diff --git a/MANIFEST.in b/MANIFEST.in
index 6b5bcc73..ba2d1d90 100644
--- a/MANIFEST.in
+++ b/MANIFEST.in
@@ -1 +1,2 @@
-recursive-include src/elli/database/refractiveindexinfo-database *.yml
\ No newline at end of file
+recursive-include src/elli/database/refractiveindexinfo-database *.yml
+include src/elli/formula_parser/dispersion_function_grammer.lark
\ No newline at end of file
diff --git a/README.md b/README.md
index 5ba430e3..fbf2d876 100644
--- a/README.md
+++ b/README.md
@@ -64,7 +64,7 @@ the folder to install it in development mode:
 ```sh
 git clone https://github.com/PyEllips/pyElli
 cd pyElli
-pip install -e .[fitting]
+pip install -e ".[fitting]"
 ```
 
 ## Acknowledgements
diff --git a/pyproject.toml b/pyproject.toml
index b25148a9..85850b1b 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -28,7 +28,9 @@ dependencies = [
     "h5py",
     "pyyaml",
     "importlib-resources",
-    "rapidfuzz"
+    "rapidfuzz",
+    "lark>=1.1.5",
+    "pint",
 ]
 
 [project.optional-dependencies]
diff --git a/requirements/dev-requirements.txt b/requirements/dev-requirements.txt
index 5b834ead..7193b689 100644
--- a/requirements/dev-requirements.txt
+++ b/requirements/dev-requirements.txt
@@ -1,6 +1,6 @@
 #
-# This file is autogenerated by pip-compile with Python 3.10
-# by the following command:
+# This file is autogenerated by pip-compile with python 3.9
+# To update, run:
 #
 #    pip-compile --extra=fitting --extra=testing --generate-hashes --output-file=requirements/dev-requirements.txt pyproject.toml requirements/fitting-requirements.txt
 #
@@ -292,6 +292,12 @@ h5py==3.7.0 \
     # via
     #   -r requirements/fitting-requirements.txt
     #   pyElli (pyproject.toml)
+importlib-metadata==6.0.0 \
+    --hash=sha256:7efb448ec9a5e313a57655d35aa54cd3e01b7e1fbcf72dce1bf06119420f5bad \
+    --hash=sha256:e354bedeb60efa6affdcc8ae121b73544a7aa74156d047311948f6d711cd378d
+    # via
+    #   -r requirements/fitting-requirements.txt
+    #   nbconvert
 importlib-resources==5.10.0 \
     --hash=sha256:c01b1b94210d9849f286b86bb51bcea7cd56dde0600d8db721d7b81330711668 \
     --hash=sha256:ee17ec648f85480d523596ce49eae8ead87d5631ae1551f913c0100b5edd3437
@@ -451,6 +457,12 @@ kiwisolver==1.4.4 \
     # via
     #   -r requirements/fitting-requirements.txt
     #   matplotlib
+lark==1.1.5 \
+    --hash=sha256:4b534eae1f9af5b4ea000bea95776350befe1981658eea3820a01c37e504bb4d \
+    --hash=sha256:8476f9903e93fbde4f6c327f74d79e9b4bd0ed9294c5dfa3164ab8c581b5de2a
+    # via
+    #   -r requirements/fitting-requirements.txt
+    #   pyElli (pyproject.toml)
 lmfit==1.0.3 \
     --hash=sha256:d067c3ea501f035af5d3c079e6e6e35dc3cc1ac7d439429a425b0aeb5a7858a2
     # via
@@ -828,6 +840,12 @@ pillow==9.3.0 \
     # via
     #   -r requirements/fitting-requirements.txt
     #   matplotlib
+pint==0.20.1 \
+    --hash=sha256:387cf04078dc7dfe4a708033baad54ab61d82ab06c4ee3d4922b1e45d5626067 \
+    --hash=sha256:68afe65665542ee3ec99f69f043b1d39bfe7c6d61b786940157138fd08b838fb
+    # via
+    #   -r requirements/fitting-requirements.txt
+    #   pyElli (pyproject.toml)
 plotly==5.10.0 \
     --hash=sha256:4d36d9859b7a153b273562deeed8c292587a472eb1fd57cd4158ec89d9defadb \
     --hash=sha256:989b13825cc974390aa0169479485d9257d37848a47bc63957251f8e1a7046ba
@@ -1382,3 +1400,10 @@ widgetsnbextension==3.6.1 \
     # via
     #   -r requirements/fitting-requirements.txt
     #   ipywidgets
+zipp==3.15.0 \
+    --hash=sha256:112929ad649da941c23de50f356a2b5570c954b65150642bccdd66bf194d224b \
+    --hash=sha256:48904fc76a60e542af151aded95726c1a5c34ed43ab4134b597665c86d7ad556
+    # via
+    #   -r requirements/fitting-requirements.txt
+    #   importlib-metadata
+    #   importlib-resources
diff --git a/requirements/fitting-requirements.txt b/requirements/fitting-requirements.txt
index c500d794..fed27aa7 100644
--- a/requirements/fitting-requirements.txt
+++ b/requirements/fitting-requirements.txt
@@ -1,6 +1,6 @@
 #
-# This file is autogenerated by pip-compile with Python 3.10
-# by the following command:
+# This file is autogenerated by pip-compile with python 3.9
+# To update, run:
 #
 #    pip-compile --extra=fitting --generate-hashes --output-file=requirements/fitting-requirements.txt pyproject.toml requirements/requirements.txt
 #
@@ -202,6 +202,10 @@ h5py==3.7.0 \
     # via
     #   -r requirements/requirements.txt
     #   pyElli (pyproject.toml)
+importlib-metadata==6.0.0 \
+    --hash=sha256:7efb448ec9a5e313a57655d35aa54cd3e01b7e1fbcf72dce1bf06119420f5bad \
+    --hash=sha256:e354bedeb60efa6affdcc8ae121b73544a7aa74156d047311948f6d711cd378d
+    # via nbconvert
 importlib-resources==5.10.0 \
     --hash=sha256:c01b1b94210d9849f286b86bb51bcea7cd56dde0600d8db721d7b81330711668 \
     --hash=sha256:ee17ec648f85480d523596ce49eae8ead87d5631ae1551f913c0100b5edd3437
@@ -338,6 +342,12 @@ kiwisolver==1.4.4 \
     --hash=sha256:f8ad8285b01b0d4695102546b342b493b3ccc6781fc28c8c6a1bb63e95d22f09 \
     --hash=sha256:f9f39e2f049db33a908319cf46624a569b36983c7c78318e9726a4cb8923b26c
     # via matplotlib
+lark==1.1.5 \
+    --hash=sha256:4b534eae1f9af5b4ea000bea95776350befe1981658eea3820a01c37e504bb4d \
+    --hash=sha256:8476f9903e93fbde4f6c327f74d79e9b4bd0ed9294c5dfa3164ab8c581b5de2a
+    # via
+    #   -r requirements/requirements.txt
+    #   pyElli (pyproject.toml)
 lmfit==1.0.3 \
     --hash=sha256:d067c3ea501f035af5d3c079e6e6e35dc3cc1ac7d439429a425b0aeb5a7858a2
     # via pyElli (pyproject.toml)
@@ -679,6 +689,12 @@ pillow==9.3.0 \
     --hash=sha256:ebf2029c1f464c59b8bdbe5143c79fa2045a581ac53679733d3a91d400ff9efb \
     --hash=sha256:f1ff2ee69f10f13a9596480335f406dd1f70c3650349e2be67ca3139280cade0
     # via matplotlib
+pint==0.20.1 \
+    --hash=sha256:387cf04078dc7dfe4a708033baad54ab61d82ab06c4ee3d4922b1e45d5626067 \
+    --hash=sha256:68afe65665542ee3ec99f69f043b1d39bfe7c6d61b786940157138fd08b838fb
+    # via
+    #   -r requirements/requirements.txt
+    #   pyElli (pyproject.toml)
 plotly==5.10.0 \
     --hash=sha256:4d36d9859b7a153b273562deeed8c292587a472eb1fd57cd4158ec89d9defadb \
     --hash=sha256:989b13825cc974390aa0169479485d9257d37848a47bc63957251f8e1a7046ba
@@ -1126,3 +1142,10 @@ widgetsnbextension==3.6.1 \
     --hash=sha256:954e0faefdd414e4e013f17dbc7fd86f24cf1d243a3ac85d5f0fc2c2d2b50c66 \
     --hash=sha256:9c84ae64c2893c7cbe2eaafc7505221a795c27d68938454034ac487319a75b10
     # via ipywidgets
+zipp==3.15.0 \
+    --hash=sha256:112929ad649da941c23de50f356a2b5570c954b65150642bccdd66bf194d224b \
+    --hash=sha256:48904fc76a60e542af151aded95726c1a5c34ed43ab4134b597665c86d7ad556
+    # via
+    #   -r requirements/requirements.txt
+    #   importlib-metadata
+    #   importlib-resources
diff --git a/requirements/requirements.txt b/requirements/requirements.txt
index 9e8cd34f..42d363c4 100644
--- a/requirements/requirements.txt
+++ b/requirements/requirements.txt
@@ -1,6 +1,6 @@
 #
-# This file is autogenerated by pip-compile with Python 3.10
-# by the following command:
+# This file is autogenerated by pip-compile with python 3.9
+# To update, run:
 #
 #    pip-compile --generate-hashes --output-file=requirements/requirements.txt pyproject.toml
 #
@@ -30,6 +30,10 @@ importlib-resources==5.10.0 \
     --hash=sha256:c01b1b94210d9849f286b86bb51bcea7cd56dde0600d8db721d7b81330711668 \
     --hash=sha256:ee17ec648f85480d523596ce49eae8ead87d5631ae1551f913c0100b5edd3437
     # via pyElli (pyproject.toml)
+lark==1.1.5 \
+    --hash=sha256:4b534eae1f9af5b4ea000bea95776350befe1981658eea3820a01c37e504bb4d \
+    --hash=sha256:8476f9903e93fbde4f6c327f74d79e9b4bd0ed9294c5dfa3164ab8c581b5de2a
+    # via pyElli (pyproject.toml)
 numpy==1.23.2 \
     --hash=sha256:17e5226674f6ea79e14e3b91bfbc153fdf3ac13f5cc54ee7bc8fdbe820a32da0 \
     --hash=sha256:2bd879d3ca4b6f39b7770829f73278b7c5e248c91d538aab1e506c628353e47f \
@@ -87,6 +91,10 @@ pandas==1.4.4 \
     --hash=sha256:e7cc960959be28d064faefc0cb2aef854d46b827c004ebea7e79b5497ed83e7d \
     --hash=sha256:ee6f1848148ed3204235967613b0a32be2d77f214e9623f554511047705c1e04
     # via pyElli (pyproject.toml)
+pint==0.20.1 \
+    --hash=sha256:387cf04078dc7dfe4a708033baad54ab61d82ab06c4ee3d4922b1e45d5626067 \
+    --hash=sha256:68afe65665542ee3ec99f69f043b1d39bfe7c6d61b786940157138fd08b838fb
+    # via pyElli (pyproject.toml)
 python-dateutil==2.8.2 \
     --hash=sha256:0123cacc1627ae19ddf3c27a5de5bd67ee4586fbdd6440d9748f8abb483d3e86 \
     --hash=sha256:961d03dc3453ebbc59dbdea9e4e11c5651520a876d0f4db161e8674aae935da9
@@ -270,3 +278,7 @@ six==1.16.0 \
     --hash=sha256:1e61c37477a1626458e36f7b1d82aa5c9b094fa4802892072e49de9c60c4c926 \
     --hash=sha256:8abb2f1d86890a2dfb989f9a77cfcfd3e47c2a354b01111771326f8aa26e0254
     # via python-dateutil
+zipp==3.15.0 \
+    --hash=sha256:112929ad649da941c23de50f356a2b5570c954b65150642bccdd66bf194d224b \
+    --hash=sha256:48904fc76a60e542af151aded95726c1a5c34ed43ab4134b597665c86d7ad556
+    # via importlib-resources
diff --git a/src/elli/database/refractive_index_info.py b/src/elli/database/refractive_index_info.py
index 72091630..44e30df6 100644
--- a/src/elli/database/refractive_index_info.py
+++ b/src/elli/database/refractive_index_info.py
@@ -21,7 +21,12 @@
     SellmeierCustomExponent,
     Table,
 )
-from ..dispersions.base_dispersion import Dispersion, DispersionSum
+from ..dispersions.base_dispersion import (
+    Dispersion,
+    DispersionSum,
+    IndexDispersion,
+    IndexDispersionSum,
+)
 from ..materials import IsotropicMaterial
 
