Optical profiler based on spectrally resolved white light interferometry

Abstract

A white light interferogram can be decomposed into its constituent monochromatic interferograms using a spectrograph. By imaging the white light interferogram on the entrance slit of the spectrograph, the intensities of the monochromatic components can be accessed at its output plane by the pixels of a CCD detector along the direction of dispersion. For a given optical path difference (OPD) in the interferometer, the phases of these constituents are different and linearly related to the wave number of the constituent spectral component. If the phases of all the constituents are determined, the OPD can be obtained as the slope of the phase versus wave number linear fit. Since the OPD is related to the height of the test object at a point, a line profile of the object can be determined if the OPD is measured along the pixels of the CCD parallel to the entrance slit of the spectrograph. To get at the line profile, we must therefore determine the optical phase at all the pixels of the CCD detector. The phase-shifting technique is an obvious choice for this. A piezoelectric transducer (PZT) phase shifter is most common in the application of the phase-shifting technique to monochromatic interferometry. We present the experimental result based on our recent proposal that the conventional PZT phase shifting, although nonachromatic, can be used for this application as well with success. © 2005 Society of Photo-Optical Instrumentation Engineers.

On-line surface inspection using cylindrical lens–based spectral domain low-coherence interferometry

“…20 sampling points along the chromaticity axis of the CCD were calibrated. Two curves, showing the calibrated wavelength with respect to each pixel, were respectively obtained by using higher-order polynomial fitting of experimental data and Hartmann's formula defined as [18] λ λ 0…”

Use of monochromatic phase data for improved profile measurement in spectrally resolved white light interferometry

“…In the present case of white light interference however the phase shift can be π/2 only at a single wavelength, say the mean wavelength. 19 For other wavelengths the phase shift will be different from π/2. It is clear that the measured phase by applying the phase shifting technique to Eqn.…”

“…For wavelength calibration of the CCD camera pixels, a cadmium spectral lamp is used. 19 Figure 2 shows the spectrally resolved white light interferogram of a line on a plane surface with a small tilt with respect to the reference surface. It should be noted from Eqn.…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14] Another white light technique is the Spectrally Resolved White Light Interferometry (SRWLI). [15][16][17][18][19] Here the white light interferogram is spectrally decomposed by passing it through a spectrometer. The interferogram displayed at the exit plane of the spectrometer has a continuous variation of wavelength along the chromaticity axis (dispersion axis).…”

“…We have suggested use of phase shifting technique with a PZT phase shifter and an appropriate error compensating algorithm to determine the phase at several wavelengths simultaneously. [18][19] In SWLI a large number of frames need to be processed to get the profile. But in SRWLI, only few frames are required.…”