CN105865370A - White-light scanning interferometry measurement method and system - Google Patents

Abstract

The invention relates to a white-light scanning interferometry measurement method and system. The system comprises a white-light scanning module, a calibration module, a fixed flat plate and a piezoelectric ceramic micro displacement platform, wherein the white-light scanning module comprises a white light source, a Kohler illumination system, a first beam splitter, a second beam splitter, a first microobjective, a second microobjective, an imaging lens, first, second, third, fourth and fifth plane mirrors and a first single-color black-and-white image sensor; the calibration module comprises a laser and a second single-color black-and-white image sensor. According to the system and the method, the central wavelength of a light source is not required to be calibrated, the calculation accuracy is not affected by enveloping shapes of interference signals, the anti-noise performance is good, and the method and the system can be widely applied to signal processing of white-light scanning interferometry measurement.

Description

A white light scanning interferometry method and system

technical field

The invention relates to the field of white light scanning interference three-dimensional shape measurement, in particular to a white light scanning interferometry method and system based on generalized correlation time delay estimation.

Background technique

As a three-dimensional shape measurement method, white light scanning interferometry is widely used in the three-dimensional shape measurement of microscopic objects and the surface roughness measurement of objects. With the development of precision manufacturing, it is necessary to measure the three-dimensional shape of some MEMS devices, semiconductor chips and other objects whose surface height jumps from hundreds of nanometers to hundreds of microns. Currently used probe-type measurement methods such as atomic force microscopes and spherometers have certain limitations and are not suitable for the three-dimensional shape measurement of such objects.

Moreover, the white light scanning interferometry technology makes up for the shortcoming that the phase jump between adjacent points of single-wavelength interferometry cannot obtain correct results when the phase jump is greater than half of the measured wavelength, and expands the range of single-wavelength interferometry. White light scanning interferometry technology not only has the advantages of non-contact, non-damage, high resolution, and high precision in single-wavelength interferometry, but also can accurately detect the surface itself with discontinuities and large gradient changes (greater than the recorded light wave). wavelength), such as objects with steps and defect hole structures. White light scanning interferometry has great significance and broad application prospects in the fields of three-dimensional shape detection, automatic processing, industrial inspection, product quality control and other fields.

White light scanning interferometry uses a wide-spectrum light source for illumination, which has a shorter coherence length than monochromatic light, so that interference fringes can only appear in a small spatial range. When the optical path difference between the measurement light and the reference light is zero, the interference signal has a maximum value, which is also called the zero optical path difference position. The zero optical path difference position represents the relative height information of the corresponding data points on the measured surface, and the relative heights of all data points are combined to form the overall shape of the tested surface. In white light scanning interferometry, the zero optical path difference positioning method is a research hotspot, and many methods have been proposed one after another. At present, the following methods are frequently used, namely: center of gravity method, Fourier transform method, Hilbert transform method, Fourier frequency domain analysis method, continuous wavelet transform method and white light phase shift interferometry. The center of gravity method locates the position of zero optical path difference by calculating the center of gravity of the white light interference signal, and its calculation speed is fast, but it can only be applied to symmetrical signals, and the calculation accuracy is greatly affected by noise. The Fourier transform method and the Hilbert transform method obtain the white light interference signal envelope through Fourier transform or Hilbert transform, and locate the zero optical path difference position by locating the extreme value of the envelope. Although these two types of methods can get envelope peaks, their anti-noise performance is weak. The Fourier frequency domain analysis method obtains the zero optical path difference position by Fourier transforming the white light interference signal to extract the phase. This algorithm has high calculation accuracy, but it needs to calibrate the center wavelength of the light source, and the calculation process is complicated. . The continuous wavelet transform method has high calculation accuracy and strong anti-noise ability, but it has certain requirements for the envelope shape of the interference signal. The white light phase-shift interferometry refers to the operation method of the single-wavelength phase-shift technique. This method is suitable for processing objects with smooth surfaces, and it will cause large errors when the phase-shift interval is not selected accurately.

The above-mentioned white light scanning interference zero optical path difference positioning methods all have their own limitations, and all of them have a certain scope of application. Therefore, designing a more accurate, simpler, and faster method of extracting the position of zero optical path difference in white light interference, and building a system with a simple optical path system and a simple interferogram acquisition operation process will help reduce the complexity of the measurement system. It is very meaningful to reduce measurement and calculation time, improve measurement accuracy and speed up measurement.

Contents of the invention

In view of this, it is necessary to propose a white light scanning interferometry method and system based on generalized correlation time delay estimation.

