Smith–Helmholtz invariant

In optics the Smith-Helmholtz invariant is an invariant quantity for light propagating through an optical system. It is defined by^[1]^[2]

H=nyu

,

where $u$ is the marginal ray angle, $y$ is the chief ray height, and $n$ is the refractive index. For a given optical system, this quantity is invariant under refraction, and implies a variety of other interesting relationships.

It is closely connected to the Abbe sine condition. The paraxial version of the sine condition is satisfied if the ratio $u/u'$ is constant, where $u'$ is the marginal ray angle in image space. The Smith-Helmholtz invariant implies that the lateral magnification, $y/y'$ is constant if and only if the sine condition is satisfied.^[3]

References

^ Born, Max; Wolf, Emil. Principles of optics : electromagnetic theory of propagation, interference and diffraction of light (6th ed.). Pergamon Press. pp. 164–166. ISBN 978-0-08-026482-0.
^ "Technical Note: Lens Fundamentals". Newport. Retrieved 16 April 2020.
^ Jenkins, Francis A.; White, Harvey E. Fundamentals of optics (4th ed.). McGraw-Hill. pp. 173–176. ISBN 0072561912.

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[1] Born, Max; Wolf, Emil. Principles of optics : electromagnetic theory of propagation, interference and diffraction of light (6th ed.). Pergamon Press. pp. 164–166. ISBN 978-0-08-026482-0.

[2] "Technical Note: Lens Fundamentals". Newport. Retrieved 16 April 2020.

[3] Jenkins, Francis A.; White, Harvey E. Fundamentals of optics (4th ed.). McGraw-Hill. pp. 173–176. ISBN 0072561912.

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See also

References