Change In Optical Path Difference Research Articles

High-sensitive quantitative phase imaging with averaged spectral domain phase microscopy

We present an averaged spectral domain phase microscopy (A-SDPM) for high-sensitive quantitative phase imaging, where multiple spectral phases from different wavenumbers are fully exploited to determine the final optical path difference (OPD). Uncertainties of recovered spectral phases and OPDs at all wavenumbers are investigated, and a threshold value for the uncertainty of OPD is set to obtain the optimized averaging. A sensitivity of 17.84pm is achieved under signal to noise ratio (SNR) of 61dB, resulting in a 4.11 fold reduction in noise compared with the single spectral phase approach. The performance of the proposed A-SDPM is further illustrated by phase imaging of a coverslip with continuous changes in OPD.

振動下で撮影された光干渉像を用いた高精度3次元形状計測

Vertical-scanning shape-measurement interferometry using white light could not be used under vertically vibrating environment. Because, it is required to repeat predefined-length vertical movement with nanometer accuracy and interferogram capturing just after the movement. We developed the technology which can measure changes of optical path difference (OPD) of an interferometer at around 20-μs interval and can trigger interferogram exposure at even the moment when predefined-length movement complets irregularly due to external vibrations. But vibration during exposure does change interferogram intensities captured. This changes result in phase extraction errors and then shape measurement errors. Then we developed the phase-extraction method which utilizes the history of OPD change during exposure and might remove the above errors. In this paper, validity of this method is estimated by shape-measurement experiments using pulse-like vertical vibrations.

振動環境下で撮影された干渉像からの高精度位相抽出

Vertical-scanning shape-measurement interferometry using white light cannot be used under vertically vibrating environment. Because, it is required to repeat predefined-length vertical movement with nanometer accuracy and interferogram capturing just after the movement. We developed the technology which can measure the changes of optical path difference (OPD) of an interferometer with nanometer resolution at around 20-μs interval. So, the technology can trigger interferogram capturing at even the moment when predefined-length movement happens to complete at an abnormal timing due to external vibrations. But vibrations in exposure time would change interferogram intensity captured. This change results in non-negligible measurement errors. Then we develop new phase extraction method which utilize history of OPD change in the exposure time and can remove the above errors. Validity of this method is also estimated by computer simulations.

Video-Based Interferogram Analysis for Measuring Influence of Vibration to White Light Interferometry

In this paper, we present a video-based interferogram analysis method for measuring the influence of vibration on white light interferometer in terms of undesired change in optical path difference between reference and sample arms. The measurement principle is based on the analysis of interferograms which involves tracking and converting change in interferograms to physical change in optical path difference. The method proposed uses the original sensor in interferometer for data acquisition as such no additional hardware is required. Such an approach ensures that the properties of interferometer such as the bandwidth of sensor are considered and the vibration pattern recorded is close to the effective influence of vibration. With our method, the influence of vibration on white light interferometer and the performance of vibration isolation system can be objectively quantified and measured.

Modified super-wide-angle Sagnac imaging interferometer based on LCoS for atmospheric wind measurement

The modified super-wide-angle Sagnac imaging interferometer (MSASII) based on liquid crystals on silicon (LCoS) is proposed as a novel device for the detection of the upper atmospheric wind field. This device employs the phase-only modulation (POM) of LCoS coupled with the MSASII, and can measure phase changes in multi-band emissions without moving mirror. It can be used to replace the conventional Michelson’s interferometer with step-moving mirror device. The optical path difference (OPD) equation of MSASII-LCoS is derived, and the four compensation conditions (field, chromatics, thermal and achromaticity of thermal compensations) are discussed within the scope of wind measurement. The real parameters of LCoS and optical glasses are selected for numerical simulation and analysis. Three aurora lines (732.0, 630.0 and 557.7 nm) are considered, and their phase variations are 3.61, 2.02 and 0.15 fringes at the same incident angle of 3°, respectively. The rate of change of OPD with temperature is the magnitude of 10 −6 cm/K, and the corresponding phase variations are within 0.09 fringes. The accuracy of phase modulation can be 0.614×10 −2 rad when LCoS of 10-bits is used. The novel model MSASII-LCoS shows its advantage for atmospheric wind measurement in the aspects of the overall structure, anti-vibration, operational flexibility and detection accuracy.

