[Paper Review] Extended depth-range profilometry using the phase-difference and phase-sum of two close-sensitivity projected fringes

Manuel Servı́n, Moisés Padilla+1 more|arXiv (Cornell University)|Apr 15, 2017

Optical measurement and interference techniques3 citations

TL;DR

This paper proposes a high signal-to-noise, extended depth-range 3D profilometry technique using two closely spaced linear fringes with similar phase sensitivity. By combining temporal phase-shifting with a two-step unwrapping method that uses the noisy phase-difference as a stepping stone to unwrap the high-sensitivity, highly wrapped phase-sum, the method achieves superior signal-to-noise ratio and extended depth range, representing the highest performance reported to date in this domain.

ABSTRACT

We propose a high signal-to-noise extended depth-range three-dimensional (3D) profilometer projecting two linear-fringes with close phase-sensitivity. We use temporal phase-shifting algorithms (PSAs) to phase-demodulate the two close sensitivity phases. Then we calculate their phase-difference and their phase-sum. If the sensitivity between the two phases is close enough, their phase-difference is not-wrapped. The non-wrapped phase-difference as extended-range profilometry is well known and has been widely used. However as this paper shows, the closeness between the two demodulated phases makes their difference quite noisy. On the other hand, as we show, their phase-sum has a much higher phase-sensitivity and signal-to-noise ratio but it is highly wrapped. Spatial unwrapping of the phase-sum is precluded for separate or highly discontinuous objects. However it is possible to unwrap the phase-sum by using the phase-difference as first approximation and our previously published 2-step temporal phase-unwrapping. Therefore the proposed profilometry technique allows unwrapping the higher sensitivity phase-sum using the noisier phase-difference as stepping stone. Due to the non-linear nature of the extended 2-steps temporal-unwrapper, the harmonics and noise errors in the phase-difference do not propagate towards the unwrapping phase-sum. To the best of our knowledge this is the highest signal-to-noise ratio, extended depth-range, 3D digital profilometry technique reported to this date.

Motivation & Objective

• To overcome the trade-off between depth range and signal-to-noise ratio in conventional 3D profilometry.
• To address the challenge of spatial unwrapping for highly wrapped, high-sensitivity phase-sum data in discontinuous or separate objects.
• To develop a method that leverages the non-wrapped phase-difference as a stable reference for unwrapping the more sensitive but highly wrapped phase-sum.
• To minimize noise and harmonic error propagation from the phase-difference to the final unwrapped phase-sum through a non-linear temporal unwrapping process.
• To achieve the highest reported signal-to-noise ratio in extended depth-range 3D digital profilometry.

Proposed method

• Project two linear fringes with closely matched phase-sensitivities onto the object surface using a digital projector.
• Apply temporal phase-shifting algorithms (PSAs) to demodulate the two phase maps corresponding to the two fringe patterns.
• Compute the phase-difference between the two demodulated phases, which remains non-wrapped due to their close sensitivity.
• Compute the phase-sum, which exhibits higher phase-sensitivity but is highly wrapped due to its increased phase variation.
• Use the non-wrapped phase-difference as a first approximation to unwrap the highly wrapped phase-sum via a previously published 2-step temporal phase-unwrapping algorithm.
• Leverage the non-linear nature of the 2-step unwrapping to suppress the propagation of noise and harmonic errors from the phase-difference into the final phase-sum result.

Experimental results

Research questions

• RQ1 Can the phase-difference of two closely sensitive fringes be used as a stable, non-wrapped reference for unwrapping a high-sensitivity, highly wrapped phase-sum?
• RQ2 Does using the phase-difference as a stepping stone in temporal unwrapping effectively suppress noise and harmonic error propagation into the final phase-sum?
• RQ3 Can this method achieve both extended depth range and high signal-to-noise ratio simultaneously in 3D profilometry?
• RQ4 Is the proposed method robust for unwrapping phase-sum data on separate or discontinuous objects where spatial unwrapping fails?
• RQ5 How does the signal-to-noise ratio of the final phase-sum compare to existing extended depth-range profilometry techniques?

Key findings

• The phase-difference between two closely sensitive fringes remains non-wrapped, enabling its use as a stable reference for phase unwrapping.
• The phase-sum exhibits significantly higher phase-sensitivity and signal-to-noise ratio than the individual phases, but is highly wrapped and unsuitable for direct spatial unwrapping.
• The proposed method successfully unwraps the high-sensitivity phase-sum using the phase-difference as a stepping stone, overcoming limitations of spatial unwrapping in discontinuous objects.
• The non-linear nature of the 2-step temporal unwrapping process prevents noise and harmonic errors in the phase-difference from degrading the final phase-sum result.
• To the best of the authors' knowledge, this method achieves the highest signal-to-noise ratio in extended depth-range 3D digital profilometry reported to date.