From 4b5ad3abfc0121aa7505ad33b6f12bb79bd7ea98 Mon Sep 17 00:00:00 2001
From: Roy Smart <roytsmart@gmail.com>
Date: Fri, 3 Apr 2026 08:36:47 -0600
Subject: [PATCH] Added `optika.systems.InterpolatedSystem` as an approximation
 to `SequentialSystem`.

---
 optika/systems/_interpolated.py | 73 +++++++++++++++++++++++++++++++++
 1 file changed, 73 insertions(+)
 create mode 100644 optika/systems/_interpolated.py

diff --git a/optika/systems/_interpolated.py b/optika/systems/_interpolated.py
new file mode 100644
index 0000000..fe7acdf
--- /dev/null
+++ b/optika/systems/_interpolated.py
@@ -0,0 +1,73 @@
+from typing import Callable, Any
+import abc
+import dataclasses
+import named_arrays as na
+import optika
+from . import AbstractSystem
+
+__all__ = [
+    "AbstractInterpolatedSystem",
+]
+
+
+@dataclasses.dataclass(eq=False, repr=False)
+class AbstractInterpolatedSystem(
+    AbstractSystem,
+):
+    """
+    Approximate an exact optical system using interpolation.
+    """
+
+    @property
+    @abc.abstractmethod
+    def distortion(self) -> Callable[
+        [na.SpectralPositionalVectorArray],
+        na.Cartesian2dVectorArray,
+    ]:
+        """
+        A distortion model which maps positions on the object plane to
+        positions on the detector.
+        """
+
+    def weights(
+        self,
+        coordinates: na.SpectralPositionalVectorArray,
+        axis_wavelength: str,
+        axis_field: tuple[str, str],
+    ) -> tuple[na.AbstractScalar, dict[str, int], dict[str, int]]:
+        """
+        Compute the weights which map the overlap of each pixel on the object
+        plane to each pixel on the detector plane.
+
+        Parameters
+        ----------
+        coordinates
+            The vertices of each pixel on the object plane.
+        axis_wavelength
+            The logical axis
+        axis_field
+            The logical axes corresponding to changing field coordinate.
+        """
+
+        position = coordinates.position
+
+        position_new = self.distortion(coordinates)
+
+        result = na.regridding.weights(
+            coordinates_input=position,
+            coordinates_output=position_new,
+            axis_input=axis_field,
+            axis_output=axis_field,
+            method="conservative",
+        )
+
+        return result
+
+
+    def image(
+        self,
+        scene: na.FunctionArray[na.SpectralPositionalVectorArray, na.AbstractScalar],
+        **kwargs: Any,
+    ) -> na.SpectralPositionalVectorArray:
+        pass
+