Low-coherence tandem interferometer for measurement of group refractive index without knowledge of the thickness of the test sample

Measurement of glass thickness and refractive index based on spectral interference technology

A non-contact glass thickness and refractive index measurement method based on spectral interferometry is proposed. The method uses the Michelson interference principle to calculate the interference signal obtained by the spectrometer using the Fourier transform algorithm to obtain the modulation period of the spectral interference fringes. The geometrical thickness and refractive index of a glass sample can be calculated from the optical path difference between the reflected light of the reference arm and that of the front and back surfaces of the glass sample before and after being placed in the measuring arm. The linear interpolation method is used to resample the interference pattern in the frequency domain to ensure uniform sampling. It also adopts an improved phase extraction algorithm in the Fourier domain, which improves the anti-interference ability of the measurement system, and it exhibits a fast detection speed and high signal-to-noise ratio. To verify the accuracy of the measurement results of this method, a high-precision coordinate measuring machine is used for comparative experiments, and the characteristics of the tested object are analyzed. The experimental results show that the measurement accuracy of the system is in good agreement with that of a high-precision coordinate measuring machine.

Low-Finesse Fabry-Pérot Interferometers Applied in the Study of the Relation between the Optical Path Difference and Poles Location

Interferometry sensors are frequently analyzed by applying the Fourier transform because the transformation separates all frequency components of its signal, making its study on a complex plane feasible. In this work, we study the relation between the optical path difference (OPD) and poles location theoretically and experimentally, using the Laplace transform and a pole-zero map. Theory and experiments are in concordance. For our study, only the cosine function was considered, which is filtered from the interference pattern. In experimental work, two unperturbed low-finesse Fabry-Pérot interferometers were used. First, a Fabry-Pérot interferometer that has a cavity length of ~1.6 mm was used. Its optical path difference was 2.33 mm and the poles were localized at points ±i12. rad/nm. Secondly, a Fabry-Pérot interferometer with a cavity length of ~5.2 mm was used, and its optical path difference was 7.59 mm and the poles were localized at points ±i40.4 rad/nm. Experimental results confirmed the theoretical analysis. Our proposal finds practical application for interferometer analysis, signal processing of optical fiber sensors, communication system analysis, and multiplexing systems based on interferometers.

High-speed combined NIR low-coherence interferometry for wafer metrology

In this investigation, we describe a combined low-coherence interferometric technique to measure the surface and thickness profiles of wafers at once with high speed. The measurement system consists of a spectrally resolved interferometer to provide and monitor the optical path difference between two incident beams of the optical source part and a low-coherence scanning interferometer to measure the dimensions of wafers with significantly shortened scanning length. In the experiments, a silicon wafer and a sapphire wafer, of which both sides are polished, were used as targets of the measurement system for verification of the proposed system. As a result, the scanning length of the low-coherence scanning interferometer was reduced from a few millimeters to a few hundreds of micrometers approximately 10 times. In addition, surface profiles of both sides and thickness profiles were simultaneously measured to reconstruct 3D shapes of wafers.

Simultaneous measurement of refractive index and thickness of multilayer systems using Fourier domain optical coherence tomography, part 2: implementation

We introduce a theoretical method for simultaneous measurement of refractive index and thickness of multilayer systems using Fourier domain optical coherence tomography (FD-OCT) without any auxiliary arrangement. The input data to the formalism are the FD-OCT measured optical path lengths (OPLs) and properly selected spectral components of FD-OCT interference spectrum. The outputs of the formalism can be affected significantly by uncertainty in measuring the OPLs. An optimization method is introduced to deal with the relatively large amount of uncertainty in measured OPLs and enhance the final results. Simulation result shows that by using the optimization method, indices can be extracted with the absolute error ? 0.001 for transparent biological samples having indices < 1.55 .

Simultaneous measurement of refractive index and thickness of multilayer systems using Fourier domain optical coherence tomography, part 1: theory

We introduce a theoretical framework for simultaneous refractive index and thickness measurement of multilayer systems using the Fourier domain optical coherence tomography (FD-OCT) system without any previous information about the item under investigation. The input data to the new formalism are the FD-OCT measured optical path lengths and properly selected spectral components of the FD-OCT interference spectrum. No additional arrangement, reference reflector, or mechanical scanning is needed in this approach. Simulation results show that the accuracy of the extracted parameters depends on the index contrast of the sample while it is insensitive to the sample’s thickness profile. For transparent biological samples with smooth interfaces, when the object is in an aqueous medium and has indices < 1.55 , this method can extract indices and thicknesses with the absolute error ? 0.001 .

