EP-4741758-A1 - WHITE LIGHT INTERFEROMETRY USING SINUSOIDAL INTERPOLATION AND SINUSOIDAL INTERPOLATION METHOD OF WHITE LIGHT INTERFEROMETRY

EP4741758A1EP 4741758 A1EP4741758 A1EP 4741758A1EP-4741758-A1

Abstract

Disclosed are: white light interferometry using sinusoidal interpolation in which interference fringes generated by measurement light and reflected light can be expressed naturally; and a sinusoidal interpolation of the white light interferometry. The white light interferometry using sinusoidal interpolation comprises: a charge coupled device (CCD) image sensor for capturing interference fringes to generate a plurality of interference fringe images; and an image analysis processor for accumulating the plurality of interference fringe images to generate a white light interference fringe signal (WLI fringe signal, I[n]).

Inventors

JO, AHJIN
LEE, Minjeung
KIM, HYOJU
AHN, BYOUNG-WOON
PARK, SANG-IL

Assignees

Park Systems Corp.

Dates

Publication Date: 20260513
Application Date: 20240704

Claims (20)

A white light interferometry using a sinusoidal interpolation comprising; a light source providing white light; a stage on which a sample is placed; a stage moving assembly for moving the stage in the direction of the path axis of the white light; a mirror having a reflective surface; a beam splitter for dividing a path of the white light provided from the light source into the sample side and the mirror side; a CCD (Charge Coupled Device) image sensor generating a plurality of interference fringe images by receiving measurement light reflected from the sample and reflected light reflected from the mirror from the beam splitter while the stage is moved in the path axis direction by the stage moving assembly and capturing interference fringes generated by the measurement light and the reflected light; and an image analysis processor for accumulating the plurality of interference fringe images to generate a white light interference fringe signal (WLI Fringe signal, I[n]), wherein the image analysis processor generates an interpolated white light interference fringe signal I[n]' by interpolating the generated white light interference fringe signal I[n] through sinusoidal interpolation..
The white light interferometry using a sinusoidal interpolation according to claim 1 characterized in that , the image analysis processor, when interpolating the white light interference fringe signal I[n] using a sinusoidal interpolation, generates an amplitude graph (Envelope, A[n]) and a phase graph (Phase, θ[n]) by dividing the white light interference fringe signal I[n] into components according to amplitude and phase, respectively, generates an interpolated amplitude graph A[n]' and an interpolated phase graph θ[n]' by interpolating the amplitude graph A[n] and the phase graph θ[n], respectively, through the sinusoidal interpolation, and generates the interpolated white light interference fringe signal I[n]' based on the interpolated amplitude graph A[n]' and the interpolated phase graph θ[n]'.
The white light interferometry using a sinusoidal interpolation according to claim 2 characterized in that , the image analysis processor, when generating the amplitude graph and the phase graph by dividing the white light interference fringe signal into components according to amplitude and phase, respectively, generates the amplitude graph (Envelope) by extracting components A[n] according to amplitude from the white light interference fringe signal I[n], and the phase graph (Phase) by extracting components θ[n] according to phase from the white light interference fringe signal I[n] based on the following Equation 1. A n Envelope = c n 2 + s n 2 1 / 2 θ n Phase = Atan s n , c n (wherein the A[n] is the Amplitude on Pixel of WLI Fringe of the white light interference fringe signal, and the θ[n] is the Phase on Pixel of WLI Fringe of the white light interference fringe signal, and the c[n] is the Cosine Component of WLI Fringe of the white light interference fringe signal calculated by c[n] = A[n] × cos(θ[n]), and the s[n] is the Sine Component of WLI Fringe of the white light interference fringe signal calculated by s[n] = A[n] × sin(θ[n]).
The white light interferometry using a sinusoidal interpolation according to claim 3 characterized in that , the image analysis processor, when generating the interpolated amplitude graph A[n]' and the interpolated phase graph θ[n]' by interpolating the amplitude graph A[n] and the phase graph θ[n] respectively through the sinusoidal interpolation, calculates the interpolation values (A[n+0.5], θ[n+0.5]) between the first measurement values (A[n], θ[n]) and the second measurement values (A[n+1], θ[n+1]) of the amplitude graph A[n] and the phase graph θ[n] respectively, based on the following Equation 2. A n + 0.5 = 0.5 * A n + A n + 1 θ n + 0.5 = 0.5 * θ n + θ n + 1 (wherein the A[n] is the Amplitude on Pixel of WLI Fringe of the white light interference fringe signal, and θ[n] is the Phase on Pixel of WLI Fringe of a white light interference fringe signal).
The white light interferometry using a sinusoidal interpolation according to claim 4 characterized in that , the image analysis processor, when generating the interpolated white light interference fringe signal I[n]' based on the interpolated amplitude graph A[n]' and the interpolated phase graph θ[n]', calculates the interpolated white light interference fringe signal I[n]' based on the each measurement values (A[n], θ[n]) of the amplitude graph A[n] and the phase graph θ[n] and each interpolation values (A[n+0.5], θ[n+0.5]) of the interpolated amplitude graph A[n]' and the interpolated phase graph θ[n]' based on the following Equation 3. I n = A n × cos θ n (wherein the A[n] is the Amplitude on Pixel of WLI Fringe of a white light interference fringe signal, and the θ[n] is the Phase on Pixel of WLI Fringe of a white light interference fringe signal).
