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. An ADC may also provide ...
(ADC) system that has the capability of
digitizing
DigitizationTech Target. (2011, April). Definition: digitization. ''WhatIs.com''. Retrieved December 15, 2021, from https://whatis.techtarget.com/definition/digitization is the process of converting information into a digital (i.e. computer- ...
very high
bandwidth
Bandwidth commonly refers to:
* Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range
* Bandwidth (computing), the rate of data transfer, bit rate or thr ...
signals
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...
that cannot be captured by conventional
electronic
Electronic may refer to:
*Electronics, the science of how to control electric energy in semiconductor
* ''Electronics'' (magazine), a defunct American trade journal
*Electronic storage, the storage of data using an electronic device
*Electronic co ...
ADCs. Alternatively, it is also known as the
photonic
Photonics is a branch of optics that involves the application of generation, detection, and manipulation of light in form of photons through emission, transmission, modulation, signal processing, switching, amplification, and sensing. Though ...
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, opticalfrontend. 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
In the pursuit of knowledge, data (; ) is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted ...
communications system
A communications system or communication system is a collection of individual telecommunications networks, transmission systems, relay stations, tributary stations, and terminal equipment usually capable of interconnection and interoperati ...
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 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
In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an information-bearing signal for the purpose of conveying information. This carrier wave usually has a m ...
) 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, opticalfrontend, stretches the signal in time. It also divides the signal into multiple segments using a
filter
Filter, filtering or filters may refer to:
Science and technology
Computing
* Filter (higher-order function), in functional programming
* Filter (software), a computer program to process a data stream
* Filter (video), a software component tha ...
, 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
Filter, filtering or filters may refer to:
Science and technology
Computing
* Filter (higher-order function), in functional programming
* Filter (software), a computer program to process a data stream
* Filter (video), a software component tha ...
, 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
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 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 is often used by so ...
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
A femtosecond is a unit of time in the International System of Units (SI) equal to 10 or of a second; that is, one quadrillionth, or one millionth of one billionth, of a second. For context, a femtosecond is to a second as a second is to about 31. ...
long), also called a
supercontinuum
In optics, a supercontinuum is formed when a collection of nonlinear processes act together upon a pump beam in order to cause severe spectral broadening of the original pump beam, for example using a microstructured optical fiber. The result is ...
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, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
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
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
is changing with time, and it is typically a few nanoseconds long. The analog signal is
modulated
In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the ''carrier signal'', with a separate signal called the ''modulation signal'' that typically contains informatio ...
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 sensors of light or other electromagnetic radiation. There is a wide variety of photodetectors which may be classified by mechanism of detection, such as Photoelectric effect, photoelectric or photoc ...
, giving the stretched replica of the original analog signal.
For continuous operation, a train of
supercontinuum
In optics, a supercontinuum is formed when a collection of nonlinear processes act together upon a pump beam in order to cause severe spectral broadening of the original pump beam, for example using a microstructured optical fiber. The result is ...
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
Channel, channels, channeling, etc., may refer to:
Geography
* Channel (geography), in physical geography, a landform consisting of the outline (banks) of the path of a narrow body of water.
Australia
* Channel Country, region of outback Austral ...
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
DSP may refer to:
Computing
* Digital signal processing, the mathematical manipulation of an information signal
* Digital signal processor, a microprocessor designed for digital signal processing
* Yamaha DSP-1, a proprietary digital signal ...
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 ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ran ...
photonic)
fiber
Fiber or fibre (from la, fibra, links=no) 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 incorporate ...
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 electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electronic ...
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
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" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
. 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 ...
frequency response
In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of sy ...
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), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that one he ...
, 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
In radio engineering, an antenna or aerial is the interface between radio waves propagating through space and electric currents moving in metal conductors, used with a transmitter or receiver. In transmission, a radio transmitter supplies a ...
wireless
Wireless communication (or just wireless, when the context allows) is the transfer of information between two or more points without the use of an electrical conductor, optical fiber or other continuous guided medium for the transfer. The most ...
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 local area networking of devices and Internet access, allowing nearby digital devices to exchange data by radio waves ...
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
lens
A lens is a transmissive optical device which 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 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. 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
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 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
Propagation can refer to:
* Chain propagation in a chemical reaction mechanism
*Crack propagation, the growth of a crack during the fracture of materials
* Propaganda, non-objective information used to further an agenda
* Reproduction, and other fo ...
(object to lens, lens to eye), this generates a magnified image. Owing to the mathematical equivalence between
paraxial
In geometric optics, the paraxial approximation is a small-angle approximation used in Gaussian optics and ray tracing of light through an optical system (such as a lens).
A paraxial ray is a ray which makes a small angle (''θ'') to the optic ...
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, 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 focusedaberration-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
An oscilloscope (informally a scope) is a type of electronic test instrument that graphically displays varying electrical voltages as a two-dimensional plot of one or more signals as a function of time. The main purposes are to display repetiti ...
.
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 t ...
. 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 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.
References
Further reading
*G. C. Valley, "Photonic analog-to-digital converters," ''Opt. Express'', vol. 15, no. 5, pp. 1955–1982, March 2007 *''Pho''tonic ''B''andwidth Compression for ''I''nstantaneous Wideband ''A''/D ''C''onversion (''PHOBIAC'') project