239 results about "Zernike polynomials" patented technology

An intraocular lens comprises optical part configured to be implanted in an eye of a subject. The intraocular lens further comprises at least one aspheric surface configured, in combination with a lens in the capsular bag of an eye, to reduce an aberration of a wavefront passing the eye. The aberrations may include astigmatism, coma, and/or spherical aberrations. An aberration of the intraocular lens may be expressed as a linear combination of Zernike polynomial terms that may include a Zernike coefficient a₁₁. The Zernike coefficient a₁₁ may be selected to reduce a spherical aberration of a wavefront passing the eye and/or to compensate for an average value resulting from a predetermined number of estimations of the Zernike coefficient a₁₁ in a population of corneas and capsular bag lenses.

A method of measuring eye refraction to achieve desired quality according to a selected vision characteristics comprising the steps of selecting a characteristic of vision to correlate to the desired quality of vision from a group of vision characteristics comprising acuity, Strehl ratio, contrast sensitivity, night vision, day vision, and depth of focus, dynamic refraction over a period of time during focus accommodation, and dynamic refraction over a period of time during pupil constriction and dilation; using wavefront aberration measurements to objectively measure the state of the eye refraction that defines the desired vision characteristic; and expressing the measured state of refraction with a mathematical function to enable correction of the pre-selected vision characteristic to achieve the desired quality of vision. The mathematical function of expression may be a Zernike polynomial having both second order and higher order terms or a function determined by spline mathematical calculations. The pre-selected desired vision characteristics may be determined using ray tracing technology.

An exposure apparatus comprises: a movable body that is arranged on an image plane side with respect to a projection optical system; a wavefront measuring unit at least a part of which is arranged on the movable body and that measures wavefront information of the projection optical system; an adjusting unit that adjusts an imaging state of a projected pattern generated on an object via the projection optical system; and a controller that determines adjustment information of the projection optical system using the least-squares method based on the wavefront information and Zernike Sensitivity corresponding to exposure conditions of the object, and controls the adjusting unit based on the adjustment information. The controller determines a coefficient in a predetermined term of a Zernike polynomial from the wavefront information, and determines an adjustment amount of an optical element of the projection optical system as the adjustment information, based on data regarding a relation between an adjustment amount of the optical element of the projection optical system and variation of the determined coefficient in a predetermined term of a Zernike polynomial.

The invention relates to a method for simulating an aero-optical effect. The method comprises the steps of conducting thermal and structural analysis to an optical window by adopting a finite element analysis method to obtain a finite element analysis result, and calculating multi-frame wave-front errors according to the finite element analysis result; fitting the current frame wave-front error to be a Zernike polynomial coefficient vector q; calculating control voltage vectors of all actuators of a deformable mirror and control voltage vectors of all actuators of a tilting mirror according to the q; and adjusting the actuators of the deformable mirror according to the control voltage of the deformable mirror, adjusting the actuators of the tiling mirror according to the control voltage of the tiling mirror, acquiring and saving distorted images on an imaging detector and again fitting the q according to the current frame wave-front error. The invention additionally discloses a system for simulating the aero-optical effect. By using the method and the system provided by the embodiment of the invention, dynamic distorted image data under the influence of the aero-optical effect can be obtained and experimental conditions are provided for researches on the correction of the aero-optical effect.

The invention relates to a beacon optical axis precision positioning system in an atmosphere laser communication system, which is characterized by comprising an optical receiving antenna (1), a vibrating mirror (2), a dispersion prism (3), a Hartmann sensor optical axis precision positioning unit (4), a vibrating mirror controller (5), a lens (6) and a common CCD camera (7). To realize the real-time correction of the pointing direction of a beacon optical axis, the beacon optical axis precision positioning system detects a beacon light beam by a Schack Hartmann sensor with microlenses array and reconstructs a real-time wavefront image by a Zernike Polynomial mode method, thereby resolving the real pointing direction of the beacon optical axis of the atmosphere laser communication system and achieving final optical axis positioning precision exceeding 2 mu rad. If a common CCD positioned at a receiving end needs to obtain same resolution ratio and measuring precision, an optical systemof the common CCD has large volume and heavier weight; in addition, compared with the traditional platform, the invention has obviously reduced volume and weight, thereby effectively meeting the requirement of future space laser communication for the light type of an onboard platform.

The invention relates to a detecting method and a detecting device of the surface-shape error of a double curved surface convex reflecting mirror, which takes an aberrationless laser convergent beam as an incident beam scanning the convex of the detected reflecting mirror and takes wavefront detector as a measuring tool to coincide the focus of the incident beam with the virtual focus of the detected double curved surface reflector; the incident beam is imaged at the real focus of the detected double curved surface reflecting mirror after being reflected by the detected reflector, an imaging beam enters in the wavefront detector after being collimated by an anaberration collimating lens, and the surface-shape error of a local area is detected by the wavefront detector; the incident beam radically scans around the virtual focus of the detected double curved surface reflector, the detected double curved surface reflecting mirror rotates a circle around an optic axis when the incident beam scans each step, and the surface-shape error of each local area inside a whole mirror surface is detected circularly; and the detected surface-shape error of the local area is subject to matching and Zernike polynomial polynomial fitting to obtain the surface-shape error of the whole double curved surface convex reflecting mirror. The invention provides a low-cost and high-precision detection means of the large-caliber double curved surface convex reflecting mirror.

