3D Spectral Image

Suhas Somnath

10/12/2018

This example illustrates how a 3D spectral image would be represented in the Universal Spectroscopy and Imaging Data (USID) schema and stored in a Hierarchical Data Format (HDF5) file, also referred to as the h5USID file.

This document is intended as a supplement to the explanation about the USID model

Please consider downloading this document as a Jupyter notebook using the button at the bottom of this document.

Prerequisites:

We recommend that you read about the USID model

We will be making use of the pyUSID package at multiple places to illustrate the central point. While it is recommended / a bonus, it is not absolutely necessary that the reader understands how the specific pyUSID functions work or why they were used in order to understand the data representation itself. Examples about these functions can be found in other documentation on pyUSID and the reader is encouraged to read the supplementary documents.

Import all necessary packages

The main packages necessary for this example are h5py, matplotlib, and sidpy, in addition to pyUSID:

import subprocess
import sys
import os
import matplotlib.pyplot as plt
from warnings import warn
import h5py

%matplotlib notebook

def install(package):
    subprocess.call([sys.executable, "-m", "pip", "install", package])


try:
    # This package is not part of anaconda and may need to be installed.
    import wget
except ImportError:
    warn('wget not found.  Will install with pip.')
    import pip
    install('wget')
    import wget

# Finally import pyUSID.
try:
    import pyUSID as usid
    import sidpy
except ImportError:
    warn('pyUSID not found.  Will install with pip.')
    import pip
    install('pyUSID')
    import sidpy
    import pyUSID as usid

h5USID File

For this example, we will be working with a Band Excitation Piezoresponse Force Microscopy (BE-PFM) imaging dataset acquired from advanced atomic force microscopes. In this dataset, a spectra was collected for each position in a two dimensional grid of spatial locations. Thus, this is a three dimensional dataset that has been flattened to a two dimensional matrix in accordance with Universal Spectroscopy and Imaging Data (USID) model.

As mentioned earlier, this dataset is available on the USID repository and can be accessed directly as well. Here, we will simply download the file using wget:

Download from GitHub

Similarly the corresponding h5USID dataset is also available on the USID repository. Here, we will simply download the file using wget:

h5_path = 'temp.h5'
url = 'https://raw.githubusercontent.com/pycroscopy/USID/master/data/BELine_0004.h5'
if os.path.exists(h5_path):
    os.remove(h5_path)
_ = wget.download(url, h5_path, bar=None)

Look at file contents

Lets open the file and look at its contents using sidpy.hdf_utils.print_tree()

h5_file = h5py.File(h5_path, mode='r')
sidpy.hdf_utils.print_tree(h5_file)

/
├ Measurement_000
  ---------------
  ├ Channel_000
    -----------
    ├ Bin_FFT
    ├ Bin_Frequencies
    ├ Bin_Indices
    ├ Bin_Step
    ├ Bin_Wfm_Type
    ├ Excitation_Waveform
    ├ Noise_Floor
    ├ Position_Indices
    ├ Position_Values
    ├ Raw_Data
    ├ Spatially_Averaged_Plot_Group_000
      ---------------------------------
      ├ Bin_Frequencies
      ├ Mean_Spectrogram
      ├ Spectroscopic_Parameter
      ├ Step_Averaged_Response
    ├ Spectroscopic_Indices
    ├ Spectroscopic_Values
    ├ UDVS
    ├ UDVS_Indices

Access the Main Dataset

We can access the first Main dataset by searching for a dataset that matches its given name using the convenient function - pyUSID.hdf_utils.find_dataset(). Knowing that there is only one dataset with the name USID_Alternate, this is a safe operation.

h5_main = usid.hdf_utils.get_all_main(h5_file)[-1]
print(h5_main)

<HDF5 dataset "Raw_Data": shape (16384, 119), type "<c8">
located at:
        /Measurement_000/Channel_000/Raw_Data
Data contains:
        Cantilever Vertical Deflection (V)
Data dimensions and original shape:
Position Dimensions:
        X - size: 128
        Y - size: 128
Spectroscopic Dimensions:
        Frequency - size: 119
Data Type:
        complex64

Here, h5_main is a USIDataset, which can be thought of as a supercharged HDF5 Dataset that is not only aware of the contents of the plain USID_Alternate dataset but also its links to the Ancillary Datasets that make it a Main Dataset.

