The task of optical 3D profilometry is to measure the value of spatial coordinate of one or more surface points of an
object. The value of measured coordinate is obtained from one or more intensity values that are recorded by a detector.
The way in which the resulting intensity is generated depends on whether the surface is optically smooth or rough. The
property of a surface to be optically smooth or rough depends on the mechanical properties of the surface and on the
parameters of the optical system. We present a detailed analysis of the conditions on which a surface can be classified as
optically smooth or optically rough. It is also discussed how the optically smooth surface and the resolved mode are
related.
Coherence scanning interferometry (CSI) is a precise and versatile method to measure the shape of objects with rough and smooth surface. However, this method requires a large amount of raw data. The demands on increasing measurement speed and camera resolution require to reduce the number of camera frames. We present an evaluation technique that allows a direct reconstruction of the interferograms envelope. An octadical wave plate is inserted into the reference arm of the interferometer. Thus two signals arise, each for one polarization state, that are shifted by 90 degrees to each other. From the two signals, a direct reconstruction of the interferograms envelope is possible.
White-light interferometry is an established and proven method for precise measurement of the shape of objects. Shape of objects with both smooth and rough surface can be measured. However, white-light interferometry suffers from some limitations. One of them is that the measured object must be mechanically moved relative to the measuring device during the measurement. We present an optical 3D sensor based on white-light interferometry that can measure the shape of objects without the mechanical movement of the object. Instead of the object, the reference plane moves and scans the shape of the object. A part of the imaging system is an electrically tunable lens that ensures that the measured part of the object is sharply imaged during the whole measuring procedure. The movement of the reference plane is done by the movement of reference mirror or by use of fiber optic modulation interferometer.
White-light interferometry is an established and proven method for the measurement of the shape of objects. It is able to measure the shape of objects with both smooth and rough surface. However, white-light interferometry suffers from some limitations. One of them is the necessity of the depth scan (the measured object is mechanically moved relative to the measuring device). We present an optical 3D sensor based on white-light interferometry that can measure the shape of objects without the mechanical depth scan. The output of a fiber optic interferometer is used as the light source for the measuring interferometer. An optical modulator inserted into one arm of the fiber optic interferometer changes the optical path difference between the interferometer arms so that the spectrum at the output is periodic. The variation of the spectral period replaces the depth scan. A focus tunable lens is a part of the imaging system. This lens secures that the object’s surface is still in the focalization plane of the imaging system.
White-light interferometry is an established method for the measurement of the shape of objects. Unlike to the classical interferometry, white-light interferometry can measure the shape of objects with rough surface. A major disadvantage of white-light interferometry is the low scanning speed and thus the long measurement time. This disadvantage can be overcome by a strong undersampling and Hilbert transform evaluation. We propose a system that measures the shape of objects with rough surface with the scanning speed of more than 100 μm/s with the standard frame rate of 25 fps. The measurement uncertainty is comparable with that obtained with standard design.
Shape from focus is a method for the accurate measurement of the geometrical shape of objects. The measurement principle is the local focus search. Therefore, the method is suitable only for objects with a texture. The shape of the object is extracted from a series of 2D images. The 2D images are acquired while the distance of the measured object from the objective lens continuously changes. The longitudinal coordinate of the corresponding surface point is determined from the maximum of the focus measure function. The focus measure function expresses the quality of focus in a small image area and is calculated from the intensity values of individual pixels of a CCD camera by means of a focus measure operator. We present experimental results that demonstrate the capability of the proposed measurement method. The influence of illumination on the measurement uncertainty is studied. The comparison of the results for various focus measure operators and various light sources is presented.
White-light interferometry is an established and proven method for the measurement of the shape of objects. White-light interferometry is able to measure the shape of objects with optically smooth as well as optically rough surfaces. A major disadvantage of white-light interferometry is its low scanning velocity and the long measurement time related. We present a system that measures the shape of object with optically rough surface and can achieve the scanning velocity up to 100 μm/s with a standard frame rate of 25 Hz. The experimental results are shown.
There are various optical methods for the measurement of the geometrical shape of objects. We calculate the measurement uncertainty for several “paradigm” methods, by means of the Cramér - Rao lower bound. Thus the parameters, on which the measurement uncertainty depends, can be found. Substantial features of individual optical measurement methods (geometrical arrangement, optically smooth or rough surface, used light, dominant source of noise) of various measurement methods are compared and their influence on the measurement uncertainty is discussed.
We propose a fast and precise optical 3D measurement method. The principle is similar to that of white-light
interferometry. The broad-band light source of white-light interferometry is replaced by two lasers with different
wavelengths. The object to be measured is placed into one arm of a Michelson interferometer and moved along the
optical axis. The intensity measured at the output of the interferometer is equal to the field autocorrelation. In the case of
two wavelengths, the autocorrelation is a periodical function with peaks as a result of their beating. The period can be
adjusted by the choice of the wavelength difference. By choosing a short period, a fast and precise measurement is
performed in the range of a single beat. However, such a measurement is ambiguous if the object has structures deeper
than the beat period. The ambiguity is removed by a fast auxiliary measurement with a long beat period covering the
whole depth range of the object. The auxiliary measurement need not be precise and can be completed quickly with a
large sampling step.
White-light interferometry is an established and proved method for the measurement of the geometrical shape of objects.
The advantage of white-light interferometry is that it is suitable for the measurement of the shape of objects with smooth
as well as rough surface. The information about the longitudinal coordinate of the surface of the measured object is
obtained from the white-light interferogram. The interferogram is the intensity at the detector expressed as the function
of the position of the object. (The object is moved along the optical axis during the measurement process.) If the shape of
an object with rough surface is measured, the phase of the interferogram is not evaluated because it is a random value.
