Autocollimation Method Research Articles

Further investigations of stitching model for annular subaperture interferometric testing based on Zernike annular polynomials

The subaperture stitching algorithm as a key step of annular subaperture interferometric testing (ASIT) is used to sew all subaperture data together to get the full aperture information. The core part of stitching algorithm is that using the stitching model to eliminate the relative misalignment errors between the adjacent subapertures to realize the stitching treatment. Obviously, the stitching accuracy is mainly determined by the performance of the stitching model. Different stitching model for existing annular stitching algorithms are briefly discussed in this paper. Based on Zernike annular polynomials (ZAP), a more accurate and stabile stitching model for ASIT is proposed. By combining standard deviation and correlation coefficient of overlapping area, we can comprehensively evaluate the stitching performance. In addition, the fitting performance of the ZAP is evaluated in some pertinent cases: different obscuration ratios and noises. By comparing the results of proposed method with that of the classical auto-collimation method, it demonstrates that the accuracy and practicability of the proposed stitching model.

Annular subaperture stitching method based on autocollimation

In this paper, we propose an annular subaperture stitching method based on an autocollimation method to relax the requirements on mechanical location accuracy. In this approach, we move a ball instead of the interferometer and the aspheric surface so that testing results for adjacent annular subapertures are registered. Thus, the stitching algorithm can easily stitch the subaperture testing results together when large mechanical location errors exist. To verify this new method, we perform a simulation experiment. The simulation results demonstrate that this method can stitch together the subaperture testing results under large mechanical location errors.

High-accuracy device for measuring the twist angle

This paper describes a high-accuracy optoelectronic device for measuring the twist angle, based on an autocollimation method and using a reflector in the form of a unit of right-angle prisms. The device makes it possible to measure the relative twist angle of objects in the range ±2.5° when there is a distance of 2.5–3.5 m between the reflector and the optoelectronic unit of the device. The rms deviation of the measured angle from the true value in this case does not exceed 2′′ in the range ±2.5°, and it does not exceed 1′′ in the range ±10′. A specially shaped mark is used in the device that makes it possible to measure the auxiliary angle between the direction of the edge of the prism reflector and a plane perpendicular to the optical axis of the device. The installation can be used to transfer the azimuthal direction vector.

Refractive indices in the whole transmission range of partially deuterated KDP crystals

Refractive indices of partially deuterated potassium dihydrogen phosphate (DKDP) crystals with 55%, 70% and 80% deuterium contents were measured by auto-collimation method at 293 K between 0.254 to 1.529 μm. Dependence of refractive indices of DKDP on deuterium content show different trend in the infrared region as in uv-visible region. Dependence of n2 (the square of refractive index) on the mole fraction of deuterium shows a difference between pure KDP and partially deuterated KDP. The Sellmeier equations were obtained by the least square method. The non-critical phase matching angles calculated from the fitted formula were in good agreement with laser experiment results, by which the reliability of these Sellmeier equations was confirmed.

Growth and optical properties of nonlinear LuAl_3(BO_3)_4 crystals

The optical properties of pure LuAl(3)(BO(3))(4) (abbreviated as LuAB) crystals were investigated for the first time. Large UV-transparent LuAl(3)(BO(3))(4) crystals were grown by a high-temperature top-seeding method with Li(2)WO(4)O(7)-B(2)O(3) as the flux. The refractive indices of LuAl(3)(BO(3))(4) at several wavelengths covering ultraviolet-visible and near-infrared regions were measured by the auto-collimation method. The parameters of Sellmeier's dispersion equation were determined from the experimental data. The phase-matching curve of second harmonic generation was measured. The nonlinear optical coefficient d(11) of LuAB crystal was determined to be 1.10 pm/V by a phase-matching method. The UV cut-off wavelength of the LuAl(3)(BO(3))(4) crystal was shorter than 190 nm.

