Принципы нанометрологии (1027506), страница 35
Текст из файла (страница 35)
PSI instruments can be used withsamples that have very low optical reflectance values (below 5 %), althoughthe signal-to-noise ratio is likely to rise as the reflectance is decreased. Anoptimal contrast is achieved when the reflectance values of the referenceand the measured surface match (see section 4.3.3).6.7.3.3 Digital holographic microscopyA digital holographic microscope (DHM) is an interferometric microscopevery similar to a PSI (see section 6.7.3.2), but with a small angle between thepropagation directions of the measurement and reference beams as shown inFigure 6.24 [78]. The acquired digital hologram, therefore, consists ofa spatial amplitude modulation with successive constructive and destructive147148C H A P T ER 6 : Surface topography measurement instrumentationFIGURE 6.24 Schematic diagram of DHM with beam-splitter (BS), mirrors (M),condenser (C), microscope objective (MO) and lens in the reference arm (RL) used tointerference fringes.
In the frequency domain, the difference between the coaxial geometry (PSI) and the off-axis geometry (DHM) is in the position of thefrequency orders of the interference. In PSI, because the three orders (thezeroth-order or non-diffracted wavefront, and 1 orders or the real andvirtual images) are superimposed, several phase shifts are necessary. Incontrast, in DHM the off-axis geometry spatially separates the differentfrequency orders, which allows simple spatial filtering to reconstruct thephase map from a single digital hologram [79]. DHM is, therefore, a real-timephase imaging technique less sensitive to external vibrations than PSI.Optical instrumentsIn most DHM instruments, contrary to most PSI instruments, the imageof the object formed by the microscope objective is not focused on thecamera.
Therefore, DHM needs to use a numerical wavefront propagationalgorithm that can use numerical optics to increase the depth of field [80], orcompensate for optical aberrations [81].The choice of source for DHM is large but is dictated by the sourcecoherence length. A source with a short coherence length is preferred tominimize parasitic interference, but the coherence length has to be sufficiently large to allow interference over the entire field of view of the detector.Typically, coherence lengths of several micrometres are necessary.DHM has a similar resolution to PSI [82] and is limited in range to halfthe central wavelength of the light source when a single wavelength is used.However, dual-wavelength [83] or multiple-wavelength DHM [84] allows thevertical range to be increased to several micrometres.
For low magnification,the field of view and the lateral resolution depends on the microscopeobjective and the camera pixel size; but for high magnification, the resolutionis diffraction limited down to 300 nm with a 100 objective. As with PSI,scanning stages and stitching software can be used to increase the fieldof view.6.7.3.4 Coherence scanning interferometryThe configuration of a coherence scanning interferometer (CSI) is similar tothat of a phase-shifting interferometer but in CSI a broadband (white light) orextended (many independent point sources) source is utilized [2,85]. CSI isoften referred to as vertical scanning white light interferometry or white lightscanning interferometry.
With reference to Figure 6.25 the light from thebroadband light source is directed towards the objective lens. The beamsplitter in the objective lens splits the light into two separate beams. Onebeam is directed towards the sample and one beam is directed towards aninternal reference mirror. The two beams recombine and the recombinedlight is sent to the detector. Due to the low coherence of the source, theoptical path length to the sample and the reference must be almost identical,for interference to be observed. Note that coherence is the measure of theaverage correlation between the values of a wave at any pair of times, separated by a given delay [41]. Temporal coherence tells us how monochromatica source is.
In other words, it characterizes how well a wave can interfere withitself at a different time (coherence in relation to CSI is discussed in moredetail in [86] and in general in section 4.3.4). The detector measures theintensity of the light as the optical path is varied in the vertical direction(z axis) and finds the interference maximum.
Each pixel of the camera149150C H A P T ER 6 : Surface topography measurement instrumentationFIGURE 6.25 Schema of a coherence scanning interferometer.measures the intensity of the light and the fringe envelope obtained can beused to calculate the position of the surface.A low-coherence source is used rather than monochromatic light because ithas a shorter coherence length and, therefore, avoids ambiguity in determiningthe fringe order.
Different instruments use different techniques to control thevariation of the optical path (by moving either the object being measured,the scanning head or the reference mirror) and some instruments havea displacement-measuring interferometer to measure its displacement [87].As the objective lens is moved a change of intensity due to interferencewill be observed for each camera pixel when the distance from the sample tothe beam-splitter is the same as the distance from the reference mirror to thebeam-splitter (within the coherence length of the source).