A spectral interferometric method to measure thickness with large range

We present a spectral interferometric method to measure the thickness of an optical plate or a film with a single layer. The system is based on the Michelson interferometer configuration, and the spectral interference signal of a broadband light source is recorded by a spectrometer. The optical path difference (OPD) between two interfering beams can be obtained by Fourier transform from the spectral interferogram. Gaussian fitting is used to find the exact peak of fringe to enhance the precision of the measurements. When the sample is inserted into the sample beam, the film’s thickness can be calculated by comparing the change of OPD, provided that the sample group refractive index is known. Only a single measurement is needed to determine a film’s thickness after the initial OPD of the system is calibrated. As no moving parts are required, the system has good stability. In particular, a large range of thicknesses, from micrometers up to several millimeters, can be measured. Such a large range is valuable for optical measurements. For demonstration, we measured the thicknesses of preservative film, cover glass and carrier glass, which were 9.6 ± 0.55, 156.1 ± 0.75, 1008.44 ± 0.96 μm, respectively.

Optical diffractometry

Interference of light has numerous metrological applications because the optical path difference (OPD) can be varied at will between the interfering waves in the interferometers. We show how one can desirably change the optical path difference in diffraction. This leads to many novel and interesting metrological applications including high-precision measurements of displacement, phase change, refractive index profile, temperature gradient, diffusion coefficient, and coherence parameters, to name only a few. The subject fundamentally differs from interferometry in the sense that in the latter the measurement criterion is the change in intensity or fringe location, while in the former the criterion is the change in the visibility of fringes with an already known intensity profile. The visibility can vary from zero to one as the OPD changes by a half-wave. Therefore, measurements with the accuracy of a few nanometers are quite feasible. Also, the possibility of changing the OPD in diffraction allows us to use Fresnel diffraction in Fourier spectrometry, to enhance or suppress diffracted fields, and to build phase singularities that have many novel and useful applications.

SIM PlanetQuest white-light fringe modeling: picometer accuracy calibration and estimation algorithms

SIM PlanetQuest will perform narrow-angle astrometry with microarcsecond accuracy using starlight interferometry requiring tens of picometers accuracy in estimating the optical path difference change between observing two stars. One challenge is to accurately model the white-light fringes and calibrate the required model parameters. Previous studies have developed algorithms based on a CCD-pixel-level calibration scheme assuming slowly varying phase-dispersion functions. However, recent measurements from the SIM PlanetQuest Spectral Calibration Development Unit (SCDU) showed that wavefront aberrations caused the phase-dispersion functions to vary by tens of nanometers across the bandwidth of a CCD pixel, making the previous CCD-pixel-based calibration scheme inadequate. We present a white-light fringe model including the extra phase dispersions caused by the wavefront aberrations together with a calibration and estimation scheme using long-stroke fringe measurements to resolve the bandwidth of pixels. Using simulated data, we show that the total systematic errors in the calibration and estimation scheme are less than a picometer. With SCDU experimental data, we demonstrate that the end-to-end accuracy of the calibration and estimation algorithm is better than 20 pm, achieving the SIM PlanetQuest Engineering Milestone 4.

振動環境でも利用できる垂直走査型光干渉応用形状計測技術

Vertical-scanning shape-measurement interferometry using white light is widely used to measure 3D shape of objects having step-like shape. This interferometry however cannot be used under vibrating environment. Because, it is required to accurately repeat predefined-step movements over vertical measurement range. We developed new technology which can measure the changes of optical path difference (OPD) of an interference microscope with nanometer resolution. This uses a line camera and a FPGA device and can measure OPD changes with around 20-μs interval. We built this technology onto a vertical-scanning interferometer and estimated performance of the developed technology using some vibration conditions.

Time-resolved vibration measurement with temporal speckle pattern interferometry

Temporal speckle pattern interferometry (TSPI) is an optical measurement procedurefor measuring the displacement of rough technical surfaces. The time-dependent speckle modulation due to optical path difference changes is tracked during the whole displacement of the surface and then evaluated pointwise without referring to neighboring pixels. This feature allows for its use as independent point sensors. This aspect of incremental phase tracking enables TSPI to be used to measure time-resolved mechanical vibrations. It also reduces the deteriorating effect of the decorrelation. Therefore large displacements can be measured. A concept for an inexpensive fiber-optical point sensor was developed and the theoretical accuracy for vibration measurement was investigated. The TSPI measurement of a loudspeaker membrane is compared with a high-precision vibrometer measurement. The first results show good agreement.

