Quantitative
QPI images quantitatively measure the optical thickness of a sample.
Iatia's QPI calculates phase values for each point in an image based on the degree of phase shift induced in light traversing through the sample. The magnitude of phase shift (changes in optical thickness) is the product of sample thickness and refractive index. When one of these properties is known, the other can be determined.
Case study - silicon sphere
The following image on the right shows a silicon sphere approximately 20nm in diameter imaged on a transmission electron microscope (TEM) at 92,000x magnification. The spherical balls of silica were mounted on holey carbon substrate and imaged. Note that the amplitude contrast of the brightfield image for this sample is substantial and indicates that the sample contains significant scattering.
A phase map of the sphere was generated by QPI from two defocused images (shown below). The line profile indicates the projected phase excursion.
QPI phase map
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Line graph - optical thickness profile
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Despite the strong scattering, the phase of the sample is accurately recovered3 and displays the structure expected for the phase shift induced by a small sphere.
Isometric plot of the QPI phase map.
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References
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Quantitative Phase Imaging Using Hard X Rays
K. A. Nugent, T. E. Gureyev, D. F Cookson, D. Paganin and Z. Barnea, Physics Review Letters 77, 2961-2964 (1996). -
Non-Interferometric Quantitative Phase Imaging with Soft X-rays
B.E. Allman, P.J. McMahon, J.B. Tiller, K.A. Nugent, D. Paganin, A. Barty, I. McNulty, S.P. Frigo, S. Wang, and C.C. Retsch, J. Opt. Soc. Am. A 17, 1732-1743 (2000). -
Quantitative Phase-Amplitude Microscopy II: Differential Interference Contrast Imaging for Biological TEM
P.J.McMahon, E.D.Barone-Nugent, B.E.Allman and K.A. Nugent, Journal of Microscopy, 206, 204-208 (2002).