Understanding Dimensionality

What is more is that the above print statement shows that this Main Dataset has two Position Dimensions - X and Y each of size 128 and at each of these locations, data was recorded as a function of 119 values of the single Spectroscopic Dimension - Frequency. Therefore, this dataset is a 3D dataset with two position dimensions and one spectroscopic dimension. To verify this, we can easily get the N-dimensional form of this dataset by invoking the get_n_dim_form()`_ of the USIDataset object:

print(h5_main.get_n_dim_form().shape)
print(h5_main.n_dim_labels)

(128, 128, 119)
['X', 'Y', 'Frequency']

Understanding shapes and flattening

The print statement above shows that the original data is of shape (128, 128, 119). Let’s see if we can arrive at the shape of the Main dataset in USID representation. Recall that USID requires all position dimensions to be flattened along the first axis and all spectroscopic dimensions to be flattened along the second axis of the Main Dataset. In other words, the data collected at each location can be laid out along the horizontal direction as is since this dataset only has a single spectroscopic dimension - Frequency. The X and Y position dimensions however need to be collapsed along the vertical axis of the Main dataset such that the positions are arranged column-by-column and then row-by-row (assuming that the columns are the faster varying dimension).

Visualize the Main Dataset

Now lets visualize the contents within this Main Dataset using the USIDataset's built-in visualize() function.

Note that the visualization below is static. However, if this document were downloaded as a jupyter notebook, you would be able to interactively visualize this dataset.

usid.plot_utils.use_nice_plot_params()
h5_main.visualize()

Here is a visualization of the spectra at evenly spaced positions:

fig, axes = sidpy.plot_utils.plot_complex_spectra(h5_main[()], num_comps=6, amp_units='V',
                                                 subtitle_prefix='Position', evenly_spaced=True,
                                                 x_label=h5_main.spec_dim_descriptors[0])

Alternatively, the spectral image dataset can be visualized via slices across the spectroscopic axis as:

fig, axes = sidpy.plot_utils.plot_map_stack(np.abs(h5_main.get_n_dim_form()), reverse_dims=True, pad_mult=(0.15, 0.15),
                                           title='Spatial maps at different frequencies', stdevs=2,
                                           color_bar_mode='single', num_ticks=3,
                                           x_vec=h5_main.get_pos_values('X'), y_vec=h5_main.get_pos_values('Y'),
                                           evenly_spaced=True, fig_mult=(3, 3), title_yoffset=0.95)
freq_vals = h5_main.get_spec_values(h5_main.spec_dim_labels[0]) *1E-3
for axis, freq_ind in zip(axes, np.linspace(0, h5_main.spec_dim_sizes[0], 9, endpoint=False, dtype=np.uint)):
    axis.set_title('{} = {}'.format(h5_main.spec_dim_labels[0], np.rint(freq_vals[freq_ind])))

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-1-637940588bce> in <module>
----> 1 fig, axes = sidpy.plot_utils.plot_map_stack(np.abs(h5_main.get_n_dim_form()), reverse_dims=True, pad_mult=(0.15, 0.15),
      2                                            title='Spatial maps at different frequencies', stdevs=2,
      3                                            color_bar_mode='single', num_ticks=3,
      4                                            x_vec=h5_main.get_pos_values('X'), y_vec=h5_main.get_pos_values('Y'),
      5                                            evenly_spaced=True, fig_mult=(3, 3), title_yoffset=0.95)

NameError: name 'np' is not defined

Ancillary Datasets

As mentioned in the documentation on USID, Ancillary Datasets are required to complete the information for any dataset. Specifically, these datasets need to provide information about the values against which measurements were acquired, in addition to explaining the original dimensionality (2 in this case) of the original dataset. Let’s look at the ancillary datasets and see what sort of information they provide. We can access the Ancillary Datasets linked to the Main Dataset (h5_main) just like a property of the object.

Ancillary Position Datasets

print('Position Indices:')
print('-------------------------')
print(h5_main.h5_pos_inds)
print('\nPosition Values:')
print('-------------------------')
print(h5_main.h5_pos_vals)

Position Indices:
-------------------------
<HDF5 dataset "Position_Indices": shape (16384, 2), type "<u4">

Position Values:
-------------------------
<HDF5 dataset "Position_Values": shape (16384, 2), type "<f4">

Recall from the USID definition that the shape of the Position Ancillary datasets is (N, P) where N is the number of Position dimensions and the P is the number of locations over which data was recorded. Here, we have two position dimensions. Therefore N is 2. P matches with the first axis of the shape of h5_main which is 16384. Generally, there is no need to remember these rules or construct these ancillary datasets manually since pyUSID has several functions that automatically simplify this process.

