Дослідження методів знешумлення інтерферограми білого світла

Abstract

Проаналізовано джерела спотворень інтерферограми білого світла. Обґрунтовано методику та досліджено ефективність знешумлення синтезованого сигналу інтерферограми з використанням цифрових фільтрів та вейвлет-перетворення. Результати апробовано на реальній інтерферометричній картині. Проанализированы источники искажений интерферограмы белого света. Обоснована методика и исследована эффективность фильтрации синтезированного сигнала интерферограмы с использованием цифровых фильтров и вейвлет-преобразования. Результаты апробированы на реальной интерферометрической картине. White light interferometry (WLI) is a non-contact measurement technique which is commonly used in determining the mechanical quantities such as geometric dimensions, position, and surface topography of the object. The main areas of use of the white light interferometers are micro- and nanotechnology, biomechanics, polymer chemistry, semiconductor equipment, and others. The measuring channel of optical interferometer includes the optical part and the computer unit. The accuracy of surface reconstruction depends on the quality of interferogram registration (optical part) and metrological properties of the reconstruction algorithm (computer unit). In practice interferogram registration is accompanied by different distortions, including optical nonlinearities and noise. Reduce of the distortions destabilizing effect can be achieved by processing the obtained interferogram in a computing unit by special algorithms. The aim of the work is analysis of methods for white light interferogram denoising. The article analyzes the distortion sources of white light interferogram and the ways of their processing. The technique of researchis based on analyzing the effectiveness of denoising the synthesized white light interferogram with signal-tonoise ratio of 30 dB. Quantitative parameter for evaluating the filtering effectiveness is signal-to-noise ratio. Firstly the researches were conducted on one-dimensional data (for the central line of interferometric pattern). This article examines the possibility of WLI denoising with digital filters (frequency domain) and wavelet transform (time-frequency domain). When using digital filters, the non-recursive filters were selected, as they are characterized by a linear phase response that will keep the shape signal. Filtering of interferogram signal using nonrecursive filter has not produced satisfactory results, as in one case with noise suppression the part of useful signalis damaged, and the signal-to-noise ratio was 15 dB. By increasing the cutoff frequency of the filter, signal shape does not undergo distortion, but there are some artifacts, especially in its central part. The reason is that the signal lies partly in the frequency dominated, where the noise predominates. The signal-to-noise ratio was 35 dB. Wavelet transform allows to decompose a signal to approximating and detailing components, with higher levels of detailing component responsible for scheduling and signal noise can be set to zero without signal distortion. Application of wavelet transformation made it possible to achieve better denoising results compared to digital filters with signal-tonoise ratio about 50 dB. Taking into account these results, the wavelet transform method is adapted to the two-dimensional data (interferometric pattern). Compared to the one-dimensional data the denoising is slightly lower, as evidenced by the signal-to-noise ratios about 40 dB. This is due to the fact that the interferogram signal intensity decreases as the distance from its center. The effectiveness of the denoising method based on wavelet transform was investigated on a real white light interferogram obtained for a spherical surface. Defects observed in the interferometric pattern after denoising are caused by optical distortions.