Littrow angle based autocollimation method for precision online monitoring three-dimensional angular drifts of chirped-pulse compression-gratings

A simple optical method for online precisely monitoring three-dimensional (3D) angular drifts of chirped-pulse compression-gratings in chirped-pulse amplification (CPA) lasers is proposed. Monitoring objects include all dimensional angular drifts of a grating, especially the grating groove in-plane-rotation. Monitoring contents contain direction and amount. And monitoring results are obtained by detecting the direction and the amount of 2D relative offsets of three focal spots formed by a ternary monitoring beam line. The theoretical model of the proposed method is set up using a matrix ray-tracing method, and a simplified monitoring equation is concluded based on numerical simulations. And the validity of this method is verified by a simple demonstration experiment. Besides, monitoring error and reliability discussion of the method are presented, as well.

Thermal refractive index coefficients of nonlinear optical crystal CsB_3O_5

The principal refractive indices of crystal CsB3O5 (CBO) at the wavelengths of 0.266, 0.355, 0.532, 0.473, 0.633, 1.064, and 1.338 μm are accurately measured by using the autocollimation method within the temperature range from 40°C to 190°C. We derive and report equations of thermal refractive index coefficients as a function of wavelength that could be used to calculate the principal thermal refractive indices at different wavelengths. Sellmeier equations at different temperatures were derived and used to calculate the phase-matching angles for the third-harmonic generation and the fourth-harmonic generation of CBO crystal at different temperatures.

Common-path design criteria for laser datum based measurement of small angle deviations and laser autocollimation method in compliance with the criteria with high accuracy and stability

Common-path design criteria for laser datum based measurement of small angle deviations are proposed to guide the implementation of common-path principle in dealing with laser beam drifts resulting from laser generation mechanism and instability of beam transmission medium. A laser autocollimation method is designed in compliance with the criteria, and can achieve an accuracy of 0.013 arcsec and a two-hour stability of 0.020 arcsec over a measurement distance of two meters. The criteria and the method proposed can be effectively used for laser datum based measurement of small angle deviations with high accuracy and stability, especially over a long measurement distance.

Gd xLa 1− xSc 3(BO 3) 4: A new nonlinear optical crystal

A new nonlinear optical material Gd x La 1− x Sc 3(BO 3) 4 (GLSB) has been synthesized in the trigonal huntite-type structure. The composition parameter x, which defines the existence region of the trigonal huntite-type structure, was determined. Large single crystals were successfully grown by a high-temperature top-seeded solution growth method using Li 6B 4O 9–LiF as a flux. Evidenced by single-crystal X-ray diffraction measurements, the member Gd 0.22La 0.78Sc 3(BO 3) 4 crystallized in space group R32 with cell dimensions a=9.7933 and c=7.9540 Å. The UV absorption edge for polished pieces exhibited at a wavelength shorter than 200 nm. Sellmeier equations were established on the basis of the refractive indices measured by the auto-collimation method. The nonlinear optical coefficient d 11 was determined to be 2.08 pm/V by the modeling and optical measurements of powders.

Growth and optical properties of UV transparent YAB crystals

Large and ultraviolet (UV) transparent YAl3(BO3)4 (YAB) crystals were grown by a high temperature top seeding method with Li2B4O7–AlBO3 as the flux. The UV cutoff wavelength of the YAB crystal was shorter than 190 nm. The refractive indices of the YAB at several wavelengths covering UV–visible and near infrared wavelength over the temperature range from 30 to 170°C were measured by the autocollimation method. The parameters of the Sellmeier dispersion equation were determined based on the experimental data. The phase matching curve of second harmonic generation was measured. The deviations of the phase matching angle for second harmonic generation at 473 nm as a function of temperature for the YAB crystals were investigated. The coefficient of frequency doubling d11 of the YAB crystal was measured to be 1·30 pm V−1 by a phase matching method.

