White-light Phase-shifting Interferometry Research Articles

Accurate white light phase-shifting interferometry under PZT scanning error

White light phase-shifting interferometry (WLPSI) has obvious advantages such as large field of view, high precision and non-contact, so it is widely used in three-dimensional (3-D) topography measurement of micro-nano photoelectric devices. In this paper, the problems for large phase unwrapping error and low phase calculation accuracy under the scanning error of piezoelectric transducer (PZT) in current phase shifting measurement are studied. The novel and effective phase-shifting measurement method under scanning error is proposed. This method can be used to accurately recover the surface phase and complete the surface reconstruction under random scanning error with maximum for 10nm. Finally, the proposed method is verified by simulation and measurement experiments.

Correction of PZT scanner errors using a phase compensation method in white-light phase-shifting interferometry

White-light phase-shifting interferometry (WLPSI) is widely used for obtaining surface profiles of inspection targets in liquid-crystal displays (LCD) and semiconductor manufacturing processes. Phase errors caused by irregular and nonlinear scanner movement are inevitable in WLPSI. Moreover, these errors affect the measurement stability. It is difficult to eliminate the mechanical and electrical delay of scanner movement entirely. A novel method, to the best of our knowledge, is proposed that consists of a scanner position tracking system and a phase correction algorithm called compensated peak detection and modified bucket algorithm. The proposed method is experimentally verified and outperforms the conventional phase corrections in both the measurement accuracy and the repeatability.

High-Stability Algorithm in White-Light Phase-Shifting Interferometry for Disturbance Suppression

A hybrid algorithm, combining a “Gauss-type” envelope algorithm with the Carré algorithm, is proposed for disturbance suppression. For white-light phase-shifting interferometry (WLPSI), this novel algorithm provides suitable performance in suppressing noise caused by external conditions, such as mechanical vibrations, low-reflectivity surfaces, and poor-contrast interferograms. The algorithm is mathematically derived, and simulation testing is performed at the micro level to demonstrate that the algorithm can position the coherence peak correctly under challenging conditions. At the macro level, the algorithm is further verified on standard samples, with the repeatability of the step height being less than 0.32% in a favorable environment and 0.59% in a noisy environment. The repeatability of the roughness was 0.23% in a favorable environment and 0.65% in a noisy environment. Note that “repeatability” = “standard deviation” / “dean value”, reflecting the stability as a percentage. The simulated and experimental results prove that the proposed algorithm is highly precise and robust. This algorithm reduces the environmental dependence of the performance of WLPSI instrumentation and expands its range of application.

Dependence of quality factor on surface roughness in crystalline whispering-gallery mode resonators.

We present an experimental study of the variation of quality factor (Q-factor) of WGM resonators as a function of surface roughness. We consider mm-size whispering-gallery mode resonators manufactured with fluoride crystals, featuring Q-factors of the order of 1 billion at 1550nm. The experimental procedure consists of repeated polishing steps, after which the surface roughness is evaluated using profilometry by white-light phase-shifting interferometry, while the Q-factors are determined using the cavity-ring-down method. This protocol permits us to establish an explicit curve linking the Q-factor of the disk-resonator to the surface roughness of the rim. We have performed measurements with four different crystals, namely, magnesium, calcium, strontium, and lithium fluoride. We have thereby found that the variations of Q-factor as a function of surface roughness is universal, in the sense that it is globally independent of the bulk material under consideration. We also discuss our experimental results in the light of theoretical estimates of surface scattering Q-factors already published in the literature.

Surface recovery algorithm in white light interferometry based on combined white light phase shifting and fast Fourier transform algorithms.

