In an ideal scenario free of intersymbol interference and noise, the waveform remains distortion-free, with each symbol perfectly overlapping one another. As a result, the resulting trace on the oscilloscope appears as a thin, clear "eye," with the "eye" opening maximally wide. However, when intersymbol interference is present, the waveform becomes distorted, causing symbols to no longer align perfectly. This leads to a blurred trace in the eye diagram, with the "eye" partially closing or even completely shutting down. If noise is also introduced, the eye diagram’s lines become even more indistinct, further reducing the size of the "eye." Consequently, the degree to which the "eye" opens directly reflects the extent of distortion—indicating the strength of intersymbol interference. From this, it’s clear that the eye diagram provides a直观 way to visualize the effects of intersymbol interference and noise, enabling a straightforward assessment of the performance quality of a baseband transmission system. Moreover, this graphical tool can be used to fine-tune the characteristics of the receiving filter, helping to minimize intersymbol interference and significantly enhance the overall system’s transmission performance.
Connect an oscilloscope across the output of the receiving filter, then adjust the oscilloscope’s sweep time so that its horizontal sweep period matches the duration of the received symbol. The resulting waveform displayed on the oscilloscope screen is known as an eye diagram. While an oscilloscope typically measures the waveform of individual bits or a short segment of time—providing detailed insights into signal behavior—the eye diagram, on the other hand, reveals the overall characteristics of all digital signals transmitted over the link.
Basic Concepts
What is an eye diagram?
"An eye diagram is a graph shaped like an eye. It’s created by accumulating and superimposing the bit patterns of serial signals captured over time, using a persistence-of-image technique. The resulting shape closely resembles an eye, hence the name 'eye diagram.' Typically, the eye diagram displays a time window of 1.25 UI. While eyes can vary in shape, so too can eye diagrams—each reflecting unique characteristics of the underlying signal. By analyzing the distinctive features of the eye diagram, you can quickly assess the quality of the signal."
Since the eye diagram succinctly captures bit information of a serial signal in a single graphic, it has become the most critical tool for assessing signal quality. As a result, eye diagram measurements are sometimes referred to as "Signal Quality Tests (SQ Tests)." Moreover, whether an eye diagram measurement passes or fails is typically determined by comparing it against a "Mask." The mask defines the allowable tolerances for the "1" and "0" levels of the serial signal, as well as constraints on rise time, fall time, and other timing parameters. This is why eye diagram testing is also commonly called "Mask Testing." Masks come in various shapes and forms; for instance, the mask for a typical NRZ signal is illustrated in blue in Figures 5 and 8. At different nodes along the serial data transmission path, the eye diagram mask may vary significantly, so it’s essential to carefully select the appropriate sub-mask type based on the specific application. Using the transmitter-side mask as the receiver-side eye diagram template could lead to constant mask violations. However, signals like Ethernet or E1/T1 do not follow NRZ coding schemes, resulting in uniquely shaped masks tailored to their characteristics. When a bit inadvertently crosses the mask boundary, it indicates poor signal quality, signaling the need to fine-tune the circuitry. Some products mandate that no mask violations should occur at all, while others allow a limited number of violations within a specified probability threshold.
In an ideal scenario free of intersymbol interference and noise, the waveform remains distortion-free, with each symbol perfectly overlapping one another. As a result, the resulting trace on the oscilloscope appears as a thin, clear "eye," with the "eye" opening maximally wide. However, when intersymbol interference is present, the waveform becomes distorted, causing symbols to no longer align perfectly. This leads to a blurred trace in the eye diagram, with the "eye" partially closing or even completely shutting down. If noise is also introduced, the eye diagram’s lines become even more indistinct, further reducing the size of the "eye." Consequently, the degree to which the "eye" opens directly reflects the extent of distortion—indicating the strength of intersymbol interference. From this, it’s clear that the eye diagram provides a直观 way to visualize the effects of intersymbol interference and noise, enabling a straightforward assessment of the performance quality of a baseband transmission system. Moreover, this graphical tool can be used to fine-tune the characteristics of the receiving filter, helping to minimize intersymbol interference and significantly enhance the overall system’s transmission performance.
Principle
Travel Principle
If the oscilloscope’s entire display screen spans 100 nanoseconds, it means that, with the instrument’s effective bandwidth, sampling rate, and memory working in harmony, waveform data for that 100-nanosecond interval has been captured. However, for a system, analyzing signals over such a short duration isn’t truly representative. For instance, if a signal experiences a spike once every million bits, the likelihood of capturing one of these spikes within those 100 nanoseconds is extremely low, potentially causing critical information to be missed entirely. Clearly, measuring data over such a brief timespan would not provide an accurate reflection of the system’s overall performance. Imagine, instead, a scenario where new signals are continuously added to the display screen through a process of repeated superposition—yet the previous waveforms are retained as well. If this accumulation continues long enough, an eye diagram can eventually take shape. This eye diagram then offers a comprehensive view of the system’s performance, revealing factors like crosstalk, noise, and other key parameters—providing valuable insights that can guide improvements across the entire system design. When analyzing the actual eye diagram alongside theoretical expectations, a complete eye diagram should ideally encompass all possible state combinations—from “000” to “111”—with each state occurring roughly the same number of times. Otherwise, certain types of information might fail to appear on the screen altogether. The illustration below shows an eye diagram formed by eight distinct states:

