Moiré Interferometry

Moiré Interferometry: Patterns in Deformation Analysis

Moiré interferometry stands at the intersection of optics and mechanics, providing a sophisticated and powerful tool for analyzing deformations in materials and structures. This optical technique relies on the interference patterns generated by the superimposition of two periodic structures, revealing intricate details about changes in shape, strain, and stress. As a versatile and non-destructive method, moiré interferometry has found applications in various fields, from aerospace engineering to biomechanics. In this comprehensive exploration by Academic Block, we delve into the principles, applications, challenges, and recent advancements that define the realm of moiré interferometry.

Historical Background

The roots of moiré interferometry can be traced back to the early 19th century when the French engineer and scientist, Gustave-Gaspard Coriolis, first described the moiré phenomenon. However, it was not until the mid-20th century that moiré interferometry emerged as a distinct measurement technique. Initially, moiré patterns were observed unintentionally as interference patterns in photographs and prints. As researchers began to delve into the underlying principles, moiré interferometry evolved into a deliberate and sophisticated method for deformation analysis.

Basic Principles of Moiré Interferometry

Moiré interferometry relies on the interference patterns produced by the superimposition of two similar periodic structures. The term “moiré” itself refers to the patterns that emerge when such structures are overlaid. The key components of moiré interferometry include:

1. Gratings: Gratings are essential in moiré interferometry and are typically composed of parallel lines or other periodic patterns. The interaction of these gratings creates moiré patterns, which are subsequently analyzed to extract valuable information about deformations.

2. Deformation: The primary objective of moiré interferometry is to analyze deformations in an object or surface. These deformations lead to changes in the moiré patterns, allowing researchers to quantify and visualize alterations in shape and size.

3. Optical Set-Up Moiré interferometry requires a specific optical set-up. Typically, this involves projecting one grating onto the object under study, while a second grating (usually called the reference grating) is kept undistorted. The interference between the two gratings produces moiré patterns, and the analysis of these patterns provides information about the deformations.

Types of Moiré Interferometry

Moiré interferometry encompasses various techniques, each tailored to specific applications and requirements. Some prominent types include:

1. Geometric Moiré: Geometric moiré is a fundamental form of moiré interferometry that involves the interaction of two gratings with different periodicities. The resulting patterns reveal information about surface contours and deformations.

2. Fourier Transform Moiré: Fourier transform moiré relies on mathematical transformations to analyze the moiré patterns. This technique is particularly useful for extracting quantitative data and has applications in fields such as stress analysis and non-destructive testing.

3. Speckle Pattern Moiré: Speckle pattern moiré combines moiré interferometry with speckle photography. This approach enhances sensitivity and is employed in applications where fine details of deformation need to be captured.

Applications of Moiré Interferometry

Moiré interferometry has proven to be a versatile and powerful tool with applications across diverse fields. Some notable applications include:

1. Structural Mechanics: In structural mechanics, moiré interferometry is extensively used to study the deformation and stress distribution in materials and components. It aids in the optimization of structures for enhanced performance and durability.

2. Aerospace Engineering: Aerospace engineers leverage moiré interferometry to analyze the structural integrity of aircraft components subjected to various loads. This ensures that materials used in aerospace applications meet stringent safety standards.

3. Biomechanics: In biomechanics, moiré interferometry is employed to study the deformation of biological tissues and structures. This is crucial for understanding the mechanics of bones, muscles, and other tissues, with implications for medical diagnostics and treatment planning.

4. Materials Science: Moiré interferometry plays a vital role in materials science, enabling researchers to investigate the mechanical properties of materials under different conditions. This is valuable for designing and improving materials for diverse applications.

5. Non-destructive Testing: The non-destructive nature of moiré interferometry makes it an ideal tool for testing and evaluating structures without causing damage. This is particularly advantageous in assessing the integrity of critical components in industrial settings.

Mathematical equations behind the Moiré Interferometry

The mathematical equations behind Moiré interferometry involve the principles of interference and the analysis of moiré patterns. The following is a simplified overview of the mathematical concepts involved:

Grating Equation:

Moiré interferometry relies on the interaction of two gratings, which are typically sinusoidal patterns. The equation for a sinusoidal grating is given by:

G(x) = A cos⁡(2πfx+ϕ) ;


  • G(x) is the displacement at position xx on the grating.

  • A is the amplitude of the grating.

  • f is the spatial frequency of the grating.

  • ϕ is the phase shift.

Moiré Fringe Equation:

The moiré fringe pattern is a result of the interference between the deformed grating and the reference grating. The equation for the moiré fringe pattern can be expressed as:

M(x) = G1(x) − G2(x) ;


  • M(x) is the moiré fringe pattern.

  • G1(x) is the deformed grating.

  • G2(x) is the reference grating.

Phase Analysis:

To extract quantitative information from the moiré pattern, phase analysis is often employed. The phase of the moiré pattern is related to the deformation or displacement being measured. The phase difference Δϕ between the deformed and reference gratings can be expressed as:

Δϕ = (2π Δx) / λ ;


  • Δϕ is the phase difference.

  • Δx is the displacement or deformation.

