## Abstract

We demonstrate a method to compensate multi-channel mismatches that intrinsically exist in a photonic analog-to-digital converter (ADC) system. This system, nominated time-wavelength interleaved photonic ADC (TWI-PADC), is time-interleaved via wavelength demultiplexing/multiplexing before photonic sampling, wavelength demultiplexing channelization, and electronic quantization. Mismatches among multiple channels are estimated in frequency domain and hardware adjustment are used to approach the device-limited accuracy. A multi-channel mismatch compensation algorithm, inspired from the time-interleaved electronic ADC, is developed to effectively improve the performance of TWI-PADC. In the experiment, we configure out a 4-channel TWI-PADC system with 40 GS/s sampling rate based on a 10-GHz actively mode-locked fiber laser. After multi-channel mismatch compensation, the effective number of bit (ENOB) of the 40-GS/s TWI-PADC system is enhanced from ~6 bits to >8.5 bits when the RF frequency is within 0.1-3.1 GHz and from ~6 bits to >7.5 bits within 3.1-12.1 GHz. The enhanced performance of the TWI-PADC system approaches the limitation determined by the timing jitter and noise.

© 2016 Optical Society of America

## 1. Introduction

Photonic analog-to-digital converter (PADC) technology has been developing rapidly in recent decades because it benefits from the low timing jitter of optical pulse trains [1–3]. The PADCs provide alternative solutions to electronic analog-to-digital converters (EADCs) for diverse applications of radar [4,5], surveillance [6], and telecommunications [7]. As comprehensively summarized in [2,3], one of the typical PADC with high speed and high resolution is called the photonic sampled and electronic quantized PADC. In this PADC [2,3], a stable pulsed laser works as a sampling source [8], an optical modulator serves as a sampling gate for RF signal, and an array of photo-detectors (PDs) is employed to convert the sampled optical signal to the sampled electronic signal that is electronically quantized by an array of EADCs. Each PD [9,10] and EADC [9] is reduced in bandwidth and sampling rate when compared to the PADC’s overall bandwidth and sampling rate because multiple channelization is carried out by multiplexing and demultiplexing processes. There are two schemes to reduce bandwidth and sampling rate: the segment-interleaved PADC [11–15] and time-interleaved (or sample-interleaved) PADC [9,16,17]. The segment-interleaved PADC is channelized by wavelength demultiplexing [14,15] and each channel is stretched in time domain or compressed in frequency domain via the dual-stage dispersive time-wavelength mapping before and after the photonic sampling [11–13]. In contrast, the time-interleaved PADC, also nominated time-wavelength interleaved PADC (TWI-PADC), is channelized by two steps. First, the sampling rate, i.e. the repetition rate of the pulsed laser, is multiplied to generate a time-wavelength interleaved high-speed sampling source by either the wavelength multiplexing [18,19] or time-wavelength mapping [3,20]. Second, the high-speed sampling source after the modulator samples optically the RF signal and the sampled optical signal is time-interleaved by wavelength demultiplexing so that each channel is correspondingly reduced in bandwidth and sampling rate. In comparison, the TWI-PADC is more advantageous than the segment-interleaved PADC because the TWI-PADC provides a higher resolution.

Up to date, various works [3,4,9,17–24] have been demonstrated to improve the performance of the TWI-PADC. For instance, more than 40-GHz sampling bandwidth with the effective number of bits (ENOB) of about 7 bits were demonstrated [3,4,22–24]. However, all the sampling rates were lower than the sampling bandwidth and didn’t satisfy the Nyquist theorem since one channel [22,24] or dual channels [3,4,23] was carried out. Ng et al. [18] four-fold multiplied the 10-GHz repetition rate of an actively mode-locked laser (AMLL) to achieve very fast sampling rate of 40 GS/s and a high ENOB of 8.3 bits whereas the sampling bandwidth was limited to be only 1.6 GHz. This is possibly because there are large mismatches among the multiple channels during the generation of the ultrahigh-speed PADC sampling source, the optical sampling, and multi-channel electronic quantization. Most recently [25], we proposed a spectral analysis and compensation method to partially overcome the mismatches during the generation of the time-wavelength interleaved PADC sampling source. In order to realize a good-performance TWI-PADC with high speed, high resolution, and wide bandwidth, there is still a well-known issue, that is, how to estimate and compensate the multi-channel mismatches. There is successful evidence to fully solve this issue in the segment-interleaved PADCs [14,15]. Besides, Khilo et al. [3] has addressed that the architecture of TWI-PADC is in principle similar with that of time-interleaved EADC and this issue in TWI-PADC might be proceeded if referred to the calibration and compensation algorithms successfully applied in modern EADCs. In [17], the effects of the multiple-channel mismatches in TWI-PADC were analyzed and estimated for hardware adjustments. However, to the best of our knowledge, there is no successful demonstration to compensate the multi-channel mismatches beyond the hardware limitation in TWI-PADC.