Based on the theoretical analysis above, combined with the actual eye diagram generation principle of an oscilloscope, we can conclude that the eye diagram typically observed on an oscilloscope closely matches the one derived from theoretical analysis—provided there are no interference effects such as crosstalk. The figure shows the eye diagram actually captured by the oscilloscope.
If any one of these eight state groups is missing, the resulting eye diagram will be incomplete. Shown below is an incomplete eye diagram observed on an oscilloscope:
 

The eye diagram reflects the overall performance of a digital system's transmission—but how can you properly grasp the methods for interpreting it? To address this, it’s essential to define the various parameters involved in the eye diagram. Once you understand these parameters, the interpretation process becomes straightforward.

Parameter Definition
There are many relevant eye diagram parameters, such as eye height, eye width, eye amplitude, eye crossing ratio, "1" level, "0" level, extinction ratio, Q-factor, average power, and more. Each parameter is illustrated in the figure below:

Parameters
There are many eye diagram parameters related to the eye plot, such as eye height, eye width, eye amplitude, eye crossing ratio, "1" level, "0" level, extinction ratio, Q-factor, and average power, among others.  
"The '1' level and the '0' level represent projecting the middle 20% of the eye diagram's horizontal axis perpendicularly onto a histogram, where the center values of the histogram correspond to the '1' level and the '0' level, respectively."
Eye amplitude represents the difference between the average distribution of "1" level signals and the average distribution of "0" level signals. It is measured by analyzing the amplitude values distributed in a region near the center of the eye diagram—typically within 20% of the distance between zero-crossing points. In essence, eye amplitude is calculated as "1" level minus "0" level.
Eye width reflects the total jitter of the signal—the horizontal opening of the eye diagram—defined as the time difference between the two crossing points where the upper and lower edges intersect. The time interval between these crossing points is calculated based on the average of histograms taken at the signal’s two zero-crossing points, while the standard deviation of each distribution is derived by subtracting the smaller average from the larger one.
Eye height refers to the vertical extent of the eye diagram on its axis—it serves as a measure of signal-to-noise ratio, closely resembling the amplitude of the eye diagram. The difference between the upper and lower histograms at 3σ represents the eye height.
Operating Steps
Basic steps for eye diagram measurement:
1. Achieve high-fidelity signal capture by following the fundamental principles of signal acquisition: oversampling, minimizing quantization error, and capturing signals over a sufficiently long duration.
2. Set the appropriate PLL;
3. Set up the eye diagram template and subtemplates;
4. Measure relevant eye diagram parameters;
Measurement method
Eye diagram testing is a crucial component of physical-layer testing for high-speed serial signals. An eye diagram is formed by overlaying waveforms from multiple bits, and it provides a visual representation that reveals key characteristics of the digital signal: the 1-level and 0-level thresholds, whether the signal exhibits overshoot or ringing, the extent of jitter, as well as the signal-to-noise ratio and the symmetry (or duty cycle) of the rise/fall times. Ultimately, the eye diagram offers a direct and intuitive way to assess signal quality and performance under high-data-rate conditions, making it an essential tool for evaluating the integrity of high-speed digital signals.
Traditional eye diagram measurement methods can be summarized in eight Chinese characters as: "Synchronous triggering + superimposed display." Modern eye diagram measurement methods, when translated into the same eight-character phrase, become: "Synchronous slicing + superimposed display." The key difference between the two approaches lies in just four characters: "triggering" versus "slicing." Traditional methods rely on triggering to capture each waveform, while modern techniques use slicing to isolate and analyze individual signal segments. "Synchronization" is crucial for accurately measuring the eye diagram, but the way synchronization is achieved differs between the two methods. In traditional methods, synchronization occurs through a single trigger event, followed by the superposition of the captured waveform. Each time a trigger is initiated, a new UI (unit interval) is added to the eye diagram—representing one bit of data arranged relative to the trigger point. Thus, with each trigger, only one additional bit is plotted on the eye diagram.
Other concepts
Extinction Ratio
The Extinction Ratio is defined as the ratio of the statistical average of the "1" level to that of the "0" level in an eye diagram, and its calculation can be expressed using any of the following three formulas:
 

