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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

・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

・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~

・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:

・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:

  • 2026-03: "Principles of solid immersion lens (SIL)" - 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.

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