Using Optical Profiling to Measure the Form of Highly Sloped Surfaces

The form of highly sloped surfaces has always been a challenging application for optical profilers using the coherence scanning interferometry (CSI) technique. In almost all industries, there are highly sloped surfaces such as machined cones, optical micro-lenses, and brightness-enhancing structures.

ZYGO’s CSI-based profilers, running on Mx™ software, now come with advanced signal detection and processing capabilities, which make it possible to obtain valid topographical data from highly sloped surfaces.

Theoretical Limits

The numerical aperture (NA) of the lens decides the theoretical limit of the slope capacity of a given microscope objective, and is given by:

    arcsine (NA) = maximum angular acceptance

Usually, a high-magnification lens is also a high NA lens. The dependence of the slope limitation on NA is the crucial factor here, as it clearly shows that high magnification alone is not sufficient to achieve the highest possible slope resolution.

For example, an objective lens with an 0.7 NA and 100x magnification would have a maximum slope acceptance of 44 degrees. An objective lens with 0.85 NA and the same 100x magnification has a maximum slope acceptance of 58 degrees, an improvement of more than 30%.

The formula provides a maximum theoretical acceptance angle for a specular test surface - a level that is very difficult to achieve in practice. As the surface slope is increased and approaches the theoretical limit, the strength of light that returns to the interferometer is observed to be weak.

This causes a low-interference signal to be produced, which can hardly be identified from the background illumination from the reference surface of the interferometer. The signal’s weak nature is the main reason why CSI profilers find it difficult to measure highly sloped specular surfaces.

In some cases of non-specular surfaces, the theoretical limit can be exceeded by over 50% due to the surface’s scattering structure. The 100x, 0.85 NA lens mentioned above enables measuring angles as high as 87 degrees on a machined surface on the Nexview™ profiler.

In Practice on a Smooth Surface

For the example measurements, a rectangular glass rod with very sharp 90-degree corners was used as a test specimen. The edge of one corner is presented by placing the rod in a V-block, so that each face is at 45 degrees with regard to the interferometer reference surface. The NewView™ 8000 profiler running Mx™ software uses the 100x, 0.85 NA objective to easily measure this surface in approximately 15 seconds (Figures 1 and 2).

Quartz rid with near-perfect 90° corners

Figure 1. Quartz rid with near-perfect 90° corners

45° slope measured on the Nexview™

Figure 2. 45° slope measured on the Nexview™

The corner is presented by rotating the V-block by 10 degrees, so that one surface is inclined away at a slope of 55 degrees, approaching the theoretical limit of 58 degrees, as determined earlier. The interference pattern has weak signal strength to such an extent that a measurement using typical settings is unable to detect the surface. On the other hand, profilers running the Mx™ software can employ Dynamic Noise Reduction to decrease signal noise and reduce the measurement speed, allowing the detection of weak signal.

For this measurement, a reduction factor of 6x was used and the surface was measured in 350 seconds, as shown in Figure 3. While the surface can also be detected using smaller noise reduction factors, this can result in more missing data.

The exact level of dynamic noise reduction is a tradeoff between measurement throughput and data density. When there is a need for detailed structure information, a higher noise reduction factor can be selected to maximize the surface.

Quartz rod tilted 10° to present one surface at 56°

Figure 3. Quartz rod tilted 10° to present one surface at 56°

In Practice on a Rough Surface

Substantially higher surface angles than the suggested theoretical specular limit can be profiled when measuring a rough, light scattering surface.

The edge of a commercial razor blade can be considered as an example. The blade has a surface slope of approximately 60 degrees, but with an extremely distinct structure. Similar to the example of the glass rod, the surface can be tilted further away using a rotation fixture.

This is demonstrated on a Nexview™ profiler with the blade rotated so that the surface is at a slope of 86 degrees; Figure 4 shows result of this measurement, which was completed in 133 seconds using a 100x, 0.85 NA lens and a 3x Dynamic Noise Reduction.

Commercial razor blade measured on edge shows a measurable surface slope of 86°

Figure 4. Commercial razor blade measured on edge shows a measurable surface slope of 86°

Conclusion and Next Steps

ZYGO’s CSI profilers, running on Mx™ software, use algorithmic advances and measurement techniques, which provide considerable improvements in measuring steep slopes.

In a majority of cases, the measurement capability is close to the theoretical limit, and on rough surfaces, the limit can be exceeded. Since many types of surfaces have variations, ZYGO specifies profilers that provide more conservative performance than those seen in the examples described above.

Overview of ZYGO Nexview™ NX2 Non-Contact Optical Profiling System

For applications requiring high-slope metrology for form and angle measurements, these new tools are very powerful, and can provide far more quantitative metrological data in a short period of time without damaging the parts when compared to competitive non-interferometric methodologies.

ZYGO recommends a free application evaluation to check whether such enhancements will solve specific slope measurement challenges. ZYGO profiler applications engineers can be contacted for an evaluation or additional information.

This information has been sourced, reviewed and adapted from materials provided by Zygo Corporation.

For more information on this source, please visit Zygo Corporation.


Please use one of the following formats to cite this article in your essay, paper or report:

  • APA

    Zygo Corporation. (2024, February 14). Using Optical Profiling to Measure the Form of Highly Sloped Surfaces. AZoOptics. Retrieved on July 20, 2024 from

  • MLA

    Zygo Corporation. "Using Optical Profiling to Measure the Form of Highly Sloped Surfaces". AZoOptics. 20 July 2024. <>.

  • Chicago

    Zygo Corporation. "Using Optical Profiling to Measure the Form of Highly Sloped Surfaces". AZoOptics. (accessed July 20, 2024).

  • Harvard

    Zygo Corporation. 2024. Using Optical Profiling to Measure the Form of Highly Sloped Surfaces. AZoOptics, viewed 20 July 2024,

Ask A Question

Do you have a question you'd like to ask regarding this article?

Leave your feedback
Your comment type

While we only use edited and approved content for Azthena answers, it may on occasions provide incorrect responses. Please confirm any data provided with the related suppliers or authors. We do not provide medical advice, if you search for medical information you must always consult a medical professional before acting on any information provided.

Your questions, but not your email details will be shared with OpenAI and retained for 30 days in accordance with their privacy principles.

Please do not ask questions that use sensitive or confidential information.

Read the full Terms & Conditions.