In this paper, we present a spectral analysis and compensation of the multi-channel mismatches in TWI-PADC. The effects of multi-channel mismatches, electro-optical modulation nonlinearity, and timing jitter on the ENOB of TWI-PADC are investigated. Inspired from modern time-interleaved EADCs [26,27], the compensation algorithm of multi-channel mismatches is developed to effectively enhance the ENOB of TWI-PADC from the hardware limitation to the timing jitter and noise determined limitation. In the experiment, high-speed and high-resolution TWI-PADC with 40-GS/s sampling rate and >7.5 ENOB covering 12.1 GHz bandwidth is successfully demonstrated.

## 2. Experimental setup

Figure 1 depicts the experimental setup of the TWI-PADC system, which is a typical architecture of the photonic sampled and electronic quantized PADC [2,18]. The laser source is an AMLL (Calmar PSL-10-TT), which is seeded by an electronic oscillator (Keysight E8257D) at 10 GHz. The pulse width of the AMLL is temporally compressed into 1.2 ps by a pulse compressor (Calmar PCS-2). After wavelength demultiplexing, multi-channel time/amplitude adjustment, and wavelength multiplexing processes, shown in Figs. 1(a) and 1(b), the repetition rate of the AMLL is four-fold multiplied to *f _{S}* = 40 GHz. Note that the generation of the sampling source was previously presented in [23]. The photonic sampling via an electro-optical modulator (EOM) is schematically depicted in Figs. 1(c) and 1(d). The RF signal to be sampled is provided by another microwave synthesizer (Rhode & Schwarz SMA 100A) and modulated to the sampling source via a Mach-Zehnder intensity modulator (EO Space AZ-1X2-AV5-40) with the bandwidth of 40 GHz and the half-wave voltage of

*V*= 3 V. As illustrated in Figs. 1(e) and 1(f), the photonic sampled signal is demultiplexed into 4 parallel channels by a wavelength division multiplexer (WDM). The WDM with 1.6-nm bandwidth in each channel is identical to the one used in Fig. 1(a). A tunable delay line (TDL) with an accuracy of ~100 fs is inserted in each channel for multi-channel time adjustment. In each channel, the average optical power into a PD with 20 GHz bandwidth (Discovery DSC-R401HG-59) is ~0 dBm. It is converted into the electronic sampled signal and digitized by a 10 GS/s real-time oscilloscope with 4 channels (Keysight MSOS804A). The oscilloscope is clocked by the electronic oscillator (Keysight E8257D) also seeding the AMLL.

_{π}The optical intensity of the sampling source (i.e. optical pulse train) of the TWI-PADC system can be expressed by

*p*(

_{n}*t*) corresponds to the pulse train in the

*n*th channel.

*A*and Δ

_{n}*t*denote its amplitude and time skew, respectively.

_{n}*δ*(·) represents the Dirac function, which is used as an approximation of the sampling source with a temporal interval of

*T*= 1/

_{S}*f*= 25 ps.

_{S}The normalized transmittance of the EOM (i.e. the relation between the output and input optical intensity), *T _{M}*, is determined by the RF signal to be sampled,${v}_{IN}\left(t\right)$, as follows [9]

*V*

_{π}and

*V*are the half-wave voltage and the DC bias of the EOM, respectively.

_{B}In mathematics, the electronic sampled signal in the *n*th channel can be described by

*R*

_{PD}_{,}

*and*

_{n}*G*are the responsivity of the PD and the transmittance gain (or loss) of the converted electronic signal in the

_{n}*n*th channel, respectively. Consequently, the peak value of the sampled signal is captured and digitized by the multiple channels, which is schematically illustrated in Fig. 1(f).

