CN103983204A - Method for calibrating effective spatial resolution of optical surface contour instrument by use of white noise PSD (power spectral density) - Google Patents

Abstract

The invention relates to a method for calibrating the effective spatial resolution of an optical surface contour instrument by use of white noise PSD (power spectral density). White noise restricts the spatial resolution of the optical surface contour instrument, the white noise PSD is a constant random signal or a random process, by use of this rule, the part, which accords with a white noise PSD curve rule, in a test result is cut off, and the residual part is corresponding to an effective space frequency scope. The advantages are as follows: the principle is simple, the operation is convenient, assistance of other devices is unnecessary, the calibration work can be finished at the time when smooth samples are detected, the calibration difficulty and cost of the optical surface contour instrument are substantially reduced, and the effective spatial resolution of the optical surface contour instrument is determined.

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 contourgraph, specifically refer to power spectrum density (PSD) curve that utilizes MATLAB simulating the white noise, the part that meets this curvilinear motion rule in optical element test result is removed, determine thus optical surface contourgraph effective spatial resolution, belong to the category of optical surface contourgraph 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 evaluate accurately these errors the raising of the processing of optical element and optical property is played to directive function, be also the key factor of accurately judging optical system imaging quality.The surface error of optical element being made to the prerequisite of accurate evaluation, be to obtain approaching most by checkout equipment the profile information of real surface, so the precision of optical element checkout equipment just becomes particularly important..

Optical surface contourgraph provides surperficial 3D region profile information by non-contact measurement, has noncontact, the advantage such as three-dimensional quick and directly perceived, in order to make measurement result more approach real surface, must determine the effective resolution of optical surface contourgraph.The intrinsic resolution of optical surface contourgraph is relevant with optical diffraction limit resolution with the lateral resolution of its detector.The maximum space wavelength that optical surface contourgraph 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 half of systematic sampling frequency.Optical diffraction resolution represents that equipment can differentiate the ability of contiguous object point.According to Rayleigh criterion, obtaining optical system can differentiate the minimum spacing r of adjacent object point and be:

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

λ is actual effectively lambda1-wavelength, the numerical aperture that NA is object lens.

Conventionally all there is certain deviation in equipment intrinsic resolution and effective resolution, need to calibrate optical surface contourgraph.Calibration steps Main Basis standard model or other checkout equipments, normally used sign sample Shi Jing international metering (the Nat ional Measurement Institutes of mechanism, NMI s) demarcated, for difference calibration geometric sense, choose different standard models, more all uncertainties is unified.Due to this method to calibration module have relatively high expectations and also expensive, seldom have optical surface contourgraph to adopt the method to calibrate.Utilize the calibration process of other calibration facilities, the requirement of standard model has been reduced, but to the having relatively high expectations of calibration facility, the comparison process of two or more equipment is more complicated also.In actual applications, need to propose a kind of new, easy method calibrates optical detection apparatus.

Summary of the invention

In order to overcome the problems referred to above of existing calibration steps existence, 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:

The harmonic wave that optical element surface contoured profile can be regarded many different space frequency, various amplitude as is formed by stacking.These harmonic waves, after checkout equipment, are subject to the interference of white noise, and 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 that each spatial frequency composition is shared.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 to be represented by N discrete z (n) value, and sampling interval is Δ x, sampling length L=N Δ x, and 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 systematic sampling frequency half, as long as the nyquist frequency of discrete system is higher than sample frequency, just can avoid overlapping phenomenon.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 of white noise (PSD) is random signal or the stochastic process of a constant, utilize this character, can by MATLAB, simulate power spectrum density (PSD) Changing Pattern of white noise, 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 being calibrated is the optical surface contourgraph 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 is calibrated three different multiples object lens of equipment optical surface contourgraph ContourGT-X3, respectively Si is tested and drawn power spectrum density (PSD) curve;

C) utilize MATLAB to simulate power spectrum density (PSD) curve of the white noise that different object lens are corresponding.And the part that meets simulation curve Changing Pattern in test curve is removed, remainder is useful space frequency range;

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

E) choose different samples and repeat above process, prove that the method chooses restricted low to standard model.Owing to having adopted such scheme, the present invention has the following advantages:

1. expense is low: alignment sample of the present invention is smooth surface, compares with the sample that needs traceability to demarcate use, and it is cheap a lot of that price is wanted.

