top of page
Unfathomed Beauty_edited.jpg

Signpost of
light rays and waves

This site provides a clear and organized overview of the fundamental theories of geometrical optics (light rays) and wave optics (light waves), along with the derivation of their underlying principles. I hope it will serve as a helpful guide (signpost) for those working in the fields of optical design and optical measurement.

Table of contents :

Geometric Optics

This theory treats light as a "ray traveling in a straight line" and systematically describes image formation by lenses and mirrors based on the path of the light ray. It provides a foundation for quantitatively understanding the structure and design of optical systems using Snell's law and ray tracing.

■Theoretical framework of light ray propagation in geometrical optics

・Ray Propagation in Spherical Lens Systems Based on Paraxial Approximation

・Ray Propagation Based on the Gaussian Imaging Equation in Ideal Lens Systems

・Focus shift in finite-conjugate optical systems

・Vector representation of ray reflection and refraction at material interfaces

■ The role and properties of the pupil in geometrical optics

・F‑Number in Imaging Optical Systems ~Geometrical Optics Derivation of Pupil Magnification and Effective F‑Number~

■ Analysis of the mechanism of optical aberration generation and practical examples of correction methods

・Ray Propagation and Aberrations in a Plane‑Parallel Plate: A Theoretical Analysis Based on Snell’s Law

・Astigmatism of a spherical mirror caused by oblique ray incidence and its correction

​・Mirror shape that focuses parallel light to a single point (paraboloid of revolution)

・Principles of solid immersion lens (SIL)

Physical Optics

This theory treats light as a "wave" and accurately explains wave phenomena such as interference, diffraction, and polarization. It is connected to Fourier optics and electromagnetic wave analysis, and is indispensable when dealing with microstructure and polarization control.

■ Electromagnetic optics and interference phenomena in non-absorbing media

・Electromagnetic wave theory of light reflection and refraction (I)

~Electromagnetic treatment of non-absorbing media~

・Transmission and Reflection Intensity in Two‑Interface Thin‑Film Interference: Derivation from the Electromagnetic Wave Equations

・Coherence Length of Optical Waves: A Theoretical Model Derived from Spectral Shape

■ Electromagnetic wave optics and material evaluation in absorbing media

・Electromagnetic wave theory of light reflection and refraction (II)

~Extension to absorbing media using complex refractive index~

・Determining Material Absorption Coefficients from Transmittance Measurements: Theory and Methods

■Fundamentals and Measurement Applications of Polarizing Optics

・The principle and description of polarization

~Understanding polarization states derived from electromagnetic wave equation~

・Principles of ellipsometry

■Fundamentals and Applications of Gaussian Beam Optics

・Gaussian Beam Propagation: A Recurrence Formula Model for Ideal Lens Systems

・Power loss of a Gaussian beam passing through a circular aperture

Appendix:

This document compiles supplementary materials necessary to describe the optical theories discussed in the main text.

・Definitions of direction and sign for one‑dimensional vectors and angles

・Representation of complex numbers using magnitude and phase

Image by The Walters Art Museum

Topics to be added in the future:

  • Aberration theory

  • Diffraction grating

*The timing of the additions is yet to be determined, and the schedule is subject to change.

Update history:

  • 2026-08:   "F‑Number in Imaging Optical Systems ~Geometrical Optics Derivation of Pupil Magnification and Effective F‑Number~"- Newly released.

  • 2026-06:  Organized the table of contents on the top page by category.

  • ​​2026-06:  "The principle and description of polarization ~Understanding polarization states derived from electromagnetic wave equation~" - Newly released.

  • 2026-06: "Transmission and Reflection Intensity in Two‑Interface Thin‑Film Interference: Derivation from the Electromagnetic Wave Equations" - Newly released.

  • 2026-03: "Principles of ellipsometry" - Newly released.

  • 2025-12: "Appendix: Representation of complex numbers using magnitude and phase" - Newly released.

  • 2025-12: "Electromagnetic wave theory of light reflection and refraction (II) ~Extension to absorbing media using complex refractive index~" - Newly released.

  • 2025-12: "Electromagnetic wave theory of light reflection and refraction ~Appendix: Regarding the Sign of Phase~" - Newly released.

  • 2025-11: "Determining Material Absorption Coefficients from Transmittance Measurements: Theory and Methods" - Newly released

  • 2025-10: "Ray Propagation in Spherical Lens Systems Based on Paraxial Approximation" Newly released.

  • 2025-10: "Appendix: Definitions of direction and sign for one‑dimensional vectors and angles" - Newly released

  • 2025-09: "Focus shift in finite-conjugate optical systems" - Newly released.

  • 2025-09: "Vector representation of ray reflection and refraction at material interfaces" - Newly released.

  • 2025-08: "Ray Propagation and Aberrations in a Plane‑Parallel Plate: A Theoretical Analysis Based on Snell’s Law" - Newly released.

  • 2025-07: "Gaussian Beam Propagation: A Recurrence Formula Model for Ideal Lens Systems" - Newly released.

  • 2025-06: "Ray Propagation Based on the Gaussian Imaging Equation in Ideal Lens Systems" - Newly released.

  • 2025-05: "Electromagnetic wave theory of light reflection and refraction (I) ~Electromagnetic treatment of non-absorbing media~" - Newly released.

  • 2025-05: "Mirror shape that focuses parallel light to a single point (paraboloid of revolution)" - Newly released.

  • 2025-04: "Power loss of a Gaussian beam passing through a circular aperture" - Newly released.

  • 2025-04: "Astigmatism of a spherical mirror caused by oblique ray incidence and its correction" - Newly released

  • 2025-04: "Coherence Length of Optical Waves: A Theoretical Model Derived from Spectral Shape" - Newly released.

  • 2025-04: "Signpost of light rays and waves" website launched.

bottom of page