Fiber-based single-channel polarization-sensitive spectral interferometry

We present a novel, to our knowledge, fiber-based single-channel polarization-sensitive spectral interferometry system that provides depth-resolved measurement of polarization transformations of light reflected from a sample. Algebraic expressions for the Stokes parameters at the output of the interferometer are derived for light reflected from a birefringent sample by using the cross-spectral density function. By insertion of a fiber-optic spectral polarimetry instrument into the detection path of a common-path spectral interferometer, the full set of Stokes parameters of light reflected from a sample can be obtained with a single optical frequency scan. The methodology requires neither polarization-control components nor prior knowledge of the polarization state of light incident on the sample. The fiber-based single-channel polarization-sensitive spectral interferometer and analysis are demonstrated by measurement of phase retardation and fast-axis angle of a birefringent mica plate.     

Electro-optic heterodyne interferometer

We propose a new configuration for using a triangle-wave signal to drive the electro-optic modulator in an electro-optic heterodyne interferometer system. The new configuration is adapted to measure the phase retardation of a wave plate and the optical rotation angle of a chiral medium. By adding optic elements, the second-harmonic component amplitude of the interferometer photodetector output signal became proportional to the phase retardation or optical rotation angle of the samples being tested.     

Grating-based real-time polarization phase-shifting interferometry: error analysis

A phase Ronchi grating-based real-time polarization phase-shifting method can be efficiently used for dynamic phase measurement in optical interferometry. A thorough error analysis is required for exhibiting how error sources influence phase-measurement results. We analyze the phase-measurement errors that are induced by the retardation error and azimuth angle error of the quarter-wave plate, the azimuth angle error of polarizers, the phase and intensity aberrations of diffractive wave fronts, and pixel mismatch of the interferometric patterns. The results will also be useful for evaluating the phase-measurement accuracy of other similar systems.     

Self-referenced rectangular path cyclic interferometer with polarization phase shifting

A polarization phase shifting interferometer using a cyclic path configuration for measurement of phase nonuniformities in transparent samples is presented. A cube beam splitter masked by two linear polarizers is used to split the source wavefront into two counter propagating linearly polarized beams that pass through the sample. At the output of the interferometer, the two orthogonally polarized beams are rendered circularly polarized in the opposite sense through the use of a quarter wave plate. Finally, phase shifting is achieved by rotating a linear polarizer before the recording plane. In a rectangular path interferometer, although the two counter propagating wavefronts are laterally folded with respect to each other in the interferometer arms, the beams finally emerge mutually unfolded at the output of the interferometer. This phenomenon is utilized to create a reference if the sample is introduced in one lateral half of the beam in any one of the interferometer arms. The polarization phase shifting technique is used to generate four phase-shifted interferograms, which are utilized to evaluate the phase profile of the phase sample. Experimental results presented validate the proposed technique.     

Simultaneous absolute measurements of principal angle and phase retardation with a new common-path heterodyne interferometer

This study demonstrates a new method for simultaneously measuring both the angle of the principal axis and the phase retardation of the linear birefringence in optical materials. We used a circular common-path interferometer (polariscope) as the basic structure modulated by an electro-optic (EO) modulator. An algorithm was developed to simultaneously measure the principal axis and the phase retardation of a lambda/4 or lambda/8 plate as a sample. In the case of a lambda/4 plate, the average absolute error of the principal axis is approximately 3.77 degrees, and that of the phase retardation is approximately 1.03 degrees (1.09%). The retardation error is within the 5% uncertainty range of a commercial wave plate. Fortunately, the nonlinear error caused by the reflection phase retardation of the beam splitter dose not appear in the new system. Therefore the error could be attributed to misalignment and defects in the EO modulator or the other optical components. As for the repeatability of this new common-path heterodyne interferometer, the average deviation for the principal axis is 0.186 degrees and the phase retardation is 0.356 degrees. For the stability, the average deviation for the principal axis is 0.405 degrees and the phase retardation is 0.635 degrees. The resolution of this new system is estimated to be approximately 0.5 degrees, and the principal axis and phase retardation could be measured up to pi and 2pi, respectively, without ambiguity.     

Precise measurement of optical phase retardation of a wave plate using modulated-polarized light

We propose a new method for precisely measuring the optical phase retardation of a wave plate using modulated-polarized light. Modulated-polarized light is used such that the zeros of the system can be accurately determined. A Babinet-Soleil compensator is employed to measure the optical phase retardation. A cross-wavelength measurement is also proposed for determining the phase retardation at a wavelength, which is not the measuring wavelength.     

