CN111811474B - Method for simultaneously measuring inclination angle and absolute distance based on optical transfer function - Google Patents

Method for simultaneously measuring inclination angle and absolute distance based on optical transfer function Download PDF

Info

Publication number
CN111811474B
CN111811474B CN202010696646.3A CN202010696646A CN111811474B CN 111811474 B CN111811474 B CN 111811474B CN 202010696646 A CN202010696646 A CN 202010696646A CN 111811474 B CN111811474 B CN 111811474B
Authority
CN
China
Prior art keywords
transfer function
absolute distance
otf
inclination angle
optical transfer
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202010696646.3A
Other languages
Chinese (zh)
Other versions
CN111811474A (en
Inventor
赵伟瑞
刘田甜
张璐
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing Institute of Technology BIT
Original Assignee
Beijing Institute of Technology BIT
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijing Institute of Technology BIT filed Critical Beijing Institute of Technology BIT
Priority to CN202010696646.3A priority Critical patent/CN111811474B/en
Publication of CN111811474A publication Critical patent/CN111811474A/en
Application granted granted Critical
Publication of CN111811474B publication Critical patent/CN111811474B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C9/00—Measuring inclination, e.g. by clinometers, by levels
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/14—Measuring arrangements characterised by the use of optical techniques for measuring distance or clearance between spaced objects or spaced apertures

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Length Measuring Devices By Optical Means (AREA)

Abstract

The invention discloses a method for simultaneously measuring an inclination angle and an absolute distance based on an optical transfer function, belonging to the technical field of photoelectric measurement. The implementation method of the invention comprises the following steps: two beams of light waves with phases are focused on a focal plane to generate an interference-diffraction or diffraction phenomenon, the light intensity distribution on the focal plane is PSF, and the PSF is subjected to Fourier transform to obtain the OTF. And selecting a side peak of the OTF under the condition of monochromatic light to calculate the ratio of the real part of the imaginary part of the OTF to obtain a corresponding side peak phase transfer function, calculating the gradient value of the phase transfer function, and calculating the inclination angle of the measured sub-mirror by using the gradient value to realize the measurement of the inclination angle. Selecting a side peak of the optical transfer function OTF under the broad spectrum condition after the differential summation method processing to obtain a corresponding side peak modulation transfer function, and obtaining MTF through normalization processingnphObtaining MTF by piecewise quartic fittingnphAnd (4) solving an absolute distance value according to the obtained functional relation with the absolute distance, so as to realize high-precision measurement of the absolute distance without being influenced by the error of the inclination angle.

