Timing and rasterization

Timing and rasterization#

TL;DR

  • Every event time in a .seq file is quantized to one of four rasters declared in [DEFINITIONS]: RF, gradient, ADC and block duration. The Opts defaults are 2 µs for the RF and ADC rasters and 20 µs for the gradient and block-duration rasters.

  • A block’s duration is independent of the extent of its events, subject to being at least as long. A block longer than its events is a delay and is not reported; a gradient that ends at a nonzero amplitude before its block ends is reported by check_timing as GRADIENT_END_NONZERO.

  • When the ADC window must coincide with the readout flat top, the smallest admissible dwell for \(N\) samples is \(d_{\min} = a\,r/\gcd(N, r)\), with \(a\) the ADC raster, \(g\) the gradient raster and \(r = g/a\). At the default rasters, 128 samples therefore admit at most 100 kHz of receiver bandwidth and 100 samples admit 500 kHz.

  • calc_adc_timing() returns the achieved dwell, so the achieved bandwidth 1 / dwell may be lower than the one requested; the readout modules report it as bandwidth_hz.

  • Raster addressability and the dead and ringdown times of the transmit and receive chains are separate constraints, and check_timing reports both. check_timing and the constraint checks establish different properties and are separate calls.

A sequencer starts and stops events on a discrete time grid. A time that is not an integer multiple of the grid period cannot be addressed, so every event time in a .seq file is quantized before it is written.

The four rasters#

[DEFINITIONS] declares four raster periods, and each class of time is quantized to one of them:

Raster

Quantizes

RF raster

RF waveform sample spacing, RF event delays and centre times

Gradient raster

arbitrary-gradient sample spacing, gradient delays, trapezoid rise, flat and fall times

ADC raster

ADC dwell time and the ADC event delay

Block-duration raster

the duration of every block

Opts holds all four. The defaults are 2 µs for the RF and ADC rasters and 20 µs for the gradient and block-duration rasters, but they are properties of the system the sequence is designed against, and a file records the values it was written with.

round_to_raster() and ceil_to_raster() quantize a single interval. Rounding up rather than to nearest is the usual choice for a delay that must not fall below a computed minimum.

Block duration against event extent#

The duration recorded for a block is independent of the extent of its events, subject to being at least as long. The difference is dead time on every channel, which is how an echo time or a repetition time is realized.

Two consequences follow. A block longer than its events is legal and silent: no check reports it, because it is a delay. A gradient that ends at a nonzero amplitude before its block ends is not silent, because the amplitude over the remaining interval is undefined; check_timing reports it as GRADIENT_END_NONZERO.

Coupling between the ADC and gradient rasters#

An acquisition window is num_samples * dwell long. The dwell is quantized to the ADC raster, and the readout gradient’s flat top is quantized to the gradient raster. Whenever the samples must be taken at constant gradient amplitude the window has to coincide with the flat top, and both conditions apply at once, and they constrain the achievable receiver bandwidth.

Write \(a\) for the ADC raster, \(g\) for the gradient raster and \(r = g / a\), an integer for any realistic pair. Admissible dwell times are the multiples \(d = k a\) for which \(N d\) is a multiple of \(g\), and the smallest is

\[ d_{\min} = \frac{a\,r}{\gcd(N, r)} . \]

The sample count therefore participates in setting the maximum receiver bandwidth, alongside the rasters themselves. At the default rasters (\(a = 2\ \mu\mathrm{s}\), \(g = 20\ \mu\mathrm{s}\), \(r = 10\)), a readout of 128 samples has \(\gcd(128, 10) = 2\) and admits no dwell shorter than 10 µs, a receiver bandwidth of 100 kHz; a readout of 100 samples has \(\gcd(100, 10) = 10\) and admits 2 µs, a bandwidth of 500 kHz. A request for 250 kHz is met in the second case and not in the first, and nothing about the first prescription is otherwise unusual.

../../_images/bandwidth_against_sample_count.png

The highest receiver bandwidth each sample count admits at the default rasters, over one range of readout lengths. The four levels are the four values \(\gcd(N, r)\) takes for \(r = 10\), and a request is met only where the ceiling reaches it.#

calc_adc_timing() performs this search and returns the dwell together with the acquisition duration, so the achieved bandwidth is 1 / dwell and may be lower than the one requested. The readout modules report what they achieved as bandwidth_hz rather than echoing the request.

Dead times and ringdown#

Raster addressability and the settling times of the transmit and receive chains are separate constraints. Three intervals in Opts state the second: rf_dead_time before a pulse, rf_ringdown_time after it, and adc_dead_time after an acquisition window. None of the three is a quantization constraint, so a sequence can satisfy every raster and still violate them.

check_timing reports both classes. Raster violations appear as RASTER; chain violations appear as RF_DEAD_TIME, RF_RINGDOWN_TIME, ADC_DEAD_TIME and POST_ADC_DEAD_TIME. The same pass also reports BLOCK_DURATION_MISMATCH, NEGATIVE_DELAY, GRADIENT_START_DELAY, GRADIENT_END_NONZERO, the soft-delay consistency conditions, and ADC_SAMPLES_DIVISOR where a vendor requires the sample count to be divisible by a fixed factor.

A sequence whose gradient waveforms are within every amplitude and slew limit can still be unplayable because one delay is off the raster. The constraint checks of Gradient, PNS and SAR constraints and check_timing establish different properties and are separate calls.

See also#