The digitized data after channel mapping can be written by

*k*is the number of digitized samples.

*a*=

_{n}*G*

_{n}R_{PD}_{,}

*and Δ*

_{n}A_{n}*t*denote the digitized amplitude and the time skew in the

_{n}*n*th channel, respectively.

## 3. Mathematical derivation

#### 3.1 Spectral analysis

Consider the RF signal to be sampled is sinusoidal, which can be expressed by ${v}_{IN}\left(t\right)={V}_{0}\mathrm{cos}({\Omega}_{IN}t)$ with a frequency of *f _{IN}* = Ω

*/2*

_{IN}*π*and an amplitude of

*V*

_{0}. When a quadrature bias (i.e.

*V*= -

_{B}*V*

_{π}/2) is applied to the EOM, the digitized data after channel mapping is derived from Eq. (4) as follows

*ω*= Ω

_{IN}*is the normalized angular frequency of the digitized data,*

_{IN}T_{S}*M*=

*πV*

_{0}/

*V*is defined as the modulation index, and

_{π}*J*

_{2}

_{m}_{+1}is the (2

*m*+ 1)th order Bessel function. In Eq. (5), the item of

*a*/2 is the offset in each channel, which can be digitally eliminated by a DC-block after digitization.

_{n}The discrete Fourier transform (DFT) of the digitized data [see Eq. (5)] after the elimination of the offset (*a _{n}*/2) can be expressed by

*ω*= 2

*πfT*is the normalized angular frequency and

_{S}*f*= (2

*m*+ 1)

*f*(

_{IN}*m*is an integer). The channel mismatch effect in frequency domain is characterized by the distortion spurs at

*f*=

*lf*4

_{S}/*±*(2

*m*+ 1)

*f*(

_{IN}*l*= 0,1,2,3). It is similar to the case in EADCs [26]. Figure 2 illustrates a typical DFT spectrum of a 4-channel TWI-PADC according to the spectral analysis in Eqs. (6) and (7). Note that only the interval of [0,

*f*/2] is plotted due to the symmetry of the spectrum.

_{S}Based on the algorithm of dual channel mismatch compensation demonstrated in Appendix, the digitized data ${v}_{Q}\left[k\right]$of a single-frequency RF signal at *f _{IN}* can be reconstructed by

*a*

_{1}and

*a*

_{2}are the amplitudes of the dual channels.

*δt =*Δ

*t*

_{2}-Δ

*t*

_{1}is the relative time skew between the dual channels, which can be calculated from the spectrum in Eq. (6) according to Appendix.

In consequence, for a 4-channel TWI-PADC, the compensation algorithm in Eq. (8) can be applied to the dual channels of the first and third or the second and fourth channel, respectively. Later, the algorithm is performed to the two data series that are previously reconstructed and thus all four channels are reconstructed eventually. Note that this algorithm can be effectively applied to a TWI-PADC with an even number of multiple channels.

#### 3.2 SINAD and ENOB estimation

According to IEEE standard for terminology and test methods for ADCs [28], the ENOB is defined by

where*SINAD*is the signal to noise and distortion ratio (SINAD) of the PADC and given by [28]

_{PADC}*P*

_{signal},

*P*

_{distortion}, and

*P*

_{noise}are the powers of the RF signal, distortion, and noise. They can be numerically derived from the DFT of the quantized data after channel mapping [see Eq. (6)].

In the TWI-PADC system, the factors of distortions and noise are the higher odd-order harmonics induced by the modulator nonlinearity, the distortion spurs induced by channel mismatch, the amplitude noise, and the timing jitter. Hence, the *SINAD _{PADC}* is a summation of the signal-to-noise ratio (SNR) and signal-to-distortion ratio (SDR) for different factors. Note that the SNR is defined by the ratio of the signal power to the power of stochastic noises whereas the SDR represents the ratio of the signal power to the power of the mismatch and nonlinearity induced distortions. The distortions are related with the RF signal to be sampled.

