In this paper, we propose a simple method for reconstructing the corneal surface profile by using the Talbot effect, projection moiré method, and heterodyne interferometry. A linear grating is obliquely illuminated by an expanding collimated light, and a self-image of this grating can be generated and projected on the corneal surface. The deformed grating fringes are imaged on the second grating to form the moiré fringes. If the first grating is moved with a constant velocity along the grating plane, a series of sampling points of the sinusoidal wave which behave like the heterodyne interferometric signal can be recorded by a CMOS camera. The phase distribution of the corneal surface then can be obtained with the IEEE 1241 least-square sine fitting algorithm and 2D phase unwrapping. Finally, the corneal surface profile can be reconstructed by substituting the phase distribution into special derived equation. This method provides the advantages of a simple optical setup, ease of operation, high stability, and high resolution.
The processes to derive the associated phase of an interference signal from the data of a series of recorded frames are performed, and we find that the sampling frequency being lower than the Nyquist sampling rate can also be applied to the full-field heterodyne interferometry. Two optimal sampling conditions for a commonly used CCD camera are proposed based on the relation between the heterodyne frequency and the contrast of the interference signal under the condition that the phase error is set to be 0.05 deg.
A simple method for measuring a step-height sample is presented with the heterodyne central fringe identification
technique and a precision translation stage. This method can accurately point out the zero optical path difference position
such that the optical path lengths of two arms of the interferometer are absolutely equivalent. Thus, the two surfaces of
the step-height sample can be identified sequentially with the translation stage. The displacement of the translation stage
is equal to the step-height of the test sample. The feasibility of the technique is demonstrated. The measurable range is
not limited by the coherence length of the light source. The measurement accuracy depends on the uncertainties of the
heterodyne central fringe identification method and the translation stage. In our setup, we have a 100 mm measurable
range and a 4 nm uncertainty. The wavelength stability of the light source has a minor effect on the measurement.
Based on the Fresnel's equations and the phase-shifting method, an alternative method for measuring the refractive index
distribution of a GRIN lens is presented. A linearly/circularly polarized light in order enters a modified Twyman-Green
interferometer, in which an electro-optical modulator is used as a phase shifter. In the interferometer, the light beam is
divided by a beam-splitter into two beams, a reference beam and a test beam. After they are reflected by a plane mirror
and the tested GRIN lens, respectively, they are combined together and pass through an analyzer. The analyzer extracts
the same polarized components to interfere each other, and the
full-field interference signals produced by the
components of the s- and the p-polarizations can be obtained. The full-field interference signals are taken by a CMOS
camera. The phase differences can be obtained by using the four-step phase-shifting interferometric method. Substituting
these two groups of data into special equations derived from Fresnel equations, and the two-dimensional refractive index
distribution of the GRIN lens can be calculated. Its validity is demonstrated and has some merits such as simple optical
configuration, easy operation and high resolution.
In this study, the optical activity of cholesteric liquid crystal and common-path heterodyne interferometry are used in a
simple measurement technique that was developed to measure small wavelength differences. A circularly polarized
heterodyne light passes through a cholesteric liquid crystal cell and an analyzer. Consequently, an interference signal is
generated. When the cholesteric liquid crystal cell is properly chosen at circular regime, it owns strongly optical activity.
Accordingly, the phase difference between the s- and p-polarized components of the interference signal depends strongly
on the wavelength. As the wavelength changed, a variation of the phase difference can be accurately detected by
heterodyne interferometry. Substituting the variation of phase difference into specially derived equations, the wavelength
variations can be estimated accurately. The feasibility of this method was demonstrated and this method provides the
advantages of a simple structure, easy operations, rapid measurement, high stability, and high sensitivity.
In this study a non-contact method for accurately measuring small concentration of solutions by surface plasmon
resonance heterodyne interferometer is proposed. Firstly, a linearly polarized heterodyne light source is transmitted
through a test box filled with pure water. The transmitted light is incident on the base of a hemi-spherical prism of a
surface plasmon resonance apparatus. Then the reflected light passes through an analyzer and generates an interference
signal on a photo-detector. Secondly, when the incident angle is chosen at resonant angle, a significant phase difference
between the s- and p-polarized components occurs. This phase difference is a function of the incident angle at the base of
the hemi-spherical prism. Finally, when the test box is filled with a test solution, the incident angle at the base of the
hemi-spherical prism is changed. This causes a variation in the phase difference that can be detected by the heterodyne
interferometry. Therefore, the concentration of the tested solution can be accurately determined with special derived
equations. The validity of this method was demonstrated experimentally. The advantages of the propose method include
a simple apparatus, rapid measurement, high stability, and high resolution. Due to the introduction of a common-path
structure, the interference signal is not affected by surrounding fluctuations and can be captured easily.
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