2.1.

Microscopes for Interferometry

Interference microscopes for areal surface structure analysis typically comprise infinity-corrected optical systems, electronic cameras, and specialized objectives that are actually compact interferometers. A familiar configuration is a mechanically robust platform with turreted interference objectives covering a range of focal lengths and corresponding magnifications. The light source most often is a light-emitting diode (LED) or a color-filtered thermal source such as a halogen bulb. Köhler illumination is also common, with optics arranged to fill the objective pupil so as to achieve a good approximation of spatially incoherent light and to extend the lateral resolution limit to the theoretical maximum achievable with each objective. A final component of importance is a mechanical focus-scanning mechanism that enables phase-shifting interferometry (PSI) and coherence scanning interferometry (CSI) by computer-controlled modulation of the optical path difference in the interferometer. Expected noise levels in final surface height data are $<0.1\mathrm{nm}/\surd \mathrm{Hz}$ in PSI mode.¹ Several comprehensive review articles detail the capabilities, measurement principles, and applications of interference microscopes.^2–5

2.2.

Classical Interference Objectives

With the exception of Fizeau-type objectives for laser-based systems,⁶ interference objectives require an equal-path geometry carefully balanced for dispersion and chromatic aberration. This is especially true for microscopes designed for CSI data acquisition, which almost by definition involves diffuse, broad spectral bandwidth light sources with coherence lengths of only a few microns. For half a century, interference microscope objectives have been the Linnik, Mirau, or the Michelson type, with the occasional specialized design for unique applications.

The Linnik interferometer is the combination of two conventional microscope objectives, one for the reference path and the other for the imaging path, usually with a cube beamsplitter.^7,8 This configuration is attractive for its large working distance at short focal lengths, e.g., 2 mm for a $100\times$ magnification, when using a 200 mm focal length ($1\times$) tube lens for the final imaging onto the camera. The Linnik design requires carefully selected objectives for balanced dispersion and compensated aberrations. Although Linnik objectives played a central historical role in the development of interference microscopy and are still commercially available today, the cost and complexity of such objectives restrict their use to specialized applications.

Mirau⁹ invented his design in the 1940s, which today is the preferred type for high magnifications. The Mirau objective shown in Fig. 1(a) has the advantage of coaxial lens, beamsplitter, and reference mirror and an inherently compact package. Assuming that the beamsplitter and reference mirror are cut from the same glass, the symmetry of this configuration brings the reference and object surfaces simultaneously into precise focus at the position of zero optical path difference, with minimal dispersion imbalance and high fringe contrast. The small reference mirror obscures the light path; however, if the pupil is filled with spatially extended illumination, a high numerical aperture (NA) accommodates the central obscuration. Typically, these objectives range in magnification from $10\times$ to $100\times$, with the field of view of a $20\times$ objective $\sim 0.45\text{-}\mathrm{mm}$ square for a $1\times$ tube lens.

Fig. 1

Classical interference objectives in common use for 3-D surface microscopy. (a) Mirau objective with a small, coaxial reference surface that partially obscures the illumination and imaging light and (b) Michelson objective using a prism and a reference path orthogonal to the measurement path.

At magnifications lower than $10\times$ and correspondingly smaller NA values, the central obscuration of the classical Mirau type blocks too much of the light. One possible solution is to use polarizing elements to control the transmission through a partially transparent reference surface, in what is referred to as an unobscured Mirau objective.^10,11 However, the polarizing elements considerably complicate the design, making it more difficult to compensate dispersion and introducing sensitivity to polarization effects that are otherwise not relevant to the Mirau because of its circular symmetry.

The Michelson geometry of Fig. 1(b) has been the preferred solution for magnifications lower than $10\times$. This configuration comprises a conventional microscope lens, a beam-splitting cube prism, and a reference arm assembly orthogonal to the main axis of the objective. The design has origins in Sagnac’s¹² proposal for interferometric texture measurement and was made popular as an interchangeable microscope objective by Watson and Sons in 1960s.¹³ There is no central obscuration as in the Mirau type, allowing for smaller NA values and larger fields of view. However, for magnifications below $2\times$, the physical size of the Michelson design, with its prism and off-axis reference path, can be unwieldy. This is particularly the case if the desire is to mount the objective on a turret with other objectives of higher magnification. As a consequence, fields of view larger than 10 mm are often associated with Twyman Green^14–16 or other custom interferometer platforms that differ from the more flexible model of a microscope with interchangeable objectives.

4.1.

Turret Mounted 1.4× Objective, Parfocal with Higher Magnifications

Figure 3 shows a first example wide-field $1.4\times$ interferometer assembled from a microscope objective lens and the tilted beamsplitter and semitransparent reference plates. The plates fit neatly between the lens and the sample, in a working space that is far too restrictive for a Michelson prism. This allows the complete objective to maintain the 60-mm parfocal length common to interference objectives from $5\times$ to $100\times$.²⁰ The new objective is more compact than a $5.5\times$ Michelson type (see Fig. 4) while providing a 17-mm diameter field of view—an image size unmatched by any commercially available objective with this parfocal length. Table 1 lists the technical specifications for this objective.