Description

Method for simultaneously measuring inclination angle and absolute distance based on optical transfer function
Technical Field
The invention relates to a method for simultaneously measuring an inclination angle and an absolute distance based on an optical transfer function, which is a method for simultaneously measuring the inclination angle and the absolute distance with large range, high precision and high efficiency and belongs to the technical field of photoelectric measurement.
Background
In the fields of astronomy, precision metrology, and the like, it is often necessary to perform high-precision measurement on a minute tilt angle (e.g., a rotation angle of a measured sub-mirror around its coordinate axis), a step height (e.g., an absolute distance between a reference sub-mirror and the measured sub-mirror along an optical axis), and the like, and correct the measured tilt angle and the step height to obtain a high-resolution image. A great deal of research has been conducted by domestic and foreign scholars on the measurement of inclination angles and step heights.
For the measurement of the tilt angle, a staged mode is widely adopted to realize a wide-range high-precision measurement of the tilt angle at present: firstly, realizing low-precision measurement of a large inclination angle by using a light spot mass center detection method, which is a rough measurement stage; then, the wavefront Phase Recovery (PR) method or the interference fringe information is used to realize high-precision measurement of small tilt angle, which is a fine measurement stage. Currently, the most representative measurement of the common phase tilt error (tip and tilt) of JWST (the James Webb Space lenses) system is to combine the center-of-mass detection method with PR method, use the center-of-mass detection method to perform rough tilt angle measurement, correct the tilt angle to a small tilt angle range satisfying PR method, and use PR method to perform fine measurement, thereby achieving high precision measurement of the tilt angle between the sub-lenses of the system (see James B. Hadaway, Conrad Wells, Gene A. Olczak, Mark Waldman, Tony L. Whitman, Joseph Cosending, Michael Zoella, Mark Connolly, David M. Chaney, random testing, "Performance of the center-of course Optical tilt error," Webb tilt error and tilt error ", and tilt error measurement, and precision measurement, JWST, the center-of course tilt error, JWST Webb Space lenses, and tilt error measurement, and precision measurement, see SPfound in 1068, J. Chase.
Methods for measuring the step height can be generally classified into two categories. The first type is a contact detection method, which is also called a direct measurement method and can be realized by using a three-coordinate measuring machine, but the method has long measurement time and is easy to damage the surface of an object; the other type is a non-contact type measuring method, and a common Optical detection method is adopted, wherein the actual step height to be measured by the Optical detection method corresponds to the Optical Path Difference (OPD) between the reference Optical Path and the measuring Optical Path, for the reflection type Optical Path, the OPD is twice of the measured step height, and the actual micro step height can be obtained by measuring the OPD. In 2016, Zhaowei and Jiang Jun Lun, the university of Beijing Physician, proposed a high-precision absolute distance measurement method based on optical transfer function, which can realize absolute measurement of step height, and its basic principle is: the method comprises the steps that discrete diaphragm holes are arranged in a light path, when only absolute distance exists between a measured sub-mirror and a reference sub-mirror, sub-light waves reflected by the two sub-mirrors are respectively collected, a Point Spread Function (PSF) of a system is obtained at a focal plane of a subsequent optical system, an optical Modulation Transfer Function (MTF) of the system is obtained according to a Fourier optical principle, a functional relation between a side peak value of a normalized MTF and the absolute distance is obtained through four-time fitting in a segmented mode, and large-range and high-precision measurement of the absolute distance can be achieved according to the functional relation. The final absolute distance measurement range is the coherence length of the light source, and the precision can reach the nanometer level (see: Jiang Junlun and Zhao Weirii, "pharmaceutical prism error in segmented descriptors," Opt. express 24, 19123-.
Interferometric methods in optical detection methods are also commonly used to achieve tilt angle and absolute distance measurements. In 2012, Anthony c.cheetham and Peter g.tuthill et al propose a fizeau interferometry method to implement common phase error (tilt angle, absolute distance) detection of a segmented primary mirror telescope, the basic principle is that discrete non-redundant diaphragm holes are arranged in an optical path, sub-light waves reflected by adjacent sub-mirrors are respectively collected, a point spread function PSF of the system can be obtained at a focal plane of a subsequent optical system, interference fringe information in the point spread function PSF is utilized, a least square method is adopted to perform multiple iterations, when the measured sub-mirrors have only absolute distance error and tilt error respectively, the tilt angle and the absolute distance of the measured sub-mirrors are solved, so as to implement high-precision measurement of the tilt angle and the absolute distance respectively, the method can achieve 0.5 arcsconds for the maximum detection range of the tilt angle, the precision is 3.7 masmrs, the maximum detection range of the absolute distance can achieve 150 μm, and the precision is 0.75nm (see Anthony c.cheetham, peter G.Tuthill, Anand Sivaramakrishnan, and James P.Lloyd, "Fizeau interactive phasing of segmented mirrors," Opt.Express 20, 29457-.
In summary, under the condition that both the tilt angle and the absolute distance exist, the tilt error can seriously affect the measurement of the absolute distance, the current measurement method firstly detects and corrects the tilt error and then detects and corrects the absolute distance error, a measurement system needs to be provided with hardware devices for measuring two errors, the method is complicated, the respective measurement needs a certain time, and the measurement and correction of the system error cannot be carried out in real time.
Disclosure of Invention
In order to solve the above-mentioned disadvantages of the prior art, the present invention provides a method for simultaneously measuring a large-range, high-precision, and high-efficiency tilt angle and an absolute distance based on an Optical Transfer Function, which obtains an Optical Transfer Function (OTF) of a system according to a Point Spread Function (PSF) which is a light intensity distribution on a focal plane of the system, obtains a Modulation Transfer Function (MTF) by modeling a side peak of the OTF and a Phase Transfer Function (PTF) by taking a Phase, obtains a tilt angle according to a relationship of the side peak tilt angle of the PTF, obtains an absolute distance by performing a quartic polynomial fitting in a segment according to a relationship of a normalized side peak and the absolute distance of the MTF, and does not affect each other when measuring two errors High precision and high efficiency.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a method for simultaneously measuring an inclination angle and an absolute distance based on an optical transfer function. Selecting a side peak of the optical transfer function OTF under the condition of monochromatic light to calculate the ratio of the real part of the imaginary part of the optical transfer function OTF to obtain the corresponding side peak phase transfer function PTFphCalculating the phase transfer function PTFphThe gradient value is used for calculating the inclination angle of the measured sub-mirror, so that the large-range and high-precision measurement of the inclination angle is realized. Selecting a side peak of the optical transfer function OTF under the broad spectrum condition after the differential summation method processing to obtain the corresponding side peak modulation transfer function MTFphFor modulation transfer function MTFphNormalized to obtain MTFnphObtaining MTF by piecewise quartic fittingnphAnd (4) solving an absolute distance value according to the obtained functional relation with the absolute distance, so as to realize high-precision measurement of the absolute distance without being influenced by the error of the inclination angle.
