.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "generated/gallery/01-pulseq-basics/01_fid.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_generated_gallery_01-pulseq-basics_01_fid.py: ==================== Free induction decay ==================== The smallest complete Pulseq sequence is a pulse-acquire experiment: one excitation pulse followed by one acquisition window. This first lesson of the course builds it and introduces the objects every later lesson extends: the system limits against which a factory designs an event, the RF and ADC events, the blocks in which events are played, the timing check, and the ``.seq`` file. A Bloch simulation of the stored pulse relates the transverse magnetisation to the flip angle. The representation these objects belong to is described in :doc:`/explanations/pulseq/events-and-blocks`. Learning objectives ------------------- After this lesson, you should be able to: - define system limits, rasters and dead times; - create a hard RF pulse and an ADC event, and relate the number of samples, the dwell time and the receiver bandwidth; - place events in blocks and set a repetition time with a delay; - read a pulse-sequence diagram of the result; - check the sequence timing and write the sequence to a ``.seq`` file. .. GENERATED FROM PYTHON SOURCE LINES 29-39 .. GENERATED FROM PYTHON SOURCE LINES 40-47 System limits ------------- Every factory solves its waveforms against a set of limits, and every event time is quantized to the rasters those limits declare. The dead times bound what the transmit and receive chains can do rather than what the sequencer can address, and the timing check reports them separately. .. GENERATED FROM PYTHON SOURCE LINES 47-62 .. code-block:: Python import numpy as np import pypulseqpp as pp system = pp.Opts( max_grad=32.0, grad_unit="mT/m", max_slew=130.0, slew_unit="T/m/s", rf_dead_time=100e-6, rf_ringdown_time=20e-6, adc_dead_time=10e-6, ) .. GENERATED FROM PYTHON SOURCE LINES 63-71 Two events ---------- A rectangular pulse of constant amplitude, and an acquisition window of 8192 samples. The dwell time is the sampling interval, and its reciprocal is the receiver bandwidth; :func:`~pypulseqpp.calc_adc_timing` moves a requested dwell onto the ADC raster and lands the acquisition duration on the gradient raster. The timing check requires both. .. GENERATED FROM PYTHON SOURCE LINES 71-99 .. code-block:: Python FLIP_ANGLES_DEG = (10.0, 30.0, 60.0, 90.0) pulses = [ pp.make_block_pulse( flip_angle=np.deg2rad(flip_angle), duration=200e-6, delay=system.rf_dead_time, system=system, use="excitation", ) for flip_angle in FLIP_ANGLES_DEG ] dwell, acquisition = pp.calc_adc_timing( 8192, 32e-6, grad_raster_time=system.grad_raster_time, adc_raster_time=system.adc_raster_time, ) adc = pp.make_adc( num_samples=8192, dwell=dwell, delay=system.adc_dead_time, system=system ) print( f"dwell {dwell * 1e6:.0f} us, receiver bandwidth {1e-3 / dwell:.1f} kHz, " f"acquisition {acquisition * 1e3:.1f} ms" ) .. rst-class:: sphx-glr-script-out .. code-block:: none dwell 40 us, receiver bandwidth 25.0 kHz, acquisition 327.7 ms .. GENERATED FROM PYTHON SOURCE LINES 100-110 Two blocks ---------- A block holds at most one event per channel, and the events in it start together on the block's clock. Blocks are played back to back, so the acquisition begins when the pulse's block ends. One repetition per flip angle. A block lasts as long as its longest event, so a delay event longer than the acquisition window in the acquisition block sets the repetition time. .. GENERATED FROM PYTHON SOURCE LINES 110-119 .. code-block:: Python seq = pp.Sequence(system=system) for pulse in pulses: seq.add_block(pulse) seq.add_block(adc, pp.make_delay(500e-3)) ok, errors = seq.check_timing() print(f"timing {ok}, {seq.num_blocks} blocks, {seq.duration()[0]:.2f} s") .. rst-class:: sphx-glr-script-out .. code-block:: none timing True, 8 blocks, 2.00 s .. GENERATED FROM PYTHON SOURCE LINES 120-125 Sequence diagram ---------------- The solid trace is one repetition; the shaded traces are the others, which differ only in the amplitude of the pulse. .. GENERATED FROM PYTHON SOURCE LINES 125-128 .. code-block:: Python seq.paper_plot() .. image-sg:: /generated/gallery/01-pulseq-basics/images/sphx_glr_01_fid_001.png :alt: 01 fid :srcset: /generated/gallery/01-pulseq-basics/images/sphx_glr_01_fid_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 129-136 Transverse magnetisation against flip angle ------------------------------------------- :func:`~pypulseqpp.sim_rf` integrates the Bloch equations over the pulse the sequence holds. On resonance a rectangular pulse rotates the magnetisation by its nominal flip angle, so the transverse component follows :math:`|M_{xy}| = \sin\alpha`. .. GENERATED FROM PYTHON SOURCE LINES 136-153 .. code-block:: Python on_resonance = [] for pulse in pulses: mz_xy, frequency = pp.sim_rf(pulse)[1:3] on_resonance.append(abs(mz_xy[int(np.argmin(abs(frequency)))])) .. image-sg:: /generated/gallery/01-pulseq-basics/images/sphx_glr_01_fid_002.png :alt: 01 fid :srcset: /generated/gallery/01-pulseq-basics/images/sphx_glr_01_fid_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 154-159 Writing the file ---------------- The definitions are written beside the block table and are what a reconstruction reads to interpret the acquisition. .. GENERATED FROM PYTHON SOURCE LINES 159-167 .. code-block:: Python from pathlib import Path from tempfile import mkdtemp seq.set_definition("Name", "fid") path = Path(mkdtemp()) / "fid.seq" seq.write(str(path)) print(path.read_text().splitlines()[0]) .. rst-class:: sphx-glr-script-out .. code-block:: none # Pulseq sequence file .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.237 seconds) .. _sphx_glr_download_generated_gallery_01-pulseq-basics_01_fid.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: 01_fid.ipynb <01_fid.ipynb>` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: 01_fid.py <01_fid.py>` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: 01_fid.zip <01_fid.zip>` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_