The invention relates to an off-focus value measuring method for a phase diversity wavefront sensor. By ensuring directional light to enter the phase diversity wavefront sensor (PD WFS), a processing algorithm utilizes an off-focus plane far-field light spot image to restrain the solving process on the basis of the conventional GS iterative operation according to the orthogonality that the off-focus plane only comprises an off-focus phase diversity and a Zernike polynomial, so that the accurate measurement of the off-focus value of a system is implemented. Relative to various current off-focus measuring methods for the PD WFS, the off-focus value measuring method for the PD WFS, which is disclosed by the invention, has the advantages that the structure is simple and stable; the solving process is rapid and reliable; the position of a photoelectric detector CCD (Charge Coupled Device) does not need to be moved in an optical path; other measuring tools are not used; in the iterative process, various prior information is sufficiently utilized to increase the constraint conditions, so that the defect that in a conventional GS algorithm, a correct result cannot be accurately obtained due to the insufficient constraint conditions is overcome; the off-focus value measuring method has higher off-focus value measuring accuracy and stability; and the foundation is laid for the PD WFS toaccurately measure the wavefront phase diversity and recover a degrade image in the actual engineering.

A system and method for converting measured wavefront data into an ablation profile for correcting visual defects includes providing measured wavefront data on an aberrated eye by a method such as known in the art. The measured wavefront data are correlated with accumulated data on previously treated eyes. Next an adjustment is applied to the measured wavefront data based upon the correlating step. This adjustment is used to form adjusted wavefront data for input to a wavefront data correction algorithm to calculate an ablation profile therefrom. The wavefront data correction algorithm may be modeled as, for example, Zernike polynomials with adjusted coefficients.

Calibration of an angularly resolved scatterometer is performed by measuring a target in two or more different arrangements. The different arrangements cause radiation being measured in an outgoing direction to be different combinations of radiation illuminating the target from ingoing directions. A reference mirror measurement may also be performed. The measurements and modeling of the difference between the first and second arrangements is used to estimate separately properties of the ingoing and outgoing optical systems. The modeling may account for symmetry of the respective periodic target. The modeling typically accounts for polarizing effects of the ingoing optical elements, the outgoing optical elements and the respective periodic target. The polarizing effects may be described in the modeling by Jones calculus or Mueller calculus. The modeling may include a parameterization in terms of basis functions such as Zernike polynomials.

A wavefront device produces adjustable amplitudes in optical path differences and adjustable axis orientation angles. two substantially identical wave plates have a wavefront profile of at least the third order Zernike polynomial function which are not circularly symmetric, as denoted by Z(i,j) where i≧3 and j≠0. The wave plates are mounted in rotatable mounts with their optical centers substantially aligned with each other. An subjective wavefront refraction instrument and method are provided to correct low and high order aberrations of the eye, using the adjustable wave plates that have astigmatism and higher order Zernike function optical path difference wavefront profiles.

An exposure method for projecting, through a projection optical system, a predetermined pattern formed on a mask onto an object to be exposed. The exposure method includes the steps of dividing an effective light source area for illuminating the mask into plural point light sources, calculating a Zernike sensitivity coefficient that represents a sensitivity of a change of image quality of the predetermined pattern to a change of a Zernike coefficient, when wave front aberration in the projection optical system is developed into a Zernike polynomial for all divided point light sources, determining an effective light source distribution based on a combination of Zernike sensitivity coefficient of all divided point light sources, and forming the effective light source distribution by intensity of each point light source.

A deformable optical lens with a lens membrane having an optically active portion that is configured to be shaped over an air-membrane interface according to a spherical cap and Zernike polynomials is provided. The spherical cap and the Zernike polynomials comprise a Zernike[4,0], (Noll[11]) polynomial and are sufficient to model the deformable optical lens to within approximately 2 micrometers.

The invention discloses a high-precision method for detecting wave aberration of a system, belonging to the field of optical detection. The method comprises the following steps of: emitting lighting beams by a light source, and generating an ideal spherical wavefront beam through diffraction after entering into a lighting system and a spatial pinhole filter with pinholes; enabling incidence beamsto enter into a detected projection objective, enabling emergent beams with aberration information to generate interference after being diffracted by an optical grating and passing through the spatial filter, acquiring the emergent beams by an image sensor, and carrying out wave surface fitting to obtain an aberration difference; enabling the incidence beams to enter into the detected projection objective through radiating and rotating by 180 DEG to obtain two wavefront measurement results, separating non-rotational symmetry components in system errors by using the characteristic of the Zernike polynomial in a unit circle field, increasing two optical axis exterior point measurements, figuring out the system errors, and subtracting the system errors by a measured value to obtain the actual wave aberration of the detected projection objective. The method for calibrating the system errors of an interferometer in the invention can be used for calibrating the system errors caused by the interferometer and improving the measuring precision of the interferometer.

