3D Visualization of Surface Structures

Vertical Resolution – Small Steps, Big Effect

September 20, 2012

One of the main features of a digital microscope is the speed and ease with which it enables surface models to be created of macroscopic and microscopic structures. In a qualitative evaluation, these provide a better understanding and a more detailed documentation of the specimen. In addition, quantification of the surface provides valuable information about the composition of the surface and its wear. Which specimens are suitable for use with a Leica digital microscope, and what are the limitations of the method used?

The three-dimensional imaging of the Leica digital microscopes is based on the principle of focus variation. The limited depth of field of the optics is utilized to determine depth information for the specimen. Vertical movement of the specimen relative to the objective determines the focus information along with the distance to the optics. For each vertical position, the area of the image that is in sharp focus is sep­ar­ated from the blurry area, and both are processed by the software to create a surface model. One of the advantages of this method is that in addition to the height information, the texture of the specimen is also documented. Which influencing factors are determinative for successful creation of a 3D surface model and how do these variables influence lateral and vertical res­olu­tion?

Optics

In microscopy, depth of field is in many cases an empirically understood metric. In practice, the correlations between the numerical aperture, resolution and magnification determine this parameter. With their adjustment options, today's microscopes create a balance between depth of field and resolution that is op­timal for the visual impression – two parameters that in theory are inversely correlated. 

In DIN/ISO standards, the specimen-side depth of field is defined as the “axial depth of the space on both sides of the specimen plane in which the specimen can be moved without detectable loss of sharpness in the image focus, while the positions of the image plane and objective are maintained.“ However, the standard does not give any clues on how to measure the detection threshold of the deterioration of focus. Particularly at low magnifications, the depth of field can be significantly increased by stopping down, i.e. reducing the numerical aperture. This is usually done using the aperture diaphragm or a diaphragm that is on a con­jug­ated plane to the aperture diaphragm. However, the smaller the numerical aperture, the lower the lateral resolution. Thus it is a matter of finding the optimum balance of resolution and depth of field depending on the structure of the specimen.

Texture of the specimen

The texture of the specimen surface encompasses all of its features and characteristics. These include color and brightness characteristics of the surface. As described above, the principle of focus variation is based on the methodical approach. The better the specimen can be divided into sharp and out-of-focus areas, the better the results of the surface model will be. This method is particularly well suited to textures that have a good contrast. As in many application areas of microscopy, the illumination is given an especially important status, as it frequently determines success or failure. Selecting a suitable illumination makes it possible to document even a specimen with little texture. For example, you can select an oblique incident illumination that makes even hidden structures visible.

Mechanical resolution in the vertical direction

The third influencing factor in this equation is the mech­anical resolution in the vertical direction. This term means the smallest possible steps in the z-direction of the focusing drive, which is usually motorized. To make full use of the performance capacity of the  optics, the smallest possible step must be smaller than the currently used depth of field, as otherwise image data are lost. A motorized focus drive with a resolution of 10 μm, for example, is suitable at a depth of field of 15 μm.

The lateral and vertical resolutions that are possible with a Leica DVM system depend on various in­flu­encing factors, such as the surface structure or illuminator, and thus must be determined depending on the application. Interpolation attains a vertical resolution of one-half of the applied depth of field. The lateral resolution is determined by the numerical aperture of the magnification used.

Depth of field – Berek’s formula

The author of the first publication on the subject of visually perceived depth of field was Max Berek, who published the results of his extensive experiments as early as 1927. Berek's formula gives practical values for visual depth of field and is therefore still used today. In simplified form, it is as follows:

TVIS: Visually perceived depth of field
n: Refractive index of the medium in which the specimen is situated. If the specimen is moved, the refractive index of the medium that forms the changing working distance is entered in the equation.
λ: Wavelength of the light used; for white light, lambda = 0.55 μm
NA: Specimen-side numerical aperture
MTOT VIS: Visual total magnification of the microscope

If in the equation above, we replace the visual total magnification with the relationship of the useful magnification (MTOT VIS = 500 to 1,000 · NA), it becomes clear that in a first approximation, the depth of field is inversely proportional to the square of the nu­mer­ical aperture.

Illumination

Selecting the suitable illumination is critical to the success of the examination. The modular design of the Leica Digital Microscopes enables you to combine the selected optics with the optimal illumination for the application. There are the following methods to choose from:

Variable oblique incident illumination

This method changes the illumination direction from vertical to lateral. This approach is particularly suitable for visualizing scratches or small recesses.

Coin in incident light
Coin in oblique incident light
Diffuser

For shiny surfaces, the dynamic range of the camera is insufficient in many cases and many areas of the specimen are overexposed. A diffuser provides reliable reduction of the overexposed area.

Solder point without a diffuser
Solder point with a diffuser
Coaxial illuminator

A coaxial illuminator is used for very shiny or reflective surfaces, such as wafers or metal sections.

Semiconductor structures with coaxial
illumination
Polarized light

Polarized light is used to suppress reflections or for documentation of plastic materials.

Plastic with polarized light
Clockwork with polarized light
Coaxial illuminator with directed light

Here, the directed light creates a three-dimensional impression of the specimen. This is helpful in many cases for determining the surface with greater accuracy.

Semiconductor structures with coaxial illumination
Semiconductor structures with directed coaxial illumination

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