diff --git a/.gitignore b/.gitignore
index 7fc851d..4c915d1 100644
--- a/.gitignore
+++ b/.gitignore
@@ -104,6 +104,3 @@ ENV/
 # IDE settings
 .vscode/
 .idea/
-
-# OS stuff
-.DS_Store
diff --git a/docs/modules.rst b/docs/modules.rst
index 52a15ec..7847e23 100644
--- a/docs/modules.rst
+++ b/docs/modules.rst
@@ -7,4 +7,4 @@ according to their modules.
 .. toctree::
    :maxdepth: 1
 
-
+   modules/imkar.diffusion
diff --git a/docs/modules/imkar.diffusion.rst b/docs/modules/imkar.diffusion.rst
new file mode 100644
index 0000000..6d54d53
--- /dev/null
+++ b/docs/modules/imkar.diffusion.rst
@@ -0,0 +1,7 @@
+imkar.diffusion
+===============
+
+.. automodule:: imkar.diffusion
+   :members:
+   :undoc-members:
+   :show-inheritance:
diff --git a/imkar/__init__.py b/imkar/__init__.py
index 2d1e55d..8ff2300 100644
--- a/imkar/__init__.py
+++ b/imkar/__init__.py
@@ -3,3 +3,7 @@
 __author__ = """The pyfar developers"""
 __email__ = 'info@pyfar.org'
 __version__ = '0.1.0'
+
+
+from . import diffusion  # noqa
+from . import utils  # noqa
diff --git a/imkar/diffusion/__init__.py b/imkar/diffusion/__init__.py
new file mode 100644
index 0000000..4f7e256
--- /dev/null
+++ b/imkar/diffusion/__init__.py
@@ -0,0 +1,7 @@
+from .diffusion import (
+    freefield,
+)
+
+__all__ = [
+    'freefield',
+    ]
diff --git a/imkar/diffusion/diffusion.py b/imkar/diffusion/diffusion.py
new file mode 100644
index 0000000..96bb392
--- /dev/null
+++ b/imkar/diffusion/diffusion.py
@@ -0,0 +1,131 @@
+import numpy as np
+import pyfar as pf
+from imkar import utils
+
+
+def freefield(sample_pressure, microphone_weights):
+    r"""
+    Calculate the free-field diffusion coefficient for each incident direction
+    after ISO 17497-2:2012 [1]_. See :py:func:`random_incidence`
+    to calculate the random incidence diffusion coefficient.
+
+    .. math::
+        d(\vartheta_S,\varphi_S) =
+            \frac{(\sum |\underline{p}_{sample}(\vartheta_R,\varphi_R)| \cdot
+            N_i)^2 - \sum (|\underline{p}_{sample}(\vartheta_R,\varphi_R)|)^2
+            \cdot N_i}
+            {(\sum N_i - 1) \cdot \sum
+            (|\underline{p}_{sample}(\vartheta_R,\varphi_R)|)^2 \cdot N_i}
+
+    with
+
+    .. math::
+        N_i = \frac{A_i}{A_{min}}
+
+    and ``A`` being the area weights ``microphone_weights``.
+
+    Parameters
+    ----------
+    sample_pressure : pyfar.FrequencyData
+        Reflected sound pressure or directivity of the test sample. Its cshape
+        need to be (..., #microphones).
+    microphone_weights : ndarray
+        An array object with all weights for the microphone positions.
+        Its cshape need to be (#microphones). Microphone positions need to be
+        same for `sample_pressure` and `reference_pressure`.
+
+    Returns
+    -------
+    diffusion_coefficients : pyfar.FrequencyData
+        The diffusion coefficient for each plane wave direction.
+
+
+    References
+    ----------
+    .. [1]  ISO 17497-2:2012, Sound-scattering properties of surfaces.
+            Part 2: Measurement of the directional diffusion coefficient in a
+            free field. Geneva, Switzerland: International Organization for
+            Standards, 2012.
+
+
+    Examples
+    --------
+    Calculate free-field diffusion coefficients and then the random incidence
+    diffusion coefficient.
+
+    >>> import imkar as ik
+    >>> diffusion_coefficients = ik.diffusion.coefficient.freefield(
+    >>>     sample_pressure, mic_positions.weights)
+    >>> random_d = ik.scattering.coefficient.random_incidence(
+    >>>     diffusion_coefficients, incident_positions)
+    """
+    # check inputs
+    if not isinstance(sample_pressure, pf.FrequencyData):
+        raise ValueError("sample_pressure has to be FrequencyData")
+    if not isinstance(microphone_weights, np.ndarray):
+        raise ValueError("weights_microphones have to be a numpy.array")
+    if not microphone_weights.shape[0] == sample_pressure.cshape[-1]:
+        raise ValueError(
+            "the last dimension of sample_pressure need be same as the "
+            "weights_microphones.shape.")
+
+    # parse angles
+    N_i = microphone_weights / np.min(microphone_weights)
+
+    # calculate according to Mommertz correlation method Equation (6)
+    p_sample_abs_sq = np.moveaxis(np.abs(sample_pressure.freq)**2, -1, 0)
+
+    p_sample_sum_sq = np.sum(
+        p_sample_abs_sq**2 * N_i, axis=-1)
+    p_sample_sq_sum = np.sum(
+        p_sample_abs_sq * N_i, axis=-1)**2
+    n = np.sum(N_i)
+    diffusion_array \
+        = (p_sample_sq_sum - p_sample_sum_sq) / ((n-1) * p_sample_sum_sq)
+    diffusion_coefficients = pf.FrequencyData(
+        np.moveaxis(diffusion_array, 0, -1),
+        sample_pressure.frequencies)
+    diffusion_coefficients.comment = 'diffusion coefficients'
+
+    return diffusion_coefficients
+
+
+def random(
+        random_diffusions, incident_directions):
+    r"""
+    Calculate the random-incidence scattering coefficient
+    according to Paris formula [2]_.
+
+    .. math::
+        d_{rand} = \sum d(\vartheta_S,\varphi_S) \cdot cos(\vartheta_S) \cdot w
+
+    with the ``random_diffusions``, and the
+    area weights ``w`` from the ``incident_directions``.
+    Note that the incident directions should be
+    equally distributed to get a valid result.
+
+    Parameters
+    ----------
+    random_diffusions : pyfar.FrequencyData
+        Diffusion coefficients for different incident directions. Its cshape
+        needs to be (..., #source_directions)
+    incident_directions : pyfar.Coordinates
+        Defines the incidence directions of each `random_diffusions` in a
+        Coordinates object. Its cshape needs to be (#source_directions). In
+        sperical coordinates the radii needs to be constant. The weights need
+        to reflect the area weights.
+
+    Returns
+    -------
+    random_diffusion : pyfar.FrequencyData
+        The random-incidence diffusion coefficient.
+
+    References
+    ----------
+    .. [2]  H. Kuttruff, Room acoustics, Sixth edition. Boca Raton:
+            CRC Press/Taylor & Francis Group, 2017.
+    """
+    random_diffusion = utils.paris_formula(
+        random_diffusions, incident_directions)
+    random_diffusion.comment = 'random-incidence diffusion coefficient'
+    return random_diffusion
diff --git a/imkar/scattering/scattering.py b/imkar/scattering/scattering.py
new file mode 100644
index 0000000..355c64d
--- /dev/null
+++ b/imkar/scattering/scattering.py
@@ -0,0 +1,135 @@
+import numpy as np
+import pyfar as pf
+from imkar import utils
+
+
+def freefield(sample_pressure, reference_pressure, microphone_weights):
+    r"""
+    Calculate the free-field scattering coefficient for each incident direction
+    using the Mommertz correlation method [1]_:
+
+    .. math::
+        s(\vartheta_S,\varphi_S) = 1 -
+            \frac{|\sum \underline{p}_{sample}(\vartheta_R,\varphi_R) \cdot
+            \underline{p}_{reference}^*(\vartheta_R,\varphi_R) \cdot w|^2}
+            {\sum |\underline{p}_{sample}(\vartheta_R,\varphi_R)|^2 \cdot w
+            \cdot \sum |\underline{p}_{reference}(\vartheta_R,\varphi_R)|^2
+            \cdot w }
+
+    with the ``sample_pressure``, the ``reference_pressure``, and the
+    area weights ``weights_microphones``. See
+    :py:func:`random_incidence` to calculate the random incidence
+    scattering coefficient.
