The time-stretch analog-to-digital converter (TS-ADC), also known as the time-stretch enhanced recorder (TiSER), is an

analog-to-digital converter In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a Digital signal (signal processing), digi ...

(ADC) system that has the capability of

digitizing Digitization is the process of converting information into a digital (i.e. computer-readable) format.Collins Dictionary. (n.d.). Definition of 'digitize'. Retrieved December 15, 2021, from https://www.collinsdictionary.com/dictionary/english ...

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 (American English) or analogue signal (British and Commonwealth English) is any continuous-time signal representing some other quantity, i.e., ''analogous'' to another quantity. For example, in an analog audio signal, the ins ...

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 Data ( , ) are a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted for ...

communications system A communications system is a collection of individual telecommunications networks systems, relay stations, tributary stations, and terminal equipment usually capable of interconnection and interoperation to form an integrated whole. Commu ...

s. 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 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 In telecommunications, a carrier wave, carrier signal, or just carrier, is a periodic waveform (usually sinusoidal) that conveys information through a process called ''modulation''. One or more of the wave's properties, such as amplitude or fre ...

) 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 multiplexing (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. Businesses *Digital bank, a form of financial institution *Digital Equipment Corporation (DEC) or Digital, a computer company *Digital Research (DR or DRI), a software ...

samples by slow electronic ADCs. Finally, these samples are collected by a digital signal processor (DSP) and rearranged in a manner such that output data is the digital representation of the original analog signal. Any

distortion In signal processing, distortion is the alteration of the original shape (or other characteristic) of a signal. In communications and electronics it means the alteration of the waveform of an information-bearing signal, such as an audio signal ...

added to the signal by the time-stretch

preprocessor In computer science, a preprocessor (or precompiler) is a Computer program, program that processes its input data to produce output that is used as input in another program. The output is said to be a preprocessed form of the input data, which i ...

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 In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...

mapping in the stretched pulse, because different wavelengths travel at different speeds in the dispersive medium. The obtained pulse is called a chirped pulse as its

frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

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 Photodetectors, also called photosensors, are devices that detect light or other forms of electromagnetic radiation and convert it into an electrical signal. They are essential in a wide range of applications, from digital imaging and optical ...

, 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 Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequency, frequencies between 300&n ...

photonic)

fiber Fiber (spelled fibre in British English; from ) is a natural or artificial substance that is significantly longer than it is wide. Fibers are often used in the manufacture of other materials. The strongest engineering materials often inco ...

links such as those used in

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

distribution. While the dispersion of fiber is a nuisance in conventional analog optical links, time-stretch technique exploits it to slow down the electrical

waveform In electronics, acoustics, and related fields, the waveform of a signal is the shape of its Graph of a function, graph as a function of time, independent of its time and Magnitude (mathematics), magnitude Scale (ratio), scales and of any dis ...

in the optical domain. In the cable TV link, the light source is a continuous-wave (CW)

laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word ''laser'' originated as an acronym for light amplification by stimulated emission of radi ...

. In PTS, the source is a chirped pulse laser. In a conventional analog optical link, dispersion causes the upper and lower modulation sidebands, ''f''_optical ± ''f''_electrical, to slip in relative phase. At certain frequencies, their beats with the optical carrier interfere destructively, creating nulls in the

frequency response In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and Phase (waves), phase of the output as a function of input frequency. The frequency response is widely used in the design and ...

of the system. For practical systems the first null is at tens of

GHz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or Cycle per second, cycle) per second. The hertz is an SI derived unit whose formal expression in ter ...

, 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 signal modulation used to transmit information, such as an audio signal, by radio waves. A refinement of amplitu ...

. 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 Wireless communication (or just wireless, when the context allows) is the transfer of information (''telecommunication'') between two or more points without the use of an electrical conductor, optical fiber or other continuous guided transm ...

communication (hence the two antennas on top of a

WiFi Wi-Fi () is a family of wireless network protocols based on the IEEE 802.11 family of standards, which are commonly used for Wireless LAN, local area networking of devices and Internet access, allowing nearby digital devices to exchange data by ...

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 (bandwidth) of a time-stretch system is limited only by the bandwidth of the electro-optic 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 A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements'') ...

, 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 the deviation of waves from straight-line propagation without any change in their energy due to an obstacle or through an aperture. The diffracting object or aperture effectively becomes a secondary source of the Wave propagation ...

and temporal dispersion, the so-called space-time duality. A lens held at a distance from an object produces a magnified

image An image or picture is a visual representation. An image can be Two-dimensional space, two-dimensional, such as a drawing, painting, or photograph, or Three-dimensional space, three-dimensional, such as a carving or sculpture. Images may be di ...

of the object. The lens imparts a quadratic phase shift to the

spatial frequency In mathematics, physics, and engineering, spatial frequency is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often sinusoidal components (as determined by the Fourier tra ...

components of the optical waves; in conjunction with the

free space A vacuum (: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective (neuter ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressur ...

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 In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the tr ...

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 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. 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 Imaging is the representation or reproduction of an object's form; especially a visual representation (i.e., the formation of an image). Imaging technology is the application of materials and methods to create, preserve, or duplicate images. ...

and

spectroscopy Spectroscopy is the field of study that measures and interprets electromagnetic spectra. In narrower contexts, spectroscopy is the precise study of color as generalized from visible light to all bands of the electromagnetic spectrum. Spectro ...

. 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) 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 ( 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.