The *SINAD _{PADC}* can be expressed as follows

*SDR*,

_{Modulation}*SDR*,

_{Mismatch}*SNR*, or

_{Noise}*SNR*corresponds to the modulation nonlinearity, channel mismatch effects, amplitude noise, and timing jitter, respectively. They can be derived from the spectrum in Eq. (6). Since the modulation nonlinearity is dominantly by the 3rd harmonics,

_{Jitter}*SDR*can be approximately expressed by

_{Modulation}*γ*(

*M*) represents the effect of the modulation nonlinearity.

*SDR _{Mismatch}* is determined by the ratio between the powers of the RF signal and mismatches as follows

*σ*is the normalized deviation of the amplitude

_{a}*a*, defined by ${\sigma}_{a}=\frac{1}{\overline{a}}\sqrt{{\displaystyle \sum _{n=1}^{4}{\left({a}_{n}-\overline{a}\right)}^{2}}/4}$, and $\overline{a}={\displaystyle \sum _{n=1}^{4}{a}_{n}}/4$.

_{n}*σ*is the root-mean-square (RMS) of time skew Δ

_{t}*t*, i.e. ${\sigma}_{t}=\sqrt{{\displaystyle \sum _{n=1}^{4}\Delta {t}_{n}^{2}}/4}$.

_{n}Similar to EADCs [29], *SNR _{Noise}* can be described by

*σ*is the noise level including the intensity noise of the optical source, the shot noise of the photodetector, and the thermal noise.

_{N}*ρ*(

_{N}*M*) represents the ratio of

*σ*to the RF amplitude.

_{N}Besides, *SNR _{Jitter}* is determined by the timing jitter as follows

*σ*is the RMS timing jitter of the TWI-PADC sampling source.

_{J}The entire SINAD of the PADC system can be derived from Eqs. (11)-(15), which is written by

## 4. Experimental details

#### 4.1 Estimation of the multi-channel mismatches

From Eqs. (12) and (14), it is found that *γ*(*M*) increases whereas *ρ _{N}*(

*M*) decreases with the modulation index of

*M*. Hence, there is a value of

*M*corresponding to the maximum

_{optimal}*SINAD*in Eq. (16) for specific parameters of

_{PADC}*σ*,

_{N}*σ*,

_{a}*σ*,

_{t}*σ*, and

_{J}*f*. To experimentally determine

_{IN}*M*, we manipulate the output power of the microwave synthesizer (RF signal) to change

_{optimal}*M*. The parameters of

*σ*and

_{a}*σ*are calculated from

_{t}*a*and Δ

_{n}*t*, which can be derived from the spectra of digitized data according to Eq. (A.1) in Appendix.

_{n}Due to the device-limited accuracy, the parameters of multi-channel mismatches are *σ _{a}* = 1.0 × 10

^{−2}and

*σ*= 95 fs, respectively. Figure 3 illustrates the single sideband (SSB) phase noise spectra of the AMLL and electronic oscillator, which are both measured by a signal analyzer (Rhode & Schwarz FSUP 50). The integral RMS timing jitters of the SSBM phase noise spectra are calculated to be

_{t}*σ*

_{J}_{,MLL}= 20.9 fs for the AMLL and

*σ*

_{J}_{,RF}= 29.3 fs for the electronic oscillator, respectively. Assuming the timing jitters of the AMLL and RF source are uncorrelated, the total RMS timing jitter of the TWI-PADC sampling source is determined by${\sigma}_{J}=\sqrt{{\sigma}_{J,\text{MLL}}^{2}+{\sigma}_{J,RF}^{2}}$ = 36 fs.

Figures 4(a)-(d) illustrate the spectra of digitized data at the RF frequency of *f _{IN}* = 3.1 GHz for

*M*= 0.05, 0.15, 0.25, and 0.50, respectively. The number of samples is 1 × 10

^{6}in each channel, corresponding to 10 kHz spectral resolution. Both the signal and the nonlinear distortion (i.e. the 3rd harmonic) increase with

*M*. The SINAD is calculated according to Eq. (10) and depicted as a function of

*M*in Fig. 4(e). According to Eqs. (14) and (15), the amplitude noise becomes dominant in the lower frequency range (i.e.

*SNR*→ + ∞ when

_{Jitter}*f*→ 0). The noise level is calculated to be ~-56 dBc, which means that

_{IN}/f_{S}*σ*= 1.4 × 10

_{N}^{−4}according to Eq. (14).

