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# Wavefront sensor

About: Wavefront sensor is a research topic. Over the lifetime, 5406 publications have been published within this topic receiving 61337 citations.

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TL;DR: The phase modulation in an interferometer can be induced by moving a mirror, tilting a glass plate, moving a grating, rotating a half-wave plate or analyzer, using an acoustooptic or electro-optic modulator, or using a Zeeman laser as mentioned in this paper.

Abstract: Publisher Summary This chapter describes the phase-measurement interferometry techniques. For all techniques, a temporal phase modulation is introduced to perform the measurement. By measuring the interferogram intensity as the phase is shifted, the phase of the wavefront can be determined with the aid of electronics or a computer. Phase modulation in an interferometer can be induced by moving a mirror, tilting a glass plate, moving a grating, rotating a half-wave plate or analyzer, using an acousto-optic or electro-optic modulator, or using a Zeeman laser. Phase-measurement techniques using analytical means to determine phase all have some common denominators. There are different equations for calculating the phase of a wavefront from interference fringe intensity measurements. The precision of a phase-measuring interferometer system can be determined by taking two measurements, subtracting them, and looking at the root-meansquare of the difference wavefront. The chapter discusses the simulation results. The elimination of the errors that reduce the measurement accuracy depends on the type of measurement being performed. Phase-measurement interferometry (PMI) can be applied to any two-beam interferometer, including holographic interferometers. Applications can be divided into: surface figure, surface roughness, and metrology.

1,283 citations

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TL;DR: In this article, a self-scanned 1024 element photodiode array and a minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100.

Abstract: A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

1,267 citations

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Bell Labs

^{1}TL;DR: The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Abstract: A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

1,145 citations

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TL;DR: This chapter discusses the development of Adaptive Optics Imaging Systems, which combines Nonlinear Optics with Linear Analysis of Random Wavefronts, and its applications in Wavefront Reconstruction and System Engineering.

Abstract: History and Background: Introduction. History. Physical Optics: Propagation with Aberrations. Imaging with Aberrations. Representing the Wavefront. Interference. Adaptive Optics Terms. Sources of Aberrations: Atmospheric Turbulence: Descriptions of Atmospheric Turbulence. Refractive Index Structure Constant. Turbulence Effects. Turbulence MTF. Thermal Blooming: Blooming Strength and Critical Power. Turbulence, Jitter, and Thermal Blooming. Non-atmospheric Sources: Optical Misalignments and Jitter. Thermally Induced Distortions of Optics. Manufacturing and Microerrors. Other Sources of Aberrations. Adaptive Optics Compensation: Phase Conjugation. Limitations of Phase Conjugation: Turbulence Spatial Error. Turbulence Temporal Error. Sensor Noise Limitations. Thermal Blooming Compensation. Artificial Guide Stars. Combining the Limitations. Linear Analysis of Random Wavefronts. Linear Analysis of Deterministic Wavefronts: Partial Phase Conjugation. Adaptive Optics Systems: Adaptive Optics Imaging Systems. Beam Propagation Systems: Local Loop Beam Cleanup Systems. Alternative Concepts. Pros and Cons of the Various Approaches. Unconventional Adaptive Optics: Nonlinear Optics. Elastic Photon Scattering, DFWM. Inelastic Photon Scattering. System Engineering. Wavefront Sensing: Directly Measuring Phase: The Non-uniqueness of the Diffraction Pattern. Determining Phase Information from Intensity. Modal and Zonal Sensing. Direct Wavefront Sensing--Modal: Importance of Wavefront Tilt. Measurement of Tilt. Focus Sensing. Modal Sensing of Higher-Order Aberrations. Direct Wavefront Sensing--Zonal: Interferometiric Wavefront Sensing. Hartman Wavefront Sensors. Curvature Sensing. Selecting a Method. Indirect Wavefront Sensing Methods: Multidither Adaptive Optics. Image Sharpening. Wavefront Sampling: Beamsplitters. Hole Gratings. Temporal Duplexing. Reflective Wedges. Diffraction Gratings. Hybrids. Sensitivities of Sampler Concepts. Detectors and Noise. WavefrontCorrection: Modal Tilt Correction. Modal Higher-Order Correction. Segmented Mirrors. Deformable Mirrors: Actuation Techniques. Actuator Influence Functions. Bimorph Corrector Mirrors. Membrane and Micromachine Mirrors. Edge Actuated Mirrors. Large Correcting Optics. Special Correction Devices: Liquid Crystal Phase Modulators. Spatial Light Modulators. Charged-large-array-mirrors. Reconstruction and Controls: Introduction. Single-Channel Linear Control: Fundamental Control Tools. Transfer Functions. Proportional Control. First- and Second-Order Lag. Feedback. Frequency Response of Control Systems. Digital Controls. Multivariate Adaptive Optics Controls: Solution of Linear Equations. Direct Wavefront Reconstruction: Phase from Wavefront Slopes. Modes from Wavefront Slopes. Phase from Wavefront Modes. Modes from Wavefront Modes. Zonal Corrector from Continuous Phase. Modal Corrector from Continuous Phase. Zonal Corrector from Modal Phase. Modal Correctors from Modal Phase. Indirect Reconstructions.Modal Corrector from Wavefront Modes. Zonal Corrector from Wavefront Slopes. Spatiotemporal Considerations. Subject Index.

1,078 citations

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TL;DR: Enhanced images of satellites are enhanced by inserting a beam splitter in collimated space behind the eyepiece and placing a plate with holes in it at the image of the pupil, which captures a snapshot of the atmospheric aberrations rather than to average over time.

Abstract: developed out of a need to solve a problem. The problem was posed, in the late 1960s, to the Optical Sciences Center (OSC) at the University of Arizona by the US Air Force. They wanted to improve the images of satellites taken from earth. The earth's atmosphere limits the image quality and exposure time of stars and satellites taken with telescopes over 5 inches in diameter at low altitudes and 10 to 12 inches in diameter at high altitudes. Dr. Aden Mienel was director of the OSC at that time. He came up with the idea of enhancing images of satellites by measuring the Optical Transfer Function (OTF) of the atmosphere and dividing the OTF of the image by the OTF of the atmosphere. The trick was to measure the OTF of the atmosphere at the same time the image was taken and to control the exposure time so as to capture a snapshot of the atmospheric aberrations rather than to average over time. The measured wavefront error in the atmosphere should not change more than /10 over the exposure time. The exposure time for a low earth orbit satellite imaged from a mountaintop was determined to be about 1/60 second. Mienel was an astronomer and had used the standard Hartmann test (Fig 1), where large wooden or cardboard panels were placed over the aperture of a large telescope. The panels had an array of holes that would allow pencils of rays from stars to be traced through the telescope system. A photographic plate was placed inside and outside of focus, with a sufficient separation, so the pencil of rays would be separated from each other. Each hole in the panel would produce its own blurry image of the star. By taking two images a known distance apart and measuring the centroid of the images, one can trace the rays through the focal plane. Hartmann used these ray traces to calculate figures of merit for large telescopes. The data can also be used to make ray intercept curves (H'-tan U'). When Mienel could not cover the aperture while taking an image of the satellite, he came up with the idea of inserting a beam splitter in collimated space behind the eyepiece and placing a plate with holes in it at the image of the pupil. Each hole would pass a pencil of rays to a vidicon tube (this was before …

717 citations