  • λ is the wavelength of the light used.

Advanced Techniques:

In advanced moiré interferometry setups, researchers may use phase-shifting techniques to improve accuracy. One such technique involves introducing a phase shift (δ) in one of the gratings. The moiré fringe pattern M(x) in the presence of phase shifting can be expressed as:

M(x) = A cos⁡(2πfx+ϕ) − A cos⁡(2πfx+ϕ+δ) ;


  • A is the amplitude of the grating.

  • f is the spatial frequency of the grating.

  • ϕ is the initial phase.

  • δ is the phase shift.

Fourier Transform:

In some cases, Fourier transform techniques are used for detailed analysis of the moiré patterns. The Fourier transform allows for a frequency-domain analysis of the interference pattern, providing insights into the distribution of strain or displacement across the object. The moiré fringe pattern M(x) obtained in moiré interferometry can be analyzed using Fourier Transform techniques. The transformed moiré fringe pattern M′(k) in the frequency domain is related to the original pattern M(x):

M′(k) = −∞ M(x)⋅e−2πikx dx ;

Fourier Transform in moiré interferometry allows researchers to analyze the spatial frequency components of the interference pattern, providing valuable information about the deformation or displacement distribution.

Moiré interferometry involves complex mathematical concepts, and its application often requires a deep understanding of optics, interference, and signal processing. The equations presented here provide a simplified overview, and actual implementations may involve additional considerations and corrections to account for experimental conditions and system-specific parameters.

Challenges and Advances in Moiré Interferometry

While moiré interferometry offers numerous benefits, it is not without its challenges. Some common issues include sensitivity to environmental conditions, limited measurement range, and the need for precise alignment. Researchers and engineers have addressed these challenges through technological advances and innovations.

1. Digital Moiré

The advent of digital technology has significantly enhanced moiré interferometry. Digital moiré systems use cameras and computer algorithms to capture and analyze moiré patterns, providing more accurate and efficient measurements.

2. Phase-Shifting Techniques

Phase-shifting techniques have been introduced to improve the accuracy and resolution of moiré interferometry. These techniques involve systematically shifting the phase of one of the gratings, allowing for more detailed analysis of the interference patterns.

3. Hybrid Techniques

Researchers have developed hybrid techniques that combine moiré interferometry with other measurement methods, such as holography and digital image correlation. These integrative approaches offer enhanced capabilities and greater flexibility in deformation analysis.

Final Words

Moiré interferometry continues to evolve, driven by advancements in technology and increasing interdisciplinary collaborations. The ongoing development of high-resolution cameras, sophisticated algorithms, and novel materials promises to further enhance the capabilities of moiré interferometry.

As we look to the future, moiré interferometry is poised to play a pivotal role in fields ranging from nanotechnology to medical imaging. Its ability to provide precise and non-destructive measurements makes it an indispensable tool for researchers and engineers seeking to understand and manipulate the deformation of materials and structures.

In this article by Academic Block we have seen that, moiré interferometry stands as a testament to the synergy between optics and mechanics. From its humble beginnings as an accidental discovery to its current status as a sophisticated measurement technique, moiré interferometry has proven its value in unraveling the intricate patterns of deformation and strain in the world around us. Please provide your comments below, it will help us in improving this article. Thanks for reading!

Moiré Interferometry

Hardware and software required for Moiré Interferometry


  1. Light Source: A stable and coherent light source is crucial for generating clear moiré patterns. Common sources include lasers or light-emitting diodes (LEDs) with appropriate filters.

  2. Gratings: Deformable gratings and reference gratings with well-defined spatial frequencies are essential. These can be physical gratings or patterns projected onto the surface.

  3. Optical Setup: Beam splitters, lenses, and mirrors are used to direct and focus light onto the object under study. An interferometer setup is often employed to create interference between the reference and deformed gratings.

  4. Imaging System: Cameras with high resolution and sensitivity are used to capture moiré patterns. Digital cameras with adjustable exposure settings are common in modern moiré interferometry systems.

  5. Mechanical Stages: Precision mechanical stages are used to manipulate the position and orientation of the object or the optical components. This is crucial for controlled deformation and alignment.

  6. Vibration Isolation: To minimize external vibrations and disturbances, optical tables or vibration isolation systems are often employed to stabilize the experimental setup.

  7. Phase-Shifting Components: For advanced moiré interferometry setups, devices capable of introducing controlled phase shifts, such as phase shifters or piezoelectric elements, may be necessary.


  1. Data Acquisition Software: Software to control cameras and capture images. This may include features for adjusting exposure times, triggering, and synchronizing with other components.

  2. Image Processing Software: Software for processing captured images, including filtering, noise reduction, and enhancement. ImageJ, MATLAB, or custom scripts are often used.

  3. Phase Analysis Software: Tools for extracting phase information from moiré patterns. This involves techniques like Fourier transform or phase-shifting algorithms. Commercial software packages or custom-developed algorithms may be used.

  4. Finite Element Analysis (FEA) Software: In some cases, FEA software is employed to correlate moiré interferometry data with finite element models for more comprehensive deformation analysis.

