 femtoseconds long), also called a supercontinuum pulse, which has a broad optical bandwidth, is time-stretched by dispersing it in a highly dispersive medium (such as a dispersion compensating fiber). This process results in (an almost) linear time-to- wavelength mapping in the stretched pulse, because different wavelengths travel at different speeds in the dispersive medium. The obtained pulse is called a

chirp A chirp is a signal in which the frequency increases (''up-chirp'') or decreases (''down-chirp'') with time. In some sources, the term ''chirp'' is used interchangeably with sweep signal. It is commonly applied to sonar, radar, and laser system ...

ed pulse as its frequency is changing with time, and it is typically a few nanoseconds long. The analog signal is modulated onto this chirped pulse using an electro-optic intensity modulator. Subsequently, the modulated pulse is stretched further in the second dispersive medium which has much higher dispersion value. Finally, this obtained optical pulse is converted to the electrical domain by a photodetector, giving the stretched replica of the original analog signal. For continuous operation, a train of supercontinuum pulses is used. The chirped pulses arriving at the electro-optic modulator should be wide enough (in time) such that the trailing edge of one pulse overlaps the leading edge of the next pulse. For segmentation, optical filters separate the signal into multiple wavelength channels at the output of the second dispersive medium. For each channel, a separate photodetector and backend electronic ADC is used. Finally the output of these ADCs are passed on to the DSP which generates the desired digital output.

Impulse response of the photonic time-stretch (PTS) system

The PTS processor is based on specialized analog optical (or microwave photonic) fiber links such as those used in

cable TV Cable television is a system of delivering television programming to consumers via radio frequency (RF) signals transmitted through coaxial cables, or in more recent systems, light pulses through fibre-optic cables. This contrasts with broadc ...

distribution. While the dispersion of fiber is a nuisance in conventional analog

optical link An optical link is a telecommunications link that consists of a single end-to-end optical circuit. A cable of optical fibers, possibly concatenated into a dark fiber link, is the simplest form of an optical link. Other forms of optical link can inc ...

s, time-stretch technique exploits it to slow down the electrical waveform in the optical domain. In the cable TV link, the light source is a

continuous-wave A continuous wave or continuous waveform (CW) is an electromagnetic wave of constant amplitude and frequency, typically a sine wave, that for mathematical analysis is considered to be of infinite duration. It may refer to e.g. a laser or particl ...

(CW) laser. In PTS, the source is a chirped pulse laser. In a conventional analog optical link, dispersion causes the upper and lower modulation

sidebands In radio communications, a sideband is a band of frequencies higher than or lower than the carrier frequency, that are the result of the modulation process. The sidebands carry the information transmitted by the radio signal. The sidebands com ...

, ''f''_optical ± ''f''_electrical, to slip in relative

phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...

. At certain frequencies, their beats with the optical

carrier Carrier may refer to: Entertainment * ''Carrier'' (album), a 2013 album by The Dodos * ''Carrier'' (board game), a South Pacific World War II board game * ''Carrier'' (TV series), a ten-part documentary miniseries that aired on PBS in April 20 ...

interfere destructively, creating nulls in the frequency response of the system. For practical systems the first null is at tens of GHz, which is sufficient for handling most electrical signals of interest. Although it may seem that the dispersion penalty places a fundamental limit on the impulse response (or the bandwidth) of the time-stretch system, it can be eliminated. The dispersion penalty vanishes with

single-sideband modulation In radio communications, single-sideband modulation (SSB) or single-sideband suppressed-carrier modulation (SSB-SC) is a type of modulation used to transmit information, such as an audio signal, by radio waves. A refinement of amplitude modul ...

. Alternatively, one can use the modulator's secondary (inverse) output port to eliminate the dispersion penalty, in much the same way as two antennas can eliminate spatial nulls in wireless communication (hence the two antennas on top of a WiFi access point). This configuration is termed phase-diversity. Combining the complementary outputs using a maximal ratio combining (MRC) algorithm results in a transfer function with a flat response in the frequency domain. Thus, the

impulse response In signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an Dirac delta function, impulse (). More generally, an impulse ...

