Analysis of Interferometer with Micro-Mirror on Beam Splitting Cube

2021 ◽  
pp. 129-143
Author(s):  
L.N. Timashova ◽  
N.N. Kulakova
Keyword(s):  
Interference Pattern ◽  
Fourier Transforms ◽  
Design Parameters ◽  
Spherical Mirror ◽  
Topographic Map ◽  
Wave Surface ◽  
Beam Splitting ◽  
Concave Mirror ◽  
Part Surface ◽  
Wave Aberration

The control of the shape of the optical part surface by the interference method has become an integral part of the process of their shaping. With a precisely focused interferometer interferometry allows obtaining an interference pattern similar to a topographic map of the error profile of the wave surface under investigation. The interferometer must form a map of the optical surface with high accuracy --- the permissible distortion of the interference fringe caused by an interferometer error should not exceed 0.1 of the distortion value caused by an error on the examined surface. The dependence of the interference pattern formation on the errors in the arrangement of the interferometer components, i.e., defocusing, was theoretically analyzed using Fourier transforms. The analysis was performed for an interferometer containing a laser illuminator, a concave spherical mirror with a central hole, coaxial to the illuminator, and a beamsplitting element in the form of a cube-prism with a semitransparent hypotenuse face. On the first flat face of the cube-prism, a microspherical concave mirror is made with the center located on the optical axis of the interferometer. A method for calculating the defocusing of a controlled spherical mirror and the corresponding wave aberration of the working wavefront is presented. An example of calculating the design parameters of the interferometer and the permissible defocusing of the controlled spherical mirror is given

Analysis of a Pot-Like Ultrasonic Sensor with an Anisotropic Beam Pattern

2010 ◽  
Vol 26 (3) ◽  
pp. 373-384 ◽  
Author(s):  
C.-C. Cheng ◽  
C.-Y. Lin ◽  
J.-H. Ho ◽  
C.-S. Chen ◽  
J. Shieh ◽  
...  
Keyword(s):  
Resonant Frequency ◽  
Fourier Transforms ◽  
Numerical Models ◽  
Beam Width ◽  
Ultrasonic Sensor ◽  
Beam Pattern ◽  
Design Parameters ◽  
Far Field ◽  
Vertical Beam ◽  
Vibrating Plate

AbstractWe investigated the design parameters of a compact pot-like ultrasonic sensor which possesses a highly anisotropic beam pattern. As the sensor size is small due to its application constraint, the parameters are thus highly coupled to one another. We analyzed the respective effects of the parameters in the case where there is a vertical beam width reduction. The parameters investigated include resonant frequency, vibrating plate width-expanded angle, and ratio of thickness discontinuity of the vibrating plate. Numerical models developed by combining finite-element analysis and spatial Fourier transforms were adopted to predict the far-field radiating beam pattern of the various design configurations. The displacement distribution of the vibrating plate was measured using a microscopic laser Doppler vibrometer and the far-field pressure beam patterns were measured using a standard microphone in a semianechoic environment. The three configurations we used to validate the simulation model resulted in an H-V ratio of 2.67, 2.68 and 3.13, respectively which all agreed well with the numerical calculations. We found that by increasing the operating resonant frequency from 40kHz to 58kHz, the vertical far-field beam width of an ultrasonic sensor can be reduced by 31.62%. We found that the vertical beam width can be significantly reduced when the ratio of the thickness discontinuity of the vibrating plate decreases from 1 to 0.4 and is incorporated with its optimal width-expanded angle of the vibrating plate. It appears that an ultrasonic sensor with this type of anisotropic beam pattern can be ideally adopted for today's automotive applications.

scholarly journals Orthogonal ray interferometer: modification for testing convex and concave mirror surfaces

2021 ◽  
Vol 2127 (1) ◽  
pp. 012067
Author(s):  
M V Askerko ◽  
A E Gavlina ◽  
V I Batshev ◽  
D A Novikov
Keyword(s):  
Point Source ◽  
Interference Pattern ◽  
Optical Method ◽  
Present Method ◽  
Rotational Symmetry ◽  
Geometrical Parameters ◽  
Concave Mirror ◽  
Entire Surface ◽  
Optical Components

Abstract A non-contact optical method for testing of large concave and convex mirrors both spherical and aspheric is presented. It is based on the orthogonal ray interferometer modification. The point source is placed near the testing mirror and the chief ray propagates normally to its axis. The information about a tangential profile of testing mirror is contained in an interference pattern that is a result of superposition between two wavefronts, the first is reflected from the mirror, the second bypasses the mirror. Testing of the entire surface is carried out by rotating the mirror. Interferogram decoding method and algorithm for determination of an error of the testing surface are presented. The proposed method does not require bulky additional optical components what differs it from existing methods and makes promising primary for testing large astronomical mirrors. Furthermore, the method is universal and suited for surfaces with various geometrical parameters. The scheme with some modification of the present method is applied for surfaces without axis of rotational symmetry or freeform surfaces.

