Richard Leach - Fundamental prinsiples of engineering nanometrology (778895), страница 30
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Commercial styli usually have tip radiiof curvature ranging from 2 mm to 10 mm, but smaller or larger styli areavailable for specialist applications and form measurement respectively.Owing to their finite shape, some styli on some surfaces will not penetrateinto valleys and will give a distorted or filtered measure of the surface texture.Consequently, certain parameters will be more affected by the stylus shapethan others. The effect of the stylus shape has been extensively coveredelsewhere (see for example [7,28–30]). The effect of the stylus force can havea significant influence on the measurement results and too high a force cancause damage to the surface being measured (see Figure 6.7). ISO 3274 [26]states that the stylus force should be 0.75 mN but this is rarely checked andcan vary significantly from the value given by the instrument manufacturer.The value of 0.75 mN was chosen so as not to cause scratches in metals witha 2 mm radius stylus, but it does cause scratches in aluminium.
Smaller forceslimit the measurement speed due to the risk of ‘stylus flight’. Someresearchers ([31,32] and, more recently [33]) have developed constant-forcestylus instruments to improve the fidelity between the surface and the stylustip plus reduce surface damage and dynamic errors.To enable a true cross-section of the surface to be measured, the stylus, asit is traversed across the surface, must follow an accurate reference path thathas the general profile of, and is parallel to, the nominal surface. SuchFIGURE 6.7 Damage to a brass surface due to a high stylus force.Surface topography measuring instrumentationa datum may be developed by a mechanical slideway; for examples see [34]and [35]. The need for accurate alignment of the object being measured iseliminated by the surface datum device in which the surface acts as its owndatum by supporting a large radius of curvature spherical (or sometimes withdifferent radii of curvature in two orthogonal directions) skid fixed to the endof the hinged pickup.
At the front end of the pickup body the skid rests on thespecimen surface (note that skids are rarely seen on modern instruments andnot covered by ISO specification standards).All the aspects of stylus instruments are discussed in great detail elsewhere [7]. The main sources of error associated with a stylus instrument aresimply listed below:-surface deformation;-amplifier distortion;-finite stylus dimensions;-lateral deflection;-effect of skid or other datum;-relocation upon repeated measurements;-effect of filters – electrical or mechanical;-quantization and sampling effects;-dynamic effects;-environmental effects;-effect of incorrect data-processing algorithms.The lateral resolution of a stylus instrument, or the shortest wavelength,l, of a sinusoidal signal where the probe can reach the bottom of the surface,is given bypffiffiffiffiffil ¼ 2p ar(6.1)where a is the amplitude of the surface and r is the radius of the stylus tip.Note that equation (6.1) only applies for a sinusoidal profile.
Quantizationeffects and the noise floor of the instrument will determine the axial, orheight, resolution.Modern stylus instruments regularly obtain measurements of surfacetexture with sub-nanometre resolution but struggle to obtain true traceabilityof these measurements in each of their axes. It is worth pointing out here thatmany of the pitfalls of mechanical stylus techniques are often highly125126C H A P T ER 6 : Surface topography measurement instrumentationexaggerated [36]. For example, the wear on the surface caused by a stylus isoften stated as its fundamental limit, but even if a stylus does cause somedamage, this may not affect the functionality of the surface.
There havebeen some proposals to speed up the performance of a stylus by vibrating itaxially [37].One drawback of a stylus instrument when operated in an areal scanningmode is the time to take a measurement. It is perfectly acceptable to takeseveral minutes to make a profile measurement, but if the same number ofpoints are required in the y direction (orthogonal to the scan direction) as aremeasured in the x direction, then measurement times can be up to severalhours. For example, if the drive mechanism can scan at 0.1 mm$s1 and1000 points are required for a profile of 1 mm, then the measurement willtake 10 s.
If a square grid of points is required for an areal measurement, thenthe measurement time will increase to 105 s or approximately 2.7 hours.This sometimes precludes the use of a stylus instrument in a production orin-line application. This is one area where some of the optical instrumentsoffer an advantage over the stylus instruments.6.7 Optical instrumentsThere are many different types of optical instrument that can measuresurface topography, both surface texture and surface form.
The techniquescan be broken down into two major areas – those that measure the actualsurface topography by either scanning a beam or using the field of view(profile or areal methods), and those that measure a statistical parameter ofthe surface, usually by analysing the distribution of scattered light (areaintegrating methods). Whilst both these methods operate in the optical farfield, there is a third area of instruments that operate in the near field – theseare discussed in chapter 7.The instruments that are discussed in sections 6.7.2 to 6.7.4 are the mostcommon instruments that are available commercially.
