CN111220971B - Method for measuring absolute distance with high precision without being influenced by inclination angle - Google Patents
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- CN111220971B CN111220971B CN201911231272.1A CN201911231272A CN111220971B CN 111220971 B CN111220971 B CN 111220971B CN 201911231272 A CN201911231272 A CN 201911231272A CN 111220971 B CN111220971 B CN 111220971B
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- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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- G01S11/12—Systems for determining distance or velocity not using reflection or reradiation using electromagnetic waves other than radio waves
Abstract
The invention relates to a high-precision absolute distance measuring method which is not influenced by an inclination angle, in particular to a high-precision and large-range absolute distance measuring method which eliminates the influence of a small inclination angle, and belongs to the technical field of photoelectric measurement. Two discrete diaphragm holes are arranged on the diaphragm and are used for respectively collecting light waves of a reference light path and a measuring light path, an Optical Transfer Function (OTF) of the system is obtained through light intensity distribution on a focal plane of the system, namely a Point Spread Function (PSF), then a Modulation Transfer Function (MTF) of the system is obtained by taking a model of the OTF, an MTF side peak value under the condition that only a residual inclination angle exists is taken as a normalization factor, the MTF side peak value when the absolute distance and the residual inclination angle exist simultaneously is normalized, and a Function relation between the normalized MTF and the absolute distance is obtained, so that the influence of the residual inclination angle is eliminated, and the high-precision and large-range measurement of the absolute distance is realized.
Description
Technical Field
The invention relates to a high-precision absolute distance measuring method which is not influenced by an inclination angle, is based on an optical transfer function and is not influenced by a residual inclination angle, is a high-precision and large-range absolute distance measuring method which is not influenced by a small inclination angle, and belongs to the technical field of photoelectric measurement.
Background introduction
In the fields of astronomy, precision measurement and the like, high-precision measurement at a nanometer level is often required to be realized on a tiny step height (such as the absolute distance between a reference sub-mirror and a measured sub-mirror along the optical axis direction), and the measured step height is used for obtaining an image with high resolution. For the measurement of the step height, scholars at home and abroad have conducted a lot of research. For the measurement of the step height, there are two major types of contact measurement methods and non-contact measurement methods, the contact measurement method is also called as a direct measurement method, and can be realized by using a three-coordinate machine, but the method has long measurement time and is easy to damage the surface of an object; an Optical detection method is commonly used in the non-contact measurement method, the actual step height to be measured by the Optical detection method corresponds to an Optical Path Difference (OPD) between a reference Optical Path and a measurement Optical Path, for a 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. The interferometry in the optical detection method is commonly used for measuring the height and the inclination angle of a tiny step, and the method can be used for detecting the common phase error (absolute distance and inclination angle) of a segmented primary mirror telescope.
In 2012, Anthony c, cheetham and Peter g, tutlill, et al, propose a fizeau interferometry method to implement common phase error (absolute distance, tilt angle) 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, a plurality of iterations are performed by using interference fringe information in the PSF and a least square method, and Δ L and Δ t of a measured sub-mirror are solved under the condition that only Δ L and Δ t exist respectively, thereby implementing high-precision measurement of absolute distance and tilt angle, the method can achieve a maximum detection range of a height of a micro-step of 150 μm, the precision is 0.75nm, the maximum detection range of a tilt angle of 0.5 areconcds, and the precision is 3.7mas (Anthony c, peter G.Tuthill, Anand Sivaramakrishnan, and James P.Lloyd, "Fizeau interactive phasing of segmented mirrors," Opt.Express 20, 29457-.
In 2015, belgium space center j.f.simar et al proposed a new method for common phase error detection of segmented primary mirror telescopes. The specific implementation method comprises the following steps: when only delta L exists between the measured sub-mirror and the reference sub-mirror, discrete diaphragm holes are arranged in the light path to respectively collect the sub-light waves reflected by the adjacent sub-mirrors, the PSF of the system can be obtained at the focal plane of the subsequent optical system, and the non-normalized side peak MTF of the system can be obtained according to the Fourier opticsphThen normalizing the obtained product to obtain
Wherein: MTFcphThe MTF central peak value is shown, and n is the number of the sub-mirrors. Obtaining MTF by Gaussian fittingnphFunctional relationship with OPD by measuring MTFnphMeasurement of the co-phase error can be achieved (see: Simar J F, Stockman Y, Surdej J. Single wavelet Co. left phase In Segmented clocks [ J)].Applied Optics,2015, 54(5):1118-1123.)。
In 2016, Zhaowei and Jiang Jun Lun, the university of Beijing Physician, proposed a high-precision absolute distance measurement method based on an optical transfer function, and the basic principle is as follows: the method comprises the steps that discrete diaphragm holes are arranged in a light path, when only absolute distance delta L exists between a measured sub-mirror and a reference sub-mirror, sub-light waves reflected by adjacent sub-mirrors are collected respectively, the PSF of a system is obtained at the focal plane of a subsequent optical system, the MTF of the system is obtained by utilizing Fourier optics and the PSF of the system, the functional relation between the side peak value of the normalized MTF and the absolute distance delta L is obtained through four-time fitting in a segmenting 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 accuracy can reach the nanometer level (see: Jiang Junlun and Zhao Weirii, "pharmaceutical prism error in segmented descriptors," Opt. Express 24, 19123-.