A white light scanning interferometry system, comprising a white light scanning module, a calibration module, a fixed plate, and a piezoelectric ceramic micro-displacement platform, the white light scanning module includes a white light source; a Koehler illumination system; a first beam splitter and a second beam splitter, the light emitted by the light source enters the first beam splitter after passing through the Koehler illumination system and is divided into object light and reference light; a first microscopic objective lens and a second microscopic objective lens; The first beam splitter is located between the Kohler illumination system and the second microscope objective lens; the imaging lens and the first, second, third, fourth, and fifth plane mirrors; a first monochrome black-and-white image sensor , the reference light is incident on the first plane mirror through the first microscopic objective lens, the object light is incident on the object to be measured through the second microscopic objective lens, and the object light and the reference light are reflected and then respectively pass through the first and second mirrors. The two microscopic objective lenses are converged behind the first beam splitter and interfere with each other, and the interference image is collected by the first monochrome black-and-white image sensor through the imaging lens. The calibration module includes a laser; a second monochromatic black and white image sensor. The laser light emitted by the laser is incident on the second beam splitter after passing through the fifth and fourth plane reflectors, and the laser light emitted by the second beam splitter interferes after passing through the second plane reflector and the third plane reflector. The generated interference fringes are collected by the second monochrome black-and-white image sensor; the fixed plate is used to fix the object to be measured; the piezoelectric ceramic micro-displacement platform is used to drive the object to be measured to be displaced.

A white light scanning interferometry method, which uses the above white light scanning interferometry system, the method comprising: collecting a series of white light interferograms and laser interferograms generated by objects to be measured, and using the laser interferograms to calculate the piezoelectric ceramic micro-displacement platform The step is to calibrate the scanning step of the white light scanning interference; select a point on the white light interferogram, and perform Fourier transform processing on the light intensity signal at this point; set the filter window to perform spectral filtering on the Fourier spectrum; The relative displacement of the light intensity signals of all pixel points and the zero optical path difference position of the light intensity signal of the selected pixel point; calculate the surface height of the object to be measured.

Compared with the prior art, in the process of calculating the signal time delay, the method and system regard the white light source as a signal source, and the interference intensity signals corresponding to different pixel points can be regarded as the same signals received by different receivers in space. Source noisy signal, through the process of calculating the time delay of the interference intensity signal between pixels to replace the process of separately transforming the interference intensity signal of each pixel to obtain the position of zero optical path difference, so that there is no need to calibrate the central wavelength of the light source, and The calculation accuracy is not affected by the envelope shape of the interference signal, and the anti-noise performance is strong, so it can be widely used in signal processing of white light scanning interferometry.

Description of drawings

In order to illustrate the technical solution of the present invention more clearly, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. As far as the skilled person is concerned, other drawings can also be obtained based on these drawings on the premise of not paying creative work.

FIG. 1 is a schematic structural diagram of a white light scanning interferometry system based on generalized correlation time delay estimation provided by the first embodiment of the present invention.

Fig. 2 is a schematic flow chart of a white light scanning interferometry method provided by the second embodiment of the present invention.

detailed description

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention.

first embodiment

As shown in FIG. 1 , the white light scanning interferometry system 500 provided by the first embodiment of the present invention includes a white light scanning module 100 , a calibration module 200 , a fixed plate 40 for fixing the object 30 to be measured, and a piezoelectric ceramic micro-displacement platform 50 , and a piezoelectric ceramic controller 60 .

Wherein said white light scanning module 100 comprises: a white light source 101, a Koehler illumination system 102, a first beam splitter 103 and a second beam splitter 104, a first microscope objective lens 105 and a second microscope An objective lens 106 , an imaging lens 107 , and a first monochromatic black and white image sensor 108 .

Wherein the calibration module 200 includes a laser 201; a first plane mirror 202, a second plane mirror 203, a third plane mirror 204, a fourth plane mirror 205, a fifth plane mirror 206, a second single color black and white image sensor 208.

On the Z-axis direction (first direction), the first beam splitter 103 is located between the Koehler illumination system 102 and the second microscope objective lens 106; in the Y-axis direction (the second direction, the Y-axis is perpendicular to Z axis), the first beam splitter 103 is located between the imaging lens 107 and the first microscope objective lens 105 .

In addition, in the Z-axis direction, the second microscope objective lens 106, the third plane mirror 204, the fixed plate 40 (and the object to be measured 30), and the piezoelectric ceramic micro-displacement platform 50 are located at the first beam splitter 103 and between the second beam splitter 104.

