As you are in Brandenburg: Check with the guys from IKT Stuttgart (https://www.ikt.uni-stuttgart.de/forschung/produktentwicklung/). This was the institute of Prof Busse, more or less the birthplace of Lock-inThermography. I have worked a long time with him and still the team there is focussed on Lock-in Thermography. Other source could be EDEVIS (https://www.edevis.com/content/de/thermography.php), This company in Stuttgart is some how a SpinOff company of IKT, Zwetschper and Dillenz, the owner of the company got their PhD from Prof Busse and have long experience in that field.
Your problem is some maybe that your excitation source (halogen lamp) even radiates not only NIR-Radiation from the lamp but also some secondary FarIR from the lamp body or the reflector. So usally you can add a filter in front of the IRSource, which just blocks this radiation.
Such a filter could be a water filled cavity, or just some transparent plates with some air blown between for cooling. (we used such solution in the IRGecko/C-Check-IR system from AT Automation Technology (https://shop.testia.com/devices/700-ir-gecko-c-checkir.html , https://www.automationtechnology.de/cms/mobile-zfp-pruefgeraete-zur-instandhaltung/, https://worldwide.espacenet.com/patent/search/family/046317160/publication/EP2664912A1?q=pn%3DEP2664912A1Conference Paper New Active Thermography Approach To Locate And Size SRM Repa...
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I guess this is your problem.
In my practical work with thermographic inspection (with hundreds of parts checked with Thermography (which are not lab samples but real aircraft structures in Hangas or even outside) we learned to deal with nasty surface reflections. If you look at the design of the C-CheckIR system, you may recognize the unusual position of the Halogen Lamp, a modified Hedler Spot, camera module, IR source and Surface have an specific oriwntation to each other. This was key for eliminating a lot of refelction problems as well a key do use this lightweight tripod with suction cups and the ability to test even at the edges of a struture like a vertical tail plane (VTP). Compare this e.g- with systems from TWI (Themeral Wave Imaging /https://www.thermalwave.com/products/ ) using amuch more simpler closed box or OPGAL (https://www.opgal.com/thermography-ndt-testing/), we checkt those configuration but could not qualify them for the Airbus maintenance needs.
Lessons learned:
decouple Wavelength of IR- Source (NIR) and Camera (Bolometer, FIR)
Use blocking filters to even filter out FIR radiation from IR Source body
optimize Camera and IR source position versus inspection surface
Finally a funny effect: we used first CFRP tubes for the "legs" of our system. Uncoated.
And we found strong reflections of a triangle pattern in our field of view.
What was the mistake?
The black CFRP.
Until we coatet them with white of silver paint things vanished.
So even keep an eye on all parts of your inspection system: avoid any black surface.
The simple things are often the trouble makers but also the key for solving the final challenges.
Another point maybe the surface finish of the part you inspect. We had sometimes trouble with uncoated CFRP parts. Mostly the side towards the inspection system is the side of the part which hade faced the mold during production, so here the surface is like being polished and strong reflecting. So everything is reflected undisturbed directly. Use a removable paint which scatters the reflected light. Socalled FingerPaint, which children are using, is washable and non-hazardous (EN 71-7/EN71-9) - it is a perfect solution. We used Staedtler, which went even into the Airbus CML materials list.
I guess that are the main trouble makes in your case. I guess you do notr need specific mathematics to eliminate your distortions. I guess it is simply a handling problem based on the points in listed here.