In summary, the current high-precision and large-range measurement method for the absolute distance is only suitable for the environment where only the absolute distance exists, and does not solve the influence caused by the residual tilt angle, so the detection of the absolute distance is still interfered by the residual tilt angle.
Disclosure of Invention
The invention aims to solve the defect that the influence of a residual inclination angle on absolute distance detection is not eliminated by the existing method, and provides a method for measuring the absolute distance with high precision without being influenced by the inclination angle. The method obtains an Optical Transfer Function (OTF) of the system according to a Point Spread Function (PSF) which is light intensity distribution on a focal plane of the system, further obtains an Optical Modulation Transfer Function (MTF) of the system by performing model selection on the OTF, takes an MTF side peak value under the condition that only an inclination angle delta t exists as a normalization factor, normalizes the MTF side peak value when the absolute distance delta L and the inclination angle delta t exist simultaneously, and obtains a functional relation between the normalized MTF and the delta L, thereby eliminating the influence of a residual inclination angle and realizing high-precision and large-range measurement on the absolute distance.
The purpose of the invention is realized by the following technical scheme.
The method for measuring the absolute distance with high precision without being influenced by the inclination angle comprises the following specific steps:
step one, light waves emitted by a broad spectrum light source are divided into two beams which respectively enter a reference light path and a measurement light path; two light waves with inclination angle delta t information generate interference-diffraction or diffraction phenomenon and then focus on a focal plane, and the light intensity distribution on the focal plane is a point spread function PSF.
According to Fourier optics, under a wide spectrum condition, the PSF expression is as follows:
wherein (x, y) is the image plane coordinate, (x, y, λ)i) Is the corresponding image plane coordinate, lambda, under the condition of different wavelengthsiIs the wavelength of the broad spectrum, Δ λ is the spectral width, n is the number of equal parts of the broad spectrum, D is the diameter of the circular aperture, J1() Is a first-order Bessel function, x is the image plane abscissa, y is the image plane ordinate, f is the focal length, and B is the distance between the centers of the two circular aperture diaphragm holes. Let (x)0,y0) As pupil plane coordinates, a is the discrete aperture x0Angle of inclination information introduced in the direction of the optical axis after rotation of the shaft, b being the discrete hole around y0Tilt angle information introduced in the direction of the optical axis after the shaft is rotated.
Step two, Fourier transform is carried out on the formula (1) to obtain an optical transfer function OTF expression as follows,
wherein λ is0Is the center wavelength of the broad spectrum, j is the imaginary unit, (f)x,fy) Is the spatial frequency domain coordinate of the PSF, fx＝x0/λf,fy＝y0The/λ f, e exponential function contains the tilt angle information, OTFsub(fx,fy) OTF for a diffraction limited system with a single aperture circular exit pupil,
where ρ is the radial coordinate in any direction on the frequency plane,
from equation (2), the OTF consists of three parts,
is the main peak part of the OTF,
and
is two side peak parts of the OTF, and as can be seen from the formula (2), the main peak part and the side peak part of the OTF both contain inclination angle information, however, the main peak part also contains the optical transfer function OTF when the diffraction of the reference optical path is limitedsub(fx,fy) This part cannot contain tilt angle information
The separation makes it difficult to calculate the tilt angle from the main peak, while the side peak part of the OTF only contains tilt angle information, so we can calculate the tilt angle using the side peak part of the OTF more conveniently and quickly.
Step three, performing modulus operation on the side peak part of the OTF to obtain the corresponding modulation transfer function MTFph，
Wherein n is the number of equal parts of the broad spectrum, and ph represents a side peak.
Wherein the MTF0Modulation transfer function, MTF, of a single circular aperture with diffraction limit0＝Δλ|OTFsubL. It can be seen from equation (4) that the tilt angle has an effect on the modulation transfer function.
Step four, taking the formula (4) as a normalization factor, normalizing the peak value of the MTF side by using the formula (4) to eliminate the influence of the inclination angle delta t on the detection absolute distance delta L, and obtaining the functional relation between the MTF and the delta L by performing four times of piecewise fitting, wherein the function relation is as follows:
wherein the MTFnphIs the normalized modulation transfer function. The normalized modulation transfer function is not influenced by the inclination angle any more, thereby realizing high-precision measurement of absolute distance.