+
+    Parameters
+    ----------
+    sample_pressure : pyfar.FrequencyData
+        Reflected sound pressure or directivity of the test sample. Its cshape
+        needs to be (..., #microphones).
+    reference_pressure : pyfar.FrequencyData
+        Reflected sound pressure or directivity of the
+        reference sample. Needs to have the same cshape and frequencies as
+        `sample_pressure`.
+    microphone_weights : np.ndarray
+        Array containing the area weights for the microphone positions.
+        Its shape needs to be (#microphones), so it matches the last dimension
+        in the cshape of `sample_pressure` and `reference_pressure`.
+
+    Returns
+    -------
+    scattering_coefficients : pyfar.FrequencyData
+        The scattering coefficient for each incident direction.
+
+
+    References
+    ----------
+    .. [1]  E. Mommertz, „Determination of scattering coefficients from the
+            reflection directivity of architectural surfaces“, Applied
+            Acoustics, Bd. 60, Nr. 2, S. 201-203, June 2000,
+            doi: 10.1016/S0003-682X(99)00057-2.
+
+    """
+    # check inputs
+    if not isinstance(sample_pressure, pf.FrequencyData):
+        raise ValueError(
+            "sample_pressure has to be a pyfar.FrequencyData object")
+    if not isinstance(reference_pressure, pf.FrequencyData):
+        raise ValueError(
+            "reference_pressure has to be a pyfar.FrequencyData object")
+    if not isinstance(microphone_weights, np.ndarray):
+        raise ValueError("microphone_weights have to be a numpy.array")
+    if sample_pressure.cshape != reference_pressure.cshape:
+        raise ValueError(
+            "sample_pressure and reference_pressure have to have the "
+            "same cshape.")
+    if microphone_weights.shape[0] != sample_pressure.cshape[-1]:
+        raise ValueError(
+            "the last dimension of sample_pressure needs be same as the "
+            "microphone_weights.shape.")
+    if not np.allclose(
+            sample_pressure.frequencies, reference_pressure.frequencies):
+        raise ValueError(
+            "sample_pressure and reference_pressure have to have the "
+            "same frequencies.")
+
+    # calculate according to mommertz correlation method Equation (5)
+    p_sample = np.moveaxis(sample_pressure.freq, -1, 0)
+    p_reference = np.moveaxis(reference_pressure.freq, -1, 0)
+    p_sample_sq = np.abs(p_sample)**2
+    p_reference_sq = np.abs(p_reference)**2
+    p_cross = p_sample * np.conj(p_reference)
+
+    p_sample_sum = np.sum(microphone_weights * p_sample_sq, axis=-1)
+    p_ref_sum = np.sum(microphone_weights * p_reference_sq, axis=-1)
+    p_cross_sum = np.sum(microphone_weights * p_cross, axis=-1)
+
+    data_scattering_coefficient \
+        = 1 - ((np.abs(p_cross_sum)**2)/(p_sample_sum*p_ref_sum))
+
+    scattering_coefficients = pf.FrequencyData(
+        np.moveaxis(data_scattering_coefficient, 0, -1),
+        sample_pressure.frequencies)
+    scattering_coefficients.comment = 'scattering coefficient'
+
+    return scattering_coefficients
+
+
+def random(
+        scattering_coefficients, incident_directions):
+    r"""
+    Calculate the random-incidence scattering coefficient
+    according to Paris formula [2]_.