The invention discloses a method for simultaneously measuring an inclination angle and an absolute distance based on an optical transfer function, which comprises the following steps:
step one, light waves emitted by a parallel light source are divided into two beams, the two beams enter a reference light path and a measurement light path respectively to obtain two beams of light waves with phase difference information, the two beams of light waves are focused on a focal plane to generate an interference-diffraction or diffraction phenomenon, and the light intensity distribution on the focal plane is a point spread function PSF. The phase difference information includes a tilt angle and an absolute distance.
Known from fourier optics, under monochromatic light conditions, the normalized point spread function PSF is:
Figure BDA0002591232410000031
wherein (x, y) is image plane coordinate, x is image plane abscissa, y is image plane ordinate, D is circular aperture diaphragm diameter, J1() Is a first-order Bessel function, lambda is the wavelength of monochromatic light, f is the focal length of the system, B is the central distance of the two circular hole diaphragms, and p is the axial distance between the measured sub-mirror and the reference sub-mirror. Definition (x)0,y0) Is the coordinate of the pupil plane, and the coordinates of the pupil plane,
Figure BDA0002591232410000032
is the normal of the measured sub-mirror and y0The included angle between the axes is set by the angle,
Figure BDA0002591232410000033
is the normal line and x of the measured sub-mirror0The angle between the axes.
And step two, performing Fourier transform on the point spread function PSF to obtain an optical transfer function OTF, wherein the optical transfer function OTF consists of a main peak and two side peaks, and the side peaks contain information of an inclination angle and an absolute distance, so that the inclination angle and the absolute distance can be conveniently calculated by using the side peaks in the subsequent steps three and six.
Performing Fourier transform on the formula (1) to obtain an optical transfer function OTF of the system:
Figure BDA0002591232410000034
wherein j is an imaginary unit, which is a convolution operation, (f)x,fy) Is the spatial frequency domain coordinate, f, of the point spread function PSFx＝x0/λf,fy＝y0/λf，OTFsub(fx,fy) Is the diffraction limited system optical transfer function OTF of a single circular aperture exit pupil:
Figure BDA0002591232410000035
where ρ is the radial coordinate in any direction on the frequency plane,
Figure BDA0002591232410000036
arccos () is an inverse cosine function.
Figure BDA0002591232410000041
Where circ () is a circular function.
From equation (2), the optical transfer function OTF consists of three parts,
Figure BDA0002591232410000042
Figure BDA0002591232410000043
is the main peak portion of the optical transfer function OTF,
Figure BDA0002591232410000044
and
Figure BDA0002591232410000045
Figure BDA0002591232410000046
is two side peak parts of the optical transfer function OTF, and is symmetrically distributed on two sides of the main peak. The peak portion of the optical transfer function OTF containsTilt angle and absolute distance information, so the tilt angle and absolute distance are calculated using the side peak portion of the optical transfer function OTF.
Selecting a side peak of the optical transfer function OTF to calculate the ratio of the real part of the imaginary part of the side peak to obtain the corresponding side peak phase transfer function PTFphCalculating PTFphAt fx、fyGradient values in two directions are used for calculating the x-direction pupil plane of the measured sub-lens0、y0The tilt angles tip and tilt in the direction realize large-range and high-precision measurement of the tilt angles.
Selecting a side peak of the optical transfer function OTF to obtain a ratio of the real part of the imaginary part of the OTF, and performing arc tangent calculation to obtain a corresponding PTFph：
Figure BDA0002591232410000047
Wherein ph represents a side peak.
PTFphAt fx、fyThe distribution in both directions changes with changes in the tilt angle. In PTFphCalculating PTF over one period of variation (. + -. pi)phAt fx、fyGradient values in two directions
Figure BDA0002591232410000048
Figure BDA0002591232410000049
The measured sub-mirrors are respectively at fx、fyTwo directions, i.e. pupil plane x0、y0The angle of inclination tip in the direction is
Figure BDA00025912324100000410
tilt is
Figure BDA00025912324100000411
Therefore, the wide-range and high-precision measurement of the inclination angle is realized.
And fourthly, performing approximate processing on the point spread function PSF in the integral form under the broad spectrum condition by using a differential summation method to obtain the point spread function PSF in the sectional summation form.
Due to PTFph is obtained by taking the inverse tangent of the ratio of real part of side peak imaginary part of the optical transfer function OTF, the tangent value has periodicity, and the value is obtained according to PTFph can only get absolute distance information of less than one wavelength, so the measurement of absolute distance is achieved by MTF. Under the broad spectrum condition, the system normalized point spread function PSF is:
Figure BDA0002591232410000051
where Δ λ is the spectral width, λ0Is the broad spectral center wavelength.
The integral is approximated by differential summation, and Δ λ is equally divided into n segments, each segment having a central wavelength λ1，λ2…λi…λnThe point spread function PSF was obtained as:
Figure BDA0002591232410000052
wherein, (x, y, λ)i) And the image plane coordinates correspond to different wavelength conditions.
And fifthly, carrying out Fourier transform on the point spread function PSF in a segmented summation mode under the broad spectrum condition to obtain an optical transfer function OTF under the broad spectrum condition.
Performing fourier transform on the formula (7) to obtain the optical transfer function OTF of the system:
Figure BDA0002591232410000053
wherein the content of the first and second substances,
Figure BDA0002591232410000056
is the spatial frequency domain coordinate, f, of the point spread function PSF under different wavelength correspondencesxi＝x0/λif,fyi＝y0/λif，
Figure BDA0002591232410000057
Is the diffraction limited system optical transfer function OTF of a single circular aperture exit pupil:
Figure BDA0002591232410000054
wherein the content of the first and second substances,
Figure BDA0002591232410000055
Figure BDA0002591232410000061
