Optical axis determination method

Due to many experimental data required and a lot of calculations involved, it is very complex and cumbersome to model prism-based liquid-refractive-index-measuring methods. By use of the feature of TE-polarized wave and TM-polarized wave and differential measurement principle, we developed a new method of mathematical modeling for measuring refractive index of a liquid based upon Fresnel formula and prism internal reflection at incident angle less than critical angle. With this method only two different concentrations measurements for a kind of solution can lead to the determination of computational model. It introduces the principle of an optic-fiber sensor system based on prism-coupler for measuring refractive index of a liquid, and it contains the configuration picture of the sensing optical path, the spectrogram of the semiconductor laser and the structure block diagram of measuring system, the system is mainly made up of the semiconductor laser with 1654.14nm in wavelength, 1×2 optical switch, Y-shaped photo-coupler with coupled rate 50:50, the detector based on isosceles prism-coupler, the data process and control system based on AT89C51 and photoelectric transformer. For TM-polarized wave and TE-polarized wave, theoretical simulations show that the ratio of sensitivity is 1.11, therefore, the beam that the component of TM-polarized wave is more than the one of TE-polarized wave is advantageous to heightening the systemۥs measurement sensitivity. Measurements are performed to examine the validity of the theoretical model and four theoretical models are given, and these results indicate the feasibility of four theoretical models with an error of 3%. In this study, a beam of light is broken down into two beams in the coupler of Y-shaped coupler, the one acts as the reference optical path, the other is known as the sensing optical path, consequently the method can limit well the fluctuation of the light source, the variation of the photodiodeۥ s dark-current of photodiode and many other interfering factors and can be used for real-time detection and online analysis of liquid refractive-index. The method is also capable of measuring even smaller changes in the optical refractive index of the material on a metal surface by the surface plasma resonance sensing techniques.

If a monochromatic linearly polarized plane wave is incident on an isotropic-uniaxial or isotropic-biaxial interface and if the incidence plane coincides with a crystal principal plane then circularly polarized light can be obtained by means of a single reflection. This result can be achieved using materials of refractive indices which are not as high as those required in isotropic devices. As is well known, in isotropic-anisotropic interfaces, there are two different incidence angles that yield circularly polarized reflected light. These angles depend on characteristics of both media (refractive indices and angle between the optical axis and the interface) and also on wavelength. In this paper a single reflection retarder is designed. Additionally, its efficiency as quarter wave retarder for non collimated or polychromatic beams is analyzed studying how the amplitudes and phases of both orthogonal components of the reflected electric field vary when the incidence angle and/or the wavelength varies.

The digital micromirror device (DMD) which is one kind of Micro-Electro-Mechanical System has been widely adapted for use in lighting projection systems, and some new imaging systems such as high-dynamic range imaging, aperture-coded spectral imaging, or medical imaging. The micromirrors on the DMD surface are non-continuous distribution and capable of tilt relative to individual rotation axis, which is different from the plane mirror. Therefore, when the DMD is applied in a convergence imaging path, there is an optical path difference (OPD) between the off-axis chief ray and the on-axis chief ray, and moreover severe non-symmetric imaging on the focal plane. Based on the geometrical optics and aberration theory, this paper proposes a calculation formula that gives the OPD as a function of the image height, the incident angle, the DMD pixel size and the DMD tilt angle in the convergent imaging path. This formula can give the OPD of the system when the optical axis is vertical to the surface of the DMD in an ideal state, which has great significance to the design and adjustment of optical path using DMD devices.

To explore the effect of optical media on digital image correlation measurement, the experiments of digital image correlation measurement under different optical media conditions were carried out. By analyzing the speckle images non-special optical path medium, common ordinary glass medium and quartz glass medium in the optical path, the effect of medium change in the optical path on digital image correlation measurement is discussed. The results show that the effect of different optical media on the accuracy of digital image correlation measurement is different, and the effect of optical media on absolute displacement measurement is much greater than that of rigid body displacement measurement. The effect of optical medium on different measuring areas is also different. The effect of quartz glass state on strain measurement is greater than that of ordinary glass. The effect of optical medium on the measurement of vertical optical axis displacement is much less than that of optical axis displacement measurement. Whether ordinary glass or quartz glass is added, the measurement error of camera optical axis direction is much larger than that of vertical optical axis direction; the stability of DIC displacement measurement in different optical path media is in turn ordinary glass medium, quartz glass medium and non-special optical path medium.