The information about the longitudinal coordinate is obtained from the center of the interferogram envelope. A classical
method for the calculation of the envelope of white-light interferogram is the demodulation by means of Hilbert
transform. However, the electric signal at the output of the camera is influenced by the noise. Therefore, as expected, the
calculated envelope is also influenced by the noise. The result is that the measured longitudinal coordinate of the surface
of the object is affected by an error. In our contribution, we look for the answer on following questions: How does the
noise of the evaluated envelope differ from the noise of the interferogram? What is the minimal measurement uncertainty
that can be achieved?
White-light interferometry measuring on rough surface commonly does not resolve the lateral structure of the surface.
Thus the height differences within one resolution cell of the imaging system can exceed one-fourth of the wavelength of
the used light. Consequently the phase of the interferogram, which is recorded at the interferometer's output during the
depth scan, becomes a random variable. In the image plane of the imaging system, a speckle pattern arises. Therefore in
white-light interferometry on rough surface, the phase is not evaluated and the zero path difference is determined by
seeking the maximal contrast of the interference fringes. Because of the rough surface, the measured value of the height
coordinate is the result of a statistical process. In this way the rough surface gives rise to a measurement error. By means
of numerical simulations we determine, how the surface roughness influences the measurement uncertainty of whitelight
interferometry.
Spatial coherence profilometry is a method for measurement of the geometrical form of objects. In addition to the
two lateral coordinates x and y, it measures the longitudinal coordinate z. In this way the complete 3D description
of the object's surface is acquired. The main piece of the presented method is a Michelson interferometer illuminated
by a monochromatic spatially extended light source. The surface of the object whose geometrical form should be
measured is used as one mirror of the Michelson interferometer. By moving of the measured object along the optical
axis, the intereference is observable only if the object's surface occurs in the vicinity of the so-called reference plane.
The reference plane is given by the position of the object mirror when the Michelson interferometer is balanced. The
described effect follows from the form of the spatial coherence function originated by the spatially extended light
source. If the intensity at the output of the interferometer is recorded as a function of the position of the measured
object, a typical correlogram arises. This correlogram is similar to that known with white-light interferometry. From
the maximum of the correlogram, the z coordinate of the object's surface can be determined. Usually a CCD camera
is used as the detector at the output of the Michelson interferometer. Then z coordinates of many surface points are
parallel measured in the course of one measurement procedure and the 3D description of the object's surface is acquired.
The scanning in the lateral direction is not necessary. Thus the described method provides a spatial coherence analogy
to white-light interferometry which is based on temporal coherence. Unlike white-light interferometry, the described
method does not require a broadband light source, the interferometer is illuminated by a monochromatic light source,
usually a laser.
An interferometer based on the spatial coherence detection has been developed for absolute height measurement. The location of a coherence peak resulting from the illumination of an extended quasi-monochromatic spatially incoherent light source with zone-plate-like spatial structure gives the longitudinal depth information. Besides simplifying the control of the light source structure, LCD-SLM eliminates the mechanical movement. Experiments of step height detection and profilometry of an object with a rough surface are presented that demonstrate the validity of the principle.
White light interferometry is an established method for height profile measurement of objects. This method, unlike classical interferometry, can be used for measurement of objects with rough surface which is an important advantage. The white light interferometer is in principle a Michelson interferometer with a broad-band light source and a CCD camera as a detector. The Michelson interferometer has the object to be measured in one arm and the reference mirror in the other arm. Due to the reflection on the rough surface, a speckle pattern arises in the detector plane. This pattern is superimposed on the reference wave. The phase in particular speckle is random, but it remains approximately constant within one speckle. This renders the white light interference observable, if the optical path lengths of the two arms differ less than the coherence length. The object to be measured is mounted on a micropositioner for translating in the longitudinal direction. Gradually, as parts of the object surface cross the reference plane, the white light interference is observable in thc corresponding speckles. The position of the micropositioner in which the interference is maximal is stored for each pixel. This value for each pixel of the object image describes the geometrical shape of thc measured object. The measurement range is theoretically unlimited, practically it is limited by the range of the micropositioner. Thc longitudinal uncertainty does not depend on the parameters of the optical setup, its value is given by the roughness of the measured surface. The height profile of the object is measured during one measurement process, unlike the scanning profilers. The illumination and the observation are coaxial which avoids shadows.
We present our experimental realization of a quantum random number generator (RNG) based on the quantum random process of division of light pulse on a fiber coupler. Our prototype consists of fiber optics elements: a pigtailcd laser diode, two mechanical attenuators, a fiber coupler, and two single photon detectors. The RNG contains all necessary electronics for the generation of light pulses, synchronized reading of detectors' states, processing of these results, and transfer of data to a host computer. The connection to the computer is done via a 25-pin parallel port, that makes our device easy to use with any personal computer (PC). The RNG can be operated in four different modes, that arc selected by the PC. The zeroth mode is just for the device control, the first mode serves for appropriate setting of generation efficiency, the second mode is designed for raw data sequence generation at a rate of 114 kByte/s, and the last mode provides balanced data sequence at a rate of 28 kByte/s utilizing von Ncumann's extraction procedure. This procedure is used to gain a properly balanced ratio between '0's and '1's. The balanced data sequence generated by the RNG in the third mode passes all kinds of tests we arc using [for example 15 tests proposed by G. Marsaglia, WWW: http://stat.fsu.edu/ geo/diehard.html 1. The raw data sequence can be used for purposes that do not need properly balanced data, because raw data passes tests that arc not inspecting the sequence balance.
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