step six, selecting a side peak of the optical transfer function OTF to obtain a corresponding side peak modulation transfer function MTFphFor modulation transfer function MTFphAnd carrying out normalization processing, wherein the normalization factor is the peak value of the peak on the MTF side of the modulation transfer function under the condition that only the inclination angle error exists, namely the absolute distance is zero. Normalized MTFphMTF by piecewise quartic fittingphAnd (4) solving the absolute distance p value according to the obtained functional relation with the absolute distance p, so as to realize high-precision absolute distance measurement without being influenced by the inclination angle error.
Obtaining a corresponding modulation transfer function MTF by performing a modulus operation on one side peak of the optical transfer function OTFph，
Figure BDA0002591232410000062
Wherein ph represents a side peak.
From equation (11), it is known that the tilt angle has an effect on the modulation transfer function, and thus on the MTFphThe normalization processing can eliminate the influence of the inclination angle on the detection of the absolute distance. The normalization factor is that the peak of the modulation transfer function MTF side only has inclination angle error,i.e. the peak value at zero absolute distance
Figure BDA0002591232410000063
Obtaining modulation transfer function MTF by four times of fitting in segmentation after normalization processingnphThe functional relationship with the absolute distance p is:
Figure BDA0002591232410000064
wherein the MTFnphIs the normalized modulation transfer function.
The absolute distance, for MTF, can be directly calculated from equation (12)phAfter normalization processing, the calculation of the absolute distance is not affected by the inclination angle, so that high-precision measurement of the absolute distance is realized.
The invention also discloses a device for simultaneously measuring the inclination angle and the absolute distance based on the optical transfer function, which is used for realizing the method for simultaneously measuring the inclination angle and the absolute distance based on the optical transfer function. The diaphragm is placed on the conjugate surface of the reference sub-mirror, and two discrete round holes are formed in the diaphragm and respectively correspond to the two sub-mirrors. The part of the light beam emitted by the parallel light source irradiates the reference sub-mirror and is called as reference light; part of the light irradiates to the measured sub-mirror and is called as detection light; the reference light and the detection light pass through the collimating lens after being reflected by the telescope secondary mirror, then pass through two discrete round holes on the diaphragm respectively, and undergo interference diffraction through the focusing lens, so that interference diffraction fringes under the wide spectrum condition are formed and are imaged on the detector through the focusing lens.
A single-wavelength filter plate is added between a diaphragm hole and a focusing lens, a system interference diffraction fringe under the condition of monochromatic light is imaged on a detector, and the light intensity distribution acquired by the detector is the point spread function PSF under the condition of the monochromatic light of the system. And performing Fourier transform on the obtained point spread function PSF to obtain an optical transfer function OTF. Selecting a side peak of the optical transfer function OTF to calculate the ratio of the real part of the imaginary part of the OTF to obtain the corresponding sidePeak phase transfer function PTFphCalculating the phase transfer function PTFphThe inclination angle of the measured sub-mirror is calculated by utilizing the relation between the gradient value and the inclination angle, so that the large-range and high-precision measurement of the inclination angle is realized. And a single-wavelength filter is not added between the diaphragm hole and the focusing lens, the image on the detector is a system interference diffraction fringe under the wide spectrum condition, and the light intensity distribution acquired by the detector is a point spread function PSF under the system wide spectrum condition. Carrying out approximate processing of a differential summation method on the obtained point spread function PSF, then carrying out Fourier transformation to obtain an optical transfer function OTF, selecting one side peak of the optical transfer function OTF to obtain a corresponding side peak modulation transfer function MTFphFor modulation transfer function MTFphNormalized to obtain MTFnphObtaining MTF by piecewise quartic fittingnphAnd (4) solving an absolute distance value according to the obtained functional relation with the absolute distance, so as to realize high-precision measurement of the absolute distance without being influenced by the error of the inclination angle.
Has the advantages that:
1. the method for measuring the inclination angle by combining the centroid detection method and the PR method has the advantages that when the inclination angle is reduced to enable the reference mirror and the detection mirror to partially overlap spots imaged by infinite star points, the centroid detection method cannot accurately judge the centroid, the PR method needs to acquire point spread functions PSF at the positions before and after the focus, the process is complex, and more time is consumed. The method for simultaneously measuring the inclination angle and the absolute distance based on the optical transfer function only needs to calculate the ratio of the real part of the side peak imaginary part of the optical transfer function OTF of the system to obtain the PTFphBy PTFphThe inclination angle can be obtained by the relation with the inclination angle, and high measurement precision is ensured. The measuring precision of the invention reaches milli-second order, and is not limited by small inclination angle, and the measuring range is related to the light path setting parameter.
2. The influence of residual inclination angle on absolute distance measurement is not eliminated by the conventional methods such as a Fizeau interferometry method, and the method for simultaneously measuring the inclination angle and the absolute distance based on the optical transfer function only needs to obtain the MTF by performing side peak modulus extraction on the optical transfer function OTF of a systemphFor MTFphNormalization processing is carried out, and MTF after normalization processingphThe absolute distance is obtained through the relation with the absolute distance p, large-range and high-precision measurement of the absolute distance is achieved, the influence of residual inclination angles on the absolute distance measurement can be eliminated, the measurement precision can reach the nanometer level, and the measurement range can reach the coherence length of a light source.
3. The invention discloses a method for simultaneously measuring an inclination angle and an absolute distance based on an optical transfer function, which can obtain a phase transfer function PTF of a side peak through an optical transfer function OTF of a systemphAnd modulation transfer function MTFphBy PTFphNormalized MTF and the sum of tilt anglesnphThe relation between the system inclination angle and the absolute distance can be calculated, the system inclination angle and the absolute distance are obtained, the two errors are measured without influencing each other, the method is simple and fast, the device is simple and easy to build, and large-range, high-precision and high-efficiency simultaneous measurement of the system inclination angle and the absolute distance is achieved.