 WavelengthFilterType = Union[
@@ -282,7 +287,9 @@ def get_mat(self, book: str, page: str) -> IsotropicMaterial:
         """
         return IsotropicMaterial(self.load_dispersion(book, page))
 
-    def load_dispersion(self, book: str, page: str) -> Dispersion:
+    def load_dispersion(
+        self, book: str, page: str
+    ) -> Union[Dispersion, IndexDispersion]:
         """Load a dispersion from the refractive index database.
         Selection by material and source identifiers.
 
@@ -307,6 +314,7 @@ def load_dispersion(self, book: str, page: str) -> Dispersion:
         )
 
         dispersion_list = []
+        contains_index_dispersion = False
 
         for dispersion_relation in yml_file["DATA"]:
             if dispersion_relation["type"] == "tabulated nk":
@@ -319,6 +327,7 @@ def load_dispersion(self, book: str, page: str) -> Dispersion:
                 df.set_index("Wavelength", inplace=True)
 
                 dispersion = Table(lbda=df.index, n=df["n"] + 1j * df["k"])
+                contains_index_dispersion = True
 
             elif dispersion_relation["type"] == "tabulated n":
                 df = pd.read_table(
@@ -330,6 +339,7 @@ def load_dispersion(self, book: str, page: str) -> Dispersion:
                 df.set_index("Wavelength", inplace=True)
 
                 dispersion = Table(lbda=df.index, n=df["n"])
+                contains_index_dispersion = True
 
             elif dispersion_relation["type"] == "tabulated k":
                 df = pd.read_table(
@@ -341,6 +351,7 @@ def load_dispersion(self, book: str, page: str) -> Dispersion:
                 df.set_index("Wavelength", inplace=True)
 
                 dispersion = Table(lbda=df.index, n=0 + 1j * df["k"])
+                contains_index_dispersion = True
 
             elif dispersion_relation["type"] == "formula 1":
                 coeffs = list(
@@ -415,6 +426,7 @@ def load_dispersion(self, book: str, page: str) -> Dispersion:
                     cauchy.add(f_i / 1e3**e_i, e_i)
 
                 dispersion = cauchy
+                contains_index_dispersion = True
 
             else:
                 raise ValueError("Unimplemented Format.")
@@ -423,6 +435,13 @@ def load_dispersion(self, book: str, page: str) -> Dispersion:
 
         if len(dispersion_list) == 1:
             return dispersion_list[0]
+
+        if contains_index_dispersion:
+            for i, dispersion in enumerate(dispersion_list):
+                if not isinstance(dispersion, IndexDispersion):
+                    dispersion_list[i] = dispersion.as_index()
+
+            return IndexDispersionSum(*dispersion_list)
         return DispersionSum(*dispersion_list)
 
     def get_reference(self, book: str, page: str) -> str:
diff --git a/src/elli/dispersions/__init__.py b/src/elli/dispersions/__init__.py
index a29bf0a1..54afb816 100644
--- a/src/elli/dispersions/__init__.py
+++ b/src/elli/dispersions/__init__.py
@@ -20,3 +20,4 @@
 from .tauc_lorentz import TaucLorentz
 from .cody_lorentz import CodyLorentz
 from .pseudo_dielectric import PseudoDielectricFunction
+from .formula import Formula, FormulaIndex
diff --git a/src/elli/dispersions/base_dispersion.py b/src/elli/dispersions/base_dispersion.py
index de4c6a69..62d4bb6d 100644
--- a/src/elli/dispersions/base_dispersion.py
+++ b/src/elli/dispersions/base_dispersion.py
@@ -1,7 +1,8 @@
 # Encoding: utf-8
 """Abstract base class and utility classes for pyElli dispersion"""
 from abc import ABC, abstractmethod
-from typing import List, Union
+from copy import deepcopy
+from typing import List, Optional, Union
 
 import numpy as np
 import numpy.typing as npt
@@ -16,13 +17,15 @@ class InvalidParameters(Exception):
     """Exception for invalid dispersion parameters."""
 
 
-class Dispersion(ABC):
+class BaseDispersion(ABC):
     """Dispersion (abstract class).
 
     Functions provided for derived classes:
     * dielectric_function(lbda) : returns dielectric constant for wavelength 'lbda'
     """
 
+    default_lbda_range = np.linspace(200, 1000, 801)
+
     @property
     @abstractmethod
     def single_params_template(self) -> dict:
@@ -43,7 +46,7 @@ def _guard_invalid_params(params1, params2):
 
     @staticmethod
     def _fill_params_dict(template: dict, *args, **kwargs) -> dict:
-        Dispersion._guard_invalid_params(list(kwargs.keys()), list(template.keys()))
+        BaseDispersion._guard_invalid_params(list(kwargs.keys()), list(template.keys()))
 
         if (len(kwargs) + len(args)) > len(template):
             raise InvalidParameters("Too many parameters")
@@ -73,6 +76,10 @@ def __init__(self, *args, **kwargs):
             self.single_params_template, *args, **kwargs
         )
 
+        for param in self.single_params:
+            if self.single_params[param] is None:
+                raise InvalidParameters(f"Please specify parameter {param}")
+
     @abstractmethod
     def dielectric_function(self, lbda: npt.ArrayLike) -> npt.NDArray:
         """Calculates the dielectric function in a given wavelength window.
@@ -101,47 +108,23 @@ def add(self, *args, **kwargs) -> "Dispersion":
 
         return self
 
-    def _check_valid_operand(self, other: Union[int, float, "Dispersion"]):
-        if not isinstance(other, (int, float, Dispersion)):
-            raise TypeError(
-                f"unsupported operand type(s) for +: '{type(self)}' and '{type(other)}'"
-            )
-
-    def _is_non_std_dispersion(self, other: Union[int, float, "Dispersion"]) -> bool:
-        return isinstance(other, (IndexDispersion, dispersions.Table))
-
-    def __radd__(self, other: Union[int, float, "Dispersion"]) -> "DispersionSum":
-        """Add up the dielectric function of multiple models"""
-        return self.__add__(other)
-
-    def __add__(self, other: Union[int, float, "Dispersion"]) -> "DispersionSum":
-        """Add up the dielectric function of multiple models"""
-        self._check_valid_operand(other)
-
-        if self._is_non_std_dispersion(other):
-            return other.__add__(self)
-
-        if isinstance(other, DispersionSum):
-            other.dispersions.append(self)
-            return other
-
-        if isinstance(other, (int, float)):
-            return DispersionSum(self, dispersions.EpsilonInf(other))
-
-        return DispersionSum(self, other)
-
-    def get_dielectric(self, lbda: npt.ArrayLike) -> npt.NDArray:
+    def get_dielectric(self, lbda: Optional[npt.ArrayLike] = None) -> npt.NDArray:
         """Returns the dielectric constant for wavelength 'lbda' default unit (nm)
         in the convention ε1 + iε2."""
+        lbda = self.default_lbda_range if lbda is None else lbda
         return np.asarray(self.dielectric_function(lbda), dtype=np.complex128)
 
-    def get_refractive_index(self, lbda: npt.ArrayLike) -> npt.NDArray:
+    def get_refractive_index(self, lbda: Optional[npt.ArrayLike] = None) -> npt.NDArray:
         """Returns the refractive index for wavelength 'lbda' default unit (nm)
         in the convention n + ik."""
+        lbda = self.default_lbda_range if lbda is None else lbda
+
+        if isinstance(self, IndexDispersion):
+            return self.refractive_index(lbda)
         return sqrt(self.dielectric_function(lbda))
 
     def get_dielectric_df(
-        self, lbda: npt.ArrayLike = None, conjugate=False
+        self, lbda: Optional[npt.ArrayLike] = None, conjugate=False
     ) -> pd.DataFrame:
         """Returns the dielectric function as a pandas dataframe
 
@@ -159,7 +142,7 @@ def get_dielectric_df(
                 A pandas dataframe containing the wavelength as index
                 and two rows containing ε1 and ε2.
         """
-        lbda = np.linspace(200, 1000, 801) if lbda is None else lbda
+        lbda = self.default_lbda_range if lbda is None else lbda
         eps = self.get_dielectric(lbda)
 
         return pd.DataFrame(
@@ -168,7 +151,7 @@ def get_dielectric_df(
         )
 
     def get_refractive_index_df(
-        self, lbda: npt.ArrayLike = None, conjugate=False
+        self, lbda: Optional[npt.ArrayLike] = None, conjugate=False
     ) -> pd.DataFrame:
         """Returns the refractive index as a pandas dataframe
 
@@ -186,7 +169,7 @@ def get_refractive_index_df(
                 A pandas dataframe containing the wavelength as index
                 and two rows containing n and k.
         """
-        lbda = np.linspace(200, 1000, 801) if lbda is None else lbda
+        lbda = self.default_lbda_range if lbda is None else lbda
         nk = self.get_refractive_index(lbda)
 
         return pd.DataFrame(
@@ -214,7 +197,58 @@ def _dict_to_str(dic):
         )
 