A white light interferometry using a sinusoidal interpolation in which white light is irradiated to a sample and a mirror, respectively, and then obtained a shape of the sample by analyzing interference fringes generated by reflected measurement light and the reflected light, wherein the white light interferometry comprising: a CCD (Charge Coupled Device) image sensor for generating a plurality of interference fringe images by capturing the interference fringe; and an image analysis processor for generating a white light interference fringe signal (WLI Fringe signal, I[n]) by accumulating the plurality of interference fringe images, wherein the image analysis processor generates an interpolated white light interference fringe signal I[n]' by interpolating the generated white light interference fringe signal I[n] through the Sinusoidal Interpolation.
The white light interferometry according to claim 6 characterized in that , the image analysis processor, when interpolating the white light interference fringe signal I[n] using a sinusoidal interpolation, generates an amplitude graph (Envelope, A[n]) and a phase graph (Phase, θ[n]) based on the white light interference fringe signal I[n], generates an interpolated amplitude graph A[n]' and an interpolated phase graph θ[n]' by interpolating the amplitude graph A[n] and the phase graph θ[n] respectively using the sinusoidal interpolation, and generates the interpolated white light interference fringe I[n]' based on the interpolated amplitude graph A[n]' and the interpolated phase graph I[n]'.
The white light interferometry according to claim 7 characterized in that , the image analysis processor, when generating the amplitude graph A[n] and the phase graph θ[n] based on the white light interference fringe signal I[n], extracts components of amplitude and phase from the white light interference fringe signal I[n], respectively, to generate an amplitude graph A[n] and a phase graph θ[n] in linear.
The white light interferometry according to claim 8 characterized in that , the linear amplitude graph A[n] is an envelope contacting all the peak points of the white light interference fringe signal I[n] among the envelopes of the white light interference fringe signal I[n].
The white light interferometry according to claim 8 characterized in that , the image analysis processor, when interpolating the amplitude graph A[n] and the phase graph θ[n] respectively using the sinusoidal interpolation, calculates interpolation values (A[n+0.5], θ[n+0.5]) between the first measurement values (A[n], θ[n]) and the second measurement values (A[n+1], θ[n+1]) of the amplitude graph A[n] and the phase graph θ[n], wherein the interpolation values (A[n+0.5], θ[n+0.5]) is average value of the first measurement values (A[n], θ[n]) and the second measurement values (A[n+1], θ[n+1]).
The white light interferometry according to claim 10 characterized in that , the image analysis processor, when generating the interpolated white light interference fringe signal I[n]' based on the interpolated amplitude graph A[n]' and the interpolated phase graph θ[n]', generate the interpolated white light interference fringe signal I[n]' based on the measured value (A[n], θ[n]) of each the amplitude graph A[n] and the phase graph θ[n], and the each interpolation values (A[n+0.5], θ[n+0.5]) of the interpolated amplitude graph A[n]' and the interpolated phase graph θ[n]'.
The white light interferometry according to claim 11 characterized in that , the measured value (A[n], θ[n]) of each the amplitude graph A[n] and the phase graph θ[n], and the measured values (A[n]', θ[n]') of each the interpolated amplitude graph A[n]' and the interpolated phase graph θ[n]' have the same value each other.
The white light interferometry according to claim 12 characterized in that , the image analysis processor, when generating the interpolated white light interference fringe signal I[n]' based on the interpolated amplitude graph A[n]' and the interpolated phase graph θ[n]', determine the intensity value of the interpolated white light interference fringe signal I[n]' based on each the measured values (A[n], θ[n]) of interpolated amplitude graph A[n]' and the interpolated phase graph θ[n]' or the interpolation values (A[n+0.5], 0[n+0.5]), when the measured value A[n] of the interpolated amplitude graph A[n]' is maximum and the phase of the interpolated phase graph θ[n]' is 0°, if the measured value θ[n] or the interpolation value (θ[n+0.5]) of the interpolated phase graph is greater than -90° to less than 90°, the intensity values of the interpolated white light interference fringe signal I[n]' have a positive (+) value corresponding to the measured value A[n] or the interpolation value (A[n+0.5]) of the interpolated amplitude graph A[n]', if the measured value θ[n] or the interpolation value (θ[n+0.5]) of the interpolated phase graph is greater than 90° to less than 270°, the intensity values of the interpolated white light interference fringe signal I[n]' have a negative (-) value corresponding to the measured value A[n] or the interpolation value (A[n+0.5]) of the interpolated amplitude graph A[n]', and if the measured value θ[n] or the interpolation value (θ[n+0.5]) of the interpolated phase graph is at -90°, 90° or 270°, the intensity values of the interpolated white light interference fringe signal I[n]' has a value of 0.
