Patent Publication Number: US-11036113-B2

Title: Photonically-sampled electronically-quantized analog-to-digital converter

Description:
RELATED APPLICATION SECTION 
     The present application is a continuation of U.S. patent application Ser. No. 15/944,042, entitled “Photonically-Sampled Electronically-Quantized Analog-to-Digital Converter”, filed on Apr. 3, 2018. The entire contents of U.S. patent application Ser. No. 15/944,042 are herein incorporated by reference. 
    
    
     The section headings used herein are for organizational purposes only and should not be construed as limiting the subject matter described in the present application in any way. 
     Introduction 
     Analog-to-digital conversion (ADC) is an important and widely-used electronic system function that transforms analog, or time-continuous, signals into digital, or discrete-time signals that are most commonly binary signals including 1&#39;s and 0&#39;s. This crucial function allows the resulting digitized signals to be further processed by a wide variety of low-cost and/or sophisticated processing only available with digital signal processing electronics. The ADC process consists of two main steps: sampling and quantization. Sampling obtains the value of the waveform at a particular instant in time; quantization determines the digital, typically binary, representation of a sample. The fidelity of the digital representation of an analog signal is related to several important performance parameters of the analog-to-digital conversion sampling and quantization system including bandwidth, speed, time and amplitude jitter, and noise. Many of these parameters are limited by the capability of the electronic sampling circuits. 
     Photonic sampling has been developed to eliminate some of the bottlenecks of electronic sampling. One feature of photonic sampling is that it can provide substantially lower timing jitter of when the sample is taken. See, for example, A. H. Nejadmalayeri, et. al,. “A 16-fs aperture jitter photonic ADC: 7.0 ENOB at 40 GHz”, Proc. Conf. on Lasers and Electro-optics (CLEO), 2011, paper CThI4. Another feature of photonic sampling is that in some architectures, photonic sampling can increase the bandwidth and reduce the noise of the analog-to-digital conversion. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present teaching, in accordance with preferred and exemplary embodiments, together with further advantages thereof, is more particularly described in the following detailed description, taken in conjunction with the accompanying drawings. The skilled person in the art will understand that the drawings, described below, are for illustration purposes only. The drawings are not necessarily to scale, emphasis instead generally being placed upon illustrating principles of the teaching. The drawings are not intended to limit the scope of the Applicant&#39;s teaching in any way. 
         FIG. 1  illustrates a schematic of a prior art photonic analog-to-digital converter architecture that has one bank of electronic, analog-to-digital converters on the output of the modulator. 
         FIG. 2  illustrates a known Mach-Zehnder modulator balanced detection system. 
         FIG. 3  illustrates a known photonic analog-to-digital converter that includes a complementary output modulator feeding a balanced output configuration that includes two banks of electronic analog-to-digital converters, one on each complementary output of the modulator. 
         FIG. 4  illustrates a known plot of the response roll-off of a known photonic analog-to-digital converter as a function of pulse width for a 20-GHz sine wave input. 
         FIG. 5  illustrates a known plot of the Effective Number of Bits (ENOB) of a known photonic analog-to-digital converter as a function of pulse width. 
         FIG. 6  illustrates an embodiment of the photonically-sampled electronically-quantized analog-to-digital converter system comprising a single-channel normalization scheme according to the present teaching. 
         FIG. 7A  illustrates an embodiment of the photonically-sampled electronically-quantized analog-to-digital converter system with passive detector-to-ADC interface according to the present teaching. 
         FIG. 7B  illustrates an embodiment of the photonically-sampled electronically-quantized analog-to-digital converter system with subtraction before the ADC according to the present teaching. 
         FIG. 7C  illustrates an embodiment of the photonically-sampled electronically-quantized analog-to-digital converter system with passive detector-to-ADC interfaces and subtraction before the ADCs, as well as single-channel normalization according to the present teaching. 
         FIG. 8  illustrates an embodiment of the photonically-sampled electronically-quantized analog-to-digital converter that uses wavelength interleaving and routing (WIR), as well as single-channel normalization, passive detector-to-ADC interfaces and subtraction before the ADCs according to the present teaching. 
         FIG. 9  illustrates an embodiment of the photonically-sampled electronically-quantized analog-to-digital converter of the present teaching comprising post-modulator dispersion. 
     
    
    
     DESCRIPTION OF VARIOUS EMBODIMENTS 
     Reference in the specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the teaching. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment. 
     It should be understood that the individual steps of the methods of the present teachings may be performed in any order and/or simultaneously as long as the teaching remains operable. Furthermore, it should be understood that the apparatus and methods of the present teachings can include any number or all of the described embodiments as long as the teaching remains operable. 
     The present teaching will now be described in more detail with reference to exemplary embodiments thereof as shown in the accompanying drawings. While the present teachings are described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives, modifications and equivalents, as will be appreciated by those of skill in the art. Those of ordinary skill in the art having access to the teaching herein will recognize additional implementations, modifications, and embodiments, as well as other fields of use, which are within the scope of the present disclosure as described herein. 
     The present teaching describes a method and apparatus for photonically-sampled, electrically-quantized analog-to-digital converters that in various embodiments can have any combination of five features that improve performance and have relatively low cost and complexity as well as relatively low power consumption. These features include single channel normalization, passive detector-to-ADC interfacing, subtraction prior to the analog-to-digital conversion, post-modulator dispersion, and low noise figure analog-to-digital conversion. 
       FIG. 1  is a schematic of a prior art photonic analog-to-digital converter architecture  100 . A pulsed laser  102  provides a high-speed, low-jitter pulse train to the modulator  104 . Pulse trains as described herein can refer to pulses that are spaced periodically, i.e. uniformly, in time. Pulse trains as described herein can also refer to pulses spaced arbitrarily in time, i.e. such that the time between pulses is variable. The output of the modulator  104  is a train of pulses representing a sampled version of the electrical input signal that is to be converted to a digital representation. These pulses are sequentially sent to an optical pulse demultiplexer  106 . A typical prior art implementation of the optical pulse demultiplexer  106  requires a massive, 1×N, optical switch. At present the only practical way to implement optical switches with the required speed is by using a binary cascade of 1×2 switches. Thus if N=32, realizing a 1×32 switch would require 31 optical switches, which would require a custom, integrated-optic assembly. This represents a major impediment to realizing this approach when the cost of fabricating such custom switch arrays is combined with the switch drive circuitry that needs to be synchronized with the sample pulses. 