With all the derived parameters *σ _{N}*,

*σ*,

_{a}*σ*, and

_{t}*σ*, the theoretical model [see Eq. (16)] is utilized to the least-squares fitting of experimental results. The fitting curve and its derivative are depicted in Fig. 4(e). It indicates that the fitting curve has a good consistence with the experimental results. The SINAD first increases and then decreases with

_{J}*M*for a certain input frequency. The maximum SINAD appears at

*M*= ~0.17, corresponding to the zero derivative of the fitting curve.

Since the amplitude and time skew of each channel can be extracted from the spectral analysis of the digitized data through Eq. (7), hardware adjustments of multi-channel mismatches are performed by manipulation of the VOAs and TDLs [see Fig. 1]. Figures 5(a)-5(d) present the spectra of digitized data after four-step hardware adjustments and Fig. 5(e) summarizes the SINAD for different multi-channel mismatches. Note that *M* = 0.17. It shows that the distortion spurs are gradually suppressed. In Fig. 5(e), the theoretical estimation based on Eq. (16) is depicted by contours and the measured SINAD values are marked in the parentheses. The SINAD increases from 26.2 dB to 41.5 dB after the hardware adjustments. The consistence of the experimental results and the theoretical estimation verifies the feasibility of the spectral analysis demonstrated above.

#### 4.2 Compensation of the multi-channel mismatches

Figure 6 shows the spectra of the digitized data at different RF frequencies of *f _{IN}* = 1.1 GHz, 3.1 GHz, 6.1 GHz, and 12.1 GHz, respectively. The modulation index is set to

*M*= 0.17. It is shown that the mismatch spurs can be effectively eliminated by the mismatch compensation algorithm [see Eq. (8)]. As an example, for

*f*= 3.1 GHz, the SINAD is enhanced from ~39 dB to ~54 dB and the ENOB is correspondingly improved from ~6.2 bits to ~8.7 bits. Note that the compensation algorithm is carried out as long as data acquisition is finished. It takes ~100 MB of memory and ~1 s (Intel Pentium P6100 CPU).

_{IN}Figure 7 represents the ENOB as a function of the RF frequency. The discrete points indicate the experimental results of TWI-PADC system, which are calculated by Eqs. (9) and (10). The ENOB without the mismatch compensation is ~6 bits within 0.1~12.1 GHz whereas the ENOB with the mismatch compensation reaches ~7.5 bits within 3.1~12.1 GHz and even approaches ~8.5 bits within 0.1-3.1 GHz. According to the theoretical analyses in Eqs. (11)-(16) and the parameters of *σ _{N}* = 1.4 × 10

^{−4},

*σ*= 1.0 × 10

_{a}^{−2},

*σ*= 95 fs, and

_{t}*σ*= 36 fs, the limitations of our TWI-PADC system determined by noise, timing jitter, and channel mismatch are estimated, respectively. Referred to [30], the ambiguity limitation can be expressed by: ENOB = log2[2ln2/π√6(

_{J}*f*)

_{IN}τ_{D}^{2}], where

*τ*= 1.2 ps is the pulse duration of the sampling source in our system. The above limitations are all compared in Fig. 7. It is found that the original performance of the TWI-PADC is mainly limited by multi-channel mismatches. After the mismatch compensation algorithm, it is essentially enhanced to the noise and timing jitter determined limitations.

_{D}In Fig. 8, the performances of our TWI-PADC system before and after mismatch compensation are compared with those of the published relevant works. Note that the reference numbers of relevant works are also marked within brackets in Fig. 8. The limitations determined by the timing jitter *σ _{J}* of 1 ps, 100 fs and 10 fs are estimated by Eq. (15) and depicted as dashed lines in Fig. 8. Juodawlkis

*et al.*achieved 9.8 bits (ENOB) at 3 GHz (bandwidth) [9] whereas the sampling rate is 505 MS/s. Similarly, 200-MS/s down-sampling with 7 bits (ENOB) and 40 GHz (bandwidth) was demonstrated [22]; a comparable performance of ENOB and bandwidth with 2 GS/s [23] or 10 GS/s [24] sampling rate was reported, respectively. In the work by W. Ng

