Optical System Design

This map uses Robert E. Fischer, Biljana Tadic-Galeb, and Paul R. Yoder, Optical System Design, second edition. Its system-engineering scope is wider than KrakenOS, but it provides a practical context for specifications, performance evaluation, Gaussian beams, tolerancing, sensors, polarization, and stray-light work.

Coverage by chapter

Fischer/Tadic-Galeb/Yoder-to-KrakenOS coverage

Book section	Match	KrakenOS implementation
Chs. 1–2, specifications, basic optics, stops, and pupils	Partial/direct	The paraxial report, surface apertures, stop flags, pupils, ray bundles, and field sampling support optical specifications, not requirements flow.
Chs. 3–5, diffraction and aberrations	Direct/partial	Exact ray aberrations, OPD, Zernike fitting, Seidel estimates, PSF, and MTF cover the optical calculations but not every design rule.
Chs. 6–8, glass, surfaces, design forms, and prisms	Direct/related	Catalog dispersion, conic/polynomial/user surfaces, exact refraction, mirrors, prisms, and layout examples are implemented.
Chs. 9–10, optimization and performance	Direct/partial	Bounded merit optimization, ray fans/spots, OPD, wavefront RMS, MTF, detector maps, and captured-image metrics are available.
Ch. 11, Gaussian beam imagery	Direct for TEM00	GaussianBeam.py propagates circular and astigmatic \(q\) parameters, clipping, and cavity modes.
Chs. 12–14, IR/UV, diffractives, and illumination	Partial/related	Wavelength-dependent rays, gratings, field propagation, and illumination layouts exist; thermal radiometry and general illumination design do not.
Ch. 15, optical testing	Partial	Simulated/captured PSF and MTF, USAF targets, and wavefront fits are present; most interferometer and laboratory reduction procedures are not.
Ch. 16, tolerancing and producibility	Direct/partial	Seeded Monte Carlo, stackups, compensators, correlations, and yield reports implement the computational core, not producibility management.
Chs. 17–18, optomechanics and manufacturing	Related/not modelled	CAD solids can participate in traces; structural design and manufacture are outside KrakenOS.
Chs. 19–20, polarization and thin films	Partial	S/P Fresnel power, normalized Jones rays, branch transport, and coating tables are available; arbitrary Mueller/Jones components and film design are absent.
Chs. 22–23, design examples and sensor systems	Partial/related	Merit operands, image simulation, detector geometry, slanted-edge MTF, and USAF MTF cover parts of these workflows.
Ch. 24, stray light and scattering	Direct/partial	Non-sequential ghosts, CAD occlusion, TIR, deterministic diffuse/BRDF branches, ancestry, and detector power support path analysis.

Aspheric sag: Chapter 7

The rotationally symmetric surface on printed p. 116 is

\[z(r)=\frac{cr^2}{1+\sqrt{1-(1+k)c^2r^2}} +\sum_i a_i r^{2i}.\]

conic__surf and aspheric__surf in MathShapesClass.py evaluate the two terms directly; SurfaceShape combines them with Zernike, error-map, axicon, and user contributions. KrakenOS’ AspherData begins at \(r^2\), while some optical-design exports begin at \(r^4\). Verify the coefficient order rather than copying a column blindly.

Performance evaluation: Chapters 3 and 10

The book separates geometrical spots and ray fans from wavefront and diffraction metrics. KrakenOS does the same:

• Exact image-plane intercepts provide transverse ray error and geometrical RMS spots.

• PhaseCalc.py and WavefrontFit.py reconstruct and fit OPD.

• PSFCalc.py forms a diffraction PSF and MTF from a complex pupil.

• EdgeMTF.py and USAFMTF.py analyze captured images rather than the ideal optical pupil.

Do not compare an RMS spot diameter directly with an Airy diameter or MTF50. They answer different questions and use different weighting. The book’s encircled-energy discussion on printed pp. 189–191 is related to integration of a normalized detector/PSF map within increasing radius; the core module does not expose one universal encircled-energy API for every analysis path.

Gaussian beams: Chapter 11

For a TEM00 beam with waist radius \(w_0\), Chapter 11 uses

\[I(r,z)=I_0(z)\exp\!\left[-\frac{2r^2}{w^2(z)}\right],\qquad z_R=\frac{\pi n w_0^2}{M^2\lambda_0},\qquad w(z)=w_0\sqrt{1+(z/z_R)^2}.\]

GaussianBeam.py stores the equivalent complex parameter and propagates it with \(q_2=(Aq_1+B)/(Cq_1+D)\). It reports beam radius, curvature, Rayleigh range, divergence, Gouy phase, clipping, and separate tangential and sagittal solutions. gaussian_beam_from_diameter_divergence is the closest entry point to the book’s diameter/divergence specification.

The implementation is direct for a paraxial TEM00 model. It is not a physical-optics calculation of arbitrary laser modes, coherence defects, thermal lensing, damage, or diffraction after severe clipping.

Tolerance analysis: Chapter 16

The book warns that RSS addition can fail when unlike aberrations and refocusing interact, and recommends Monte Carlo trials for realistic production prediction. KrakenOS supports both summaries. For independent linearized contributors,

\[\sigma_P\simeq \sqrt{\sum_i\left(\frac{\partial P}{\partial x_i}\sigma_i\right)^2}.\]

The tolerance service perturbs radius, thickness, index, decentre, tilt, and other configured variables; rebuilds and retraces the system; applies an optional compensator; and reports distributions, percentiles, yield, and ranked sensitivities. docs/source/tutorials/tolerance_monte_carlo.rst contains the reproducible UI/API workflow.

Polarization: Chapter 19

At an isotropic interface, Physics/optics.py calculates S/P Fresnel power and phase. Non-sequential branch records can carry complex Jones components, and detector analysis can sum projected fields coherently. This covers the interface part of the chapter and supports polarization-sensitive beam splitters.

The match is partial: KrakenOS does not provide a general sequence of Jones or Mueller matrices for retarders, diattenuators, depolarizers, birefringent crystals, stress birefringence, or polarization aberration. A scalar coating table is not automatically a complex thin-film polarization model.

Stray light: Chapter 24

The book’s scatter-path workflow on printed pp. 714–715 maps closely to system.NsTrace: launch representative in-field and out-of-field bundles, include the mechanical geometry, trace nearest physical hits, and inspect paths that reach a detector. Fresnel/coating branches reveal ghosts and TIR; diffuse-object settings spawn Lambertian, cosine-lobe, Oren–Nayar, or optional pySCATMECH BRDF children. Branch paths and depth expose the number and kind of interactions.

The veiling-glare contrast relation, Eq. (24.4), is

\[C=\frac{I_{\max}-I_{\min}}{I_{\max}+I_{\min}}.\]

Adding a uniform stray-light pedestal to both levels lowers this contrast. KrakenOS can form relative detector maps needed for that experiment, but a calibrated prediction requires source radiance, BSDF/BTDF normalization, throughput, spectral transmission, pixel response, and noise. See Stray Light Analysis and Control for the sharper radiometric boundary.

Important gaps

Requirements allocation, cost and schedule trades, optomechanical stress and thermal analysis, fabrication planning, coatings design, detector electronics, absolute radiometry, illumination optimization, and test-equipment design are not KrakenOS capabilities. The code is strongest from an optical prescription through rays, fields, relative power, image metrics, and tolerances.