CN103047928A - Random error mode evaluation method of phase shifting interferometer - Google Patents

Abstract

The invention discloses a random error mode evaluation method of a phase shifting interferometer, and the method belongs to the field of the error evaluation of interferometers. The method comprises the following steps that a certain inclination quantity is led in during a testing process; the average value of a plurality of measuring results serves as a reference value; the random testing error of one testing result is obtained by subtracting the reference value from one testing result; and the error is analyzed according to the characteristics of different error sources, so as to obtain the main error sources in an interference measuring process by analysis. According to the random error mode evaluation method of the phase shifting interferometer, the categories of the random error sources in the phase shifting interferometer are quickly obtained by analyzing the modes of the random errors and comparing the difference among the random error modes caused by various error sources, so as to provide convenient and quick guidance for the maintenance and the use of the interferometer.

Description

A kind of appraisal procedure to phase-shifting interferometer stochastic error mode

Technical field

The invention belongs to the evaluation areas of interferometric error, be specifically related to a kind of appraisal procedure to phase-shifting interferometer stochastic error mode.

Background technology

Phase-shifting interferometer is a kind of high-accuracy optical measuring apparatus, is widely used in the research and production.As a kind of high-accuracy optical instrument, phase-shifting interferometer utilizes himself high-accuracy optics and mechanical part to guarantee its measuring accuracy.Through using for a long time, ever-increasing stochastic error can exert an influence to the measuring accuracy of interferometer.Generally, need to adopt the highly sophisticated device of multiple costliness to analyze the stochastic error source of seeking.This has increased maintenance and the use cost of interferometer widely.

Summary of the invention

In order to solve problems of the prior art, the invention provides a kind of appraisal procedure to phase-shifting interferometer stochastic error mode, the method is analyzed by the mode to stochastic error, obtain fast the kind in stochastic error source in the phase-shifting interferometer by comparing difference between the stochastic error mode that various error sources cause, for maintenance and the use of interferometer provides simple and efficient guidance.

The technical scheme that technical solution problem of the present invention adopts is as follows:

A kind of appraisal procedure to phase-shifting interferometer stochastic error mode is characterized in that the method comprises the steps:

Step 1: use phase-shifting interferometer that one good wavefront is taken multiple measurements, introduce in the measuring process, get and introduce after the inclination repeatedly the mean value of measurement result as the reference phase place; Then get at random wherein test phase, deduct fixed phase, obtain a random measurement result's test error:

Step 2: by the analysis to phase-shifting interferometer stochastic error source, obtain the relation between different types of error source and the test error, the error characteristics that the unstable stochastic error that causes of position noise error, light source power that the inaccurate stochastic error that causes of acquisition phase shift of deriving, vibration cause and light source center frequency drift cause;

Step 3: the characteristic of the stochastic error that the different error sources that obtain according to analysis cause, obtain the test error in the test result in the contrast step 1, determine the main error source in the interferometer.

The invention has the beneficial effects as follows: the present invention is by mathematical analysis and analogue simulation, determine the characteristic of the stochastic error that different error sources cause, can help the related personnel to identify fast in the searching instrument and have error source, greatly saved by the expense of highly sophisticated device to plant maintenance and detection, convenient succinct.

Description of drawings

A kind of tested wavefront of appraisal procedure to phase-shifting interferometer stochastic error mode of Fig. 1 the present invention.

Introduce the interference fringe of certain tilt quantity in Fig. 2 test process.

The stochastic error that causes is forbidden in Fig. 3 phase shift.

The stochastic error that Fig. 4 vibration causes.

The unstable stochastic error that causes of Fig. 5 intensity of light source.

The unstable stochastic error that causes of Fig. 6 light source center frequency.

Embodiment

Below in conjunction with drawings and Examples the present invention is described in further details.