     A plurality of optical detectors  108 ,  108 ′ is optically coupled to the output of the optical pulse demultiplexer  106 . Each of the plurality of detectors  108 ,  108 ′ is electrically connected to one of a plurality of electronic receivers  110 ,  110 ′ which contain active electronic devices and/or circuits that amplify, provide impedance transformation, etc. The electronic receivers provide the interface between the output of the detectors  108 ,  108 ′ and the input to the ADC  112 ,  112 ′. In addition to the cost of the high-speed digital amplifiers in the electronic receivers, such amplifiers can consume a considerable amount of power. Each of the plurality of electronic receivers  110  is then electronically connected to one of a plurality of electronic analog-to-digital converters  112 ,  112 ′ so that each electronic analog-to-digital converter only sees pulses at its electronic sampling rate. The electronic sampling rate of each analog-to-digital converter is many times slower than the optical sampling rate. A digital back end process unit  114  is then used for various processing tasks. 
       FIG. 1  illustrates a prior art photonic analog-to-digital converters that uses short optical pulses to sample electrical signal applied to the optical modulator. The pulses are converted from optical to electrical pulses to enable sampling by the electronic analog-to-digital converters  112 ,  112 ′ using a detector  108 ,  108 ′ followed by the electronic receiver circuits  110 ,  110 ′. The sampling function works best with short pulses for reasons that will be discussed in conjunction with  FIG. 4 . 
       FIG. 2  illustrates a known Mach-Zehnder modulator balanced detection system  200 . The balanced detection system  200  includes Mach-Zehnder modulator  202  having an RF input and an optical input that is coupled to the output of a laser  204 . The Mach-Zehnder modulator  202  outputs shown in  FIG. 2  are complementary, i.e. they are, at least ideally, of equal amplitudes that are 180° out of phase with respect to one another. The two arms of the Mach-Zehnder modulator  202  are optically coupled to a balanced detector  206  that includes a first and second detector  208 ,  210  in a balanced configuration having an output that is electrically connected to an input of a receiver  212 . 
     In operation, an input signal causes a so-called positive-polarity signal in the first detector  208  and a so-called negative-polarity signal in the second detector  210 . Noise at the input, however, appears as common-mode noise in the two outputs. That is the noise has the same polarity in both outputs. Thus, when the first and second detector  208 ,  210  outputs are subtracted, the noise is cancelled and the signal is doubled as compared to the output of one of the first and the second detectors  208 ,  210 . The details of the balanced detection system  200  are described in E. I. Ackerman, et al, “Signal-to-noise performance of two analog photonic links using different noise reduction techniques,” 2007 International Microwave Symposium Conference Digest, pp. 51-54, Jun. 3-8, 2007. 
       FIG. 3  illustrates a known photonic analog-to-digital converter  300  that includes a balanced output configuration that includes a bank of N electronic analog-to-digital converters on each complementary-output of the modulator  302 . The photonic analog-to-digital converter  300  is similar to the photonic analog-to-digital converter  100  that was described in connection with  FIG. 1 . However, the photonic analog-to-digital converter  300  includes a complementary output optical modulator  302  such as the Mach-Zehnder modulator  202  that was described in connection with  FIG. 2 . 
     A pulsed laser  304  provides a high-speed, low-jitter pulse train to the input of the complementary output optical modulator  302 . Complementary trains of pulses representing a sampled version of the electrical input signal propagate on each of a first  306  and second arm  308  of the output of the modulator  302 . These pulses are sequentially sent to a first optical pulse demultiplexer  310  and second optical pulse demultiplexer  312 . Hence this approach requires two of the massive, optical switch arrays that were described in conjunction with  FIG. 1 . A first and second plurality of optical detectors  314 ,  314 ′  316 ,  316 ′ are optically coupled to the output of the first and second optical pulse demultiplexers  310 ,  312 . Each of the plurality of detectors in the first and second plurality of optical detectors  314 ,  314 ′,  316 ,  316 ′ is electrically connected to one of a plurality of the first and second plurality of electronic receivers  318 ,  318 ′,  320 ,  320 ′. Each of the plurality of electronic receivers in the first and second plurality of electronic receivers  318 ,  318 ′,  320 ,  320 ′ is then electronically connected to one of a plurality of electronic analog-to-digital converter in the first and the second plurality of analog-to-digital converters  322 ,  322 ′,  324 ,  324 ′ so that each electronic analog-to-digital converter (ADC) only sees pulses at its electronic sampling rate. A digital back end process unit  326  is then used for various processing tasks. 
     The subtraction of the complementary outputs is done digitally with signal processing hardware after the analog-to-digital conversion process. This configuration has been used on prior art photonic analog-to-digital converter demonstrations. See, for example, P. W. Juodawlkis, et al, “Optically sampled analog-to-digital converters,” IEEE Trans. Microwave Theory Tech., vol. 49, pp. 1840-1853, 2001. See also reference, S. J. Spector, et al, “Integrated Optical Components in Silicon for High Speed Analog to Digital Conversion,” Proc. SPIE, vol. 6477, pp. 647700-1-647700-14, 2007. 
     The subtraction of complementary outputs substantially improves the signal integrity of the digital representation of the analog signal. In addition to noise cancellation, the full-complementary configuration shown in  FIG. 3  allows recovery of the input intensity by summing the outputs from the two complementary analog-to-digital converters corresponding to the same pulse on each output. This enables more complex linearization and normalization methods, such as the arcsine linearization of the Mach-Zehnder modulator, and cancellation of AM noise sidebands on large signals when they come from optical intensity noise. See, for example, J. C. Twichell and R. Helkey, “Phase-encoded optical sampling for analog-to-digital converters,” IEEE Photon. Technol. Lett., vol. 12, pp. 1237-1239, Sep. 2000. However, these advantages come at the expense of doubling the number of electronic ADCs required, which in turn increases the size, weight, power and/or cost of the overall unit. 
     One feature of the photonically-sampled, electrically-quantized analog-to-digital converters of the present teaching is optimizing for both less roll-off and high detection efficiency.  FIG. 4  illustrates a plot  400  of the response roll-off of a prior art photonic analog-to-digital converter as a function of pulse width for a 20-GHz sine wave input. Short pulses are favored because they experience less roll-off. Reducing the roll-off becomes more important as the analog input frequency increases. On the other hand, detection is more efficient with longer pulses. This is because of two factors. First, short pulses can result in high peak power which causes the detector to become nonlinear. Second, the timing jitter of the electronic analog-to-digital converter sampler leads to increased noise when the input signal to the electronic analog-to-digital converter is varying rapidly. 
     One feature of the photonically-sampled, electrically-quantized analog-to-digital converters of the present teaching is optimizing for both high bandwidth and high Effective Number of Bits (ENOB).  FIG. 5  illustrates a plot  500  of the ENOB of a prior art photonic analog-to-digital converter as a function of pulse width. The effective number of bits is a measure of the signal-to-noise and distortion ratio of an analog-to-digital converter. The plot in  FIG. 5  shows how the effective number of bits increases with increasing pulse width for a simple low-pass-filter circuit following the detector. A higher effective number of bits is desirable. Thus from the point of view of increasing ENOB longer pulses are preferred, which is counter to the need for short pulses to increase bandwidth. The present teaching describes a system and method that resolves these opposing constraints. 