 
-class IndexDispersion(Dispersion):
+class Dispersion(BaseDispersion):
+    """A dispersion based on a dielectric function formulation."""
+
+    def _check_valid_operand(self, other: Union[int, float, "Dispersion"]):
+        if not isinstance(other, (int, float, Dispersion, dispersions.TableEpsilon)):
+            raise TypeError(
+                f"unsupported operand type(s) for +: '{type(self)}' and '{type(other)}'"
+            )
+
+    def __radd__(self, other: Union[int, float, "Dispersion"]) -> "DispersionSum":
+        """Add up the dielectric function of multiple models"""
+        return self.__add__(other)
+
+    def __add__(self, other: Union[int, float, "Dispersion"]) -> "DispersionSum":
+        """Add up the dielectric function of multiple models"""
+        if isinstance(other, IndexDispersion):
+            raise TypeError(
+                "Cannot add refractive index and dielectric function based dispersions."
+            )
+        self._check_valid_operand(other)
+
+        if isinstance(other, dispersions.TableEpsilon):
+            return other.__add__(self)
+
+        if isinstance(other, DispersionSum):
+            other.dispersions.append(self)
+            return other
+
+        if isinstance(other, (int, float)):
+            return DispersionSum(self, dispersions.EpsilonInf(other))
+
+        return DispersionSum(self, other)
+
+    def as_index(self):
+        """
+        Returns this class as IndexDispersion.
+        This method may be used to add dielectric and index based dispersions.
+        Please ensure that you know what you are doing as building dielectric
+        and index based dispersions is normally mathematically wrong.
+        """
+        index_class = deepcopy(self)
+        # pylint: disable=attribute-defined-outside-init
+        index_class.refractive_index = lambda lbda: sqrt(
+            index_class.dielectric_function(lbda)
+        )
+        index_class.__class__ = IndexDispersion  # pylint: disable=invalid-name
+        index_class.dielectric_function = self.dielectric_function
+
+        return index_class
+
+
+class IndexDispersion(BaseDispersion):
     """A dispersion based on a refractive index formulation."""
 
     @abstractmethod
@@ -228,29 +262,63 @@ def refractive_index(self, lbda: npt.ArrayLike) -> npt.NDArray:
             npt.NDArray: The refractive index for each wavelength point.
         """
 
-    def __add__(self, other: Union[int, float, "Dispersion"]) -> "DispersionSum":
-        self._check_valid_operand(other)
+    def _check_valid_operand(self, other: Union[int, float, "IndexDispersion"]):
+        if not isinstance(other, (int, float, IndexDispersion, dispersions.Table)):
+            raise TypeError(
+                f"unsupported operand type(s) for +: '{type(self)}' and '{type(other)}'"
+            )
 
-        if isinstance(other, IndexDispersion):
-            raise NotImplementedError(
-                "Adding of index based dispersions is not supported yet"
+    def __radd__(
+        self, other: Union[int, float, "IndexDispersion"]
+    ) -> "IndexDispersionSum":
+        """Add up the dielectric function of multiple models"""
+        return self.__add__(other)
+
+    def __add__(
+        self, other: Union[int, float, "IndexDispersion"]
+    ) -> "IndexDispersionSum":
+        if isinstance(other, Dispersion):
+            raise TypeError(
+                "Cannot add refractive index and dielectric function based dispersions."
             )
 
-        raise TypeError(
-            "Cannot add refractive index and dielectric function based dispersions."
-        )
+        self._check_valid_operand(other)
+
+        if isinstance(other, dispersions.Table):
+            return other.__add__(self)
+
+        if isinstance(other, IndexDispersionSum):
+            other.index_dispersions.append(self)
+            return other
+
+        if isinstance(other, (int, float)):
+            return IndexDispersionSum(self, dispersions.ConstantRefractiveIndex(other))
+
+        return IndexDispersionSum(self, other)
 
     def dielectric_function(self, lbda: npt.ArrayLike) -> npt.NDArray:
         return self.refractive_index(lbda) ** 2
 
+    def as_dielectric(self):
+        """
+        Returns this class as Dispersion.
+        This method may be used to add dielectric and index based dispersions.
+        Please ensure that you know what you are doing as building dielectric
+        and index based dispersions is normally mathematically wrong.
+        """
+        diel_disp = deepcopy(self)
+        diel_disp.__class__ = Dispersion  # pylint: disable=invalid-name
+        diel_disp.dielectric_function = self.dielectric_function
+        return diel_disp
+
 
 class DispersionFactory:
     """A factory class for dispersion objects"""
 
     @staticmethod
     def get_dispersion(identifier: str, *args, **kwargs) -> Dispersion:
-        """Creates a Dispersion object identified by its string name and initializes it with the
-        given parameters.
+        """Creates a Dispersion object identified by its string name and initializes it
+        with the given parameters.
 
         Args:
             identifier (str): Identifier of the Dispersion object, e.g. Cauchy.
@@ -275,14 +343,14 @@ class DispersionSum(Dispersion):
 
     def __init__(self, *disps: Dispersion) -> None:
         super().__init__()
-        self.dispersions = list(disps)
+
+        self.dispersions = []
+        for disp in disps:
+            self += disp
 
     def __add__(self, other: Union[int, float, "Dispersion"]) -> "DispersionSum":
         self._check_valid_operand(other)
 
-        if self._is_non_std_dispersion(other):
-            return other.__add__(self)
-
         if isinstance(other, DispersionSum):
             self.dispersions += other.dispersions
             return self
@@ -298,7 +366,7 @@ def dielectric_function(self, lbda: npt.ArrayLike) -> npt.NDArray:
         dielectric_function = sum(
             disp.dielectric_function(lbda) for disp in self.dispersions
         )
-        return dielectric_function
+        return np.array(dielectric_function)
 
     def __repr__(self):
         return (
@@ -307,3 +375,48 @@ def __repr__(self):
             + "\n\n"
             + "\n\n".join(map(str, self.dispersions))
         )
+
+
+class IndexDispersionSum(IndexDispersion):
+    """Represents the sum of two index dispersions"""
+
+    single_params_template: dict = {}
+    rep_params_template: dict = {}
+    index_dispersions: List[IndexDispersion]
+
+    def __init__(self, *disps: IndexDispersion) -> None:
+        super().__init__()
+
+        self.index_dispersions = []
+        for disp in disps:
+            self += disp
+
+    def __add__(
+        self, other: Union[int, float, "IndexDispersion"]
+    ) -> "IndexDispersionSum":
+        self._check_valid_operand(other)
+
+        if isinstance(other, IndexDispersionSum):
+            self.index_dispersions += other.index_dispersions
+            return self
+
+        if isinstance(other, (int, float)):
+            self.index_dispersions.append(dispersions.ConstantRefractiveIndex(n=other))
+            return self
+
+        self.index_dispersions.append(other)
+        return self
+
+    def refractive_index(self, lbda: npt.ArrayLike) -> npt.NDArray:
+        refractive_index = sum(
+            disp.refractive_index(lbda) for disp in self.index_dispersions
+        )
+        return np.array(refractive_index)
+
+    def __repr__(self):
+        return (
+            "IndexDispersionSum\n"
+            + "=" * 13
+            + "\n\n"
+            + "\n\n".join(map(str, self.index_dispersions))
+        )
diff --git a/src/elli/dispersions/cauchy.py b/src/elli/dispersions/cauchy.py
index 0bea46c6..d12ca3c4 100644
--- a/src/elli/dispersions/cauchy.py
+++ b/src/elli/dispersions/cauchy.py
@@ -22,7 +22,8 @@ class Cauchy(IndexDispersion):
     Output:
         .. math::
             \varepsilon^{1/2}(\lambda) =
-            \boldsymbol{n_0} + 100  \boldsymbol{n_1}/\lambda^2 + 10^7 \boldsymbol{n_2}/\lambda^4
+            \boldsymbol{n_0} + 100  \boldsymbol{n_1}/\lambda^2 +
+            10^7 \boldsymbol{n_2}/\lambda^4
             + i (\boldsymbol{k_0} + 100 \boldsymbol{k_1}/\lambda^2
             + 10^7 \boldsymbol{k_2}/\lambda^4)
     """
diff --git a/src/elli/dispersions/epsilon_inf.py b/src/elli/dispersions/epsilon_inf.py
index c33eecef..bc6c9591 100644
--- a/src/elli/dispersions/epsilon_inf.py
+++ b/src/elli/dispersions/epsilon_inf.py
@@ -1,5 +1,6 @@
 # Encoding: utf-8
 """Constant epsilon infinity."""
+from typing import Any, Dict
 import numpy.typing as npt
 
 from .base_dispersion import Dispersion
@@ -20,7 +21,7 @@ class EpsilonInf(Dispersion):
     """
 
     single_params_template = {"eps": 1}
-    rep_params_template = {}
+    rep_params_template: Dict[str, Any] = {}
 