(bandwidth) of a time-stretch system is limited only by the bandwidth of the

electro-optic Electro–optics is a branch of electrical engineering, electronic engineering, materials science, and material physics involving components, electronic devices such as lasers, laser diodes, LEDs, waveguides, etc. which operate by the propag ...

modulator, which is about 120 GHz—a value that is adequate for capturing most electrical waveforms of interest. Extremely large stretch factors can be obtained using long lengths of fiber, but at the cost of larger loss—a problem that has been overcome by employing Raman amplification within the dispersive fiber itself, leading to the world's fastest real-time digitizer. Also, using PTS, capture of very high-frequency signals with a world record resolution in 10-GHz bandwidth range has been achieved.

Comparison with time lens imaging

Another technique, temporal imaging using 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 Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...

and temporal dispersion, the so-called space-time

duality Duality may refer to: Mathematics * Duality (mathematics), a mathematical concept ** Dual (category theory), a formalization of mathematical duality ** Duality (optimization) ** Duality (order theory), a concept regarding binary relations ** Dual ...

. A lens held at a distance from an object produces a magnified

image An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensiona ...

of the object. The lens imparts a quadratic phase shift to the spatial frequency components of the optical waves; in conjunction with the

free space A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...

propagation (object to lens, lens to eye), this generates a magnified image. Owing to the mathematical equivalence between paraxial

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 A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...

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 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: (1) high dispersion to loss ratio, (2) uniform dispersion, and (3) 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.

Relation to phase stretch transform

The

phase stretch transform Phase stretch transform (PST) is a computational approach to signal and image processing. One of its utilities is for feature detection and classification.M. H. Asghari, and B. Jalali, "Edge detection in digital images using dispersive ph ...

or PST is a computational approach to signal and image processing. One of its utilities is for feature detection and classification. phase stretch transform is a spin-off from research on the

time stretch dispersive Fourier transform Time stretch dispersive Fourier transform (TS-DFT), otherwise known as time-stretch transform (TST), temporal Fourier transform or photonic time-stretch (PTS) is a spectroscopy technique that uses optical dispersion instead of a grating or prism to ...

. It transforms the image by emulating propagation through a diffractive medium with engineered 3D dispersive property (refractive index).

Application to imaging and spectroscopy

In addition to wideband A/D conversion, photonic time-stretch (PTS) is also an enabling technology for high-throughput real-time instrumentation such as imaging and

spectroscopy Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...

. The first artificial intelligence facilitated high-speed phase microscopy is demonstrated to improve the diagnosis accuracy of cancer cells out of blood cells by simultaneous measurement of phase and intensity spatial profiles. The world's fastest optical imaging method called

serial time-encoded amplified microscopy (STEAM) Time Stretch Microscopy also known as Serial time-encoded amplified imaging/microscopy or stretched time-encoded amplified imaging/microscopy' (STEAM) is a fast real-time optical imaging method that provides MHz frame rate, ~100 ps shutter speed, ...

makes use of the PTS technology to acquire image using a single-pixel photodetector and commercial ADC. Wavelength-time spectroscopy, which also relies on photonic time-stretch technique, permits real-time single-shot measurements of rapidly evolving or fluctuating spectra.

Time stretch quantitative phase imaging Time Stretch Microscopy also known as Serial time-encoded amplified imaging/microscopy or stretched time-encoded amplified imaging/microscopy' (STEAM) is a fast real-time optical imaging method that provides MHz frame rate, ~100 ps shutter speed, ...

( TS-QPI) is an imaging technique based on time-stretch technology for simultaneous measurement of phase and intensity spatial profiles. In time stretched imaging, the object's spatial information is encoded in the spectrum of laser pulses within a pulse duration of sub-nanoseconds. Each pulse representing one frame of the camera is then stretched in time so that it can be digitized in real-time by an electronic analog-to-digital converter (ADC). The ultra-fast pulse illumination freezes the motion of high-speed cells or particles in flow to achieve blur-free imaging.