Investigation of an optical sensor for small tilt angle detection of a precision linear stage

This paper presents evaluation results of the characteristics of the angle sensor based on the laser autocollimation method for small tilt angle detection of a precision linear stage. The sensor consists of a laser diode (LD) as the light source, and a quadrant photodiode (QPD) as the position-sensing detector. A small plane mirror is mounted on the moving table of the stage as a target mirror for the sensor. This optical system has advantages of high sensitivity, fast response speed and the ability for two-axis angle detection. On the other hand, the sensitivity of the sensor is determined by the size of the optical spot focused on the QPD, which is a function of the diameter of the laser beam projected onto the target mirror. Because the diameter is influenced by the divergence of the laser beam, this paper focuses on the relationship between the sensor sensitivity and the moving position of the target mirror (sensor working distance) over the moving stroke of the stage. The main error components that influence the sensor sensitivity are discussed and the optimal conditions of the optical system of the sensor are analyzed. The experimental result about evaluation of the effective working distance is also presented.

The accurate refractive indices of BIBO crystal at different temperatures

The principal refractive indices of BiB3O6 (BIBO) crystal at different wavelengths in the temperature range from 30 to 170 °C were measured by the autocollimation method. The Sellmeier equations at different temperatures have been obtained. In order to check their reliability, the refractive indices at 0.532 µm and 1.319 µm at different temperatures are calculated by the Sellmeier equations and compared with the measured values. As a result, the difference between the calculated results and the measured results is less than 2 × 10−4. The calculated type I second harmonic generation angle of BIBO at 1.0640 µm is consistent with the measured result.

High-accuracy device for the spatial orientation of objects

This paper describes the design of an optoelectronic device for high-accuracy transfer of the direction of a vector from one plane to another, based on the autocollimation method, using a reflector in the form of a prism unit. The device makes it possible to determine the relative rotation angle of objects within the limits ±1.5° to within 5″. When the device is used as a vertical channel of direction transfer, the limiting error of azimuth transfer is no more than 7″ when the distance between the objects is 2.5–3.5 m.

Detection of three-axis angles by an optical sensor

This article describes an optical method for measurement of three-axis angles (roll angle Δ θ X , pitch angle Δ θ Y , yaw angle Δ θ Z ). The laser autocollimation method is improved from two-axis angle measurement to three-axis angle measurement by employing a diffraction grating instead of a plane mirror as the target reflector. The three-axis angle components can be calculated by three methods of using different diffraction light spots reflected from the diffraction grating. Method 1 uses three beams, which are the 0th-order and the ±1st-order diffraction light spots. Both Method 2 and Method 3 use two light spots. The former uses the ±1st-order diffraction light spots and the latter combines the 0th-order with the +1st-order or the −1st-order diffraction light spots. A prototype three-axis angle sensor is also designed and fabricated to compare the characteristics of the three methods from the viewpoints of sensitivity, linearity and resolution of the sensor output.

Accurate measurement of refractive indices of Ca 9La(VO 4) 7 crystal

The principal refractive indices of Ca 9La(VO 4) 7 crystal for wavelengths of 0.488, 0.6328, 1.064 and 1.338 μm under the temperature range from 30 °C to 170 °C were measured by auto-collimation method. The Sellmeir-equations of Ca 9La(VO 4) 7 crystal at different temperatures have been obtained based on the experimental data, and the refractive indices of some wavelengths in different temperatures are calculated by the Sellmeir-equations and compared with the corresponding measured values in order to check their reliability. As a result, the difference between the calculated results and the measured results is not more than 1 × 10 −4. The theoretical PM (phase matching) angles of SHG (second harmonic generation) built on the experimental refractive indices are also given.

Theoretical Study on Self-Calibration for the Wide-Range Laser Auto-Collimation Method

A wide-range laser auto-collimation method to measure the surface profiles of targets with steep slopes has been proposed. This method employs a deflecting optical system to enlarge the measurement range of the angle sensor. However, this optical system also changes the sensitivity property of the angle sensor. Therefore, we propose a new in-situ self-calibration method that includes the geometrical designed data of the target and can be applied to wide-range laser auto-collimation method. In the proposed method, the calibration sensitivities at each measurement point are obtained with two sets of measured data, which are acquired before and after performing minute rotation or translation with respect to the measured target, and the simulated shift of the normal angle at each point. The present paper describes the calibration procedure and specific calculation method used in the proposed method.