Quality control of micro-nano structured and freeform surfaces is becoming increasingly important, which leads to challenging requirements in the measurement and characterization of rough and highly reflective surfaces. As an important measurement technique, white light scanning interferometry (WLSI) is a fast noncontact method to measure three-dimensional (3D) surface profiles. Nevertheless, the existing WLSI 3D surface reconstruction algorithms are prone to environmental vibrations and phase changes caused by reflections on the tested surface. A novel peak detecting algorithm that combines the white light phase-shifting interferometry (WLPSI) method and fast Fourier transform (FFT) coherence-peak-sensing technique is proposed in this paper, which can accurately determine the local fringe peak and improve the vertical resolution of the measurement. A microcomponent (10μm standard step height) and a spherical surface were used as test specimens to evaluate the proposed method. Both simulated and experimental results show that the proposed algorithm improves the precision and anti-interference ability of the WLPSI and FFT methods, which can effectively reduce the batwing effects at the edges and solve the problem of positioning error in the maximum modulation.

Fringe-Order Determination Method in White-Light Phase-Shifting Interferometry for the Compensation of the Phase Delay and the Suppression of Excessive Phase Unwrapping

White-light phase-shifting interferometry (WLPSI) is widely recognized as a standard method to measure shapes with high resolution over a long distance. In practical applications, WLPSI, however, is associated with some degree of ambiguity of its phase, which occurs due to a phase delay, which is the offset between the phase of the fringes and the fringe envelope peak position. In this paper, a new algorithm is proposed for the determination of a fringe order suitable for samples in which the phase delay mainly occurs due to noise, diffraction and a steep angle. The concepts of the decouple factor and the connectivity are introduced and a method for calculating the decouple factor and the connectivity is developed. With the phase-unwrapping procedure which considers these values, it is demonstrated that our algorithm determines the correct fringe order. To verify the performance of the algorithm, a simulation was performed with the virtual step height under noise. Some specimens such as step height standard and a column spacer with a steep angle are also measured with a Mirau interference microscope, after which the algorithm is shown to be effective and robust.

New algorithm of white-light phase shifting interferometry pursing higher repeatability by using numerical phase error correction schemes of pre-processor, main processor, and post-processor

White-light phase shifting interferometry (WLPSI) is frequently used for the precision measurement of 3D patterns in various fields. Phase error is one of the most dominant errors in WLPSI, and it is mainly generated by the scanner positioning error and mechanical vibrations. In this paper, phase error detection method by image analysis is proposed, and the numerical correction method for minimizing the phase error is also proposed. The image reconstruction method (IRM), iterative IRM (IIRM) as pre-processors, partial IRM (PIRM), least squares method (LSM) as a main processor, and surface compensation method (SCM) as a post-processor were developed for correcting phase errors. The five methods are implemented and simulated, and the pros and cons of each method are explained. Mirau type interferometry and the phase error generator using a PZT stage were used, and the measurements by WLPSI were done under various vibration conditions. The captured images were analyzed by the five correction methods, and the results were compared. Phase error was effectively minimized by the correction methods, and repeatability of 0.2 nm was obtained in the case of the specimen of 500 nm in height. Repeatability of 10 nm was obtained by conventional WLPSI algorithms for the same specimen.

Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry

This paper proposes a white-light phase-shifting method for interferometry, in which the absolute phase of each point is measured individually. During the axial scanning of the sample, eight phase-shifted intensities are recorded, while the fringe visibility is maximum. A seven-point algorithm, which compensates for the variation in the fringe visibility due to the coherence envelope, allows the computation of the relative phase. Then, the absolute phase is computed from this relative phase, the piezoelectric transducer (PZT) position at the beginning of the data recording and from the fringe order. The fringe order is deduced from the evolution of the fringe envelope between two consecutive PZT positions and from the computed relative phase. This method allows unambiguous profilometry with a nanometric resolution by using a phase-shifting method. Furthermore, both the necessary storage memory and the computation time can be significantly reduced by comparing with already-demonstrated white-light profilers working in the same resolution range.

Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry

Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry

An algorithm for profilometry by white-light phase-shifting interferometry

Abstract In the case of white-light interferometry, the usual phase shifting methods cannot be used because the modulation in the interference intensity is due to both the phase variation and to the coherence envelope. We propose a practical approach in which the coherence envelope is considered as locally linear. The classical four-point calculation algorithm is adapted to a set of seven intensities which are weighted with adapted coefficients in order to compensate for the effect of the coherence envelope. The capabilities of this method are described theoretically.