This study proposes an alternative and simple method for measuring full-field refractive index. This method is based on the phase-shifting technique with a modulated electro-optical (EO) modulator and the phenomenon of total internal reflection. To this purpose, a linear polarized light is expanded and incident on the interface between the prism and the tested specimen, and the reflected light passes through an analyzer for interference. The phase difference between the s- and p-polarized light is sensitive to the refractive index of the tested specimen when the total internal reflection appears on this interface. Based on this effect, the resulting phase differences make it possible to analyze the refractive index of the tested specimen through a phase-shifting technique with a modulated EO modulator. The feasibility of this method was verified by experiment, and the measurement resolution can reach a value of refractive index unit of at least 3.552×10−4. This method has advantages of simple installation, ease of operation, and fast measurement.
This study proposes a simple method for measuring two-dimensional temperature distributions. Using the significant
phase difference between p- and s-polarizations of the reflected light of a surface plasmon resonance (SPR) detector, the
variation in the phase difference, which is caused by a variation in the temperature, can be accurately measured by
phase-shifting interferometry. Then, by substituting the phase distribution into special derived equation, the temperature distribution can be determined. In order to show the feasibility of this method, different temperature distributions were
measured. The measurement resolution is about 0.186°C. Due to the introduced common-path configuration and the high-sensitivity characteristic of surface plasmon resonance, this method should have merits of easy operation, high sensitivity, high accuracy and rapidly measurement.
Measurements of glucose concentration are important parts of biochemical analyses. Based on the principles of the
common-path heterodyne interferometry, we develop a high sensitivity optical sensor for measuring glucose
concentration. A heterodyne light beam after transmitted through a glucose solution passes through some polarization
components for interference. The phase difference determined with heterodyne interferometric technique of the
interference signal is greatly enhanced as a result of proper azimuth angles of some polarization components, and a high
sensitivity measurement of glucose concentration can be achieved. The feasibility of the measuring method was
demonstrated by our experimental results. This optical sensor should bear the merits of high accuracy, short sample
medium length, and simpler operational endeavor.
In this study, the optical activity of cholesteric liquid crystal and common-path heterodyne interferometry are used in a
simple measurement technique that was developed to measure small wavelength differences. A circularly polarized
heterodyne light passes through a cholesteric liquid crystal cell and an analyzer. Consequently, an interference signal is
generated. When the cholesteric liquid crystal cell is properly chosen at circular regime, it owns strongly optical activity.
Accordingly, the phase difference between the s- and p-polarized components of the interference signal depends strongly
on the wavelength. As the wavelength changed, a variation of the phase difference can be accurately detected by
heterodyne interferometry. Substituting the variation of phase difference into specially derived equations, the wavelength
variations can be estimated accurately. The feasibility of this method was demonstrated and this method provides the
advantages of a simple structure, easy operations, rapid measurement, high stability, and high sensitivity.
In this study a non-contact method for accurately measuring small concentration of solutions by surface plasmon
resonance heterodyne interferometer is proposed. Firstly, a linearly polarized heterodyne light source is transmitted
through a test box filled with pure water. The transmitted light is incident on the base of a hemi-spherical prism of a
surface plasmon resonance apparatus. Then the reflected light passes through an analyzer and generates an interference
signal on a photo-detector. Secondly, when the incident angle is chosen at resonant angle, a significant phase difference
between the s- and p-polarized components occurs. This phase difference is a function of the incident angle at the base of
the hemi-spherical prism. Finally, when the test box is filled with a test solution, the incident angle at the base of the
hemi-spherical prism is changed. This causes a variation in the phase difference that can be detected by the heterodyne
interferometry. Therefore, the concentration of the tested solution can be accurately determined with special derived
equations. The validity of this method was demonstrated experimentally. The advantages of the propose method include
a simple apparatus, rapid measurement, high stability, and high resolution. Due to the introduction of a common-path
structure, the interference signal is not affected by surrounding fluctuations and can be captured easily.
The feasibility of conventional polarization-selective substrate-mode holograms is usually limited by the finite refractive index modulation strength. Therefore, in this study, a novel design of polarization selective element with a large diffraction angle is proposed based on the coupled-wave theory. The polarization selective element for 632.8nm is fabricated with VRP-M silver-halide recording material. The diffraction efficiencies of s- and p- components are 83% and 5%, and the calculated extinction ratios are 5.58 and 275, respectively. Polarization selective elements fabricated by the proposed method have all the merits of conventional substrate-mode hologram but not limited by the finite refractive index modulation of common recording materials.
In this study, a simple method for measuring the small displacements is presented. When a circularly polarized
heterodyne light beam reflected from a mirror is incident into a hemi-spherical prism and is reflected at the base of the
prism. Then the reflected light beam passes through an analyzer for interference. With properly chosen azimuth angles of
transmission axis of the analyzer, the phase difference between s- and p- polarized light is sensitive to the incident angle
near the internal reflection polarization angle. The phase difference can be accurately measured with the heterodyne
interferometry. The small displacement of the mirror causes a small variation of incident angle and a phase change.
Therefore, substituting the phase difference into special derived equations; the small displacement can be determined.
