Sanjit K. Debnath

Real-time quantitative phase imaging with a spatial phase-shifting algorithm

This Letter reports on the use of a spatial phase-shifting algorithm in a fast, straightforward method of real-time quantitative phase imaging. The computation time for phase extraction is five times faster than a Fourier transform and twice as fast as a Hilbert transform. The fact that the phase extraction from an interferogram of 512 × 512 pixels takes less than 8.93 ms with a typical desktop computer suggests the proposed method can be readily applied to high-speed dynamic quantitative phase imaging. The proposed method of quantitative phase imaging is effective and sufficiently general for application to the dynamic phenomena of biological samples.

Spectrally resolved white-light phase-shifting interference microscopy for thickness-profile measurements of transparent thin film layers on patterned substrates

We describe how spectrally-resolved white-light phase-shifting interference microscopy with a windowed 8-step algorithm can be used for rapid and accurate measurements of the thickness profile of transparent thin film layers with a wide range of thicknesses deposited upon patterned structures exhibiting steps and discontinuities. An advantage of this technique is that it can be implemented with readily available hardware.

Spectrally resolved phase-shifting interferometry of transparent thin films: sensitivity of thickness measurements

Spectrally resolved white-light phase-shifting interference microscopy can be used for rapid and accurate measurements of the thickness profile of transparent thin-film layers deposited upon patterned structures exhibiting steps and discontinuities. We examine the sensitivity of this technique and show that it depends on the thickness of the thin-film layer as well as its refractive index. The results of this analysis are also valid for any other method based on measurements of the spectral phase such as wavelength scanning or white-light interferometry.

Optical profiler based on spectrally resolved white light interferometry

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.

Improved optical profiling using the spectral phase in spectrally resolved white-light interferometry

In spectrally resolved white-light interferometry (SRWLI), the white-light interferogram is decomposed into its monochromatic constituent. The phase of the monochromatic constituents can be determined using a phase-shifting technique over a range of wavelengths. These phase values have fringe order ambiguity. However, the variation of the phase with respect to the wavenumber is linear and its slope gives the absolute value of the optical-path difference. Since the path difference is related to the height of the test object at a point, a line profile can be determined without ambiguity. The slope value, though less precise helps us determine the fringe order. The fringe order combined with the monochromatic phase value gives the absolute profile, which has the precision of phase-shifting interferometry. The presence of noise in the phase may lead to the misidentification of fringe order, which in turn gives unnecessary jumps in the precise profile. The experimental details of measurement on standard samples with SRWLI are discussed in this paper.

Experimental study of the phase-shift miscalibration error in phase-shifting interferometry: use of a spectrally resolved white-light interferometer

The white-light interferogram in a spectrally resolved white-light interferometer is decomposed in its constituent spectral components by a spectrometer and displayed along its chromaticity axis. A piezoelectric transducer phase shifter in such an interferometer can give a desired phase shift of pi/2 only at one wavelength. The phase shift varies continuously at all other wavelengths along the chromaticity axis. This situation is ideal for an experimental study of the phase error due to the phase-shift error in the phase-shifting technique, as it will be shown in this paper.

Spectrally resolved phase-shifting interference microscopy: technique based on optical coherence tomography for profiling a transparent film on a patterned substrate

Spectrally resolved white-light phase-shifting interference microscopy has been used for measurements of the thickness profile of a transparent thin-film layer deposited upon a patterned structure exhibiting steps and discontinuities. We describe a simple technique, using an approach based on spectrally resolved optical coherence tomography, that makes it possible to obtain directly a thickness profile along a line by inverse Fourier transformation of the complex spectral interference function.

Analysis of spectrally resolved white light interferometry by Hilbert transform method

Scanning White Light Interferometry (SWLI) is a tool for measuring discontinuous surface profile. A short coherence length white light source is used in the interferometer so that the fringes are localized in the vicinity of zero Optical Path Difference (OPD). The object surface is scanned along the height axis to get the height variation over the object field. Another technique using white light is Spectrally Resolved White Light Interferometry (SRWLI) in which the white light interferogram is spectrally decomposed by a spectrometer. The interferogram displayed at the exit plane of the spectrometer has a continuous variation of wavelength along the chromaticity axis. This interferogram encodes the phase as a function of wave number. For a given OPD, the phase is different for different spectral component of the source. The OPD can be determined as the slope of the phase versus wave number linear fit. To determine the phase of the different spectral components, temporal phase shifting technique which typically uses five frames has been proposed. Since the OPD is related to the height of the test object at a point, a line profile of the object can be determined. In this paper we discuss the Hilbert Transform method for determination of phase in SRWLI. This procedure requires only one spectrally resolved white light interferogram.

White light diffraction phase microscopy as profilometry tool

Abstract. A reflection type white light diffraction phase microscope for full field surface profiling of opaque samples is proposed. The system can extract surface profile from one recorded interferogram without any mechanical movement and the use of white light makes it free from speckle noise. We validated the performance of our system by measuring a known step sample and a high-quality plane sample. The step height of the step sample is found to be 88.5 nm with a standard deviation of 1.4 nm, and the surface peak to valley value of the plane sample is found to be 28.6 nm with a standard deviation of 3 nm.

Spectrally resolved phase-shifting interferometry for accurate group-velocity dispersion measurements

We report an accurate method to measure the group-velocity dispersion (GVD) of transparent materials by use of spectrally resolved phase-shifting interferometry. The GVD of silica glass slide measured using an eight-step phase-shifting algorithm agrees well with that calculated using the Sellmeier dispersion equation over the entire visible wavelength region, with a rms error of < or =0.0036 microm(-2), better than that of other measurement methods reported so far.