Orthogonal Fringe Research Articles

Compact and stable real-time dual-wavelength digital holographic microscopy with a long-working distance objective.

We propose a compact dual wavelength digital holographic Microscopy (DHM) based on a long working distance objective, which enabling quantitative phase imaging of opaque samples with extended measurement range in one shot. The compactness of the configuration is achieved by constructing a miniature modified Michelson interferometer between the objective and the sample, and as a result it provides higher temporal stability than conventional dual wavelength DHM. In the setup, the propagation directions of two reference beams of different wavelengths can be independently adjusted, and thus two off axis interferograms having orthogonal fringe directions can be simultaneously captured through a monochrome CCD camera. The unambiguous vertical measurement range in optical path length is extended to 8.338 μm, the length of a synthetic wavelength, by selecting two wavelengths with a gap of 52 nm. The capability of the proposed setup is demonstrated with measurements of a standard 1.8 μm height step as well as a moving micro staircase structure.

Random phase-shifting algorithm by constructing orthogonal phase-shifting fringe patterns.

The intensity distribution of fringe patterns becomes nonsinusoidal in real testing environments. Thus, the performance of existing phase shift extraction algorithms, which usually compute the desired phase shift by arccosine function or arcsine function, may be affected. In the presented paper, we report an arctangent-function-based technique to solve this disturbance. First, two orthogonal fringe patterns are constructed through subtraction and addition of two background-removed images. Second, the unequal amplitude between two new fringe patterns is eliminated using a normalization process. Third, the phase shift is determined by computing the norms of the two new images. The proposed method is fast and can be implemented easily in many applications. We verify the algorithm performance and robustness using both simulated and experimental data, indicating the high accuracy of the presented method.

A 3D shape retrieval method for orthogonal fringe projection based on a combination of variational image decomposition and variational mode decomposition

The orthogonal fringe projection technique has as wide as long practical application nowadays. In this paper, we propose a 3D shape retrieval method for orthogonal composite fringe projection based on a combination of variational image decomposition (VID) and variational mode decomposition (VMD). We propose a new image decomposition model to extract the orthogonal fringe. Then we introduce the VMD method to separate the horizontal and vertical fringe from the orthogonal fringe. Lastly, the 3D shape information is obtained by the differential 3D shape retrieval method (D3D). We test the proposed method on a simulated pattern and two actual objects with edges or abrupt changes in height, and compare with the recent, related and advanced differential 3D shape retrieval method (D3D) in terms of both quantitative evaluation and visual quality. The experimental results have demonstrated the validity of the proposed method.

One-shot 3D gradient field scanning

Three-dimensional (3D) shape profiling is an important and practical problem that is being widely studied in the academia and applied in industrial field. In the present work we propose a 3D scanning technique based on the combination of orthogonal fringe projection. It allows us to compute depth field gradient maps in a fast and efficient manner by measuring the local bending of the projected fringes. In the present work we extend the ideas presented in our previous work (di Martino et al. (2014) [1]), obtaining a more general analytical description and evaluating in-depth the different parameters and steps involved in the proposed approach. In addition, extensive validation experiments are presented which show the potential and limitations of the proposed framework.

Improved differential 3D shape retrieval

Phase unwrapping is a complex step in three-dimensional (3D) surface measurement. To simplify the computation process, Martino et al. proposed a differential algorithm. However, it will result in large error when the orthogonal fringes are not in horizontal or vertical direction. To solve this problem, the relationship between projector׳s and camera׳s coordinate systems is introduced. With the data obtained from coordinate transformation, the improved differential algorithm can be used for orthogonal fringes in any direction. Besides that, taking advantage of Fourier differentiation theorem makes operation and calculation simpler. By contrast, the results of experiments show that the proposed method is applicable to the patterns with orthogonal fringes in every direction. In addition, Fourier differentiation theorem effectively increases the speed of differential process.

Electrostatic focal spot correction for x-ray tubes operating in strong magnetic fields.

A close proximity hybrid x-ray/magnetic resonance (XMR) imaging system offers several critical advantages over current XMR system installations that have large separation distances (∼5 m) between the imaging fields of view. The two imaging systems can be placed in close proximity to each other if an x-ray tube can be designed to be immune to the magnetic fringe fields outside of the MR bore. One of the major obstacles to robust x-ray tube design is correcting for the effects of the MR fringe field on the x-ray tube focal spot. Any fringe field component orthogonal to the x-ray tube electric field leads to electron drift altering the path of the electron trajectories. The method proposed in this study to correct for the electron drift utilizes an external electric field in the direction of the drift. The electric field is created using two electrodes that are positioned adjacent to the cathode. These electrodes are biased with positive and negative potential differences relative to the cathode. The design of the focusing cup assembly is constrained primarily by the strength of the MR fringe field and high voltage standoff distances between the anode, cathode, and the bias electrodes. From these constraints, a focusing cup design suitable for the close proximity XMR system geometry is derived, and a finite element model of this focusing cup geometry is simulated to demonstrate efficacy. A Monte Carlo simulation is performed to determine any effects of the modified focusing cup design on the output x-ray energy spectrum. An orthogonal fringe field magnitude of 65 mT can be compensated for using bias voltages of +15 and -20 kV. These bias voltages are not sufficient to completely correct for larger orthogonal field magnitudes. Using active shielding coils in combination with the bias electrodes provides complete correction at an orthogonal field magnitude of 88.1 mT. Introducing small fields (<10 mT) parallel to the x-ray tube electric field in addition to the orthogonal field does not affect the electrostatic correction technique. However, rotation of the x-ray tube by 30° toward the MR bore increases the parallel magnetic field magnitude (∼72 mT). The presence of this larger parallel field along with the orthogonal field leads to incomplete correction. Monte Carlo simulations demonstrate that the mean energy of the x-ray spectrum is not noticeably affected by the electrostatic correction, but the output flux is reduced by 7.5%. The maximum orthogonal magnetic field magnitude that can be compensated for using the proposed design is 65 mT. Larger orthogonal field magnitudes cannot be completely compensated for because a pure electrostatic approach is limited by the dielectric strength of the vacuum inside the x-ray tube insert. The electrostatic approach also suffers from limitations when there are strong magnetic fields in both the orthogonal and parallel directions because the electrons prefer to stay aligned with the parallel magnetic field. These challenging field conditions can be addressed by using a hybrid correction approach that utilizes both active shielding coils and biasing electrodes.