Dual low coherence scanning interferometry for rapid large step height and thickness measurements

In this investigation, we propose a dual low coherence scanning interferometer as the novel concept to measure large height steps on the topographic surface of a specimen and the thickness profile of a transparent optical plate. Dual low coherence characteristics by the tandem interferometric configuration can generate several discrete correlograms for the measured surfaces, which provide the possibility to reduce the scanning length of typical low coherence scanning interferometry significantly. Also, the spectrally-resolved interferometric method is combined to monitor the distance gaps between correlograms caused by the dual low coherence. To verify the proposed interferometry, a large height step specimen and a silicon wafer were used and the 3D surface and thickness profiles were rapidly and successfully measured. In addition, the technique which can identify each correlogram by the insertion of dispersive plates are suggested in this paper.

Glass thickness and index measurement using optical sampling by cavity tuning

In this paper, we describe a method based on optical sampling by cavity tuning, which is capable of high-accuracy glass thickness and index measurement. By tuning the repetition frequency of the frequency comb, a series of cross-correlation patterns can be obtained that correspond to the front and rear surfaces of the specimen and the co-operation mirror. Both the geometrical thickness and the optical thickness of the specimen can be measured via the cross-correlation patterns, and consequently, the glass refractive index can be determined at the same time. The comparison with the reference value shows an agreement within 1.3 μm for the thickness measurement, and within 5×10^-4 for the refractive index measurement.

Research Progress on F-P Interference-Based Fiber-Optic Sensors

We review our works on Fabry-Perot (F-P) interferometric fiber-optic sensors with various applications. We give a general model of F-P interferometric optical fiber sensors including diffraction loss caused by the beam divergence and the Gouy phase shift. Based on different structures of an F-P cavity formed on the end of a single-mode fiber, the F-P interferometric optical sensor has been extended to measurements of the refractive index (RI) of liquids and solids, temperature as well as small displacement. The RI of liquids and solids can be obtained by monitoring the fringe contrast related to Fresnel reflections, while the ambient temperature and small displacement can be obtained by monitoring the wavelength shift of the interference fringes. The F-P interferometric fiber-optic sensors can be used for many scientific and technological applications.

Air etalon facilitated simultaneous measurement of group refractive index and thickness using spectral interferometry

A simple method based on air etalons of a transparent cavity is proposed to simultaneously measure the group refractive index and thickness of a transparent optical plate by spectral domain low coherence interferometry. In this method, only a single beam path is needed in contrast to the two beam paths, the reference and sample arms, of the conventional Michelson interferometer. An empty cavity is first constructed in the beam path by two glass plates. Then the transparent plate under test is inserted into the cavity, so that two air gaps are formed in the cavity. A beam of light of low coherence length is then transmitted through the cavity in the normal direction. Measurements of the reflected waves by the air gaps before and after the sample plate is put into the cavity allow us to determine the group refractive index (n_g) and thickness (d) of the sample simultaneously. The relative precision of the results for d and n_g are both approximately 7×10^-4.

Interference enhancement in spectral domain interferometric measurements on transparent plate

In spectral domain interferometry, the interference signal generated by directly reflected waves from the two surfaces of a sample plate under test is greatly enhanced by the blockage of those light waves reflected by the two arm mirrors in the Michelson interferometer. This sample surface-reflected interference signal, being the optical path length of the plate, is therefore identifiable directly from the Fourier-transformed interference spectrum. Consequently, the group refractive index and physical thickness of the plate can be obtained simultaneously without any prior information of them. Moreover, subsequent in situ angular scanning on the interference spectra helps to retrieve the wavelength-dependent phase refractive index and first-order dispersion. The order of magnitude of the relative error for the group refractive index is 10(-4), while that for the phase refractive index and the physical thickness is 10(-3).

Sub-sampling low coherence scanning interferometry and its application: refractive index measurements of a silicon wafer

In this investigation, refractive indices of a silicon (Si) wafer were measured by low-coherence scanning interferometry adopting the sub-sampling technique to reduce measurement time. Based on Fourier domain analysis method, the sub-sampled correlogram was analyzed and the refractive indices were calculated by the simple refractive index model and curve fitting of the phase extracted from the sub-sampled correlogram. In the experiment to verify the proposed technique, near-infrared light emitted by a super-luminescent diode with 1050 nm center wavelength was used as an optical source because it is partially transparent to an undoped Si wafer. As the result of measuring an undoped double-side polished Si wafer, group and phase refractive indices were successfully obtained with the sub-sampled correlogram, and the deviations from the reference value were within 0.001.

