Polarization and Spectral Interferometric Techniques for Quantitative Phase Microscopy - Biomedical Optical Phase Microscopy and Nanoscopy - page 291

wavelength. Thus, with a reasonable assumption regarding the average RI, the linear phase
term yields the value d and provides quantitative structural information. Lastly, the third
term contains the variations in the RI with respect to wavelength, ), and is identified

in Eqs. (14.7) and (14.8) by its nonlinear phase. This nonlinear phase term is the source of
information for NLDS, which grants access to the dispersion-causing biochemical properties
of samples. It is important to note that even though multiple parameters are embedded in
the sampled signal—specifically,

Δ n ( ω

μ tot in the intensity modulated term, d , in the linear phase

term, and n in the nonlinear phase term—each is present in only one of the three parts of

Eq. (14.8) and hence can be retrieved independently.

Δ

We demonstrate the NDLS technique using a super continuum laser source (Fianium, MA,
USA) and a 4 f Michelson interferometer. A similar setup was described previously in Ref .
[63] , which used collimated light to probe the sample. To match beam dispersion between
the sample and reference arms of the interferometer, identical MO (40

3

, 0.66 NA, infinity-
corrected, L-40 3 , Newport Corp., CA, USA) are used in each arm, producing a lateral
resolution of 0.46 μ m. The samples are plated on a silvered surface such that input light
passes through the cell media and the sample and is reflected by the silver coating and then
imaged onto the entrance slit of an imaging spectrograph. The use of the imaging
spectrograph allows for acquisition of multiple spectral interferograms across one lateral
dimension. To obtain sample information in the other dimension, the sample is then
translated using a motorized actuator. The imaging spectrograph spans the visible spectrum
of the super continuum source, with 575 nm central wavelength, 240 nm bandwidth, and
0.2 nm spectral resolution.

14.5.1 Fluorescent and Nonfluorescent Polystyrene Beads

To verify the concept of NDLS, we measured fluorescent (Invitrogen F8833) and
nonfluorescent (Thermo Scientific), 10 m polystyrene beads. Samples were prepared by

drying bead solutions on a silver-coated coverglass followed by immersion with glycerol,
mimicking the environment of cell culture. To prepare the raw interferograms for further
processing, they were resampled from the wavelength domain to the wavenumber domain
with linearly spaced sampling points.

μ

The linear phase is processed using SDPM to acquire structural information. To achieve this,
an FFT of the interferograms needs to be computed, but dispersion effects must be eliminated
first. This can be accomplished by first unwrapping the phase of each interferogram and then
fitting it to a line of the form of φ lin 5 ( ω / c 0 ) L2 2 πq [64] , where L is the best estimate of
2 n 0 ml c , and q is an integer describing the initial phase. Figure 14.10A shows the unwrapped
phase of I ( ω ), along with the corresponding linear fit, φ lin , for a point located at the center of
the fluorescent bead. The residual phase,

), which is the difference between the
unwrapped phase and its linear fit, is removed from each interferogram and stored for

Δφ ( ω