The device for realizing the method comprises the following steps: the device comprises a parallel light source, a reference sub-mirror, a measured sub-mirror, a diaphragm, a focusing lens and a detector, wherein the diaphragm is arranged on a 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 light beam emitted by the broad spectrum parallel light source is partially irradiated to 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 are reflected by the telescope secondary mirror, then pass through the collimating lens, then pass through two discrete round holes on the diaphragm and the focusing lens in sequence, and are subjected to interference diffraction after passing through the focusing lens, and formed interference diffraction fringes are imaged on the detector by the focusing lens.
Advantageous effects
1) Fizeau interferometry and the like do not eliminate the influence of the residual tilt angle on the measurement of the absolute distance, and the method for measuring the absolute distance with high precision, which is not influenced by the residual tilt angle and is based on the optical transfer function, can eliminate the influence of the residual tilt angle on the high-precision measurement of the absolute distance only by obtaining the OTF of the system.
2) The measurement precision is high, and after the influence of the residual inclination angle is eliminated, the measurement precision of the absolute distance obtained by adopting the four-time fitting in a segmentation mode can reach the nanometer level.
3) The measuring range is large, and after the influence of the residual inclination angle is eliminated, the measuring range of the absolute distance can reach the coherence length of a light source used for measurement.
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 system point spread function;
FIG. 3 is a modulation transfer function of the system;
FIG. 4 is a variation curve of the MTF side peak of the system under the influence of Δ t when only Δ t exists and the tilt angle ranges from 0 to 0.23arcsec sides;
FIG. 5 is a graph showing the relationship between the set value and the calculated value of Δ L when Δ t is 3.7 mas;
FIG. 6 is an error curve of the set value and the calculated value of Δ L when Δ t is 3.7 mas;
fig. 7 is a flow chart of the measurement process of the present invention.
Wherein, 1-telescope secondary mirror; 2-reference sub-mirror; 3-the sub-mirror to be tested; 4-a collimating lens; 5, a diaphragm; 6-a focusing lens; 7-detector.
Detailed Description
The invention is further illustrated by the following figures and examples.
Example 1
The method is used for measuring the common phase error of the segmented primary mirror telescope, and the light path schematic diagram is shown in figure 1. The flow chart is shown in fig. 7.
The initial common phase error of the primary mirror of the segmented mirror telescope comprises the following steps: the absolute distance is in the sub-millimeter magnitude, the residual inclination angle is in the milli-second magnitude, and the absolute distance corresponds to the axial distance between the measured sub-mirror and the reference sub-mirror, and the normal direction and the x of the measured sub-mirror0Axis or y0The angle of inclination between the axes.
The light source of the telescope is starlight which can be regarded as parallel light, wherein one sub-mirror is used as a reference sub-mirror, the plane wave is reflected by the reference sub-mirror and a measured sub-mirror, the reflected light wave carries the information of the common phase error between the two sub-mirrors, and then is reflected by the telescope sub-mirror 1, and is changed into two parallel light waves by the collimating lens 4. The conjugate surface of the primary mirror of the telescope system is provided with a diaphragm 5, 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 placed 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 the light intensity distribution detected on the detector 7 is PSF (particle swarm optimization), which is shown in figure 2.
Step two, when the optical path difference information only has an inclination angle Δ t, the PSF is known from fourier optics under a broad spectrum condition as follows:
step three, carrying out Fourier transform on the formula (1) to obtain the OTF of the system as follows,
step four, obtaining the corresponding modulation transfer function MTF by taking the module of the side peak part of the OTFph，
The MTF of the system is shown in fig. 3, an inclination angle with a step of 0.0015arcsec and a range of 0-0.23 arcsec is introduced into the sub-mirror 3 to be measured, the MTF side peak value changes after being affected by Δ t as shown in fig. 4, the abscissa is Δ t, and the ordinate is the MTF side peak value.
Step five, taking the formula (3) as a normalization factor, normalizing the peak value of the MTF side by using the formula (3), and obtaining a function relation corresponding to the normalized MTF and the delta L formula by performing piecewise four-time fitting, wherein the function relation is as follows:
introducing delta t into the sub-mirror 3 to be tested, wherein the delta t is 3.7mas, introducing delta L with the step size of 0.06328 μm and the range of 0-195 μm, obtaining normalized MTF by taking a formula (3) as a normalization factor, and substituting the MTF into a formula (4) to obtain a calculated value of the delta L, as shown in FIG. 5, the horizontal axis is the calculated value of the delta L, and the vertical axis is a set value of the delta L, which are very close to each other.
