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.

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

・Vector representation of ray reflection and refraction at material interfaces

・Paraxial ray propagation in a spherical lens system and the Lagrange invariant

・Ray propagation in an ideal lens system based on Newton’s formula

・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)

・Focus shift in finite-conjugate optical systems

・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 wave theory of light reflection and refraction (I)

　　~Electromagnetic treatment of non-absorbing media~

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

　　~Extension to absorbing media using complex refractive index~

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

・Principles of ellipsometry

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

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

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

・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

Update history:

  • 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: "Paraxial ray propagation in a spherical lens system and the Lagrange invariant" 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 in an ideal lens system based on Newton’s formula" - 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