From 9fa4bea2e13590b5d95e730692b58571a375147a Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Mon, 29 Apr 2024 16:40:39 +0000
Subject: [PATCH 01/21] [pre-commit.ci] pre-commit autoupdate
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

updates:
- [github.com/pre-commit/pre-commit-hooks: v4.5.0 → v4.6.0](https://github.com/pre-commit/pre-commit-hooks/compare/v4.5.0...v4.6.0)
- [github.com/psf/black: 24.3.0 → 24.4.2](https://github.com/psf/black/compare/24.3.0...24.4.2)
---
 .pre-commit-config.yaml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index f66b8cca..f7c36a21 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -3,7 +3,7 @@
 
 repos:
   - repo: https://github.com/pre-commit/pre-commit-hooks
-    rev: v4.5.0
+    rev: v4.6.0
     hooks:
       - id: trailing-whitespace
       - id: check-docstring-first
@@ -25,7 +25,7 @@ repos:
       - id: end-of-file-fixer
       - id: sort-simple-yaml
   - repo: https://github.com/psf/black
-    rev: 24.3.0
+    rev: 24.4.2
     hooks:
       - id: black
         args: ['--line-length=119']

From 3ce8e2cb54ebad652276b15ed0dde0fae9615552 Mon Sep 17 00:00:00 2001
From: Chen Zhang <zhangc@ornl.gov>
Date: Thu, 11 Jul 2024 14:15:28 -0400
Subject: [PATCH 02/21] Update data.py

Fix outdated docstring
---
 src/imars3d/backend/dataio/data.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/imars3d/backend/dataio/data.py b/src/imars3d/backend/dataio/data.py
index ebbdd648..2591f1fd 100644
--- a/src/imars3d/backend/dataio/data.py
+++ b/src/imars3d/backend/dataio/data.py
@@ -100,7 +100,7 @@ class load_data(param.ParameterizedFunction):
     dc_fnmatch: Optional[str]
         Unix shells-style wild card (``*.tiff``) for selecting dark current
     max_workers: Optional[int]
-        maximum number of processes allowed during loading, default to use as many as possible.
+        maximum number of processes allowed during loading, default to use a single core.
     tqdm_class: panel.widgets.Tqdm
         Class to be used for rendering tqdm progress
 

From ce35005671939ff3bc175231c2d7509b7d193cd3 Mon Sep 17 00:00:00 2001
From: Chen Zhang <zhangc@ornl.gov>
Date: Thu, 11 Jul 2024 14:21:41 -0400
Subject: [PATCH 03/21] Update environment.yml

Pin numpy to v1.x until we fixed the deprecation issue.
---
 environment.yml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/environment.yml b/environment.yml
index c159f939..126933f2 100644
--- a/environment.yml
+++ b/environment.yml
@@ -11,6 +11,7 @@ dependencies:
   - astropy
   - tomopy
   - algotom
+  - numpy < 2.0
   # plot
   - holoviews
   - bokeh

From 5d2e7271f590748373deec8c84d0c78b216ffc13 Mon Sep 17 00:00:00 2001
From: Chen Zhang <chenzhang8722@gmail.com>
Date: Thu, 11 Jul 2024 14:50:05 -0400
Subject: [PATCH 04/21] put pin in meta.yaml as well

---
 .gitignore             | 1 -
 conda.recipe/meta.yaml | 1 +
 environment.yml        | 2 +-
 3 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/.gitignore b/.gitignore
index bff69f29..eb6f33c0 100644
--- a/.gitignore
+++ b/.gitignore
@@ -12,7 +12,6 @@
 /build
 /dist
 /python/imars3d.egg-info
-conda.recipe/
 
 # temp files and dirs
 _tmp
diff --git a/conda.recipe/meta.yaml b/conda.recipe/meta.yaml
index 98175aec..db957acb 100644
--- a/conda.recipe/meta.yaml
+++ b/conda.recipe/meta.yaml
@@ -47,6 +47,7 @@ requirements:
     - bokeh
     - datashader
     - hvplot
+    - numpy < 2
 
 test:
   imports:
diff --git a/environment.yml b/environment.yml
index 126933f2..ff269027 100644
--- a/environment.yml
+++ b/environment.yml
@@ -11,7 +11,7 @@ dependencies:
   - astropy
   - tomopy
   - algotom
-  - numpy < 2.0
+  - numpy < 2
   # plot
   - holoviews
   - bokeh

From 8d0dbdf3dfff6d580390ea4d5e328510b6fa2038 Mon Sep 17 00:00:00 2001
From: Chen Zhang <chenzhang8722@gmail.com>
Date: Thu, 11 Jul 2024 15:14:07 -0400
Subject: [PATCH 05/21] add dask explicitly

---
 environment.yml | 1 +
 1 file changed, 1 insertion(+)

diff --git a/environment.yml b/environment.yml
index ff269027..55fc4247 100644
--- a/environment.yml
+++ b/environment.yml
@@ -17,6 +17,7 @@ dependencies:
   - bokeh
   - datashader
   - hvplot
+  - dask
   # GUI
   - panel
   - param

From de356911e4ca354c5a85d2648a7a0754d4668a90 Mon Sep 17 00:00:00 2001
From: Chen Zhang <chenzhang8722@gmail.com>
Date: Thu, 11 Jul 2024 15:43:28 -0400
Subject: [PATCH 06/21] install glibc from conda

---
 .readthedocs.yaml | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/.readthedocs.yaml b/.readthedocs.yaml
index e303aa84..3e82d7fb 100644
--- a/.readthedocs.yaml
+++ b/.readthedocs.yaml
@@ -7,6 +7,8 @@ build:
   jobs:
     pre_build:
       - mkdir ~/tmp
+    post_install:
+      - conda install -c conda-forge glibc=2.32
 
 sphinx:
   builder: html

From 4f571b1553161d5fcefae5191f2975830c3f764a Mon Sep 17 00:00:00 2001
From: Chen Zhang <chenzhang8722@gmail.com>
Date: Thu, 11 Jul 2024 15:57:49 -0400
Subject: [PATCH 07/21] conda-forge no longer provides glibc

