Eye diagram

An eye diagram is the display made by overlaying many symbol periods of a digital signal on one time axis, each trace starting at the same point of the symbol clock. For a binary (NRZ) signal the traces of all the bit sequences leave an open region between the one and zero levels that looks like an eye. The height of that opening is the margin against noise at the instant the receiver decides each bit, its width the margin against errors in the timing of that instant, and its shape shows what the transmitter, the fiber and the receiver have done to the signal: limited bandwidth, chromatic dispersion, noise and jitter. An optical eye is displayed after conversion to an electrical signal, in units of optical power.

How an eye is captured

The signal is driven with a long pseudo-random bit sequence (PRBS) so that every short pattern of bits appears. A PRBS of order $n$ contains every $n$-bit pattern except all zeros, so its longest run of ones is $n$ bits: PRBS7 repeats every 127 bits, and PRBS31 every 2,147,483,647 bits, 0.21 s at 10.3125 Gbit/s. Long runs of identical bits expose low-frequency effects such as the droop of AC-coupled parts, which a short pattern never excites.

A sampling oscilloscope with an optical input takes one sample per trigger, stepping the sampling time across the symbol period, and builds up the eye from millions of samples; the trigger comes from the pattern generator's clock or from a clock recovered from the data. Real-time oscilloscopes capture a continuous record and fold it into an eye using a clock recovered in software. For compliance measurements the signal first passes through a reference receiver of standardized response, so that every laboratory sees the same eye: a fourth-order Bessel-Thomson filter with a −3 dB bandwidth of 0.75 times the bit rate for NRZ eye masks (7.73 GHz at 10.3125 Gbit/s), and half the symbol rate for PAM4 measurements of TDECQ (26.5625 GHz at 53.125 GBd). The unit interval (UI), one symbol period, is 97.0 ps at 10.3125 Gbit/s, 38.8 ps at 25.78125 Gbit/s and 18.8 ps at 53.125 GBd.

Reading the eye

Average power, extinction ratio and OMA are tied together. With a linear extinction ratio $r$ and average power $P_{\text{avg}}$, the one and zero levels are $2P_{\text{avg}}r\mathrm{/}(r+1)$ and $2P_{\text{avg}}\mathrm{/}(r+1)$, so

$$\text{OMA}=2P_{\text{avg}}\frac{r-1}{r+1}\mathrm{.}$$

A transmitter at 0 dBm average power with a 5 dB extinction ratio has levels of 1.52 and 0.48 mW and an OMA of 1.04 mW (+0.17 dBm). The extinction ratio is sensitive to the zero level, so the oscilloscope's reading with no light at its input, its dark level, has to be calibrated out before the ratio is measured; an uncorrected offset of a few percent of the one level changes a high extinction ratio by decibels.

Jitter closes the eye from the sides. Because random jitter has no peak value, total jitter is quoted at a target bit error ratio, in the dual-Dirac model as the deterministic part plus 14.07 times the rms random part at ${10}^{-12}$; the timing jitter entry works an example.

What the shape shows

From the eye to a bit error rate

With Gaussian noise on the two levels and the decision threshold placed optimally between them, the bit error rate follows from the Q factor alone:

$$\text{BER}=\frac{1}{2}\mathrm{erfc}\text{\hspace{0.17em}⁣}\left(\frac{Q}{\sqrt{2}}\right),$$

which gives $1.0\times {10}^{-9}$ at $Q=6.0$, $1.0\times {10}^{-12}$ at $Q=7.03$ and $1.0\times {10}^{-3}$ at $Q=3.1$. The last is close to the error rates before correction that modern forward error correction accepts ($2.4\times {10}^{-4}$, or $Q=3.5$, for the KP4 code of 400G Ethernet), which is why the eyes of links protected by FEC may look far worse than those of the older links that had to reach ${10}^{-12}$ unaided. The Gaussian assumption fails for the dominant noise of amplified links (ASE beat noise follows a chi-squared distribution) and for pattern-dependent closure, so a Q read off an eye is a figure for comparison rather than a prediction; the measured error rate decides.

Mask tests

Transmitter standards test the eye against a mask rather than a Q. IEEE 802.3 and ITU-T G.957 and G.959.1 define a polygonal keep-out region at the center of the eye, and regions above the one level and below the zero level, scaled to the unit interval and to the one and zero levels, and a transmitter passes if no sample, or no more than a stated fraction of samples, falls inside them. The mask margin is how far the mask can be enlarged before that limit is reached, a single figure for how much room a transmitter has. The mask is applied to the eye seen through the reference receiver described above.

PAM4 eyes

A PAM4 signal has four levels and shows three eyes stacked one above another. Each is one third of the outer opening, which costs $10{\log }_{10}3$ = 4.8 dB against NRZ at the same outer modulation amplitude, and the three must be evenly spaced, since a compressed upper eye closes first. A mask on a raw PAM4 eye says little, because real receivers equalize the signal before deciding, so PAM4 transmitters are scored by TDECQ, a penalty computed from the captured waveform through the reference receiver and a reference equalizer. The PAM4 Eye & TDECQ Explorer builds such an eye from adjustable impairments and computes TDECQ as they change.

Eye diagrams describe intensity-modulated signals received by direct detection. A coherent signal carries its data in the phase and amplitude of the optical field, and is displayed as a constellation diagram and judged by its error vector magnitude (modulation format).

How this fits into the full path from host bits to light and back, with the 100G lane arithmetic, is traced in Bits to Light.

Common questions

What is an eye diagram?

A display of a digital signal in which many symbol periods are overlaid on one time axis, aligned to the symbol clock. The open region between the levels, the eye, shows how much noise and timing error the signal can tolerate at the receiver's decision point.

What does an open eye mean?

That the one and zero levels are well separated compared with the noise on them and that the transitions are well defined in time, so that a receiver sampling at the center of the eye makes few errors. A closed eye means the noise, jitter or intersymbol interference is large enough to cause errors.

What are eye height and eye width?

Eye height is the vertical opening at the center of the eye after the noise on the levels is allowed for, commonly the distance from three standard deviations below the one level to three above the zero level. Eye width is the horizontal opening between the crossings, less three standard deviations of the jitter on each.

How is an eye diagram measured on an optical signal?

The transmitter is driven with a pseudo-random pattern, its light is converted to an electrical signal by the optical input of a sampling or real-time oscilloscope, passed through a standardized reference receiver, and sampled in step with the symbol clock or a clock recovered from the data. The oscilloscope overlays the samples into the eye and reads its levels, noise, jitter and mask margin.

What is an eye mask test?

A test in which the eye must stay clear of keep-out regions defined by the standard for the interface: a polygon in the center of the eye and bands above and below it. The transmitter passes if no sample, or fewer than a stated fraction, fall inside them.

References: G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley, 2010), section 4.5 (Q factor and BER). IEEE Std 802.3, clauses 52, 121, 122 and 124 (transmitter eye masks and TDECQ). ITU-T G.957 and G.959.1 (eye masks and reference receivers for optical interfaces). D. Derickson (ed.), Fiber Optic Test and Measurement (Prentice Hall, 1998), chapter 8. M. P. Li, Jitter, Noise, and Signal Integrity at High-Speed (Prentice Hall, 2007).