     def dielectric_function(self, _: npt.ArrayLike) -> npt.NDArray:
         return self.single_params.get("eps")
diff --git a/src/elli/dispersions/formula.py b/src/elli/dispersions/formula.py
new file mode 100644
index 00000000..fba98333
--- /dev/null
+++ b/src/elli/dispersions/formula.py
@@ -0,0 +1,127 @@
+"""A formula dispersion to parse dispersion values from a formula string."""
+from typing import Dict, List, Optional
+
+import numpy as np
+import numpy.typing as npt
+
+from elli.units import ureg
+from elli.dispersions.base_dispersion import BaseDispersion, Dispersion, IndexDispersion
+from elli.formula_parser.parser import formula_parser, transformation_formula_parser
+
+
+class FormulaParser(BaseDispersion):
+    r"""A formula dispersion"""
+
+    @property
+    def single_params_template(self) -> dict:
+        return self.f_single_params
+
+    @property
+    def rep_params_template(self) -> dict:
+        return self.f_rep_params
+
+    def __init__(
+        self,
+        formula: str,
+        wavelength_axis_name: str,
+        single_params: Dict[str, float],
+        rep_params: Dict[str, npt.ArrayLike],
+        unit: Optional[str] = None,
+    ):
+        self.f_single_params: Dict[str, float] = single_params
+        self.f_axis_name: str = wavelength_axis_name
+        rep_params_len: Optional[int] = None
+        rep_params_sets: List[Dict[str, float]] = []
+
+        for key, values in rep_params.items():
+            if not isinstance(values, (np.ndarray, list)):
+                raise ValueError(
+                    "Repeated parameters must be given as dict of lists or numpy arrays"
+                )
+            for i, value in enumerate(values):
+                if i >= len(rep_params_sets):
+                    rep_params_sets.append({})
+                rep_params_sets[i][key] = value
+
+            if rep_params_len is None:
+                rep_params_len = len(values)
+                continue
+            if len(values) != rep_params_len:
+                raise ValueError(
+                    f"All repeated parameters must have the same length."
+                    f"Found {values} with length {len(values)}, "
+                    f"but previous length was {rep_params_len}."
+                )
+
+        self.f_rep_params = {}
+        if rep_params_sets:
+            self.f_rep_params = rep_params_sets[0]
+        super().__init__()
+
+        for rep_params_set in rep_params_sets:
+            self.add(**rep_params_set)
+
+        self.rep_params_dl = {}
+        if self.rep_params:
+            self.rep_params_dl = {
+                k: np.array([dic[k] for dic in self.rep_params])
+                for k in self.rep_params[0]
+            }
+
+        self.formula = formula
+
+        self._check_repr()
+
+        self._dispersion_function = self.__dispersion_function
+        if unit is not None:
+            self._set_unit_conversion(unit)
+
+    def _set_unit_conversion(self, unit: str):
+        quantity = ureg(unit)
+        if quantity.check("[length]"):
+            scaling = ureg("nm").to(unit).magnitude
+            self._dispersion_function = lambda lbda: self.__dispersion_function(
+                scaling * lbda
+            )
+            return
+
+        if quantity.check("[energy]"):
+            scaling = ureg("nm").to(unit).magnitude
+            self._dispersion_function = lambda lbda: self.__dispersion_function(
+                scaling / lbda
+            )
+            return
+
+        raise ValueError(f"Unsupported unit `{unit}`.")
+
+    def _check_repr(self):
+        representation = formula_parser().parse(self.formula).data
+
+        if isinstance(self, FormulaIndex) and not representation == "n":
+            raise ValueError(
+                f"Representation `{representation}` not supported by FormulaIndex"
+            )
+
+        if isinstance(self, Formula) and not representation == "eps":
+            raise ValueError(
+                f"Representation `{representation}` not supported by Formula"
+            )
+
+    def __dispersion_function(self, lbda: npt.ArrayLike) -> npt.NDArray:
+        return transformation_formula_parser(
+            self.f_axis_name, lbda, self.single_params, self.rep_params_dl
+        ).parse(self.formula)[1]
+
+
+class Formula(Dispersion, FormulaParser):
+    r"A formula dispersion"
+
+    def dielectric_function(self, lbda: npt.ArrayLike) -> npt.NDArray:
+        return self._dispersion_function(lbda)
+
+
+class FormulaIndex(IndexDispersion, FormulaParser):
+    r"""A formula dispersion in refractive index formulation"""
+
+    def refractive_index(self, lbda: npt.ArrayLike) -> npt.NDArray:
+        return self._dispersion_function(lbda)
diff --git a/src/elli/dispersions/pseudo_dielectric.py b/src/elli/dispersions/pseudo_dielectric.py
index d06d853d..f0c6a7f0 100644
--- a/src/elli/dispersions/pseudo_dielectric.py
+++ b/src/elli/dispersions/pseudo_dielectric.py
@@ -45,10 +45,6 @@ class PseudoDielectricFunction(Dispersion):
     def __init__(self, *args, **kwargs):
         super().__init__(*args, **kwargs)
 
-        for param in self.single_params:
-            if self.single_params[param] is None:
-                raise InvalidParameters(f"Please specify parameter {param}")
-
         rho = np.tan(np.deg2rad(self.single_params.get("psi"))) * np.exp(
             -1j * np.deg2rad(self.single_params.get("delta"))
         )
diff --git a/src/elli/dispersions/sellmeier.py b/src/elli/dispersions/sellmeier.py
index e95c798c..668e06eb 100644
--- a/src/elli/dispersions/sellmeier.py
+++ b/src/elli/dispersions/sellmeier.py
@@ -13,7 +13,7 @@ class Sellmeier(Dispersion):
 
     Repeated parameters:
         :A: Coefficient for n\ :sup:`2` contribution. Defaults to 0.
-        :B: Resonance wavelength. Defaults to 0. Unit in µm\ :sup:`-2`.
+        :B: Resonance wavelength. Defaults to 0. Unit in µm\ :sup:`2`.
 
     Output:
         .. math::
diff --git a/src/elli/dispersions/sellmeier_custom.py b/src/elli/dispersions/sellmeier_custom.py
index 0698b9a1..b611dd68 100644
--- a/src/elli/dispersions/sellmeier_custom.py
+++ b/src/elli/dispersions/sellmeier_custom.py
@@ -13,9 +13,9 @@ class SellmeierCustomExponent(Dispersion):
 
     Repeated parameters:
         :A: Coefficient for n\ :sup:`2` contribution. Defaults to 0.
+        :e_A: Exponent for the wavelength in the numerator. Defaults to 1.
         :B: Resonance wavelength. Defaults to 0. Unit in µm\ :sup:`-2`.
-        :e_A:
-        :e_B:
+        :e_B: Exponent for B. Defaults to 1.
 
     Output:
         .. math::
@@ -26,7 +26,7 @@ class SellmeierCustomExponent(Dispersion):
     """
 
     single_params_template = {}
-    rep_params_template = {"A": 0, "B": 0, "e_A": 1, "e_B": 1}
+    rep_params_template = {"A": 0, "e_A": 1, "B": 0, "e_B": 1}
 
     def dielectric_function(self, lbda: npt.ArrayLike) -> npt.NDArray:
         lbda = lbda / 1e3
diff --git a/src/elli/dispersions/table_epsilon.py b/src/elli/dispersions/table_epsilon.py
index 57afa6da..b9c6a22b 100644
--- a/src/elli/dispersions/table_epsilon.py
+++ b/src/elli/dispersions/table_epsilon.py
@@ -1,11 +1,11 @@
 # Encoding: utf-8
 """Dispersion specified by a table of wavelengths (nm) and dielectric function values."""
-from typing import Union
-import numpy as np
+from typing import Any, Dict, Union
 import numpy.typing as npt
 import scipy.interpolate
 
-from .base_dispersion import Dispersion, InvalidParameters
+from .epsilon_inf import EpsilonInf
+from .base_dispersion import Dispersion, InvalidParameters, DispersionSum
 
 
 class TableEpsilon(Dispersion):
@@ -14,9 +14,9 @@ class TableEpsilon(Dispersion):
     wavelength range.
 
     Single parameters:
-        :lbda (list): Wavelengths in nm. Defaults to np.linspace(0, 3000, 1000).
+        :lbda (list): Wavelengths in nm. This value must be provided.
         :epsilon: Complex dielectric function values in the convention ε1 + iε2.
-            Defaults to np.ones(1000).
+            This value must be provided.
 
     Repeated parameters:
         --
@@ -25,11 +25,8 @@ class TableEpsilon(Dispersion):
         The interpolation in the given wavelength range.
     """
 
-    single_params_template = {
-        "lbda": np.linspace(0, 3000, 1000),
-        "epsilon": np.ones(1000),
-    }
-    rep_params_template = {}
+    single_params_template = {"lbda": None, "epsilon": None}
+    rep_params_template: Dict[str, Any] = {}
 
     def __init__(self, *args, **kwargs) -> None:
         super().__init__(*args, **kwargs)
@@ -50,8 +47,27 @@ def __init__(self, *args, **kwargs) -> None:
             kind="cubic",
         )
 
-    def __add__(self, _: Union[int, float, "Dispersion"]) -> "DispersionSum":
-        raise NotImplementedError("Adding of tabular dispersions is not yet supported")
+        self.default_lbda_range = self.single_params.get("lbda")
+
+    def __add__(self, other: Union[int, float, "Dispersion"]) -> "DispersionSum":
+        if isinstance(other, (int, float)):
+            return DispersionSum(self, EpsilonInf(eps=other))
+
+        if isinstance(other, TableEpsilon):
+            raise NotImplementedError(
+                "Adding of tabular dispersions is not yet supported"
+            )
+
+        if isinstance(other, Dispersion):
+            return DispersionSum(self, other)
+
+        if isinstance(other, DispersionSum):
+            other.dispersions.append(self)
+            return other
+
+        raise TypeError(
+            f"unsupported operand type(s) for +: '{type(self)}' and '{type(other)}'"
+        )
 
     def dielectric_function(self, lbda: npt.ArrayLike) -> npt.NDArray:
         return self.interpolation(lbda)
diff --git a/src/elli/dispersions/table_index.py b/src/elli/dispersions/table_index.py
index e6281c79..2eea0fe3 100644
--- a/src/elli/dispersions/table_index.py
+++ b/src/elli/dispersions/table_index.py
@@ -1,10 +1,12 @@
 # Encoding: utf-8
 """Dispersion specified by a table of wavelengths (nm) and refractive index values."""
-import numpy as np
+from typing import Union
 import numpy.typing as npt
 import scipy.interpolate
 
-from .base_dispersion import IndexDispersion, InvalidParameters
+from elli.dispersions.constant_refractive_index import ConstantRefractiveIndex
+
+from .base_dispersion import IndexDispersion, IndexDispersionSum, InvalidParameters
 
 
 class Table(IndexDispersion):
@@ -13,9 +15,9 @@ class Table(IndexDispersion):
     wavelength range.
 
     Single parameters:
-        :lbda (list): Wavelengths in nm. Defaults to np.linspace(0, 3000, 1000).
+        :lbda (list): Wavelengths in nm. This value must be provided.
         :n: Complex refractive index values in the convention n + ik.
-            Defaults to np.ones(1000).
+            This value must be provided.
 
     Repeated parameters:
         --
@@ -24,7 +26,7 @@ class Table(IndexDispersion):
         The interpolation in the given wavelength range.
     """
 
-    single_params_template = {"lbda": np.linspace(0, 3000, 1000), "n": np.ones(1000)}
+    single_params_template = {"lbda": None, "n": None}
     rep_params_template = {}
 
     def __init__(self, *args, **kwargs) -> None:
@@ -44,5 +46,29 @@ def __init__(self, *args, **kwargs) -> None:
             kind="cubic",
         )
 
