Improved signal model for confocal sensors accounting for object depending artifacts

Differential Confocal Optical Probes with Optimized Detection Efficiency and Pearson Correlation Coefficient Strategy Based on the Peak-Clustering Algorithm

Quantifying free-form surfaces using differential confocal microscopy can be challenging, as it requires balancing accuracy and efficiency. When the axial scanning mechanism involves sloshing and the measured surface has a finite slope, traditional linear fitting can introduce significant errors. This study introduces a compensation strategy based on Pearson's correlation coefficient to effectively reduce measurement errors. Additionally, a fast-matching algorithm based on peak clustering was proposed to meet real-time requirements for non-contact probes. To validate the effectiveness of the compensation strategy and matching algorithm, detailed simulations and physical experiments were conducted. The results showed that for a numerical aperture of 0.4 and a depth of slope < 12°, the measurement error was <10 nm, improving the speed of the traditional algorithm system by 83.37%. Furthermore, repeatability and anti-disturbance experiments demonstrated that the proposed compensation strategy is simple, efficient, and robust. Overall, the proposed method has significant potential for application in the realization of high-speed measurements of free-form surfaces.

Influence of Surface Tilt Angle on a Chromatic Confocal Probe with a Femtosecond Laser

This paper presents an intentional investigation of the effect of the object tilt angle on the tracking local minimum method (TL method), which is the one for detecting the measurement target position of the object optical axis, in a chromatic confocal probe employing a differential dual-fiber-detector optical system with a mode-locked femtosecond laser as the light source. The effect of the object tilt angle on dual-detector confocal probes, and even chromatic confocal probes, has not been investigated in detail so far, although the effect of object tilt angle on scanning confocal probes has been studied. At first, to examine the influence of the object tilt angle on the TL method, a theoretical model is established, and numerical simulations are performed based on the established theoretical equation. Then, the effect of aberrations in confocal optics on the confocal response curve is investigated in experiments. Finally, investigations on the effect of the object tilt angle on the TL method are demonstrated in experiments.

Bidirectional confocal measurement of a microsphere

This paper presents the bidirectional confocal measurement of a microsphere, which enables the simple measurement of the sphere with a similar number of measuring points taken on its upper and its lower hemispheres. The innovative measuring strategy is the placement of the sphere above a mirror and the subsequent measurement of the upper hemisphere on the real sphere and the lower hemisphere on the mirrored sphere. While theoretical explanations are given first, the main focus of the paper is the presentation of the idea itself and the very promising empirical findings. We believe these findings prove that the measuring strategy presented has the potential to become a prime method for the optical characterization of microspheres.

Multi-view object topography measurement with optical sectioning structured illumination microscopy

Various optical instruments have been developed for three-dimensional (3D) surface topography, including the white light interference, reflectance confocal microscopes, and digital holographic microscopes, etc. However, the steep local slope of objects may cause the light to be reflected in a way that it will not be captured by the objective lens because of the finite collection angle of the objective. To solve this "shadow problem," we report a method to enlarge the collection angle range of optical sectioning structured illumination microscopy by capturing sectioned images of the objects from multiple angle of views. We develop a multi-view image fusion algorithm to reconstruct a single 3D image. Using this method, we detect previously invisible details whose slopes are beyond the collection angle of the objective. The proposed approach is useful for height map measurement and quantitative analyses in a variety of fields, such as biology, materials science, microelectronics, etc.

Influence of sample surface height for evaluation of peak extraction algorithms in confocal microscopy

The axial resolution of confocal microscopy is not only dependent on optical characteristics but also on the utilized peak extraction algorithms. In previous evaluations of peak extraction algorithms, sample surface height is generally assumed to be zero, and only sampling-noise-induced peak extraction uncertainty was analyzed. Here we propose a sample surface-height-dependent (SHD) evaluation model that takes the combined considerations of sample surface height and noise for comparisons of algorithms' performances. Monte Carlo simulations were first conducted on the centroid algorithm and several nonlinear fitting algorithms such as the parabola fitting algorithm, Gaussian fitting algorithm, and sinc² fitting algorithm. Subsequently, the evaluation indicators, including mean peak extraction error and mean uncertainty were suggested for the algorithms' performance ranking. Finally, experimental verifications of the SHD model were carried out using a fiber-based chromatic confocal system. From our simulations and experiments, we demonstrate that sample surface height is a critical influencing factor in peak extraction computation in terms of both the accuracy and standard deviations. Compared to the conventional standard uncertainty evaluation model, our SHD model can provide a more comprehensive characterization of peak extraction algorithms' performance and offer a more flexible and consistent reference for algorithm selection.

Coherence scanning and phase imaging optical interference microscopy at the lateral resolution limit

To get physical insight into the 3D transfer characteristics of interference microscopy at high numerical apertures we study reflecting rectangular grating structures. In general, the height obtained from phase information seems to be reduced, whereas height values resulting from coherence scanning sometimes seem to be systematically overestimated. Increasing the numerical aperture of an interference microscope broadens the spectra of the resulting interference signals, thus offering a broad variety of wavelength contributions to be analyzed. If phase analysis of a measured far-field interference wavefront is performed at very short wavelengths the periodical profiles obtained from coherence scanning and phase shifting analysis differ only by the measured amplitude. However, at longer wavelength there is a 180° phase shift of the measured profiles obtained from phase analysis compared to coherence peak analysis. Increasing the evaluation wavelength improves the lateral resolution since the long wavelength contributions are related to electromagnetic waves of high angles of incidence. This behavior is to the best of our knowledge not documented in literature so far. It was first observed experimentally and could be confirmed by simulation results obtained from either Kirchhoff diffraction theory or an extended Richards-Wolf model developed in our group. Compared to original input profiles used for the simulation the profiles obtained from phase evaluation correspond quite well at longer wavelength, whereas the results obtained from coherence peak analysis are typically inverted with respect to height.

