What a time interval measurement is
The core of a modern counter is not counting pulses but time stamping. Every time the input signal crosses the set trigger level, the instrument records that instant relative to its internal time base, with a granularity equal to the single-shot time resolution (better than 7 ps on the CNT-104S and CNT-104R, 14 ps on the CNT-102, 35 ps on the CNT-91/91R, 70 ps on the CNT-90 and 100 ps on the CNT-90XL). A time interval is the difference between two time stamps. Take an edge on channel A as start and an edge on channel B as stop and you measure the propagation delay or phase difference from A to B; take adjacent rising edges on one channel as start and stop and you measure the period; take a rising edge as start and the following falling edge as stop and you measure pulse width.
Frequency measurement is an extension of the same idea: count N periods within the gate time and divide by the difference between the first and last time stamp. Frequency resolution and time resolution on one instrument are therefore tied together, since a finer time stamp yields more digits of frequency at the same gate time. Conversely, a time interval happens only once and there is no gate to lengthen, which is the most fundamental difference between it and a frequency measurement.
Multichannel instruments can also do one start against several stops. The CNT-104S supports 1 start and 3 stops, which is used for time-of-flight in physics experiments and for delay verification in multi-output trigger systems. All the channels share one time axis, so the time differences between channels hold intrinsically and no correction for offsets between instruments is needed afterwards.
TIE, period jitter and cycle-to-cycle jitter
Jitter is the deviation of a clock edge from the instant at which it should have appeared, and the three definitions differ only in what you take as should. Picture a continuous series of time stamps t₁, t₂, t₃ and so on, each of them a rising edge.
Period jitter: each period Pₙ = tₙ₊₁ − tₙ compared with the mean period. It describes how much longer or shorter an individual period can be, it is the quantity most used in setup and hold analysis of digital circuits, and it is normally reported as σ (rms) and peak-to-peak.
Cycle-to-cycle jitter: the difference between two adjacent periods, Pₙ₊₁ − Pₙ. It is insensitive to slow frequency drift and reflects abrupt changes from one period to the next, which suits looking at PLL switching and coupled power supply noise. Note that it has to be computed from consecutive adjacent periods; if periods are missing from the measurement, the quantity has no meaning.
TIE (time interval error): the difference between each edge tₙ and the ideal clock instant n×P₀, where the ideal clock can be fitted from the mean period of the whole record. TIE is an accumulated quantity, the running sum of period jitter, so it exposes long-term drift, slow modulation and PLL tracking error, and it is the jitter definition that appears most often in communication interface and synchronization standards. The three are not three phenomena but three statistical views of the same set of time stamps, and as long as the data is continuous they convert into one another.
The measurement floor: single-shot resolution and trigger noise
Every time stamp carries two kinds of error. The first comes from the interpolation circuit inside the instrument and is the single-shot time resolution on the data sheet. The second comes from triggering: if voltage noise moves the instant at which the signal crosses the trigger level, the time stamp moves with it. The timing error from trigger noise is approximately the noise voltage divided by the slew rate of the edge, so a slower edge, a smaller amplitude or more noise all mean a larger timing error. This is why jitter measurements use a 50 Ω input, use as much of the signal amplitude as possible, set the trigger level at the steepest part of the edge, and avoid long unterminated cables.
The two errors combine as a root sum of squares and form the measurement floor of the instrument. When the jitter of the device under test is of the same order as that floor, the σ you read is mostly the contribution of the instrument; only when signal jitter is clearly above the floor does the reading represent the signal. A rough rule is that the floor should be several times smaller than the value you want to measure, which is why evaluating low-jitter clocks and oscillators favors the CNT-104S and CNT-104R with their better than 7 ps single-shot resolution, while the 35 ps CNT-91/91R suits general clock, delay and period measurement.
A time interval cannot be improved by lengthening the gate, but if the event repeats you can average several measurements: averaging N times lowers the random part of the floor by roughly √N. That is the basis of the statistical measurement discussed in the next section, and it explains why measuring fast is a real resolution advantage for jitter work and not merely a saving of time.