scholarly journals Computational program to evaluate local defects type Chalmers Test on a reflective optical surface

2021 ◽  
pp. 18-24
Author(s):  
Benito CANALES-PACHECO ◽  
Esteban RUEDA-SORIANO ◽  
Luis Alberto RUIZ-AGUILAR ◽  
Raymundo Sergio NORIEGA-LOREDO
Keyword(s):  
Interference Pattern ◽  
Radius Of Curvature ◽  
Spherical Mirror ◽  
Fizeau Interferometer ◽  
Optical Surface ◽  
Computational Tool ◽  
Optical Surfaces ◽  
Computational Program ◽  
Local Defects ◽  
Local Deformations

A computational tool is developed to measure the local deformations in optical surfaces from the interference patterns obtained by the Chalmers test principle and from the analysis of a reflective optical surface using a commercial Fizeau interferometer of the ZYGO. The tests were made on a concave spherical mirror with a radius of curvature of 60 cm and a diameter of 13 cm. To obtain the measurements of local deformations, a computational tool proposed for the localization of dark fringes is used by evaluating the maximum and minimum of the image obtained in the interference patterns. The results obtained show that the computational tool allows locating fringes within an interference pattern, allowing faster inter-fringe measurements and assigning an error on the surface in terms of wavelength.

scholarly journals Optical Image Encryption Using a Nonlinear Joint Transform Correlator and the Collins Diffraction Transform

Photonics ◽  
2019 ◽  
Vol 6 (4) ◽  
pp. 115 ◽  
Author(s):  
Juan M. Vilardy O. ◽  
Ronal A. Perez ◽  
Cesar O. Torres M.
Keyword(s):  
Fourier Transforms ◽  
Lateral Displacement ◽  
Random Phase ◽  
Design Parameters ◽  
Invariance Property ◽  
Joint Transform Correlator ◽  
Optical Processing ◽  
Optical Wave ◽  
Special Cases ◽  
Nonlinear Joint

The Collins diffraction transform (CDT) describes the optical wave diffraction from the generic paraxial optical system. The CDT has as special cases the diffraction domains given by the Fourier, Fresnel and fractional Fourier transforms. In this paper, we propose to describe the optical double random phase encoding (DRPE) using a nonlinear joint transform correlator (JTC) and the CDT. This new description of the nonlinear JTC-based encryption system using the CDT covers several optical processing domains, such as Fourier, Fresnel, fractional Fourier, extended fractional Fourier and Gyrator domains, among others. The maximum number of independent design parameters or new security keys of the proposed encryption system using the CDT increases three times in comparison with the same encryption system that uses the Fourier transform. The proposed encryption system using the CDT preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of both the key random mask in the decryption process and the retrieval of the primary image. The viability of this encryption system is verified and analysed by numerical simulations.

Physical Parameter Identification of Laminates Based on Thermal Deformation Measurements

1995 ◽  
Author(s):  
Werner Konrad ◽  
Bernd Caesar
Keyword(s):  
Parameter Identification ◽  
Physical Parameter ◽  
High Precision ◽  
Model Updating ◽  
Nodal Point ◽  
Design Parameters ◽  
Physical Parameters ◽  
Spherical Mirror ◽  
Load Case ◽  
Space Applications

Abstract High precision structures, as telescope mirrors for space applications, require high thermal stability and structural stiffness combined with low weight. Laminate structures with their special properties can satisfy these stringent requirements. Model updating and physical parameter identification on the basis of measurements can be applied to optimize such structures or define correction measures w.r.t. manufacturing inaccuracies. In classic update procedures correction factors are used to improve physical parameters. The definition of correction differences which are suitable for parameters with zero starting values or values changing from positive to negative as it may be the case for the layer orientations of a laminate is presented. High precision structures require high accurate measuring methods for the test. Thermal deformations can be measured by holographic, interferometric methods with high precision in the μm range. An interferometric contour map can be compared with the nodal point displacements of a Finite Element model by special spline functions called Zernike’s polynomials. The equations to determine the various design parameters or material properties may not be linear independent, depending on the applied thermal load case. The degree of correlation between the various parameters is investigated. The results are used to optimize the load case selection and to improve error localization methods. The proposed method is applied to a segment of a high stability spherical mirror plate with real measuring data.

