Traceable Reference Full Metrology Chain for Innovative Aspheric and Freeform Optical Surfaces Accurate at the Nanometer Level.

The design of innovative reference aspheric and freeform optical elements was investigated with the aim of calibration and verification of ultra-high accurate measurement systems. The verification is dedicated to form error analysis of aspherical and freeform optical surfaces based on minimum zone fitting. Two thermo-invariant material measures were designed, manufactured using a magnetorheological finishing process and selected for the evaluation of a number of ultra-high-precision measurement machines. All collected data sets were analysed using the implemented robust reference minimum zone (Hybrid Trust Region) fitting algorithm to extract the values of form error. Agreement among the results of several partners was observed, which demonstrates the establishment of a traceable reference full metrology chain for aspherical and freeform optical surfaces with small amplitudes.

Spectral Reflectance Estimation Using Gaussian Processes and Combination Kernels.

This paper explores hyperspectral reflectance factor estimation using Gaussian process regression with multispectral- and trichromatic measurements. Estimations are performed in visible- (400-700 nm) or visible-near infrared (400-980 nm) wavelength ranges using the learning-based approach, where sensor and light spectral characteristics are not required. We first construct new estimation models via Gaussian processes, show connection to previous kernel-based models, and then evaluate new models by using marginal likelihood optimization within the probabilistic interpretation. By using standard spectral ensembles and several images in experiments, we evaluate new models with anisotropic radial- and combination kernels (process covariance), marginal likelihood optimization (parameter selection), as well as with input data transformations (pre-processing). Several new Gaussian process models provide spectral accuracy improvements for simulated and real data, when compared with the previous kernel-based models. Most versatile new model is using spectral subspace coordinate learning and combination kernels, and can be efficiently optimized via marginal likelihood. Preliminary results suggest that new models provide uncertainty estimates, which can be used for iterative training set augmentation.

Transfer standard for traceable dynamic calibration of stroboscopic scanning white light interferometer.

The reconstructed image of a moving sample always shows a distorted representation of reality. Therefore, one needs to calibrate, for example, out-of-plane nano-videos for quality control of nano-microelectromechanical systems (N-MEMS). Here we discuss how to calibrate and obtain confidence limits for stroboscopic scanning white light interferometry (SSWLI) data when there are differences in speed and amplitude across the field of view. Many N-MEMS devices rely on oscillating structures; consequently, one must calibrate movie recordings of these structures to have global standards and to allow inter-device comparison. We propose to use a quartz tuning fork driven off-resonance as a transfer standard. This approach allows a broad range of traceable frequencies and out-of-plane amplitudes to be introduced into selected parts of the field of view of the SSWLI device featuring similar optical surface properties to many N-MEMS devices without demanding an additional reference surface.

Spectral imaging using consumer-level devices and kernel-based regression.

Hyperspectral reflectance factor image estimations were performed in the 400-700 nm wavelength range using a portable consumer-level laptop display as an adjustable light source for a trichromatic camera. Targets of interest were ColorChecker Classic samples, Munsell Matte samples, geometrically challenging tempera icon paintings from the turn of the 20th century, and human hands. Measurements and simulations were performed using Nikon D80 RGB camera and Dell Vostro 2520 laptop screen as a light source. Estimations were performed without spectral characteristics of the devices and by emphasizing simplicity for training sets and estimation model optimization. Spectral and color error images are shown for the estimations using line-scanned hyperspectral images as the ground truth. Estimations were performed using kernel-based regression models via a first-degree inhomogeneous polynomial kernel and a Matérn kernel, where in the latter case the median heuristic approach for model optimization and link function for bounded estimation were evaluated. Results suggest modest requirements for a training set and show that all estimation models have markedly improved accuracy with respect to the DE00 color distance (up to 99% for paintings and hands) and the Pearson distance (up to 98% for paintings and 99% for hands) from a weak training set (Digital ColorChecker SG) case when small representative training data were used in the estimation.

Evaluating logarithmic kernel for spectral reflectance estimation-effects on model parametrization, training set size, and number of sensor spectral channels.

In this work, we evaluate the conditionally positive definite logarithmic kernel in kernel-based estimation of reflectance spectra. Reflectance spectra are estimated from responses of a 12-channel multispectral imaging system. We demonstrate the performance of the logarithmic kernel in comparison with the linear and Gaussian kernel using simulated and measured camera responses for the Pantone and HKS color charts. Especially, we focus on the estimation model evaluations in case the selection of model parameters is optimized using a cross-validation technique. In experiments, it was found that the Gaussian and logarithmic kernel outperformed the linear kernel in almost all evaluation cases (training set size, response channel number) for both sets. Furthermore, the spectral and color estimation accuracies of the Gaussian and logarithmic kernel were found to be similar in several evaluation cases for real and simulated responses. However, results suggest that for a relatively small training set size, the accuracy of the logarithmic kernel can be markedly lower when compared to the Gaussian kernel. Further it was found from our data that the parameter of the logarithmic kernel could be fixed, which simplified the use of this kernel when compared with the Gaussian kernel.

Identifying diagonal cutter marks on thin wires using 3D imaging.

We present work on matching 2-mm-thick wires using optical 3D imaging methods. Marks on such small surfaces are difficult to match using a comparison microscope as this 2D imaging method does not provide height data about the sample surface. Moreover, these 2D microscopy images may be affected by illumination. Hence, the reference and investigated sample should be present at the same time. We employed scanning white light interferometry and confocal microscopy to provide quantitative 3D profiles for reliable comparison of samples that are unavailable for simultaneous analysis. We show that 3D profiling offers a solution by allowing illumination-independent sample comparison. We correctly identified 74 of 80 profiles using consecutive matching striae (CMS) criteria, and we were able to match samples based on profiles measured using different 3D imaging devices. The results suggest that the used methods allow matching cutter marks on thin wires, which has been difficult previously.

Link functions and Matérn kernel in the estimation of reflectance spectra from RGB responses.

We evaluate three link functions (square root, logit, and copula) and Matérn kernel in the kernel-based estimation of reflectance spectra of the Munsell Matte collection in the 400-700 nm region. We estimate reflectance spectra from RGB camera responses in case of real and simulated responses and show that a combination of link function and a kernel regression model with a Matérn kernel decreases spectral errors when compared to a Gaussian mixture model or kernel regression with the Gaussian kernel. Matérn kernel produces performance similar to the thin plate spline model, but does not require a parametric polynomial part in the model.

Stroboscopic scanning white light interferometry at 2.7 MHz with 1.6 µm coherence length using a non-phosphor LED source.

Stroboscopic scanning white light interferometry (SSWLI) allows precise three dimensional (3D) measurements of oscillating samples. Commercial SSWLI devices feature limited pulsing frequency. To address this issue we built a 400-620 nm wideband 150 mW light source whose 1.6 µm wide interferogram is without side peaks. The source combines a non-phosphor white LED with a cyan LED. We measured a calibration artifact with 10 nm precision and obtained 40 nm precision when measuring the 3D profile of a capacitive micromachined ultrasonic transducer membrane operating at 2.72 MHz. This source is compatible with solid state technology.

Evaluation and unification of some methods for estimating reflectance spectra from RGB images.

The problem of estimating spectral reflectances from the responses of a digital camera has received considerable attention recently. This problem can be cast as a regularized regression problem or as a statistical inversion problem. We discuss some previously suggested estimation methods based on critically undersampled RGB measurements and describe some relations between them. We concentrate mainly on those models that are using a priori information in the form of high-resolution measurements. We use the "kernel machine" framework in our evaluations and concentrate on the use of multiple illuminations and on the investigation of the performance of global and locally adapted estimation methods. We also introduce a nonlinear transformation of reflectance values to ensure that the estimated reflection spectra fulfill physically motivated boundary conditions. The reported experimental results are derived from measured and simulated camera responses from the Munsell Matte, NCS, and Pantone data sets.

Regularized learning framework in the estimation of reflectance spectra from camera responses.

For digital cameras, device-dependent pixel values describe the camera's response to the incoming spectrum of light. We convert device-dependent RGB values to device- and illuminant-independent reflectance spectra. Simple regularization methods with widely used polynomial modeling provide an efficient approach for this conversion. We also introduce a more general framework for spectral estimation: regularized least-squares regression in reproducing kernel Hilbert spaces (RKHS). Obtained results show that the regularization framework provides an efficient approach for enhancing the generalization properties of the models.