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,

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

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,

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

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.