     Prior art photonic analog-to-digital converters choose either a compromise pulse width that is not ideal for either the sampling or the detection function, or they use a complex circuit between the detector and the analog-to-digital converter. See, for example, P. W. Juodawlkis, et al, “Optically sampled analog-to-digital converters,” IEEE Trans. Microwave Theory Tech., vol. 49, pp. 1840-1853, 2001. Generally, using a complex circuit becomes very difficult to implement as the speed of the electronic analog-to-digital converter increases. The disadvantages of prior art photonic analog-to-digital converter technology are the cost, complexity, and the power required for the large amount of digital back end electronics used for sampling, calibration, combining, cancellation, and linearization. 
     What is needed are analog-to-digital converter systems and methods that perform more functions in the optical domain as compared to prior art photonic analog-to-digital converter technology. Furthermore, what is needed is a photonic analog-to-digital converter system and method that eliminates the challenges associated with handling short-optical-pulse samples in the electronic domain. 
     One feature of the photonically-sampled electronically-quantized analog-to-digital converter of the present teaching is that it provides a photonic analog-to-digital converter that uses a smaller quantity of components in a less complex configuration of sampling and quantizing electronics than known photonic analog-to-digital converters while achieving substantially the same improvement in signal integrity of the sampled signal by cancelling noise, linearizing the signal, and suppressing AM sidebands. 
       FIG. 6  illustrates an embodiment of the photonically-sampled electronically-quantized analog-to-digital converter system  600  comprising a single-channel normalization scheme according to the present teaching. The embodiment illustrated in  FIG. 6  includes a laser  602 , or other optical transmitter, that generates a series of nominally equal amplitude short optical pulses of light in an optical pulse train  604 . An optical splitter, or tap  606 , splits the optical pulse train into two or more paths. One path proceeds to an optical modulator  608 . The optical modulator  608  can be any type of optical modulator. In some embodiments, the optical modulator  608  is a Mach-Zehnder-type optical modulator. 
     The portion of the optical pulse train  604  that passes through the optical modulator  608  is modulated with an RF input signal  610  whose digital representation is desired. The optical modulator  608  imposes an RF input modulation  610  onto the optical pulses of the optical pulse train  604  to produce an optically-sampled pulse train  612 . The RF-modulated optically-sampled pulse train  612  is incident on an optical pulse demultiplexer  614 , which splits incoming optical signals into multiple output ports. One skilled in the art will appreciate that numerous types of optical pulse demultiplexer  614  architectures can be used. In some embodiments, the optical demultiplexer  614  splits the incoming optical signal into different output ports based on the time slot of the optical pulse. Demultiplexed optically-sampled signals  616  from each output of the optical pulse demultiplexer  614  are passed to respective detectors  620 ,  620 ′ that convert the optical signals into electrical signals. 
     The electrical signals are then passed to electronic receivers  626 ,  626 ′ that condition the signal, and then to analog-to-digital converters  630 ,  630 ′, that quantize the electrical analog signals to a digital signals. These signals are then input into N inputs  634 ,  634 ′ of a digital signal processor  650  comprising a bank of digital back-end electronics and processing that provides various functions such as combining, calibration, and linearization. The digital signal processor  650  provides a digital output  652 . The digital output  652  is a digital representation of the RF input modulation  610 . The digital output  652  can be in any one of numerous formats, such as serial or parallel, straight binary or Gray code, high bandwidth, and/or low bandwidth, depending on the particular known digital back end signal processing used. 
     The portion of the optical pulse train  604  that follows path  640  forms the single-channel normalization path. The optical pulses in path  640  propagate to detector  618 . The detected signal is then passed to the electrical receiver  624  that conditions the signal, and then to a reference analog-to-digital converter  628  that converts the electrical analog signal to a digital signal to produce a reference input at input  632  to the digital signal processor  650 . 
     The embodiment of  FIG. 6  is referred to herein as a single-channel normalization. The single-channel normalization architecture advantageously uses a single detector  618  and a single analog-to-digital converter  628  to perform the functions that in prior art implementations, such as shown in  FIG. 3 , required a second optical pulse demultiplexer,  312 , as well as a whole bank of N complementary detectors,  316 , N receivers,  320  and N analog-to-digital converters,  324 . 
     A feature of the present teaching is that essentially all the optical intensity noise from the laser is at frequencies that are less than half the optical pulse train repetition rate because any higher frequency noise is aliased back into this frequency range according to the Nyquist sampling theory. Single-channel normalization is thus able to cover the entire frequency range of the input optical intensity noise. Within this bandwidth, it will perform the full normalization and noise cancellation functions. That is, the single-channel normalization scheme will suppress input optical intensity noise, AM sideband noise due to input optical intensity noise, and the reference input  632  will provide the reference signal at a signal level that enables arcsine and other linearization algorithms. While single-channel normalization will not suppress noise at frequencies above half the electronic analog-to-digital sample rate, which is the bandwidth of the photonically-sampled, electronically quantized analog-to-digital converter, this limitation is usually not significant because most optical intensity noise and intensity variation important for normalization is at low frequency. Differences in channel transmission through the pulse demultiplexer  614  appear as channel gain offsets, not as noise. These differences in channel transmission can be compensated by routine analog-to-digital converter calibration algorithms. 
     As compared to the configuration shown in  FIG. 3 , only about half of the number of analog-to-digital converters  630 ,  630 ′ and consequently only about half the number of inputs to the digital signal processor is required in the single-channel normalization architecture. The electronic analog-to-digital converters account for a large fraction of both the electrical power consumed and the total system cost for photonic analog-to-digital converters of the prior art. Thus, the embodiment shown in  FIG. 6  of the current teaching advantageously provides a substantial reduction in cost, complexity and electrical power. 
     One skilled in the art will appreciate that the single-channel normalization scheme described herein can be used in combination with any type of photonic analog-to-digital converter architecture. Using the single-channel normalization scheme of the present teaching with known photonic analog-to-digital converter substantially reduces overall cost, complexity and power consumption, with only a small reduction in performance. 
     One feature of some of the photonically-sampled electronically-quantized analog-to-digital converter system embodiments of the present teaching is that some embodiments eliminate the need for an active receiver interface between the photodetector and ADC.  FIG. 7A  illustrates an embodiment of the photonically-sampled electronically-quantized analog-to-digital converter  700  with passive detector-to-ADC interface according to the present teaching. The laser  702 , or other optical source, generates an optical signal that is a train of optical pulses  704 . The laser  702  is connected to an optical modulator  706 . The optical modulator  706  can be any type of optical modulator. In some embodiments, the optical modulator  706  is a Mach-Zehnder-type optical modulator. An RF input signal  708  whose digital representation is desired is input to the modulator  706 . The optical modulator  706  imposes the RF input modulation  708  onto the optical pulses of the optical pulse train  704  to produce an optically-sampled pulse train  710 . 