A kind of appraisal procedure to phase-shifting interferometer stochastic error mode is characterized in that the method comprises the steps:

Step 1: use phase-shifting interferometer that one good wavefront is taken multiple measurements, the root-mean-square error of wavefront is at 1/10 ~ 1/20 wavelength, introduce a certain amount of inclination in the measuring process, two to three vertical bar lines are arranged in the interference fringe, get after introducing repeatedly the mean value of measurement result as the reference phase place, repeatedly measure the operation of averaging and to eliminate preferably most of stochastic error, therefore get repeatedly the mean value of measurement result as with reference to value, be convenient to extract the stochastic error in certain this measuring process; Then get at random wherein test phase, deduct fixed phase, obtain a random measurement result's test error:

The mode of phase-shifting interferometer by phase shift produces the interference fringe in the out of phase situation, to obtain different light intensity system of equations, by finding the solution of this Series of Equations obtained required phase place in the interferometry.The interference fringe that the phase-shifting interferometer phase shift obtains can obtain by following formula:

Wherein V is the interference fringe contrast, φ _nBe t fixed phase constantly,

Be tested phase place.

According to document Peter de Groot " Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window ". APPLIED OPTICS, 34, the phase-shifting interferometer broad sense phase extraction algorithms of mentioning among the 4723-4730 (1995), tested phase place

Can be obtained by following formula:

For window function w _nBe real function, Re is for getting real part, and Im represents to get imaginary part, can get following formula:

$s_n=\mathrm{Im}\left[w_n\exp (-i{\mathrm{\φ}}_n)\right]=w_n\sin (-{\mathrm{\φ}}_n)---\left(3\right)$

$c_n=\mathrm{Re}\left[w_n\exp (-i{\mathrm{\φ}}_n)\right]=w_n\cos \left({\mathrm{\φ}}_n\right)---\left(4\right)$

The extraction formula of the phase place in the interferometer is like this:

When there was error source in interferometer, the image of the interference fringe that collects was

Obtain

According to formula $\mathrm{arc}{\tan }^{\′}\left(x\right)=\frac{1}{1+x^2}$ ，

，

The error of test is:

Because

, following formula becomes:

Wherein k is constant for same phase shift algorithm, and under the prerequisite of paying close attention to the measuring error concrete form, k can be considered to 1.

Step 2: by the in-depth analysis to phase-shifting interferometer stochastic error source, obtain the relation between different types of error and the test error, the error characteristics that the unstable stochastic error that causes of position noise error, light source power that the inaccurate stochastic error that causes of acquisition phase shift of deriving, vibration cause and light source center frequency drift cause;

The stochastic error source that exists in the phase-shifting interferometer has: the unstable Intensity Unstable of position noise Position Error, light source power, light source center frequency drift Frequency Unstable that the non-linear stochastic error Phase Shift Error that causes of phase shift, vibration cause.The interferometer test error directly translates into the change of interference fringe light intensity, so between the size of light intensity variable quantity and error source following relation is arranged:

$\mathrm{\ΔI}=\frac{\mathrm{dI}\left(x\right)}{\mathrm{dx}}\×\mathrm{\Δx}---\left(10\right)$

Wherein x is the size of error source.Discuss according to light intensity variation and measuring error that following formula just can cause four kinds of stochastic error sources respectively.

1, Phase-shifting Errors:

At this moment calculating the test error that obtains is

Wherein, Δ P _nBe Phase-shifting Errors.This error with

Item is directly proportional, and the inaccurate stochastic error that causes of this explanation phase shift shows as a kind of striped of rule in test result, and fringe number is the twice of interference fringe

2, vibrate the position noise error that causes:

Wherein,

Derivative for wavefront.The error form that vibration causes with

With

Two are directly proportional, the direction of vibration and the size with

Direction and size close contact is arranged therefore, the stochastic error that causes of vibration shows as frequency multiplication striped (with respect to interference fringe) in test result, but the peak value of same ripple and inconsistent.

3, the unstable error of light source power:

Wherein, Δ _nIntensity is the unstable error of light intensity.The error of the unstable introducing of light source power with

With Relevant, so the unstable stochastic error that causes of light source power shows as the striped of frequency multiplication in test result, the peak value of different cycles is also inconsistent, and the peak value of different cycles changes as wave (key player on a team's curve).

4, the error that causes of light source center frequency drift:

Wherein, Δ _nFreq is the error of light source center frequency drift.This error with Be directly proportional, simultaneously quilt

Modulate, so the light source center frequency drift causes that the peak value that stochastic error shows as different cycles in the striped of frequency multiplication increases or reduces in mutually same direction.

Step 3: the characteristic of the stochastic error that the different error sources that obtain according to analysis cause, obtain the test error in the test result in the contrast step 1, determine the main error source in the interferometer.

