Hyperspectral interferometry for single-shot absolute measurement of two-dimensional optical path distributions

Abstract

Abstract.We propose a method that we call Hyperspectral Interferometry (HSI) to resolve the 2 phase unwrapping problem in the analysis of interferograms recorded with a narrow-band light source. By using a broad-band light source and hyperspectral imaging system, a set of interferograms at different wavenumbers are recorded simultaneously on a high resolution image sensor. These are then assembled to form a three-dimensional intensity distribution. By Fourier transformation along the wavenumber axis, an absolute optical path difference is obtained for each pixel independently of the other pixels in the field of view. As a result, interferograms with spatially distinct regions are analysed as easily as continuous ones. The approach is illustrated with a HSI system to measure 3-D profiles of optically smooth or rough surfaces. Compared to existing profilometers able to measure absolute path differences, the single shot nature of the approach provides greater immunity from environmental disturbance.

Single-shot areal profilometry using hyperspectral interferometry with a microlens array

“…We denote the sampling points along the wavenumber axis by k p where p = 0, 1, 2,..., N k -1, and N k is the total number of sample points. Strictly speaking there should be two additional subscripts m, n on k p because, unlike the etalon-based system described in [6], the positions of the sample points along the k axis vary from one lenslet to another. However this variation introduces only an additional variable phase term in the depth reconstruction and does not alter the position of the Fourier-domain peak so can be neglected for depth measurement applications.…”

“…Known as hyperspectral interferometry (HSI), it is based on the combination of an interferometer and a hyperspectral imaging system [6,7]. HSI uses a hyperspectral imager to spatially separate a set of narrowband interferograms from a single white-light interferogram.…”

“…Prototype HSI systems and sample profiles from both optically smooth and rough surfaces have been reported in [6] and [7], respectively. A white-light image of the sample was recombined with a reference beam at the entrance of an imaging spectrometer which spread the image along a spectral axis by means of a diffraction grating.…”

Depth-resolved Imaging and Displacement Measurement Techniques Viewed as Linear Filtering Operations

“…Hyperspectral interferometry has been recently proposed for the measurement of surface profiles [7]. By using a broad-band light source and a hyperspectral imaging system, a set of interferograms at different wave numbers are recorded simultaneously on a high resolution image sensor.…”

“…An alternative to the '2 spatial + time' axes, involves the acquisition of time independent data that allows phase volumes to be reconstructed along all three spatial coordinates. 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 3 Wavelength scanning interferometry [1,2], tilt scanning interferometry [3,4], phase contrast spectral optical coherence tomography [5,6] and hyperspectral interferometry [7] have been developed over the past five years and can be regarded as a combination of the depth-sensing capabilities of optical coherence tomography and the phasesensitive capabilities of traditional 2-D full-field interferometric techniques [1-3, 5, 6].…”