Принципы нанометрологии (1027506), страница 34
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Due to the small depth of field of the optics, only smallregions of the object are sharply imaged. To perform a complete detection ofthe surface with full depth of field, the precision optical arrangement ismoved vertically along the optical axis while continuously capturing datafrom the surface. This ensures that each region of the object is sharplyfocused. Algorithms convert the acquired sensor data into 3D informationand a true colour image with full depth of field. This is achieved by analysingthe variation of focus along the vertical axis.Various methods exist to analyse this variation of focus, usually based onthe computation of the sharpness at a specific position.
Typically, thesemethods rely on evaluating the sensor data in a small local area. In general, asan object point is focused sharper, the larger the variation of sensor values ina local neighbourhood. As an example, the standard deviation of the sensorvalues could be used as a simple measure for the sharpness.The vertical resolution of a focus variation instrument depends on thechosen objective and can be as low as 10 nm.
The vertical scan rangedepends on the working distance of the objective and ranges from a fewmillimetres to approximately 20 mm or more. The vertical resolution is notdependent upon the scan height, which can lead to a high dynamic range.The xy range is determined by the objective and typically ranges from 0.14mm by 0.1 mm to 5 mm by 4 mm for a single measurement.
By usingspecial algorithms and a motorised stage the xy range can be increased toaround 100 mm by 100 mm.In contrast to other optical techniques that are limited to coaxial illumination, the maximum measurable slope angle is not dependent on thenumerical aperture of the objective. Focus variation can be used with a largerange of different illumination sources (such as a ringlight), which allows themeasurement of slope angles exceeding 80 .Focus variation is applicable to surfaces with a large range of differentoptical reflectance values.
Specimens can vary from shiny to diffuse143144C H A P T ER 6 : Surface topography measurement instrumentationreflecting, from homogeneous to compound materials, and from smooth torough surface properties (but see below). Focus variation overcomes theaspect of limited measurement capabilities in terms of reflectance by usinga combination of a modulated illumination source, controlling the sensorparameters and integrated polarization. In addition to the scanned heightdata, focus variation also delivers a colour image with full depth of field thatis registered to the 3D data points.Since focus variation relies on analysing the variation of focus, it isonly applicable to surfaces where the focus varies sufficiently during thevertical scanning process.
Surfaces not fulfilling this requirement, such astransparent specimens or components with only a small local roughness, aredifficult and sometimes impossible to measure. Typically, focus variationgives repeatable measurement results for surfaces with a local Ra of 10 nm orgreater at a lc of 2 mm (see section 8.2.3).6.7.3.2 Phase-shifting interferometryA phase-shifting interferometer (PSI) consists of an interferometer integratedwith a microscope (see Figure 6.21) [72,43]. Within the interferometer,a beam-splitter directs one beam of light down a reference path, which hasa number of optical elements including an ideally flat and smooth mirrorfrom which the light is reflected.
The beam-splitter directs a second beam ofFIGURE 6.21 Schema of a phase-shifting interferometer.Optical instrumentslight to the sample where it is reflected. The two beams of light return to thebeam-splitter and are combined forming an image of the measured surfacesuperimposed by an interference pattern on the image sensor array (camera).Usually a PSI uses a co-axial alignment, i.e. the two beams propagate in thesame direction, but off-axis arrangements can be used [73]. The image of thesurface can be either focused onto the detector or not.
In the latter casea digital propagation algorithm is employed allowing numerical focusing[74]. The optical path in the reference arm is adjusted to give the maximuminterference contrast. During measurement, several known shifts betweenthe optical path to the measured surface and the optical path to the referencemirror are introduced and produce changes in the fringe pattern. Phase mapsare then constructed from each shifted interferogram. There are several waysto shift the difference in optical paths.
For example, the objective and reference mirror of the system are translated with the use of a piezoelectricactuator. 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.
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