+        self.default_lbda_range = self.single_params.get("lbda")
+
+    def __add__(
+        self, other: Union[int, float, "IndexDispersion"]
+    ) -> "IndexDispersionSum":
+        if isinstance(other, (int, float)):
+            return IndexDispersionSum(self, ConstantRefractiveIndex(eps=other))
+
+        if isinstance(other, Table):
+            raise NotImplementedError(
+                "Adding of tabular dispersions is not yet supported"
+            )
+
+        if isinstance(other, IndexDispersion):
+            return IndexDispersionSum(self, other)
+
+        if isinstance(other, IndexDispersionSum):
+            other.dispersions.append(self)
+            return other
+
+        raise TypeError(
+            f"unsupported operand type(s) for +: '{type(self)}' and '{type(other)}'"
+        )
+
     def refractive_index(self, lbda: npt.ArrayLike) -> npt.NDArray:
         return self.interpolation(lbda)
diff --git a/src/elli/formula_parser/__init__.py b/src/elli/formula_parser/__init__.py
new file mode 100644
index 00000000..e69de29b
diff --git a/src/elli/formula_parser/dispersion_function_grammar.lark b/src/elli/formula_parser/dispersion_function_grammar.lark
new file mode 100644
index 00000000..7524723a
--- /dev/null
+++ b/src/elli/formula_parser/dispersion_function_grammar.lark
@@ -0,0 +1,51 @@
+?assignment: "eps" "=" kkr_expression -> eps
+             | "n" "=" kkr_expression -> n
+
+?kkr_expression: expression
+                | "<kkr>" "+" "1j" "*" term -> kkr_term
+
+?expression: term
+            | expression "+" term -> add
+            | expression "-" term -> sub
+
+?term: factor
+       | term "*" factor -> mul
+       | term "/" factor -> div
+
+?factor: power
+       | power "**" power -> power
+
+
+?power: "(" expression ")"
+        | FUNC "(" expression ")" -> func
+        | "sum" "[" repeated_expression "]" -> sum_expr
+        | NAME -> single_param_name
+        | SIGNED_NUMBER -> number
+        | BUILTIN -> builtin
+
+?repeated_expression: repeated_term
+                    | repeated_expression "+" repeated_term -> add
+                    | repeated_expression "-" repeated_term -> sub
+
+
+?repeated_term: repeated_factor
+                | repeated_term "*" repeated_factor -> mul
+                | repeated_term "/" repeated_factor -> div
+
+?repeated_factor: repeated_power
+                  | repeated_power "**" repeated_power -> power
+
+?repeated_power: "(" repeated_expression ")"
+                 | FUNC "(" repeated_expression ")" -> func
+                 | SIGNED_NUMBER -> number
+                 | NAME -> param_name
+                 | BUILTIN -> builtin
+
+FUNC.1: "sin" | "cos" | "tan" | "sqrt" | "dawsn" | "ln" | "log" | "heaviside" 
+BUILTIN.1: "1j" | "pi" | "eps_0" | "hbar" | "h" | "c" 
+
+%import common.CNAME -> NAME
+%import common.SIGNED_NUMBER
+%import common.WS_INLINE
+
+%ignore WS_INLINE
\ No newline at end of file
diff --git a/src/elli/formula_parser/parser.py b/src/elli/formula_parser/parser.py
new file mode 100644
index 00000000..29d99a63
--- /dev/null
+++ b/src/elli/formula_parser/parser.py
@@ -0,0 +1,239 @@
+#
+# Copyright The NOMAD Authors.
+#
+# This file is part of NOMAD. See https://nomad-lab.eu for further info.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#
+"""This modules creates a formula parser"""
+import os
+from operator import add, mul, neg, sub, truediv
+from typing import Dict
+
+import numpy as np
+import numpy.typing as npt
+import scipy.constants as sc
+from lark import Lark, Transformer, v_args
+from scipy.special import dawsn  # pylint: disable=no-name-in-module
+
+
+@v_args(inline=True)
+class FormulaTransformer(Transformer):
+    """Transformer class for parsing formulas"""
+
+    single_params: Dict[str, float]
+    repeated_params: Dict[str, np.ndarray]
+    no_repeated_params: int
+
+    number = float
+    add = add
+    sub = sub
+    mul = mul
+    div = truediv
+    neg = neg
+    power = pow
+
+    def _check_and_set(self, repeated_params):
+        if not repeated_params:
+            self.no_repeated_params = 0
+            return
+
+        if not isinstance(repeated_params, dict):
+            raise ValueError(
+                f"Repeated parameters must be a dict but found {type(repeated_params)}"
+            )
+
+        params = iter(repeated_params.items())
+        length = len(next(params)[1])
+        for name, param in params:
+            if not isinstance(param, np.ndarray):
+                raise TypeError(
+                    f"Expected {name} to be of type numpy ndarray but found type {type(param)}"
+                )
+            if length != len(param):
+                raise ValueError("Repeated parameters must have all the same length.")
+
+        self.no_repeated_params = length
+
+    def _check_and_set_single(self, single_params):
+        for name, param in single_params.items():
+            if not isinstance(param, (float, int)):
+                raise TypeError(
+                    f"Expected {name} to be of type float but found type {type(param)}."
+                )
+        self.single_params = single_params
+
+    def __init__(
+        self,
+        x_axis_name: str,
+        x_axis_values: np.ndarray,
+        single_params: Dict[str, float],
+        repeated_params: Dict[str, np.ndarray],
+    ):
+        super().__init__()
+        if not isinstance(x_axis_name, str):
+            raise TypeError("x_axis_name must be a string.")
+
+        if not isinstance(x_axis_values, np.ndarray):
+            raise TypeError("x_axis_values must be a numpy array.")
+
+        self.x_axis_name = x_axis_name
+        self.x_axis_values = x_axis_values
+
+        self._check_and_set(repeated_params)
+        self._check_and_set_single(single_params)
+
+        self.repeated_params = repeated_params
+        self.single_params = single_params
+
+    def eps(self, inp):
+        """Return an epsilon type formula"""
+        return "eps", inp
+
+    # pylint: disable=invalid-name
+    def n(self, inp):
+        """Return an index type formula"""
+        return "n", inp
+
+    def kkr_term(self, term):
+        """Calculate the kramers kronig transformation on the function"""
+        raise NotImplementedError("kkr transformation not yet implemented")
+
+    def func(self, name, val):
+        """Evaluates a function"""
+        names = {
+            "sin": np.sin,
+            "cos": np.cos,
+            "tan": np.tan,
+            "sqrt": np.emath.sqrt,
+            "dawsn": dawsn,
+            "ln": np.log,
+            "log": np.log10,
+            "heaviside": np.heaviside,
+        }
+
+        if name in names:
+            return names[name](val)
+
+        raise ValueError(f"Unknown function: {name}")
+
+    def builtin(self, name):
+        """Returns the values for builtin tokens"""
+        names = {
+            "1j": 1j,
+            "pi": sc.pi,
+            "eps_0": sc.epsilon_0,
+            "hbar": sc.hbar,
+            "h": sc.h,
+            "c": sc.c,
+        }
+
+        if name in names:
+            return names[name]
+
+        raise ValueError(f"Unknown constant: {name}")
+
+    def sum_expr(self, expr):
+        """Sum an expression"""
+        return expr.sum(axis=1)
+
+    def single_param_name(self, name):
+        """Return a parameter inside a non-repeated section"""
+        if name == self.x_axis_name:
+            return self.x_axis_values
+
+        if name in self.single_params:
+            return self.single_params[name]
+
+        raise ValueError(f"No such parameter {name}")
+
+    def param_name(self, name):
+        """Return a parameter inside a repeated section"""
+        if name == self.x_axis_name:
+            return np.einsum(
+                "i,j->ij", self.x_axis_values, np.ones(self.no_repeated_params)
+            )
+
+        if name in self.single_params:
+            return self.single_params[name]
+
+        if name in self.repeated_params:
+            return self.repeated_params[name]
+
+        raise ValueError(f"No such parameter {name}")
+
+
+def formula_parser(transformer=None):
+    """Creates a formula parser.
+
+    Args:
+        transformer (lark.Transformer, optional):
+            A transformer to use with this parsing.
+            If set to None it generates the AST.
+            Defaults to None.
+
+    Returns:
+        lark.Lark: The parsing object.
+    """
+    __location__ = os.path.realpath(
+        os.path.join(os.getcwd(), os.path.dirname(__file__))
+    )
+
+    with open(
+        f"{__location__}/dispersion_function_grammar.lark", encoding="utf-8"
+    ) as formula_grammar:
+        if transformer is None:
+            return Lark(
+                formula_grammar,
+                start="assignment",
+                parser="lalr",
+            )
+
+        return Lark(
+            formula_grammar, start="assignment", parser="lalr", transformer=transformer
+        )
+
+
+def transformation_formula_parser(
+    x_axis_name: str,
+    x_axis_values: npt.ArrayLike,
+    single_params: Dict[str, float],
+    repeated_params: Dict[str, np.ndarray],
+):
+    """Creates a formula parser with the given parameters.
+    This parser is automatically evaluated based on the given parameters.
+    This is done directly whitout creating the abstract syntax tree.
+
+    Args:
+        x_axis_name (str): The name of the x-axis to use replace in the formula string.
+        x_axis_values (np.ndarray): The value array of the x-axis to replace in the formula string.
+        single_params (Dict[str, float]):
+            A dictionary of parameter name and value of single parameters.
+        repeated_params (Dict[str, np.ndarray]):
+            A dictionary of parameter name and values of repeated paremters.
+
+    Returns:
+        str, np.ndarray:
+            The evaluated formula.
+            The first tuple element indicates the type of dispersion
+            and may either be `n` for refractive index or `eps` for dielectric function.
+            The second element is the evluated formula one point for each x-axis input point.
+    """
+    return formula_parser(
+        FormulaTransformer(
+            x_axis_name=x_axis_name,
+            x_axis_values=x_axis_values,
+            single_params=single_params,
+            repeated_params=repeated_params,
+        )
+    )
diff --git a/src/elli/importer/nexus.py b/src/elli/importer/nexus.py
index 136799ec..504fbd4d 100644
--- a/src/elli/importer/nexus.py
+++ b/src/elli/importer/nexus.py
@@ -8,7 +8,12 @@
 import numpy as np
 import pandas as pd
 
-from ..utils import calc_rho
+from elli.dispersions.formula import Formula, FormulaIndex
+from elli.dispersions.table_epsilon import TableEpsilon
+from elli.dispersions.table_index import Table
+from elli.materials import BiaxialMaterial, IsotropicMaterial, UniaxialMaterial
+
+from ..utils import calc_rho, conversion_wavelength_energy
 