     The RF-modulated optically-sampled pulse train  710  is incident on an optical pulse demultiplexer  712 , which splits incoming optical signals into multiple output ports. One skilled in the art will appreciate that numerous types of optical pulse demultiplexer  712  architectures can be used. In some embodiments, the optical demultiplexer  712  splits the incoming optical signal into different output ports based on the time slot of the optical pulse. Demultiplexed optically-sampled signals  714  from each output of the optical pulse demultiplexer  712  are passed to respective detectors  716 ,  716 ′ that convert the optical signals into electrical signals. 
     The electrical signal output of the detectors  716 ,  716 ′ are input to an interface  718 ,  718 ′. The interface  718 ,  718 ′ connects to an ADC  720 ,  720 ′, that quantize the electrical analog signals to digital signals. These signals are then input into N inputs  724 ,  724 ′ of a digital signal processor  726  comprising a bank of digital back-end electronics and processing that provides various functions such as combining, calibration, and linearization. The digital signal processor  726  provides a digital output  728 . The digital output  728  is a digital representation of the RF input modulation  708 . The digital output  728  can be in any one of numerous formats, such as serial or parallel, straight binary or Gray code, high bandwidth, and/or low bandwidth, depending on the particular known digital back end signal processing used. 
     In some embodiments, the interface  718 ,  718 ′ performs passive frequency response shaping and impedance transformation on the respective electrical signal output from the detectors  716 ,  716 ′. In various other embodiments, interface  718 ,  718 ′ performs other passive filter functions. Interface  718 ,  718 ′ contains only passive elements and does not contain any active electronic devices and/or circuits that amplify. The reason the amplifier can be eliminated is because the optical path from laser  702  to photodetector  716 ,  716 ′ is designed such that the photodetector  716 ,  716 ′ produces sufficient current, when combined with the sensitivity of the ADC  720 ,  720 ′, to drive the ADC  720 ,  720 ′ to full scale. Eliminating the need for post-detector amplification can significantly reduce the cost, complexity and power consumption of the photonically-sampled, electrically quantized ADC  700 . 
     In some embodiments, the interface  718 ,  718 ′ between the output of the detector  716 ,  716 ′ and the input to the ADC  720 ,  720 ′ is a separate component. In some embodiments, the interface  718 ,  718 ′ is integrated with the detector  716 ,  716 ′ output and/or ADC  720 ,  720 ′ input. For example, in embodiments for which the interface  718 ,  718 ′ needs to include low pass filtering, then a separately identifiable low pass filter can be included. Alternatively a low pass filter function of the interface  718 ,  718 ′ can be realized using the output resistance of the detector  716 ,  716 ′ output together with the input capacitance of the ADC  720 ,  720 ′. Similarly, in embodiments for which the interface  718 ,  718 ′ performs a function that requires inductance, then the inductance of the photodetector  716 ,  716 ′ bond wire alone, or a length of conductor alone, or a combination of both can be used for the interface  718 ,  718 ′. It should be understood that the interface element that performs only passive function according to the present teaching can be used in various other embodiments that do not include a demultiplexer. It will be understood by those skilled in the art that these embodiments only include a single detector and single analog-to-digital converter that are connected via the passive interface. 
     One feature of the present teaching is performing subtraction prior to, or at the input to, the analog-to-digital converters. This subtraction provides, for example, cancellation of input optical intensity noise.  FIG. 7B  illustrates an embodiment of the photonically-sampled electronically-quantized analog-to-digital converter  730  with subtraction before the ADC according to the present teaching. The laser  732 , or other optical source, generates an optical signal that is a train of optical pulses  734 . 
     The output of the laser  732  is optically coupled to an input of an optical modulator  736  with balanced outputs. The optical modulator  736  with balanced or complementary outputs is shown as a Mach-Zehnder modulator  736 . The optical modulator  736  imposes an RF input  738  on the train of optical pulses  734 , and generates optically-sampled signals at complementary outputs  735 ,  737 . The complementary outputs  735 ,  737  represent equal and opposite amplitudes, i.e., a so-called positive output  735  and a so-called negative output  737 . 
     The optically-sampled signals generated at the positive complementary output  735  of the optical modulator  736  passes to a first pulse demultiplexer  740 , and the optically-sampled signals generated at the negative complementary output  737  of the optical modulator  736  passes to a second pulse demultiplexer  740 ′. The demultiplexers  740 ,  740 ′ can use any one of various demultiplexer architectures, such as wavelength-division and time-division demultiplexing. The outputs of the demultiplexers  740 ,  740 ′ generate separate demultiplexed optically-sampled signals  741 ,  741 ′,  742 ,  742 ′ from the optically-sampled signals at the input of the demultiplexers  740 ,  740 ′. 
     The outputs of the demultiplexers  740 ,  740 ′ are optically coupled to the optical detectors  743 ,  743 ′,  744 ,  744 ′ where they are converted to electrical signals. The outputs of the optical detectors  743 ,  743 ′,  744 ,  744 ′ are electrically connected to receivers  745 ,  745 ′,  746 ,  746 ′. The receivers  745 ,  745 ′,  746 ,  746 ′ provide the detected signals to the respective positive and negative inputs of the ADC  747 ,  747 ′. In some embodiments, the receivers  745 ,  745 ′,  746 ,  746 ′ are replaced by interfaces, such as the interfaces  718 ,  718 ′ described in connection with  FIG. 7A . 
     Performing subtraction prior to, or at the input to, the analog-to-digital converters advantageously reduces the number of ADC&#39;s  474 ,  474 ′. The outputs of the receivers  745 ,  746  are electrically connected to positive inputs of analog-to-digital-converters  747 ,  747 ′. The outputs of the receivers  745 ′,  746 ′ are electrically connected to negative inputs of analog-to-digital-converters  747 ,  747 ′. By performing subtraction prior to, or at the input to, the analog-to-digital converters  747 ,  747 ′, the present teaching uses N ADCs  747 ,  747 ′. This is half the number of analog-to-digital converters of known apparatus, such as the apparatus shown in  FIG. 3 , which required 2 N ADCs. In some embodiments balanced detectors are used to perform the subtraction function prior to being interfaced to single-ended analog-to-digital converters as an alternative to the use of balanced or differential input analog-to-digital converters that is shown in  FIG. 7B . Since the total power consumed by the photonically-sampled, electronically quantized ADC  730  is often dominated by the power consumed by the electronic ADCs, cutting the number of electronic ADCs in half will substantially reduce the overall power consumed by the photonically-sampled, electronically-quantized ADC of the present teaching. 