A method of sinusoidal interpolation of a white light interferometry in which an image analysis processor interpolates a white light interference fringe signal I[n] through a sinusoidal interpolation to generate an interpolated white light interference fringe signal I[n]', the method of sinusoidal interpolation comprising: generating an amplitude graph (Envelope, A[n]) and a phase graph (Phase, θ[n]) based on the white light interference fringe signal I[n] by image analysis processor, generating an interpolated amplitude graph A[n]' and an interpolated phase graph θ[n]' by interpolating the amplitude graph A[n] and the phase graph θ[n] respectively through the sinusoidal interpolation by the image analysis processor, and generating the interpolated white light interference fringe signal I[n]' based on the interpolated amplitude graph A[n]' and the interpolated phase graph θ[n]' by the image analysis processor.
The method of sinusoidal interpolation of a white light interferometry according to claim 14, the generating an amplitude graph (Envelope, A[n]) and a phase graph (Phase, θ[n]) based on the white light interference fringe signal I[n] by the image analysis processor comprising: generating a linear phase graph θ[n] and the amplitude graph A[n], by extracting a component depending on the Amplitude and Phase of the white light interference fringe signal I[n], respectively, by the image analysis processor generating.
The method of sinusoidal interpolation of a white light interferometry according to claim 15, the generating a linear phase graph θ[n] and the amplitude graph A[n], by extracting a component depending on the Amplitude and Phase of the white light interference fringe signal I[n], respectively, by the image analysis processor comprising: generating the amplitude graph (Envelope) by extracting component A[n] depending on the amplitude of the white light interference fringe signal I[n] and generating phase graph (Phase) by extracting component θ[n] depending on the phase of the white light interference fringe signal I[n] the white light interference fringe signal I[n], based on the Equation 1 below by the image analysis processor. A n Envelope = c n 2 + s n 2 1 / 2 θ n Phase = Atan s n , c n . (wherein A[n] is the Amplitude on Pixel of WLI Fringe, and θ[n] is the Phase on Pixel of WLI Fringe, and c[n] is the Cosine Component of the WLI Fringe calculated by c[n] = A[n] × cos(θ[n], and the s[n] is the Sine Component of WLI Fringe calculated by s[n] = A[n] × sin(θ[n]).
The method of sinusoidal interpolation of a white light interferometry according to claim 14, the generating an interpolated amplitude graph A[n]' and an interpolated phase graph θ[n]' by interpolating the amplitude graph A[n] and the phase graph θ[n] respectively through the sinusoidal interpolation by the image analysis processor comprising: calculating interpolation values (A[n+0.5], θ[n+0.5]) between first measured values (A[n], θ[n]) and second measured values (A[n+1], θ[n+1]) of each of the amplitude graph A[n] and the phase graph θ[n] by the image analysis processor, wherein the interpolation values (A[n+0.5], θ[n+0.5]) are characterized by being average values of the first measurement values (A[n], θ[n]) and the second measurement values (A[n+1], θ[n+1]).
The method of sinusoidal interpolation of a white light interferometry according to claim 17, the calculating interpolation values (A[n+0.5], θ[n+0.5]) between first measured values (A[n], θ[n]) and second measured values (A[n+1], θ[n]) of each of the amplitude graph A[n] and the phase graph θ[n] by the image analysis processor comprising: calculating interpolation values (A[n+0.5], θ[n+0.5]) between first measured values (A[n], θ[n]) and second measured values (A[n+1], θ[n+1]) of each of the amplitude graph A[n] and the phase graph θ[n] based in Equation 2 below by the image analysis processor. A n + 0.5 = 0.5 * A n + A n + 1 θ n + 0.5 = 0.5 * θ n + θ n + 1 . (wherein A[n] is the Amplitude on Pixel of WLI Fringe, and θ[n] is the Phase on Pixel of WLI Fringe.)
The method of sinusoidal interpolation of a white light interferometry according to claim 14, the generating an interpolated white light interference fringe signal I[n]' based on the interpolated amplitude graph A[n]' and the interpolated phase graph θ[n]' by the image analysis processor comprising: generating the interpolated white light interference fringe signal I[n]' based on the measured values (A[n], θ[n]) of each of the amplitude graph A[n] and the phase graph θ[n], and the interpolation values (A[n+0.5], θ[n+0.5]) of each of the interpolated amplitude graph A[n]' and the interpolated phase graph θ[n]' by the image analysis processor.
The method of sinusoidal interpolation of a white light interferometry according to claim 19, the generating the interpolated white light interference fringe signal I[n]' based on the measured values (A[n], θ[n]) of each of the amplitude graph A[n] and the phase graph θ[n], and the interpolation values (A[n+0.5], θ[n+0.5]) of each of the interpolated amplitude graph A[n]' and the interpolated phase graph θ[n]' by the image analysis processor comprising: generating the interpolated white light interference pattern signal I[n]' based on the measured values (A[n], θ[n]) of each of the amplitude graph A[n] and the phase graph θ[n], and the interpolation values (A[n+0.5], θ[n+0.5]) of each the interpolated amplitude graph A[n]' and the interpolated phase graphs θ[n]' based on Equation 3 below by the image analysis processor. I n = A n × cos θ n (wherein A[n] is the Amplitude on Pixel of WLI Fringe, and θ[n] is the Phase on Pixel of WLI Fringe.)