 
 def read_nexus_psi_delta(nxs_filename: str) -> pd.DataFrame:
@@ -63,3 +68,119 @@ def read_nexus_rho(nxs_filename: str) -> pd.DataFrame:
         and the wavelength as second column.
     """
     return calc_rho(read_nexus_psi_delta(nxs_filename))
+
+
+def read_nexus_materials(filename: str):
+    """Read the optical materials from a nexus file.
+
+    Args:
+        filename (str): The nexus filename.
+    """
+
+    def get_dispersion_function(dataset: h5py.Dataset):
+        single_params = {}
+        rep_params = {}
+
+        def get_params(_: str, dataset: h5py.Dataset):
+            if dataset.attrs.get("NX_class", "") in ["NXdispersion_single_parameter"]:
+                param_name = dataset["name"][()].decode("utf-8")
+                single_params[param_name] = dataset["value"][()]
+
+            if dataset.attrs.get("NX_class", "") in ["NXdispersion_repeated_parameter"]:
+                param_name = dataset["name"][()].decode("utf-8")
+                rep_params[param_name] = dataset["values"][()]
+
+        identifier = None
+        if "wavelength_identifier" in dataset:
+            identifier = dataset["wavelength_identifier"][()].decode("utf-8")
+            unit = (
+                f"{dataset['wavelength_unit'][()]} "
+                f"{dataset['wavelength_unit'].attrs.get('units', '')}"
+            )
+
+        if "energy_identifier" in dataset:
+            raise NotImplementedError(
+                "Using dispersions with an energy axis is not yet supported."
+            )
+
+        representation = dataset["representation"][()].decode("utf-8")
+        formula = dataset["formula"][()].decode("utf-8")
+        dataset.visititems(get_params)
+
+        if representation == "eps":
+            return Formula(formula, identifier, single_params, rep_params, unit)
+
+        if representation == "n":
+            return FormulaIndex(formula, identifier, single_params, rep_params, unit)
+
+        raise ValueError(f"Unsupported representation {representation}")
+
+    def get_dispersion_table(dataset: h5py.Dataset):
+        wavelength = None
+        if "wavelength" in dataset:
+            wavelength = dataset["wavelength"]
+
+        if "energy" in dataset:
+            wavelength = conversion_wavelength_energy(dataset["energy"])
+
+        if wavelength is None:
+            raise ValueError("No wavelength array found in dataset.")
+
+        if "refractive_index" in dataset:
+            return Table(lbda=wavelength, n=dataset["refractive_index"][()])
+
+        if "dielectric_function" in dataset:
+            return TableEpsilon(
+                lbda=wavelength, epsilon=dataset["dielectric_function"][()]
+            )
+
+        raise ValueError(
+            "Invalid dispersion table, neither `refractive_index` "
+            "nor `dielectric_function` found."
+        )
+
+    def get_dispersion(dataset: h5py.Dataset):
+        dispersion = None
+        for data in dataset.values():
+            if data.attrs.get("NX_class") in ["NXdispersion_function"]:
+                dispersion = (
+                    get_dispersion_function(data)
+                    if dispersion is None
+                    else dispersion + get_dispersion_function(data)
+                )
+
+            if data.attrs.get("NX_class") in ["NXdispersion_table"]:
+                dispersion = (
+                    get_dispersion_table(data)
+                    if dispersion is None
+                    else dispersion + get_dispersion_table(data)
+                )
+
+        return dispersion
+
+    def get_material(dataset: h5py.Dataset):
+        dispersions = {}
+        for dispersion in [f"dispersion_{axis}" for axis in ["x", "y", "z"]]:
+            if dispersion not in dataset:
+                if dispersion == "dispersion_x":
+                    raise ValueError("Invalid dispersion file. `dispersion_x` missing")
+                continue
+            dispersions[dispersion] = get_dispersion(dataset[dispersion])
+
+        if len(dispersions) == 1:
+            return IsotropicMaterial(dispersions["dispersion_x"])
+        if len(dispersions) == 2:
+            return UniaxialMaterial(
+                dispersions["dispersion_x"], dispersions["dispersion_z"]
+            )
+        if len(dispersions) == 3:
+            return BiaxialMaterial(**dispersions)
+
+        raise ValueError("Could not create material from nexus file.")
+
+    entries = {}
+    with h5py.File(filename) as h5file:
+        for entry, data in h5file.items():
+            entries[entry] = get_material(data)
+
+    return entries
diff --git a/src/elli/units.py b/src/elli/units.py
new file mode 100644
index 00000000..b47b0079
--- /dev/null
+++ b/src/elli/units.py
@@ -0,0 +1,5 @@
+"""The pint unit registry for pyElli"""
+from pint import UnitRegistry
+
+ureg = UnitRegistry()
+ureg.enable_contexts("spectroscopy")
diff --git a/tests/fixtures.py b/tests/fixtures.py
new file mode 100644
index 00000000..125899e3
--- /dev/null
+++ b/tests/fixtures.py
@@ -0,0 +1,19 @@
+import os
+from distutils import dir_util
+from pytest import fixture
+
+
+@fixture
+def datadir(tmp_path, request):
+    """
+    Fixture responsible for searching a folder with the same name of test
+    module and, if available, moving all contents to a temporary directory so
+    tests can use them freely.
+    """
+    filename = request.module.__file__
+    test_dir, _ = os.path.splitext(filename)
+
+    if os.path.isdir(test_dir):
+        dir_util.copy_tree(test_dir, str(tmp_path))
+
+    return tmp_path
diff --git a/tests/test_dispersion_adding.py b/tests/test_dispersion_adding.py
index 172f7346..4740cf60 100644
--- a/tests/test_dispersion_adding.py
+++ b/tests/test_dispersion_adding.py
@@ -1,26 +1,63 @@
 """Test adding of dispersions"""
 import pytest
+import numpy as np
 from numpy.testing import assert_array_almost_equal
 from elli import Cauchy, Sellmeier
-from elli.dispersions.base_dispersion import DispersionSum
+from elli.dispersions.base_dispersion import DispersionSum, IndexDispersionSum
 from elli.dispersions.table_epsilon import TableEpsilon
 
 
-def test_fail_on_adding_index_dispersion():
-    """Test whether adding for an index based model fails"""
-    cauchy_err_str = "Adding of index based dispersions is not supported yet"
-    with pytest.raises(NotImplementedError) as sum_err:
-        _ = Cauchy() + Cauchy()
+def test_adding_index_dispersion():
+    """Test correct adding of index based dispersions"""
+    index_dispersion_sum = Cauchy() + Cauchy()
 
-    assert cauchy_err_str in str(sum_err.value)
+    assert_array_almost_equal(
+        index_dispersion_sum.get_dielectric(),
+        (Cauchy().get_refractive_index() * 2) ** 2,
+    )
 
 
 def test_fail_on_adding_index_and_diel_dispersion():
     """Test whether the adding fails for an index based and dielectric dispersion"""
 
-    for disp in [1, Sellmeier()]:
-        with pytest.raises(TypeError) as sum_err:
-            _ = disp + Cauchy()
+    with pytest.raises(TypeError) as sum_err:
+        _ = Sellmeier() + Cauchy()
+
+    assert (
+        "Cannot add refractive index and dielectric function based dispersions."
+        in str(sum_err.value)
+    )
+
+
+@pytest.mark.parametrize(
+    "dispersions",
+    [
+        (DispersionSum(Sellmeier(), Sellmeier()), Cauchy()),
+        (IndexDispersionSum(Cauchy(), Cauchy()), Sellmeier()),
+        (
+            DispersionSum(Sellmeier(), Sellmeier()),
+            IndexDispersionSum(Cauchy(), Cauchy()),
+        ),
+        (Sellmeier(), Cauchy()),
+    ],
+)
+def test_fail_on_adding_index_and_diel_dispersion_sum(dispersions):
+    """Adding of index based and diel based dispersion sums fails"""
+
+    with pytest.raises(TypeError):
+        _ = dispersions[0] + dispersions[1]
+
+    with pytest.raises(TypeError):
+        _ = dispersions[1] + dispersions[0]
+
+
+def test_fail_on_adding_index_and_diel_dispersion_as_args():
+    """
+    The adding of dispersion fails for an index based and dielectric dispersion
+    when provided as args to DispersionSum
+    """
+    with pytest.raises(TypeError) as sum_err:
+        DispersionSum(Sellmeier(), Cauchy())
 
         assert (
             "Cannot add refractive index and dielectric function based dispersions."
@@ -62,11 +99,112 @@ def test_flat_dispersion_sum_on_multiple_add():
     )
 
 
-def test_adding_of_tabular_dispersions():
-    """Tests correct adding of tabular dispersions"""
+def test_flat_dispersion_on_adding_with_dispersion_sum():
+    """
+    DispersionSum is kept flat even when a mixture of
+    Dispersions and DispersionSums are added
+    """
+    dispersion_sum = (
+        Sellmeier()
+        + DispersionSum(DispersionSum(Sellmeier(), Sellmeier()), Sellmeier())
+        + Sellmeier()
+    )
+
+    assert isinstance(dispersion_sum, DispersionSum)
+    assert len(dispersion_sum.dispersions) == 5
+
+    for disp in dispersion_sum.dispersions:
+        assert isinstance(disp, Sellmeier)
+
+    assert_array_almost_equal(
+        dispersion_sum.get_dielectric_df().values,
+        5 * Sellmeier().get_dielectric_df().values,
+    )
+
+
+def test_multiple_dispersion_sum_args():
+    """Multiple Dispersions can be provided via the DispersionSum args"""
+    dispersion_sum = DispersionSum(Sellmeier(), Sellmeier(), Sellmeier())
+
+    assert isinstance(dispersion_sum, DispersionSum)
+    assert len(dispersion_sum.dispersions) == 3
+
+    for disp in dispersion_sum.dispersions:
+        assert isinstance(disp, Sellmeier)
+
+    assert_array_almost_equal(
+        dispersion_sum.get_dielectric_df().values,
+        3 * Sellmeier().get_dielectric_df().values,
+    )
+
+
+def test_nested_dispersion_sum_args():
+    """
+    DispersionSum is kept flat even for nested
+    DispersionSum args
+    """
+    dispersion_sum = DispersionSum(
+        DispersionSum(DispersionSum(Sellmeier(), Sellmeier()), Sellmeier()), Sellmeier()
+    )
+
+    assert isinstance(dispersion_sum, DispersionSum)
+    assert len(dispersion_sum.dispersions) == 4
+
+    for disp in dispersion_sum.dispersions:
+        assert isinstance(disp, Sellmeier)
+
+    assert_array_almost_equal(
+        dispersion_sum.get_dielectric_df().values,
+        4 * Sellmeier().get_dielectric_df().values,
+    )
+
+
+def test_flattening_of_dispersion_sum_args():
+    """When a DispersionSum is passed via a DisperionSum arg it is flattened."""
+    dispersion_sum = DispersionSum(Sellmeier(), DispersionSum(Sellmeier(), Sellmeier()))
+
+    assert isinstance(dispersion_sum, DispersionSum)
+    assert len(dispersion_sum.dispersions) == 3
+
+    for disp in dispersion_sum.dispersions:
+        assert isinstance(disp, Sellmeier)
+
+    assert_array_almost_equal(
+        dispersion_sum.get_dielectric_df().values,
+        3 * Sellmeier().get_dielectric_df().values,
+    )
+
+
+def test_adding_of_float_to_tabular_epsilon_dispersion():
+    """Tests correct adding of a float value to tabular dispersions"""
+
+    table_eps = TableEpsilon(lbda=np.linspace(200, 1000, 801), epsilon=np.ones(801)) + 1
+
+    assert_array_almost_equal(
+        table_eps.get_dielectric(),
+        np.ones(801) * 2,
+    )
+
+
+def test_adding_of_dispersion_function_and_table():
+    """Dispersion function and table can be added"""
+
+    table = TableEpsilon(lbda=np.linspace(200, 1000, 801), epsilon=np.ones(801))
+    sellmeier = Sellmeier().add(1, 1)
+
+    assert_array_almost_equal(
+        (table + sellmeier).get_dielectric(),
+        table.get_dielectric() + sellmeier.get_dielectric(),
+    )
+
+
+def test_fail_on_adding_tabular_dispersions():
+    """Adding two tabular dispersions should return an NotImplementedError"""
 
