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Mountains® allows you to analyze simple but also composite data obtained using a very wide range of surface analysis instruments & microscopes.

The following are some of the most common data types managed.

### Topography and images from profilometers, optical profilers, microscopes etc.

 Data type Formula Description Suitable for… Example application Profile z=f(x) A profile is a measurement of heights along a line on a surface. The height Z is expressed according to a position X. Roughness Waviness Simple forms Roughness of sanded mold used for plastic injection Series of profiles z=f(x,t) Several profiles packed together as a single data set Roughness or waviness changing over time Roughness or waviness parameters calculated on several profiles scanned at different positions or in different directions in order to increase the stability of parameter values. Tribology: successive stages of surface wear (2D cross section) Automotive: control of “orange peel” defect on painted body parts. Parametric profile (“contour”) (x,z) = f(t) The outer line of one or several objects. Contrary to the standard profile (in which only one side is studied), a parametric profile may contain overhangs and closed contours. Form analysis Comparison of shapes to CAD drawings (DXF) Control of mechanical components (bearings, cams, nozzles etc.) Surface z=f(x,y) A surface is a measurement of heights over a rectangular area of a surface. The height Z is expressed according to a position X,Y. Topography Calculation of the volume of material rejected by a laser impact Control of geometry in nanotechnologies Series of surfaces z=f(x,y,t) Several surfaces packed together as a single data set Surface change over time (wear, bow under a changing constraint) Wear: successive stages of surface wear, calculation of missing volume (3D). Electronic packaging: study of chip carrier distortion when applying a heating cycle Shell Freeform surface Meshes representing the outer shell of an object Outer texture of a 3D object Surface texture of a component that has no particular flat area Multiple-angle reconstruction of an object under the microscope in order to 3D print it Multi-channel image (z1,z2,…zn) = f(x,y) Multiple signal analysis over a rectangular area. Note: Prior to V9.0, this data type was called “Multilayer surface”. Data from multi-channel microscopes, i.e. those which supply more than one value for each pixel (one of the channels is often topography, i.e. map of Z heights, but this is not mandatory) Analyzing data from multi-channel scanning probe microscopes Locating proteins on a 3D topographic representation of a material using the conductivity signal in addition to the height Image (R,G,B) = f(x,y) or G = f(x,y) A common image where each X,Y pixel has a “true” color (RGB) or possibly just a gray level (G) “True color” image or grayscale image Analysis of rust spots Counting objects Measuring nano-objects visible on SEM images Series of images (R,G,B) = f(x,y,t) A collection of images packed into a single data set An animated view of images In Mountains®, a series of images is often used for 3D reconstruction. This can be : a multi-focus image stack a multiple angle view for stereo reconstruction 4 4-quadrant SEM images. The result can then be studied as a surface-image data type (see below). Surface-image (Z,R,G,B) = f(x,y) or (Z,G) = f(x,y) An association of a surface and an image packed into a single data set The image can be a true color image (RGB) or a gray level image (G) This is the standard type of data produced by most optical profilers supplying both topography (Z height) and an image (RGB color) This allows 3D representations of the surface in its true original color (contrary to the “surface” data type above which contains only topography and for which only false-color may be added) All applications of topography, plus the ability to see the 3D surface in its true color Mountains® 3D reconstruction from scanning electron microscopy (2D) images Point cloud (x,y,z) A set of space coordinates with no established order nor relation between them Outer shape of any object, as raw data digitized in 3D by a scanning instrument Import 3D scanner data into Mountains® and convert point clouds into continuous surfaces (Shell or Surface studiable types)

### AFM Force curve analysis

 Data type Description Force curve Used in Atomic Force Microscopy (AFM), force curves represent the deflection of the cantilever according to its vertical distance from the sample. The measurement consists of two curves, the approach curve (blue) and the retract curve (red). Series of force curves A collection of force curves packed into a single data set Force volume A force volume studiable is a grid of equally spaced force curves. Each point in the image corresponds to a force curve that contains an approach and a retract curve. This set of force curves is considered as a single object. Note: this type of studiable has the structure of a “data cube” (virtual multi-dimensional structure, with only two metric axes).

### Spectral and hyperspectral analysis

 Data type Formula Description Suitable for… Example application Spectrum curve(s) Generated by a spectrometer. Peaks in the spectrum curve are detected automatically. A spectrum generated by any type of spectrometer: Raman, FTIR, EDX etc. Mountains® offers advanced tools for analyzing hyperspectral data, such as blind unmixing functions allowing dissociation of the original spectrum curves from an image. Hyperspectral image In a hyperspectral image, each pixel represents a full spectrum. The color of the pixel in a slice gives information about the intensity or amplitude of the spectrum at the given wavenumber. Note: this type of studiable has the structure of a “data cube” (virtual multi-dimensional structure, with only two metric axes) Note: Prior to V9.0, this data type was called “hyperspectral cube”. Raman, FTIR, EDX, cathodoluminescence etc. or simply hyperspectral visible light cameras supplying hyperspectral images requiring analysis Multi-channel cube (i1,i2,…iN) = f(x,y,z) A cube of voxels encoding the chemical composition of a material. Each voxel located at (x,y,z) encodes one value per channel, each channel (1 to N) representing the abundance of a given material. FIB-SEM tomography based on BSE (a single gray level channel) or on EDS/EDX (several channels, one per material) Confocal Raman microscopes Particle/porosity analysis in full 3D Distribution of grains/particles in heterogeneous materials, material by material Form/texture analysis of objects/grains embedded inside other objects

### What if my instrument data type is not listed above?

The above list contains data types available in currently released versions of Mountains®.