     The output of the analog-to-digital converters  747 ,  747 ′ provide N inputs  748 ,  748 ′, etc. to the digital signal processor  749 . The digital signal processor  749  provides a digital output  751 . The digital output  751  is a digital representation of the RF input  738  that can be one of numerous types of data formats, including serial or parallel, straight binary or Gray code, high bandwidth and/or low bandwidth depending on the particular known digital back end electronics used. It should be understood that performing subtraction prior to, or at the input to, the analog-to-digital converters according to the present teaching can be used in various other embodiments that do not include a demultiplexer. It will be understood by those skilled in the art that these embodiments only include a single detector and single analog-to-digital converter in which subtraction is performed at the input or prior to the input. 
     The photonically-sampled electronically-quantized analog-to-digital converter  730  shown in  FIG. 7B  uses complementary detection. Therefore, every channel separately has the input optical intensity noise cancelled. Consequently, the input intensity noise is cancelled over the full bandwidth of the photonic analog-to-digital converter. The balanced detectors do not provide AM sideband noise suppression, nor do they provide normalization for the arcsine or other linearization algorithms. In some embodiments, these functions are accomplished by a single-channel normalization up to the bandwidth of a single analog-to-digital converter, which is half its sample rate. A key insight of the present teaching is that a complementary detection results in a level of cancellation that is good enough for most practical systems because they are able to tolerate a higher level of uncancelled AM sideband noise and un-normalized high-frequency fluctuations than they can tolerate uncancelled baseband optical intensity noise. 
       FIG. 7C  illustrates an embodiment of the photonically-sampled electronically-quantized analog-to-digital converter  750  with passive detector-to-ADC interface and subtraction before the ADC as well as single-channel normalization according to the present teaching. The laser  752 , or other optical source, generates an optical signal that is a train of optical pulses  766 . The optical signal is split by a tap or splitter  754 . The first portion of the optical beam from the splitter  754  is directed to an input to an optical detector  756 . An output of the optical detector  756  is electrically connected to a passive detector-to-ADC interface  758 . The laser pulse power, optical path impairments from the laser to the detector, detector response, and ADC sensitivity are chosen such that no electrical amplification is required in the interface  758 , and yet the ADC is driven at full scale. In some embodiments, the ADC is driven with sufficient current to produce a drive at greater than half-scale of the ADC. The output of the interface  758  is electrically connected to an input of a reference analog to digital converter  760 . The output of the reference analog-to-digital converter  760  is electrically coupled to an input  778  of the digital signal processor  790 . 
     In some embodiments, interface  758  performs passive frequency response shaping and impedance transformation. In various other embodiments, interface  758  performs other passive filter functions. Interface  758  contains only passive elements and does not contain any active electronic devices and/or circuits that amplify. The reason the amplifier can be eliminated is because the optical path from laser to photodetector  756  is designed such that the photodetector  756  produces sufficient current, when combined with the sensitivity of the ADC  760 , to drive the ADC  760  to full scale. Eliminating the need for post-detector amplification can significantly reduce the cost, complexity and power consumption of the photonically-sampled, electrically quantized ADC. 
     In some embodiments, the interface  758  between the output of the detector  756  and the input to the ADC  760  is a separate component. In some embodiments, the interface  758  is integrated with the detector  756  output and/or ADC  760  input. For example, in embodiments for which the interface  758  needs to include low pass filtering, then a separately identifiable low pass filter can be included. Alternatively a low pass filter function of the interface  758  can be realized using the output resistance of the detector  756  output together with the input capacitance of the ADC  760 . Similarly, in embodiments for which the interface  758  performs a function that requires inductance, then the inductance of the photodetector  756  bond wire alone, or a length of conductor alone, or a combination of both can be used for the interface  758 . 
     The second output of the splitter  754  is optically coupled to an input of the optical modulator  764  with balanced outputs. The optical modulator  764  with balanced or complementary outputs is shown as a Mach-Zehnder modulator  764 . The optical modulator  764  imposes an RF input  762  on the train of optical pulses  766 , and generates optically-sampled signals  765 ,  767  at complementary outputs. The optically-sampled signals  765 ,  767  at complementary outputs represent equal and opposite amplitudes, i.e., a so-called positive output and a so-called negative output. 
     The optically-sampled signals  765  generated at the positive complementary output of the optical modulator  764  passes to a first pulse demultiplexer  768 , and the optically-sampled signals  767  generated at the negative complementary output of the optical modulator  764  passes to a second pulse demultiplexer  768 ′. The demultiplexers  768 ,  768 ′ can use any one of various demultiplexer architectures, such as wavelength-division and time-division demultiplexing. The outputs of the demultiplexers  768 ,  768 ′ generate separate demultiplexed optically-sampled signals  771 ,  771 ′,  781 ,  781 ′ from the optically-sampled signals  765 ,  767 . 
     The outputs of the demultiplexers  768 ,  768 ′ are optically coupled to the optical detectors  770 ,  770 ′,  780 , and  780 ′ where they are converted to electrical signals. The outputs of the optical detectors  770 ,  770 ′,  780 , and  780 ′ are electrically connected to passive detector-to-ADC interfaces  772 ,  772 ′,  782 , and  782 ′. These passive interfaces  772 ,  772 ′,  782 , and  782 ′ are similar in design to the interface  758  described above. The interfaces  772 ,  772 ′,  782 , and  782 ′ provide the detected signals to the respective ADC  774 ,  774 ′. In some applications, the interfaces  772 ,  772 ′,  782 , and  782 ′ can be low-pass filters (LPF), in other applications the interfaces  772 ,  772 ′,  782 , and  782 ′ can be band-pass filters (BPF). Also the interfaces  772 ,  772 ′,  782 , and  782 ′ can be either a separate element as shown in  FIG. 7C , or they can be incorporated into one of the existing elements. An example of the latter case would be to implement a low pass filter function by selecting the frequency response of the detector to roll off at the desired frequency. 
     One feature of the present teaching is performing subtraction prior to, or at the input to, the analog-to-digital converters. The outputs of the interfaces  772 ,  782  are electrically connected to positive inputs of analog-to-digital-converters  774 ,  774 ′. The outputs of the interfaces  772 ′,  782 ′ are electrically connected to negative inputs of analog-to-digital-converters  774 ,  774 ′. By performing subtraction prior to, or at the input to, the analog-to-digital converters, the present teaching uses N ADCs  774 ,  774 ′. This is half the number of analog-to-digital converters of prior art apparatus, such as the apparatus shown in  FIG. 3 , which required 2 N ADCs. In some embodiments balanced detectors are used to perform the subtraction function prior to being interfaced to single-ended analog-to-digital converters as an alternative to the use of balanced or differential input analog-to-digital converters that is shown in  FIG. 7C . Since the total power consumed by the photonically-sampled, electronically quantized ADC is often dominated by the power consumed by the electronic ADCs, cutting the number of electronic ADCs in half will substantially reduce the overall power consumed by the photonically-sampled, electronically-quantized ADC of the present teaching. 