+
+    .. math::
+        s_{rand} = \sum s(\vartheta_S,\varphi_S) \cdot cos(\vartheta_S) \cdot w
+
+    with the ``scattering_coefficients``, and the
+    area weights ``w`` from the ``incident_directions``.
+    Note that the incident directions should be
+    equally distributed to get a valid result.
+
+    Parameters
+    ----------
+    scattering_coefficients : pyfar.FrequencyData
+        Scattering coefficients for different incident directions. Its cshape
+        needs to be (..., #source_directions)
+    incident_directions : pyfar.Coordinates
+        Defines the incidence directions of each `scattering_coefficients` in a
+        Coordinates object. Its cshape needs to be (#source_directions). In
+        sperical coordinates the radii needs to be constant. The weights need
+        to reflect the area weights.
+
+    Returns
+    -------
+    random_scattering : pyfar.FrequencyData
+        The random-incidence scattering coefficient.
+
+    References
+    ----------
+    .. [2]  H. Kuttruff, Room acoustics, Sixth edition. Boca Raton:
+            CRC Press/Taylor & Francis Group, 2017.
+    """
+    random_scattering = utils.paris_formula(
+        scattering_coefficients, incident_directions)
+    random_scattering.comment = 'random-incidence scattering coefficient'
+    return random_scattering
diff --git a/imkar/utils/__init__.py b/imkar/utils/__init__.py
new file mode 100644
index 0000000..eaf3a04
--- /dev/null
+++ b/imkar/utils/__init__.py
@@ -0,0 +1,7 @@
+from .utils import (
+    paris_formula,
+)
+
+__all__ = [
+    'paris_formula',
+    ]
diff --git a/imkar/utils/utils.py b/imkar/utils/utils.py
new file mode 100644
index 0000000..6eb8697
--- /dev/null
+++ b/imkar/utils/utils.py
@@ -0,0 +1,57 @@
+import numpy as np
+import pyfar as pf
+
+
+def paris_formula(coefficients, incident_directions):
+    r"""
+    Calculate the random-incidence coefficient
+    according to Paris formula [2]_.
+
+    .. math::
+        c_{rand} = \sum c(\vartheta_S,\varphi_S) \cdot cos(\vartheta_S) \cdot w
+
+    with the ``coefficients``, and the
+    area weights ``w`` from the ``incident_directions``.
+    Note that the incident directions should be
+    equally distributed to get a valid result.
+
+    Parameters
+    ----------
+    coefficients : pyfar.FrequencyData
+        coefficients for different incident directions. Its cshape
+        needs to be (..., #incident_directions)
+    incident_directions : pyfar.Coordinates
+        Defines the incidence directions of each `coefficients` in a
+        Coordinates object. Its cshape needs to be (#incident_directions). In
+        sperical coordinates the radii needs to be constant. The weights need
+        to reflect the area weights.
+
+    Returns
+    -------
+    random_coefficient : pyfar.FrequencyData
+        The random-incidence scattering coefficient.
+
+    References
+    ----------
+    .. [2]  H. Kuttruff, Room acoustics, Sixth edition. Boca Raton:
+            CRC Press/Taylor & Francis Group, 2017.
+    """
+    if not isinstance(coefficients, pf.FrequencyData):
+        raise ValueError("coefficients has to be FrequencyData")
+    if not isinstance(incident_directions, pf.Coordinates):
+        raise ValueError("incident_directions have to be None or Coordinates")
+    if incident_directions.cshape[0] != coefficients.cshape[-1]:
+        raise ValueError(
+            "the last dimension of coefficients needs be same as "
+            "the incident_directions.cshape.")
