Optics Fundamentals for Ray Tracing and Lens Design

Explore optical ray tracing as a precise method to model light in lenses and imaging systems, emphasizing sequential ray tracing, aberration minimization, and applications in lens design and retina imaging.

Understand optics basics to model refraction, reflection, and dispersion in optical systems for ray tracing. Use first-order calculations and optimization in spreadsheets or software to predict results and guide design.

Apply Snell's law to predict refraction at interfaces, using plane of incidence and refractive indices in materials like air, water, glass, and silicon; explore total internal reflection and critical angles.

Apply the law of reflection: incident rays, reflected rays, and the normal lie in the plane of incidence, with equal angles of incidence and reflection, forming a virtual image.

Explore the lens optical axis and its distinction from the mechanical axis, explain centers C1 and C2 and radii of curvature, and show how misalignment affects centered versus non-centered lenses.

Define the lens coordinate system and optical axis, emphasizing a right-handed z-forward convention for light propagating from left to right. Focus on the y z plane for rotationally symmetric systems.

Adopt a universal sign convention for optical design, used in Zmax and other software, with left-to-right propagation, positive right-side values, and negative left-side values for radii, thickness, and angles.

Explore reflection concepts and sign conventions, using positive and negative angles to apply Snell's law in optical simulations, including negative refractive indices for accurate optical path length.

Propagate rays as straight lines in media with constant refractive index, using height y and angle u to compute y' = y + t' tan(u'), yielding 20.05 mm.

Explore paraxial rays near optical axis and apply a radian-based small-angle approximation to relate ray height and axis angle with refractive indices via phi = (n'−n)/r, distinguishing radius from curvature.

Explore optical power in two senses: total energy delivered and lens power, defined as diopters, equal to one over the focal length, with examples from convex, concave, and window lenses.

Apply the small-angle approximation to sine, tangent, and cosine for radians-only angles, noting the rule of thumb to use it under about ten degrees to keep errors under ~1%.

Explore thin lens focal length concepts, radii of curvature, and sign conventions, for convex and concave lenses, using the lens maker equation to compute focal length.

Explore singlet lens types, a single piece of glass or plastic used in eyeglasses, cameras, and microscopes, with plano convex, plano concave, bi-convex, bi-concave, and positive or negative meniscus varieties.

Explore the structure of a simple lens and its geometrical parameters, including semidiameter, diameter, focal length, optical power (diopter), radius of curvature, center thickness, and edge thickness.

Learn how lens shape factor, calculated from the curvatures of a singlet, can produce the same focal length with different shapes and influence spherical aberration optimization.

Explore lensmaker's equation through practical examples, highlighting sign conventions for r1 and r2. Learn how these signs affect focal length f by applying the n minus one rule.

Explore object and image locations using first order optics and the thin lens equation 1/t' = 1/f + 1/t, with left negative and right positive.

Analyze how object and image sizes relate to positions using tangent relations, sign conventions, and the paraxial approximation, and define magnification as h' over h.

Explore magnification in optical systems and its calculation as h'/h or t'/t. Understand sign conventions: negative magnification yields inverted real images, while positive magnification yields upright images.

Explore how real images form when light rays converge through lenses or mirrors, enabling screen projection, while noting that real images are inverted relative to the object.

Explore virtual images formed when light rays diverge from a point passing a lens or mirror, which cannot be projected on a screen and remain upright relative to the object.

Conclude by exploring practical optics topics with Zmax simulations, including sequential basics, field of view, f-number stop, and imaging. Learn about aberrations, spherical aberration, and AI modeling in Zmax.