Point Diffraction Interferometer Research Articles

基于Levenbery-Marquardt算法的点衍射三维坐标测量方法

基于Levenbery-Marquardt算法的点衍射三维坐标测量方法

Radius of curvature measurement based on wavefront difference method by the point diffraction interferometer

A method for measuring the radius of curvature with a pinhole point diffraction interferometer (PDI) is proposed. Using the wavefront difference method and the Gaussian imaging equation, the longitudinal displacement of the converging rays passing through a standard plane-parallel-plate sample in PDI interference cavity is determined. Based on this longitudinal displacement, a precise formula for radius of curvature calculation is deduced. An experimental system for radius of curvature measurements is set up to verify the principle. With this testing system, the radius of curvature of spherical mirrors and the surface figure can be measured in a higher precision simultaneously. Some sources of uncertainty in measurement are discussed based on detailed error analysis. The experimental results indicate that the measurement accuracy ΔR/R0 is in the order of 10−4.

Analysis of diffraction wavefront in visible-light point-diffraction interferometer

As a key element in point-diffraction interferometer (PDI), the diffraction pinhole determines the sphericity of the reference wavefront and achievable precision of the testing system. The point-diffraction wavefront error, aperture angle, and light transmittance in the PDI operating at visible light, which are determined by pinhole dimension, are analyzed based on finite difference time domain (FDTD) method. The study shows that an aperture angle about 75° can be obtained with a 1 μm pinhole diameter, and the corresponding testing precision is better than root mean square λ/1000 within 0.35 NA. Both the numerical simulation and experiments have been carried out to demonstrate the feasibility of the proposed analysis approach, and a good agreement is obtained between calculated and measured parameters in visible-light PDI. The proposed simulation approach with the FDTD method provides a feasible way to analyze the diffraction wavefront in visible-light PDI, as well as a powerful tool for the design and optimization of PDI system.

Synthetic phase-shifting for optical testing: Point-diffraction interferometry without null optics or phase shifters

An innovative iterative search method called the synthetic phase-shifting (SPS) algorithm is proposed. This search algorithm is used for maximum-likelihood (ML) estimation of a wavefront that is described by a finite set of Zernike Fringe polynomials. In this paper, we estimate the coefficient, or parameter, values of the wavefront using a single interferogram obtained from a point-diffraction interferometer (PDI). In order to find the estimates, we first calculate the squared-difference between the measured and simulated interferograms. Under certain assumptions, this squared-difference image can be treated as an interferogram showing the phase difference between the true wavefront deviation and simulated wavefront deviation. The wavefront deviation is the difference between the reference and the test wavefronts. We calculate the phase difference using a traditional phase-shifting technique without physical phase-shifters. We present a detailed forward model for the PDI interferogram, including the effect of the finite size of a detector pixel. The algorithm was validated with computational studies and its performance and constraints are discussed. A prototype PDI was built and the algorithm was also experimentally validated. A large wavefront deviation was successfully estimated without using null optics or physical phase-shifters. The experimental result shows that the proposed algorithm has great potential to provide an accurate tool for non-null testing.

Measuring of temperatures of a candle flame using four multidirectional point-diffraction interferometers

An optical system formed by four point-diffraction interferometers is used for measuring the temperature distribution of a candle flame. It is assumed that the phase can be expressed in terms of the Radon transform, and it is processed with a tomographic iterative algorithm to obtain the temperatures. The interferograms show the asymmetry of the candle flame, justifying the use of a tomographic iterative algorithm instead of the Abel inversion. The resulting temperature distribution verifies the usefulness of the proposed method.

Modified polarization point diffraction interferometer with extended measurable NA for spherical surface testing

The small pinhole of point diffraction interferometer based on pinhole-point diffraction places ultra-high requirement on both the adjustment of testing system and performance of CCD camera. Besides, poor fringe contrast due to the low reflectivity of test spherical surface would limit the measurement precision in the processing of fringe pattern. A modified polarization point diffraction interferometer with extended measurable numerical aperture (NA) is presented for testing the spherical surfaces with low reflectivity. Measurement error factors as well as the corresponding calibration procedure are introduced in detail. Comparing with the results of Zygo interferometer, measurement accuracy with root-mean-square (RMS) value about 0.0026λ and peak-to-valley (PV) 0.0134λ is achieved. The system has good measurement repeatability, and the standard deviation of measurement results RMS better than 0.0010λ is obtained. The proposed interferometer reduces the difficulty in the adjustment of the system and provides a feasible way for testing the surfaces with low reflectivity and high NA.

Wavefront local curvature evaluation by multiple point diffraction interferometry

The principal objective of this work is modify the classical point diffraction interferometer to measure simultaneously local curvatures of a wavefront at different points on a plane transversal o the direction of propagation of an aberrated beam. On the other hand we propose a new and easy method of calculus that will allow optimize the design of the fundamental component of the interferometer for a specific application.