Differential 3D shape retrieval

We are presenting a differential three-dimensional (3-D) shape profiling method that is based on the combination of orthogonal fringe projection. It allows us to compute depth gradient maps in a fast and efficient manner. What we are demonstrating is that depth gradients can be computed in a simple way by measuring fringe deformation throughout a novel single-shot approach. We show the usefulness and potential applications of the proposed approach. Validation experiments are presented as well.

Deflectometry for phase retrieval using a composite fringe

An improved deflectometry for wavefront measurement using a composite fringe is proposed to reduce the projection fringes and improve the accuracy. The single composite fringe contains four fringes in different directions. It goes through the tested objects and then is captured by a CCD camera. Two high frequency orthogonal fringe patterns and two single period orthogonal fringe patterns can be obtained from the composite fringe by fast Fourier transform. The unwrapping of the wrapped phase of the high frequency fringe is accomplished by the corresponding single period fringe using a heterodyne method. The wavefront is reconstructed by the integration of partial derivatives. Using only one fringe, the proposed method is more applicable to dynamic wavefront measurement. The experimental results demonstrate that the proposed method can retrieve the complex wavefronts more accurately.

One-frame two-dimensional deflectometry for phase retrieval by addition of orthogonal fringe patterns

Deflectometry is a well-known method to characterize pure phase objects by measuring the deformation of fringes. In principle, the retrieved magnitude is the partial derivative of the phase along the coordinate orthogonal to the fringes. In order to recover the phase it is necessary to know the derivatives in two orthogonal directions, which is usually achieved by rotating 90° the original fringes and acquiring a new deformed pattern. This "time-multiplexed" two-dimensional deflectometry is a time-consuming operation if the goal is to characterize phase objects in real time. In the present paper we propose a kind of two-dimensional deflectometry that allows acquisition of fringe patterns in two orthogonal directions in a single frame. The proposed procedure utilizes a two-dimensional ("additive") fringe pattern that allows the application of Takeda's method to each coordinate independently. The advantage of the method (with respect to the traditional one) is that it simplifies the setup and reduces the acquisition time. Validation experiments are presented.

Single image orthogonal fringe technique for resolution enhancement of the Fourier transform fringe analysis method

Gradient range and spatial resolution in Fourier Transform Profilometry depend on the size of the filter window in reciprocal space. The proposed methods to date for the elimination of the fundamental frequency and enlargement of the filter window are either too computationally complex or depend on the possibility of using two frames, thus disabling the method's ability to cope with dynamic situations and subjecting the results to possible intensity changes between the two frame acquisitions. This article describes a simple method for using a single crossed fringe pattern to accomplish that objective, greatly improving the previously reported technique, whilst retaining its main advantages.

Advanced bidirectional subdivision algorithm for orthogonal fringes in precision optical measurement instruments

Subdivision is one of the essential methods to improve the measurement resolution of optical instruments. A novel method is studied to solve the λ/2n+2 bidirectional counting of orthogonal interference signals by constructing n sets of reference signals and using the zero-cross detection. The advantage of this method is that the effective bidirectional fringe counting can be achieved easily by the computer programming. This method can be used widely in the signal processing system of the optical measurement instruments, such as the Moiré fringe measurement instruments and the laser interferometers.

Subdivision and direction recognition of λ/16 of orthogonal fringes for nanometric measurement

Subdivision is one of the essential methods to improve the measurement resolution of optical instruments. A new method is proposed to solve lambda/16 bidirectional subdivision and direction recognition for orthogonal interference signals by constructing two sets of reference signals and using zero-cross detection. The experimental results prove that the method is efficient for orthogonal signals and has good real-time performance by field-programmable gate array realization. This method is easy to realize by use of electronic design automation tools and can be widely used in the signal processing system of optical measurement instruments such as a moiré fringe measurement system and laser interferometer.

Fast phase-map recovery from large shears in an electronic speckle-shearing pattern interferometer using a Fourier least-squares estimation

Electronic speckle-shearing pattern interferometry offers the possibility of analyzing out-of-plane and in-plane deformations in experimental mechanics. However, to obtain high-contrast fringes this technique must introduce large shears into the speckle patterns. Several techniques have recently been proposed to recover the phase from these data, but they all suffer limitations due to the slow convergence of the proposed algorithms or to the low precision of the recovered phase. This paper presents a least-squares estimation method in the frequency domain that allows wavefront recovery from two orthogonal shearing fringe patterns when a large shear is applied. This method is based on the application of a single Fourier filter using the fast Fourier transform process. The experimental results obtained by using electronic speckleshearing pattern interferometry for the analysis of a finite circular plate deformed at the center illustrate the advantages of the proposed technique.