Richard Leach - Fundamental prinsiples of engineering nanometrology (778895), страница 34
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Finally, the vertical height data are deduced from the phase maps.For specimens with vertical heights greater than half the wavelength [72], the2p ambiguity can be suppressed by phase-unwrapping algorithms or the useof dual-wavelength methods [73,75].PSI instruments usually come in one of two configurations depending onthe arrangement of the microscope objective. Figure 6.22 shows a MirauFIGURE 6.22 Schematic diagram of a Mirau objective.145146C H A P T ER 6 : Surface topography measurement instrumentationFIGURE 6.23 Schematic diagram of a Linnik objective.configuration, where the components A, B and C are translated withreference to D, and Figure 6.23 shows a Linnik configuration, wherecomponents B and C are translated with reference to D and E. The Mirau ismore compact and needs less adjustment than the Linnik.
For both objectives, there must be white light interference when both the reference mirrorand the object are in focus. For the Mirau objective this is accomplished inone setting of the tilt and position of the reference mirror. For the Linnikobjective, both the reference mirror and the object must be in focus, but inaddition both arms of the Linnik objective must be made equal withina fringe. Also, a Linnik objective consists of two objectives that must matchtogether, at least doubling the manufacturing costs. An advantage of theLinnik is that no central area of the objective is blocked and no spaceunderneath the objective is needed for attaching an extra mirror and beamsplitter. Therefore, with the Linnik objective, magnifications and resolutions can be achieved as with the highest-resolution standard opticalmicroscope objectives. A further objective is based on a Michelson interferometer (see section 4.4.1).
These are produced by placing a cube beamsplitter under the objective lens directing some of the beam to a referencesurface. The advantage of the Michelson configuration is that the centralpart of the objective is not blocked. However, the cube beam-splitter isplaced in a convergent part of the beam, which leads to aberrations andlimits the instrument to small numerical apertures and large workingdistances.Optical instrumentsThe light source used for PSI measurements typically consists of a narrowband of optical wavelengths as provided by a laser, light-emitting diode (LED),narrow-band filtered white light source, or spectral lamp. The accuracy of thecentral wavelength and the bandwidth of the illumination are important tothe overall accuracy of the PSI measurement. The measurement of a surfaceprofile is accomplished by using an image sensor composed of a linear arrayof detection pixels.
Areal measurements of the surface texture may beaccomplished by using an image sensor composed of a matrix array ofdetection pixels. The spacing and width of the image sensor pixels areimportant characteristics, which determine attributes of instrument lateralresolution (see section 6.7.1).PSI 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. Most PSI instruments usually require thatadjacent points on a surface have a height difference of l/4. The range of PSIis limited to one fringe, or approximately half the central wavelength of thelight source, so PSI instruments are usually only used for measuringapproximately flat surfaces (a rule of thumb is that only surfaces with an Raor Sa less than l/10 would be measured using PSI).
This limitation can beovercome by combining the PSI instrument with a CSI instrument (seesection 6.7.3.4), usually referred to as a vertical scanning mode. Theaccuracy of a PSI instrument can be enhanced to allow highly flat surfacesto be measured (surfaces that are flatter than the reference surface) usinga process known as reference surface averaging [76]. Alternatively, it may bepossible to characterize the reference surface using a liquid surface [77]. Thexy range will be determined by the field of view of the objective and thecamera size. Camera pixel arrays range from 256 by 256 to 1024 by 1024 ormore, and the xy range can be extended to several tens of centimetres usingscanning stages and stitching software.
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.
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