Parallel on-axis phase-shifting holographic phase microscopy based on reflective point-diffraction interferometer with long-term stability

Parallel on-axis two-step phase-shifting reflective point-diffraction interferometry for holographic phase microscopy based on Michelson architecture is proposed. A cube beamsplitter splits the object wave into two copies within the two arms. The reference wave is rebuilt by low-pass filtering with a pinhole-masked mirror. Both object and reference waves are split into two beams by a grating in a 4f imaging system; thus, two interferograms with quadrature phase-shift can be acquired simultaneously with the aid of polarization elements. The approach has the merit of nanometers-scale phase stability over hours due to its quasi-common-path geometry. It can make full use of camera spatial bandwidth while its temporal resolution is as fast as the camera frame rate. Phase imaging on microscale specimen is implemented, and the experimental results demonstrate that the proposed approach is suitable for investigating dynamic processes.

Point diffraction interferometer with a liquid crystal monopixel

In this work a novel point diffraction interferometer based on a variable liquid crystal wave plate (LCWP) has been implemented. The LCWP consists of a 3x3 cm(2) monopixel cell with parallel alignment. The monopixel cell was manufactured such that the electrode covers the entire surface except in a centered circular area of 50 μm of diameter. This circle acts as a point perturbation which diffracts the incident wave front giving rise to a spherical reference wave. By applying a voltage to the LCWP we can change the phase of the wave front that passes through the monopixel, except at the center. Phase shifting techniques are used in order to calculate the amplitude and phase distribution of the object wave front. The system allows a digital hologram to be obtained, and by using the Fresnel diffraction integral it is possible to digitally reconstruct the different planes that constitute the three dimensional object.

Analysis of spatial resolution and pinhole size for single-shot point-diffraction interferometer using in closed-loop adaptive optics

A closed-loop adaptive optics system using a single-shot point-diffraction interferometer (PDI) and a liquid crystal spatial light modulator is presented. Only one CCD camera is required to achieve simultaneous acquisition of four phase-stepped interference patterns, and then the aberrated wavefront is directly reconstructed with a simple algorithm. To reasonably choose or utilize the photosensitive area of a single camera using in this class of single-shot interferometers, the relationship of the spatial resolution and the reconstructed accuracy is analyzed. Additionally, to increase the intensity transmission to the utmost extent and thus improve the visibility of interference patterns especially in the beginning of closed-loop correction, the maximal pinhole size allowed in a closed-loop adaptive optics is studied. Numerical simulation and closed-loop correction experiments are performed.

Lens aberrations and their relationship with lens sutures for species with Y-suture branches

Work remains to be done to understand the origins of ocular aberrations. We analyze lens aberrations of several species with Y-suture branches (bovine, ovine, and porcine) and their relationship with suture distribution. Aberrations are measured in vitro with a point diffraction interferometer in 10 different eyes of each species. The minimum number of Zernike polynomials minimizing the root mean square error of the wavefront is estimated by processing the interferograms. Through this we find significant amounts of astigmatism, coma, spherical aberration, and trefoil in the lenses of the three species. Moreover, we observe a high degree of correlation between the orientation of the lens sutures and the axis of nonrotationally symmetric aberrations. Our results point to lens sutures as the histological origin of the most significant lens aberrations: astigmatism, coma, and trefoil, but we are unable to find a major suture governing all the axes.

Research on System Error Calibration Algorithm of Point Diffraction Interferometer

In order to evaluate absolute accuracy of point diffraction interferometer(PDI),a system error calibration method based on tilting and rotation of test mirror is used and calibration algorithm are discussed in detail.Calibration formulas are deduced and a verified simulation is conducted.In the method,figure errors of spherical test mirror are measured in N equal position around an initial axis and a tilt axis.The rotationally asymmetric component of real figure about test mirror in each axis position can be calculated through rotation method.As system errors in same coordinate are constant in two rotate measurements,subtract one from another,an equation can be acquired without system error term.The rotationally symmetric component of real figure which expressed in Zernike rotationally items can be evaluated in solving this differential equation with least square.System error can be acquired through deprive real figure error of test mirror from measurement data.The simulation results shows that figure error of test mirror and system error which calculated through this algorithm are consistent with the simulation input values,difference of errors are less than 0.03 nm and residual errors are less than 0.3 nm,it can meet the requirement of the calibration accuracy.