Drawings
FIG. 1 is a schematic diagram of an optical path for measuring a common phase error of a blocking mirror;
FIG. 2 is a point spread function of the system;
FIG. 3 is a phase transfer function of the system;
FIG. 4 is a normalized modulation transfer function of the system;
FIG. 5 is a graph showing a relationship between a set value and a measured value of tilt tip when p is 126.56nm and a tilt angle is measured in a range of 0 to 1.06 arcsec;
FIG. 6 is an error curve of a set value and a measured value of a tilt tip when p is 126.56nm and a tilt angle measurement range is 0 to 1.06 arcsec;
FIG. 7 is a graph showing a relationship between a set value and a calculated value of an absolute distance p when the inclination angle is 3.7mas and the absolute distance measurement range is 0 to 195 μm;
FIG. 8 is a graph showing the error between the set value and the calculated value of the absolute distance p when the tilt angle is 3.7mas and the absolute distance measurement range is 0 to 195 μm;
FIG. 9 is a graph showing the error between the set value and the calculated value of the absolute distance p when the tilt angle is 3.7mas and the absolute distance measurement range is 0 to 3.164 μm;
FIG. 10 is a flowchart of a method for simultaneously measuring a tilt angle and an absolute distance based on an optical transfer function according to the present disclosure.
Wherein, 1-telescope secondary environment; 2-reference sub-mirror; 3-the sub-mirror to be tested; 4-a collimating lens; 5-diaphragm hole; 6-a focusing lens; 7-a detector; p is the axial distance between the measured sub-mirror and the reference sub-mirror; and delta t is the included angle between the normal direction of the measured sub-mirror and the optical axis.
Detailed Description
The invention is further illustrated by the following figures and examples.
Example 1:
the embodiment is used for measuring the common phase error of the segmented primary mirror telescope, and a light path schematic diagram taking two secondary mirrors as an example is shown in fig. 1. The flow chart is shown in fig. 10.
The initial common-phase error of the primary mirror of the segmented mirror telescope comprises the following steps: the inclination angle is in the order of arc second, the absolute distance is in the order of sub-millimeter, which respectively corresponds to the normal and y of the measured sub-mirror0Axis or x0The angle of inclination between the axes and the axial distance between the measured and reference sub-mirrors. When the telescope works, a light source of the telescope is starlight and can be regarded as parallel light, wherein one sub-mirror is used as a reference sub-mirror, plane waves are reflected by the reference sub-mirror and a measured sub-mirror, and the reflected light waves carry information of common phase errors between two adjacent sub-mirrors.
As shown in fig. 10, the method for simultaneously measuring an inclination angle and an absolute distance based on an optical transfer function disclosed in this embodiment includes the following specific steps:
step one, a diaphragm 5 is arranged on a conjugate surface of a reference sub-mirror, two discrete circular diaphragm holes are arranged on the diaphragm, light waves of a reference light path and a measuring light path are respectively collected, a detector is arranged on a focal plane of a focusing lens 6, a plane light wave carrying optical path difference information passes through the diaphragm holes and then is subjected to interference diffraction under the action of the focusing lens 6, and light intensity distribution detected on the detector 7 is a point spread function PSF, as shown in figure 1.
And secondly, adding a single-wavelength filter between the diaphragm 5 and the focusing lens 6, wherein the light intensity distribution acquired by the detector 7 is a point spread function PSF under the condition of single wavelength and contains common phase error information of an inclination angle and an absolute distance.
Known from fourier optics, under monochromatic light conditions, the normalized point spread function PSF is:
Figure BDA0002591232410000091
wherein (x, y) is image plane coordinate, x is image plane abscissa, y is image plane ordinate, D is circular aperture diaphragm diameter, J1() Is a first-order Bessel function, lambda is the wavelength of monochromatic light, f is the focal length of the system, B is the central distance of the two circular hole diaphragms, and p is the axial distance between the measured sub-mirror and the reference sub-mirror. Definition (x)0,y0) Is the coordinate of the pupil plane, and the coordinates of the pupil plane,
Figure BDA0002591232410000092
is the normal of the measured sub-mirror and y0The included angle between the axes is set by the angle,
Figure BDA0002591232410000093
is the normal line and x of the measured sub-mirror0The angle between the axes.
And step three, performing Fourier transform on the point spread function PSF to obtain an optical transfer function OTF, wherein the optical transfer function OTF consists of a main peak and two side peaks, and the side peaks contain information of an inclination angle and an absolute distance, so that the inclination angle and the absolute distance can be conveniently calculated by using the side peaks in the subsequent steps four and seven.
Performing Fourier transform on the formula (1) to obtain an optical transfer function OTF of the system:
Figure BDA0002591232410000094
wherein j is an imaginary unit, which is a convolution operation, (f)x,fy) Is the spatial frequency domain coordinate, f, of the point spread function PSFx＝x0/λf,fy＝y0/λf，OTFsub(fx,fy) Is the diffraction limited system optical transfer function OTF of a single circular aperture exit pupil:
Figure BDA0002591232410000095
where ρ is the radial coordinate in any direction on the frequency plane,
Figure BDA0002591232410000096
arccos () is an inverse cosine function.
Figure BDA0002591232410000097
Where circ () is a circular function.
From equation (2), the optical transfer function OTF consists of three parts,
Figure BDA0002591232410000098
Figure BDA0002591232410000099
is the main peak portion of the optical transfer function OTF,
Figure BDA00025912324100000910
and
Figure BDA00025912324100000911
Figure BDA00025912324100000912
is two side peak parts of the optical transfer function OTF, and is symmetrically distributed on two sides of the main peak. The optical transfer function OTF side peak portion contains the tilt angle and absolute distance information, so the tilt angle and absolute distance are calculated using the side peak portion of the optical transfer function OTF.
Selecting a side peak of the optical transfer function OTF to calculate the ratio of the real part of the imaginary part of the side peak to obtain the corresponding side peak phase transfer function PTFphCalculating PTFphAt fx、fyGradient values in two directions are used for calculating the x-direction pupil plane of the measured sub-lens0、y0The tilt angles tip and tilt in the direction realize large-range and high-precision measurement of the tilt angles. Introducing an absolute distance of 126.56nm into the sub-mirror 3 to be measured, introducing a tilt angle with the stepping of 8.706mas and the range of 0-1.06 arcsec, and analyzing the relation between the setting error and the measurement error.
Selecting a side peak of the optical transfer function OTF to obtain a ratio of the real part of the imaginary part of the OTF, and performing arc tangent calculation to obtain a corresponding PTFph：
Figure BDA0002591232410000101
Wherein ph represents a side peak.