A cancellation technique for the validation of the reference profile of an interferometer

There are a number of methods by which to measure the surface flatness profile using an interferometer. These methods involve obtaining a fringe image that displays the surface profile by the interference between a reflected beam from the measured surface and a reflected beam from a reference surface. Since the reference functions as a datum, the accuracy of the measured results depends on the accuracy of the reference. The authors previously proposed a differential laser auto-collimation method with zero-point compensation for canceling the parabolic error caused by the systematic error of the measurement system. The extension of the differential laser auto-collimation with zero-point compensation is a cancellation technique for the validation of the reference for the interferometer. This measurement method consists of two steps. First, the measured surface is not irradiated by the laser beam, and the systematic error is obtained. Next, the measured surface is irradiated, and the surface profile that includes the systematic error is obtained. Finally, the surface profile is estimated using the difference between these two steps. In this article, the principle and the experimental results are shown.

Growth and optical properties of bulk KTP crystals by hydrothermal method

The high-quality bulk potassium titanyl phosphate (KTiOPO4 or KTP) crystals have been grown successfully by the hydrothermal method using an improved mixed solution of K2HPO4 (2.0 mol/l), KH2PO4 (0.1 mol/l) and H2O2 (1 wt%) as mineralizer, and spontaneous flux KTP crystals as nutrients. The growing rate of KTP crystals along (0 1 1) was 0.15 mm/day. The size of the biggest grown crystal was up to 26×83×25 mm3, 132 g in weight. The transmittance was over 80% in the range of 450–2500 nm. The optical homogeneity was up to 4.15×10−6 cm−1. The precise principal refractive indices were measured by the auto-collimation method and compared with those of KTP grown by the flux method. The Sellmeir equations were fitted with the experimental data. The test of bulk absorption at strong CW green radiation 532 nm was performed with the photo-thermal common-path interferometer. The results showed that the hydrothermal KTP crystals have great ability to anti-gray track.

Growth, refractive index and spectroscopic characteristic of Yb 3+:Ca 2La 2/3(VO 4) 2 crystal

An Yb 3+:Ca 2La 2/3(VO 4) 2 crystal with dimensions of Ø18×30 mm 3 has been grown by the Czochralski method. The principal refractive indices of the Yb 3+:Ca 2La 2/3(VO 4) 2 crystal have been measured by the auto-collimation method. The experimentally obtained room temperature values of the refractive indices are: n o=1.8546, n e=1.8322 at the 1.064 μm wavelength. The specific heat of the Yb 3+:Ca 2La 2/3(VO 4) 2 crystals is 0.053 J/g K at 308 K. The hardness of the Yb 3+:Ca 2La 2/3(VO 4) 2 crystal is 946.1 VDH. Spectroscopic characterization of the Yb 3+:Ca 2La 2/3(VO 4) 2 crystal has been performed as well. The polarized absorption cross-sections are 2.05×10 −20 cm 2 for E∥ c and 2.47×10 −20 cm 2 for E⊥ c, respectively. The polarized emission cross-sections are 1.55×10 −20 cm 2 for E∥ c and 1.61×10 −20 cm 2 for E⊥ c, respectively. The Yb 3+:Ca 2La 2/3(VO 4) 2 crystal has a broad operating laser wavelength, which is useful for generating femtosecond pulses.

Experimental study on measurement of aspheric surface shape with complementary annular subaperture interferometric method

Based on our previously reported annular subaperture reconstruction algorithm with Zernike annular polynomials and matrix method, we provide an experimental demonstration by testing a parabolic mirror with the complementary annular subaperture interferometric method. By comparing the results of annular subaperture method with that of the classical auto-collimation method, it is shown that the reconstruction results are in good agreement with the auto-collimation measurement. In addition, we discuss some limitations of characterizing annular subaperture measurement data with finite Zernike coefficients in our algorithm, and also show the possibility of characterizing higher spatial frequency information with adequate Zernike coefficients. It is believable that the reported method can be extended to test the surface shape of some large concave aspheric mirrors with acceptable accuracy.