Why large sample counts matter: mean, standard deviation and Allan deviation
Jitter is a random process, so a single time interval reading means nothing and the distribution is what matters: the mean tells you about systematic delay or phase offset, the standard deviation σ is the rms jitter, and the minimum and maximum give peak-to-peak. Peak-to-peak in particular depends on sample count, because the more samples you take the better the chance of catching a rare outlier, which is why standards that quote a peak-to-peak value normally also state the sample count or measurement time.
How many samples you can accumulate is set by the measurement rate and memory depth of the instrument. The CNT-91/91R runs at 250,000 measurements per second with up to 3.5M results of internal memory; the CNT-104S runs at 20 million per second; the CNT-104R holds up to 32M samples internally. On a CNT-104R a single capture can therefore cover tens of millions of consecutive periods, which is enough for a credible histogram and for finding an outlier that occurs once in ten thousand.
For long-term stability the statistical tool changes to Allan deviation (ADEV): the data is divided into segments of averaging time τ and the statistic is formed from the differences between the mean frequencies of adjacent segments. Standard deviation grows without bound in the presence of drift, whereas ADEV separates white noise, flicker noise and drift, and it is the standard language of oscillator and reference specifications. The short-term stability of the 6688, for example, is quoted as ADEV 5×10⁻¹² (τ=1 s / 10 s) and that of the 6689 as 3×10⁻¹¹ / 1×10⁻¹¹. Measuring at that level requires a counter whose time base is more stable than the device under test, which is the subject of "Laboratory Time and Frequency References: GNSS-disciplined Rubidium and Standalone Sources" Laboratory Time and Frequency References: GNSS-disciplined Rubidium and Standalone Sources.
Why gapless measurement matters
A traditional counter works in a cycle of measure, process, measure again, with a stretch of time in between during which it is not watching the signal. For an average frequency that does not matter, but for jitter it is fatal: cycle-to-cycle jitter needs adjacent periods and TIE needs the accumulation of every edge, so periods lost in the dead time leave both quantities undefined. What you get is a sample of the signal, and sampling systematically misses short transients.
Gapless measurement means putting a time stamp on every trigger edge and writing the stream into memory without interruption. The four channels of the CNT-104S do this in parallel with a 50 ns sampling interval per channel and a total rate of 20 million per second, and the CNT-102 does it on 2 channels at 1 million per second. With a continuous series of time stamps, period jitter, cycle-to-cycle jitter, TIE, the modulation domain plot of frequency against time and the histogram all come out of the same capture, and you can go back and identify which period went wrong.
The CNT-90 and CNT-91 families do not time stamp every period, but with TimeView software they perform modulation domain analysis at 250 kSa/s free-running or an equivalent 100 MSa/s in repetitive sampling, recording how frequency or time interval varies over time into 1.9M (CNT-91/91R) or 375k (CNT-90/90XL) results of memory. That is sufficient for trend work such as periodic modulation, PLL lock behavior and sweep linearity. For cycle-to-cycle statistics on every single period, choose the gapless architecture.
Counter and oscilloscope: two tools for the same job
An oscilloscope records voltage against time at a fixed sample rate and interpolates the edge instant from adjacent sample points, so its time resolution is limited by sample rate, vertical noise and the interpolation algorithm. Its memory holds the whole waveform, including long flat stretches that carry no information, so the number of consecutive periods it can cover is comparatively limited. Its advantage is that it shows shape: overshoot, ringing, crosstalk and the marks power supply noise leaves on an edge are visible only on an oscilloscope.
A counter records one time stamp when an edge crosses the trigger level, so all of its memory holds meaningful events, which lets it record millions of consecutive periods at ps resolution over spans from microseconds to hours and output statistics and ADEV directly. Its limitation is that it cannot see the waveform and cannot tell whether trigger noise came from the signal or from the measurement setup, so trigger settings and connection quality are the responsibility of the user.
In practice the two go together: use the oscilloscope to confirm edge quality and where to put the trigger level, and the counter to accumulate the large sample counts needed for jitter statistics and long-term stability. When the task is comparing the phase relationship of several clocks at once, a multichannel gapless counter (CNT-104S, CNT-102) is the most direct tool. For the trade-offs between models see "Frequency Counter Selection Guide: Resolution, Channels and Time Base" Frequency Counter Selection Guide: Resolution, Channels and Time Base.