     The output of the analog-to-digital converters  774 ,  774 ′ provide N inputs  776 ,  776 ′, etc. to the digital signal processor  790 . The digital signal processor  790  provides a digital output  792 . The digital output  792  is a digital representation of the RF input  762  that can be one of numerous types of data formats, including serial or parallel, straight binary or Gray code, high bandwidth and/or low bandwidth depending on the particular known digital back end electronics used. The digital signal processor  790  uses the output of the reference analog-to-digital converter  760  to improve signal integrity of the digital representation of the input RF signal by normalization, linearization, noise cancellation and AM sideband suppression. 
     The photonically-sampled electronically-quantized analog-to-digital converter  750  shown in  FIG. 7C  uses complementary detection. Therefore, every channel separately has the input optical intensity noise cancelled. Consequently, the input intensity noise is cancelled over the full bandwidth of the photonic analog-to-digital converter. The balanced detectors do not provide AM sideband noise suppression, nor do they provide normalization for the arcsine or other linearization algorithms. These functions are accomplished by the single-channel normalization, up to the bandwidth of a single analog-to-digital converter, which is half its sample rate. A key insight of the present teaching is that this results in a level of cancellation that is good enough for most practical systems because they are able to tolerate a higher level of uncancelled AM sideband noise and un-normalized high-frequency fluctuations than they can tolerate uncancelled baseband optical intensity noise. 
       FIG. 8  illustrates an embodiment of the photonically-sampled electronically-quantized analog-to-digital converter  800  according to the present teaching that advantageously uses multiple wavelengths to achieve both interleaving and routing (WIR) of the sample pulses. The photonically-sampled electronically-quantized analog-to-digital converter  800  uses a complementary-output optical modulator, such the Mach-Zehnder modulator  814  shown in  FIG. 8  with a passive detector-to-ADC interface and subtraction prior to the ADC, both of which were described in connection with  FIG. 7  combined with the single-channel normalization described in connection with  FIG. 6 . 
     Ideally the sampling waveform would be a train of impulse functions, i.e. pulses of zero width in time. Since no such waveform can be generated by an actual system, the sampling waveform of the present teaching approximates this ideal case by sampling with a pulse width that is less than a particular fraction of a period of the frequency of the sampled waveform. In one particular embodiment of the present teaching, a waveform is sampled with a sampling pulse that is &lt; 1/10 of the period of the highest frequency in the waveform to be sampled. This has been found to effective. 
     There are two key design parameters that determine the number of pulses that can be interleaved from a single laser pulse: (1) the spectral bandwidth of the laser pulse; and (2) the desired width of the sampling pulse, which is related to the maximum electrical frequency to be sampled. Consider, for example, an electrical waveform with a bandwidth of 10 GHz. The period of this waveform is 1/10 10  Hz=10 −10  seconds, or 100 picoseconds. To effectively sample this waveform would require a sampling pulse of width Δt&lt;10 picoseconds. If one assumes that the shape of the pulses in the sampling waveform is approximately Gaussian, then it is well known to those skilled in the art that the product of the minimum time and the bandwidth product of a Gaussian pulse, Δt×Δf=0.441. Hence, the bandwidth of the sampling waveform Δf=0.441/10 −11 =44.1 GHz, or equivalently 0.35 nm in wavelength, where we have converted the bandwidth in frequency in Hz to a bandwidth in wavelength in meters using the well-known relationship Δf/f=Δλ/λ and assuming a nominal center wavelength of λ=1.55×10 −6  m. Lasers are presently commercially available that generate narrow pulses that have an optical bandwidth of &gt;30 nm. Hence using such a laser, it is possible to divide each laser pulse into 30/Δλ=85 separate pulses, each with a different wavelength. Various embodiments will use a number of wavelengths that is based on the spectral bandwidth of the laser pulse and on the electrical frequency of the signal to be sampled, as described herein. 
     A laser  802 , or other optical source known in the art, generates an optical signal including a train of optical pulses where each of the pulses includes multiple wavelengths. The optical signal is split by a tap or splitter  804 . A first output of the splitter  804 , which feeds the single-channel normalization channel, is optically coupled to a detector  860 . An output of the detector  860  is electrically coupled to a passive detector-to-ADC interface  862 . In some embodiments, the interface  862  is a low-pass filter (LPF). An output of the interface  862  is electrically connected to an analog input of the reference analog-to-digital converter  864 . The digital output of the reference analog-to-digital converter  864  is electrically connected to an input  866  of the digital signal processor  840 . 
     Referring back to  FIGS. 6-7C , in some embodiments of the photonically-sampled, electronically quantized ADC the rate of optical pulses from the optical source  602 ,  702  is equal to the rate of optical pulses in the sampling pulse train  612 ,  716 . In other embodiments, it may be desirable or necessary to achieve a faster rate from pulse train  612 ,  716  than the rate of pulses from the optical source  602 ,  702 ,  732 ,  752 . Referring to  FIG. 7C , to achieve a faster sampling pulse train rate, an interleaver can be inserted between the output of the tap  754  and the input to the modulator  764 . Both time and wavelength interleavers can be used in the photonically-sampled, electronically-quantized ADC of the present teaching. 
     Referring again to  FIG. 8 , a second output of the splitter  804  is optically coupled to a wavelength interleaver portion of the wavelength interleaver and router (WIR). The wavelength interleaver includes the wavelength division demultiplexer (WDD)  818 . The WDD  818  separates each of the multiple wavelength pulses into separate outputs. The outputs of the WDD  818  are optically coupled to a plurality of optical delay elements that can be implemented in a number of ways;  FIG. 8  shows using optical fibers  870 ,  872 , and  874 . Each of the plurality of optical delay elements comprising optical fibers  870 ,  872 , and  874  provides a desired relative time delay between each of the different wavelength optical pulse trains. An output of each of the plurality of optical delay elements comprising optical fibers  870 ,  872 , and  874  is optically coupled to a respective input of a wavelength division multiplexer (WDM)  822  so that the relative time-delay optical pulse trains with different wavelengths are recombined in the WDM  822 . The WDM  822  generates at an output a pulse train consisting of multiple optical pulses each with different wavelengths, each in a different time slot. The resulting output of the wavelength interleaver provides an interleaved optical sampling signal  816 . A wavelength interleaver has the additional advantage that the wavelength encoding of the sampling pulses means that a wavelength demultiplexer can be used to implement a particularly simple form of the optical pulse demultiplexer. For an example of wavelength demultiplexing in a system using photonic ADC, see A. H. Nejadmalayeri, et. al,. “A 16-fs aperture jitter photonic ADC: 7.0 ENOB at 40 GHz”, Proc. Conf. on Lasers and Electro-optics (CLEO), 2011, paper CThI4. 
