diff --git a/README.md b/README.md
index aa433980..204c5719 100644
--- a/README.md
+++ b/README.md
@@ -9,6 +9,13 @@
 
 A Python library for simulating optical systems, similar to Zemax.
 
+`optika` computes the spectral response and resolution of an arbitrary optical system, and can optimize it using `scipy.optimize`.
+Surfaces carry their own sag profile, aperture, material, and rulings, and are placed in global coordinates, so a system is an ordinary Python object that can be built, modified, and swept over programmatically.
+
+Because every parameter can be an array from [`named-arrays`](https://github.com/sun-data/named-arrays), a whole configuration space of designs propagates through the raytrace at once, and an uncertain parameter carries its uncertainty through to the performance of the system.
+
+More information is available in the [documentation](https://optika.readthedocs.io/en/latest/).
+
 ## Installation
 
 Optika can be installed using pip:
@@ -18,13 +25,35 @@ pip install optika
 ```
 
 ## Features
-- Sequential raytrace modeling
-- Spherical, conical and toroidal surface sag profiles
-- Ruled surfaces, constant, variable, and holographic line spacing
+
+- Sequential raytrace modeling of an optical system
+- Stratified random sampling of input rays for faster convergence
+- Image simulation of a given scene using an optical system
+- A fast linear forward model approximating a raytraced system, for imaging many scenes without raytracing each one
+- Spherical, conical, and toroidal surface sag profiles
 - Circular, rectangular, and polygonal apertures
-- multilayer reflectivity and transmissivity
+- Mirrors and arbitrary multilayer coatings
+- Refractive glass materials with Sellmeier dispersion (e.g. N-BK7, F2)
+- Diffraction gratings, with constant, polynomial, and holographic ruling spacing, and sinusoidal, square, rectangular, sawtooth, and triangular ruling profiles
+- CCD/CMOS sensor simulation, including quantum efficiency, noise, and charge diffusion
 - n-dimensional configurations of the optical system using [named-arrays](https://github.com/sun-data/named-arrays)
-- uncertainity propagation using [named-arrays](https://github.com/sun-data/named-arrays)
+- Uncertainty propagation using [named-arrays](https://github.com/sun-data/named-arrays)
+
+## Key concepts
+
+**Surfaces are placed in global coordinates.**
+Unlike Zemax, where each surface is positioned relative to the one before it, an `optika` surface carries a `transformation` giving its position and orientation in the coordinate system of the whole instrument.
+Moving one surface therefore does not move everything downstream of it.
+
+**The field of view and entrance pupil are computed, not specified.**
+The apertures of the surfaces determine them, so marking a surface with `is_pupil_stop` or `is_field_stop` is enough.
+
+**Rulings are a property of a surface.**
+A diffraction grating is an ordinary surface with a `rulings` field, so switching between ruling designs does not mean switching to a different type of surface.
+
+**Any parameter can be an array.**
+Giving a parameter an extra named axis sweeps the system over that axis, and every ray traced through it carries that axis along, which is how `optika` explores a configuration space without a loop.
+An [`UncertainScalarArray`](https://named-arrays.readthedocs.io/en/latest/_autosummary/named_arrays.UncertainScalarArray.html) parameter propagates its uncertainty through the raytrace by the Monte Carlo method.
 
 ## Example Gallery
 
@@ -42,3 +71,54 @@ by specifying the materials and thicknesses of the layers.
 Model the [quantum efficiency of a backilluminated CCD](https://optika.readthedocs.io/en/latest/_autosummary/optika.sensors.quantum_efficiency_effective.html#optika.sensors.quantum_efficiency_effective)
 
 ![QE example](https://optika.readthedocs.io/en/latest/_images/optika.sensors.quantum_efficiency_effective_0_0.png)
+
+Compute the [transmissivity of a thin filter](https://optika.readthedocs.io/en/latest/#examples),
+such as the aluminum filters used to reject visible light on solar instruments.
+
+```python
+import matplotlib.pyplot as plt
+import astropy.units as u
+import named_arrays as na
+import optika
+
+# Define the wavelengths at which to compute the transmissivity
+wavelength = na.geomspace(100, 800, axis="wavelength", num=201) * u.AA
+
