Bayesian uncertainty evaluation applied to the tilted-wave interferometer.

The tilted-wave interferometer is a promising technique for the development of a reference measurement system for the highly accurate form measurement of aspheres and freeform surfaces. The technique combines interferometric measurements, acquired with a special setup, and sophisticated mathematical evaluation procedures. To determine the form of the surface under test, a computational model is required that closely mimics the measurement process of the physical measurement instruments. The parameters of the computational model, comprising the surface under test sought, are then tuned by solving an inverse problem. Due to this embedded structure of the real experiment and computational model and the overall complexity, a thorough uncertainty evaluation is challenging. In this work, a Bayesian approach is proposed to tackle the inverse problem, based on a statistical model derived from the computational model of the tilted-wave interferometer. Such a procedure naturally allows for uncertainty quantification to be made. We present an approximate inference scheme to efficiently sample quantities of the posterior using Monte Carlo sampling involving the statistical model. In particular, the methodology derived is applied to the tilted-wave interferometer to obtain an estimate and corresponding uncertainty of the pixel-by-pixel form of the surface under test for two typical surfaces taking into account a number of key influencing factors. A statistical analysis using experimental design is employed to identify main influencing factors and a subsequent analysis confirms the efficacy of the method derived.

Evaluation of absolute form measurements using a tilted-wave interferometer.

Tilted-wave interferometry is a promising measurement technique for the highly accurate measurement of aspheres and freeform surfaces. However, the interferometric fringe evaluation of the sub-apertures causes unknown patch offsets, which currently prevent this measurement technique from providing absolute measurements. Simple strategies, such as constructing differences of optical path length differences (OPDs) or ignoring the piston parameter, can diminish the accuracy resulting from the absolute form measurement. Additional information is needed instead; in this paper, the required accuracy of such information is explored in virtual experiments. Our simulation study reveals that, when one absolute OPD is known within a range of 500 nm, the accuracy of the final measurement result is significantly enhanced.

Analytical Jacobian and its application to tilted-wave interferometry.

Tilted-wave interferometry (TWI) is a novel optical measurement principle for the measurement of aspherical surfaces. For the reconstruction of the wavefront and the surface under test, respectively, perturbation methods are applied, which require the calculation of the Jacobian matrix. For the practical use of the instrument, a fast and exact calculation of the Jacobian matrices is crucial, since this strongly influences the calculation times of the TWI. By applying appropriate approaches in optical perturbation methods we are able to calculate the required Jacobian matrices analytically when the nominal optical path through the system is given. As a result, calculation times for the TWI can be considerably reduced. We finally illustrate the improved TWI procedure and apply methods of optimal design to determine optimal positions of the surface under test. For such applications the fast calculation of the Jacobian matrices is essential.

Preoperative characterization of basal cell carcinoma comparing tumour thickness measurement by optical coherence tomography, 20-MHz ultrasound and histopathology.

Optical coherence tomography (OCT) is a new imaging method with promising results for several dermatological indications, including preoperative skin tumour characterization. While high-frequency ultrasound (HFUS) is frequently used for this purpose, overestimation of tumour thickness is a problem, due to subtumoral inflammatory infiltration that cannot be differentiated from tumour tissue. The aim of this single-centre study was to describe OCT features of basal cell carcinoma (BCC) and to determine vertical tumour thickness accurately, including a comparison with HFUS and histopathology. Tumour thickness values of 10 BCCs measured by OCT did not differ significantly from those measured by histopathology (median difference 0.12 mm). By contrast, the difference between HFUS and histopathology was greater (median difference 0.3 mm). A Pearson's correlation coefficient of 0.83 showed a stronger correlation of OCT in measuring tumour thickness compared with HFUS (0.59). Bland-Altman plots revealed a better agreement of OCT and histopathology concerning tumour thickness measurements. On the basis of this explorative study cohort, OCt was more exact than HFUS in preoperative tumour thickness estimation of BCCs compared with histopathological measurements.

Assessment of tumor thickness in melanocytic skin lesions: comparison of optical coherence tomography, 20-MHz ultrasound and histopathology.

BACKGROUND: Accurate assessment of vertical tumor size is important for surgical treatment planning of melanocytic skin lesions. High-frequency ultrasound (HFUS) is frequently used for this purpose, but overestimation of tumor thickness is known as a problem especially in thin melanocytic lesions. Optical coherence tomography (OCT) as a new imaging technique might be a promising alternative. OBJECTIVE: To evaluate the ability of OCT to accurately determine the vertical tumor thickness of melanocytic skin lesions and to compare it with HFUS and histopathology in order to improve surgical planning. METHODS: In this single-center study, 26 melanocytic lesions were imaged by OCT and HFUS. Vertical lesion dimensions of both methods were compared with histopathological measurements. RESULTS: Bland-Altman plots for OCT and histopathology as well as for HFUS and histopathology revealed better agreement for OCT and histopathology concerning tumor thickness measurements. Tumor thickness values for the melanocytic lesions measured by OCT presented a median tumor thickness of 0.31 mm (range 0.10-0.77) compared to a median tumor thickness of 0.25 mm (range 0.06-1.5) measured by histopathology. The median tumor thickness of HFUS was 0.44 mm (range 0.23-1.1). A Spearman correlation procedure including the correlation coefficient (r) showed a stronger relationship between OCT and histopathology (r = 0.734) compared to HFUS and histopathology (r = 0.390). CONCLUSIONS: On the basis of this smaller study cohort, OCT seems to be more exact than HFUS as far as thickness determination of thin melanocytic skin lesions is concerned.