The present invention provides a coherent laser communication system based on wavefront correction. The device is composed of a polarizer (1), a telescope system (2), a beam splitter prism (3), a Hartmann-Shack wavefront sensor (4), a computer system (5), a wavefront controller (6), a spatial light modulator (7), a local oscillator laser (8), an optical coupler (9) and a detector (10). The telescope system (2) receives the laser which passes through the atmosphere. The Hartmann-Shack wavefront sensor (4) detects the deformed wavefrotn signal. The computer system (5) applies the Zernike polynomial for reconstructing the non-deformed wavefront signal. After the correction of spatial light modulator (7), the non-deformed wavefront signal is executed with frequency mixing with the light beam emitted from the local oscillator laser (8) for generating the coherent intermediate frequency signal and transmitting to the detector (10). The whole system corrects the laser which passes through the atmosphere through the above mode for causing that the detector (10) obtains the coherent laser signal after correcting the deformed wavefront signal.

A variable near-null compensator for measuring aspheric surfaces by subaperture stitching includes a pair of counter-rotating CGH phase plates, each of the phase plates having a phase function including two terms Z5 and Z7 of Zernike polynomials. The phase plates are mounted on a pair of precision rotary center-through tables, wherein rotational axes of the pair of precision rotary center-through tables coincide with the optical axes of the phase plates. A figure metrology apparatus includes a wavefront interferometer, the test mirror mount, the near-null compensator and the mechanical adjustment components therefor. The optical axis of the near-null compensator coincides with the optical axis of the interferometer. A method for measuring aspheric surfaces by subaperture stitching includes the steps of mounting the test mirror, measuring the subapertures with the figure metrology apparatus, and finally processing the data by stitching.

The invention discloses a single focal plane high-precision testing method for optical wavefront of an optical imaging system, relates to the technical field of optical testing, solves the problems that exit pupil amplitudes are not distributed uniformly and calculation errors are introduced by fast Fourier transform in the conventional phase retrieval algorithm, and provides the scheme for eliminating the influence of vibration in the process of image acquisition on detection accuracy. The method comprises the following steps of: establishing a detection platform of the optical imaging system; detecting the position of the focal plane of a lens to be detected by using a detection device in the detection platform and acquiring an out-of-focus stellar image of the lens to be detected by the detection device; selecting effective data according to the acquired out-of-focus stellar image and calculating a pupil function of an optical system; and extracting the phase of the acquired pupil function to obtain the optical wavefront of the optical imaging system. The pupil function of the optical system is calculated by a Zernike multinomial, an extended Nijboer-Zernike multinomial, and a generalized inverse matrix. The single focal plane high-precision testing method is low in cost, and high in accuracy and is suitable for manufacturing enterprises, scientific research and detection units of the optical imaging system.

The invention discloses a high speed aberration correction method based on machine learning. The incident parallel beam passes through the spatial light modulator that does not load the wavefront phase distribution to obtain the ideal focused spot. A series of wavefront phase distributions are obtained using the Zenike polynomial processing, and each wavefront phase distribution is loaded into the spatial light modulator to obtain a distorted focused spot. The light intensity distribution of each distorted focused spot and the respective Zenike coefficients under the incident wave wavefront distribution are input to the machine learning training to obtain the correction model. The intensity distribution of the distorted focused spot pattern of the scattering medium to be measured is input to the calibration model to obtain the values of the respective Zenike coefficients, and by taking the negative value calculation, the corrected phase distribution is obtained and loaded into the spatial light modulator to achieve aberration correction. The method can realize the high speed optical aberration correction of the optical path, the correction speed is fast and the accuracy is high, and the problem that the traditional adaptive optical algorithm is slow is solved.

The invention discloses a high-speed and high-resolution scanning microscopic imaging system and method based on machine learning. The phase distribution is obtained by combination of Zernike polynomial coefficients and loaded into a spatial light modulator to obtain distortion focus spots; the light intensity distribution of all the distortion focus spots and the corresponding Zernike polynomialcoefficients are input into machine learning network, and training is performed to obtain a correction model; the light intensity distribution of the distortion focus spots is input into the correction model, and calculation is performed to obtain various Zernike polynomial coefficients and obtain the corrected phase distribution; the corrected phase is loaded on the spatial light modulator to achieve aberration correction so as to reconstruct a high-quality focus spot. The correction speed of optical aberration is improved, fast aberration correction in the process of optical microscopic imaging is achieved, a new idea is provided for high resolution imaging and high precision detection deep inside a living biological tissue, and a good application prospect is achieved in the field of biomedical research.