Background:The refractive index (RI) of cellular material provides fundamental biophysical information about the composition and organizational structure of cells. Efforts to describe the refractive properties of cells have been significantly impeded by the experimental difficulties encountered in measuring viable cell RI. In this report we describe a procedure for the application of quantitative phase microscopy in conjunction with confocal microscopy to measure the RI of a cultured muscle cell specimen. Methods: The experimental strategy involved calculation of cell thickness by using confocal optical sectioning procedures, construction of a phase map of the same cell using quantitative phase microscopy, and selection of cellular regions of interest to solve for the cell RI. Results: Mean cell thickness and phase values for six cell regions (five cytoplasmic and one nuclear) were deter-

One of the significant successes in the field of neutron interferometry has been the experimental observation of the phase shift of a neutron de Broglie wave due to the action of the Earth's gravitational field. Past experiments have clearly demonstrated the effect and verified the quantum-mechanical equivalence of gravitational and inertial masses to a precision of about 1%. In this experiment the gravitationally induced phase shift of the neutron is measured with a statistical uncertainty of order 1 part in 1000 in two different interferometers. Nearly harmonic pairs of neutron wavelengths are used to measure and compensate for effects due to the distortion of the interferometer as it is tilted about the incident beam direction. A discrepancy between the theoretically predicted and experimentally measured values of the phase shift due to gravity is observed at the 1% level. Extensions to the theoretical description of the shape of a neutron interferogram as a function of tilt in a gravitational field are discussed and compared with experiment. ͓S1050-2947͑97͒04109-7͔PACS number͑s͒: 03.30.ϩp, 03.65.

Since the Transport Intensity Equation (TIE) has been applied to electron microscopy only recently, there are controversial discussions in the literature regarding the theoretical concepts underlying the equation and the practical techniques to solve the equation. In this report we explored some of the issues regarding the TIE, especially bearing electron microscopy in mind, and clarified that: (i) the TIE for electrons exactly corresponds to the Schrödinger equation for high-energy electrons in free space, and thus the TIE does not assume weak scattering; (ii) the TIE can give phase information at any distance from the specimen, not limited to a new field; (iii) information transfer in the TIE for each spatial frequency g will be multiplied by g2 and thus low frequency components will be dumped more with respect to high frequency components; (vi) the intensity derivative with respect to the direction of wave propagation is well approximated by using a set of three symmetric images; and (v) a substantially larger defocus distance than expected before can be used for high-resolution electron microscopy. In the second part of this report we applied the TIE down to atomic resolution images to obtain phase information and verified the following points experimentally: (i) although low frequency components are attenuated in the TIE, all frequencies will be recovered satisfactorily except the very low frequencies; and (ii) using a reconstructed phase and the measured image intensity we can correct effectively the defects of imaging, such as spherical aberrations as well as partial coherence.

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The scalar version of the Aharonov-Bohm effect predicts a phase shift for de Broglie waves due to the action of a scalar potential in an otherwise field-free (i.e., force-free) region of space. Unlike the more familiar effect due to the magnetic vector potential, the scalar effect has hitherto remained unverified due, presumably, to technical difficulties in electron interferometry. Rather than using electrons acted on by electrostatic potentials, we have performed an analogous interferometry experiment with thermal neutrons subject to pulsed magnetic fields. The expected phase shifts have been observed to a high degree of accuracy.PACS numbers: 03.65.Bz, 42.50.-p In classical electrodynamics, potentials are merely a convenient mathematical tool for calculating electromagnetic fields of force. In quantum mechanics, however, potentials have a primary physical significance and are an essential ingredient which cannot be readily eliminated from the Schrodinger equation. In a paper entitled "Significance of Electromagnetic Potentials in Quantum Theory" published in 1959, Aharonov and Bohm [1] proposed two types of actual electron interference experiments aimed at exhibiting these conclusions. The phenomena predicted came to be known as the AharonovBohm (AB) effect, and have given rise to a literature of almost 400 journal articles over the last thirty-odd years.The essence of the AB experiments [2] is that electrons suffer phase shifts in passing through regions of space of zero fields but nonzero potentials. The effects are of two types, the usual magnetic (or vector) AB effect, and the less often cited electric (or scalar) AB effect which is conceptually quite simple. It concerns the phase shift caused by the scalar potential V= -eU in the Schrodinger equation:(H 0 +V)yr=ihdifr/dt.(1) Figure 1 (a) shows a divided electron wave packet traveling down two conducting cylinders which act as Faraday cages, i.e., have a field-free interior irrespective of their electrostatic potentials U\ and Ui* To exhibit the scalar AB effect, the potential of cylinder 2 alone is pulsed during a time when the wave packet is contained inside it. In spite of the absence of a force at all times, a relative phase shift A# is expected, A = (\/h)feU 2 (t)dt.(2)The correctness of this AB prediction is of such importance to the consistency of quantum mechanics [3] that the actual experiment deserves a serious attempt. However, such an experiment has not yet been performed because of technical difficulties with existing types of electron interferometers. The closely related experiment of Mateucci and Pozzi [4] involves forces acting on the electron and is not, therefore, a clear-cut test of the effect. Realizations with protons or ions are hindered by the lack of suitable interferometers for such particles.In the present experiment with neutrons, the phase shift is due to a scalar potential, V s -JI * B, which is the analog of V*= -eU, the scalar potential in the scalar AB effect for electrons. (This parallels a previous situation in which th...