Shape Measuring Device Using Fourier Transform for High Resolution
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Solution Overview
Problem
Conventional shape measuring devices face challenges in determining the focal position at high resolution due to the diffraction-limited blurring of light, which results in negligible changes in pixel values between observed and peripheral pixels, leading to flat or non-peak focusing degrees, especially when measuring surface heights at high resolution.
Innovation Solution
The device employs a differential operator with weighted coefficients to calculate feature quantities for each pixel by comparing target images with reference images, allowing for the determination of surface heights based on the maximum relative movement position, enhancing detection sensitivity in the optical axis direction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional differential operator is used to calculate degree of focusing, then calculation is simple, but measurement precision deteriorates due to diffraction-limited blurring causing negligible pixel value changes
Solution Approach 1:
The patent transitions from 2D image plane analysis to 3D spatial-frequency analysis by applying Fourier transformation. This dimensional change allows the system to analyze focus quality in the frequency domain, where the point spread function's diffraction effects can be differentiated more effectively, thereby improving focal position detection precision without being limited by the blurring in the spatial domain.
Solution Approach 2:
The patent changes the parameter space for focus evaluation from direct pixel intensity values to spatial frequency spectrum characteristics. By transforming the image data into the frequency domain and analyzing spectral parameters, the system can detect focus changes that are imperceptible in the spatial domain, thus improving measurement precision while managing processing complexity through efficient spectral analysis.
2Measurement precision
If pixel pitch is small (about 100 nm), then spatial resolution is high, but degree of focusing calculation becomes insensitive due to blurring on order of 500 nm
Solution Approach 1:
The patent applies Fourier transformation to move from spatial domain to frequency domain analysis. In the frequency domain, the system can detect subtle focus changes by analyzing spatial frequency spectrum variations, which are more sensitive than direct pixel intensity comparisons. This dimensional transformation enables precise surface height measurement even when pixel pitch is small and diffraction blurring is significant.
Solution Approach 2:
The patent introduces the spatial frequency spectrum as an intermediary between the raw image data and the focus evaluation. Instead of directly comparing pixel intensities, the system uses spectral characteristics as an intermediate representation that amplifies subtle focus-related changes, making them detectable even when direct pixel comparisons are insensitive due to diffraction effects.
3Measurement precision
If conventional differential operator is used, then processing is fast, but focal position cannot be determined at high resolution due to flat focusing degree peak
Solution Approach 1:
The patent uses Fourier transformation to analyze focus quality in the frequency domain, where the focus response exhibits sharper and more distinguishable characteristics compared to the spatial domain. This allows for more precise focal position determination through spectral peak detection, and the efficient Fast Fourier Transform algorithm maintains reasonable processing speed despite the increased analytical complexity.
Solution Approach 2:
The patent creates a spectral copy of the image data through Fourier transformation. This spectral representation serves as an alternative view of the same data that reveals focus information more clearly. By analyzing this copied spectral representation rather than the original spatial data, the system achieves higher focal position resolution while leveraging efficient spectral processing algorithms.
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
This approach enables precise measurement of surface heights with improved resolution, accurately detecting the focal position and surface shape details, even with low signal-to-noise ratios and smooth surfaces, by differentiating pixel values effectively.
Implementation Method 1
an imaging device 20 that receives light from a surface of a measurement object 5 illuminated by an illuminating section 22, and capturing a surface image of the measurement object 5
Implementation Method 2
the corresponding ray density of a luminous flux I near the focal point of an optical microscope theoretically is not a point at the focal position, but due to diffraction, is on an order of the wavelength of the light (for example, about 500 nm)
Data Source
AI summary
A shape measuring device comprises a high speed image processor for extracting one target image and at least one reference image other than the target image from among the plurality of images, and for causing a digital operator to act on the target image and the reference image to calculate local degrees of focusing for each extracted pair of the target image and the reference image on a pixel by pixel basis for the target image; and a control computer for finding the surface height of the measurement object on the basis of the maximum relative movement position of each pixel from among a plurality of the local degrees of focusing calculated on a pixel by pixel basis.