Application of space periodic variation of light polarization in imaging polarimetry

The application of space periodic variation of light polarization for measurement and calculation of the distribution of the phase retardation between two eigenwaves propagating inside a linearly birefringent media and the distribution of the azimuth angle of the first eigenvector is described. The measuring method proposed does not require any mechanical movements or rotations of any optical elements. Application of a liquid crystal (LC) modulator instead of a quarter-wave plate gives an opportunity to introduce the required phase shift. The space periodic modulation of the polarization of light is achieved by the use of a Wollaston prism placed inside the path of the light beam. Then a fast Fourier transform is used for further calculations. The number of measurements of the light intensity at the output of the system is minimized to two. These assumptions make the proposed method very fast, which is especially important in measurements of the objects with optical anisotropy that is changing in time.     

Application of phase-to-amplitude conversion technique to linear birefringence measurements

A novel technique that measures the linear birefringence of crystal quartz within the configuration of a Soliel-Babinet compensator (SBC) is proposed. A characteristic of this technique is that phase retardation introduced by quartz is amplitude modulation (AM) instead of phase modulation (PM). The linear birefringence is measured regardless of the azimuth angle of the SBC and the orientation of the linear polarization laser beam. Compared with the single-wedge method, the SBC is similar to a parallel plate that allows for a wider range of refracttive index of the test material to be measured. This proposed method uses a conventional amplitude demodulation method in conjunction with an optical heterodyne technique and a bandpass filter to produce a better signal-to-noise ratio. Although the SBC configuration is more complex than a single element, the independence of azimuth angle and the orientation of the linear polarized laser beam can enhance the sensitivity of the linear birefringence measurement.     

Polariscope for simultaneous measurement of the principal axis and the phase retardation by use of two phase-locked extractions

A novel polariscope with electro-optic modulation that is capable of simultaneous measurement of the principal axis and the phase retardation of an optical linear birefringent medium by means of two phase-locked extractions is described. A phase compensator is used to suppress the transmission phase-retardation effect of the beam splitter, thereby enhancing the precision of the measuring performance. The validity of the proposed design is demonstrated by measurement of the principal axis and phase retardation of a quarter-wave plate sample. There are absolute errors of 0.25 degrees on average and 0.58 degrees at maximum in the principal-axis measurement and of 0.75 degrees (0.83%) on average and 3.11 degrees at maximum in the phase-retardation measurement. Meanwhile, the retardation error lies within a 5% uncertainty range of a commercial wave plate. The root-mean-square resolutions for the principal-axis angle and phase-retardation measurements are 0.042 degrees and 0.081 degrees, respectively. Finally, the dynamic ranges of the principal-axis angle measurement and the phase-retardation measurement extend as far as 180 degrees.     

Optical method for measuring optical rotation angle and refractive index of chiral solution

Based on the phenomena of Brewster's angle and the principles of common-path heterodyne interferometry, we present an optical method for measuring the optical rotation angle and the refractive index of a chiral solution simultaneously in one optical configuration. A heterodyne light beam and a circularly polarized heterodyne light beam are separately guided to project onto the interface of a semicircle glass and a chiral solution. One of the beams is transmitted through the solution, and the other is reflected near Brewster's angle at the interface. Then the two beams pass through polarization components respectively for interference. The phase differences of the two interference signals used to determine the rotation angle and the refractive index become very high with the proper azimuth angles of some polarization components, hence achieving an accurate rotational angle and a refractive index. The feasibility of the measuring method was demonstrated by our experimental results. This method should bear the merits of high accuracy, short sample medium length, and simpler operational endeavor.     

Improved angle interferometer based on total internal reflection

We describe an improved interferometer for angle measurement based on the internal reflection effect. The improvement is achieved by eliminating the influence of wave-plate rotation on the measurement. In the proposed angle interferometer the wave plate is fixed and placed between a rhomb assembly and a retroreflector. This scheme not only allows the angle interferometer to keep the optical configuration compact but also doubles the resolution and can measure the pitch and yaw of moving objects. Both a theoretical analysis and an experimental verification have been conducted on the interferometer. The results indicate that the performance of the modified angle interferometer is greatly improved, especially when the rotation angle is large. The nonlinearity error of the measurement equation is also addressed.     

Highly sensitive wave-front sensor with a non-zero-order phase plate

We propose a novel highly sensitive wave front detection method for a quick check of a flat wave front by taking advantage of a non-zero-order pi phase plate that yields a non-zero-order diffraction pattern. When a light beam with a flat wave front illuminates a phase plate, the zero-order intensity is zero. When there is a slight distortion of the wave front, the zero-order intensity increases. The ratio of first-order intensity to that of zero-order intensity is used as the criterion with which to judge whether the wave front under test is flat, eliminating the influence of background light. Experimental results demonstrate that this method is efficient, robust, and cost-effective and should be highly interesting for a quick check of a flat wave front of a large-aperture laser beam and adaptive optical systems.     

