Experimental verification of reconstruction of two interfering wavefronts using the transport of intensity equation (original) (raw)
Related papers
Application of transport-of-intensity equation in fringe analysis
Optics Letters, 2014
The transport-of-intensity equation (TIE) is applied in the reconstruction of two interfering wavefronts by analyzing the interference patterns and their derivatives along their common propagation directions. The TIE is extended from one wave to two waves and is then applied to calculate the phase of the interference field. Finally, the phase shift concept is applied to reconstruct the phase distribution of two waves. The consistency of the method is verified by simulation. Fig. 6. (a) Profiles of the calculated PIFs and (b) the error of the reconstructed phase distributions.
Scanning, 2017
Phase measurements obtained by high-coherence interferometry are restricted by the 2π ambiguity, to height differences smaller than λ/2. A further restriction in most interferometric systems is for focusing the system on the measured object. We present two methods that overcome these restrictions. In the first method, different segments of a measured wavefront are digitally propagated and focused locally after measurement. The divergent distances, by which the diverse segments of the wavefront are propagated in order to achieve a focused image, provide enough information so as to resolve the 2π ambiguity. The second method employs an interferogram obtained by a spectrum constituting a small number of wavelengths. The magnitude of the interferogram’s modulations is utilized to resolve the 2π ambiguity. Such methods of wavefront propagation enable several applications such as focusing and resolving the 2π ambiguity, as described in the article.
Wavefront reconstruction by spatial-phase-shift imaging interferometry
Applied Optics, 2006
Common-path imaging interferometers offer some advantages over other interferometers, such as insensitivity to vibrations and the ability to be attached to any optical system to analyze an imaged wavefront. We introduce the spatial-phase-shift imaging interferometry technique for surface measurements and wavefront analysis in which different parts of the wavefront undergo certain manipulations in a certain plane along the optical axis. These manipulations replace the reference-beam phase shifting of existing interferometry methods. We present the mathematical algorithm for reconstructing the wavefront from the interference patterns and detail the optical considerations for implementing the optical system. We implemented the spatial phase shift into a working system and used it to measure a variety of objects. Measurement results and comparison with other measurement methods indicate that this approach improves measurement accuracy with respect to existing quantitative phase-measurement methods.
Computational Method for Wavefront Sensing Based on Transport-of-Intensity Equation
Photonics, 2021
Recently the transport-of-intensity equation as a phase imaging method turned out as an effective microscopy method that does not require the use of high-resolution optical systems and a priori information about the object. In this paper we propose a mathematical model that adapts the transport-of-intensity equation for the purpose of wavefront sensing of the given light wave. The analysis of the influence of the longitudinal displacement z and the step between intensity distributions measurements on the error in determining the wavefront radius of curvature of a spherical wave is carried out. The proposed method is compared with the traditional Shack–Hartmann method and the method based on computer-generated Fourier holograms. Numerical simulation showed that the proposed method allows measurement of the wavefront radius of curvature with radius of 40 mm and with accuracy of ~200 μm.
Generalized method for wave-front analysis
Optics Letters, 2004
We suggest and demonstrate a new method for wave-front analysis based on common-path phase-shift interferometry. We introduce a formalism and an iterative mathematical algorithm in which the wave front is transformed, modified, and inversely transformed. The resulting intensity data are sufficient to reconstruct the entire wave front. In a more restricted case, in which the wave-front modifications are arbitrarily applied over arbitrary spatial regions of the wave front, the wave front is reconstructed semianalytically by use of a model that allows a local solution, followed by an iterative algorithm. Measurement results indicating that the suggested approach has an improved measurement accuracy with respect to existing quantitative phase measurement methods are presented.
Error analysis and correction in wavefront reconstruction from the transport-of-intensity equation
Optical Engineering, 2006
Wavefront reconstruction from the transport-of-intensity equation ͑TIE͒ is a well-posed inverse problem given smooth signals and appropriate boundary conditions. However, in practice experimental errors lead to an ill-condition problem. A quantitative analysis of the effects of experimental errors is presented in simulations and experimental tests. The relative importance of numerical, misalignment, quantization, and photodetection errors are shown. It is proved that reduction of photodetection noise by wavelet filtering significantly improves the accuracy of wavefront reconstruction from simulated and experimental data.
Wave-front reconstruction of optical disturbances using digital image processing
1995
This thesis is concerned with the development of a practical digital image processing system for recording and subsequent reconstruction of the magnitude and phase of an optical wave-front arriving from a coherently illuminated object disturbance. Since the wave-fronts of concern are coherent, the magnitude and phase of such waves are generally independent functions in the sense that the knowledge of one is not sufficient to uniquely deduce the other. To uniquely reconstruct and characterize optical disturbances both the magnitude and phase are required. In general, all recording media respond only to light intensity and no difficulty is encountered in recording the intensity and therefore the magnitude, because it is the square root of the intensity. It is therefore necessary that the phase information be somehow converted to light intensity variations for recording purposes. Several techniques, such as interferometric techniques, are normally • used to convert phase information into light changes. The practical implementations of such techniques are not always simple. An alternative to these techniques, based on digital Fourier transformations, is proposed and applied to the phase retrieval problem. Computer simulations and practical results show that the Gerchberg and Saxton iterative algorithm is suitable for recovering the phase information from single measurements of the intensity in both the image and Fourier domains in an optical system. A considerable improvement in the experimental results is obtained when non-linear image sensors are used to perform quasi-magnitude measurements instead of the usual intensity measurements. The magnitude and phase of the digitally reconstructed wave-front are used to characterize the corresponding optical disturbance. In general, optical disturbances are created in transparent media and they are characterized by refractive index changes that deviate the incident light from its normal trajectory and consequently the phase of the wave-front is changed. Knowing the phase it is possible to perform measurements of the refractive index, density, and some other parameters of the medium under study. The generation of schlieren images on the computer screen is also possible and the method proved to be a good complement to the conventional schlieren technique due to the high sensitivity that is normally not achievable in practice.