     The output of the wavelength interleaver at the output of WDM  822  is optically coupled to an input of an optical modulator  814  with balanced outputs, which is shown in  FIG. 8  as a Mach-Zehnder modulator. The optical sampling signals  816  are then modulated by the modulator  814 . The modulator  814  imposes an RF modulation signal from RF input  812  on the optical sampling signals  816 , and generates complementary outputs of an optically-sampled signal, so-called positive optically-sampled signal  824  and so-called negative optically-sampled signal  826 . These complementary outputs represent sampled, equal and opposite amplitudes of the RF signal. 
     A first output of the optical modulator  814 , which generates a positive optically-sampled signal  824 , is optically coupled to an input of a WDD  828 , which provides the routing portion of the WIR. The WDD  828  generates a plurality of wavelength demultiplexed outputs  832 ,  832 ′ of the positive optically-sampled signal  824  at a plurality of outputs. A second output of the optical modulator  814 , which generates a negative optically-sampled signal  826 , is optically coupled to an input of a WDD  830 . The WDD  830  generates a plurality of wavelength demultiplexed signals  834 ,  834 ′ of the negative optically-sampled stream  826  at a plurality of outputs. The router part of the WIR uses a readily available component, a WDD, to perform the function of the optical pulse demultiplexer without the need for a massive, custom optical switch. Such a switch is shown in prior art presented in  FIG. 1  element  106  and  FIG. 3  element  310 . Hence, embodiments of the present teaching including WIR removes one of the main impediments to a practical realization of a photonically-sampled, electronically-quantized ADC. 
     Each of the plurality of outputs of the WDD  828  is optically coupled to an input of a respective one of a plurality of optical detectors  836 ,  836 ′ that detect a respective one of the plurality of wavelength demultiplexed signals  832 ,  832 ′. Each electrical output of the plurality of optical detectors  836 ,  836 ′ is electrically connected to an input of a respective one of a plurality of passive detector-to-ADC interfaces  838 ,  838 ′. Similarly, each of the plurality of outputs of the WDD  830  is optically coupled to an input of a respective one of a plurality of optical detectors  837 ,  837 ′ that detect a respective one of the plurality of wavelength demultiplexed signals  834 ,  834 ′. Each electrical output of the plurality of optical detectors  837 ,  837 ′ is electrically connected to an input of a respective one of a plurality of passive detector-to-ADC interfaces  839 ,  839 ′. 
     Each output of the plurality of interfaces  838 ,  838 ′ is electrically connected to a positive input of a respective one of a plurality of analog-to-digital-converters  850 ,  850 ′. Each output of the plurality of interfaces  839 ,  839 ′ is electrically connected to a negative input of a respective one of a plurality of analog-to-digital-converters  850 ,  850 ′. Each of the plurality of analog-to-digital converters  850 ,  850 ′ is receiving one particular sample of the RF signal  812  that was encoded on a particular wavelength. The plurality of analog-to-digital-converters  850  generates N outputs  852 ,  852 ′, which are electrically connected to N inputs of digital signal processor  840 . The digital signal processor  840  provides a digital output  842 . The digital output  842  is a digital representation of the RF modulation signal at the RF input  812 , which can be one of various known formats, including serial or parallel, high bandwidth and/or low bandwidth, depending on the particular known digital signal processing electronics that is used. The digital signal processor  840  uses the output of the reference analog-to-digital converter  864  to improve signal integrity of the digital representation of the input RF signal by normalization, linearization, noise cancellation and AM sideband suppression. 
     A key insight of the present teaching is that essentially all the optical intensity noise from the laser is at frequencies that are less than half the pulse repetition rate because any higher frequency noise is aliased back into this frequency range according to the Nyquist sampling theory. The single-channel normalization is thus able to cover the entire frequency range of the input optical intensity noise. Differences in channel transmission through the pulse demultiplexer, such as demultiplexer  768  in  FIG. 7C  or the WIR as shown in  FIG. 8 , appear as channel gain offsets, not as noise. These differences in channel transmission can be compensated by routine analog-to-digital converter calibration algorithms. 
       FIG. 9  illustrates an embodiment of the photonically-sampled electronically-quantized analog-to-digital converter  900  of the present teaching that includes a dispersive component located after the modulator. The analog-to-digital converter  900  includes an optical source, such as a laser  902  that generates a train of optical sampling pulses  904 . The output of the laser  902  is optically coupled to an input of the optical modulator  908 . The optical modulator  908  modulates an RF modulation signal applied to the input  910  onto the sampling pulses generated by the laser  902  to produce the optically sampled signal  912 . The optical sampling pulses, and resulting optically sampled signal comprise short duration optical pulses. 
     The output of the optical modulator is coupled to an input of the optical pulse demultiplexer  920  with a dispersive optical element  914 . The dispersive optical element  914  increases the width of the pulses. The dispersive optical element can be any dispersive element known in the art. A fiber Bragg grating can be used to implement the dispersive optical element. The dispersive optical element can also be a length of dispersive optical fiber in which the amount of dispersion in the dispersive optical fiber  914  and the length of the optical dispersive fiber  914  are chosen so as to provide an appropriate pulse length for a given application and/or to optimize detection. Because short pulses have large optical bandwidths in some embodiments, only a few hundred meters of dispersive fiber  914  are required. 
     The dispersive optical element  914  can be positioned anywhere between the optical modulator  908  and the plurality of detectors  924 ,  924 ′. In some embodiments, the dispersive optical element  914  is positioned immediately after the optical modulator  908  as shown in  FIG. 9 . In other embodiments, the dispersive optical element  914  is positioned immediately before the plurality of optical detectors  924 ,  924 ′. In some embodiments, the total dispersion may be achieved by using multiple dispersive optical elements. Continuing the example of using dispersive optical fiber to implement the dispersive optical element  914 , some of the length of the dispersive optical fiber is positioned at one location in the photonic analog-to-digital converter, and the remainder of the length of dispersive fiber is positioned at one or more other locations in the photonic analog-to-digital converter. It should be understood that the dispersive element of the present teaching can be used in various other embodiments that do not include a demultiplexer. It will be understood by those skilled in the art that these embodiments only include a single detector and single analog-to-digital converter. 
     In the embodiment shown in  FIG. 9 , the output of the dispersive optical element  914  is optically coupled to an input of the optical pulse demultiplexer  920 . The optical pulse demultiplexer  920  demultiplexes the sampled, and if preceded by a dispersive optical element, dispersed optical pulse train  916  into multiple output ports. In some embodiments, the optical demultiplexer  920  splits the incoming optical signal into a plurality of output ports based on the time slot of the optical pulse. Each of the plurality of demultiplexer output ports is optically coupled to a respective one of a plurality of optical detectors  924 ,  924 ′. The optical detectors  924 ,  924 ′ convert the demultiplexed dispersed optical pulse trains  922 ,  922 ′ into an electrical signal. The dispersed optical pulse trains comprise longer-duration pulses than the short pulses of optically sampled signal  912 . 
