Fringe pattern analysis using deep learning (1807.02757v1)

Abstract: In many optical metrology techniques, fringe pattern analysis is the central algorithm for recovering the underlying phase distribution from the recorded fringe patterns. Despite extensive research efforts for decades, how to extract the desired phase information, with the highest possible accuracy, from the minimum number of fringe patterns remains one of the most challenging open problems. Inspired by recent successes of deep learning techniques for computer vision and other applications, here, we demonstrate for the first time, to our knowledge, that the deep neural networks can be trained to perform fringe analysis, which substantially enhances the accuracy of phase demodulation from a single fringe pattern. The effectiveness of the proposed method is experimentally verified using carrier fringe patterns under the scenario of fringe projection profilometry. Experimental results demonstrate its superior performance in terms of high accuracy and edge-preserving over two representative single-frame techniques: Fourier transform profilometry and Windowed Fourier profilometry.

• The paper presents a two-stage CNN that estimates background intensity and reconstructs phase maps from a single fringe pattern.
• The proposed method outperforms traditional Fourier-based techniques by reducing computational complexity and preserving high-frequency details.
• Experimental results show lower mean absolute errors and superior 3D reconstructions, confirming its efficacy in optical metrology.

Analysis of "Fringe pattern analysis using deep learning"

This paper presents a significant advancement in the field of optical metrology through the integration of deep learning for fringe pattern analysis. The authors propose a novel method that leverages deep neural networks to enhance phase demodulation accuracy from a single fringe pattern, specifically applied to fringe projection profilometry.

Methodology and Network Architecture

The authors develop a two-stage convolutional neural network (CNN) architecture designed to emulate and improve traditional phase demodulation processes. The first CNN (CNN1) estimates the background intensity from captured fringe patterns, essential for isolating the signal from noise. The second CNN (CNN2) leverages this information, alongside the original fringe pattern, to predict the numerator and denominator required for the arctangent function used in phase calculation. This two-stage approach enables the network to effectively handle and preserve high-frequency details and edges in the resulting phase map.

A notable aspect of the methodology is the use of deep networks to learn implicit representations of complex demodulation processes, which traditionally require multiple images for phase-shifting techniques. This approach significantly reduces the computational complexity and resource requirements by eliminating the multi-frame dependencies inherent in phase-shifting methods.

Experimental Verification and Results

The method's efficacy is demonstrated through rigorous experimental setups involving fringe projection profilometry. Training data was collected via a 12-step phase-shifting method to ensure accurate ground truth phase maps. The authors detail an extensive testing regime, comparing their proposed approach against conventional Fourier transform (FT) and windowed Fourier transform (WFT) methods. The deep learning approach outperforms these traditional methods, as evidenced by lower mean absolute errors (MAE) in phase retrieval and superior geometric reconstructions in 3D renderings of complex surfaces.

Statistical analysis revealed the superiority of the proposed networks in preserving edge details and handling phase discontinuities, which are common challenges in existing single-frame analysis techniques. Additionally, the reconstruction of standard ceramic spheres demonstrated the method's practical applicability and accuracy in quantitative measurements, with minimal deviations from known ground truth values.

Implications and Future Directions

The integration of deep learning into fringe pattern analysis as exhibited by this research represents a compelling shift towards more efficient, single-measurement optical metrology solutions. By relying on a trained neural network to perform phase demodulation, this approach promises not only enhanced accuracy but also robustness in dynamic environments where traditional multi-frame techniques may falter due to movement or external perturbations.

Further refinement of the model and training on diverse fringe patterns could extend its applicability to a wider range of optical measurement techniques, including those with complex fringe forms such as exponential phase or closed fringes. Additionally, incorporating adaptive learning mechanisms to better handle noise and varying image qualities could further improve performance.

In conclusion, this paper offers a significant contribution to the field, prompting a reevaluation of single-image analysis capabilities within optical metrology and setting a foundation for further exploration into deep learning applications in this domain.