---
 .readthedocs.yaml | 2 --
 1 file changed, 2 deletions(-)

diff --git a/.readthedocs.yaml b/.readthedocs.yaml
index 3e82d7fb..e303aa84 100644
--- a/.readthedocs.yaml
+++ b/.readthedocs.yaml
@@ -7,8 +7,6 @@ build:
   jobs:
     pre_build:
       - mkdir ~/tmp
-    post_install:
-      - conda install -c conda-forge glibc=2.32
 
 sphinx:
   builder: html

From 34161495ea9a65fde44b5018e591f0c88331e95d Mon Sep 17 00:00:00 2001
From: Chen Zhang <chenzhang8722@gmail.com>
Date: Thu, 11 Jul 2024 16:04:24 -0400
Subject: [PATCH 08/21] switch to the example version from rtd documentation

---
 .readthedocs.yaml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/.readthedocs.yaml b/.readthedocs.yaml
index e303aa84..3cb4e8da 100644
--- a/.readthedocs.yaml
+++ b/.readthedocs.yaml
@@ -1,9 +1,9 @@
 version: 2
 
 build:
-  os: ubuntu-20.04
+  os: "ubuntu-22.04"
   tools:
-    python: "mambaforge-4.10"
+    python: "mambaforge-22.9"
   jobs:
     pre_build:
       - mkdir ~/tmp

From f57eca3b7536bcd4bc27ef1e92cb8b51cf383c61 Mon Sep 17 00:00:00 2001
From: Chen Zhang <zhangc@ornl.gov>
Date: Thu, 18 Jul 2024 13:34:23 -0400
Subject: [PATCH 09/21] Update meta.yaml

Quick patch to fix the version syntax
---
 conda.recipe/meta.yaml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/conda.recipe/meta.yaml b/conda.recipe/meta.yaml
index db957acb..1a668f04 100644
--- a/conda.recipe/meta.yaml
+++ b/conda.recipe/meta.yaml
@@ -47,7 +47,7 @@ requirements:
     - bokeh
     - datashader
     - hvplot
-    - numpy < 2
+    - numpy<2
 
 test:
   imports:

From 4337101b5ec9b7cddda6eb47db111f150c3fb974 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Mon, 5 Aug 2024 16:43:43 +0000
Subject: [PATCH 10/21] [pre-commit.ci] pre-commit autoupdate
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

updates:
- [github.com/psf/black: 24.4.2 → 24.8.0](https://github.com/psf/black/compare/24.4.2...24.8.0)
---
 .pre-commit-config.yaml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index f7c36a21..73faa5ac 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -25,7 +25,7 @@ repos:
       - id: end-of-file-fixer
       - id: sort-simple-yaml
   - repo: https://github.com/psf/black
-    rev: 24.4.2
+    rev: 24.8.0
     hooks:
       - id: black
         args: ['--line-length=119']

From 6996a91ad57794b415bc2234d585d628053b1e40 Mon Sep 17 00:00:00 2001
From: Chen Zhang <zhangc@ornl.gov>
Date: Thu, 5 Sep 2024 11:59:32 -0400
Subject: [PATCH 11/21] disable memmap as requested

---
 src/imars3d/backend/dataio/data.py | 12 +++++++++++-
 1 file changed, 11 insertions(+), 1 deletion(-)

diff --git a/src/imars3d/backend/dataio/data.py b/src/imars3d/backend/dataio/data.py
index 2591f1fd..86c27d50 100644
--- a/src/imars3d/backend/dataio/data.py
+++ b/src/imars3d/backend/dataio/data.py
@@ -296,7 +296,17 @@ def _load_images(filelist: List[str], desc: str, max_workers: int, tqdm_class) -
     file_ext = Path(filelist[0]).suffix.lower()
     if file_ext in (".tif", ".tiff"):
         # use tifffile directly for a faster loading
-        reader = partial(tifffile.imread, out="memmap")
+        # NOTE: Test conducted on 09-05-2024 on bl10-analysis1 shows that using
+        #       memmap is faster, which contradicts the observation from the instrument
+        #       team.
+        #                       | Method | Time (s) |
+        #                       |--------|----------|
+        #                       | `imread(out="memmap")` | 2.62 s ± 24.6 ms |
+        #                       | `imread()` | 3.59 s ± 13.6 ms |
+        #       The `memmap` option is removed until we have a better understanding of the
+        #       discrepancy.
+        # reader = partial(tifffile.imread, out="memmap")
+        reader = tifffile.imread
     elif file_ext == ".fits":
         reader = dxchange.read_fits
     else:

From 7b511aec3e1d28462ff29465ebc752353a7adb32 Mon Sep 17 00:00:00 2001
From: Chen Zhang <zhangc@ornl.gov>
Date: Mon, 16 Sep 2024 14:23:53 -0400
Subject: [PATCH 12/21] allow both tif and tiff for TIFF images

---
 src/imars3d/backend/dataio/data.py | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/src/imars3d/backend/dataio/data.py b/src/imars3d/backend/dataio/data.py
index 86c27d50..745fa3c7 100644
--- a/src/imars3d/backend/dataio/data.py
+++ b/src/imars3d/backend/dataio/data.py
@@ -568,21 +568,21 @@ def _extract_rotation_angles(
     # Note
     # ----
     #   For the following file
-    #       20191030_ironman_small_0070_300_440_0520.tiff
+    #       20191030_ironman_small_0070_300_440_0520.tif(f)
     #   the rotation angle is 300.44 degrees
     # If all given filenames follows the pattern, we will use the angles from
     # filenames. Otherwise, we will use the angles from metadata.
-    regex = r"\d{8}_\S*_\d{4}_(?P<deg>\d{3})_(?P<dec>\d{3})_\d*\.tiff"
+    regex = r"\d{8}_\S*_\d{4}_(?P<deg>\d{3})_(?P<dec>\d{3})_\d*\.tif{1,2}"
     matches = [re.match(regex, Path(f).name) for f in filelist]
     if all(matches):
         logger.info("Using rotation angles from filenames.")
         rotation_angles = np.array([float(".".join(m.groups())) for m in matches])
     else:
         # extract rotation angles from metadata
-        file_ext = set([Path(f).suffix for f in filelist])
-        if file_ext != {".tiff"}:
-            logger.error("Only tiff files are supported.")
-            raise ValueError("Rotation angle from metadata is only supported for Tiff.")
+        file_exts = set(Path(f).suffix.lower() for f in filelist)
+        if not file_exts.issubset({".tiff", ".tif"}):
+            logger.error("Only .tiff and .tif files are supported.")
+            raise ValueError("Rotation angle from metadata is only supported for .tiff and .tif files.")
         # -- read metadata
         # img = tifffile.TiffFile("test_with_metadata_0.tiff")
         # img.pages[0].tags[65039].value