Visualize the contents of the Position Ancillary Datasets

Notice below that there are two sets of lines, one for each dimension. The blue lines on the left-hand column appear solid simply because this dimension (X or columns) varies much faster than the other dimension (Y or rows). The first few rows of the dataset are visualized on the right-hand column.

fig, all_axes = plt.subplots(ncols=2, nrows=2, figsize=(8, 8))

for axes, h5_pos_dset, dset_name in zip(all_axes,
                                        [h5_main.h5_pos_inds, h5_main.h5_pos_vals],
                                        ['Position Indices', 'Position Values']):
    axes[0].plot(h5_pos_dset[()])
    axes[0].set_title('Full dataset')
    axes[1].set_title('First 512 rows only')
    axes[1].plot(h5_pos_dset[:512])
    for axis in axes.flat:
        axis.set_xlabel('Row in ' + dset_name)
        axis.set_ylabel(dset_name)
        axis.legend(h5_main.pos_dim_labels)

for axis in all_axes[1]:
    usid.plot_utils.use_scientific_ticks(axis, is_x=False, formatting='%1.e')
    axis.legend(h5_main.pos_dim_descriptors)

fig.tight_layout()

Making sense of the visualization

Given that the columns vary faster than the rows means that the contents of each row of the image have been stored end-to-end in the Main Dataset as opposed to on top of each other as in the original 3D dataset.

Attributes associated with the Position Indices Dataset

Just looking at the shape and values of the Position ancillary datasets does not provide all the information. Recall that the ancillary datasets need to have some mandatory attributes like labels and units that describe the quantity and units for each of the dimensions:

for key, val in sidpy.hdf_utils.get_attributes(h5_main.h5_pos_inds).items():
    print('{} : {}'.format(key, val))

X : <HDF5 region reference>
Y : <HDF5 region reference>
labels : ['X' 'Y']
units : ['m' 'm']

Ancillary Spectroscopic Datasets

Recall that the spectrum at each location was acquired as a function of 119 values of the single Spectroscopic dimension - Frequency. Therefore, according to USID, we should expect the Spectroscopic Dataset to be of shape (M, S) where M is the number of spectroscopic dimensions (1 in this case) and S is the total number of spectroscopic values against which data was acquired at each location (119 in this case).

print('Spectroscopic Indices:')
print('-------------------------')
print(h5_main.h5_spec_inds)
print('\nSpectroscopic Values:')
print('-------------------------')
print(h5_main.h5_spec_vals)

Spectroscopic Indices:
-------------------------
<HDF5 dataset "Spectroscopic_Indices": shape (1, 119), type "<i4">

Spectroscopic Values:
-------------------------
<HDF5 dataset "Spectroscopic_Values": shape (1, 119), type "<f4">

Visualize the contents of the Spectroscopic Datasets

Observe the single curve that is associated with the single spectroscopic variable Frequency. Also note that the contents of the Spectroscopic Indices dataset are just a linearly increasing set of numbers starting from 0 according to the definition of the Indices datasets which just count the nth value of independent variable that was varied.

fig, axes = plt.subplots(ncols=2, figsize=(8, 4))
for axis, data, title, y_lab in zip(axes.flat,
                                    [h5_main.h5_spec_inds[()].T, h5_main.h5_spec_vals[()].T],
                                    ['Spectroscopic Indices', 'Spectroscopic Values'],
                                    ['Index', h5_main.spec_dim_descriptors[0]]):
    axis.plot(data)
    axis.set_title(title)
    axis.set_xlabel('Row in ' + title)
    axis.set_ylabel(y_lab)

sidpy.plot_utils.use_scientific_ticks(axis, is_x=False, formatting='%.1e')
# fig.suptitle('Ancillary Spectroscopic Datasets', y=1.05)
fig.tight_layout()

Attributes within the Spectroscopic Indices Dataset

Again, the attributes of Spectroscopic Datasets show mandatory information about the Spectroscopic dimensions such as the quantity (labels) and units:

for key, val in sidpy.hdf_utils.get_attributes(h5_main.h5_spec_inds).items():
    print('{} : {}'.format(key, val))

Frequency : <HDF5 region reference>
be_line_Plot_Group : <HDF5 region reference>
labels : ['Frequency']
units : ['Hz']

Clean up

Finally lets close the HDF5 file.

h5_file.close()

Here, we will even delete the HDF5 file. Please comment out the line below if you want to look at the HDF5 file using software like HDFView.

os.remove(h5_path)