*et al.*[18], a 10-GHz AMLL was adopted for a 4-channel TWI-PADC system with 40 GS/s sampling rate. However, the sampling range covers only 1.6 GHz and a narrow-bandwidth filter used in the EADC reduces the sampling bandwidth. Based on the time-stretched scheme, J. Chou

*et al.*reported 4.5 bits (ENOB) at 95 GHz (bandwidth) with an effective sampling rate of 10 TS/s [31]. Note that the original sampling rate 40 GS/s at 95 GHz is illustrated in Fig. 8 to take full advantage of the horizontal axis. It is reasonable because the sampling rate after time-stretching is multiplied whereas the bandwidth after time-stretching is compressed. Compared to the works with high resolutions [4,9,22–24,32,33], our work achieves a high resolution of >7.5 bits and higher sampling rate of 40 GS/s. In comparison to [18,34,35], the sampling rate of our TWI-PADC is comparable but the bandwidth of 12.1 GHz is more dominant. Moreover, the time-stretched scheme shows significant advantages in both the bandwidth and sampling rate whereas the time aperture is intrinsically limited.

## 5. Conclusion

We have demonstrated a multi-channel mismatch compensation to improve the performance of the TWI-PADC system with 40 GS/s sampling rate. First, the dependence of multi-channel mismatches, modulation nonlinearity, noise, and timing jitter on the ENOB is analyzed in frequency domain. Second, the compensation of multi-channel mismatches is effectively applied to enhance the ENOB. In consequence, the TWI-PADC is experimentally increased from ~6 bits to >8.5 bits within the bandwidth of 0.1~3.1 GHz and from ~6 bits to >7.5 bits within the bandwidth of 3.1~12.1 GHz. The experimental results are in good agreement with the theoretical analysis and the enhanced performance of the TWI-PADC approaches the limitation determined by the noise level of −56 dBc and timing jitter of 36 fs. In terms of the sampling rate, ENOB, and bandwidth, the performance of the TWI-PADC is comparable and even superior to the published relevant works [9,18,22–24,31–35].

## Appendix Dual channel mismatch compensation algorithm

Eq. (7) presents a formula of *N*-length DFT. *a _{n}* and Δ

*t*in each channel can be derived from ${\beta}_{l}^{+}$or ${\beta}_{l}^{-}$ by an inverse DFT. It means that 2

_{n}*N*number of amplitude and time skew can be derived from both real and imaginary parts of ${\beta}_{l}^{+}$ or ${\beta}_{l}^{-}$. Taking ${\beta}_{l}^{+}$ as example, it can be expressed as

*f = lf*±

_{S}/N*f*as shown in Eq. (15). Hence, Eq. (A. 1) indicates that the amplitude and time skew in each channel can be calculated from the distortion spurs on the digitization spectrum.

_{IN}For a dual channel TWI-PADC system, the relation between the mismatch-free spectrum ${\tilde{V}}_{Q}\left[\omega \right]$and the mismatched spectrum ${V}_{Q}\left[\omega \right]$ can be derived from Eqs. (4) and (7) as follows

*a*

_{1}and

*a*

_{2}are the amplitudes of the two channels and

*δ =*Δ

*t*

_{2}-Δ

*t*

_{1}is the relative time skew between two channels which can be derived from Eq. (17). With an inverse DFT, Eq. (18) can be converted to

*h*

_{0}[

*k*] = F

^{−1}{

*H*

_{0}[

*ω*]},

*h*

_{1}[

*k*] = F

^{−1}{

*H*

_{1}[

*ω*]}, and the compensated data ${\tilde{v}}_{Q}\left[k\right]\text{=}{\tilde{v}}_{Q}^{+}\left[k\right]\text{+}{\tilde{v}}_{Q}^{-}\left[k\right]$. For a single-tone input at

*ω*, Eq. (20) can be expressed by

_{IN}**H**≠ 0, i.e. cosΩ

*≠ 0 (which is always tenable for*

_{IN}δ*δ*much smaller than

*T*), the compensated data can be reconstructed according to Eq. (21), which is represented by Eq. (8).

_{S}## Funding

National Natural Science Foundation of China (NSFC) (61571292, 61535006, and 61505105); SRFDP of MOE (grant no. 20130073130005).

## Acknowledgments

We are grateful to all the referees for helpful criticisms of earlier versions of this paper.

