CN103983204B - Utilize the method for white noise PSD collimation optical surface profiler effective spatial resolution - Google Patents

Abstract

The present invention relates to the method that one utilizes Power Spectrum of White Noise density (PSD) collimation optical surface profiler effective spatial resolution.White noise can limit the spatial resolution of optical surface profiler, random signal or the stochastic process of its to be a kind of power spectrum density be constant, utilize this rule, the part meeting Power Spectrum of White Noise density (PSD) curved rule in test result is blocked, the corresponding effective spatial frequency range of remainder.The principle of the invention is simple, simple operation, do not need by other equipment, while detection smooth specimen, just can complete calibration operation, significantly reduce difficulty and the cost of optical surface profiler calibration, determine the effective spatial resolution of optical surface profiler.

Description

Utilize the method for white noise PSD collimation optical surface profiler effective spatial resolution

Technical field

The present invention relates to the calibration steps of the actual effective spatial resolution of a kind of optical surface profiler, specifically refer to power spectrum density (PSD) curve utilizing MATLAB simulating the white noise, the partial removal of this curvilinear motion rule will be met in optical element test result, determine optical surface profiler effective spatial resolution thus, belong to the category of optical surface profiler calibration.

Background technology

The development of detection technique is the vital expulsive forces of scientific domain such as physics, mechanics and medical science.The surface error of optical element is divided into surperficial face shape error, percent ripple and surfaceness, and evaluating these errors accurately and play directive function to the processing of optical element and the raising of optical property, is also the key factor accurately judging optical system imaging quality.The surface error of optical element is made to the prerequisite of accurate evaluation, be the profile information that will obtain closest to real surface by checkout equipment, therefore the precision of optical element checkout equipment just becomes particularly important..

Optical surface profiler provides the 3D region profile information on surface by non-contact measurement, having noncontact, the advantage such as three-dimensional quick and directly perceived, in order to make measurement result closer to real surface, must determine the effective resolution of optical surface profiler.The intrinsic resolution of optical surface profiler is relevant with optical diffraction limit resolution with the lateral resolution of its detector.The maximum space wavelength that optical surface profiler detects is relevant with object lens test specification.The lateral resolution of detector is the minimum space wavelength of distinguishable picture point, depends on the nyquist frequency f of system _ny(Nyquist frequency), f _nyfor the half of system sampling frequency.Optical diffraction resolution represents the ability that equipment can differentiate contiguous object point.Obtaining according to Rayleigh criterion the minimum spacing r that optical system can differentiate adjacent object point is:

$r=0.61\frac{\mathrm{\λ}}{\mathrm{NA}}---\left(1\right)$

λ is actual effective lambda1-wavelength, and NA is the numerical aperture of object lens.

All there is certain deviation in usual equipment intrinsic resolution and effective resolution, needs to calibrate optical surface profiler.Calibration steps Main Basis standard model or other checkout equipments, normally used characterizing sample is through international metering mechanism (Nat ional Measurement Institutes, NMI s) calibrated, different standard models is chosen for difference calibration geometric sense, more all uncertainties is unified.Because the requirement of this method to calibration module is higher and expensive, optical surface profiler is seldom had to adopt the method to calibrate.Utilize the calibration process of other calibration facilities, the requirement of standard model is reduced, but higher to the requirement of calibration facility, the comparison process also more complicated of two or more equipment.In actual applications, need to propose a kind of newly, easy method calibrates optical detection apparatus.

Summary of the invention

In order to overcome the problems referred to above that existing calibration steps exists, the invention provides a kind of method of the actual effective spatial resolution of collimation optical surface profiler of simple possible.

The main thought of this method is:

Optical element surface contoured profile can regard many different space frequency as, the harmonic superposition of various amplitude forms.These harmonic waves are after checkout equipment, and by the interference of white noise, the transmission capacity of system in some spatial frequencys is poor, can not reflect the real information in this spatial frequency range.Power spectral density function can reflect the proportion shared by each spatial frequency composition.The discrete Fourier transformation of one dimension surface profile power spectrum density (PSD) can be write as

$\mathrm{PSD}\left(f_m\right)=\frac{\mathrm{\Δx}}{N}{|\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}z\left(n\right)\·\exp \left({-i2\mathrm{\πf}}_m\mathrm{n\Δx}\right)|}^2---\left(2\right)$