The proposed method has advantages of common-path configuration and heterodyne interferometry.
A simple method is presented to determine small wavelength differences based on the dispersion properties of a uniaxial crystal and circularly polarized heterodyne interferometry. A circularly polarized heterodyne light beam is incident on a uniaxial crystal at the Brewster's angle, and the reflected light beam passes through an analyzer for interference. Owing to proper azimuth angles of the transmission axis of the analyzer and the optical axis of the crystal, the variation of the phase difference determined with the heterodyne interferometric technique of the interference signal is significantly enhanced, resulting in an accurate wavelength variation. The feasibility of this method was demonstrated, and the sensitivity of wavelength differences is about 0.001 nm. The proposed approach has a simple structure, straightforward operation, high stability, and high sensitivity.
We derive the phase difference equation between the p- and s-polarizations of reflection light based on the Kretschmann-Raether configuration. This phase difference equation is used to examine the relationship of the incident angle and metal film thickness versus the phase differences under a small refractive index variation. For a fixed incident angle, the phase difference has a higher measurement sensitivity than the reflectivity change. At the critical angle, there is a higher sensitivity when the metal film thickness is smaller than the skin depth. The surface plasmon resonant (SPR) angle dominates when the metal film thickness is greater than the skin depth. The phase measuring sensitivity at the SPR angle is higher than that at the critical angle by 1 order.
When a light coming from a circularly polarized heterodyne light source incidents on an optical material, a phase difference between s- and p- polarization components of the reflected light occurs. This phase difference can be measured accurately with the heterodyne interferometry. The measured data are substituted into the special equations derived from Fresnel equations, the refractive index can be estimated. This method bears both merits of a common-path interferometer and a heterodyne interferometer. The refractive indices of three optical glasses and two birefringent crystals were measured to show the validity of this method.
Based on the heterodyne interferometry and Fresnel equations, an alternative method for measuring the complex refractive index of a turbid medium. A light beam is incident on the boundary between a right-angle prism and a turbid medium. The phase difference between s- and p- polarizations of the reflected light occurs. The phase difference depends on then incident angle and the complex refractive index of a turbid medium; their relation can be derived from Fresnel equations. The phase difference can be measured accurately with the heterodyne interferometry. Because there are two unknown parameters to be estimated, at least the phase differences under two different conditions should be measured. Then, these measured data are substituted into the derived relation, and a set simultaneous equation is obtained. If the simultaneous equation is solved, the complex refractive index can be estimated. Because the reflected light from the boundary is measured, the scattering noises coming from the turbidity of the tested medium can be greatly reduced. In addition, this method has some merits such as simple optical setup, high sensitivity, high stability, and suitability for a little amount of the tested medium in its native state (without dilution).
First, the phase differences between s- and p-polarizations of a circularly polarized heterodyne light beam reflected from the emulsion layer, and that from its substrate, are measured, respectively. The measured data are substituted into specially derived equations, so the refractive indices of the emulsion layer and its substrate can be calculated. Second, the variations of phase differences between s- and p-polarizations due to the wavelength shifts and the extraction of the holographic plate in a modified Michelson interferometer are measured. Then, the thickness of the emulsion layer and its substrate can be estimated based on the measured values of refractive indices, the wavelength shifts, and the phase difference variations. This method has some advantages, such as high resolution and easy operation in only one optical configuration.
A light beam is incident on the boundary surface between the thin metal film of a surface-plasmon-resonance (SPR) apparatus and the test medium. If the incident angle is equal or very near to the resonant angle, then the phase difference between p- and s- polarizations of the reflected light is related to the associated physical parameter. The phase difference can be measured accurately by the heterodyne interferometry. If the relation between the phase difference and the associated physical parameter is specified, the associated physical parameter can be estimated with the data of the phase difference. This method has the advantages of both common-path interferometry and heterodyne interferometry.
A light beam coming from a circularly polarized heterodyne light source passes through a chiral medium, its rotation angle is just half of the phase difference between p- and s- polarization components. And this phase difference can be measured accurately with heterodyne interferometric technique. The rotatory power is obtained by dividing the estimated rotation angle with its path length. This method has many advantages, such as, high stability, high resolution, easy operation, and real-time measurement.
A novel method for measuring small displacements based on the total-internal-reflection-heterodyne interferometry is presented. In this method, a common-path heterodyne interferometer is applied to measure the phase differences between s and p polarizations at total-internal reflection. The phase differences depend on the incident angles which are the function of displacements by using the image formula. Hence, small displacements can be evaluated only by measuring the phase differences. In our optical setup, a heterodyne light source with a frequency difference 800 Hz between s and p polarizations is used. A light beam passing through a lens is reflected from a mirror located near the focal plane of the objective lens and is driven by a piezo- electric transducer. If the mirror shifts from the focal plane of the lens, the reflected beam deflects with a small angular deviation to a phase difference measurement system. From Fresnel's equations, the phase difference between s and p polarizations is the function of incident angle and the numbers of TIR at total-internal reflection condition. To compare this test signal with a reference signal using a phase meter, the phase difference can be measured in real- time. Consequently, the displacement also can be calculated.
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