Modern Optical Engineering
==========================

Reference: Warren J. Smith, *Modern Optical Engineering: The Design of
Optical Systems*, fourth edition.

Use this reference to connect paraxial imaging, aberrations, diffraction,
optical layouts, and practical engineering decisions.

Cardinal points and mechanical distances
----------------------------------------

Effective focal length is measured from a principal plane. Back focal
distance is measured from the last optical vertex. Working distance uses
a stated mechanical or optical reference.

For a thin lens in air, with positive real-object and real-image distances,

.. math::

   \frac{1}{s}+\frac{1}{s'}=\frac{1}{f},
   \qquad m=-\frac{s'}{s}.

Use the principal planes for the equivalent conjugate relation of a thick
system.

Aperture and image quality
--------------------------

For an unobscured circular pupil in diffraction-limited incoherent imaging,

.. math::

   N=\frac{f}{D_{\mathrm{EP}}},
   \qquad d_{\mathrm{Airy}}=2.44\lambda N.

The Airy diameter is measured to the first dark ring. It is not an RMS spot
diameter. Evaluate field, wavelength, focus, and tolerance dependence
separately from the on-axis nominal result.

Related documentation
---------------------

* :doc:`../../cardinal_points`
* :doc:`../../lens_design_intro`
* :doc:`../../aberration_polynomial`
* :doc:`../../pupil_sampling`