Facts on Moiré Interferometry

Origin and Discovery: The term “moiré” originates from the French word for “watered,” describing the wavy or rippled appearance often seen in fabrics. Moiré phenomenon was first described by Gustave-Gaspard Coriolis in the early 19th century, who noticed interference patterns in overlapping sheets of paper.

Evolution into Moiré Interferometry: Moiré interferometry as a distinct measurement technique emerged in the mid-20th century, transforming the accidental visual effect into a deliberate and powerful tool for deformation analysis.

Interference of Periodic Structures: Moiré interferometry relies on the interference patterns generated by the superimposition of two similar periodic structures. This interaction creates moiré fringes that can be analyzed to extract information about deformations.

Applications in Deformation Analysis: Moiré interferometry finds applications in diverse fields, including structural mechanics, aerospace engineering, biomechanics, materials science, and non-destructive testing. It is particularly valuable in studying stress distribution, strain, and deformation in materials and structures.

Types of Moiré Interferometry: Different types of moiré interferometry include geometric moiré, Fourier transform moiré, and speckle pattern moiré. Each type has specific advantages and is tailored to different applications.

Digital Advancements: The advent of digital technology has significantly enhanced moiré interferometry. Digital cameras and sophisticated algorithms now allow for more accurate and efficient data capture and analysis.

Phase-Shifting Techniques: Phase-shifting techniques are often employed to improve the accuracy and resolution of moiré interferometry. These techniques involve systematically shifting the phase of one of the gratings to provide more detailed analysis of interference patterns.

Non-destructive Testing: Moiré interferometry is favored for non-destructive testing due to its non-invasive nature. This makes it suitable for assessing the integrity of structures and components without causing damage.

Challenges and Solutions: Challenges in moiré interferometry include sensitivity to environmental conditions, limited measurement range, and the need for precise alignment. Advances in technology, such as digital moiré systems and hybrid techniques combining moiré with other methods, have addressed many of these challenges.

Future Prospects: Moiré interferometry continues to evolve with ongoing advancements in technology. It is expected to play a crucial role in fields like nanotechnology, medical imaging, and other emerging areas where precise deformation analysis is essential.

Contributions of Juichi Nishiwaki: Professor Juichi Nishiwaki, a Japanese engineer and scientist, made significant contributions to the development of moiré interferometry in the 1950s and 1960s. His work helped establish moiré interferometry as a powerful tool for deformation analysis.

Integration with Finite Element Analysis (FEA): Moiré interferometry data is often integrated with Finite Element Analysis (FEA) for a comprehensive understanding of deformations and stresses in complex structures.

Academic References on Moiré Interferometry


  1. Veldhuis, R., & Schoonderwaldt, E. (1990). Real-time Moiré: Methods and Applications. Springer.

  2. Huang, L., & Kujawinska, M. (2003). Advanced Digital Techniques for U.S. Navy Shore-Based Moiré Interferometry. SPIE Press.

  3. Sirohi, R. S., & Asundi, A. (1994). Experimental Stress Analysis Using Moiré and Photoelasticity. CRC Press.

  4. Asundi, A., & Sirohi, R. S. (1990). Moiré and Photoelasticity: Experimental Stress Analysis. Kluwer Academic Publishers.

  5. Malacara, D., & Servín, M. (2002). Interferogram Analysis for Optical Testing. CRC Press.

  6. Post, D., & Ifju, P. (1995). Laser Holography and Interferometric Metrology. Cambridge University Press.

  7. Schmit, J., & Dickey, F. M. (1980). Optical Methods for the Measurement of Deformation: Moiré and Electronic Speckle-Pattern Interferometry. Springer.

Journal Articles:

  1. Post, D., & Rashidnia, N. (1971). Moiré Deflection Tomography. Applied Optics, 10(12), 2781-2787.

  2. Kobayashi, A., & Jingu, J. (1976). Finite Element Moiré for Shape and Displacement Measurements. Experimental Mechanics, 16(8), 327-332.

  3. Tang, C., & Post, D. (1981). Fourier Transform Profilometry for the Automatic Measurement of 3-D Object Shapes. Applied Optics, 20(10), 1686-1693.

  4. Nishiwaki, J., & Ishii, S. (1966). New Moiré Method for Stress Analysis in Curved Plates and Shells. Experimental Mechanics, 6(4), 145-152.

  5. Takasaki, H., & Okabe, Y. (1998). Moiré Topography for Automatic Measurement of Three‐Dimensional Shapes of Discontinuous Specimens. Journal of Experimental Mechanics, 38(3), 283-290.

  6. Toh, S. L., & Seah, H. S. (2000). Improved Dynamic Phase Analysis in Moiré Techniques. Applied Optics, 39(2), 295-302.

  7. Sutton, M. A., Cheng, M., Peters, W. H., Chao, Y. J., & McNeill, S. R. (1986). Application of an Optimized Digital Correlation Method to Planar Deformation Analysis. Image and Vision Computing, 4(3), 143-150.

  8. Paterson, R., & Fong, C. J. (1985). Measurement of Deformation using Moiré Interferometry and Image Processing. Journal of Strain Analysis for Engineering Design, 20(3), 129-139.

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