PTFphAt fx、fyThe distribution in both directions changes with changes in the tilt angle. In PTFphCalculating PTF over one period of variation (. + -. pi)phAt fx、fyGradient values in two directions
Figure BDA0002591232410000102
Figure BDA0002591232410000103
The measured sub-mirrors are respectively at fx、fyTwo directions, i.e. pupil plane x0、y0The angle of inclination tip in the direction is
Figure BDA0002591232410000104
tilt is
Figure BDA0002591232410000105
Therefore, the wide-range and high-precision measurement of the inclination angle is realized.
Introducing an absolute distance of 126.56nm into the sub-mirror 3 to be measured, introducing a tilt angle with the stepping of 8.706mas and the range of 0-1.06 arcsec, and analyzing the relation between the setting error and the measurement error. As shown in fig. 5, the abscissa indicates the actually measured tilt amount, and the ordinate indicates the introduced tilt amount, and it can be seen from the graph that the measured value of the tilt angle is very close to the set value. And comparing the set value and the calculated value of the inclination angle to obtain the measurement error of the method. FIG. 6 is an error curve of the set value and the measured value of the tilt tip in the range of 0 to 1.06arcsec, wherein the abscissa is the set value of the tilt angle, and the ordinate is the error of the set value and the calculated value of the tilt angle, so as to obtain the measurement precision of 2.468mas RMS.
And step five, removing a single-wavelength filter added between the diaphragm 5 and the focusing lens 6, wherein the light intensity distribution acquired by the detector 7 is a point spread function PSF under the broad spectrum condition. And (3) carrying out approximate processing on the point spread function PSF in the integral form under the wide spectrum condition by using a differential summation method to obtain the point spread function PSF in the sectional summation form.
Due to PTFphThe ratio of real part of side peak imaginary part of the optical transfer function OTF is obtained by taking inverse tangent, the tangent value has periodicity, and the method is based on PTFphOnly absolute distance information of less than one wavelength can be obtained, so the measurement of absolute distance is achieved by MTF. Under the broad spectrum condition, the system normalized point spread function PSF is:
Figure BDA0002591232410000106
where Δ λ is the spectral width, λ0Is the broad spectral center wavelength.
The integral is approximated by differential summation, and Δ λ is equally divided into n segments, each segment having a central wavelength λ1，λ2…λi…λnThe point spread function PSF was obtained as:
Figure BDA0002591232410000111
wherein, (x, y, λ)i) And the image plane coordinates correspond to different wavelength conditions.
And sixthly, performing Fourier transform on the point spread function PSF in a segmented summation mode under the broad spectrum condition to obtain an optical transfer function OTF under the broad spectrum condition.
Performing fourier transform on the formula (7) to obtain the optical transfer function OTF of the system:
Figure BDA0002591232410000112
wherein the content of the first and second substances,
Figure BDA0002591232410000116
is the spatial frequency domain coordinate, f, of the point spread function PSF under different wavelength correspondencesxi＝x0/λif,fyi＝y0/λif，
Figure BDA0002591232410000117
Is the diffraction limited system optical transfer function OTF of a single circular aperture exit pupil:
Figure BDA0002591232410000113
wherein the content of the first and second substances,
Figure BDA0002591232410000114
Figure BDA0002591232410000115
step seven, selecting a side peak of the optical transfer function OTF to obtain a corresponding side peak modulation transfer function MTFphFor modulation transfer function MTFphAnd carrying out normalization processing, wherein the normalization factor is the peak value of the peak on the MTF side of the modulation transfer function under the condition that only the inclination angle error exists, namely the absolute distance is zero. Normalized MTFphMTF by piecewise quartic fittingphAnd (4) solving the absolute distance p value according to the obtained functional relation with the absolute distance p, so as to realize high-precision absolute distance measurement without being influenced by the inclination angle error. To the measured sub-mirror 3And introducing an absolute distance p with the step size of 0.06328 mu m and the range of 0-195 mu m into an inclination angle of 3.7mas, and analyzing the relation between the setting error and the measurement error.
Obtaining a corresponding modulation transfer function MTF by performing a modulus operation on one side peak of the optical transfer function OTFph，
Figure BDA0002591232410000121
Wherein ph represents a side peak.
From equation (11), it is known that the tilt angle has an effect on the modulation transfer function, and thus on the MTFphThe normalization processing can eliminate the influence of the inclination angle on the detection of the absolute distance. The normalization factor is the peak value of the side peak of the modulation transfer function MTF under the condition that only the inclination angle error exists, namely the absolute distance is zero
Figure BDA0002591232410000122
Obtaining modulation transfer function MTF by four times of fitting in segmentation after normalization processingnphThe functional relationship with the absolute distance p is:
Figure BDA0002591232410000123
wherein the MTFnphIs the normalized modulation transfer function.
The absolute distance, for MTF, can be directly calculated from equation (12)phAfter normalization processing, the calculation of the absolute distance is not affected by the inclination angle, so that high-precision measurement of the absolute distance is realized.
An inclination angle of 3.7mas is introduced to the sub-mirror 3 to be tested, and then an absolute distance p with the step of 0.06328 mu m and the range of 0-195 mu m is introduced. Obtaining the normalized MTF of the system according to the normalization factor required by the methodnphThe MTF at this timenphSubstituting into equation (12) results in a calculated value for p. As shown in FIG. 7, the abscissa indicates the actually measured absolute distance p and the ordinate indicates the introduced absolute distance, from which the measured values and settings can be seenThe values are very close. And comparing the set value and the calculated value of p to obtain the measurement error of the method. When the inclination angle is 3.7mas and p ranges from 0 to 195 μm, the error curve of the set value and the calculated value of the inclination angle is distributed between +/-0.05 μm as shown in FIG. 8, and the RMS of the error of the set value and the calculated value of p is 0.0102 μm. As can be seen from fig. 8, when the value of p is less than 0.5 wavelength, the error is large, and the maximum error can reach 178 nm. To verify the measurement accuracy, the reduction introduces an error step size to measure the p-value over a range of 0.5 wavelengths. Introducing small p value error with the step of 0.006328 μm and the range of 0-3.164 μm, wherein the error curve of the set value and the calculated value of the inclination angle is shown in FIG. 9, the p value measurement error is extremely small in the range, and the RMS of the error of the set value and the calculated value of the obtained p is 9.6 multiplied by 10-9And mu m. The method is proved to ensure the measurement precision under the condition of small error, and the whole measurement precision can reach the nanometer level.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (1)