From 79460caaba171a1bda8852d03731186f9ee9d6e7 Mon Sep 17 00:00:00 2001
From: Chen Zhang <zhangc@ornl.gov>
Date: Mon, 16 Sep 2024 14:53:49 -0400
Subject: [PATCH 13/21] make dark field optional

---
 src/imars3d/backend/preparation/normalization.py | 13 +++++++++----
 1 file changed, 9 insertions(+), 4 deletions(-)

diff --git a/src/imars3d/backend/preparation/normalization.py b/src/imars3d/backend/preparation/normalization.py
index 49692213..9e03e2b1 100644
--- a/src/imars3d/backend/preparation/normalization.py
+++ b/src/imars3d/backend/preparation/normalization.py
@@ -41,7 +41,7 @@ class normalization(param.ParameterizedFunction):
     flats = param.Array(
         doc="3D array of flat field images (aka flat field, open beam), axis=0 is the image number axis.", default=None
     )
-    darks = param.Array(doc="3D array of dark field images, axis=0 is the image number axis.", default=None)
+    darks = param.Array(doc="3D array of optional dark field images, axis=0 is the image number axis.", default=None)
     max_workers = param.Integer(
         default=0,
         bounds=(0, None),
@@ -59,10 +59,15 @@ def __call__(self, **params):
         self.max_workers = clamp_max_workers(params.max_workers)
         logger.debug(f"max_worker={self.max_workers}")
 
-        # use median filter to remove outliers from flats and darks
-        # NOTE: this will remove the random noises coming from the environment.
+        # process flats (formerly known as open beam, white field)
         self.flats = np.median(params.flats, axis=0)
-        self.darks = np.median(params.darks, axis=0)
+
+        # process darks (formerly known as black field)
+        if params.darks is None:
+            self.darks = np.zeros_like(self.flats)
+        else:
+            self.darks = np.median(params.darks, axis=0)
+
         # apply normalization
         _bg = self.flats - self.darks
         _bg[_bg <= 0] = 1e-6

From a43db286885008a6768967ceba8d05e10961ec07 Mon Sep 17 00:00:00 2001
From: Chen Zhang <zhangc@ornl.gov>
Date: Mon, 16 Sep 2024 15:21:36 -0400
Subject: [PATCH 14/21] add missing unit test

---
 .../backend/preparation/test_normalization.py  | 18 ++++++++++++++++++
 1 file changed, 18 insertions(+)

diff --git a/tests/unit/backend/preparation/test_normalization.py b/tests/unit/backend/preparation/test_normalization.py
index b0f9ee84..94b7a062 100644
--- a/tests/unit/backend/preparation/test_normalization.py
+++ b/tests/unit/backend/preparation/test_normalization.py
@@ -124,6 +124,24 @@ def test_normalization_bright_dark():
     assert diff < 0.01
 
 
+def test_normalization_no_darks():
+    """Test normalization routine without providing dark field images."""
+    raw, _, flats, proj = prepare_synthetic_data()
+
+    # Process with normalization, passing None for darks
+    proj_imars3d = normalization(arrays=raw, flats=flats, darks=None)
+
+    # Compare results
+    diff = np.absolute(proj_imars3d - proj).sum() / np.prod(proj.shape)
+    assert diff < 0.02  # Increased tolerance from 0.01 to 0.02 to account for the lack of dark field images
+
+    # Additional check: Ensure the shape of the output matches the input
+    assert proj_imars3d.shape == raw.shape
+
+    # Check that values are within expected range (0 to 1 for normalized data)
+    assert np.all(proj_imars3d >= 0) and np.all(proj_imars3d <= 1)
+
+
 class TestMinusLog:
     @pytest.mark.parametrize("ncore", [1, 2])
     def test_execution(self, ncore: int) -> None:

From 6d79fbf94e9a9b141cd2b72487f22ada894e6ff3 Mon Sep 17 00:00:00 2001
From: Chen Zhang <zhangc@ornl.gov>
Date: Tue, 17 Sep 2024 13:08:38 -0400
Subject: [PATCH 15/21] relax rotation angle extraction process

---
 src/imars3d/backend/dataio/data.py     | 109 ++++++++++++++++++++-----
 tests/unit/backend/dataio/test_data.py |  27 ++++++
 2 files changed, 116 insertions(+), 20 deletions(-)

diff --git a/src/imars3d/backend/dataio/data.py b/src/imars3d/backend/dataio/data.py
index 745fa3c7..601a47c1 100644
--- a/src/imars3d/backend/dataio/data.py
+++ b/src/imars3d/backend/dataio/data.py
@@ -125,6 +125,9 @@ class load_data(param.ParameterizedFunction):
 
         Currently, we are using a forgiving reader to load the image where a corrupted file
         will not block reading other data.
+
+        The rotation angles are extracted from the filenames if possible, otherwise from the
+        metadata embedded in the tiff files. If both failed, the angle will be set to None.
     """
 
     #
@@ -544,7 +547,7 @@ def _get_filelist_by_dir(
 def _extract_rotation_angles(
     filelist: List[str],
     metadata_idx: int = 65039,
-) -> np.ndarray:
+) -> Optional[np.ndarray]:
     """
     Extract rotation angles in degrees from filename or metadata.
 
@@ -558,40 +561,106 @@ def _extract_rotation_angles(
     Returns
     -------
         rotation_angles
+            Array of rotation angles if successfully extracted, None otherwise.
     """
     # sanity check
-    if filelist == []:
+    if not filelist:
         logger.error("filelist is [].")
         raise ValueError("filelist cannot be empty list.")
 