High-stability white-light interferometry with reference signal for real-time correction of scanning errors

White-light interferometry (WLI) for object topography measurements relies on an accurate rate of change of the optical path difference (OPD) between the object and reference beams. However, the motion of the scanner realizing the OPD change is not perfect, and scanning errors directly impact measurement accuracy. We describe a white-light interferometer that is capable of accounting for these errors and correcting them in real time through the monitoring of the scanner motion. This monitoring is achieved by embedding an additional high-coherence interferometer into the system. Besides allowing for monitoring the scanning progress, this system also provides the means to automatically calibrate the WLI. Significant improvements both in the accuracy and repeatability are demonstrated experimentally. Data analysis is discussed as well.

High-precision shape measurement by white-light interferometry with real-time scanner error correction.

White-light interferometric techniques allow high-precision shape measurement of objects with discontinuous structures by detecting the peak of the coherence envelope. These techniques assume a specific change in the optical path difference (OPD) between the interfering beams; however, the scanning device effecting that change often introduces OPD errors that are carried over to the measurements. We present a technique for measuring OPD changes from the collected interference fringes during each measurement. Information about the scan is directly fed into the algorithm, which compensates for the errors, resulting in improved measurement accuracy. The method corrects not only the scanner errors but also slowly varying vibrations. In addition, this technique can be easily adapted to any existing low-coherence interferometer because no large data storage or postprocessing is required.

Birefringence in gradient-index rod lenses: a direct measurement method and interferometric polarization effects

Gradient-index (GRIN) media can contain stress birefringence resulting from the variation in material composition. Anisotropy in a GRIN rod lens affects ray propagation and can degrade image quality. A technique, believed to be new, for measuring birefringence in GRIN rod lenses has been developed. The change in optical path difference (OPD) for orthogonal polarizations is measured directly. With this method, effects on OPD from standard imaging aberrations are excluded. Birefringence measurements for various GRIN rod samples are presented. The data are compared with results obtained previously by use of a Twyman-Green measurement method. Also, the polarization effects on tilt fringes observed with the direct measurement method and the Twyman-Green method are presented and modeled theoretically. Tilt fringes for large birefringence test cases are also modeled.

Anaylsis of Birefringence during Wound Healing and Remodeling following Alkali Burns in Rabbit Cornea

The use of synthetic inhibitors of metalloproteinases (SIMP) or medroxyprogesterone (MP) can prevent or significantly delay the ulceration of alkali-injured corneas by influencing collagen degradation. We have examined the remodeling of rabbit corneal stroma following alkali injury and have assessed the effect of SIMP and MP treatment. Following a defined alkali injury to the rabbit cornea, animals were divided into three subgroups, one group treated with topical β-mercaptomethyl tripeptide (SIMP), one treated by subconjunctival injection of MP and one treated with a control solution. The corneal tissue was taken at 3 days, 1, 2, 3, 4, 9 and 26 weeks after alkali injury and prepared for light microscopy and transmission electron microscopy (TEM). A quantitative measurement of birefringence, in terms of the optical path difference (OPD), was made using a modified polarized microscopy technique based on the analysis of interference colours. The results showed that SIMP effectively prevented deep corneal ulceration. MP could delay the ulceration and the corneas treated with MP appeared to have better transparency than the other groups. There was a significant difference of the OPD between the anterior (5.8±0.3nm) and posterior (7.8±0.4nm) stroma of the normal cornea (P<0.001). The OPD values from the central corneas from alkali-injured eyes were generally lower than normal during the first 4 weeks and then gradually recovered to the normal level or above, except for the posterior stroma of the MP-treated eyes. We found that the OPD changes were very dependent on the presence of corneal lesions. The stroma near corneal ulceration, scar tissue, calcified stroma and the retro-corneal collagen layer showed a significant reduction of birefringence (lower OPD values). These OPD values remained much lower than normal up to the end of the experiment. TEM showed disrupted corneal stroma in all three groups, with thinner scar tissue in the MP group. The fibril diameters did not change significantly 3 days and 1 week after the alkali burns (27.1±2.3nm in the control group, 27.3±2.2nm in the SIMP group and 27.7±2.1nm in the MP group) and there were no differences compared with 29.7±1.7nm of the normal cornea (P>0.05). After 2 weeks of tissue remodeling, the fibril diameters in alkali-injured corneas showed a large variation (the range was between 11.5 and 80nm) with a bimodal distribution, especially in the control group. The technique presented here for birefringence evaluation can provide an alternative way to monitor wound healing and tissue remodeling, both visually and quantitatively.