1. Method for simultaneously measuring an inclination angle and an absolute distance based on an optical transfer function, characterized in that: comprises the following steps of (a) carrying out,
step one, light waves emitted by a parallel light source are divided into two beams, the two beams enter a reference light path and a measurement light path respectively to obtain two beams of light waves with phase difference information, the two beams of light waves are focused on a focal plane to generate an interference-diffraction or diffraction phenomenon, and the light intensity distribution on the focal plane is a point spread function PSF; the phase difference information comprises an inclination angle and an absolute distance;
step two, carrying out Fourier transform on the point spread function PSF to obtain an optical transfer function OTF, wherein the optical transfer function OTF consists of a main peak and two side peaks, and the side peaks contain information of an inclination angle and an absolute distance, so that the inclination angle and the absolute distance can be conveniently calculated by utilizing the side peaks in the subsequent steps;
step three, selecting a side peak of the optical transfer function OTF to calculate the ratio of the real part of the imaginary part of the side peak to obtain the corresponding side peak phase transfer function PFFphCalculating PTFphAt fx、fyGradient values in two directions are used for calculating the x-direction pupil plane of the measured sub-lens0、y0The tilt angles tip and tilt in the direction realize large-range and high-precision measurement of the tilt angles;
performing approximate processing on the point spread function PSF in the integral form under the wide spectrum condition by using a differential summation method to obtain the point spread function PSF in the sectional summation form;
fifthly, carrying out Fourier transform on the point spread function PSF in a segmented summation mode under the broad spectrum condition to obtain an optical transfer function OTF under the broad spectrum condition;
step six, selecting a side peak of the optical transfer function OTF to obtain a corresponding side peak modulation transfer function MTFphFor modulation transfer function MTFphCarrying out normalization processing, wherein the normalization factor is the modulation transfer function MTFphThe peak value of the side peak under the condition that only the inclination angle error exists, namely the absolute distance is zero; normalized MTFphMTF by piecewise quartic fittingphThe function relation with the absolute distance p is obtained according to the obtained function relation, and high-precision absolute distance measurement which is not influenced by the error of the inclination angle is realized;
the first implementation method comprises the following steps:
known from fourier optics, under monochromatic light conditions, the normalized point spread function PSF is:
Figure FDA0003075684850000011
wherein (x, y) is image plane coordinate, x is image plane abscissa, y is image plane ordinate, D is circular aperture diaphragm diameter, J1() Is a first order Bessel function, and λ is a single colorThe optical wavelength, f is the focal length of the system, B is the central distance between two circular hole diaphragms, and p is the axial distance between the measured sub-mirror and the reference sub-mirror, namely the absolute distance p; definition (x)0,y0) Is the coordinate of the pupil plane, and the coordinates of the pupil plane,
Figure FDA0003075684850000012
is the normal of the measured sub-mirror and y0The included angle between the axes is set by the angle,
Figure FDA0003075684850000013
is the normal line and x of the measured sub-mirror0The included angle between the axes;
the second step is realized by the method that,
performing Fourier transform on the formula (1) to obtain an optical transfer function OTF of the system:
Figure FDA0003075684850000021
wherein j is an imaginary unit, which is a convolution operation, (f)x,fy) Is the spatial frequency domain coordinate, f, of the point spread function PSFx＝x0/λf,fy＝y0/λf，OTFsub(fx,fy) Is the diffraction limited system optical transfer function OTF of a single circular aperture exit pupil:
Figure FDA0003075684850000022
where ρ is the radial coordinate in any direction on the frequency plane,
Figure FDA0003075684850000023
arccos () is an inverse cosine function;
Figure FDA0003075684850000024
wherein, circ () is a circle function;
from equation (2), the optical transfer function OTF consists of three parts,
Figure FDA0003075684850000025
Figure FDA0003075684850000026
is the main peak portion of the optical transfer function OTF,
Figure FDA0003075684850000027
and
Figure FDA0003075684850000028
two side peak parts of the optical transfer function OTF are symmetrically distributed on two sides of the main peak; the side peak portion of the optical transfer function OTF contains the tilt angle and absolute distance information, so the tilt angle and absolute distance are calculated using the side peak portion of the optical transfer function OTF;
the third step is to realize the method as follows,
selecting a side peak of the optical transfer function OTF to obtain a ratio of the real part of the imaginary part of the OTF, and performing arc tangent calculation to obtain a corresponding PTFph：
Figure FDA0003075684850000029
Wherein ph represents a side peak;
PTFphat fx、fyThe distribution in the two directions changes along with the change of the inclination angle; in PTFphCalculating PTF over one period of variation (. + -. pi)phAt fx、fyGradient values in two directions
Figure FDA00030756848500000210
Figure FDA00030756848500000211
The measured sub-mirrors are respectively at fx、fyTwo directions, i.e. pupil plane x0、y0The angle of inclination tip in the direction is
Figure FDA00030756848500000212
tilt is
Figure FDA00030756848500000213
Thereby realizing the large-range and high-precision measurement of the inclination angle;
the implementation method of the fourth step is that,
due to PTFphThe ratio of real part of side peak imaginary part of the optical transfer function OTF is obtained by taking inverse tangent, the tangent value has periodicity, and the method is based on PTFphAbsolute distance information can only be obtained for less than one wavelength, so the absolute distance measurement passes the MTFphThe implementation is carried out;
under the broad spectrum condition, the system normalized point spread function PSF is:
Figure FDA0003075684850000031
where Δ λ is the spectral width, λ0Is the broad spectral center wavelength;
the integral is approximated by differential summation, and Δ λ is equally divided into n segments, each segment having a central wavelength λ1，λ2…λi…λnThe point spread function PSF was obtained as:
Figure FDA0003075684850000032
wherein, (x, y, λ)i) The image plane coordinates correspond to the different wavelength conditions;
the fifth step is to realize that the method is that,
performing fourier transform on the formula (7) to obtain the optical transfer function OTF of the system:
Figure FDA0003075684850000033
wherein the content of the first and second substances,
Figure FDA0003075684850000034
is the spatial frequency domain coordinate of the point spread function PSF corresponding to different wavelengths,
Figure FDA0003075684850000035
Figure FDA0003075684850000036
is the diffraction limited system optical transfer function OTF of a single circular aperture exit pupil:
Figure FDA0003075684850000037
wherein the content of the first and second substances,
Figure FDA0003075684850000038
Figure FDA0003075684850000041
the sixth realization method comprises the following steps of,
obtaining a corresponding modulation transfer function MTF by performing a modulus operation on one side peak of the optical transfer function OTFph，
Figure FDA0003075684850000042
Wherein ph represents a side peak;
from equation (11), it is known that the tilt angle has an effect on the modulation transfer function, and thus on the MTFphThe normalization processing is carried out, so that the influence of the inclination angle on the detection of the absolute distance can be eliminated; the normalization factor is the modulation transfer function MTFphSide peaks where only the angle of inclination is presentError, i.e. peak value with zero absolute distance
Figure FDA0003075684850000043
Obtaining modulation transfer function MTF by four times of fitting in segmentation after normalization processingnphThe functional relationship with the absolute distance p is:
Figure FDA0003075684850000044
wherein the MTFnphIs the normalized modulation transfer function;
the absolute distance, for MTF, can be directly calculated from equation (12)phAfter normalization processing, the calculation of the absolute distance is not influenced by the inclination angle, so that high-precision measurement of the absolute distance is realized;
the device comprises a parallel light source, a reference sub-mirror, a measured sub-mirror, a spectroscope, a diaphragm, a single-wavelength filter, a focusing lens and a detector; wherein the diaphragm is arranged on the conjugate surface of the reference sub-mirror, and two discrete round holes are arranged on the diaphragm and respectively correspond to the two sub-mirrors; the part of the light beam emitted by the parallel light source irradiates the reference sub-mirror and is called as reference light; part of the light irradiates to the measured sub-mirror and is called as detection light; the reference light and the detection light pass through the collimating lens after being reflected by the telescope secondary mirror, then pass through two discrete round holes on the diaphragm respectively, and undergo interference diffraction through the focusing lens to form interference diffraction fringes under the wide spectrum condition, and the interference diffraction fringes are imaged on the detector through the focusing lens;
adding a single-wavelength filter plate between the diaphragm hole and the focusing lens, imaging a system interference diffraction fringe on the detector under the condition of monochromatic light, and acquiring light intensity distribution by the detector, namely a point spread function PSF under the condition of the monochromatic light of the system; carrying out Fourier transform on the obtained point spread function PSF to obtain an optical transfer function OTF; selecting a side peak of the optical transfer function OTF to calculate the ratio of the real part of the imaginary part of the side peak to obtain the corresponding side peak phase transfer function PTFphCalculating the phase transfer function PTFphThe inclination angle of the measured sub-mirror is calculated by utilizing the relation between the gradient value and the inclination angle, so that the large-range and high-precision measurement of the inclination angle is realized; a single-wavelength filter is not added between the diaphragm hole and the focusing lens, the image on the detector is a system interference diffraction fringe under the wide spectrum condition, and the light intensity distribution acquired by the detector is a point spread function PSF under the system wide spectrum condition; carrying out approximate processing of a differential summation method on the obtained point spread function PSF, then carrying out Fourier transformation to obtain an optical transfer function OTF, selecting one side peak of the optical transfer function OTF to obtain a corresponding side peak modulation transfer function MTFphFor modulation transfer function MTFphNormalized to obtain MTFnphObtaining MTF by piecewise quartic fittingnphAnd (4) solving an absolute distance value according to the obtained functional relation with the absolute distance, so as to realize high-precision measurement of the absolute distance without being influenced by the error of the inclination angle.
CN202010696646.3A 2020-07-20 2020-07-20 Method for simultaneously measuring inclination angle and absolute distance based on optical transfer function Active CN111811474B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010696646.3A CN111811474B (en) 2020-07-20 2020-07-20 Method for simultaneously measuring inclination angle and absolute distance based on optical transfer function

