Modern Optical Engineering

This map uses Warren J. Smith, Modern Optical Engineering: The Design of Optical Systems, fourth edition. It is the closest reference for the classical imaging core of KrakenOS, and Chapter 19 is also a direct source of numerical prescriptions in the repository.

Coverage by chapter

Smith-to-KrakenOS coverage
Book section	Match	KrakenOS implementation
Chs. 2–4, Gaussian and paraxial optics	Direct/partial	`ParaxialMatrix.py` evaluates gap, refracting-surface, mirror, and thin-lens matrices, cardinal quantities, stops, and pupils.
Chs. 5–6, primary and third-order aberrations	Direct/partial	Exact ray intercepts and OPD are direct; `SeidelTool.py` estimates Seidel sums and the knowledge base derives Smith’s ray polynomial.
Chs. 7 and 9, prisms, mirrors, stops, and diffraction	Direct/partial	Refraction, reflection, TIR, coordinate breaks, stops, pupil tools, Gaussian beams, and diffraction PSF/MTF are available.
Chs. 10–12, materials, coatings, and radiometry	Partial/related	Catalog dispersion, absorption, metal reflectance, Fresnel power, and coating tables are present; absolute radiometry is not.
Chs. 13–14, system layout	Related/direct	The UI and common layout library support complete sequential and non-sequential systems, folded paths, CAD solids, and detectors.
Ch. 15, image evaluation	Direct/partial	OPD, fitted wavefronts, geometrical spots, PSF, MTF, and energy maps are implemented, but not every chart and tolerance criterion in the book.
Chs. 16–18, lens, mirror, and catadioptric forms	Related	KrakenOS can model and optimize these forms; it does not automatically synthesize the book’s starting points.
Ch. 19, selected designs	Direct data	All 62 printed prescriptions are encoded in `common_optical_layouts/_modern_optical_engineering_ch19.py`.
Ch. 20, manufacture, tolerances, mounts, and laboratory practice	Partial/related	Monte Carlo tolerance and compensator tools cover part of the chapter; manufacture, mounts, drawings, and laboratory practice are not solvers.
App. A, ray tracing and aberration calculation	Direct	KrakenOS uses equivalent three-dimensional vector intersection and refraction methods for meridional and skew rays, including aspheres.

Paraxial refraction and system matrices

Sections 3.1–3.6 develop refraction, translation, several-surface tracing, thin lenses, and mirrors. In the conventional ray order \(\boldsymbol r=(y,u)^T\), KrakenOS’ component matrices are

\[\begin{split}M_{\rm gap}=\begin{bmatrix}1&d\\0&1\end{bmatrix},\qquad M_{\rm surface}=\begin{bmatrix} 1&0\\(n_1-n_2)/(n_2R)&n_1/n_2 \end{bmatrix}.\end{split}\]

build_paraxial_matrix_trace multiplies these in ray order. The legacy internal matrices use \((u,y)^T\); kraken_to_abcd performs the permutation. ParaxialMatrixTrace reports effective focal length, front and back focal lengths, principal planes, entrance/exit pupils, and magnification. This is a direct matrix equivalent of the book’s paraxial trace, not its row-by-row scalar worksheet.

Aberration polynomial: Eqs. (5.1) and (5.2)

Section 5.2, printed pp. 62–67, expands the transverse ray intercept in field height, pupil radius, and pupil azimuth. KrakenOS does not use the series to propagate a real ray: it traces exact surfaces. The relationship is therefore best used to interpret a traced spot or fit its symmetry and orders.

The full invariant derivation and coefficient meanings are given in Deriving the Axially Symmetric Aberration Polynomial. It shows why centred systems contain odd transverse orders and connects the third-order coefficients to spherical aberration, coma, astigmatism, Petzval curvature, and distortion. SeidelTool.Seidel.calculate supplies a lower-order diagnostic, while PhaseCalc.py and WavefrontFit.py recover OPD and fitted wavefront coefficients from exact rays. These are complementary analyses, not identical coefficient normalizations.

Stops, diffraction, and Gaussian beams: Chapter 9

Sections 9.2–9.7 define the aperture stop, pupils, field stop, vignetting, telecentricity, \(f\)-number, and numerical aperture. These map to surface clear apertures, stop flags, pupil analysis, ray acceptance, and paraxial reports. A CAD face that blocks a non-sequential ray is a physical occluder; it is not automatically the paraxial aperture stop.

Sections 9.9–9.11 cover aperture diffraction, resolution, and TEM00 beams. The implemented Gaussian relations are

\[q_2=\frac{Aq_1+B}{Cq_1+D},\qquad \frac{1}{q}=\frac{1}{R}-j\frac{\lambda_0 M^2}{\pi n w^2}.\]

GaussianBeam.propagate_gaussian_beam evaluates these through the paraxial trace and reports waist radius, curvature, Rayleigh range, divergence, Gouy phase, and clipping. PSFCalc.py separately evaluates a sampled diffraction PSF. A Gaussian \(1/e^2\) beam radius, geometrical RMS spot radius, and Airy radius are three different quantities.

Image evaluation: Chapter 15

Sections 15.2–15.4 connect focus, spherical aberration, wavefront error, and tolerances. KrakenSys accumulates OPL per ray, PhaseCalc removes a reference sphere/tilt, and WavefrontFit fits the residual. The wavelength must be converted from micrometres to millimetres before an OPL in millimetres is expressed in waves.

Sections 15.5–15.10 cover energy distributions, spread functions, MTF, and square-wave targets. PSFCalc supplies the diffraction path; EdgeMTF and USAFMTF supply captured-image paths. For the detailed transform and measurement equations, see Modulation Transfer Function.

Chapter 19: exact prescriptions in the repository

KrakenOS/common_optical_layouts/_modern_optical_engineering_ch19.py cites Smith Chapter 19, figures 19.1–19.62, book pp. 534–596. It encodes every surface row in propagation order, including radii, spacings, glass index and Abbe number, apertures, stops, wavelength, image surface, and the two aspheric Schwarzschild designs.

The translation rules are explicit:

A blank radius becomes a plane surface.
Historical or discontinued glasses use embedded nvk index/Abbe data so that a catalog rename cannot silently change the prescription.
Smith’s printed conic value \(p\) becomes KrakenOS \(\kappa=p-1\) for figures 19.61–19.62.
Smith’s AD, AE, AF, and AG coefficients become radial \(A_4\), \(A_6\), \(A_8\), and \(A_{10}\) terms.

The designs are exposed through the UI layout library. Run python -m KrakenOS.UI.validate_modern_optical_engineering_layouts to check construction and traceability. Numerical reproduction of a prescription is not proof that a plotted ray fan matches the book: wavelength, focus plane, field sampling, aperture normalization, and glass data must also match.

Important gaps

KrakenOS has no automatic first-order architecture generator, glass-map search, thermal/structural finite-element solver, optomechanical mount analysis, manufacturing drawing generator, coating-stack optimizer, or laboratory test planner. Chapter 19 prescriptions are source data, not licensed substitutes for the book’s design commentary and plots.