## References and links

**1. **H. F. Taylor, “An optical analog-to-digital converter-design and analysis,” IEEE J. Quantum Electron. **15**(4), 210–216 (1979). [CrossRef]

**2. **G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express **15**(5), 1955–1982 (2007). [CrossRef] [PubMed]

**3. **A. Khilo, S. J. Spector, M. E. Grein, A. H. Nejadmalayeri, C. W. Holzwarth, M. Y. Sander, M. S. Dahlem, M. Y. Peng, M. W. Geis, N. A. DiLello, J. U. Yoon, A. Motamedi, J. S. Orcutt, J. P. Wang, C. M. Sorace-Agaskar, M. A. Popović, J. Sun, G. R. Zhou, H. Byun, J. Chen, J. L. Hoyt, H. I. Smith, R. J. Ram, M. Perrott, T. M. Lyszczarz, E. P. Ippen, and F. X. Kärtner, “Photonic ADC: overcoming the bottleneck of electronic jitter,” Opt. Express **20**(4), 4454–4469 (2012). [CrossRef] [PubMed]

**4. **P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, and A. Bogoni, “A fully photonics-based coherent radar system,” Nature **507**(7492), 341–345 (2014). [CrossRef] [PubMed]

**5. **W. Zou, H. Zhang, X. Long, S. Zhang, Y. Cui, and J. Chen, “All-optical central-frequency-programmable and bandwidth-tailorable radar,” Sci. Rep. **6**, 19786 (2016). [CrossRef] [PubMed]

**6. **K. G. Merkel and A. L. Wilson, “A survey of high performance analog-to-digital converters for defense space applications,” in IEEE Aerospace Conference (2003), pp. 2415–2427. [CrossRef]

**7. **J. A. Wepman, “Analog-to-digital converters and their applications in radio receivers,” IEEE Commun. Mag. **33**(5), 39–45 (1995). [CrossRef]

**8. **G. E. Villanueva, M. Ferri, and P. Pérez-Millán, “Active and passive mode locked fiber lasers for high-speed high-resolution photonic analog-to-digital conversion,” IEEE J. Quantum Electron. **48**(11), 1443–1452 (2012). [CrossRef]

**9. **P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microw. Theory Tech. **49**(10), 1840–1853 (2001). [CrossRef]

**10. **F. Su, G. Wu, and J. Chen, “Photonic analog-to-digital conversion with equivalent analog prefiltering by shaping sampling pulses,” Opt. Lett. **41**(12), 2779–2782 (2016). [CrossRef] [PubMed]

**11. **A. S. Bhushan, F. Coppinger, and B. Jalali, “Time-stretched analogue-to-digital conversion,” Electron. Lett. **34**(11), 1081–1082 (1998). [CrossRef]

**12. **Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: fundamental concepts and practical considerations,” J. Lightwave Technol. **21**(12), 3085–3103 (2003). [CrossRef]

**13. **K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics **7**(2), 102–112 (2013). [CrossRef]

**14. **G. Sefler, J. Chou, J. Conway, and G. Valley, “Distortion correction in a high-resolution time-stretch ADC scalable to continuous time,” J. Lightwave Technol. **28**(10), 1468–1476 (2010). [CrossRef]

**15. **S. Gupta and B. Jalali, “Time-warp correction and calibration in photonic time-stretch analog-to-digital converter,” Opt. Lett. **33**(22), 2674–2676 (2008). [CrossRef] [PubMed]

**16. **A. Yariv and R. G. M. P. Koumans, “Time interleaved optical sampling for ultra-high speed A/D conversion,” Electron. Lett. **34**(21), 2012–2013 (1998). [CrossRef]

**17. **R. C. Williamson, P. W. Juodawlkis, J. L. Wasserman, G. E. Betts, and J. C. Twichell, “Effects of crosstalk in demultiplexers for photonic analog-to-digital converters,” J. Lightwave Technol. **19**(2), 230–236 (2001). [CrossRef]

**18. **W. Ng, L. Luh, D. L. Persechini, D. Le, Y. M. So, M. Mokhtari, and J. E. Jensen, “Ultrahigh-speed photonic analog-to-digital conversion technologies,” in Proceedings of Defense and Security ISOP (2004), pp. 171–177.