Measurement method of Stokes parameters using a quarter-wave plate with phase difference errors

The Stokes parameters (S0, S1, S2, and S3) of monochromatic light can be measured using the adjustable azimuth settings of a quarter-wave plate and a polarizer. When measuring the Stokes parameters of light of an arbitrary wavelength, the measurement of S3 is affected by the phase difference error Δq(λi), due to the mismatch with respect to wavelength with the quarter-wave plate. In this method, Δq(λi), due to such a mismatch of incident light of arbitrary wavelength, can be overcome by a judicious choice of azimuth settings of the quarter-wave plate and the use of a polarizer; however, the use of a precision quarter-wave plate is necessary. The present paper proposes a measurement method of Stokes parameters of incident light of arbitrary wavelength using a quarter-wave plate with phase difference errors.     

Effects of birefringence on Fizeau interferometry that uses a polarization phase-shifting technique

Interferometers that use different states of polarization for the reference and the test beams can modulate the relative phase shift by using polarization optics in the imaging system. Thus the interferometer can capture simultaneous images that have a fixed phase shift, which can be used for phase-shifting interferometry. As all measurements are made simultaneously, the interferometer is not sensitive to vibration. Fizeau interferometers of this type have an advantage compared with Twyman-Green-type systems because they are common-path interferometers. However, a polarization Fizeau interferometer is not strictly common path when both wavefronts are transmitted by an optic that suffers from birefringence. The two polarized beams see different phases owing to birefringence; as a result, an error can be introduced in the measurement. We study the effect of birefringence on measurement accuracy when different polarization techniques are used in Fizeau interferometers. We demonstrate that measurement error is reduced dramatically and can be eliminated if the reference and test beams are circularly polarized rather than linearly polarized.     

Novel method for determining the fast axis and phase retardation of a wave plate using Fresnel Rhomb

In this study, an optical scheme based on the measurement of light intensity and a proper orientation of the Fresnel Rhomb is successfully developed for simultaneous determination of the phase retardation and fast axis of a wave plate. The theoretical analysis of the principle of measuring the reflection-induced retardance of the Fresnel Rhomb and the phase retardation of a wave plate is given taking Stokes–Mueller Formalism as a mathematical tool. In this method, the fast axis position of the wave plate need not be determined in advance. In addition, the measured result is free of the intensity fluctuation of light source. An application example is also demonstrated. The measured result of the example is verified with an experiment. Some of the merits of the method, such as, a simple optical set-up, high stability and high accuracy, low cost and easier operation, are presented, and the validity of the method is demonstrated.     

Balanced detector interferometric ellipsometer

A novel balanced detector interferometric ellipsometer (BDIE), composed of a polarized common-path optical heterodyne interferometer incorporating a novel balanced detector, provides an amplitude-sensitive method for measurement of the elliptical parameters of a thin film. The requirement for equal amplitude of the polarized heterodyne signals for balanced detection results in the simultaneous measurement of the elliptical parameters in terms of the azimuth angle of a half-wave plate and the output intensity from the differential amplifier, respectively. The common-path feature of BDIE shows a common phase noise rejection mode and this enhances the sensitivity of the phase measurement. At the same time, the balanced detector configuration of BDIE reduces excess noise of laser intensity fluctuation to give better sensitivity during measurement. The error of measurement of BDIE is derived and analyzed. Finally, the elliptical polarization effect of the laser beam is found to be independent of the measurement of the elliptical parameters.     

Simple technique for the measurement of two-dimensional linear retardation distributions of wave plates with a phase-shifting Nomarski prism

What we believe to be a new technique for the measurement of two-dimensional retardation distributions of a wave plate (WP) is presented. Phase-shifting interferometry has been applied for determining the relative retardation distribution using a Nomarski prism (NP) as a phase shifter. Absolute retardation distribution is obtained by accurately determining the position of zero retardation in the interference field using white light interference fringes and adjusting the phase distribution with respect to the zero retardation position. The measured absolute retardation distribution of the NP is subtracted from that obtained for the combination of the WP and NP, to get the desired retardation distributions for the WP. The technique is suitable for the measurement of phase retardation of both single and multiple order WPs, as the actual phase retardation distributions are obtained. Results obtained for WPs are presented.     

一种新型单频激光干涉系统的研究

这种单频激光干涉系统采用共光路设计布局,通过偏振分束器以及1/4波长片等光学器件对干涉条纹进行空间移相,提取相位依次相差90°的三路干涉输出信号,进行比较放大,解决了常规单频激光干涉仪中的光强“零漂”问题。利用共模抑制技术,提高了干涉系统的测量稳定性和重复性。采用光程差放大技术,提高了干涉系统的分辨力。     

Circularly polarized optical heterodyne interferometer for optical activity measurement of a quartz crystal

Phase retardation between two orthogonal circularly polarized light waves that propagate in an optical active medium is proportional to its optical activity. The measurement of optical activity of a quartz depolarizer in terms of the phase difference of two orthogonal circularly polarized waves is proposed. A circularly polarized optical heterodyne interferometer with a Zeeman laser to measure the optical activity of a quartz crystal is demonstrated experimentally. The accuracy of the measurement is discussed. In addition, the effect of elliptical polarization and nonorthogonality of linearly polarized light waves of a Zeeman laser on the optical activity measurement is analyzed.