Defect detection and property evaluation of indium tin oxide conducting glass using optical coherence tomography

This study demonstrates a new approach for evaluating the properties of indium tin oxide (ITO) conducting glass and identifying defects using optical coherence tomography (OCT). A swept-source OCT system was implemented to scan the ITO conducting glass to enable two-dimensional or three-dimensional imaging. With OCT scanning, the defects can be clearly identified at various depths. Several parameters in addition to morphological information can be estimated simultaneously, including the thickness of the glass substrate, the refractive index, reflection coefficient, and transmission coefficient, all of which can be used to evaluate the quality of ITO conducting glass. This study developed a modified method for evaluating the refractive index of glass substrates without having to perform multiple scans as well as a segmentation algorithm to separate the interfaces. The results show the potential of OCT as an imaging tool for the inspection of defects in ITO conducting glass.

Extrinsic fiber-optic Fabry-Perot interferometer sensor for refractive index measurement of optical glass

A simple fiber-optic sensor based on Fabry-Perot interference for refractive index measurement of optical glass is investigated both theoretically and experimentally. A broadband light source is coupled into an extrinsic fiber Fabry-Perot cavity formed by the surfaces of a sensing fiber end and the measured sample. The interference signals from the cavity are reflected back into the same fiber. The refractive index of the sample can be obtained by measuring the contrast of the interference fringes. The experimental data meet with the theoretical values very well. The proposed technique is a new method for glass refractive index measurement with a simple, solid, and compact structure.

Thickness and refractive index measurement of a silicon wafer based on an optical comb

We have proposed and demonstrated a novel method that can determine both the geometrical thickness and refractive index of a silicon wafer at the same time using an optical comb. The geometrical thickness and refractive index of a silicon wafer was determined from the optical thickness using phase information obtained in the spectral domain. In a feasibility test, the geometrical thickness and refractive index of a wafer were measured to be 334.85 microm and 3.50, respectively. The measurement uncertainty for the geometrical thickness was evaluated as 0.95 microm (k = 1) using a preliminary setup.

Simultaneous measurement of group refractive index and thickness of optical samples using optical coherence tomography

Optical coherence tomography (OCT), based on a Michelson interferometer and utilizing low coherence light as the optical source, is a novel technique for the noninvasive imaging of optical scattering media. A simple OCT scheme based on a 3 x 3 fiber coupler is presented for the simultaneous measurement of the refractive index and thickness of optical samples. The proposed system enables the refractive index and thickness to be determined without any prior knowledge of the sample parameters and is characterized by a simple and compact configuration, a straightforward measurement procedure, and a low cost. The feasibility of the proposed approach is demonstrated experimentally using BK7 and B270 optical glass samples.

Thickness measurement system for transparent plates using dual digital versatile disc (DVD) pickups

A low-cost high-precision thickness measurement system for transparent plates that uses dual digital versatile disc (DVD) pickups is proposed. The two DVD pickups are used as the transmitter and the receiver in the measurement system, respectively. One of the DVD pickups emits a laser to the other DVD pickup (receiver) and projects on the photodiode integrated circuit of the receiver. The transparent plate is placed in the optical path to change the focused point that will affect the focusing error signal (FES) of the receiver. Using the FES, a mathematical model for thickness measurement based on the geometric optical method is developed. The experimental results show that the accuracy is 1.5 microm, and the uncertainty is estimated to be +/-1.37 microm for the measured thickness of 150 microm.

Refractive index measurement by spectrally resolved interferometry using a femtosecond pulse laser

We describe a measurement method of refractive indices by way of spectrally resolved interferometry using a femtosecond pulse laser. The method is dispersion insensitive and requires no prior precise knowledge of the geometrical thickness of the specimen. Not only the group but also the phase refractive index can be determined over the wide spectral range covered by the optical comb of the femtosecond pulse laser in use.

Measurement of group refractive index wavelength dependence using a low-coherence tandem interferometer

A technique for the measurement of the group refractive index wavelength dependence of optical materials using a low-coherence tandem interferometer and a spectrometer is proposed. Four channeled spectra resulting from interferences of light beams from different pairs of optical paths are used for the calculation of optical path differences. The group refractive index wavelength dependence is calculated from these optical path differences generated from the sample under measurement. No a priori information of the geometric thickness of a sample is required. The wavelength dependence of the group refractive index of the samples BK7 parallel plate of 5.200 and 10.025 mm from 675 to 850 nm is experimentally measured with an accuracy of the order of 10(-5) and a repeatability of the order of 10(-9).

Simultaneous measurement of various optical parameters in a multilayer optical waveguide by a Michelson precision reflectometer

A novel reflectometer based on Michelson interference is proposed and used to measure various optical parameters of homogeneous multilayer optical waveguides. Refractive indices, thickness, insertion loss, absorbed loss, Fresnel reflectance, and diffuse reflection coefficients of optical waveguides can be measured simultaneously.