-    # extract rotation angles from file names
+    # process one file at a time
+    rotation_angles = []
+    for filename in filelist:
+        file_ext = Path(filename).suffix.lower()
+        angle = None
+        if file_ext == ".tiff":
+            # first, let's try to extract the angle from the filename
+            angle = extract_rotation_angle_from_filename(filename)
+            if angle is None:
+                # if failed, try to extract from metadata
+                angle = extract_rotation_angle_from_tiff_metadata(filename, metadata_idx)
+            if angle is None:
+                # if failed, log a warning and move on
+                logger.warning(f"Failed to extract rotation angle from {filename}.")
+        elif file_ext in (".tif", ".fits"):
+            # for tif and fits, we can only extract from filename as the metadata is not reliable
+            angle = extract_rotation_angle_from_filename(filename)
+            if angle is None:
+                # if failed, log a warning and move on
+                logger.warning(f"Failed to extract rotation angle from {filename}.")
+        else:
+            # if the file type is not supported, raise value error
+            logger.error(f"Unsupported file type: {file_ext}")
+            raise ValueError("Unsupported file type.")
+
+        rotation_angles.append(angle)
+
+    # this means we have a list of None
+    if all(angle is None for angle in rotation_angles):
+        logger.warning("Failed to extract any rotation angles.")
+        return None
+
+    # warn users if some angles are missing
+    if any(angle is None for angle in rotation_angles):
+        logger.warning("Some rotation angles are missing. You will see nan in the rotation angles array.")
+
+    return np.array(rotation_angles, dtype=float)
+
+
+def extract_rotation_angle_from_filename(filename: str) -> Optional[float]:
+    """
+    Extract rotation angle in degrees from filename.
+
+    Parameters
+    ----------
+    filename:
+        Filename to extract rotation angle from.
+
+    Returns
+    -------
+        rotation_angle
+            Rotation angle in degrees if successfully extracted, None otherwise.
+    """
+    # extract rotation angle from file names
     # Note
     # ----
     #   For the following file
     #       20191030_ironman_small_0070_300_440_0520.tif(f)
+    #       20191030_ironman_small_0070_300_440_0520.fits
     #   the rotation angle is 300.44 degrees
-    # If all given filenames follows the pattern, we will use the angles from
-    # filenames. Otherwise, we will use the angles from metadata.
-    regex = r"\d{8}_\S*_\d{4}_(?P<deg>\d{3})_(?P<dec>\d{3})_\d*\.tif{1,2}"
-    matches = [re.match(regex, Path(f).name) for f in filelist]
-    if all(matches):
-        logger.info("Using rotation angles from filenames.")
-        rotation_angles = np.array([float(".".join(m.groups())) for m in matches])
+    regex = r"\d{8}_\S*_\d{4}_(?P<deg>\d{3})_(?P<dec>\d{3})_\d*\.(?:tiff?|fits)"
+    match = re.match(regex, Path(filename).name)
+    if match:
+        rotation_angle = float(".".join(match.groups()))
     else:
-        # extract rotation angles from metadata
-        file_exts = set(Path(f).suffix.lower() for f in filelist)
-        if not file_exts.issubset({".tiff", ".tif"}):
-            logger.error("Only .tiff and .tif files are supported.")
-            raise ValueError("Rotation angle from metadata is only supported for .tiff and .tif files.")
+        rotation_angle = None
+    return rotation_angle
+
+
+def extract_rotation_angle_from_tiff_metadata(filename: str, metadata_idx: int = 65039) -> Optional[float]:
+    """
+    Extract rotation angle in degrees from metadata of a tiff file.
+
+    Parameters
+    ----------
+    filename:
+        Filename to extract rotation angle from.
+    metadata_idx:
+        Index of metadata to extract rotation angle from, default is 65039.
+
+    Returns
+    -------
+        rotation_angle
+            Rotation angle in degrees if successfully extracted, None otherwise.
+    """
+    try:
         # -- read metadata
         # img = tifffile.TiffFile("test_with_metadata_0.tiff")
         # img.pages[0].tags[65039].value
         # >> 'RotationActual:0.579840'
-        rotation_angles = np.array(
-            [float(tifffile.TiffFile(f).pages[0].tags[metadata_idx].value.split(":")[-1]) for f in filelist],
-            dtype="float",
-        )
-    return rotation_angles
+        return float(tifffile.TiffFile(filename).pages[0].tags[metadata_idx].value.split(":")[-1])
+    except Exception:
+        return None
 
 
 def _save_data(filename: Path, data: np.ndarray, rot_angles: np.ndarray = None) -> None:
diff --git a/tests/unit/backend/dataio/test_data.py b/tests/unit/backend/dataio/test_data.py
index efbe04fb..0bd677a3 100644
--- a/tests/unit/backend/dataio/test_data.py
+++ b/tests/unit/backend/dataio/test_data.py
@@ -15,6 +15,8 @@
     load_data,
     save_checkpoint,
     save_data,
+    extract_rotation_angle_from_filename,
+    extract_rotation_angle_from_tiff_metadata,
 )
 
 
@@ -181,6 +183,31 @@ def test_extract_rotation_angles(data_fixture):
     rst = _extract_rotation_angles([metadata_tiff] * 3)
     ref = np.array([0.1, 0.1, 0.1])
     np.testing.assert_array_almost_equal(rst, ref)
+    # case_2: mixed file types
+    rst = _extract_rotation_angles([good_tiff, metadata_tiff, generic_tiff, generic_fits])
+    ref = np.array([10.02, 0.1, np.nan, np.nan])
+    np.testing.assert_array_equal(rst, ref)
+    # case_3: all files without extractable angles
+    rst = _extract_rotation_angles([generic_tiff, generic_fits])
+    assert rst is None
+
+
+def test_extract_rotation_angle_from_filename():
+    # Test cases for extract_rotation_angle_from_filename
+    assert extract_rotation_angle_from_filename("20191030_sample_0070_300_440_0520.tiff") == 300.44
+    assert extract_rotation_angle_from_filename("20191030_sample_0071_301_441_0521.tif") == 301.441
+    assert extract_rotation_angle_from_filename("20191030_sample_0072_302_442_0522.fits") == 302.442
+    assert extract_rotation_angle_from_filename("generic_file.tiff") is None
+
+
+def test_extract_rotation_angle_from_tiff_metadata(tmpdir):
+    # Create a TIFF file with rotation angle in metadata
+    data = np.ones((3, 3))
+    filename = str(tmpdir / "metadata.tiff")
+    tifffile.imwrite(filename, data, extratags=[(65039, "s", 0, "RotationActual:0.5", True)])
+
+    assert extract_rotation_angle_from_tiff_metadata(filename) == 0.5
+    assert extract_rotation_angle_from_tiff_metadata("non_existent_file.tiff") is None
 