In this embodiment, the white light source 101 is a tungsten-halogen white light source. The laser 201 is a He-Ne laser with a wavelength of 632.8nm.

During operation, the light emitted by the tungsten-halogen white light source 101 is collimated by the Koehler illumination system 102 and then enters the first beam splitter 103, where it is divided into reference light L1 and object light L2.

The reference light L1 is incident on the first plane reflector 202 through the first microscopic objective lens 105, and the objective light L2 is incident on the object to be measured 30 through the second microscopic objective lens 106, after the object light L2 and the reference light L1 are reflected Then pass through the first and second microscopic objective lenses 105 and 106 , and then gather at the first beam splitter 103 to generate interference. The interference image is collected by the first monochromatic black and white image sensor 108 through the imaging lens 107 .

In this embodiment, the object to be measured 30 and the second plane mirror 203 are fixed by the fixed plate 40 , specifically, the object to be measured 30 and the second plane mirror 203 are respectively located on two sides of the fixed plate 40 . When in use, adjust the object 30 to be measured and the second plane mirror 203 to have the same vertical scanning displacement.

In this embodiment, except that the second plane mirror 203 is located on one side of the second beam splitter 104, on the other two sides of the second beam splitter 104, a third plane mirror 204, a fourth plane mirror 205 .

The laser light emitted by the He-Ne laser 201 is incident on the second beam splitter 104 after passing through the fifth and fourth plane reflectors 206, 205, and the laser light emitted by the second beam splitter 104 passes through the second plane reflector 203, the third Interference occurs behind the plane mirror 204 , and the interference fringes generated by it are collected by the second monochrome black-and-white image sensor 208 .

In this embodiment, the first and second beam splitters 103 and 104 are beam splitters with the same parameters; the magnification of the first microscopic objective lens 105 and the second microscopic objective lens 106 is 10, and the numerical aperture is 0.25 .

The first monochrome black-and-white image sensor 108 and the second monochrome black-and-white image sensor 208 are two image sensors with the same specification.

In addition, in this embodiment, the object 14 to be measured specifically adopts an OAMEM103 MEMS device produced by MEMSCAP.

When in use, in the white light scanning interference optical path, the piezoelectric ceramic micro-displacement platform 50 drives the object 30 to be measured to realize scanning in the vertical direction of the object 30 to be measured. The light reflected from points at different heights on the surface of the measurement object 30 reaches the zero optical path difference position of interference with the reference light at different times.

Thus, measuring the surface height of the object to be measured 30 is determined by extracting the position of zero optical path difference. If accurate measurement of the height of the object to be measured 30 is to be realized, it is necessary to accurately calibrate the displacement of the piezoelectric ceramic micro-displacement platform 50. The present invention In the method of laser interference calibration, the second plane mirror 203 and the object to be measured 30 are fixed by the fixed plate 40, and driven by the piezoelectric ceramic micro-displacement platform 50, the object to be measured 30 and the second plane mirror 203 have For the same vertical scanning displacement, only the vertical scanning displacement of the second plane mirror 203 can be measured, and the corresponding vertical scanning displacement of the object 30 to be measured can be obtained.

In the actual measurement process, every time the piezoelectric ceramic micro-displacement platform 50 (controlled by the piezoelectric ceramic micro-displacement controller 60) moves once, the first black-and-white image sensor 108 and the second black-and-white image sensor 208 will respectively collect an image. , the first black and white image sensor 108 collects white light interference fringes containing information about the object 30 to be measured, and the second black and white image sensor 208 collects laser interference fringes. By calculating the interference fringes collected by the second black-and-white image sensor 208 through the phase shift extraction algorithm, the phase shift of the interference fringes generated by each movement of the micro-displacement scanning stage can be obtained, thereby calculating the corresponding displacement. Using this method can achieve accurate calibration of the displacement of the piezoelectric ceramic micro-displacement scanning stage.

For the white light interference image collected by the first black-and-white image sensor 108, a pixel in the interference image is selected, the light intensity function of the pixel is extracted, and the light intensity functions of all pixels on the interference image are compared with the selected pixel in turn. The light intensity function of the point calculates the displacement difference through the generalized correlation time delay estimation algorithm, and the relative displacement between each pixel point and the zero optical path difference position of the selected pixel point can be obtained, so as to obtain the height of the object to be measured. The specific implementation Details will be given in the second embodiment.

second embodiment

Please refer to FIG. 2 together. The white light scanning interferometry method based on generalized correlation time delay estimation will be further described in conjunction with this embodiment in conjunction with the accompanying drawings and embodiments. In this method, the white light scanning described in the first embodiment is used. The measurement performed by the interferometric system 500 includes the following steps S101-S106.