     with pytest.raises(NotImplementedError) as not_impl_err:
-        _ = TableEpsilon() + 1
+        _ = TableEpsilon(
+            lbda=np.linspace(200, 1000, 801), epsilon=np.ones(801)
+        ) + TableEpsilon(lbda=np.linspace(200, 1000, 801), epsilon=np.ones(801))
 
     assert (
         str(not_impl_err.value) == "Adding of tabular dispersions is not yet supported"
diff --git a/tests/test_dispersions.py b/tests/test_dispersions.py
index 3ddb107c..dc36a643 100644
--- a/tests/test_dispersions.py
+++ b/tests/test_dispersions.py
@@ -59,8 +59,6 @@ def test_regression_dispersions_default(datadir):
         "Sellmeier",
         "Tanguy",
         "TaucLorentz",
-        "Table",
-        "TableEpsilon",
     ]
     lbda = np.linspace(400, 1000, 500)
 
diff --git a/tests/test_dispersions/TableEpsilon_default.csv b/tests/test_dispersions/TableEpsilon_default.csv
deleted file mode 100644
index 3a5a6f9f..00000000
--- a/tests/test_dispersions/TableEpsilon_default.csv
+++ /dev/null
@@ -1,501 +0,0 @@
-Wavelength,ϵ1,ϵ2
-400.0,0.9999999999999998,0.0
-401.2024048096192,1.0,0.0
-402.40480961923845,1.0000000000000002,0.0
-403.60721442885773,1.0000000000000002,0.0
-404.80961923847696,1.0000000000000002,0.0
-406.0120240480962,1.0000000000000002,0.0
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-408.4168336673347,1.0000000000000004,0.0
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-414.42885771543087,1.0,0.0
-415.6312625250501,1.0000000000000002,0.0
-416.8336673346693,1.0000000000000002,0.0
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-438.47695390781564,1.0,0.0
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diff --git a/tests/test_dispersions/Table_default.csv b/tests/test_dispersions/Table_default.csv
deleted file mode 100644
index 3a5a6f9f..00000000
--- a/tests/test_dispersions/Table_default.csv
+++ /dev/null
@@ -1,501 +0,0 @@
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-907.4148296593187,1.0,0.0
-908.6172344689379,1.0,0.0
-909.8196392785571,1.0000000000000002,0.0
-911.0220440881765,1.0,0.0
-912.2244488977956,1.0,0.0
-913.4268537074149,1.0,0.0
-914.6292585170341,0.9999999999999999,0.0
-915.8316633266534,1.0,0.0
-917.0340681362726,1.0,0.0
-918.2364729458918,1.0,0.0
-919.438877755511,1.0,0.0
-920.6412825651303,1.0000000000000004,0.0
-921.8436873747495,0.9999999999999999,0.0
-923.0460921843688,0.9999999999999999,0.0
-924.248496993988,1.0,0.0
-925.4509018036073,0.9999999999999999,0.0
-926.6533066132265,1.0,0.0
-927.8557114228457,0.9999999999999999,0.0
-929.058116232465,0.9999999999999999,0.0
-930.2605210420842,0.9999999999999998,0.0
-931.4629258517034,0.9999999999999998,0.0
-932.6653306613227,1.0,0.0
-933.867735470942,0.9999999999999999,0.0
-935.0701402805612,1.0,0.0
-936.2725450901804,1.0,0.0
-937.4749498997996,0.9999999999999999,0.0
-938.6773547094189,0.9999999999999997,0.0
-939.8797595190381,1.0,0.0
-941.0821643286573,0.9999999999999999,0.0
-942.2845691382765,1.0,0.0
-943.4869739478959,0.9999999999999999,0.0
-944.6893787575151,1.0000000000000002,0.0
-945.8917835671343,1.0000000000000002,0.0
-947.0941883767536,1.0,0.0
-948.2965931863728,1.0,0.0
-949.498997995992,1.0000000000000004,0.0
-950.7014028056112,1.0000000000000002,0.0
-951.9038076152304,1.0,0.0
-953.1062124248498,0.9999999999999999,0.0
-954.308617234469,1.0,0.0
-955.5110220440882,1.0,0.0
-956.7134268537075,1.0,0.0
-957.9158316633267,1.0,0.0
-959.1182364729459,1.0,0.0
-960.3206412825651,1.0000000000000002,0.0
-961.5230460921844,1.0,0.0
-962.7254509018037,1.0,0.0
-963.9278557114229,0.9999999999999999,0.0
-965.1302605210421,1.0,0.0
-966.3326653306614,1.0,0.0
-967.5350701402806,1.0,0.0
-968.7374749498998,1.0000000000000002,0.0
-969.939879759519,1.0,0.0
-971.1422845691383,1.0,0.0
-972.3446893787576,1.0000000000000002,0.0
-973.5470941883768,1.0000000000000002,0.0
-974.749498997996,1.0000000000000002,0.0
-975.9519038076153,1.0,0.0
-977.1543086172345,0.9999999999999998,0.0
-978.3567134268537,0.9999999999999999,0.0
-979.559118236473,1.0000000000000002,0.0
-980.7615230460922,1.0000000000000002,0.0
-981.9639278557115,1.0,0.0
-983.1663326653307,1.0,0.0
-984.36873747495,1.0,0.0
-985.5711422845692,1.0,0.0
-986.7735470941884,1.0000000000000002,0.0
-987.9759519038076,1.0,0.0
-989.1783567134269,1.0000000000000002,0.0
-990.3807615230461,1.0000000000000002,0.0
-991.5831663326654,0.9999999999999999,0.0
-992.7855711422847,0.9999999999999998,0.0
-993.9879759519039,1.0,0.0
-995.1903807615231,1.0,0.0
-996.3927855711423,1.0000000000000002,0.0
-997.5951903807616,1.0000000000000002,0.0
-998.7975951903808,1.0000000000000002,0.0
-1000.0,0.9999999999999999,0.0
diff --git a/tests/test_formula_dispersion.py b/tests/test_formula_dispersion.py
new file mode 100644
index 00000000..43b24b42
--- /dev/null
+++ b/tests/test_formula_dispersion.py
@@ -0,0 +1,68 @@
+"""Tests for the formula dispersion"""
+import numpy as np
+from numpy.testing import assert_array_almost_equal
+import pytest
+
+from elli.dispersions import Sellmeier, Formula
+from elli.dispersions.cauchy import Cauchy
+from elli.dispersions.formula import FormulaIndex
+
+
+@pytest.mark.parametrize(
+    "ref_model, formula_model, formula, single_params, rep_params, unit",
+    [
+        (
+            Sellmeier,
+            Formula,
+            "eps = 1 + sum[A * (lbda * 1e-3)**2 / ((lbda * 1e-3)  ** 2 - B)]",
+            {},
+            {"A": [1, 1, 1], "B": [0.1, 0.1, 0.1]},
+            "nm",
+        ),
+        (
+            Sellmeier,
+            Formula,
+            "eps = 1 + sum[A * lbda**2 / (lbda** 2 - B)]",
+            {},
+            {"A": [1, 1, 1], "B": [0.1, 0.1, 0.1]},
+            "micrometer",
+        ),
+        (
+            Cauchy,
+            FormulaIndex,
+            (
+                "n = n0 + 1e2 * n1 / lbda ** 2 + 1e7 * n2 / lbda ** 4 + "
+                "1j * (k0 + 1e2 * k1 / lbda ** 2 + 1e7 * k2 / lbda ** 4)"
+            ),
+            {"n0": 1.5, "n1": 1, "n2": 1, "k0": 1, "k1": 1, "k2": 1},
+            {},
+            "nm",
+        ),
+    ],
+)
+def test_formula_reproduces_predefined(
+    ref_model, formula_model, formula, single_params, rep_params, unit
+):
+    """The formula dispersion reproduces other dispersion models"""
+    lbda = np.linspace(400, 1500, 500)
+
+    disp = ref_model(**single_params)
+    for params in zip(*rep_params.values()):
+        disp.add(*params)
+
+    formula_disp = formula_model(formula, "lbda", single_params, rep_params, unit)
+
+    assert_array_almost_equal(
+        disp.get_dielectric(lbda), formula_disp.get_dielectric(lbda)
+    )
+
+
+def test_formula_fails_on_wrong_repr():
+    """The formula dispersion fails when it is tried to be
+    initialized with the wrong represenation"""
+
+    with pytest.raises(ValueError):
+        Formula("n = 1", "", {}, {})
+
+    with pytest.raises(ValueError):
+        FormulaIndex("eps = 1", "", {}, {})
diff --git a/tests/test_nexus.py b/tests/test_nexus.py
index 8e649106..700aff75 100644
--- a/tests/test_nexus.py
+++ b/tests/test_nexus.py
@@ -1,27 +1,10 @@
 """Tests for a TiO2/SiO2/Si reference layer"""
 from __future__ import unicode_literals
 
-import os
-from distutils import dir_util
-
-import elli
 from pytest import fixture
 
-
-@fixture
-def datadir(tmpdir, request):
-    """
-    Fixture responsible for searching a folder with the same name of test
-    module and, if available, moving all contents to a temporary directory so
-    tests can use them freely.
-    """
-    filename = request.module.__file__
-    test_dir, _ = os.path.splitext(filename)
-
-    if os.path.isdir(test_dir):
-        dir_util.copy_tree(test_dir, str(tmpdir))
-
-    return tmpdir
+from fixtures import datadir  # pylint: disable=unused-import
+import elli
 
 
 @fixture
@@ -30,7 +13,7 @@ def nexus_psi_delta_file(datadir):
     """
     Fixture which returns the nexus file containting the psi / delta measurement data.
     """
-    return datadir.join("ellips.test.nxs")
+    return datadir / "ellips.test.nxs"
 