A dielectric lens antenna becomes a promising candidate for 5G mobile system in the range of millimeter wave frequency band because of the simplicity of the structure and ease of installation. Special radiation pattern such as low sidelobe, high gain and multibeam are expected to achieve many radiation patterns. This paper describes the verification of lens shaping based on refraction angles at lens surfaces. The lens surface shaping program was developed using a MATLAB software. The ratio of sinusoidal function of incident angle and the refracted angle should be equal to the refractive index. The angular relations are checked for various sample points. At points where lens curvature is sufficient, angle relations agree very well with the refractive index. At point where lens surface becomes flat, incident and refracted angles become small thus rendering the agreement of angle relation and refractive index insufficient. As a whole, surface designing accuracy is verified by comparing the refraction angles for both lens surfaces obtained from MATLAB simulation and angular calculation.

Brewster’s law in the light of the refined unambiguous angles of incidence, reflection, and refraction

Refinement of the theory of formation of rainbow with incorporation of the refined unambiguous angles of incidence, reflection, and refraction

Fringe test is the method which can detect the relative optical path difference in optical synthetic aperture telescope array. To get to the interference fringes, the two beams of light in the meeting point must be within the coherence length. Step scanning method is within its coherence length, selecting a specific step, changing one-way's optical path of both by changing position of micro displacement actuator. At the same time, every fringe pattern can be recorded. The process of fringe patterns is from appearing to clear to disappearing. Firstly, a particular pixel is selected. Then, we keep tract of the intensity of every picture in the same position. From the intensity change, the best position of relative optical path difference can be made sure. The best position of relative optical path difference is also the position of the clearest fringe. The wavelength of the infrared source is 1290nm and the bandwidth is 63.6nm. In this experiment, the coherence length of infrared source is detected by cube reflection experiment. The coherence length is 30μm by data collection and data processing, and that result of 30μm is less different from the 26μm of theoretical calculated. In order to further test the relative optical path of optical synthetic aperture using step scanning method, the infrared source is placed into optical route of optical synthesis aperture telescope double aperture. The precision position of actuator can be obtained when the fringe is the clearest. By the experiment, we found that the actuating step affects the degree of precision of equivalent optical path. The smaller step size, the more accurate position. But the smaller the step length, means that more steps within the coherence length measurement and the longer time.

On the law of the partial polarization of light by reflexion

In geometrical optics, light is described by rays that propagate according to three laws: rectilinear propagation, refraction, and reflection. Their direction of propagation indicates the direction of the flow of light energy. They are normal to a wavefront. They are not a physical entity in the sense that we cannot isolate a ray, yet they are very convenient for describing the process of imaging by a system. We begin this chapter with a brief introduction of the Cartesian sign convention for the distances and heights of the object and image points, and the angles of incidence and refraction or reflection and slope angles of the rays. We discuss Fermat’s principle that the optical path length of a ray from one point to another is stationary, and derive the laws of rectilinear propagation in a homogeneous medium, refraction by a refracting surface, and reflection by a reflecting surface (first in 2D and then in 3D). These laws are used to obtain ray-tracing equations representing the propagation of a ray exactly from a certain point to a point on a refracting or a reflecting surface, or refraction or reflection of the ray by the surface, and propagation of the refracted or reflected ray to the next surface. The purpose of exact ray tracing is to determine the aberrations of a system consisting of a series of refracting and/or reflecting surfaces that generally have a common axis of rotational symmetry called the optical axis. Such a system is called a centered or a rotationally symmetric system. Its surfaces bend light rays from an object according to the three laws to form its image.