Interferometric straightness measurement system using triangular prisms

A new interferometric system for measuring straightness is developed. In the system, triangular prisms are used to generate two converging beams. A straightness reflector is used to reflect back the converging beams along their respective paths to form a combined beam. The combined beam is received by a detector system to count the interference fringes. Being different from the traditional straightness re- flector, the new straightness reflector consists of not only reflecting sur- faces but also refractive surfaces. The refractive surfaces cause a change in optical path difference (OPD) when a relative lateral displace- ment between the triangular prisms and the straightness reflector takes place. The relationship between the OPD and the lateral displacement is derived. The expected results agree with the results in the experiments. A straightness measurement with an accuracy of 0.1 mm is obtained over a travel range of 120 mm. © 1998 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(98)00706-5)

Optical Soppler imaging with field-widened Michelson interferometers

In a field widened interferometer, the optical path difference changes by less than one wavelength over a field of view of ten degrees or more, making it particularly suitable for imaging. The Wide Angle Michelson Interferometer (WAMI) is a conceptually simple device, constructed for a single path difference, that generates a cosinusoidal output whose phase yields the Doppler velocity, and whose modulation depth gives the temperature. In practice, such a field widened configuration involves refractive material, but by careful selection the assembly can be compensated for thermal and wavelength variations of the glass constants. In this mode the WAMI provides an extremely efficient way of extracting Doppler information from a simple known spectrum, such as an isolated Gaussian line, or even a doublet. However, when additional spectral information is required, it is necessary to combine the WAMI with a low resolution Fabry-Perot etalon. Two spaceflight imaging WAMIs now under construction are described; the space shuttle WAMDII, and WINDII, which will fly on the Upper Atmosphere Research Satellite.

Flow-measurements of the viscosity coefficients of two nematic liquid crystalline azoxybenzenes

To determine the Miesowicz viscosity coefficients a shear-flow set-up has been built, which allows the measurement of η1, η2, η3 and η12. These coefficients are determined by pressing the liquid crystal through a rectangular capillary which forms part of a thermostated set-up placed between the poles of a magnet in order to control the director n. In addition, the flow-alignment angle θ 0 is determined from the change in optical path difference between the ordinary and extraordinary components of polarized light, comparing the situation with n aligned along the flow-direction and with flow-alignment, respectively. Results are given for the complete set of viscosity coefficients of p-methoxy-p'-butylazoxybenzene and p, p'-dibutylazoxybenzene. The results show good agreement with visco-elastic ratios found with light-scattering techniques. Within the experimental accuracy the Onsager-Parodi relation is well fulfilled.

Changes in optical path difference in the oesophageal region and the excretory cells during exsheathment in Haemonchus contortus

Davey K. G. and Sommerville R. I. 1982. Changes in optical path difference in the oesophageal region and the excretory cells during exsheathment in Haemonchus contortus. International Journal for Parasitology 12: 503–507. Changes in the optical path difference (opd) between various parts of the worm and the medium in which the worms were immersed were determined by quantitative interference microscopy. The opd of the oesophagus and the excretory cells both increased upon stimulation of the worms with CO 2 at 38.5°C, suggesting a decrease in volume of those structures. The oesophagus decreased markedly in length and slightly in diameter, yielding a decrease in volume of approximately 15 to 17 pl. Desheathing the worms with NaOCl produced changes in the oesophagus but not the excretory cells. This confirms previous findings that exsheathment involves at least two parallel processes, both of which are initiated by CO 2 and only one of which is stimulated by exposure to NaOCl.

Interference method of measuring transparent dielectric film thickness

The change in optical path difference caused by rotation of a plate with respect to incident light flux is examined in [4]. The thickness of a transparent dielectric film is dedetermined by estimating the shift in the interference pattern that is due to the change in optical path difference during rotation of the film placed on one of the arms of a two-beam interferometer, perpendicularly to the light flux: h = A/{2ne[(n 2-sin = i) I/2 -cos i -n + i]}, where h is the film thickness, A is the shift in the interference pattern, A = m%/2 (l is the wavelength, m is the number of interference fringes), n and n e are, respectively, the indices of refraction of the film and the environment, and i is the angle of film rotation.

Some applications of interference microscopy in enzyme cytochemistry: With particular reference to alkaline phosphatase

The interference microscope can be applied to the quantitative cytochemical study of enzymes provided that some change in optical path difference is produced as a result of enzyme action. Microscopical interferometry has been applied to the study of alkaline phosphatase in various tissues, especially in the brush borders of renal tubules and intestinal epithelium. It has been possible to study the effects of hydrogen-ion and substrate concentrations, buffers, activators, and inhibitors. The properties of the enzyme in tissue sections are similar to those of the enzyme in homogenates and purified preparations.