Surface profile height distribution function is represented by N number of discrete z (n) value, and sampling interval is Δ x, and sampling length L=N Δ x, m is spatial frequency index, f _m=m/ (N Δ x) is m rank spatial frequencys.The minimum spatial frequency that system can respond is relevant with sampling length, and maximal value depends on nyquist frequency f _ny(Nyquist frequency), f _nyfor the half of system sampling frequency, as long as the nyquist frequency of discrete system is higher than sample frequency, just overlapping phenomenon can be avoided.So the intrinsic spatial frequency range of system is

$f_{\min }=\frac{1}{N{\mathrm{\Δ}}_X}\≤f_m=\frac{m}{N{\mathrm{\Δ}}_X}\≤\frac{1}{2{\mathrm{\Δ}}_X}=f_{\mathrm{Ny}}---\left(3\right)$

Be subject to the interference of white noise, the effective spatial resolution of system does not reach the requirement of intrinsic resolution, noise

Power spectrum density (PSD) curve different with optical element surface power spectrum density (PSD) curvilinear motion rule, the power spectrum density (PSD) of white noise is random signal or the stochastic process of a constant, utilize this character, power spectrum density (PSD) Changing Pattern of white noise can be simulated by MATLAB, it is separated from useful information.

The step of the actual effective spatial resolution of collimation optical surface profiler of the present invention is:

A) equipment be calibrated is the optical surface profiler ContourGT-X3 of Brooker, first calculates the inherent spatial resolution of this equipment and spatial frequency range in table 1 and table 2;

B) standard model is Si.Use three the different multiples object lens being calibrated equipment optical surface profiler ContourGT-X3, respectively Si tested and draw power spectrum density (PSD) curve;

C) MATLAB is utilized to simulate power spectrum density (PSD) curve of white noise corresponding to different object lens.And the partial removal of simulation curve Changing Pattern being met in test curve, remainder is useful space frequency range;

D) contrast with the useful space frequency range result utilizing fractal surface power spectrum density (PSD) calibration steps to obtain, the accuracy of the result;

E) choose different sample and repeat above process, prove that the method is chosen standard model restricted low.Owing to have employed such scheme, the present invention has the following advantages:

1. expense is low: alignment sample of the present invention is smooth surface, and compared with the sample needing traceability to demarcate, price wants cheap a lot.

2. easy to operate: calibration process does not need to use other correcting devices, only need the power spectrum density (PSD) with MATLAB simulating the white noise, without the need to unified uncertainty again after each geometric sense of system (as the linearity of platform, system noise and objective lens aberration etc.) calibration.

3. accuracy is high, practical: for the useful space frequency range utilizing fractal surface power spectrum density (PSD) calibration steps to obtain, both results are consistent.Whether be that fractal surface does not limit to sample, smooth surface.

Accompanying drawing explanation

Fig. 1 uses and is calibrated equipment ContourGT-X3 tests power spectrum density (PSD) under the logarithmic coordinate obtained result to Si-I;

Fig. 2 uses ContourGT-X3 Si-II to be tested to the result of power spectrum density (PSD) under the logarithmic coordinate obtained;

The power spectrum density of white noise under logarithmic coordinate (PSD) that Fig. 3 is simulated the test result of Si-I and MATLAB by contourgraph;

The power spectrum density of white noise under logarithmic coordinate (PSD) that Fig. 4 is simulated the test result of Si-II and MATLAB by contourgraph;

The power spectrum density of white noise under logarithmic coordinate (PSD) that Fig. 5 is simulated the test result of fused quartz and MATLAB by contourgraph;

The power spectrum density of white noise under logarithmic coordinate (PSD) that Fig. 6 is simulated the test result of D263 and MATLAB by contourgraph;

The power spectrum density of white noise under logarithmic coordinate (PSD) that Fig. 7 is simulated the test result of SiC and MATLAB by contourgraph.

Embodiment

Below in conjunction with accompanying drawing and instantiation, the present invention is described in detail.The equipment of being calibrated is the optical surface profiler ContourGT-X3 of Brooker.Its three object lens 2.5 ×, 10 × and 50 × test zone be respectively 2.55 × 1.91mm ², 0.62 × 0.47mm ²with 0.13 × 0.10mm ², in table 1, provide each object lens parameter.