**19. **G. Wu, S. Li, X. Li, and J. Chen, “18 wavelengths 83.9Gs/s optical sampling clock for photonic A/D converters,” Opt. Express **18**(20), 21162–21168 (2010). [CrossRef] [PubMed]

**20. **F. X. Kärtner, J. Kim, J. Chen, and A. Khilo, “Photonic Analog-to-Digital Conversion with Femtosecond Lasers,” Frequenz (Bern) **62**(7–8), 171–174 (2008).

**21. **M. P. Fok, K. L. Lee, and C. Shu, “4× 2.5 GHz repetitive photonic sampler for high-speed analog-to-digital signal conversion,” IEEE Photonics Technol. Lett. **16**(3), 876–878 (2004). [CrossRef]

**22. **J. Kim, M. J. Park, M. H. Perrott, and F. X. Kärtner, “Photonic subsampling analog-to-digital conversion of microwave signals at 40-GHz with higher than 7-ENOB resolution,” Opt. Express **16**(21), 16509–16515 (2008). [CrossRef] [PubMed]

**23. **A. H. Nejadmalayeri, M. E. Grein, A. Khilo, J. Wang, M. Y. Sander, M. Peng, C. M. Sorace, E. P. Ippen, and F. X. Kaertner, “A 16-fs aperture-jitter photonic ADC: 7.0 ENOB at 40 GHz,” in *CLEO 2011*, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CThI6.

**24. **D. J. Esman, A. O. J. Wiberg, N. Alic, and S. Radic, “Highly linear broadband photonic-assisted Q-Band ADC,” J. Lightwave Technol. **33**(11), 2256–2262 (2015). [CrossRef]

**25. **G. Yang, W. Zou, X. Li, and J. Chen, “Theoretical and experimental analysis of channel mismatch in time-wavelength interleaved optical clock based on mode-locked laser,” Opt. Express **23**(3), 2174–2186 (2015). [CrossRef] [PubMed]

**26. **C. Vogel, “The impact of combined channel mismatch effects in time-interleaved ADCs,” IEEE Trans. Instrum. Meas. **54**(1), 415–427 (2005). [CrossRef]

**27. **N. Kurosawa, H. Kobayashi, K. Maruyama, H. Sugawara, and K. Kobayashi, “Explicit analysis of channel mismatch effects in time-interleaved ADC systems,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. **48**(3), 261–271 (2001).

**28. **IEEE Standard for Terminology and Test Methods for Analog-to-Digital Converters, IEEE Standard 1241, 2000. http://ieeexplore.ieee.org/xpl/ articleDetails.jsp?arnumber = 929859&contentType = Standards.

**29. **B. Brannon, “Sampled systems and the effects of clock phase noise and jitter.” Analog Devices App. Note, AN-756, (2004).

**30. **G. C. Valley, J. P. Hurrell, and G. A. Sefler, “Photonic analog-to-digital converters: fundamental and practical limits,” Proc. SPIE **5618**, 96–106 (2004). [CrossRef]

**31. **J. Chou, O. Boyraz, D. Solli, and B. Jalali, “Femtosecond real-time single-shot digitizer,” Appl. Phys. Lett. **91**(16), 161105 (2007). [CrossRef]

**32. **O. Golani, L. Mauri, F. Pasinato, C. Cattaneo, G. Consonnni, S. Balsamo, and D. M. Marom, “A photonic analog-to-digital converter using phase modulation and self-coherent detection with spatial oversampling,” Opt. Express **22**(10), 12273–12282 (2014). [CrossRef] [PubMed]

**33. **T. R. Clark, J. U. Kang, and R. D. Esman, “Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion,” IEEE Photonics Technol. Lett. **11**(9), 1168–1170 (1999). [CrossRef]

**34. **W. Ng, R. Stephens, D. Persechini, and K. V. Reddy, “Ultra-low jitter mode locking of Er-fibre laser at 10GHz and its application in photonic sampling for analogue-to-digital conversion,” Electron. Lett. **37**(2), 113–114 (2001). [CrossRef]

**35. **Q. Wu, H. Zhang, Y. Peng, X. Fu, and M. Yao, “40GS/s Optical analog-to-digital conversion system and its improvement,” Opt. Express **17**(11), 9252–9257 (2009). [CrossRef] [PubMed]