Extinction ratio is a critically important parameter in the measurement of optical communication transmitters, as its value directly determines the quality of the communication signal. A higher extinction ratio indicates better logic discrimination at the receiver end, while a lower ratio suggests that the signal is more susceptible to interference, leading to an increased bit-error rate in the system.
The extinction ratio directly affects the sensitivity of the optical receiver. From the perspective of enhancing receiver sensitivity, we aim for the highest possible extinction ratio, as this helps minimize power penalties. However, a higher extinction ratio isn’t always better—excessively high ratios can actually increase pattern-dependent jitter in the laser. Therefore, for typical FP/DFB directly modulated lasers, the minimum required extinction ratio is 8.2 dB or higher, while EML electro-absorption lasers should maintain an extinction ratio of at least 10 dB. As a general guideline, it’s recommended that the actual extinction ratio be set 0.5 to 1.5 dB above the minimum requirement. This isn’t a rigid threshold, but rather a precautionary measure: going too far beyond the minimum could lead to excessive signal degradation after transmission, potentially resulting in bit errors or pushing channel costs beyond acceptable limits.
Eye-crossing ratio
The eye diagram cross ratio measures the relationship between the amplitude of the crossing point and the signal levels corresponding to "1" and "0." Consequently, different cross ratio values can convey distinct signal levels. Typically, a standard signal has a cross ratio of 50%, indicating that "1" and "0" signals each occupy exactly half of the vertical span. To measure this ratio, the statistical method shown in the figure below is employed. The cross level is calculated as the average value derived from the central window used for vertical statistics at the crossing point, and the proportional equation is as follows (where the "1" and "0" reference levels are determined by averaging the middle 20% of the eye diagram—specifically, calculating from 40% to 60%):
As the crosspoint ratio varies, it indicates the signal's ability to reliably convey either a '1' or a '0'. As shown in the figure below, the left-hand graph displays eye diagrams corresponding to different crosspoint ratios, which align with the associated 1 and 0 pulse signals on the right. Additionally, you can observe how the width of each pulse signal relates to the crosspoint ratio depicted in the diagram.

For typical signals, an evenly distributed representation of signal levels—both 1 and 0—is most common. Generally, the eye diagram crossing ratio is required to be 50%, meaning that the verification of related parameters is based on equal-length signal pulses representing both 1s and 0s. Consequently, by analyzing the distribution of the eye crossing ratio, it becomes possible to effectively measure and assess the relative amplitude loss caused by deviations in the signal levels of 1s and 0s. For instance, if the eye crossing ratio is excessively high—indicating an overabundance of 1-level signals—the ratio can then be used to evaluate signal errors, masking effects, and their corresponding thresholds. On the other hand, if the eye crossing ratio is too low—suggesting an excess of 0-level signals—it often leads to difficulties for the receiver in extracting the underlying frequency, potentially resulting in synchronization failure and, ultimately, a loss of timing recovery.