Straightness measurement is a very important technique in the field of Mechanical Engineering. A particular applicationwould be very high accuracy machining on a diamond turning lathe. In this paper a novel optical method for measuringstraightness of motion using reflection confocal optics is proposed. The advantage of this method in comparison with thetransmission optical systems used by Burch and Williams' is that the lateral displacements in the direction of the two axesperpendicular to the optical axis, and the rotation angles around all three axes, can be measured simultaneously. This can bevery useful for straightness measurement. Also, reflection optical systems are more compact in length.Keywords: straightness measurement, optical alignment, reflection confocal optical system, straightness measurement ofmotion, geometrical optics SUMMARY When a table moves along a guide way, lateral displacement occurs which often needs to be measured. There have beenseveral proposals to measure this displacement using optical, rather than mechanical methods. Optical methods are classifedaccording to the optical principle used: interference, Moire gratings, or geometrical optics. The optical methods offer theadvantages of being non-contacting and able to measure lateral displacements accurately over a long distance.Burch and Williams' (1974) developed a geometrical optical system using a transmission confocal design. Using theirmethod, lateral displacements in the direction of the two axes perpendicular to the optical axis can be measured, along withrotation angles around those axes. The method described here is based on reflection confocal systems. The advantage of thismethod is that lateral displacements in the direction of the two axes to the optical axis can be measured, along with rotationangles around all three axes. Also shorter length optical systems may be measured using a reflection optical system. Theaccuracy of the lateral displacement measurement is several micrometres for movements of the order of a metre. In thefuture we plan to improve the accuracy to better than one hundred nanometres using a position displacement magnifyingdevice that is being developed by our group.The figure shows top and side views of a table MT which moves along a guide way GW and an optical arrangement formeasuring its motion using a reflection confocal optical system. The light beam from a He-Ne laser HL is divided intotwo beams by a beam splitter BS and a mirror M .

Deviation problems in ray optics in the light of the refined unambiguous definitions of angles of incidence, reflection and refraction

This paper researches the calculation method of space target optical characteristics to improve performance and sensitivity of the photoelectric detection target. In accordance with the detection principle of the photoelectric detection target and the detection screen thickness geometrical relationship, this paper sets up the space target spectral characteristic model using the surface element mesh analysis method and the bidirectional reflection distribution function. It provides the incident radiation energy calculation function in the optical lens entrance pupil of the photoelectric detection target detection area in order to determine the total spectral radiance intensity calculation function of the space target. The paper also reports on the minimum flux calculation function detected by the photoelectric detection target based on the definition of detection sensitivity and the change curve of the target's radiation energy when entering the detection area at different incident angles. Lastly, it demonstrates the spectral illuminations of an optical detection system under different radiation wavelengths and reflection radiation angles, as well as change curves of the target's spectral radiation intensity passing through the detection screen area and at different incident angles from the same distance.

Using ray tracing and optical path iteration, this section present a mathematical model for light transmission, absorption, and loss in fiber-based organic photovoltaics (Reprinted with permission from [1], Copyright 2009, American Institute of Physics). Simulations based on this model give an optimum incident angle, position and an optimum aspect ratio in terms of other parameters of the fiber photocell. Further, the predicted relationship between current generation and incident angle correlates well with experimental data for a given fiber length. Finally, we show that experimental results on current generation versus fiber diameter are well reproduced by our simulation for fiber diameters of the order of the wavelength of incident light.

It is well known that components with dissimilar compatibility factors cannot be combined by segmentation into an efficient thermoelectric generator, since each component needs a unique optimal current density. Based on the complex variable method, the thermal-electric field within a bi-layered thermoelectric composite has been analyzed, and the field distributions have been obtained in closed-form. Our analysis shows that current refraction occurs at the interface, both the refraction angle and current density vary with the incidence angle. Further analysis proves that the current densities in two components can be adjusted independently by adjusting the incidence current density and incidence angle, thus the optimal current density can be matched in both components, and the conversion efficiency can be significantly increased. These results point to a new route for high efficiency thermoelectric composites.