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010696646.3A CN111811474B (en) 2020-07-20 2020-07-20 Method for simultaneously measuring inclination angle and absolute distance based on optical transfer function

Publications (2)

Publication Number Publication Date
CN111811474A CN111811474A (en) 2020-10-23
CN111811474B true CN111811474B (en) 2021-07-09

Family

ID=72866413

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010696646.3A Active CN111811474B (en) 2020-07-20 2020-07-20 Method for simultaneously measuring inclination angle and absolute distance based on optical transfer function

Country Status (1)

Country Link
CN (1) CN111811474B (en)

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105806240A (en) * 2016-05-25 2016-07-27 北京理工大学 Method capable of simultaneously measuring multiple absolute distances based on optical transfer functions
CN109668526A (en) * 2019-01-29 2019-04-23 北京理工大学 The method at the high-acruracy survey inclination angle based on optical transfer function
CN111220971A (en) * 2019-10-22 2020-06-02 北京理工大学 Method for measuring absolute distance with high precision without being influenced by inclination angle
EP3680851A1 (en) * 2019-01-09 2020-07-15 Agfa Nv Method and system to calculate the point spread function of a digital image detector system based on a mtf modulated quantum-noise measurement

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR3024539B1 (en) * 2014-08-01 2016-07-22 Morpho METHOD FOR ESTIMATING THE DISTANCE OF AN OBJECT TO AN IMAGING SYSTEM

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105806240A (en) * 2016-05-25 2016-07-27 北京理工大学 Method capable of simultaneously measuring multiple absolute distances based on optical transfer functions
EP3680851A1 (en) * 2019-01-09 2020-07-15 Agfa Nv Method and system to calculate the point spread function of a digital image detector system based on a mtf modulated quantum-noise measurement
CN109668526A (en) * 2019-01-29 2019-04-23 北京理工大学 The method at the high-acruracy survey inclination angle based on optical transfer function
CN111220971A (en) * 2019-10-22 2020-06-02 北京理工大学 Method for measuring absolute distance with high precision without being influenced by inclination angle

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
Phasing piston error in segmented telescopes;JIANG JUNLUN等;《OPTICS EXPRESS》;20160822;第24卷(第17期);全文 *
Tip–tilt error for extremely large segmented telescopes: detailed theoretical point-spread-function analysis and numerical simulation results;Natalia Yaitskova等;《Optical Society of America》;20020731;第19卷(第7期);全文 *

Also Published As

Publication number Publication date
CN111811474A (en) 2020-10-23

Similar Documents

Publication Publication Date Title
Sykora et al. Instantaneous measurement Fizeau interferometer with high spatial resolution
CN108507495B (en) Free-form surface detection method based on reverse Hartmann detection
CN109668526B (en) High-precision inclination angle measuring method based on optical transfer function
US20190271532A1 (en) Method for measuring a spherical-astigmatic optical surface
Trivedi et al. Measurement of focal length using phase shifted moiré deflectometry
Miks et al. Dependence of camera lens induced radial distortion and circle of confusion on object position
CN104655053A (en) Device and method for measuring curvature radius of spherical mirror based on pinhole type point diffraction interferometer
CN111307063A (en) Method for eliminating symbol ambiguity problem in single-amplitude interference fringe wave surface recovery
Yang et al. Radius of curvature measurement based on wavefront difference method by the point diffraction interferometer
Huang et al. X-ray mirror metrology using SCOTS/deflectometry
Guzhov et al. Eliminating phase-shift errors in interferometry
CN113820104A (en) Method for adjusting interference inspection light path of meniscus lens
CN111811474B (en) Method for simultaneously measuring inclination angle and absolute distance based on optical transfer function
CN111220971B (en) Method for measuring absolute distance with high precision without being influenced by inclination angle
CN112013972B (en) Shearing quantity calibration device and method for transverse shearing interference wavefront sensor
JP2002213930A (en) Method of measuring shape, and method of manufacturing highly precise lens
US10705437B2 (en) Metrology method and apparatus, computer program and lithographic system
EP3470923A1 (en) Metrology method
Han et al. The absolute flatness measurements of two aluminum coated mirrors based on the skip flat test
Doerband et al. Characterizing lateral resolution of interferometers: the Height Transfer Function (HTF)
Chu et al. Measuring the phase transfer function of a phase-shifting interferometer
Wang et al. Modified polarization point diffraction interferometer with extended measurable NA for spherical surface testing
Burge et al. Optical alignment with computer-generated holograms
Kim Development of aspheric surface profilometry using curvature method
WO2020007588A1 (en) Sensor apparatus and method for lithographic measurements

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant