Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Continuous K/S minimizing distributions in Kubelka-Munk systems

Not Accessible

Your library or personal account may give you access

Abstract

The phenomenological model of Kubelka and Munk (KM) for describing the reflection and transmission of diffuse radiation in turbid, plane parallel media is utilized in investigating the nature of inhomogeneous distributions (i.e., the ratio of the absorption and scattering coefficients, K/S, is not necessarily constant) which satisfy certain constraints in finitely thick slabs. The distributions are constrained to be continuous and to minimize the integral of K2/S2 across the slab, while resulting in a specified reflectance when the slab rests upon a backing of specified reflectance. The form of the inhomogeneous distributions is obtained as the solution to the corresponding variational problem, and the associated Lagrange multiplier is found to be algebraically related to the transmittance. The sufficiency of the approach is justified a posteriori by direct comparison with the closed-form solutions of KM for homogeneous distributions. The qualitative nature of such optimal inhomogeneous distributions is discussed with regard to the effects of the boundary conditions and the scattering thickness and is found to be approximately exponential.

© 1977 Optical Society of America

Full Article  |  PDF Article
More Like This
Kubelka–Munk Coefficients from Transmittance*

B. Patrick Caldwell
J. Opt. Soc. Am. 58(6) 755-758 (1968)

Extension of the Kubelka–Munk theory of light propagation in intensely scattering materials to fluorescent media

Leonid Fukshansky and Nina Kazarinova
J. Opt. Soc. Am. 70(9) 1101-1111 (1980)

Kubelka-Munk optical properties of a barium sulfate white reflectance standard

E. M. Patterson, C. E. Shelden, and B. H. Stockton
Appl. Opt. 16(3) 729-732 (1977)

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (7)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (2)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (31)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved