Spectral characteristics of chromatic confocal imaging systems

Fiber chromatic confocal method with a tilt-coupling source module for axial super-resolution

Current fiber chromatic confocal probes suffer from a low axial resolution. This study proposes a fiber chromatic confocal method with a tilt-coupling source module for axial super-resolution. An annular intensity distribution is generated at the fiber port of the probe by adjusting the tilt-coupling angle between the fiber and source module to reduce the width of the confocal axial response characteristic curve at each wavelength and to enhance the intensity contrast of the spectral signal. Compared with the coaxial coupling state, the developed 21° tilt-coupling state can reduce the FWHM by approximately 17%, and the axial resolution increases by 1.7 times.

Thickness measurement method for self-supporting film with double chromatic confocal probes

With the randomness and immeasurability properties of zero point, the conventional self-supporting film thickness measurement model must calibrate the distance between two chromatic confocal sensors using a standard part whose thickness needs to be measured by other methods in advance. The measurement performance is easily disturbed by the calibration process, and by the accuracy of sample thickness or its uniformity. In order to overcome these limitations, a new thickness measurement model was developed by adding an auxiliary transparent film in the initial position of the dispersion field. The lower plane of the reference film is not only applied as the zero point of the first sensor but also can be measured by another sensor, whose value is equal to the sensor distance. Theoretical analysis and simulation showed that the proposed method does not change the linear relationship of the displacement coefficient. In order to verify the proposed measurement model, a laboratory thickness measurement system was developed based on two commercial chromatic confocal sensors with a displacement accuracy less than 0.2 µm. A set of self-supporting film was measured using the proposed system, the traditional method, and the reference system. These experiments indicated that the standard deviation of the calibration results of the sensor distance based on the proposed method was reduced to 0.1 µm, which can be concluded that its stability was improved significantly compared to the conventional model. In addition, the proposed method was able to achieve a measurement accuracy of 0.4 µm, which can demonstrate its efficiency and practicability.

Thickness Measurement for Glass Slides Based on Chromatic Confocal Microscopy with Inclined Illumination

Chromatic confocal microscopy is a widely used method to measure the thickness of transparent specimens. In conventional configurations, both the illumination and imaging axes are perpendicular to the test specimen. The reflection will be very weak when measuring high-transparency specimens. In order to overcome this limitation, a special chromatic confocal measuring system was developed based on inclined illumination. This design was able to significantly improve the signal-to-noise ratio. Compared with conventional designs, the proposed system was also featured by its biaxial optical scheme, instead of a coaxial one. This biaxial design improved the flexibility of the system and also increased the energy efficiency by avoiding light beam splitting. Based on this design, a prototype was built by the authors’ team. In this paper, the theoretical model of this specially designed chromatic confocal system is analyzed, and the calculating formula for the thickness of transparent specimen is provided accordingly. In order to verify its measurement performance, two experimental methodology and results are presented. The experimental results show that the repeatability is better than 0.54 μm, and the axial measurement accuracy of the system could reach the micron level.

Characterization of a chromatic confocal displacement sensor integrated with an optical laser head

In this paper, the results of experimental characterization of an optical system consisting of a chromatic confocal displacement sensor integrated with an optical laser head are presented. As a result of integration, the part of the optical path of the displacement sensor was combined with the optical path of the laser beam. Consequently, a working distance of 250 mm for the optical system was achieved. The main aim of the characterization was to determine the calibration curve, as well as the application parameters of the system. The methodology for spectral data processing with particular emphasis on the effectiveness of various extraction algorithms is presented. The Lorentzian fitting was considered as the optimal algorithm for the optical system. Consequently, a large measuring range of 10 mm was obtained with perfect linear tendency of the calibration curve. The optical system was characterized by high accuracy equal to ±0.11% of the measuring range, as well as 1 µm resolution. Moreover, the functionality of the system was verified on materials commonly used in laser processing and additive manufacturing. Finally, the system was validated through a comparative measurement with a laser profiler.

Locally adaptive thresholding centroid localization in confocal microscopy

We introduce an iteration-free approach, based on a centroid algorithm with a locally adaptive threshold, for nanometer-level peak position localization of the axial response signal in confocal microscopy. This approach has localization accuracies that are near theoretical limits, especially when there is a small number of sampling points within the discrete signal. The algorithm is also orders of magnitude faster compared to fitting schemes based on maximum likelihood estimation. Simulations and experiments demonstrate the localization performance of the approach.

Two-dimensional spectral signal model for chromatic confocal microscopy

In chromatic confocal microscopy, the signal characteristics influence the accuracy of the signal processing, which in turn determines measurement performance. Thus, a full understanding of the spectral characteristics is critical to enhance the measurement performance. Existing spectral models only describe the signal intensity-wavelength characteristics, without taking the displacement-wavelength relation into consideration. These models require prior knowledge of the optical design, which reduces the effectiveness in the optical design process. In this paper, we develop a two-dimensional spectral signal model to describe the signal intensity-wavelength-displacement characteristics in chromatic confocal microscopy without prior knowledge of the optical design layout. With this model, the influence of the dimensional characteristics of the confocal setup and the displacement-wavelength characteristics and monochromatic aberrations of the hyperchromatic objective are investigated. Experimental results are presented to illustrate the effectiveness of our signal model. Using our model, further evaluation of the spectral signal can be used to enhance the measurement performance of chromatic confocal microscopy.

Adaptive modal decomposition based overlapping-peaks extraction for thickness measurement in chromatic confocal microscopy

Accurate overlapping-peaks extraction plays a critical role in chromatic confocal thickness measurement of ultra-thin transparent film. However, the current algorithms usually appear as a perceptible extraction error resulting from the disturbing influence among peaks in the process of fitting the spectral axial response signal (sARS) of the two measuring surfaces. In this paper, we propose an adaptive modal decomposition method to extract multi peaks for the ultra-thin materials. With this method, the sARS can be firstly decomposed into several sub-modes, which can be used to obtain the peak wavelength of each measuring surface by the existing single peak extraction algorithms, such as the centroid method and Gauss fitting method. Monte Carlo simulations and experimental tests demonstrate that the proposed algorithm has significant improvements over the existing nonlinear fitting algorithms in terms of peak extraction accuracy and precision.

Design of a chromatic confocal displacement sensor integrated with an optical laser head

In this paper, the methodology for design of the system consisting of chromatic confocal displacement sensor integrated with an optical laser head was presented. Furthermore, the results of experimental characterization of optical components of the laser head were also included in the numerical analysis. The designed chromatic confocal displacement sensor was analyzed as an assembly of components widely available on the optical market. Nevertheless, the main goal of the numerical optimization was to determine the influence of individual components of the optical path of the system on its parameters, i.e., measuring range, FWHM of the characteristic spectral peak, and intensity that reaches the detector. The optimized solution was characterized in order to determine the calibration curve, as well as other important application parameters of the system. Moreover, taking into consideration the integration aspect the caustic of the laser beam shaped by the laser head was measured. Finally, the versatility of the system was presented and discussed.

Characterization of the displacement response in chromatic confocal microscopy with a hybrid radial basis function network

Characterization of the displacement response is critical for accurate chromatic confocal measurement. Current characterization methods usually provide a linear or polynomial relationship between the extracted peak wavelengths of the spectral signal and displacement. However, these methods are susceptible to errors in the peak extraction algorithms and errors in the selected model. In this paper, we propose a hybrid radial basis function network method to characterise the displacement response. With this method, the peak wavelength of the spectral signal is firstly extracted with a state-of-art peak extraction algorithm, following which, a higher-accuracy chromatic dispersion model is applied to determine the displacement-wavelength relationship. Lastly, a radial basis function network is optimized to provide a mapping between the spectral signals and the residual fitting errors of the chromatic dispersion model. Using experimental tests, we show that the hybrid radial basis function network method significantly improves the measurement accuracy, when compared to the existing characterizing methods.

Corrected parabolic fitting for height extraction in confocal microscopy

Accurate and reliable peak extraction of axial response signals plays a critical role in confocal microscopy. For axial response signal processing, nonlinear fitting algorithms, such as parabolic, Gaussian or sinc² fitting may cause significant systematic peak extraction errors. Also, existing error compensation methods require a priori knowledge of the full-width-at-half-maximum of the axial response signal, which can be difficult to obtain in practice. In this paper, we propose a generalised error compensation method for peak extraction from axial response signals. This full-width-at-half-maximum-independent method is based on a corrected parabolic fitting algorithm. With the corrected parabolic fitting algorithm, the systematic error of a parabolic fitting is characterised using a differential equation, following which, the error is estimated and compensated by solving this equation with a first-order approximation. We demonstrate, by Monte Carlo simulations and experiments with various axial response signals with symmetrical and asymmetrical forms, that the corrected parabolic fitting algorithm has significant improvements over existing algorithms in terms of peak extraction accuracy and precision.

Method of thickness measurement for transparent specimens with chromatic confocal microscopy

In this paper, a new method for measuring the thickness of transparent specimens using chromatic confocal microscopy (CCM) is presented. The conventional CCM thickness measurement model relies on capturing the focal points on the upper and lower surfaces of a transparent specimen. This model has strict specimen placement tolerance and a limited measurement range. In order to overcome these limitations, a new thickness measurement model was developed by adding an auxiliary reflector below the specimen. The thickness of the specimen can be determined by comparing the wavelengths of light focused on the auxiliary reflector before and after placing the measurement specimen. Theoretical analysis and simulation showed that the proposed method has twice the measurement range of the conventional model. In order to verify the proposed CCM measurement model, a laboratory thickness measurement system was developed by the authors' team. A commercial laser scanning confocal microscope (Carl Zeiss LSM780) was used as the reference system. A set of quartz glasses was measured using both the proposed system and the reference system. Experimental comparison showed that the proposed method was able to achieve a measurement accuracy of 0.25 μm. In addition, repeated measurements conducted at different heights showed negligible variation. Thus, it can be concluded that the specimen placement tolerance was improved significantly compared with the conventional model.

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.

An imaging spectrometer employing tunable hyperchromatic microlenses

We present the design, fabrication and characterization of hydraulically-tunable hyperchromatic lenses for two-dimensional (2D) spectrally-resolved spectral imaging. These hyperchromatic lenses, consisting of a positive diffractive lens and a tunable concave lens, are designed to have a large longitudinal chromatic dispersion and thus axially separate the images of different wavelengths from each other. 2D objects of different wavelengths can consequently be imaged using the tunability of the lens system. Two hyperchromatic lens concepts are demonstrated and their spectral characteristics as well as their functionality in spectral imaging applications are shown.

Chromatic confocal matrix sensor with actuated pinhole arrays

We present two versions of a chromatic confocal matrix sensor for the snapshot acquisition of three-dimensional objects. The first version contains separate illumination and detection pinhole arrays, while the second version uses a single pinhole array in double pass. The discrete lateral measurement points defined by the illumination and detection pinhole arrays are evaluated in parallel with a hyperspectral detection module. As this approach enables the spectrometric evaluation of all lateral channels, multilayer objects can be analyzed. To increase the lateral resolution the pinhole arrays are moved by micromechanical actuators. The paper includes a quantitative evaluation of the chromatic confocal module and proof-of-principle experiments with the full sensor system.