Exact analysis beats numerical analysis

In principle, analytical solutions of the radiative transfer equation have the advantage that the results are exact compared to numerical solutions and that the computing time is considerably shorter for many applications. At the ILM, exact analytical solutions of the (generalised)

radiative transfer equation were derived, validated and efficiently implemented, resulting in a speed gain of several orders of magnitude compared to numerical methods for many practical applications.

Geometries for which analytical solutions were found

  • Infinitely extended (2D and 3D)
  • Semi-infinit (2D and 3D)
  • Layered (2D and 3D)
  • Circle

These solutions are available for all spatial and spatial frequency domains (continuous wave, frequency and time domains), for all relevant quantities (radiance, fluence, flux, reflection and transmission) and for elastically and inelastically scattered light (fluorescence, Raman).

Analytical solutions
Analytical solutions


Prof. Dr. Alwin Kienle

Prof. Dr. Alwin Kienle

Director Materials Optics & Imaging

Tel: +49 (0)731 / 1429 224

Ihr Kontakt zu uns

Wir sind jederzeit gerne für Sie da.

Ganz egal, ob Sie uns lieber online, telefonisch oder persönlich erreichen möchten – wir helfen Ihnen immer gerne weiter.

I have read the privacy policy and agree that the data I have provided may be collected and stored electronically. My data will only be used strictly for the purpose of processing and answering my request. By submitting the contact form, I agree to the processing of my data.

Privacy policy settings

Cookie settings
This website uses cookies that enable services offered by external providers, such as YouTube or Google Maps. The legal basis here is Art. 6 GDPR (1) a.

You can object to the anonymized recording of your user behavior by MATOMO here. For this purpose, we store a cookie on your computer in order to respect this decision on subsequent visits.

Please note that, depending on your settings, some functions may not be available.

You can find more information in our privacy policy

Matomo settings

Please note: When you object to tracking, a Matomo deactivation cookie is set that remembers your objection.