And step six, comparing the set value and the calculated value of the delta L to obtain the measurement error of the method. When the Δ t is 3.7mas and the Δ L ranges from 0 μm to 195 μm, an error curve of a set value and a calculated value of the Δ L is as shown in fig. 6, and it can be seen from the graph that when the value of the Δ L is less than 0.5 wavelength, the error is large, the maximum error can reach 178nm, in order to ensure the detection accuracy of the Δ L, the MTF and the PTF can be obtained by using the OTF of the system, the PTF is an interference factor item in the PSF, and the measurement accuracy is comparable to the accuracy of the interference measurement. And obtaining a constant term of PTF by means of Zernike polynomial fitting, and realizing high-precision detection of the delta L. When Δ L is greater than 0.5 wavelength, as Δ L increases gradually, Δ L is detected by the method of the present invention, and the error between the set value and the calculated value of Δ L is distributed between ± 0.05 μm as shown in fig. 6, and finally the RMS of the error between the set value and the calculated value of Δ L is 0.0102 μm.
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 (2)
1. A method for measuring absolute distance with high precision without being affected by an inclination angle, characterized in that: the method comprises the following specific steps:
step one, light waves emitted by a broad spectrum light source are divided into two beams which respectively enter a reference light path and a measurement light path; two beams of light waves with inclination angle delta t information generate interference-diffraction or diffraction phenomenon, and then are focused on a focal plane, and the light intensity distribution on the focal plane is a point spread function PSF;
according to Fourier optics, under a wide spectrum condition, the PSF expression is as follows:
wherein (x, y) is the image plane coordinate, (x, y, λ)i) Is the corresponding image plane coordinate, lambda, under the condition of different wavelengthsiIs the wavelength of the broad spectrum, Δ λ is the spectral width, n is the number of equal parts of the broad spectrum, D is the diameter of the circular aperture, J1() Is a first-order Bessel function, x is an image plane abscissa, y is an image plane ordinate, f is a focal length, and B is a central distance of two circular aperture diaphragm holes; let (x)0,y0) As pupil plane coordinates, a is the discrete aperture x0Angle of inclination information introduced in the direction of the optical axis after rotation of the shaft, b being the discrete hole around y0Tilt angle information introduced in the direction of the optical axis after the shaft is rotated;
step two, Fourier transform is carried out on the formula (1) to obtain an optical transfer function OTF expression as follows,
wherein λ is0Is the center wavelength of the broad spectrum, j is the imaginary unit, (f)x，fy) Is the spatial frequency domain coordinate of the PSF, fx＝x0/λf，fy＝y0The/λ f, e exponential function contains the tilt angle information, OTFsub(fx，fy) OTF being a diffraction limited System with a Single-Aperture circular exit pupil, OTFsub(fx，fy) As shown in equation (3):
where ρ is the radial coordinate in any direction on the frequency plane,
from equation (2), the OTF consists of three parts,
is the main peak part of the OTF,
and
is two side peak parts of the OTF, and as can be seen from the formula (2), the main peak part and the side peak part of the OTF both contain inclination angle information, however, the main peak part also contains the optical transfer function OTF when the diffraction of the reference optical path is limitedsub(fx，fy) The main peak portion not containing information on the inclination angle
The separation makes the calculation of the inclination angle by the main peak difficult, and the side peak part of the OTF only contains the inclination angle information, so the calculation of the inclination angle by the side peak part of the OTF is more convenient and faster;
step three, performing modulus operation on the side peak part of the OTF to obtain the corresponding modulation transfer function MTFph，
Wherein n is the number of equal parts of the broad spectrum, and ph represents a side peak;
wherein the MTF0Modulation transfer function, MTF, of a single circular aperture with diffraction limit0＝Δλ|OTFsubL, |; from equation (4), it can be seen that the tilt angle has an effect on the modulation transfer function;
step four, taking the formula (4) as a normalization factor, normalizing the peak value of the MTF side by using the formula (4) to eliminate the influence of the inclination angle delta t on the detection absolute distance delta L, and obtaining the functional relation between the MTF and the delta L by performing four times of piecewise fitting, wherein the function relation is as follows:
wherein the MTFnphIs the normalized modulation transfer function; the normalized modulation transfer function is not influenced by the inclination angle any more, thereby realizing high-precision measurement of absolute distance.
2. An apparatus for implementing the method of claim 1, wherein: the method comprises the following steps: the device comprises a telescope secondary mirror, a reference secondary mirror, a measured secondary mirror, a collimating lens, a diaphragm, a focusing lens and a detector; the light beam emitted by the broad spectrum parallel light source is partially irradiated to 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 are reflected by the telescope secondary mirror, then pass through the collimating lens, then pass through two discrete round holes on the diaphragm and the focusing lens in sequence, and are subjected to interference diffraction after passing through the focusing lens, and formed interference diffraction fringes are imaged on the detector by the focusing lens.
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