 
 @pytest.fixture(scope="module")

From d6ce446513a9e34cdb864c482cf67a7ef87cfda5 Mon Sep 17 00:00:00 2001
From: Chen Zhang <zhangc@ornl.gov>
Date: Tue, 17 Sep 2024 13:59:37 -0400
Subject: [PATCH 16/21] allow passing rotation center for tilt

---
 src/imars3d/backend/diagnostics/tilt.py | 35 ++++++++++++++++++++++---
 1 file changed, 31 insertions(+), 4 deletions(-)

diff --git a/src/imars3d/backend/diagnostics/tilt.py b/src/imars3d/backend/diagnostics/tilt.py
index 79389f04..4275f2b5 100644
--- a/src/imars3d/backend/diagnostics/tilt.py
+++ b/src/imars3d/backend/diagnostics/tilt.py
@@ -6,7 +6,7 @@
 import multiprocessing
 from imars3d.backend.util.functions import clamp_max_workers
 import numpy as np
-from typing import Tuple
+from typing import Tuple, Union, Optional
 from functools import partial
 from scipy.optimize import minimize_scalar
 from scipy.optimize import OptimizeResult
@@ -103,6 +103,7 @@ def calculate_dissimilarity(
     tilt: float,
     image0: np.ndarray,
     image1: np.ndarray,
+    center: Optional[Tuple[Union[float, int], Union[float, int]]] = None,
 ) -> float:
     """Calculate the dissimilarity between two images with given tilt.
 
@@ -119,6 +120,9 @@ def calculate_dissimilarity(
     image1:
         The second image for comparison, which is often the radiograph taken at
         omega + 180 deg
+    center:
+        The center of the rotation axis, default is None, which means the center
+        of the image. This will be passed to the rotation function from skimage.
 
     Returns
     -------
@@ -168,6 +172,7 @@ def calculate_dissimilarity(
         resize=True,
         preserve_range=True,
         order=1,  # use default bi-linear interpolation for rotation
+        center=center,
     )
     # since 180 is flipped, tilting back -2 deg of the original img180 means tilting +2 deg
     # of the flipped one
@@ -178,6 +183,7 @@ def calculate_dissimilarity(
         resize=True,
         preserve_range=True,
         order=1,  # use default bi-linear interpolation for rotation
+        center=center,
     )
 
     # p-norm
@@ -198,6 +204,7 @@ def calculate_tilt(
     image180: np.ndarray,
     low_bound: float = -5.0,
     high_bound: float = 5.0,
+    center: Optional[Tuple[Union[float, int], Union[float, int]]] = None,
 ) -> OptimizeResult:
     """
     Use optimization to find the in-plane tilt angle.
@@ -214,13 +221,16 @@ def calculate_tilt(
         The lower bound of the tilt angle search space
     high_bound:
         The upper bound of the tilt angle search space
+    center:
+        The center of the rotation axis, default is None, which means the center
+        of the image. This will be passed to the rotation function from skimage.
 
     Returns
     -------
         The optimization results from scipy.optimize.minimize_scalar
     """
     # make the error function
-    err_func = partial(calculate_dissimilarity, image0=image0, image1=image180)
+    err_func = partial(calculate_dissimilarity, image0=image0, image1=image180, center=center)
     # use bounded uni-variable optimizer to locate the tilt angle that minimize
     # the dissimilarity of the 180 deg pair
     res = minimize_scalar(
@@ -249,6 +259,9 @@ class tilt_correction(param.ParameterizedFunction):
     cut_off_angle_deg: float
         The angle in degrees to cut off the rotation axis tilt correction, i.e.
         skip applying tilt correction for tilt angles that are too small.
+    center: Any
+        The center of the rotation axis, default is None, which means the center
+        of the image. This will be passed to the rotation function from skimage.
     max_workers:
         Number of cores to use for parallel median filtering, default is 0,
         which means using all available cores.
@@ -275,6 +288,10 @@ class tilt_correction(param.ParameterizedFunction):
         default=2.0,
         doc="The angle in degrees to cut off the rotation axis tilt correction, i.e. skip applying tilt correction for tilt angles that are too small.",
     )
+    center = param.Parameter(
+        default=None,
+        doc="The center of the rotation axis, default is None, which means the center of the image. This will be passed to the rotation function from skimage.",
+    )
     # NOTE:
     # The front and backend are sharing the same computing unit, therefore we can
     # set a hard cap on the max_workers.
@@ -329,6 +346,7 @@ def __call__(self, **params):
                     calculate_tilt,
                     low_bound=params.low_bound,
                     high_bound=params.high_bound,
+                    center=params.center,
                 ),
                 [shm_arrays[il] for il in idx_lowrange],
                 [shm_arrays[ih] for ih in idx_highrange],
@@ -349,6 +367,7 @@ def __call__(self, **params):
             corrected_array = apply_tilt_correction(
                 arrays=params.arrays,
                 tilt=tilt,
+                center=params.center,
                 max_workers=self.max_workers,
             )
         return corrected_array
@@ -366,6 +385,8 @@ class apply_tilt_correction(param.ParameterizedFunction):
         The array for tilt correction
     tilt: float
         The rotation axis tilt angle in degrees
+    center: Any
+        The center of the rotation axis, default is None, which means the center
     max_workers: int
         Number of cores to use for parallel median filtering, default is 0, which means using all available cores.
     tqdm_class: panel.widgets.Tqdm
@@ -379,6 +400,10 @@ class apply_tilt_correction(param.ParameterizedFunction):
 
     arrays = param.Array(doc="The array for tilt correction", default=None)
     tilt = param.Number(doc="The rotation axis tilt angle in degrees", default=None)
+    center = param.Parameter(
+        default=None,
+        doc="The center of the rotation axis, default is None, which means the center of the image. This will be passed to the rotation function from skimage.",
+    )
     # NOTE:
     # The front and backend are sharing the same computing unit, therefore we can
     # set a hard cap on the max_workers.
@@ -406,7 +431,9 @@ def __call__(self, **params):
         # dimensionality check
         if params.arrays.ndim == 2:
             logger.info(f"2D image detected, applying tilt correction with tilt = {params.tilt:.3f} deg")
-            corrected_array = rotate(params.arrays, -params.tilt, resize=False, preserve_range=True)
+            corrected_array = rotate(
+                params.arrays, -params.tilt, resize=False, preserve_range=True, center=params.center
+            )
         elif params.arrays.ndim == 3:
             logger.info(f"3D array detected, applying tilt correction with tilt = {params.tilt:.3f} deg")
             with SharedMemoryManager() as smm:
@@ -420,7 +447,7 @@ def __call__(self, **params):
                 if params.tqdm_class:
                     kwargs["tqdm_class"] = params.tqdm_class
                 rst = process_map(
-                    partial(rotate, angle=-params.tilt, resize=False, preserve_range=True),
+                    partial(rotate, angle=-params.tilt, resize=False, preserve_range=True, center=params.center),
                     [shm_arrays[idx] for idx in range(params.arrays.shape[0])],
                     **kwargs,
                 )

From 6f2419d2c5525b4e2ea3db4afbeba977579e8f49 Mon Sep 17 00:00:00 2001
From: Chen Zhang <zhangc@ornl.gov>
Date: Tue, 17 Sep 2024 14:27:54 -0400
Subject: [PATCH 17/21] add new helper function to calculate chunksize

---
 src/imars3d/backend/util/functions.py | 20 +++++++++++
 tests/unit/backend/util/test_util.py  | 48 ++++++++++++++++++++++++++-
 2 files changed, 67 insertions(+), 1 deletion(-)

diff --git a/src/imars3d/backend/util/functions.py b/src/imars3d/backend/util/functions.py
index 39a83ba7..e5b4f396 100644
--- a/src/imars3d/backend/util/functions.py
+++ b/src/imars3d/backend/util/functions.py
@@ -29,6 +29,26 @@ def clamp_max_workers(max_workers: Union[int, None]) -> int:
     return result
 
 
+def calculate_chunksize(num_elements: int, max_workers: Union[int, None] = None, scale_factor: int = 4) -> int:
+    """Calculate an optimal chunk size for multiprocessing.
+
+    Parameters:
+    - num_elements: The total number of elements to process.
+    - max_workers: The number of workers (processes) to use. Defaults to clamped max.
+    - scale_factor: A factor to fine-tune chunk size (default 4).
+
+    Returns:
+    - int: Suggested chunk size.
+    """
+    # Calculate the number of workers
+    workers = clamp_max_workers(max_workers)
+
+    # Calculate chunk size based on number of elements and workers
+    chunksize = max(1, num_elements // (workers * scale_factor))
+
+    return chunksize
+
+
 def to_time_str(value: datetime = datetime.now()) -> str:
     """
     Convert the supplied datetime to a formatted string.
diff --git a/tests/unit/backend/util/test_util.py b/tests/unit/backend/util/test_util.py
index 19f609c4..ea384eef 100644
--- a/tests/unit/backend/util/test_util.py
+++ b/tests/unit/backend/util/test_util.py
@@ -1,8 +1,9 @@
 # package imports
-from imars3d.backend.util.functions import clamp_max_workers, to_time_str
+from imars3d.backend.util.functions import clamp_max_workers, to_time_str, calculate_chunksize
 
 # third party imports
 import pytest
+from unittest.mock import patch
 
 # standard imports
 from datetime import datetime
@@ -13,6 +14,51 @@ def test_clamp_max_workers():
     assert clamp_max_workers(-10) >= 1
 
 
+@patch("multiprocessing.cpu_count", return_value=8)
+def test_chunksize_with_small_number_of_elements(mock_cpu_count):
+    num_elements = 10
+    max_workers = None
+    chunksize = calculate_chunksize(num_elements, max_workers)
+    assert chunksize == 1
+
+
+@patch("multiprocessing.cpu_count", return_value=8)
+def test_chunksize_with_large_number_of_elements(mock_cpu_count):
+    num_elements = 10000
+    max_workers = None
+    chunksize = calculate_chunksize(num_elements, max_workers)
+    expected_chunksize = max(1, num_elements // (6 * 4))  # 6 workers, scale factor 4
+    assert chunksize == expected_chunksize
+
+
+@patch("multiprocessing.cpu_count", return_value=4)
+def test_chunksize_with_different_cpu_count(mock_cpu_count):
+    num_elements = 10000
+    max_workers = None
+    chunksize = calculate_chunksize(num_elements, max_workers)
+    expected_chunksize = max(1, num_elements // (2 * 4))  # 2 workers (cpu_count - 2), scale factor 4
+    assert chunksize == expected_chunksize
+
+
+@patch("multiprocessing.cpu_count", return_value=8)
+def test_chunksize_with_max_workers(mock_cpu_count):
+    num_elements = 10000
+    max_workers = 4
+    chunksize = calculate_chunksize(num_elements, max_workers)
+    expected_chunksize = max(1, num_elements // (4 * 4))  # 4 workers manually set
+    assert chunksize == expected_chunksize
+
+
+@patch("multiprocessing.cpu_count", return_value=8)
+def test_chunksize_with_custom_scale_factor(mock_cpu_count):
+    num_elements = 10000
+    max_workers = None
+    scale_factor = 2
+    chunksize = calculate_chunksize(num_elements, max_workers, scale_factor=scale_factor)
+    expected_chunksize = max(1, num_elements // (6 * 2))  # 6 workers, scale factor 2
+    assert chunksize == expected_chunksize
+
+
 @pytest.mark.parametrize(
     "timestamp",
     [

From 9eb8049996e4c55ac9f5c65eff6b1b0a47e9073f Mon Sep 17 00:00:00 2001
From: Chen Zhang <zhangc@ornl.gov>
Date: Tue, 17 Sep 2024 14:56:39 -0400
Subject: [PATCH 18/21] explicit specify chunksize for multiprocess

---
 .../backend/corrections/beam_hardening.py     |  3 ++-
 src/imars3d/backend/corrections/denoise.py    |  3 ++-
 .../intensity_fluctuation_correction.py       |  3 ++-
 .../backend/corrections/ring_removal.py       |  3 ++-
 src/imars3d/backend/dataio/data.py            |  3 ++-
 src/imars3d/backend/diagnostics/rotation.py   |  3 ++-
 src/imars3d/backend/diagnostics/tilt.py       |  4 ++-
 src/imars3d/backend/util/functions.py         | 26 ++++++++++++++-----
 8 files changed, 35 insertions(+), 13 deletions(-)

diff --git a/src/imars3d/backend/corrections/beam_hardening.py b/src/imars3d/backend/corrections/beam_hardening.py
index 9338fabe..69be5a77 100644
--- a/src/imars3d/backend/corrections/beam_hardening.py
+++ b/src/imars3d/backend/corrections/beam_hardening.py
@@ -4,7 +4,7 @@
 import logging
 import param
 import numpy as np
-from imars3d.backend.util.functions import clamp_max_workers
+from imars3d.backend.util.functions import clamp_max_workers, calculate_chunksize
 from multiprocessing.managers import SharedMemoryManager
 from functools import partial
 from tqdm.contrib.concurrent import process_map
@@ -83,6 +83,7 @@ def __call__(self, **params):
                 # mp
                 kwargs = {
                     "max_workers": self.max_workers,
+                    "chunksize": calculate_chunksize(params.arrays.shape[0], self.max_workers),
                     "desc": "denoise_by_bilateral",
                 }
                 if self.tqdm_class:
diff --git a/src/imars3d/backend/corrections/denoise.py b/src/imars3d/backend/corrections/denoise.py
index 67c980cc..2f45b9d2 100644
--- a/src/imars3d/backend/corrections/denoise.py
+++ b/src/imars3d/backend/corrections/denoise.py
@@ -3,7 +3,7 @@
 """Image noise reduction (denoise) module."""
 import logging
 import param
-from imars3d.backend.util.functions import clamp_max_workers
+from imars3d.backend.util.functions import clamp_max_workers, calculate_chunksize
 import numpy as np
 import tomopy
 from multiprocessing.managers import SharedMemoryManager
@@ -153,6 +153,7 @@ def denoise_by_bilateral(
             # mp
             kwargs = {
                 "max_workers": max_workers,
+                "chunksize": calculate_chunksize(arrays.shape[0], max_workers),
                 "desc": "denoise_by_bilateral",
             }
             if tqdm_class:
diff --git a/src/imars3d/backend/corrections/intensity_fluctuation_correction.py b/src/imars3d/backend/corrections/intensity_fluctuation_correction.py
index 44276362..64a8c229 100644
--- a/src/imars3d/backend/corrections/intensity_fluctuation_correction.py
+++ b/src/imars3d/backend/corrections/intensity_fluctuation_correction.py
@@ -2,7 +2,7 @@
 # -*- coding: utf-8 -*-
 """iMars3D's intensity fluctuation correction module."""
 import logging
-from imars3d.backend.util.functions import clamp_max_workers
+from imars3d.backend.util.functions import clamp_max_workers, calculate_chunksize
 import numpy as np
 import param
 import tomopy
@@ -93,6 +93,7 @@ def _intensity_fluctuation_correction(self, ct, air_pixels, sigma, max_workers,
                 # map the multiprocessing calls
                 kwargs = {
                     "max_workers": max_workers,
+                    "chunksize": calculate_chunksize(ct.shape[0], max_workers),
                     "desc": "intensity_fluctuation_correction",
                 }
                 if tqdm_class:
diff --git a/src/imars3d/backend/corrections/ring_removal.py b/src/imars3d/backend/corrections/ring_removal.py
index dd39c6e3..aef0fcf6 100644
--- a/src/imars3d/backend/corrections/ring_removal.py
+++ b/src/imars3d/backend/corrections/ring_removal.py
@@ -3,7 +3,7 @@
 """iMars3D's ring artifact correction module."""
 import logging
 import param
-from imars3d.backend.util.functions import clamp_max_workers
+from imars3d.backend.util.functions import clamp_max_workers, calculate_chunksize
 import scipy
 import numpy as np
 
@@ -238,6 +238,7 @@ def _remove_ring_artifact(
             # invoke mp via tqdm wrapper
             kwargs = {
                 "max_workers": max_workers,
+                "chunksize": calculate_chunksize(arrays.shape[1], max_workers),
                 "desc": "Removing ring artifact",
             }
             if tqdm_class:
diff --git a/src/imars3d/backend/dataio/data.py b/src/imars3d/backend/dataio/data.py
index 601a47c1..4e762cd5 100644
--- a/src/imars3d/backend/dataio/data.py
+++ b/src/imars3d/backend/dataio/data.py
@@ -3,7 +3,7 @@
 
 # package imports
 from imars3d.backend.dataio.metadata import MetaData
-from imars3d.backend.util.functions import clamp_max_workers, to_time_str
+from imars3d.backend.util.functions import clamp_max_workers, to_time_str, calculate_chunksize
 
 # third party imports
 import numpy as np
@@ -329,6 +329,7 @@ def _load_images(filelist: List[str], desc: str, max_workers: int, tqdm_class) -
         #       - there are a lot of cores available
         kwargs = {
             "max_workers": max_workers,
+            "chunksize": calculate_chunksize(len(filelist), max_workers),
             "desc": desc,
         }
         rst = process_map(partial(_forgiving_reader, reader=reader), filelist, **kwargs)
diff --git a/src/imars3d/backend/diagnostics/rotation.py b/src/imars3d/backend/diagnostics/rotation.py
index 22f2f5b8..2674e357 100644
--- a/src/imars3d/backend/diagnostics/rotation.py
+++ b/src/imars3d/backend/diagnostics/rotation.py
@@ -5,7 +5,7 @@
 import numpy as np
 
 import param
-from imars3d.backend.util.functions import clamp_max_workers
+from imars3d.backend.util.functions import clamp_max_workers, calculate_chunksize
 from multiprocessing.managers import SharedMemoryManager
 from tqdm.contrib.concurrent import process_map
 from tomopy.recon.rotation import find_center_pc
@@ -139,6 +139,7 @@ def _find_rotation_center(
             # map the multiprocessing calls
             kwargs = {
                 "max_workers": max_workers,
+                "chunksize": calculate_chunksize(len(idx_low), max_workers),
                 "desc": "Finding rotation center",
             }
             if tqdm_class:
diff --git a/src/imars3d/backend/diagnostics/tilt.py b/src/imars3d/backend/diagnostics/tilt.py
index 4275f2b5..8cd61fbe 100644
--- a/src/imars3d/backend/diagnostics/tilt.py
+++ b/src/imars3d/backend/diagnostics/tilt.py
@@ -4,7 +4,7 @@
 import logging
 import param
 import multiprocessing
-from imars3d.backend.util.functions import clamp_max_workers
+from imars3d.backend.util.functions import clamp_max_workers, calculate_chunksize
 import numpy as np
 from typing import Tuple, Union, Optional
 from functools import partial
@@ -336,6 +336,7 @@ def __call__(self, **params):
 
             kwargs = {
                 "max_workers": self.max_workers,
+                "chunksize": calculate_chunksize(len(idx_lowrange), self.max_workers),
                 "desc": "Calculating tilt correction",
             }
             if params.tqdm_class:
@@ -442,6 +443,7 @@ def __call__(self, **params):
                 np.copyto(shm_arrays, params.arrays)
                 kwargs = {
                     "max_workers": self.max_workers,
+                    "chunksize": calculate_chunksize(params.arrays.shape[0], self.max_workers),
                     "desc": "Applying tilt corr",
                 }
                 if params.tqdm_class:
diff --git a/src/imars3d/backend/util/functions.py b/src/imars3d/backend/util/functions.py
index e5b4f396..9ce5f83b 100644
--- a/src/imars3d/backend/util/functions.py
+++ b/src/imars3d/backend/util/functions.py
@@ -16,6 +16,15 @@ def clamp_max_workers(max_workers: Union[int, None]) -> int:
     """Calculate the number of max workers.
 
     If it isn't specified, return something appropriate for the system.
+
+    Parameters
+    ----------
+    max_workers:
+        The maximum number of workers to use
+
+    Returns
+    -------
+        The number of maximum
     """
     if max_workers is None:
         max_workers = 0
@@ -32,13 +41,18 @@ def clamp_max_workers(max_workers: Union[int, None]) -> int:
 def calculate_chunksize(num_elements: int, max_workers: Union[int, None] = None, scale_factor: int = 4) -> int:
     """Calculate an optimal chunk size for multiprocessing.
 
-    Parameters:
-    - num_elements: The total number of elements to process.
-    - max_workers: The number of workers (processes) to use. Defaults to clamped max.
-    - scale_factor: A factor to fine-tune chunk size (default 4).
+    Parameters
+    ----------
+    num_elements:
+        The number of elements to process
+    max_workers:
+        The maximum number of workers to use
+    scale_factor:
+        The factor to scale the chunk size by
 
-    Returns:
-    - int: Suggested chunk size.
+    Returns
+    -------
+        The optimal chunk size
     """
     # Calculate the number of workers
     workers = clamp_max_workers(max_workers)

From 0b7f190554a782f4048373843950376d54637080 Mon Sep 17 00:00:00 2001
From: Chen Zhang <zhangc@ornl.gov>
Date: Thu, 19 Sep 2024 11:55:08 -0400
Subject: [PATCH 19/21] Update src/imars3d/backend/dataio/data.py

provide file type in error messages as suggested

Co-authored-by: Pete Peterson <petersonpf@ornl.gov>
---
 src/imars3d/backend/dataio/data.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/imars3d/backend/dataio/data.py b/src/imars3d/backend/dataio/data.py
index 4e762cd5..718dd878 100644
--- a/src/imars3d/backend/dataio/data.py
+++ b/src/imars3d/backend/dataio/data.py
@@ -592,7 +592,7 @@ def _extract_rotation_angles(
         else:
             # if the file type is not supported, raise value error
             logger.error(f"Unsupported file type: {file_ext}")
-            raise ValueError("Unsupported file type.")
+            raise ValueError(f"Unsupported file type: {file_ext}")
 
         rotation_angles.append(angle)
 

From 683e02e457b3794892b4ff15c93cac0f565bd61b Mon Sep 17 00:00:00 2001
From: Chen Zhang <zhangc@ornl.gov>
Date: Thu, 19 Sep 2024 12:00:22 -0400
Subject: [PATCH 20/21] Update src/imars3d/backend/util/functions.py

use consistent type hinting

Co-authored-by: Pete Peterson <petersonpf@ornl.gov>
---
 src/imars3d/backend/util/functions.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/imars3d/backend/util/functions.py b/src/imars3d/backend/util/functions.py
index 9ce5f83b..3c0ca24c 100644
--- a/src/imars3d/backend/util/functions.py
+++ b/src/imars3d/backend/util/functions.py
@@ -38,7 +38,7 @@ def clamp_max_workers(max_workers: Union[int, None]) -> int:
     return result
 
 
-def calculate_chunksize(num_elements: int, max_workers: Union[int, None] = None, scale_factor: int = 4) -> int:
+def calculate_chunksize(num_elements: int, max_workers: Optional[int] = None, scale_factor: int = 4) -> int:
     """Calculate an optimal chunk size for multiprocessing.
 
     Parameters

From 50d64c763200d6b29100477dbb5ad078726a17d6 Mon Sep 17 00:00:00 2001
From: Chen Zhang <zhangc@ornl.gov>
Date: Thu, 19 Sep 2024 12:09:17 -0400
Subject: [PATCH 21/21] add missing import

---
 src/imars3d/backend/util/functions.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/imars3d/backend/util/functions.py b/src/imars3d/backend/util/functions.py
index 3c0ca24c..ac5097ab 100644
--- a/src/imars3d/backend/util/functions.py
+++ b/src/imars3d/backend/util/functions.py
@@ -6,7 +6,7 @@
 import logging
 import multiprocessing
 import resource
-from typing import Union
+from typing import Optional, Union
 
 
 logger = logging.getLogger(__name__)