+# Compute the efficiency of a 100 nm layer of aluminum
+reflectivity, transmissivity = optika.materials.multilayer_efficiency(
+    wavelength=wavelength,
+    layers=optika.materials.Layer(
+        chemical="Al",
+        thickness=1000 * u.AA,
+    ),
+)
+
+# Plot the transmissivity, which drops sharply at the aluminum L edge
+fig, ax = plt.subplots(constrained_layout=True)
+na.plt.plot(wavelength, transmissivity.average, ax=ax, axis="wavelength");
+ax.set_xscale("log");
+ax.set_xlabel(f"wavelength ({wavelength.unit:latex_inline})");
+ax.set_ylabel("transmissivity");
+```
+![aluminum filter example](https://optika.readthedocs.io/en/latest/_images/index_0_0.png)
+
+## Development
+
+Install the package in editable mode along with its test dependencies, and run the test suite using [pytest](https://docs.pytest.org):
+```bash
+pip install -e .[test]
+pytest
+```
+
+This project is formatted using [black](https://black.readthedocs.io), linted using [ruff](https://docs.astral.sh/ruff), and type-checked using [mypy](https://mypy-lang.org), all of which are checked by continuous integration:
+```bash
+black .
+ruff check .
+mypy optika
+```
+
+To build the documentation locally:
+```bash
+pip install -e .[doc]
+sphinx-build docs docs/_build/html
+```
diff --git a/docs/index.rst b/docs/index.rst
index 4a948282..d2489a30 100644
--- a/docs/index.rst
+++ b/docs/index.rst
@@ -1,5 +1,5 @@
-Introduction
-============
+optika
+======
 
 :mod:`optika` is a Python package for designing optical systems inspired by
 `Zemax <https://en.wikipedia.org/wiki/Zemax>`_.
@@ -27,6 +27,14 @@ Furthermore, :mod:`named_arrays` provides an implementation of a 3D vector,
 :class:`~named_arrays.Cartesian3dVectorArray`, which is convenient to use since
 many of the inputs and outputs of :mod:`optika` can be represented as 3D vectors.
 
+Installation
+------------
+
+:mod:`optika` is published on PyPI and can be installed using::
+
+    pip install optika
+
+
 Features
 --------
 
@@ -77,6 +85,77 @@ Differences from Zemax
   designs.
 
 
+Examples
+========
+
+Compute the transmissivity of a thin filter, such as the aluminum filters used
+to reject visible light on solar instruments.
+
+.. jupyter-execute::
+
+    import matplotlib.pyplot as plt
+    import astropy.units as u
+    import named_arrays as na
+    import optika
+
+    # Define the wavelengths at which to compute the transmissivity
+    wavelength = na.geomspace(100, 800, axis="wavelength", num=201) * u.AA
+
+    # Compute the efficiency of a 100 nm layer of aluminum
+    reflectivity, transmissivity = optika.materials.multilayer_efficiency(
+        wavelength=wavelength,
+        layers=optika.materials.Layer(
+            chemical="Al",
+            thickness=1000 * u.AA,
+        ),
+    )
+
+    # Plot the transmissivity, which drops sharply at the aluminum L edge
+    fig, ax = plt.subplots(constrained_layout=True)
+    na.plt.plot(wavelength, transmissivity.average, ax=ax, axis="wavelength");
+    ax.set_xscale("log");
+    ax.set_xlabel(f"wavelength ({wavelength.unit:latex_inline})");
+    ax.set_ylabel("transmissivity");
+
+|
+
+Compute the effective quantum efficiency of a back-illuminated CCD, and compare
+it to the theoretical maximum for the same sensor.
+
+.. jupyter-execute::
+
+    # Define the wavelengths at which to compute the quantum efficiency
+    wavelength = na.geomspace(10, 10000, axis="wavelength", num=1001) * u.AA
+
+    # Compute the effective quantum efficiency of the sensor
+    eqe = optika.sensors.quantum_efficiency_effective(
+        wavelength=wavelength,
+    )
+
+    # Compute the quantum efficiency of an ideal back surface
+    eqe_max = optika.sensors.quantum_efficiency_effective(
+        wavelength=wavelength,
+        cce_backsurface=1,
+    )
+
+    # Plot both
+    fig, ax = plt.subplots(constrained_layout=True)
+    na.plt.plot(wavelength, eqe, ax=ax, axis="wavelength", label="effective");
+    na.plt.plot(wavelength, eqe_max, ax=ax, axis="wavelength", label="ideal back surface");
+    ax.set_xscale("log");
+    ax.set_xlabel(f"wavelength ({wavelength.unit:latex_inline})");
+    ax.set_ylabel("quantum efficiency");
+    ax.legend();
+
+|
+
+For a complete optical system, including a raytrace and a simulated image, see
+the worked Newtonian telescope in
+:class:`optika.systems.SequentialSystem`.
+
+|
+
+
 Tutorials
 =========