For the difference between the stochastic error that above-mentioned different random error source causes is described more in detail accurately, below by to a tested wavefront, as shown in Figure 1, artificially introduce stochastic error, as shown in Figure 2, carry out analog simulation.Difference between the different random error can obtain by Fig. 3 to Fig. 6.

1, for Phase-shifting Errors, in Fig. 3, found the regular streaks of frequency multiplication, and with interference fringe relevant (error has 4 cycles, and interference fringe has 2 cycles) shown in Figure 1.Obviously in this and the formula (17)

Corresponding.

2, for vibration error, the striped of frequency multiplication is arranged equally, but the peak value of same ripple is also inconsistent on the frequency multiplication striped in Fig. 4.Item in this phenomenon and the formula (20)

With

Consistent.

3, decide error for flashing, the striped that discovery has frequency multiplication in Fig. 5, the peak value of different cycles is also inconsistent, and the peak value of different cycles changes as wave (key player on a team's curve).This phenomenon and formula (23) middle term

With

Relevant.

4, for the unstable error that causes of light source frequency, in Fig. 6, find striped with frequency multiplication, in this striped peak value of different cycles in continuous growth, this and formula (26) middle term

Relevant.

Claims (2)

1. the appraisal procedure to phase-shifting interferometer stochastic error mode is characterized in that the method comprises the steps:

Step 1: use phase-shifting interferometer that one good wavefront is taken multiple measurements, introduce in the measuring process, get and introduce after the inclination repeatedly the mean value of measurement result as the reference phase place; Then get at random wherein test phase, deduct fixed phase, obtain a random measurement result's test error:

Step 2: by the analysis to phase-shifting interferometer stochastic error source, obtain the relation between different types of error source and the test error, the error characteristics that the unstable stochastic error that causes of position noise error, light source power that the inaccurate stochastic error that causes of acquisition phase shift of deriving, vibration cause and light source center frequency drift cause;

Step 3: the characteristic of the stochastic error that the different error sources that obtain according to analysis cause, obtain the test error in the test result in the contrast step 1, determine the main error source in the interferometer.

2. as claimed in claim 1ly a kind ofly the phase-shifting interferometer random error characteristics be is characterized in that the relation in the step 2 of the method between error source and the test error obtains by following derivation:

The interference fringe I that the phase-shifting interferometer phase shift obtains _nBe expressed as:

Wherein V is the interference fringe contrast, φ _nBe fixed phase, Be tested phase place.

Tested phase place Can be obtained by following formula:

The window function w that wherein uses in the derivation algorithm _nBe real function, Re is for getting real part, and Im represents to get imaginary part, can get following formula:

$s_n=\mathrm{Im}\left[w_n\exp (-i{\mathrm{\φ}}_n)\right]=w_n\sin (-{\mathrm{\φ}}_n)---\left(3\right)$

$c_n=\mathrm{Re}\left[w_n\exp (-i{\mathrm{\φ}}_n)\right]=w_n\cos \left({\mathrm{\φ}}_n\right)---\left(4\right)$

Phase extraction formula (2) becomes:

When there was error source in interferometer, the image of the interference fringe that collects was

,

Strength Changes for the interference fringe that caused by error source obtains the result:

According to formula

,

, the error of test is:

Because

, following formula becomes:

Wherein k is constant for same phase shift algorithm, and under the prerequisite of paying close attention to the measuring error concrete form, k can be considered to 1,

Different to the interference fringe influencing characteristic according to the different random error source, the error that can be derived the test result that the different random error source causes by following formula is:

The stochastic error that causes for phase shift,

Wherein, Δ P _nBe Phase-shifting Errors.As seen this error with Item is directly proportional;

The position noise error that vibration causes,

Wherein,

Derivative for wavefront.The stochastic error that vibration causes with

With

Two are directly proportional, the direction of vibration and the size with

Direction and size close contact arranged;

The unstable stochastic error that causes of light source power,

Wherein, Δ _nIntensity is the unstable error of light intensity.The error of the unstable introducing of light source power with

With

Relevant;

The error that the light source center frequency drift causes,

Wherein, Δ _nFreq is the error of light source center frequency drift.This error with

Be directly proportional, simultaneously quilt

Item is modulated.

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