Calculation formula
Generally, the measurement of rise and fall times focuses primarily on the portion of the eye diagram between 20% and 80%. The rise time is illustrated in the figure below, where the transition signal's rising slope is calculated by converting the time interval between the left-hand crossing point (20%) and the right-hand crossing point (80%), using the following formula:
Fall time = Average (20% time point) - Average (80% time point)

Just like with the rise time, the shorter the fall time, the better the white block in the center of the eye diagram is revealed, resulting in improved signal transmission and a higher tolerance for bit-error rates.
Q Factor
The Q-factor is a parameter used to measure the signal-to-noise ratio of an eye diagram. It is defined as the ratio of signal power to noise power at the receiver’s optimal decision threshold and can be applied to digital signals of various formats and rates. The calculation formula is as follows: 

"Here, the difference between the average value of the '1' level and the average value of the '0' level is defined as the eye amplitude, while the sum of the root-mean-square (RMS) value of noise in the '1' signal and the RMS value of noise in the '0' signal is referred to as the total signal noise RMS."
The Q-factor comprehensively reflects the quality of an eye diagram. The higher the Q-factor, the better the eye diagram quality and the greater the signal-to-noise ratio. Typically, the Q-factor is influenced by factors such as noise, optical power, and whether the electrical signal maintains impedance matching from the source to the destination. Generally speaking, the thinner and smoother the 1-level line in the eye diagram, the higher the Q-factor. Under normal conditions—without optical attenuation—the Q-factor of the transmitted-side optical eye diagram should not fall below 12, while the Q-factor at the receiver side should remain above 6.
Average power
The average power, as reflected by the eye diagram, represents the mean value of the entire data stream. Unlike eye diagram amplitude measurements, which focus on peak-to-peak variations, the average power is calculated as the mean of the histogram. If the data encoding is functioning correctly, the average power should correspond to 50% of the total eye diagram amplitude.
Jitter
Jitter is timing noise in high-speed data transmission lines that leads to bit errors. As the system's data rate increases, the amplitude of jitter measured over several seconds remains roughly constant—but when measured over just a fraction of the bit period, it scales proportionally with the data rate, ultimately causing bit errors. Therefore, it’s crucial to minimize this type of correlated jitter within the system to enhance overall performance.
Jitter describes the horizontal fluctuations of a signal—specifically, its short-term deviation at a given moment from its ideal time position.
The image shows the intersection point of a highly jittery eye diagram, with its corresponding histogram appearing as a single-pixel-wide block projected onto the time axis. Ideally, this should be a single point, but due to horizontal fluctuations in the symbol waveform, it instead forms a small area.

The inherent jitter generated by the device is referred to as jitter output. Its primary sources can be categorized into two main types: random jitter (RJ) and deterministic jitter (DJ). Deterministic jitter itself can be further divided into periodic jitter, duty cycle distortion, inter-symbol interference, and crosstalk. DCD arises from asymmetries within the clock period, while ISI results from variations in edge response caused by data-dependent effects and dispersion. PJ originates from electromagnetic coupling due to periodic sources, such as power supply feedthrough, and crosstalk is induced by the pickup of other signals. A key characteristic of DJ is that its peak-to-peak value has upper and lower bounds. DCD and ISI are classified as bounded correlated jitter, whereas PJ and crosstalk fall under the category of unbounded correlated jitter. In contrast, RJ is considered unbounded uncorrelated jitter. Additionally, the overall jitter distribution is determined by the convolution of the probability density functions for RJ and DJ.
Analyzing jitter and identifying its specific causes will help minimize the impact of jitter during system design. At the same time, this analysis can determine how jitter affects the Bit Error Rate (BER), ensuring that the system’s BER remains below a certain maximum value—typically . Therefore, the root causes of jitter are visually illustrated in the figure below:

System Performance
When the received signal is affected simultaneously by intersymbol interference and noise, quantitative analysis of system performance becomes challenging. In such cases, an oscilloscope can typically be used to visually estimate the system's performance qualitatively by examining the "eye diagram" of the received signal. The eye diagram allows you to observe the effects of intersymbol interference and noise, as described below: 