Step S101, collect a series of white light interferograms and laser interferograms generated by the object to be measured, use the laser interferogram to calculate the step of the piezoelectric ceramic micro-displacement platform 50, and calibrate the scanning step of the white light scanning interference:

During specific measurement, a computer is used to drive the first monochrome black-and-white image sensor 108 and the second monochrome black-and-white image sensor 208 to simultaneously collect a series of white light interferograms and laser interferograms containing information about the object 30 to be measured.

Use the phase shift extraction algorithm (refer to the literature "Two step demodulation algorithm based on the orthogonality of diamond diagonal vectors" Applied Physics B 119:387–391 (2015)), calculate the laser interferogram, and obtain the measured object 30 piezoelectric ceramics The amount of phase shift of the interference fringes generated by each movement of the micro-displacement platform 50 is used to calibrate the scanning step of the white light scanning interference.

Step S102, select a point on the white light interferogram, and perform Fourier transform processing on the light intensity signal of the point:

For example, the light intensity signal I(x ₀ ,y ₀ ,z) of the selected pixel point (x ₀ ,y ₀ ) can be expressed as:

$\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, (x ₀ , y ₀ ) represents the coordinates of a single pixel point in the interferogram, z is the scanning position of the micro-displacer along the optical axis, h(x ₀ , y ₀ ) represents the surface height distribution of the measured object, a (x ₀ ,y ₀ ) is the background intensity, b(x ₀ ,y ₀ ) is the modulation amplitude, and g[zh(x ₀ ,y ₀ )] is the envelope function of the interference signal. λ ₀ is the center wavelength of the light source, and η is the random noise in the experiment. The effect of additional phase delay is ignored here.

Perform Fourier transform on the light intensity signal represented by formula (1):

In the formula, G(x ₀ , y ₀ , f _z ) is the Fourier transform spectrum of g(z).

Step S103, setting a filtering window to perform spectral filtering on the Fourier spectrum in step S102.

Specifically, the filter window H(f _z ) composed of two central bandpass rectangular filter windows is set to filter out the spectrum of the background term in formula (2) and eliminate part of the noise. This process can be expressed as:

Step S104 , extracting the light intensity signals of all pixels and performing transform filtering processing.

In this embodiment, the light intensity signals of all pixel points (x, y) can be expressed as:

$\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Perform Fourier transform on the light intensity signal represented by formula (4):

The result after filtering window H(f _z ) is:

Step S105, sequentially calculate the relative displacement of the light intensity signal of all pixels and the zero optical path difference position of the light intensity signal of the selected pixel:

Perform the following operations on formula (3) and formula (6):

where * denotes complex conjugation. Perform inverse Fourier transform on C(f _z ), get:

According to the principle of generalized correlation delay estimation, when When the maximum value is obtained, the That is, the relative displacement Δh between the zero optical path difference position between the (x, y) pixel point and the (x ₀ , y ₀ ) pixel point. The reason why the relative displacement Δh of the position of zero optical path difference can be obtained by obtaining the maximum value in formula (8) is as follows:

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&ap;</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; \&CircleTimes;</span>\\ <span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; \}</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

In the formula, Indicates convolution. From equation (8), we can put Expressed as:

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&ap;</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}^{<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; \&times;</span>\\ \mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; z</span>}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

Let Δh=h(x,y)-h(x ₀ ,y ₀ ) be the relative displacement of the zero optical path difference between the (x,y) pixel and the (x ₀ ,y ₀ ) pixel, then the formula (10) It can be expressed as:

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&ap;</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}^{<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&infin;</span>}}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; \&times;</span>\\ \mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; \}</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; z</span>}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

From (11), it can be concluded that when hour, Get the maximum value.

Step S106, calculating the surface height of the object to be measured:

The relative displacement between all the pixels and the zero optical path difference position of the selected pixel is calculated sequentially, which is equivalent to calculating the surface height of the object to be measured.

So far, through the method and system 500 proposed by the present invention, the three-dimensional shape of the object to be measured can be recovered from a series of collected white light interferograms.