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

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

Accompanying drawing explanation

Fig. 1 is used the result that is calibrated power spectrum density (PSD) under the equipment ContourGT-X3 logarithmic coordinate that test obtains to Si-I;

Fig. 2 is used the result of power spectrum density (PSD) under the ContourGT-X3 logarithmic coordinate that test obtains to Si-II;

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

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

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

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

Fig. 7 by contourgraph to the white noise of the test result of SiC and MATLAB simulation the power spectrum density (PSD) under logarithmic coordinate.

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 contourgraph 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 contourgraph ContourGT-X3

2.5 * and the intrinsic spatial frequency maximal value of 10 * object lens depend on nyquist frequency, and 50 * depend on its optical diffraction resolution.By above-mentioned calculative determination intrinsic spatial frequency range and the spatial resolution situation of system, relevant parameter is shown in and table 2.

Intrinsic spatial frequency range and the resolution of table 2 ContourGT-X3

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

Fig. 1 and Fig. 2 are for passing through three different multiples object lens of contourgraph to the power spectrum density of Si-I and Si-II (PSD) test result, in figure, the power spectrum density (PSD) in each self-corresponding higher-spatial frequencies part of each object lens does not almost change as seen, and this feature meets the Changing Pattern of Power Spectrum of White Noise density (PSD).The distribution situation of utilizing MATLAB to simulate Power Spectrum of White Noise density (PSD) under intrinsic spatial frequency range is shown in Fig. 3 and Fig. 4.The tail end of each power spectrum density recording (PSD) curve in two width figure and Power Spectrum of White Noise density (PSD) is overlapping separately, lap is not useful space frequency part, and burble point is effective spatial resolution.Table 3 is the value of burble point place spatial frequency.

The spatial frequency corresponding to burble point of table 3 actual measurement and corresponding Power Spectrum of White Noise density (PSD) curve

By table 3, the 50 * effective spatial resolution definite with 10 * object lens is identical, 2.5 * deviation slightly, 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 ", power spectrum density (PSD) curve of fractal surface under logarithmic coordinate is straight line, utilize this rule to use the atomic force microscope (AFM) of calibrating to obtain this rule and do not do calibration straight line with this, optical surface contourgraph is calibrated, the resulting result with it result of Power Spectrum of White Noise density (PSD) method contrasts, in Table 4.

Two kinds of contrasts of judging effective spatial resolution methods and results of table 4

The fine difference of the useful space frequency range that two kinds of methods are definite is negligible, so the useful space frequency range that two kinds of methods obtain 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 obtaining is as Fig. 5-Fig. 7, and effective spatial resolution is in Table 5.

The spatial frequency corresponding to burble point of table 5 actual measurement and corresponding Power Spectrum of White Noise density (PSD) curve

As shown in Table 5, under 50 * object lens, the definite effective spatial resolution of 5 samples is identical, and under 10 * object lens, effective spatial resolution changes from 0.05-0.09 μ m ^-1, 2.5 * object lens are 0.02-0.06 μ m ^-1, the root-mean-square value of the surfaceness calculating between these two spatial frequency range is identical, thus the deviation of the two effective spatial resolution on result without impact.Can choose less value as useful space frequency range.Finally obtain using definite useful space frequency range and the effective spatial resolution of method of Power Spectrum of White Noise density (PSD), in Table 6.

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

In table 6, between the inherent spatial resolution of visible system and actual effective spatial resolution, there is relatively large deviation, the information that has comprised a large amount of white noises in surface profile information, must after having determined actual effective spatial resolution, just can obtain approaching most the profile information of real surface, so just can the processing of guiding optics element and the raising of optical property, reach the object of accurate judgement optical system imaging quality.As can be seen here, the calibration of the actual effective spatial resolution of optical surface contourgraph is very necessary.

Claims (4)

1. a method of utilizing Power Spectrum of White Noise density (PSD) collimation optical surface profiler effective spatial resolution, it is characterized in that: use three different multiples object lens that are calibrated equipment optical surface contourgraph to test optical element surface, describe power spectrum density (PSD) curve of its result under logarithmic coordinate.

2. the method for collimation optical surface profiler effective spatial resolution according to claim 1, is characterized in that: utilize MATLAB to simulate under each object lens, the power spectrum density of test result white noise (PSD) curve.

3. the method for collimation optical surface profiler effective spatial resolution according to claim 1, it is characterized in that: MATLAB analog result and optical element surface test result are compared, meet analog result and partly remove, remaining part is useful space frequency range.

4. 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.