+
+    theta = incident_directions.get_sph().T[1]
+    weight = np.cos(theta) * incident_directions.weights
+    norm = np.sum(weight)
+    coefficients_freq = np.swapaxes(coefficients.freq, -1, -2)
+    random_coefficient = pf.FrequencyData(
+        np.sum(coefficients_freq*weight/norm, axis=-1),
+        coefficients.frequencies,
+        comment='random-incidence coefficient'
+    )
+    return random_coefficient
diff --git a/tests/conftest.py b/tests/conftest.py
new file mode 100644
index 0000000..8a443c9
--- /dev/null
+++ b/tests/conftest.py
@@ -0,0 +1,73 @@
+import pytest
+import pyfar as pf
+import numpy as np
+
+
+@pytest.fixture
+def half_sphere():
+    """return 42th order gaussian sampling for the half sphere and radius 1.
+    Returns
+    -------
+    pf.Coordinates
+        half sphere sampling grid
+    """
+    mics = pf.samplings.sph_gaussian(42)
+    # delete lower part of sphere
+    return mics[mics.get_sph().T[1] <= np.pi/2]
+
+
+@pytest.fixture
+def quarter_half_sphere():
+    """return 10th order gaussian sampling for the quarter half sphere
+    and radius 1.
+    Returns
+    -------
+    pf.Coordinates
+        quarter half sphere sampling grid
+    """
+    incident_directions = pf.samplings.sph_gaussian(10)
+    incident_directions = incident_directions[
+        incident_directions.get_sph().T[1] <= np.pi/2]
+    return incident_directions[
+        incident_directions.get_sph().T[0] <= np.pi/2]
+
+
+@pytest.fixture
+def pressure_data_mics(half_sphere):
+    """returns a sound pressure data example, with sound pressure 0 and
+    two frequency bins
+    Parameters
+    ----------
+    half_sphere : pf.Coordinates
+        half sphere sampling grid for mics
+    Returns
+    -------
+    pyfar.FrequencyData
+        output sound pressure data
+    """
+    frequencies = [200, 300]
+    shape_new = np.append(half_sphere.cshape, len(frequencies))
+    return pf.FrequencyData(np.zeros(shape_new), frequencies)
+
+
+@pytest.fixture
+def pressure_data_mics_incident_directions(
+        half_sphere, quarter_half_sphere):
+    """returns a sound pressure data example, with sound pressure 0 and
+    two frequency bins
+    Parameters
+    ----------
+    half_sphere : pf.Coordinates
+        half sphere sampling grid for mics
+    quarter_half_sphere : pf.Coordinates
+        quarter half sphere sampling grid for incident directions
+    Returns
+    -------
+    pyfar.FrequencyData
+        output sound pressure data
+    """
+    frequencies = [200, 300]
+    shape_new = np.append(
+        quarter_half_sphere.cshape, half_sphere.cshape)
+    shape_new = np.append(shape_new, len(frequencies))
+    return pf.FrequencyData(np.zeros(shape_new), frequencies)
diff --git a/tests/test_diffusion.py b/tests/test_diffusion.py
new file mode 100644
index 0000000..80e535d
--- /dev/null
+++ b/tests/test_diffusion.py
@@ -0,0 +1,45 @@
+import pytest
+import numpy as np
+import pyfar as pf
+from imkar import diffusion
+
+
+def test_freefield(half_sphere, pressure_data_mics):
+    mics = half_sphere
+    p_sample = pressure_data_mics.copy()
+    p_sample.freq.fill(1)
+    d = diffusion.freefield(p_sample, mics.weights)
+    np.testing.assert_allclose(d.freq, 1)
+
+
+@pytest.mark.parametrize("radius",  [
+    (1), (10)])
+@pytest.mark.parametrize("magnitude",  [
+    (1), (10)])
+def test_freefield_with_theta_0(
+        half_sphere, pressure_data_mics, radius, magnitude):