 
 # pylint: disable=redefined-outer-name
diff --git a/tests/test_nexus_formula.py b/tests/test_nexus_formula.py
new file mode 100644
index 00000000..e941980d
--- /dev/null
+++ b/tests/test_nexus_formula.py
@@ -0,0 +1,216 @@
+"""Test loading optical models from nexus dispersive material files"""
+import numpy as np
+from numpy.testing import assert_array_almost_equal
+import h5py
+
+from fixtures import datadir  # pylint: disable=unused-import
+from elli.dispersions.table_index import Table
+from elli.importer.nexus import read_nexus_materials
+from elli.dispersions.base_dispersion import IndexDispersionSum
+from elli.dispersions.polynomial import Polynomial
+from elli.dispersions.sellmeier import Sellmeier
+from elli.dispersions.sellmeier_custom import SellmeierCustomExponent
+from elli.materials import BiaxialMaterial, IsotropicMaterial, UniaxialMaterial
+
+
+def test_read_nexus_without_errors(datadir):
+    """All dispersive materials are loaded without errors"""
+    for file in datadir.iterdir():
+        read_nexus_materials(file)
+
+
+def test_read_nexus_nk_table(datadir):
+    """An isotropic nk table is loaded properly"""
+    nk_file = datadir / "MoTe2-Beal.nxs"
+
+    with h5py.File(nk_file, "r") as h5file:
+        dispersion_path = "/entry/dispersion_x/dispersion_table_nk"
+        lbda = h5file[f"{dispersion_path}/wavelength"][()]
+
+        table_manual = Table(
+            lbda=lbda,
+            n=h5file[f"{dispersion_path}/refractive_index"][()],
+        )
+
+    nexus_material = read_nexus_materials(nk_file)["entry"]
+
+    assert isinstance(nexus_material, IsotropicMaterial)
+
+    assert_array_almost_equal(
+        table_manual.get_dielectric(lbda),
+        nexus_material.dispersion_x.get_dielectric(lbda),
+    )
+
+
+def test_read_nexus_uniaxial_material_with_table(datadir):
+    """An uniaxial material with tabulated data is loaded correctly."""
+    uniaxial_file = datadir / "MoSe2-Munkhbat-o.nxs"
+
+    with h5py.File(uniaxial_file, "r") as h5file:
+        dispersion_x_path = "/entry/dispersion_x/dispersion_table_nk"
+        lbda = h5file[f"{dispersion_x_path}/wavelength"][()]
+
+        table_x_manual = Table(
+            lbda=lbda,
+            n=h5file[f"{dispersion_x_path}/refractive_index"][()],
+        )
+
+        dispersion_z_path = "/entry/dispersion_z/dispersion_table_n"
+        lbda = h5file[f"{dispersion_z_path}/wavelength"][()]
+
+        table_z_manual = Table(
+            lbda=lbda, n=h5file[f"{dispersion_z_path}/refractive_index"][()]
+        )
+
+    nexus_material = read_nexus_materials(uniaxial_file)["entry"]
+
+    assert isinstance(nexus_material, UniaxialMaterial)
+
+    assert_array_almost_equal(
+        table_x_manual.get_dielectric(lbda),
+        nexus_material.dispersion_x.get_dielectric(lbda),
+    )
+
+    assert_array_almost_equal(
+        table_z_manual.get_dielectric(lbda),
+        nexus_material.dispersion_z.get_dielectric(lbda),
+    )
+
+
+def test_read_nexus_for_sellmeier_table_sum(datadir):
+    """A sum of sellmeier and a table is read correctly"""
+    nexus = datadir / "Si-Chandler-Horowitz.nxs"
+
+    def read_sellmeier(h5file: h5py.File):
+        sellmeier_path = "/entry/dispersion_x/sellmeier"
+        params_A = h5file[f"{sellmeier_path}/A/values"][()]
+        params_B = h5file[f"{sellmeier_path}/B/values"][()]
+        params_e1 = h5file[f"{sellmeier_path}/e1/values"][()]
+        params_e2 = h5file[f"{sellmeier_path}/e2/values"][()]
+        eps_inf = h5file["/entry/dispersion_x/sellmeier/eps_inf/value"][()]
+
+        sellmeier = SellmeierCustomExponent()
+        for A, B, e1, e2 in zip(params_A, params_B, params_e1, params_e2):
+            sellmeier.add(A, e1, B, e2)
+
+        return (sellmeier + eps_inf).as_index()
+
+    with h5py.File(nexus, "r") as h5file:
+        table_path = "/entry/dispersion_x/dispersion_table_k"
+        lbda = h5file[f"{table_path}/wavelength"][()]
+
+        table = Table(lbda=lbda, n=h5file[f"{table_path}/refractive_index"][()])
+
+        dispersion = table + read_sellmeier(h5file)
+
+    nexus_material = read_nexus_materials(nexus)["entry"]
+
+    assert isinstance(nexus_material, IsotropicMaterial)
+    assert isinstance(nexus_material.dispersion_x, IndexDispersionSum)
+
+    assert_array_almost_equal(
+        dispersion.get_dielectric(lbda),
+        nexus_material.dispersion_x.get_dielectric(lbda),
+    )
+
+
+def test_read_nexus_sellmeier(datadir):
+    """A sellmeier dispersion is read correctly"""
+    nexus = datadir / "Si-Salzberg.nxs"
+    lbda = np.linspace(1357, 11040, 100)
+
+    with h5py.File(nexus, "r") as h5file:
+        sellmeier_path = "/entry/dispersion_x/sellmeier"
+        params_A = h5file[f"{sellmeier_path}/A/values"][()]
+        params_B = h5file[f"{sellmeier_path}/B/values"][()]
+
+        sellmeier = Sellmeier()
+        for A, B in zip(params_A, params_B):
+            sellmeier.add(A, B**2)
+
+    nexus_material = read_nexus_materials(nexus)["entry"]
+
+    assert isinstance(nexus_material, IsotropicMaterial)
+
+    assert_array_almost_equal(
+        sellmeier.get_dielectric(lbda), nexus_material.dispersion_x.get_dielectric(lbda)
+    )
+
+
+def test_read_nexus_biaxial_material(datadir):
+    """A biaxial material is read correctly"""
+    nexus = datadir / "WTe2-Munkhbat-alpha.nxs"
+
+    with h5py.File(nexus, "r") as h5file:
+        table_x_path = "/entry/dispersion_x/dispersion_table_nk"
+        table_y_path = "/entry/dispersion_y/dispersion_table_nk"
+        table_z_path = "/entry/dispersion_z/dispersion_table_n"
+        lbda = h5file[f"{table_x_path}/wavelength"][()]
+
+        table_x = Table(lbda=lbda, n=h5file[f"{table_x_path}/refractive_index"][()])
+        table_y = Table(
+            lbda=h5file[f"{table_y_path}/wavelength"][()],
+            n=h5file[f"{table_y_path}/refractive_index"][()],
+        )
+        table_z = Table(
+            lbda=h5file[f"{table_z_path}/wavelength"][()],
+            n=h5file[f"{table_z_path}/refractive_index"][()],
+        )
+
+    nexus_material = read_nexus_materials(nexus)["entry"]
+
+    assert isinstance(nexus_material, BiaxialMaterial)
+
+    assert_array_almost_equal(
+        table_x.get_dielectric(lbda), nexus_material.dispersion_x.get_dielectric(lbda)
+    )
+
+    assert_array_almost_equal(
+        table_y.get_dielectric(lbda), nexus_material.dispersion_y.get_dielectric(lbda)
+    )
+
+    assert_array_almost_equal(
+        table_z.get_dielectric(lbda), nexus_material.dispersion_z.get_dielectric(lbda)
+    )
+
+
+def test_read_nexus_dispersion_sum(datadir):
+    """A dispersion sum is read correctly"""
+    nexus = datadir / "YVO4-Shi-e-20C.nxs"
+    lbda = np.linspace(480, 1340, 100)
+
+    def read_sellmeier(h5file: h5py.File):
+        sellmeier_path = "/entry/dispersion_x/sellmeier"
+        params_A = h5file[f"{sellmeier_path}/A/values"][()]
+        params_B = h5file[f"{sellmeier_path}/B/values"][()]
+        params_e1 = h5file[f"{sellmeier_path}/e1/values"][()]
+        params_e2 = h5file[f"{sellmeier_path}/e2/values"][()]
+        eps_inf = h5file["/entry/dispersion_x/sellmeier/eps_inf/value"][()]
+
+        sellmeier = SellmeierCustomExponent()
+        for A, B, e1, e2 in zip(params_A, params_B, params_e1, params_e2):
+            sellmeier.add(A, e1, B, e2)
+
+        return sellmeier + eps_inf
+
+    def read_poly(h5file: h5py.File):
+        polynomial_path = "/entry/dispersion_x/polynomial"
+        params_e = h5file[f"{polynomial_path}/e/values"][()]
+        params_f = h5file[f"{polynomial_path}/f/values"][()]
+
+        poly = Polynomial(0)
+        for e, f in zip(params_e, params_f):
+            poly.add(f / 1e3**e, e)
+
+        return poly
+
+    with h5py.File(nexus, "r") as h5file:
+        disp = read_sellmeier(h5file) + read_poly(h5file)
+
+    nexus_material = read_nexus_materials(nexus)["entry"]
+
+    assert isinstance(nexus_material, IsotropicMaterial)
+
+    assert_array_almost_equal(
+        disp.get_dielectric(lbda), nexus_material.dispersion_x.get_dielectric(lbda)
+    )
diff --git a/tests/test_nexus_formula/MoSe2-Munkhbat-o.nxs b/tests/test_nexus_formula/MoSe2-Munkhbat-o.nxs
new file mode 100644
index 00000000..f040c24d
Binary files /dev/null and b/tests/test_nexus_formula/MoSe2-Munkhbat-o.nxs differ
diff --git a/tests/test_nexus_formula/MoTe2-Beal.nxs b/tests/test_nexus_formula/MoTe2-Beal.nxs
new file mode 100644
index 00000000..35884bd3
Binary files /dev/null and b/tests/test_nexus_formula/MoTe2-Beal.nxs differ
diff --git a/tests/test_nexus_formula/Si-Chandler-Horowitz.nxs b/tests/test_nexus_formula/Si-Chandler-Horowitz.nxs
new file mode 100644
index 00000000..202a2a53
Binary files /dev/null and b/tests/test_nexus_formula/Si-Chandler-Horowitz.nxs differ
diff --git a/tests/test_nexus_formula/Si-Salzberg.nxs b/tests/test_nexus_formula/Si-Salzberg.nxs
new file mode 100644
index 00000000..536d79ab
Binary files /dev/null and b/tests/test_nexus_formula/Si-Salzberg.nxs differ
diff --git a/tests/test_nexus_formula/WTe2-Munkhbat-alpha.nxs b/tests/test_nexus_formula/WTe2-Munkhbat-alpha.nxs
new file mode 100644
index 00000000..ff59aba0
Binary files /dev/null and b/tests/test_nexus_formula/WTe2-Munkhbat-alpha.nxs differ
diff --git a/tests/test_nexus_formula/YVO4-Shi-e-20C.nxs b/tests/test_nexus_formula/YVO4-Shi-e-20C.nxs
new file mode 100644
index 00000000..a7eab6d8
Binary files /dev/null and b/tests/test_nexus_formula/YVO4-Shi-e-20C.nxs differ
diff --git a/tests/test_refractive_index_info.py b/tests/test_refractive_index_info.py
index b95aefb7..a5c4ba18 100644
--- a/tests/test_refractive_index_info.py
+++ b/tests/test_refractive_index_info.py
@@ -72,10 +72,10 @@ def test_formula_4(self):
         disp = self.RII.load_dispersion("AgCl", "Tilton")  # formula 4
 
         np.testing.assert_almost_equal(
-            disp.get_refractive_index(1024), 2.0213900020277, decimal=3
+            disp.get_refractive_index(1024), 2.0213900020277, decimal=12
         )
         np.testing.assert_almost_equal(
-            disp.get_refractive_index(10080), 1.9799748188746, decimal=4
+            disp.get_refractive_index(10080), 1.9799748188746, decimal=12
         )
 
     def test_formula_5(self):