Performance of Oversampled Polyphase Filterbank Inversion via Fourier Transform

2020 ◽  
Vol 09 (01) ◽  
pp. 2050004 ◽  
Author(s):  
I. S. Morrison ◽  
J. D. Bunton ◽  
W. van Straten ◽  
A. Deller ◽  
A. Jameson
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Fourier Transforms ◽  
Perfect Reconstruction ◽  
Design Parameters ◽  
High Temporal Resolution ◽  
Spectral Leakage ◽  
Design Considerations ◽  
Near Perfect Reconstruction ◽  
Selection Of

Frequency channelization is a fundamental signal processing operation employed across various domains, including communications and radio astronomy. The polyphase filterbank (PFB) represents an efficient and versatile means of channelization. When strict constraints are placed on the allowable spectral leakage between neighboring channels, an oversampled PFB design is advantageous. A helpful consequence of the oversampling is that inversion of the PFB to recover high temporal resolution is simplified and can be accomplished accurately using Fourier transforms. We describe this inversion approach and identify key design considerations. We examine the residual error and spectral/temporal leakage behavior when a channelizer and its corresponding inverter are cascaded, concluding that near-perfect reconstruction can be approached with appropriate selection of PFB and inverter design parameters.

Computer analysis of side-band holography in STEM

1991 ◽  
Vol 49 ◽  
pp. 684-685
Author(s):  
M.A. Gribelyuk ◽  
J.M. Cowley
Keyword(s):  
Interference Pattern ◽  
Computer Analysis ◽  
Side Band ◽  
Diffraction Plane ◽  
Illumination System ◽  
Probe Size

Recently the use of a biprism in a STEM instrument has been suggested for recording of a hologram. A biprism is inserted in the illumination system and creates two coherent focussed beams at the specimen level with a probe size d= 5-10Å. If one beam passes through an object and another one passes in vacuum, an interference pattern, i.e. a hologram can be observed in diffraction plane (Fig.1).

Computer processing of high-resolution images of periodic specimens

1986 ◽  
Vol 44 ◽  
pp. 2-5
Author(s):  
W. Chiu ◽  
M.F. Schmid ◽  
T.-W. Jeng
Keyword(s):  
High Resolution ◽  
Fourier Transforms ◽  
Complex Structure ◽  
Distribution Functions ◽  
Multiple Image ◽  
Cryo Electron Microscopy ◽  
Structure Factors ◽  
Unit Cells ◽  
High Resolution Images ◽  
Phase Probability Distribution

Cryo-electron microscopy has been developed to the point where one can image thin protein crystals to 3.5 Å resolution. In our study of the crotoxin complex crystal, we can confirm this structural resolution from optical diffractograms of the low dose images. To retrieve high resolution phases from images, we have to include as many unit cells as possible in order to detect the weak signals in the Fourier transforms of the image. Hayward and Stroud proposed to superimpose multiple image areas by combining phase probability distribution functions for each reflection. The reliability of their phase determination was evaluated in terms of a crystallographic “figure of merit”. Grant and co-workers used a different procedure to enhance the signals from multiple image areas by vector summation of the complex structure factors in reciprocal space.

The influence of confocal microscope design on imaging performance

1993 ◽  
Vol 51 ◽  
pp. 144-145
Author(s):  
C J R Sheppard
Keyword(s):  
Image Quality ◽  
Fluorescence Imaging ◽  
Confocal Microscope ◽  
Industrial Applications ◽  
Three Dimensions ◽  
Design Parameters ◽  
Weak Signals ◽  
Size And Shape ◽  
Imaging Performance ◽  
Fundamental Limitation

The confocal microscope is now widely used in both biomedical and industrial applications for imaging, in three dimensions, objects with appreciable depth. There are now a range of different microscopes on the market, which have adopted a variety of different designs. The aim of this paper is to explore the effects on imaging performance of design parameters including the method of scanning, the type of detector, and the size and shape of the confocal aperture.It is becoming apparent that there is no such thing as an ideal confocal microscope: all systems have limitations and the best compromise depends on what the microscope is used for and how it is used. The most important compromise at present is between image quality and speed of scanning, which is particularly apparent when imaging with very weak signals. If great speed is not of importance, then the fundamental limitation for fluorescence imaging is the detection of sufficient numbers of photons before the fluorochrome bleaches.

The extended Fourier algorithm: Application in discrete optics and electron holography

1994 ◽  
Vol 52 ◽  
pp. 918-919
Author(s):  
E. Voelkl ◽  
L. F. Allard
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Sampling Rate ◽  
Electron Holography ◽  
Optical Bench ◽  
Fourier Space ◽  
Ccd Cameras ◽  
Simulated Image ◽  
Initial Sampling ◽  
Fourier Algorithm

The conventional discrete Fourier transform can be extended to a discrete Extended Fourier transform (EFT). The EFT allows to work with discrete data in close analogy to the optical bench, where continuous data are processed. The EFT includes a capability to increase or decrease the resolution in Fourier space (thus the argument that CCD cameras with a higher number of pixels to increase the resolution in Fourier space is no longer valid). Fourier transforms may also be shifted with arbitrary increments, which is important in electron holography. Still, the analogy between the optical bench and discrete optics on a computer is limited by the Nyquist limit. In this abstract we discuss the capability with the EFT to change the initial sampling rate si of a recorded or simulated image to any other(final) sampling rate sf.

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