Description

Technical Field The present invention relates to a white light interferometry using a Sinusoidal Interpolation and a sinusoidal interpolation method of the white light interferometry, more particularly, to a white light interferometry using a sinusoidal interpolation and a sinusoidal interpolation method of the white light interferometry in which the white light is irradiated to a sample and a mirror, respectively, and then interference fringes generated by reflected measurement light and the reflected light are interpolated through a sinusoidal interpolation. Background Art In recent fields of nanoscience, semiconductors, nanophysics, nanochemistry, nanomaterials, nanooptics, surface science, medical imaging, biology, biophysics, medical physics, or biomedical optics, there is a growing demand to measure three-dimensional shape information of samples with a three-dimensional nanostructures or micrometer structures. A white light interferometry that uses interference phenomenon of white light has been used to measure the three-dimensional shape information of the sample. A general white light interferometry uses a beam splitter that separates a white light source and generates a path toward the sample and the mirror, respectively. The white light irradiated to the sample and the mirror, respectively by the beam splitter is reflected and then recombined and transmitted to the CCD (charge-coupled device) image sensor, which captures interference fringe images by the combined light reflected from the sample and the mirror, respectively. The image analysis processor analyzes the interference fringe image captured by the CCD image sensor to generate 3D shape information of the sample. At this time, the sample is placed on the stage, and the stage is moved along the path axis (generally the Z-axis) of the light source by a separate driving assembly to generate a path difference between the sample side and the mirror side. The interference fringe image captured by the CCD image sensor forms different interference fringe images according to a change in the path difference between the sample side and the mirror side, and the image analysis processor generates three-dimensional shape information of the sample based on the interference fringes from which the different interference fringe images are accumulated. On the other hand, conventional white light interferometry has a problem in that the shape of the white light interference fringe (WLI Fringe) is expressed unnaturally according to the physically limited minimum movable length of the driving assembly that moves the stage to generate a path difference between the sample side and the mirror side, i.e., the Z Step Size. The problem due to the unnatural shape of the white light interference fringe (WLI Fringe) according to this limited Z Step Size has been solved by interpolating according to the Cubic Spline, but the Cubic Spline has a large amount of calculation, while the accuracy is low. Disclosure of Invention Technical Problem An object of the present invention for solving the above-described problem is to provide a white light interferometry using a sinusoidal interpolation, which can naturally express the shape of an interference fringe by interpolating an interference fringe generated by measurement light and reflected light that are reflected after white light split by a beam splitter is irradiated to a sample and a mirror, respectively, through sinusoidal interpolation, and a sinusoidal interpolation method of the white light interferometry. Another object of the present invention is to provide a white light interferometry using a sinusoidal interpolation capable of providing a fast and accurate interpolation by using a mathematical condition of a sinusoidal wavelength, and sinusoidal interpolation method of the white light interferometry. Solution to Problem In order to achieve the above-described object, a white light interferometry using a sinusoidal interpolation according to an embodiment of the present invention includes a light source providing white light, a stage on which a sample is placed, a stage moving assembly for moving the stage in a path axis direction of the white light, a mirror having a reflective surface, a beam splitter for dividing a path of the white light provided from the light source into the sample side and the mirror side, and a CCD (Charge Coupled Device) image sensor generating a plurality of interference fringe images by receiving measurement light reflected from the sample and reflected light reflected from the mirror from the beam splitter and capturing the interference fringes generated by the measurement light and reflected light while the stage is moved in the path axis direction by the stage movement assembly, and an image analysis processor for accumulating the plurality of interference fringe images to generate a white light interference fringe signal (WLI Fringe signal, I[n]), wherein the image analysis processor