---
title: "Improved Solutions of the Steady-State and the Time-Resolved Diffusion Equations for Reflectance from a Semi-Infinite Medium"
authors: ["Alwin Kienle", "Michael S. Patterson"]
year: 1997
venue: "JOSA A"
arxiv: null
doi: "10.1364/josaa.14.000246"
source: "https://doi.org/10.1364/josaa.14.000246"
topics: [subsurface-scattering]
seed_rank: 1296
seed_batch: "sss-translucent-2026-08-25"
reviewed: "2026-08-25"
pool: "graphics"
relevance_score: 8
lineage: subsurface-scattering
cites:
  - title: "A Diffusion Theory Model of Spatially Resolved, Steady-State Diffuse Reflectance for the Noninvasive Determination of Tissue Optical Properties in Vivo"
    url: "https://doi.org/10.1118/1.596777"
    year: 1992
    arxiv: null
    doi: "10.1118/1.596777"
see:
  - "1249-a-diffusion-theory-model-of-spatially-resolved-steady-state-diffuse"
---

# Improved Solutions of the Steady-State and the Time-Resolved Diffusion Equations for Reflectance from a Semi-Infinite Medium

## One-sentence takeaway

Improved extrapolated-boundary dipole.

## Problem

Predecessor chain Farrell92 → Kienle97 → better graphics dipoles. This paper's job: Improved extrapolated-boundary dipole.

## Design

Improved extrapolated-boundary dipole. Lineage: Farrell92 → Kienle97 → better graphics dipoles.

## Evidence

JOSA A 1997. DOI `10.1364/josaa.14.000246`. Improved extrapolated-boundary dipole.

## Limitations

Diffusion / dipole assumption: homogeneous or layered-homogeneous, weak at edges and high absorption unless a later paper fixes it.

## Implications for Broadside

Anoptic has a forward+ mesh renderer and is betting on FMM+RC 3D GI. Translucent materials / SSS is the missing appearance model for skin, marble, wax, leaves, and interiors. Do not claim they already have SSS.

## Bottom line

Mint this 1997 JOSA A paper. Improved extrapolated-boundary dipole.

## Links

- DOI: [10.1364/josaa.14.000246](https://doi.org/10.1364/josaa.14.000246)