There are many moreoptical instruments, or variations on the instruments presented here, mostof which are listed in [27] with appropriate references. At the time of writing,only the methods described in sections 6.7.2.2, 6.7.3.1, 6.7.3.2 and 6.7.3.4are being actively standardized in the appropriate ISO committee (ISO 213working group 16).Optical instruments have a number of advantages over stylus instruments. They do not physically contact the surface being measured and hencedo not present a risk of damaging the surface. This non-contact nature canalso lead to much faster measurement times for the optical scanningOptical instrumentsinstruments. The area-integrating and scattering methods can be faster still,sometimes only taking some seconds to measure a relatively large area.However, more care must be taken when interpreting the data from an opticalinstrument.
Whereas it is relatively simple to predict the output of a stylusinstrument by modelling it as a ball of finite diameter moving across thesurface, it is not such a trivial matter to model the interaction of an electromagnetic field with the surface. Often many assumptions are made aboutthe nature of the incident beam or the surface being measured that can bedifficult to justify in practice [38]. The beam-to-surface interaction is socomplex that one cannot decouple the geometry or material characteristics ofthe surface being measured from the measurement. For this reason, it is oftennecessary to have an a priori understanding of the nature of the surface beforean optical measurement is attempted.6.7.1 Limitations of optical instrumentsOptical instruments have a number of limitations, some of which aregeneric, and some that are specific to instrument types.
This section brieflydiscusses some of these limitations and section 6.12 discusses a number ofcomparisons that show how the limitations may affect measurements and towhat magnitude.Many optical instruments use a microscope objective to magnify thefeatures on the surface being measured. Magnifications vary from 2.5 to100 depending on the application and the type of surface being measured.Instruments employing a microscope objective will have two fundamentallimitations. Firstly, the numerical (or angular) aperture (NA) determines thelargest slope angle on the surface that can be measured and affects the opticalresolution. The NA of an objective is given byNA ¼ n sin a(6.2)where n is the refractive index of the medium between the objective and thesurface (usually air, so n can be approximated by unity) and a is the acceptance angle of the aperture (see Figure 6.8, where the objective is approximated by a single lens).
The acceptance angle will determine the slopes onthe surface that can physically reflect light back into the objective lens andhence be measured.For instruments based on interference microscopy it may be necessary toapply a correction to the interference pattern due to the effect of the NA.Effectively the finite NA means that the fringe distance is not equal to half thewavelength of the source radiation [39]. This effect also accounts for the aperture correction in gauge block interferometry (see section 4.5.4.6), but it has127128C H A P T ER 6 : Surface topography measurement instrumentationFIGURE 6.8 Numerical aperture of a microscope objective lens.a larger effect here; it may cause a step height to be measured up to 15 % short.This correction can usually be determined by measuring a step artefact witha calibrated height value and it can be directly determined using a grating [40].The second limitation is the optical resolution of the objective.
Theresolution determines the minimum distance between two lateral features ona surface that can be measured. The resolution is approximately given byr ¼l2NA(6.3)where l is the wavelength of the incident radiation [41]. For a theoreticallyperfect optical system with a filled objective pupil, the optical resolution isgiven by the Rayleigh criterion, where the ½ in equation (6.3) is replaced by0.61. Yet another measure of the optical resolution is the Sparrow criterion,or the spatial wavelength where the instrument response drops to zero andwhere the ½ in equation (6.3) is replaced by 0.82. Equation (6.3), and theRayleigh and Sparrow criteria, can be used almost indiscriminately, so theuser should always check which expression has been used where opticalresolution is a limiting factor. Also, equation (6.3) sets a minimum value.
Ifthe objective is not optically perfect (i.e. aberration-free) or if a part of thebeam is blocked (for example, in a Mirau interference objective, or whena steep edge is measured) the value becomes higher (worse).Optical instrumentsTable 6.1Minimum distance between features for different objectivesMagnificationNAResolution/mmPixel spacing/mm1020500.30.40.51.000.750.601.750.880.35For some instruments, it may be the distance between the pixels (determined by the image size and the number of pixels in the camera array) in themicroscope camera array that determines the lateral resolution. Table 6.1gives an example for a commercial microscope – for the 50 objective, it isthe optical resolution that determines the minimum distance betweenfeatures, but with the 10 objective it is the pixel spacing.The optical resolution of the objective is an important characteristic of anoptical instrument, but its usefulness can be misleading.
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