The eye diagram provides valuable insights into the performance of digital signal transmission systems: it allows you to visually assess the extent of intersymbol interference and the strength of noise, offering a clear understanding of how these factors affect system performance and enabling an objective evaluation of a baseband system's quality. Additionally, it can guide adjustments to the receiver filter, helping to minimize intersymbol interference—for example:
The "eye" of the eye diagram—how wide it opens—directly reflects the strength of intersymbol interference. The wider the "eye" and the more symmetric and upright the eye diagram appears, the weaker the intersymbol interference; conversely, a narrower "eye" indicates stronger interference. When noise is present, it gets superimposed onto the signal, causing the lines in the eye diagram to appear blurred and indistinct. If intersymbol interference is also present, the "eye" will close even further, shrinking significantly compared to its appearance without interference. Compared to an ideal eye diagram free of both noise and interference, the originally crisp, well-defined thin lines now transform into broader, more hazy bands—and these bands lose their neat alignment as well. The greater the noise, the wider and fuzzier the lines become; similarly, the stronger the intersymbol interference, the more distorted and asymmetrical the eye diagram appears.
Theoretical analysis yields the following key conclusions, which should serve as a reference in practical applications when discussing system performance based on the eye diagram.
(1) The optimal sampling moment should be when the "eye" is widest open.
(2) The sensitivity to timing errors can be determined by the slope of the eye diagram's diagonal edge. The steeper the slope, the more sensitive the system is to timing errors.
(3) At the sampling instant, the vertical height of the shaded areas on the upper and lower branches of the eye diagram represents the maximum signal distortion.
(4) The horizontal axis position at the center of the eye diagram should correspond to the decision threshold level.
(5) At the sampling moment, the distance from the closest trace in each of the upper and lower branches to the threshold represents the noise margin for the corresponding level. If the instantaneous noise value exceeds this margin, an erroneous decision may occur.
(6) For a receiving system that uses signal zero-crossing averaging to obtain timing information, the size of the region where the eye diagram's tilted branches intersect the horizontal axis indicates the range of variation in the zero-point location. This variation range significantly impacts the accuracy of timing information extraction.
Bit Error Rate
In digital circuit systems, the transmitting end sends out multiple bits of data. Due to various factors, the receiving end may encounter some erroneous bits—commonly referred to as bit errors. The ratio of the number of erroneous bits to the total number of bits transmitted is known as the Bit Error Rate, or BER for short. The BER is the most critical parameter for characterizing the performance of digital circuit systems. In communication circuits operating at gigahertz-level bit rates—such as Fibre Channel, PCIe, SONET, and SATA—it is typically required that the BER be less than or equal to [a specific value]. When the BER is high, the communication system becomes inefficient and its performance becomes unstable. Factors influencing the BER include jitter, noise, channel attenuation, and the signal's bit rate, among others.
In the Bit Error Rate (BER) test, the pattern generator produces billions of data bits and sends them to the input device, where they are then received at the output end. The BER analyzer subsequently compares the received data bit by bit with the original transmitted data, identifying which bits were received incorrectly. Based on this comparison, it calculates the BER over a specific period of time. To ensure the accuracy of the BER test, we use the actual eye diagram obtained from our reference test as a benchmark for generating the final BER plot.
The BER plot is a function of the bit error rate at specific time positions, BER(t), and is commonly referred to as a BERT scan or bathtub curve. Simply put, it represents the BER measured at various times t relative to a reference clock—either the signal transmitter’s clock or a clock recovered from the received signal, depending on the system being tested. Referencing the eye diagram mentioned above, the relationship between eye opening and the bit error rate, along with its corresponding BER plot, is illustrated below: 