Progressive Addition Lens Measurement by Point Diffraction Interferometry

Design a device for accurate measurements of local optical properties of progressive addition lenses (PALs). A point diffraction interferometer has been adapted to measure local prescriptions of PALs. The most basic configuration of the interferometer for the measurement of PALs showed in this work presents high dynamic range and accuracy as well as the possibility of choosing the number and position of measurement points. Measurements are taken within a region of interest within a radius of about 0.4 to 1.5 mm. Different PAL designs are measured by the method proposed here and compared with results by a last generation commercial lens mapper. With the point diffraction interferometer we also compared several PAL designs in order to analyze their properties in the progression zone. The device is compact, robust, and fairly accurate, and the operational principle is very simple. By direct measurements it provides the local dioptric power, i.e., the second order wavefront properties, of the lens for selected regions of interest. The position and area can be chosen by the user. The only mobile part of the setup allows for the selection of the measurement points without any additional prismatic correction or movement of the PAL.

Circular common-path point diffraction interferometer

A simple and compact point-diffraction interferometer with circular common-path geometry configuration is developed. The interferometer is constructed by a beam-splitter, two reflection mirrors, and a telescope system composed by two lenses. The signal and reference waves travel along the same path. Furthermore, an opaque mask containing a reference pinhole and a test object holder or test window is positioned in the common focal plane of the telescope system. The object wave is divided into two beams that take opposite paths along the interferometer. The reference wave is filtered by the reference pinhole, while the signal wave is transmitted through the object holder. The reference and signal waves are combined again in the beam-splitter and their interference is imaged in the CCD. The new design is compact, vibration insensitive, and suitable for the measurement of moving objects or dynamic processes.

Real-time determination of beam propagation factor by Mach–Zehnder point diffraction interferometer

Based on a novel Mach–Zehnder point diffraction interferometer, a real-time method to determinate beam propagation factor M2 of laser beams is presented. By using the proposed point diffraction interferometer, the intensity profile and wavefront of laser beam are completely extracted from a single interferogram in one-shot measurement. Knowing the complex field of laser beam yields the beam's propagation parameters such as beam propagation factor M2 conform to the ISO standard method. The experimental method is simple, fast and operates without movable parts, which is allowed to investigate laser beams in conditions inaccessible using the existing method.

A single-mode-fiber-based point diffraction interferometer

Based on the modification of a point diffraction interferometer, a method for measuring the optical fields from remote objects and external sources is developed. In this method, the reference beam is obtained from the studied beam by filtration of its spatial spectrum with a single-mode optical fiber. To eliminate the effect of phase errors caused by the nonideality of elements of the optical scheme on the measurement results, we developed a procedure of interferometer calibration that permits one to determine these errors with the aim of subtracting them from the measured field phase distributions.

Optical pressure sensor based on the combined system of a variable liquid lens and a point diffraction interferometer

We propose an experimental efficient optical pressure sensor based on a variable liquid lens and a modified point diffraction interferometer. The working principle of the sensor is based on the fact that a variation in pressure induces a change in lens curvature and hence in its focal length, which can be tracked and measured with the interferometer. The pressure is then measured by recording and processing the interferometric images. The sensor in this proposal can change its dynamic range by the simple axial movement of one of the components of the optical system. In this work we show the performance of the system within three working ranges: from 0 to 1 kPa with accuracy of approximately 0.01 kPa, from 0 to 7 kPa with 0.05 kPa accuracy, and from 0 to 30 kPa with 0.3 kPa accuracy.

点衍射干涉仪波前参考源标定算法的研究

点衍射干涉仪波前参考源标定算法的研究

Key Factors in Fiber Point Diffraction Interference Technology for Measuring Surface

The point diffraction interferometer (PDI), which generates the nearly ideal spherical wavefront with the pinhole method, is realized the absolute interferometric measurement without the use of reference surface. But it is hard to detect the diameter of the pinhole and hard for use of phase shifting interferometers in PDI. However the advanced fiber point diffraction interferometer (FPDI) not only replaces the pinhole with the fiber, but also makes it possible to implement phase shifting and maintain advantage of traditional PDI. In this paper, the different methods of measuring surface are proposed according to different experimental conditions and different targets (such as concave spherical surface, convex spherical surface, flat surface) with the fiber point diffraction interferometer built in the laboratory. Base on these experiments, there are several key factors in the measurement process such as measurement configuration, laser source, polarization beamsplitter, optical fiber. And these factors, affecting the experiment accuracy, were analyzed seriously.

Micro-hole drilling in thin films with cw low power lasers

In this work, we perform drilling of micro-holes and micro-patterning in indium tin oxide (ITO) and titanium thin films. In ITO films the drilling is performed by thermocavitation only; meanwhile in titanium two competing processes are identified: (i) laser-induced sublimation producing high-quality micro-holes comparable to those produced with femtosecond pulses but at a reduced cost and (ii) erosion by thermocavitation which tend to degrade the quality of the micro-holes. The micro-holes can be employed as micrometer light sources for use in point-diffraction interferometers or spatial filters; in addition, micron-sized resolution patterning can be performed.