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翻译一下这篇英文文献呀,是关于用相称干涉法测表面粗糙度的
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文章如下：
Surface Roughness Measurement Using Infrared Phase-Shifting Digital Interferometer
You He*,Lei Chen,Qing Wang,Jingbangchen
Institute of Electronic Engineering&
oto-electric Technology of
Nanjing University of Science&Technology
ABSTRACT
The design of far infrared phase-shifting Twyman-Green interferometer is described in this paper.An IR interferometric method is used to evaluate the surface roughness of ground glass. It is conducted that a rigorous mathematical analysis to describe the contrast of the interference fringes patterns and surface roughness. The experiment is run at the instrument of self-developed interferometer which aperture is 30mm with accuracy better than /50( =10.6 m).The mathematical derivation is verified with experimental data obtained from various values of roughness.
Keyword:infrared interferometer,surface roughness,phase-shifting
1.INSTRODUCTION
Optical interferometric techniques is an important instrumentality for optical shop testing,because it provides full-field,real-time and non-contacting measurements.Far infrared interferometry has an advantage that there is no need for elaborate preparation of the material surface under investigation,preferably with little or no surface preparation.For example,far infrared Fizeau interferometry was developed for warpage measurement of rough reflective surfaces of microelectronic decices as a function of temperature and for surface topography measurement of rough reflective surface,far infractive Twyman-Green interferometry was developed for determining the transmission,refractive index, dn\dT,refractive index homogeneity,and the modulation transfer function(M.T.F).Phase shifting interfermetry,proposed by Brunning et al.,has been proved to be a high-accuracy and effective phase measurement method,which is not only extensively used in interferomerters operating at visible wavelength,but alse in IR interferometers.
In this paper a Twyman-Green IR phase-shifting inerferometer pyroelectric vidicon(PEV) as detector is developed,and the aperture is 30mm.The goal of this paper is to derive a math expression for the intensity distribution of Twyman-Green interferometer on rough reflective surface. We verify the results from the math derivation experimentally using data obtained from the specimens with various roughness.
2.INFRARED INTERFEROMETER
The diagram of the IR Twyman-Green interferometer is shown in Fig.1.The instrument uses a 7.8W CO2 laser as light
source.Because of light at 10.6 m is invisible,a He-Ne laser operating at 0.6328m is introduced into the IR interferometer to solve alignment problems.The CO2 laser is a highly stable TEM00 single longitudinal mode laser that has excellent coherence properties for use in an unequal path Twyman-Green interferometer.The beam is vertically polarized with a beam diameter of 4mm.The IR interferogram can be detected and converted into video signal by PEV,then displayed in real-time on monitor.The video signal can be grabbed by an image grabber,through which the interferogram is converted into a digital image with 8-bit digitization depth and then analyzed by computer,A series of software packages will give the results of tested wavefront.
Fig.2 is the schematic diagram of the IR interferometric optical system.Two znse lens(6) and lens(7),are used as a beam expander to obtain a 30mm effective beam diameter.There are two beam aplitters made of ZnSe(3 and 8).Splitter (3) works as a reflector for the low-power He-Ne laser and transmits the IR radiation to the subsequent beam paths .The ZnSe beam splitter is chosen because is too is transparent at the 0.6328 wavelength of the alignment He-Ne laser.Both beam splitter have enough wedges to avoid unwanted secondary reflection .Mirrors (2),(5) are made by K9 which coating with silver because of the silver mirror is a high reflector for both 0.6328 mand 10.6m.In test arm there are a F/4 diverger for testing for testing roughness surface and a plane mirror for testing IR optical system respectively .Imaging lens (16) is consists of a two-lens finite fonjugates sustem that images the surface of test optic onto the detectoer target (17). It provides a sharply defined image of the pupil and eliminates uncertainties caused by frenel diffraction .Mirror (14) in is for testing,concave mirror (15) is for alignment the optical quality requirement for the components is mostly demanding for the reference mirror(9),(12),the major beam splitter(8),and the diverger(10).While the spherical aberration introduced by a singlet diverger is acceptable for large f-number.,a singlet cannot be used for small f-number.Therefore,we have to use a doublet lens for faster divergers.
3.SURFACE ROUGHNESS
2.1The relationship of surface roughness and contrast
According to the scattering theory of electromagnetic wave,the specular component of the scattered light increases with increasing wavelength for random rough surface.Identifying the degree of roughness depends on both the geometry and the wacelength of the incident.Roughness is generally classified as periodic roughness.When a surface is illuminated with coherent light,the surface roughness and the the orientation of the surface determine the general scattering pattern .
In the following analysis of the interferometer,waves are considered for normal incidence of light on the beam object surface.Let l1,l2 and l3 denote geometric path lengths of the interferometer as shown in Fig.2.The test object of roughness surface is replace by mirror(12) .The complex amplitudes corresponding to the reference and the test paths can be expressed by
where k(=2 / ) is the wave numeber and h(x,y) is the local surface height measured relative to the zero mean.Also,in eq.(2),w(x,y) represent out-of-plane deformation of the mean surface of the object .Then the intensity distribution is:
In order to quantify contrast while dealing with random rough surface ,we assume a Gaussian probability density function of the surface height distribution.A Gaussian surface height distribution with standard deviation has a probability distribution function
The expression for intensity simplifies to
The fringe contrast c can be obtained as
Where
in the above, C0 is due to maximum amplitudes in the reference and test paths od the optical setup,while C0 is due to surface roughness.For simplicity,let us assume l1=l2=l then for constructive interference,the eq(6)_should be:
The eq.(8)is the relation of C and / .the C decreases with increasing of / .
2.2 The calculation of contrast
The contrast of interferogram can calculate by arithmetic of phase shifting.The intensity distribution is
where a(x,y) is the average intensity,b(x,y) is the fringer or intensity modulation. (x,y) is the wave-front phase. (k)is the introduced phase shift by PZT phase shifter.
The contrast can express:
If the reference mirror is moved an amount equal to /4, Eq.(10) can be rewritten for four conseutive steps of the mirror.
Then
4. EXPERIMENTS
The experiments to determine the ability of the interfermeter to deal with various degrees of random roughness are carried out.Some example is showm in Fig3.These intensity profiles were subsequently annalyzed to quantify the fringe contrast .Plots of the normalized fringe contrast as a grit size are shown in Fig.3 (a) and Fig.3(b),respectively. Evidently,as the roughness of the surface increases,the contrast of the fringes deteriorates,as one would expect.The surface quality after polishing with W10 abrasive was found good enough to obtain reasonable fringe contrast .In many of experiment reported in this work either w28 and w40 abrasive grit size were used.Fig.4 illustrates the relationship between contrast C and scaled roughness / .
The comparisons of the contrasts of the fringes and the standard deviation of surface roughness obtained by Taylor-Hobson and interfermetric measurements are listde in Table1.It shows that the standard deviations obtained from two measurement are in good agreement within a few percent.
4.CONCLUSIONS
A far infrared Twyman-Green interferomerter has been developed for surfaces roughness .The ability of method to perform real-time measurements on rough surfaceis demonstrated.Far infrared Tywman-Greenm interferometer are used to test IR transmitting materials and aspheric.We have tested IR lenses,optical substrate disk.The instrument designed for this research is capable of measuring wavefronts to within /25 RMS.The instruments is proven to br repeatable to /50 RMS.