Fig. 3

Compact $1.4\times$ interference objective based on a 144-mm focal length microscope objective and the configuration of Fig. 2.

Fig. 4

The $1.4\times$ interferometer (to the right in the figure) mounted on a turret with parfocal $2.75\times$ and $5.5\times$ Michelson objectives and a $20\times$ Mirau objective. These lenses all have the same 60-mm parfocal distance.

Table 1

Turret-mounted wide-field 1.4× objective.

Figure 5 illustrates the range of magnification made possible by the $1.4\times$ objective with a fixed $1\times$ tube lens with minimal refocusing, using the objective turret. The images are for a lateral calibration sample having a variety of grid sizes. In the $1.4\times$ image, the coarse grid has a 0.5-mm pitch, easily accommodated in the $6\times 6\mathrm{mm}$ field at $1\times$ zoom. The finest grid, with a 0.03-mm pitch, is just barely resolved, but we can observe the overall form of the sample on a nanometer height scale. A motorized turret moves into place the $100\times$ objective with a $0.083\times 0.083\mathrm{mm}$ field that images detail of the individual squares of the 0.03-mm pitch grating. This figure demonstrates the ability to easily switch between millimeter-scale form and micron-scale structure and texture using parfocal objectives. Software switchable tube lenses available on some systems further extend the range of field sizes, enabling system magnifications from $0.7\times$ to $200\times$ using $0.5\times$ to $2\times$ zoom settings, respectively. [Software selectable tube lenses (also referred to as zoom lenses) are available on the ZYGO Nexview™ and NewView™ 8300 interference microscopes].

Fig. 5

Illustration of the dynamic range in field of view between two parfocal objectives mounted on the same turret: The new $1.4\times$ (upper figure) and a Mirau $100\times$ (lower figure). The tube lens in this example has a fixed $1\times$ magnification. The feature height is $0.04\mu \mathrm{m}$.

4.2.

Dovetail-Mount 0.5× lens

It is reasonable to ask how large a field of view is achievable with the new design if we set aside the requirements of 60-mm parfocal distance. An answer is provided by a $0.5\times$ lens for measuring large surface areas on a standard CSI microscope platform. An objective at this low magnification presents many challenges—the focal length is 400 mm, and the large field requires a beamsplitter with a clear aperture of 80 mm. Figure 6 shows the considerable advantages in size, weight, and manageability of the new design when compared with what would be the required in the Michelson geometry.

Fig. 6

Comparison of (a) the new wide-field and (b) the traditional Michelson geometries for a $0.5\times$ interference objective. At low magnification and corresponding low NA, the new design is more compact and easier to handle.

A $0.5\times$ objective is now available commercially with a 48-mm diameter field of view when using a $0.5\times$ (100-mm focal length) tube lens. Table 2 lists the technical specifications for this objective. The optical design achieves well-controlled lateral chromatic aberration $<8\mu \mathrm{m}$ through the tilted beamsplitter and reference plates, and a distortion $<0.1\%$ over the full field at 0.015 NA. A dovetail mount allows for installing the objective interchangeably with objectives of other magnifications on a complete CSI system for both form and texture measurements. A megapixel camera provides lateral sampling of $32\mu \mathrm{m}$ over a $32\times 32\mathrm{mm}$ area.

Table 2

Dovetail-mounted wide-field 0.5× objective.

A primary target application is the measurement of technical surfaces using CSI. Figure 7 shows the measurement result for a metal part having a ground, unpolished surface finish. The surface roughness is such that there are no continuous fringes visible in the instrument. The full 3-D image with 1 million data points requires only a few seconds to measure with CSI and the new $0.5\times$ objective.

Fig. 7

False-color 3-D areal topography map of a machined fuel injector component, measured with one field of view using the new $0.5\times$ objective.

The combination of the new objective and field stitching²¹ allows for the measurement of areas well beyond the size usually considered accessible to a microscope platform. The benefits of the wide-field objective in this case are significantly reduced data acquisition time and improved form metrology as a consequence of fewer stitched fields. As an example, Fig. 8 shows an assembly of gears in a housing with variable surface textures and discrete surface heights and reflectivities. Figure 9 shows the surface topography of this assembly measured with the $0.5\times$ objective. The measurement is the composite of 29 overlapping CSI image fields acquired and aligned automatically in less than a minute under computer control.

Fig. 8

Photograph of a 150-mm diameter transmission pump assembly.

Fig. 9

Measured 3-D image of the part shown in the Fig. 8, using the $0.5\times$ objective. For this image, the height range is $Sz=119.8\mu \mathrm{m}$.