+    mics = half_sphere
+    spherical = mics.get_sph().T
+    mics.set_sph(spherical[0], spherical[1], radius)
+    p_sample = pressure_data_mics.copy()
+    p_sample.freq.fill(magnitude)
+    d = diffusion.freefield(p_sample, mics.weights)
+    np.testing.assert_allclose(d.freq, 1)
+
+
+@pytest.mark.parametrize("frequencies",  [
+    ([100, 200]), ([100])])
+@pytest.mark.parametrize("radius",  [
+    (1), (10)])
+def test_freefield_not_one(frequencies, radius):
+    # validate with code from itatoolbox
+    mics = pf.samplings.sph_equal_angle(10, radius)
+    mics.weights = pf.samplings.calculate_sph_voronoi_weights(mics)
+    mics = mics[mics.get_sph().T[1] <= np.pi/2]  # delete lower part of sphere
+    theta_is_pi = mics.get_sph().T[1] == np.pi/2
+    mics.weights[theta_is_pi] /= 2
+    data = np.ones(mics.cshape)
+    p_sample = pf.FrequencyData(data[..., np.newaxis], [100])
+    p_sample.freq[1, :] = 2
+    d = diffusion.freefield(p_sample, mics.weights)
+    np.testing.assert_allclose(d.freq, 0.9918, atol=0.003)
diff --git a/tests/test_imkar.py b/tests/test_imkar.py
index e6d07f7..f801097 100644
--- a/tests/test_imkar.py
+++ b/tests/test_imkar.py
@@ -1,5 +1,24 @@
-def test_import_imkar():
-    try:
-        import imkar           # noqa
-    except ImportError:
-        assert False
+#!/usr/bin/env python
+
+"""Tests for `imkar` package."""
+
+import pytest
+
+
+from imkar import imkar
+
+
+@pytest.fixture
+def response():
+    """Sample pytest fixture.
+
+    See more at: http://doc.pytest.org/en/latest/fixture.html
+    """
+    # import requests
+    # return requests.get('https://github.com/mberz/cookiecutter-pypackage')
+
+
+def test_content(response):
+    """Sample pytest test function with the pytest fixture as an argument."""
+    # from bs4 import BeautifulSoup
+    # assert 'GitHub' in BeautifulSoup(response.content).title.string
diff --git a/tests/test_utils.py b/tests/test_utils.py
new file mode 100644
index 0000000..1440c0b
--- /dev/null
+++ b/tests/test_utils.py
@@ -0,0 +1,34 @@
+import pytest
+import numpy as np
+import pyfar as pf
+
+from imkar import utils
+
+
+@pytest.mark.parametrize("c_value",  [
+    (0), (0.2), (0.5), (0.8), (1)])
+@pytest.mark.parametrize("frequencies",  [
+    ([100, 200]), ([100])])
+def test_random_constant_coefficient(
+        c_value, frequencies, half_sphere):
+    incident_directions = half_sphere
+    shape = np.append(half_sphere.cshape, len(frequencies))
+    coefficient = pf.FrequencyData(np.zeros(shape)+c_value, frequencies)
+    c_rand = utils.paris_formula(coefficient, incident_directions)
+    np.testing.assert_allclose(c_rand.freq, c_value)
+    assert c_rand.comment == 'random-incidence coefficient'
+
+
+def test_random_non_constant_coefficient():
+    data = pf.samplings.sph_gaussian(10)
+    incident_directions = data[data.get_sph().T[1] <= np.pi/2]
+    incident_cshape = incident_directions.cshape
+    s_value = np.arange(
+        incident_cshape[0]).reshape(incident_cshape) / incident_cshape[0]
+    theta = incident_directions.get_sph().T[1]
+    actual_weight = np.cos(theta) * incident_directions.weights
+    actual_weight /= np.sum(actual_weight)
+    coefficient = pf.FrequencyData(s_value.reshape((50, 1)), [100])
+    c_rand = utils.paris_formula(coefficient, incident_directions)
+    desired = np.sum(s_value*actual_weight)
+    np.testing.assert_allclose(c_rand.freq, desired)