     The output of each of the plurality of optical detectors  924 ,  924 ′ is electrically connected to an input of a respective one of a plurality of electrical receivers  926 ,  926 ′ that condition the signals. The output of each of the plurality of the electrical receivers  926 ,  926 ′ is electrically connected to the input of a respective one of the plurality of analog-to-digital converters  930 ,  930 ′. 
     The embodiment illustrated in  FIG. 9  shows a bank of electrical receivers  926 ,  926 ′ that connect the detectors  924 ,  924 ′ to the ADC  930 ,  930 ′. Alternatively, other embodiments may utilize a passive interface instead of the receiver  926 ,  926 ′ to connect the detector  924 ,  924 ′ to the ADC  930 ,  930 ′. The dispersive optical element may be utilized in conjunction with any of the embodiments shown in  FIGS. 6, 7 and/or 8 . 
     The plurality of analog-to-digital converters  930 ,  930 ′ convert the electrical analog signals to digital signals. The plurality of analog-to-digital-converters  930 ,  930 ′ generates N outputs  934 , 934 ′, which are electrically connected to N inputs of a digital signal processor  950 . The digital signal processor  950  provides a digital output  952 . The resulting digital output  952  is a digital representation of the RF modulation at input  910 , which can be one of various known formats, including serial or parallel, straight binary or Gray code, high bandwidth and/or low bandwidth, depending on the particular known digital back end signal processing used. 
     One feature of the embodiment shown in  FIG. 9  is that it beneficially avoids what was heretofore believed to be fundamentally opposing constraints on the width of the optical sampling pulse that forced designers to either compromise on optical pulse width and/or the complex circuitry required to manage the performance with regard to pulse width of prior art photonic analog-to-digital converters. The analog-to-digital converter of the present teaching performs sampling with short pulses, but the detection and subsequent processing are conducted on longer, dispersed pulses. As such, the response roll-off of known systems as described in connection with  FIG. 4  takes on substantially the value associated with the sampling, short, pulse durations. However, detection is efficient using the longer dispersed pulses with lower peak power avoiding detector nonlinearity and lower noise owing to lower bandwidth pulse leading and trailing edges. Furthermore, the effective number of bits for the embodiment shown in  FIG. 9  would take on the substantially the value associated with the longer pulses in the receive chain of the system, thus the effective number of bits is higher, as described in conjunction with  FIG. 5 . 
     As the performance of analog-to-digital converters improves, it has become possible to move the analog-to-digital converter forward in the receive chain, i.e. move it closer to the antenna with the ultimate objective to have the analog-to-digital converter connected directly to the antenna output. One factor that is presently limiting achieving this objective is the noise figure of prior art analog-to-digital converters, which is presently limited to about 20 dB. The noise figure of state-of-the-art RF receivers is less than 6 dB. Hence at a minimum, a low noise amplifier is needed between the antenna and the analog-to-digital converter. The present lower bound on the noise figure of prior-art, high-speed, analog-to-digital converters is fundamentally set by a combination of electronic sampling and the flash topology used to implement them. 
     Unlike electronic sampling, photonic sampling can provide the necessary gain, with low noise figure, prior to the electronic analog-to-digital converter. As is well known in the art, inserting a stage with sufficient low-noise gain before a stage with higher noise figure can reduce the overall noise figure of the gain plus high noise figure stage. One feature of the present teaching is the recognition that the gain that photonic sampling can provide, can make it possible to sample directly the output of an antenna and do so with sufficiently low noise figure to make such an approach competitive with the noise figure that can be achieved with a low noise amplifier. 
     Wide bandwidth photonic links with gain and low noise figure have been demonstrated; see for example E. I. Ackerman, et al, “Signal-to-noise performance of two analog photonic links using different noise reduction techniques,” 2007 International Microwave Symposium Conference Digest, pp. 51-54, Jun. 3-8, 2007. Prior art system designs fail to realize that photonic sampling can be considered to be a type of optical link, but unlike a conventional optical link where both the input and output are continuous signals, a photonic sampler performs equivalent functions of an optical link in which the input is continuous but the output occurs only at discrete instants in time, which are commonly referred to as samples. A photonic sampler with gain and low noise figure in conjunction with an electronic quantizer, i.e. an electronic analog-to-digital converter, can produce a system with a sufficiently low noise figure to sample directly the output of an antenna. 
     Architecture of the electronically-quantized analog-to-digital converter system with low noise figure can be similar to the known photonic analog-to-digital converter architecture of  FIG. 1 , or to any of the new architectures described in connection with  FIGS. 6 through 9 . A pulsed laser provides a high-speed, low-jitter pulse train to the modulator. The output of the modulator is a train of pulses representing a sampled version of the electrical input signal that is to be converted to a digital representation. These pulses are sequentially sent to an optical pulse demultiplexer. A plurality of optical detectors is optically coupled to the output of the optical pulse demultiplexer. Each of the plurality of detectors is electrically connected to one of a plurality of electronic receivers which typically contain active electronic devices and/or circuits that amplify, provide impedance transformation. The electronic receivers provide the interface between the output of the detectors and the input to the electronic ADC. In some embodiments, the receivers are replaced by passive interfaces described earlier. Each of the plurality of electronic receivers is then electronically connected to one of a plurality of electronic analog-to-digital converters so that each electronic analog-to-digital converter only sees pulses at its electronic sampling rate. The electronic sampling rate of each analog-to-digital converter is many times slower than the optical sampling rate. A digital back end process unit is then used for various processing tasks. The optical pulse power is chosen to be large enough so that the equivalent input noise of the photonic ADC (at the RF input  610  shown in  FIG. 6 , for example) is smaller than the equivalent input noise at the input of the electronic ADCs (at the inputs to the ADCs  630  shown in  FIG. 6 , for example). This is possible because, as the optical power increases, the variation in the pulse amplitude at the output of the receivers  626  caused by a varying voltage at the photonic ADC input  610  to become larger. When the output pulse amplitude variation becomes larger than the input voltage variation of the signal, there is gain and the equivalent input noise at the photonic ADC input becomes smaller than the equivalent input noise of the electronic ADC. This simple description assumes the equivalent input noise of the photonic ADC is dominated by the equivalent input noise of the electronic ADC. This is possible by careful design of the photonic front end to minimize photonic noise sources, such as laser intensity noise and optical amplifier noise. Techniques for this are well known; see, for example, E. I. Ackerman, et al, “Signal-to-noise performance of two analog photonic links using different noise reduction techniques,” 2007 International Microwave Symposium Conference Digest, pp. 51-54, Jun. 3-8, 2007. 
     Equivalents 
     While the Applicant&#39;s teaching is described in conjunction with various embodiments, it is not intended that the Applicant&#39;s teaching be limited to such embodiments. On the contrary, the Applicant&#39;s teaching encompass various alternatives, modifications, and equivalents, as will be appreciated by those of skill in the art, which may be made therein without departing from the spirit and scope of the teaching.