To sum up, the method and system 500 regard the white light source 101 as a signal source in the process of calculating the signal delay, and the interference intensity signals corresponding to different pixel points can be regarded as the same signal received by different receivers in space. Source noisy signal, through the process of calculating the time delay of the interference intensity signal between pixels to replace the process of separately transforming the interference intensity signal of each pixel to obtain the zero optical path difference position, so that there is no need to calibrate the central wavelength of the white light source 101 , and the calculation accuracy is not affected by the envelope shape of the interference signal, and has strong anti-noise performance, and can be widely used in signal processing of white light scanning interferometry.

Compared with prior art, the present invention has following advantage:

(1) Compared with the single-wavelength measurement method, the method provided by the present invention can realize the measurement of objects with large gradient changes, greatly increases the measurement range, and expands the application field of interferometry.

(2) Compared with other white light scanning interference zero optical path difference positioning algorithms, the light intensity signal of a single pixel needs to be transformed and processed. The method proposed in the present invention converts the zero optical path difference position extraction process into a generalized correlation time delay estimation method To calculate the relative displacement of the interference signal between different pixels. In addition, the method proposed by the invention has simple operation, high calculation accuracy, strong anti-noise performance, no need to calibrate the central wavelength of the light source, and no requirement for the envelope shape of the white light interference signal.

(3) The system 500 used in the method of the present invention is simple, and the scanning step of the piezoelectric ceramic micro-displacement platform is calibrated by means of a single-wavelength laser phase shift, which is more accurate than the method of step calibration through electrical feedback.

The above description is a preferred embodiment of the present invention, and it should be pointed out that for those skilled in the art, without departing from the principle of the present invention, some improvements and modifications can also be made, and these improvements and modifications are also considered Be the protection scope of the present invention.

Claims (7)

1. A white light scanning interferometry system, characterized in that the system includes a white light scanning module, a calibration module, a fixed plate, and a piezoelectric ceramic micro-displacement platform, wherein the white light scanning module includes: a white light source; A Koehler lighting system; A first beam splitter and a second beam splitter, the light emitted by the light source enters the first beam splitter after passing through the Koehler illumination system and is divided into object light and reference light; A first microscopic objective lens and a second microscopic objective lens; the first beam splitter is located between the Kohler illumination system and the second microscopic objective lens; an imaging lens and first, second, third, fourth and fifth flat mirrors; and A first monochromatic black-and-white image sensor, the reference light is incident on the first plane reflector through the first microscopic objective lens, the object light is incident on the object to be measured through the second microscopic objective lens, and the object light and the reference light are reflected Then pass through the first and second microscopic objective lenses respectively, and then converge after the first beam splitter to generate interference, and the interference image is collected by the first monochrome black-and-white image sensor through the imaging lens; Wherein said calibration module comprises: a laser; A second monochrome black-and-white image sensor, the laser light emitted by the laser is incident on the second beam splitter mirror after passing through the fifth and fourth plane mirrors, and the laser light emitted by the second beam splitter passes through the second plane mirror, the fourth plane mirror Interference occurs behind the three-plane mirror, and the interference fringes generated by it are collected by the second monochrome black-and-white image sensor; Wherein the fixed plate is used to fix the object to be measured; the piezoelectric ceramic micro-displacement platform is used to drive the object to be measured to be displaced. 2. A white light scanning interferometry system according to claim 1, wherein the light source is a white light source of a tungsten halogen lamp. 3. A white light scanning interferometry system as claimed in claim 1, wherein the laser is a He-Ne laser. 4. The white light scanning interferometry system according to claim 1, in the first direction, the first beam splitter is located between the Koehler illumination system and the second microscope objective lens. 5. A kind of white light scanning interferometry system as claimed in claim 4, is characterized in that, in the second direction perpendicular to the first direction, the first beam splitter is located between the image lens and the first display. between microscopic lenses. 6. A white light scanning interferometry system as claimed in claim 1, wherein the magnification of the first microscopic objective lens and the second microscopic objective lens is 10, and the numerical aperture is 0.25. 7. A white light scanning interferometry method, which uses the white light scanning interferometry system according to claim 1-6, wherein the method comprises: Collect a series of white light interferograms and laser interferograms generated by the object to be measured, use the laser interferogram to calculate the step of the piezoelectric ceramic micro-displacement platform, and calibrate the scanning step of the white light scanning interference; Select a point on the white light interferogram, and perform Fourier transform processing on the light intensity signal of the point; Setting the filtering window to perform spectral filtering on the Fourier spectrum; Extract the light intensity signals of all pixels for transformation and filtering; Sequentially calculate the relative displacement of the light intensity signals of all pixels and the zero optical path difference position of the light intensity signal of the selected pixel; and Calculate the surface height of the object to be measured.