First-Order Optics: Rays, Stops, and Pupil Analysis

Learn why understanding optics is essential before using raytracing software to design, analyze, and optimize optical systems, and to interpret results and predict performance for lenses and mirrors.

Explain Snell's law and the plane of incidence, linking refractive indices to refraction, and illustrate critical angles and total internal reflection with material examples.

Explore the law of reflection: incident rays, reflected rays, and the normal vector lie in the plane of incidence, with the angle of reflection equaling the angle of incidence.

Explore how light travels as rays and wavefronts, relate rays to wavefronts using Snell's law, and use ray tracing to locate focal points and assess optical aberrations.

Understand optical path length, equal to light phase, defined as the integral of refractive index over distance for continuous media or the sum of n_i d_i for discrete segments.

Explore how rotational symmetry simplifies manufacturing and analysis. Identify the optical axis as the line through centers of surfaces and distinguish it from the mechanical axis.

Differentiate the object side and image side in imaging systems, explain object and image space and planes, and define the optical axis with a left-to-right z-axis convention for analysis.

Identify how the aperture stop limits light in an optical system, whether at the lens edge or a mechanical stop, and how its diameter and location shape system behavior.

The field of view is constrained by image sensor size and shape; rectangular sensors use their diagonal to define the field, while rotational symmetry keeps the optical spot circular.

Explore image sensor formats by size and aspect ratio, from full frame 36 by 24 mm to 3 by 2, 4 by 3, and square 1 by 1 sensors.

Define the entrance pupil as the image of the aperture stop seen from the object space, and image it through the optics to locate its position, real or virtual.

Understand the exit pupil, the image of the aperture stop seen from the image space, and its ability to lie anywhere from infinity to inside the optical train.

Examine paraxial rays and their two subcategories, marginal and chief rays, to model all other rays and determine image location, size, magnification, aberrations, and pupil positions.

Use paraxial rays for first-order optics with the small-angle approximation to estimate focal length and aberrations; switch to trigonometric rays for exact wide-angle, off-axis solutions with Zemax.

Marginal rays start at an object point, pass the edge of the aperture stop, and reach the image plane, defining the system's acceptance angle and focus via U and Y.

Examine chief rays and marginal rays, their passage through the center of the aperture stop and optical axis, and how the edge of field of view defines the pupil.

Compare real rays using exact Snell's law at interfaces with first-order rays, a linear approximation that reveals focus, aberrations, magnification, and the entrance and exit pupils.

Explore first-order ray tracing for transfer and refraction at spherical surfaces, using small-angle approximations to relate ray height and angles across interfaces with optical power φ.

Explore invariants in physics and their role in optics and imaging systems. See how conserved quantities like energy, momentum, angular momentum, and charge stay constant across reference frames.

Investigate first-order ray invariants, including the refraction invariant n' I' = n I, and the Lagrange invariant linking marginal and chief rays across the optical system.

Explore sign conventions in first-order optics: ray height, thickness, and radii of curvature; angles, reflections, and refractive index sign rules; plus primed, unprimed, and barred ray quantities.

Define the focal length from the optical center to the focal point, and explain how marginal rays and collimated light reveal f for lenses.

Define the field of view (FOV) in angular and physical terms, and derive the angular FOV from focal length and CCD height using full FOV = 2 arctan(h/(2f)).

Explore how the f-number relates focal length to entrance pupil diameter, the physical aperture, using effective focal length when applicable to determine the f-number of an optical system.

this bonus lecture reviews core optics concepts and workflows, including field of view, f-number, stops, and Zmax surface assembly, plus nodal points and principal planes.