Confocal signal evaluation algorithms for surface metrology: uncertainty and numerical efficiency

Confocal microscopy is one of the dominating measurement techniques in surface metrology, with an enhanced lateral resolution compared to alternative optical methods. However, the axial resolution in confocal microscopy is strongly dependent on the accuracy of signal evaluation algorithms, which are limited by random noise. Here, we discuss the influence of various noise sources on confocal intensity signal evaluating algorithms, including center-of-mass, parabolic least-square fit, and cross-correlation-based methods. We derive results in closed form for the uncertainty in height evaluation on surface microstructures, also accounting for the number of axially measured intensity values and a threshold that is commonly applied before signal evaluation. The validity of our results is verified by numerical Monte Carlo simulations. In addition, we implemented all three algorithms and analyzed their numerical efficiency. Our results can serve as guidance for a suitable choice of measurement parameters in confocal surface topography measurement, and thus lead to a shorter measurement time in practical applications.

Measurement of steep edges and undercuts in confocal microscopy

Confocal microscopy is widely used to measure the surface topography of specimen with a precision in the micrometer range. The measurement uncertainty and quality of the acquired data of confocal microscopy depends on various effects, such as optical aberrations, vibrations of the measurement setup and variations in the surface reflectivity. In this article, the influence of steep edges and undercuts on measurement results is examined. Steep edges on the specimen's surface lead to a reduced detector signal which influences the measurement accuracy and undercuts cause surface regions, which cannot be captured in a measurement. The article describes a method to overcome the negative effects of steep edges and undercuts by capturing several measurements of the surface with different angles between the surface and the optical axis of the objective. An algorithm is introduced which stitches different angle measurements together without knowledge of the exact position and orientation of the rotation axis. Thus, the measurement uncertainty due to steep edges and undercuts can be avoided without expensive high-precision rotation stages and time consuming adjustment of the measurement setup.

Super-aperture metrology: overcoming a fundamental limit in imaging smooth highly curved surfaces

The imaging of smooth, highly curved or tilted surfaces is widely recognized as one of the most challenging and unsolved problems in optical imaging and metrology today. The reason is that even when such surfaces are imaged using high aperture microscope objectives the steepness of the features causes the light to be reflected in such a way that it is not captured by the lens. This is true even in the limiting case of unity numerical aperture since the illuminating light may also be reflected in the forward direction. In order to overcome this fundamental problem we have developed a method whereby such specimens are covered with a readily removable organic fluorescent film thereby creating an isotropic scattering surface. We show that we are readily able to detect slopes with angles close 90° using a 0.75 NA objective--an 82% improvement over the theoretical aperture limit. Issues of variation in film thickness deposition are shown to be readily accommodated. This approach may be used with other fluorophore materials, organic or inorganic, since there is no need for biocompatibility in this application.

Systematic errors on curved microstructures caused by aberrations in confocal surface metrology

Optical aberrations of microscope lenses are known as a source of systematic errors in confocal surface metrology, which has become one of the most popular methods to measure the surface topography of microstructures. We demonstrate that these errors are not constant over the entire field of view but also depend on the local slope angle of the microstructure and lead to significant deviations between the measured and the actual surface. It is shown by means of a full vectorial high NA numerical model that a change in the slope angle alters the shape of the intensity depth response of the microscope and leads to a shift of the intensity peak of up to several hundred nanometers. Comparative experimental data are presented which support the theoretical results. Our studies allow for correction of optical aberrations and, thus, increase the accuracy in profilometric measurements.

Topographic optical profilometry of steep slope micro-optical transparent surfaces

Optical profilometers based on light reflection may fail at surfaces presenting steep slopes and highly curved features. Missed light, interference and diffraction at steps, peaks and valleys are some of the reasons. Consequently, blind areas or profile artifacts may be observed when using common reflection micro-optical profilometers (confocal, scanning interferometers, etc…). The Topographic Optical Profilometry by Absorption in Fluids (TOPAF) essentially avoids these limitations. In this technique an absorbing fluid fills the gap between a reference surface and the surface to profile. By comparing transmission images at two different spectral bands we obtain a reliable topographic map of the surface. In this contribution we develop a model to obtain the profile under micro-optical observation, where high numerical aperture (NA) objectives are mandatory. We present several analytical and experimental results, validating the technique's capabilities for profiling steep slopes and highly curved micro-optical surfaces with nanometric height resolution.

Spectral characteristics of chromatic confocal imaging systems

We present signal-generation models for chromatic confocal imaging systems with illumination and detection pinholes of finite size: a collinear model that considers neither aberrations nor diffraction effects, a geometrical model that accounts for aberrations, and a wave optical model covering both aberrations and diffraction effects. These models are aimed at describing the spectral response of multipoint sensor systems with field-dependent aberrations and vignetting effects. They are suitable for single- and double-pass systems with either diffusely or specularly reflecting surfaces under test. We show experimental results to verify our models.

Digital differential confocal microscopy based on spatial shift transformation

Differential confocal microscopy is a particularly powerful surface profilometry technique in industrial metrology due to its high axial sensitivity and insensitivity to noise. However, the practical implementation of the technique requires the accurate positioning of point detectors in three-dimensions. We describe a simple alternative based on spatial transformation of a through-focus series of images obtained from a homemade beam scanning confocal microscope. This digital differential confocal microscopy approach is described and compared with the traditional Differential confocal microscopy approach. The ease of use of the digital differential confocal microscopy system is illustrated by performing measurements on a 3D standard specimen.