The intrinsic parameter of table 1 optical surface profiler ContourGT-X3

2.5 × depend on nyquist frequency with the intrinsic spatial frequency maximal value of 10 × object lens, and 50 × depend on its optical diffraction resolution.Determined intrinsic spatial frequency range and the spatial resolution situation of system by above-mentioned calculating, relevant parameter is shown in and table 2.

The intrinsic spatial frequency range of table 2 ContourGT-X3 and resolution

In order to test result and fractal surface power spectrum density (PSD) calibration steps be compared, we adopt identical calibration sample, and thickness is respectively the Si of 1mm and 3mm, is Si-I and Si-II respectively.

Fig. 1 and Fig. 2 is by power spectrum density (PSD) test result of contourgraph three different multiples object lens to Si-I and Si-II, have almost no change in the power spectrum density (PSD) of each self-corresponding higher-spatial frequencies part of each object lens as seen in figure, this feature meets the Changing Pattern of Power Spectrum of White Noise density (PSD).Utilize MATLAB to simulate the distribution situation of Power Spectrum of White Noise density (PSD) under intrinsic spatial frequency range and see Fig. 3 and Fig. 4.The tail end of each power spectrum density (PSD) curve recorded in two width figure and respective Power Spectrum of White Noise density (PSD) overlap, lap is not useful space frequency-portions, and burble point is effective spatial resolution.Table 3 is the value of burble point place spatial frequency.

The spatial frequency that table 3 is surveyed and the burble point of corresponding Power Spectrum of White Noise density (PSD) curve is corresponding

By table 3,50 × identical with the effective spatial resolution that 10 × object lens are determined, 2.5 × slightly deviation, but the root-mean-square value of effects on surface roughness is without impact.

In patent " a kind of method of collimation optical surface profiler effective spatial resolution ", the power spectrum density of fractal surface under logarithmic coordinate (PSD) curve is straight line, the atomic force microscope (AFM) utilizing this rule to use to calibrate obtains this rule and does not do calibration straight line with this, optical surface profiler is calibrated, the result of the result obtained Power Spectrum of White Noise density (PSD) method with it contrasts, in table 4.

Two kinds, table 4 judges the contrast of effective spatial resolution methods and results

The fine difference of the useful space frequency range that two kinds of methods are determined is negligible, and the useful space frequency range obtained in two ways is consistent.

In order to further illustrate the practicality of this method, we use fused quartz, D263 and SiC to carry out identical research, and the result obtained is as Fig. 5-Fig. 7, and effective spatial resolution is in table 5.

The spatial frequency that table 5 is surveyed and the burble point of corresponding Power Spectrum of White Noise density (PSD) curve is corresponding

As shown in Table 5, the effective spatial resolution that 5 samples are determined under 50 × object lens is identical, and under 10 × object lens, effective spatial resolution change is from 0.05-0.09 μm ^-1, 2.5 × object lens are 0.02-0.06 μm ^-1, the root-mean-square value of the surfaceness calculated between these two spatial frequency range is identical, thus the deviation of the effective spatial resolution of both on result without impact.Less value can be chosen as useful space frequency range.The useful space frequency range that the method finally obtaining use Power Spectrum of White Noise density (PSD) is determined and effective spatial resolution, in table 6.

Intrinsic and the useful space frequency range of table 6 optical surface profiler

Relatively large deviation is there is between the inherent spatial resolution of visible system and actual effective spatial resolution in table 6, the information of a large amount of white noise is contained in surface profile information, the profile information closest to real surface just must can be obtained after determining actual effective spatial resolution, so just can the processing of guiding optics element and the raising of optical property, reach the object accurately judging optical system imaging quality.As can be seen here, the calibration of the actual effective spatial resolution of optical surface profiler is very necessary.

Claims (2)

1. one kind utilizes the method for Power Spectrum of White Noise Density Calibration optical surface profiler effective spatial resolution, it is characterized in that: use three the different multiples object lens being calibrated equipment optical surface profiler to test optical element surface, describe the power spectral density plot of its result under logarithmic coordinate, under utilizing MATLAB to simulate each object lens, the power spectral density plot of test result white noise, MATLAB analog result and optical element surface test result are compared, meet analog result partial removal, remaining part is useful space frequency range; Described optical element is the Si of smooth surface.

2. the method for collimation optical surface profiler effective spatial resolution according to claim 1, is characterized in that: use different optical element to carry out revision test, the repeatability of the result and accuracy.