In the two figures above, the BER plot shares the same time axis as the eye diagram, with the edges of the eye diagram aligning on either side, while the sampling points are positioned at the center. At a given BER, the distance between the curves reflects the degree of eye opening corresponding to that BER. When the sampling points are close to the intersection, jitter can cause the BER to rise, reaching a maximum of 0.5.
Generate discussion
Generally speaking, generating an eye diagram requires measuring a large amount of data and then reconstructing the signal from that data. In oscilloscope-based eye diagram measurements, after initial data acquisition, the oscilloscope’s memory stores a complete record of the captured data. Next, either hardware or software is used to recover or extract the clock signal, aligning it with the incoming data stream bit by bit. By triggering on the recovered clock, multiple 1 UI (unit interval, equivalent to one clock cycle) signals within the data stream are overlapped—essentially superimposing the waveform of each individual bit. This process ultimately yields the characteristic eye diagram.
As shown in the formation diagram above, an eye diagram is created by triggering the signals in the data record at equal intervals using the recovered clock signal, and then superimposing these captured unit UI waveforms on top of one another.
Through the analysis above, recovering the clock signal from the collected data is crucial for generating the eye diagram. Therefore, the relationship between the eye diagram and CLK is as follows:
(1) The CLK of a sampling oscilloscope can typically be either a user-provided clock, a recovered clock, or a code-synchronization signal synchronized with the data signal itself.
(2) The real-time oscilloscope completes the sampling of all data with a single trigger, eliminating the need for additional synchronization or trigger signals. Typically, the clock is recovered using a software-based PLL method.
Therefore, it is necessary here to introduce the function of the clock recovery circuit (refer to the English version below):
Clock and Data Recovery (CDR) circuit functions:
First, recover the clock signal (CR) from the received data stream (input signal).
Use the CR to make timing and amplitude-level decisions on the incoming signal.
Regenerate the data stream (DR), ensuring its timing and amplitude characteristics are synchronized with the recovered clock (CR) or the regenerated system clock.
Translated as:
(1) Recover the original sampling clock signal from the received data stream
(2) Use the recovered clock signal to measure performance metrics of the input signal, such as timing and amplitude levels.
(3) Reconstruct the data stream based on the input signal's characteristics, such as timing and amplitude, and synchronize it with either the recovered clock signal or the newly generated system clock.
Currently, most clock recovery methods rely on phase-locked loop (PLL)-based techniques. A PLL consists of three fundamental components: a phase detector, a loop filter, and a voltage-controlled oscillator (VCO). The basic principle is illustrated in the block diagram below: 

Overall, the importance of phase-locked loops for clock recovery can be seen in the following aspects:
(1) Fully integrated and requiring no external reference clock signal
(2) Ensure that the clock signal is synchronized with the data.
(3) Provides monitoring of the clock signal and issues an alert when the phase-locked loop loses lock.
(4) Optimizing Bit Error Rate—Adjusting the Clock Phase for Data Signals
Refer to the following article:
Phase-Locked Loop (PLL) required for clock recovery:
"Fully integrated and does not require an external reference clock."
Ensure the clock is aligned with the middle of a data word.
"Monitors the CR and provides a Loss-of-Lock (LOL) alarm when the PLL loses lock."
For Optimized Bit Error Rate (BER) – adjust the clock phase relative to the data signal.
The instruments used for testing high-speed serial data signals—specifically eye diagrams and jitter measurements—all employ a phase-locked loop (PLL)-based clock recovery method. In particular, real-time oscilloscopes typically rely on software PLLs to recover the reference clock, while sampling oscilloscopes and bit-error-rate testers utilize hardware PLLs for clock recovery. By employing software-based clock recovery, these tools can capture long-duration data waveforms, compare the incoming data bits against the recovered clock one by one, and thereby perform precise eye diagram, jitter, and bit-error-rate tests. This approach allows for detailed analysis of every individual bit in the captured serial data stream, eliminating inaccuracies caused by trigger-induced jitter or hardware-clock recovery jitter. As a result, both CDR jitter and trigger jitter are theoretically reduced to zero.
Currently, Tektronix offers the following eye diagram generation solution:

(1) Data recovery clock (CDR) and eye diagram template testing can be categorized into hardware CDR (PLL) and software CDR (PLL + others).
(2) Measuring eye diagram parameters such as eye height and eye width
(3) Based on the data measured above, plot the corresponding graphs:
Jitter: Trends, Spectrum
Histogram, Bathtub Curve
In a real-time oscilloscope, the continuous bit-eye diagram generation method is typically used. First, the oscilloscope captures a long sequence of consecutive data waveforms; then, software-based CDR (Clock Data Recovery) is employed to recover the clock signal, which is subsequently used to slice each bit’s waveform—starting from the 1st, 2nd, 3rd, and continuing all the way up to the (n-1)th and nth bits. Finally, all the individual bit waveforms are overlapped to produce the eye diagram. The real-time eye diagram generation process works as follows:
Software Clock Recovery
Eye Diagram Parameter Measurement
Comprehensive range of standard parameter measurements tailored for specific applications, including amplitude, timing, and jitter
Low jitter, low noise
Single-trigger event, rather than the multiple-trigger events used in the ET method—where continuous sampling occurs after a single trigger—helps reduce jitter and noise that might otherwise be introduced.
"Supports different clock recovery models"
Phase-Locked Loop (PLL)