Deflectometry: sub-nm precision with „a-few-dollar equipment“
Deflectometry measures the local slope of a specular surface, intrinsically. This means, there is no a posteriori calculation of the spatial derivative. The spatial derivative is „intrinsically“ done optically. In terms of information theory, there is a source encoding which strong redundancy reduction, before the noise is added. As the illumination is completely incoherent, deflectometry is limited only by photon noise. The precision of the slope is virtually unlimited.
The fundamental limit for the slope precision δα is given by the uncertainty product:
δα δx ≈ λ / SNR, where δx is the diffraction limited lateral resolution and SNR the Signal-to-Noise Ratio.
Basic publications:
Patent PMD: G. Häusler, „Verfahren und Vorrichtung zu Ermittlung der Form oder der Abbildungseigenschaften von spiegelnden oder transparenten Objekten“
Deutsches Patent DE19944354 (1999)
T 166 M. Knauer, J. Kaminski und G. Häusler. „Phase Measuring Deflectometry: a new approach to measure specular free-form surfaces“,
in Optical Metrology in Production Engineering, Proceedings of SPIE Vol. 5457, pp 366-376 Strasbourg, 04.2004
T 167 M. Knauer, J. Kaminski und G. Häusler. „Absolute Phasenmessende Deflektometrie“, in DGaO-Proceedings 2004
T 274. (87881C) pdf Häusler, C. Faber, E. Olesch, S. Ettl: „Deflectometry vs. interferometry,“ in: Proceedings SPIE 8788, Optical Measurement Systems for Industrial Inspection VIII, 8788-47, 2013 (11pp)
https://www.optik.nat.fau.de/files/2022/02/t-274-87881c.pdf
https://www.optik.nat.fau.de/forschung/osmin-former-group/test-fuer-pdf-upload/