This paper presents a method for measuring the three-dimensional (3-D) displacement of an image point based on point-diffraction interferometry. An object Point-light-source (PLS) interferes with a fixed PLS and its interferograms are captured by an exit pupil. When the image point of the object PLS is slightly shifted to a new position, the wavefront of the image PLS changes. And its interferograms also change. Processing these figures (captured before and after the movement), the wavefront difference of the image PLS can be obtained and it contains the information of three-dimensional (3-D) displacement of the image PLS. However, the information of its three-dimensional (3-D) displacement cannot be calculated until the distance between the image PLS and the exit pupil is calibrated. Therefore, we use a plane-parallel-plate with a known refractive index and thickness to determine this distance, which is based on the Snell’s law for small angle of incidence. Thus, since the distance between the exit pupil and the image PLS is a known quantity, the 3-D displacement of the image PLS can be simultaneously calculated through two interference measurements. Preliminary experimental results indicate that its relative error is below 0.3%. With the ability to accurately locate an image point (whatever it is real or virtual), a fiber point-light-source can act as the reticle by itself in optical measurement.
A new laser differential reflection-confocal lens thickness measurement (DRCTM) method is proposed for the high-accuracy measurement of the lens thickness. DRCTM uses the test beam reflected from the lens first and last surface to determine the vertex positions of the two surfaces. Differential confocal technology is used to precisely identify the lens vertexes of the lens first and last surfaces, thereby enabling the precise measurement of the lens thickness. Compared with the existing measurement methods, DRCTM has high accuracy and strong anti-interference capability. Theoretical analysis and experimental results indicate that the DRCTM measurement error can be limited to 0.0015%.
We present a two-step program for point-by-point flat surface measurements with a fiber point diffraction interferometer (FPDI). The point diffraction wavefront reflected by a flat mirror under test is an aberrated spherical wavefront carrying the surface information of the flat mirror. The aberrated spherical wavefront interferes with a reference point diffraction wavefront through a plate beamsplitter (BS). The aberrations of the plate BS are also measured by the FPDI method. The figure of the flat mirror can be evaluated point by point after correcting the aberrations of the plate BS. This method makes use of the nearly perfect point diffraction wavefront, thus it can assure accurate flatness measurement on the optic under test. This research extends to the field of FPDI applications, and provides a new route for the high precision measurement of flat optics.
Critical dimension measurement based on scatterometry is expected to be the key technology in current and future
semiconductor manufacturing processes. Scatterometry has strong dependence on modeling. The paper compares the
Integral Equation Solver and the Rigorous Coupled Waveguide Analysis (RCWA) technique from convergence, and
chooses the RCWA method to simulate the critical dimension measurement. The paper introduces an angle resolved
scatterometry technology constructed on microscope. The back focal plane of a bright field reflection microscope
contains diffraction information about the sample, and positions in the back focal plane map to diffraction angles from
the sample. With suitable control of the angle of the incident illumination, back focal plane imaging can provide
information similar to that obtained from angle resolved scatterometry. The paper simulates the reflectance of the
rectangular grating at a fixed wavelength (λ=532nm) versus angle of incidence, measured for both s polarization and p
polarization. The silicon gratings are 10nm difference with line width, pitch, line height and sidewall angle. The
simulations reveal that the p polarization light is more sensitive than the s polarization light to the changes of the grating
size, and the scatterfield microscopy has nanometer level sensitivity to the line width variations.
An advanced fiber point diffraction interferometer (FPDI) is built for measuring spherical mirror surface and spherical
lens wave front aberration with high precision. This new interferometer is based on point diffraction technique. Using
short coherence length laser as light source, the perfect spherical wave diffracts from fiber point resource as reference
wave. And the spherical wave is interfered with object wave to achieve higher accuracy. A phase shifting point
diffraction interferometer with one single-mode-optical-fiber is built for measuring concave spherical mirror surface. A
concave spherical mirror is measured by the experimental facility. The interferograms are collected by CCD and
analyzed by computer. The PV values and RMS values of resulted surface error are compared with the result acquired by
digital wave front interferometer. The measured surface is fitted and represented by Zernike polynomials. The results
compared with Zygo GPI interferometer are proximately the same. Finally the differences between them are discussed in
detail. To measure the aberration of spherical lens, a two single-mode-optical-fibers point diffraction interferometer is
built by adding another single mode optical fiber. A convex lens is measured. The interferograms is presented.
Due to the phasing effects, the measurements of Minimum Resolvable Temperature Difference (MRTD) for Staring
array thermal imagers often get abnormal results when the targets approaching system Nyquist frequency (fn). To
simulate the relations between MRTD values and four-bar targets' frequencies, this paper introduces the concept of best
contrast. Clearly, the MRTD results are inversely proportional to the best contrasts under optimum phases, higher
contrast corresponding to a lower MRTD. On the other hand, with the spatial frequencies increasing, the target's
opening area shrinking and leads the effective infrared eradiation decreasing, this means the MRTD results are inversely
proportional to the opening area of the target. Based on these two assumptions, and through numerical simulations, this
paper depicts the tendency chart of MRTD under optimum phases to the four-bar targets' spatial frequencies. The
tendency chart adequately explains the hump curve happens at frequencies between 0.6fn and fn. From the simulations,
the maximum of MRTD values can be predicted at the frequency of 0.89fn. The tendency chart illustrated by numerical
simulation is consistent with the MRTD results get in laboratory. While in Dynamic Minimum Resolvable Temperature
Difference (DMRTD) testing, moving the four-bar targets introduces temporal effects not present in static MRTD test.
Simulation reveals that DMRTD test can get more realistic shape of the curve between 0.6fn and fn, the characteristic
hump in the static MRTD curve between 0.6fn and fn is not seen.
An absolute measurement method of spherical lens with Fiber Point Diffraction Interferometer (FPDI) was developed.
To achieve a high accuracy, several key techniques are discussed such as: short coherence length laser, interferogram
collecting, experiment set up, and reconstruction of wave front. Through these techniques an experiment system has been
built. The 5-step phase shifting interferograms are collected. The wave front is fitted by Zernike polynomials and
reconstructed. The repeated measurement result has a good performance compared to a Zygo GPI interferometer.
Due to the imperfectness of the reference wavefront produced by standard lens, the spherical figure measurement
precision of the traditional interferometer is limited. The fiber point diffraction interferometer (FPDI) provides a method
to produce the nearly perfect reference wavefront for the spherical figure measurement. The diverging wavefront
diffracting from the fiber tip can serve as an ideal reference for the concave spherical surface measurement. However, it
can not serve for the convex surface measurement until an auxiliary positive lens is introduced. This paper presents the
different FPDI configurations for the concave and convex spherical surface measurement. The measurement uncertainty
of the FPDI comes from the following factors: the spherical figure error of the reference wavefront diffracting from the
fiber tips; the flatness of the fiber tips; the phase shifting error of PZT; the tilting error introduced by adjustment during
measurement; the environmental influences such as temperature, vibration, and air turbulence. In all of these factors, the
flatness of the fiber tips mostly affects the measurement uncertainty. The estimation of the expanded uncertainty is about
λ/95 for the concave and λ/40 (λ=532nm) for the convex spherical figure measurement by FPDI.
This paper presents Zernike polynomials fitting wave front which is detected by fiber point diffraction interferometer (FPDI). To confirm that Zernike polynomials are suitable for fitting concave spherical mirror surface, different orders of Zernike polynomials were used to fit several different surfaces which are produced by computer. Fitting result errors were evaluated by residual standard deviation. It is illuminated that Zernike polynomials are suitable for fitting surface which changes smoothly but not suitable for fitting surface with sharp fluctuating. When the shape changes dramatically Zernike polynomials are unable to correctly fit. Choosing appropriate term of polynomials, more terms don't mean higher precision. A metal coated concave spherical mirror, curvature radius 580mm, caliber 70mm, was measured as a sample. The five-step phase shifting interferograms of good quality were detected by an experimental FPDI which was built in lab. Measured wave front was fitted by 36 terms of Zernike polynomials from phase map which were unwrapped from five-step phase shifting interferograms. The measurement result was obtained and compared with that by Zygo interferometer when measured the same mirror. The 2 represented wave fronts have same characters such as centers bulging and marginal trough.
The point diffraction interferometer (PDI) is the technology which realizes the absolute interferometric measurement
without the use of reference surface. Pinhole is mostly used to generate the ideal spherical wavefront traditionally. While
using the single mode optical fiber instead of pinhole can easily introduce phase-shifting ability for PDI measurement.
This paper mainly discusses the merits and disadvantages of two kinds of fiber phase shifting point diffraction
interferometer (FPS/PDI). Two fibers FPS/PDI is a separated-path configuration. Although it's easy to adjust, it's more
sensitive to environment influence, and the thickness of fiber cladding will induce an off-axis error during measurement.
Single fiber FPS/PDI is a common-path configuration, thus it is robuster than the front, but the maximum visibility is
now one half. Its accuracy is mainly affected by factors such as the fiber core diameter, slight ellipticity and oblique face.
The paper lastly compares the single fiber PDI with ZYGO interferometer based on measurement data about a sphere
surface, the single interference pattern collected by our experimental fiber PDI apparatus is analyzed and the major error
sources are also discussed.
The primary restriction on the precision of spherical figure measurement is the imperfectness of the reference spherical
wavefront. Using the nearly perfect spherical wavefront diffracting from a single mode fiber as the reference, the
accuracy of spherical figure measurement can be greatly improved. To get good contrast of interference fringe, the
extraneous interference should be eliminated, and the intensity of the reference beam must match to the measuring beam
at the same time. Using the short coherence length laser source can avoid most of the extraneous interference. The
principles through stretching the resonant cavity length to shorten the coherence length are discussed; the effects are
validated by constructing a Twymann-Green interferometer using the cavity length tunable YAG solid state laser.
Calculations on light intensity show that only through controlling the attenuation of the measuring beam, can it match to
the reference beam. Coating the fiber tips with semi-metallic film can substantially improve the contrast of the
interference fringe. Comparing to the measurement results of ZYGO interferometer, the single interference pattern
collected by our experimental fiber PDI apparatus is analyzed and the major error sources are also discussed.
A multi-parameter Measurement Assurance Program (MAP) aim at laser interferometer is discussed detailedly in this paper. Firstly, we summarize the basic implementation process of MAP. After analyzing the measurement parameters of the laser interferometer, we design a set of transfer standard and check standard. Then, the mathematical statistic model of the whole MAP process is presented including the statistic process control and the evaluation of the measurement uncertainty. Lastly, we demonstrate the MAP software we programmed for this process in order to facilitate the implementation. It's clear that our MAP implementation has greatly improved the attending laboratories' confidence for their measurement results.