Height Map Calculation for Inclined Transparent Surfaces
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Solution Overview
Problem
Optical profilers with limited numerical apertures cannot measure height maps of transparent materials with inclined surfaces effectively, as the reflected measurement beam is reflected outside the numerical aperture, preventing accurate determination of the surface height.
Innovation Solution
A method involving an optical profiler with a limited numerical aperture, where a height map of an inclined surface is calculated using the refractive index and measured height maps of a first area on the inclined surface and a second area of the underlying surface, applying the formula HIS = (ZUS - ZIS)/(n - 1) + ZUS, to account for the optical path length and refraction effects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If an optical profiler with limited numerical aperture is used to measure transparent materials with inclined surfaces, then the measurement capability is restricted, but the device complexity and cost are reduced
Solution Approach 1:
The patent introduces an intermediary calculation method that uses the measured height map of the underlying surface and the known refractive index as mediators to derive the height map of the inclined surface. Instead of directly measuring the inclined surface (which fails due to numerical aperture limitations), the method measures the underlying surface through the transparent material and calculates the inclined surface height using optical path length relationships. This intermediary approach enables measurement of inclined surfaces without requiring the profiler to directly detect reflected beams from steep angles.
Solution Approach 2:
The patent changes the measurement parameter from direct surface reflection (which fails for inclined surfaces) to transmission through the transparent material. By measuring the underlying surface through the transparent body and using the refractive index parameter to correct the optical path length, the method transforms an impossible direct measurement into a feasible indirect measurement. The key parameter change is measuring through the material rather than reflecting from the inclined surface.
2Adaptability or versatility
If the numerical aperture of the objective is increased to capture reflected beams from inclined surfaces, then measurement capability improves, but the device complexity and cost increase
Solution Approach 1:
Instead of changing the physical parameter of numerical aperture to expand measurement capability, the patent changes the measurement approach parameter from reflection-based to transmission-based. By measuring through the transparent material and using refractive index correction, the method achieves inclined surface measurement with standard numerical apertures, avoiding the need for complex high-NA objectives.
Solution Approach 2:
The patent uses the underlying surface measurement and refractive index as intermediaries to avoid the need for high numerical aperture. Rather than directly capturing reflected beams from inclined surfaces (which would require high NA), the method measures the underlying surface through the transparent material and calculates the inclined surface geometry, eliminating the need for complex optical hardware.
3Productivity
If direct measurement of inclined surfaces is attempted, then measurement speed is maintained, but measurement accuracy is lost due to beam reflection outside numerical aperture
Solution Approach 1:
The patent introduces an intermediary calculation step that processes the underlying surface measurement data using refractive index relationships. This calculation intermediary transforms the transmitted light measurement (which captures all rays regardless of inclination) into accurate inclined surface height information, maintaining measurement speed while ensuring precision through optical path length correction.
Solution Approach 2:
The patent replaces the mechanical/optical constraint of direct beam reflection with a computational approach. Instead of relying on the optical system to physically capture reflected beams (which fails for inclined surfaces), the method uses computational processing of transmission data through refractive index correction to derive accurate surface geometry, substituting optical mechanical capability with computational analysis.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Enables the calculation of height maps for inclined surfaces even when the reflected radiation falls outside the numerical aperture, providing accurate surface height measurements by accounting for the refractive index and underlying surface offset.
Implementation Method 1
a detector for receiving an interference radiation intensity from the reflected reference beam from the reference reflector and the reflected measurement beam from the surface
Implementation Method 2
a body of a transparent material having a refractive index n with an inclined or curved surface
Data Source
Figure 1a
Figure 1b~3
Figure 4~5c
AI summary
The invention relates to a method for calculating a height map of a sample comprising a body of a transparent material having a refractive index (n) with an inclined or curved surface, the body being provided on an underlying surface extending laterally from underneath the body. The method comprising: positioning a first area of a body of a transparent material with an inclined or curved surface and a second area of the underlying surface extending laterally from underneath the body under an optical profiler; measuring a height map of the first area (ZIS) and the second area (ZUS) with the optical profiler; and, calculating a height map of the inclined or curved surface (HIS) by using the refractive index, the measured height map of the first area (ZIS) and the second area (ZUS).