If the objective ismoved downwards the highest points on the surface will cause interferencefirst. This information can be used to build up a three-dimensional map ofthe surface. Figure 6.26 shows how the interference is built up at each pixel inthe camera array.There are a number of options for extracting the surface data from the CSIoptical phase data. Different fringe analysis methods give advantages withOptical instrumentsFIGURE 6.26 Schematic of how to build up an interferogram on a surface using CSI.different surface types, and many instruments offer more than one method.These are simply listed here but more information can be found in [85] and[86].
The fringe analysis methods include:-envelope detection;-centroiding;-envelope detection with phase estimation;-scan domain convolution;-frequency domain analysis.CSI instruments can have sub-nanometre resolution and repeatabilitybut it is very difficult to determine their accuracy, as this will be highlydependent on the surface being measured. Most of their limitations werediscussed in section 6.7.1 and are reviewed in [47]. The range of the opticalpath actuator, usually around 100 mm, will determine their axial range,although this can be increased to several millimetres using a long-rangeactuator and stitching software.
The xy range will be determined by the fieldof view of the objective and the camera size. Camera pixel arrays range from256 by 256 to 1024 by 1024 or more, and the xy range can be extended toseveral tens of centimetres using scanning stages and stitching software. CSIinstruments can be used with samples that have very low optical reflectancevalues (below 5 %), although, as with PSI, the signal-to-noise ratio is likely torise as the reflectance is decreased.To avoid the need to scan in the axial direction, some CSI instrumentsoperate in a dispersive mode. Dispersive CSI generates the spectral distributions of the interferograms directly by means of dispersive optics without151152C H A P T ER 6 : Surface topography measurement instrumentationthe need for depth scanning [88].
This method is well suited to in-lineapplications with high immunity to external vibration and high measurement speed. Researchers have recently developed a CSI technique that can beused to measure relatively large areas (several centimetres) without the needfor lateral scanning [89]. As such a full-field method does not use a microscope objective, the lateral resolution is necessarily limited.Some CSI instruments have been configured to measure the dynamicbehaviour of oscillating structures by using a stroboscopic source to essentially freeze the oscillating structure [90]. (Note that confocal instrumentshave also been used to measure the motion of vibrating structures [91].)CSI (and PSI) is often used for the measurement of the thickness ofoptical films by making use of the interference between reflections from thetop surface and the different film interfaces [92,93].
Recent advances can alsomeasure the individual thickness of a small number of films in a multilayerstack and the interfacial surface roughness [94].6.7.4 Scattering instrumentsThere are various theories to describe the scattering of light from a surface(see [95] for a thorough introduction and review). The theories are based onboth scalar and vector scattering models and many were developed todescribe the scattering of radio waves from the ocean surface. Light scatteredfrom a surface can be both specular, i.e.
the reflection as predicted bygeometrical optics, and diffuse, i.e. reflections where the angle of reflection isnot equal to the angle of incidence. Diffuse reflection is caused by surfaceirregularities, local variations in refractive index and any particulates presentat the surface (for this reason cleanliness is important). From the theoreticalmodels, the distribution of light scattered from smooth surfaces is found tobe proportional to a statistical parameter of the surface (often Rq or Sq),within a finite bandwidth of spatial wavelengths [96,97].
Hence, scatteringinstruments do not measure the actual peaks and valleys of the surfacetexture; rather they measure some aspect of the surface height distribution.There are various methods for measuring light scatter and there are manycommercially available instruments [98,99]. As scattering instrumentssample over an area (they are area-integrating methods) they can be very fastand relatively immune to environmental disturbance. For these reasons,scattering methods are used extensively in on-line or in-process situations,for example measuring the effects of tool wear during a cutting process ordamage to optics during polishing. It can be difficult to associate an absolutevalue to a surface parameter measured using a scattering technique, soscattering is often used to investigate process change.Optical instrumentsThe function that describes the manner in which light is scattered froma surface is the bi-directional scatter distribution function (BSDF) [95].
Thereflective properties of a surface are governed by the Fresnel equations [41].Based upon the angle of incidence and material properties of a surface (opticalconstants), the Fresnel equations can be used to calculate the intensity andangular distribution of the reflected waves. The BSDF describes the angulardistribution of scatter.The total integrated scatter (TIS) is equal to the light power scattered intothe hemisphere above the surface divided by the power incident on thesurface. The TIS is equal to the integral of the BSDF over the scatteringhemisphere multiplied by a correction factor (known as the obliquity factor).Reference [100] derived a relationship between the TIS and Rq (or Sq)given byRqzl pffiffiffiffiffiffiffiffiTIS4p(6.6)where the TIS is often approximated by the quotient of the diffusely scatteredpower to the specularly reflected power.The instrumentation for measuring TIS [101] consists of a light source(usually a laser), various filters to control the beam size, a device for collectingthe scattered light, and detectors for measuring the scattered light andspecularly reflected light.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
