Higher accuracy of optical surface measurement is needed with the rapid development of optical industry and technology, especially in the field of optical manufacture and optical metrology. Fizeau interferometery is widely recognized as one of the most important measurement techniques currently in use. Results of the Fizeau interferometeric testing contain the reference surface errors and test surface errors. The test accuracy is restricted by the error of reference surface. As a result, so-called absolute flatness testing technology must be used to eliminate the system error such as reference surface error and higher accuracy of the surface profile testing. In this paper, the theory formula of even and odd functions is deduced, and the method are programmed for simulation. Based on HOOL phase-shifting interferometer, experiments are done to achieve high accuracy flatness measurement. The experiment shows that with high-accuracy interferometer, absolute flatness testing technology can effectively calibrate reference surface and improve the accuracy of flatness surface testing. An important result of this experiment is that the accuracy of the test surface can be reached λ/50.
The phase diversity wave-front sensing (PDWFS) technique is a posteriori image-based wave-front sensing method which utilizes two images collected simultaneously whose pupil phase differs from each other in a known manner, typically the defocus phase diversity. Here, we present a new method of implementing phase diversity on the sparse aperture imaging system that adds an intentional piston phase to one subaperture. The objective function is firstly derived for the sparse aperture imaging system, then the genetic algorithm is used to minimize the objective function to estimate the piston errors of the subapertures. Digital simulations are conducted for varying amounts of piston phase diversity and levels of noise, the performance of sub-aperture phase diversity is evaluated by comparing with the conventional defocus phase diversity. The results show that the conventional defocus phase diversity performs better than the sub-aperture phase diversity when there is no noise, while the sub-aperture phase diversity outperforms the conventional defocus phase diversity when the noise strength increases. Sub-aperture phase diversity may be an useful alternative if the conventional defocus phase diversity method fails.
A method of measuring water colority based on HSV chromaticity (H hue, S saturation, V value) system is proposed. The measurement system is composed of halogen lamp, sample cell and spectrometer. The spectrum data of transmission light captured by spectrometer is used to calculate the XYZ tristimulus values which is then converted to HSV chromaticity. The colority and saturation value shows a good functional relationship which is calibrated in the experiment. Therefore the water colority can be calculated by the saturation in the HSV chromaticity. Since the hue value is acquired at the same time, the method can be adopted to test water sample with different hue. Moreover, the V value is an independent component, so the instability of light source has no influence on the measurement. The colority obtained by the calibrated function coincides with the standard solution.
This paper analyzes the modulation transfer function of three sub-mirror sparse aperture optical system (Golay3) among the low contrast with the central part, the side lobe peak and the sub-mirror aperture. It is shown that the sparse aperture system can be achieved higher frequency information while the optical imaging system is designed and the side lobe is moved or low contrast of the central part is reduced or contrast of the higher frequency part is increased by changing the position of sub mirrors or size of surrounded apertures.
The existence of Gravitational Wave (GW) is one of the greatest predictions of Einstein’s relative theory. It has played an important part in the radiation theory, black hole theory, space explore and so on. The GW detection has been an important aspect of modern physics. With the research proceeding further, there are still a lot of challenges existing in the interferometer which is the key instrument in GW detection especially the measurement of the super large radius optics. To solve this problem, one solution , Fizeau interference, for measuring the super large radius has been presented. We change the tradition that curved surface must be measured with a standard curved surface. We use a flat mirror as a reference flat and it can lower both the cost and the test requirement a lot. We select a concave mirror with the radius of 1600mm as a sample. After the precision measurement and analysis, the experimental results show that the relative error of radius is better than 3%, and it can fully meet the requirements of the measurement of super large radius optics. When calculating each pixel with standard cylinder, the edges are not sharp because of diffraction or some other reasons, we detect the edge and calculate the diameter of the cylinder automatically, and it can improve the precision a lot. In general, this method is simple, fast, non-traumatic, and highly precision, it can also provide us a new though in the measurement of super large radius optics.
In order to eliminate the noise in images acquired by the sparse aperture system, the modeling and filtering of electrical and optical noise are analyzed by the case of three-mirror aperture optical system. The study shows that the median filter can be applied to remove Gauss and salt & pepper noise, meanwhile high-pass filter with Gauss function can eliminate the influence of non-uniform illuminating on imaging. The Lucy-Richardson algorithm is used to restore the image, by which the resolution is heightened.
The phase diversity wavefront sensing (PDWFS) technique is an a posteriori image-based wavefront sensing technique which has been successfully implemented to the Hubble Space Telescope. The analytical form for the phase diversity Cramér-Rao lower bound(CRLB) of Golay3 aperture is firstly derived. Monte Carlo analysis of the PDWFS CRLB is used due to the dependence of CRLB on the true values of aberration parameters being estimated. Then the ensemble average of mean-squared errors(MSE) quantities of CRLB is used to evaluate the performance of imaging schemes with different photon distributions and different amounts of defocus. The numerical simulation shows that for a point source target, if a third image implies the inclusion of extra photons, the MSE would be reduced to a degree in accordance with the amount of the extra photons, the MSE remains nearly unchanged if the totoal photons is finite, no matter for a two-channel or a three-channel system. We also find that varying the defocus of one image becomes meaningless if the defocus of the other image is at a high level.
Pentaprism scanning system has been widely used in the measurement of large flat and wavefront, based on its property that the deviated beam will have no motion in the pitch direction. But the manufacturing and position errors of pentaprisms will bring error to the measurement and so a good error analysis method is indispensable. In this paper, we propose a new method of building mathematic models of pentaprism and through which the size and angle errors of a pentaprism can be put into the model as parameters. 4 size parameters are selected to determine the size and 11 angle parameters are selected to determine the angles of a pentaprism. Yaw, Roll and Pitch are used to describe the position error of a pentaprism and an autocollimator. A pentaprism scanning system of wavefront test is simulated by ray tracing using matlab. We design a method of separating the constant from the measurement results which will improve the measurement accuracy and analyze the system error by Monte Carlo method. This method is simple, rapid, accurate and convenient for computer programming.
In the field of optical information security, the research of double random phase encoding is becoming deeper with each passing day, however the encryption system is linear, and the dependencies between plaintext and ciphertext is not complicated, with leaving a great hidden danger to the security of the encryption system. In this paper, we encrypted the higher dimensional Wigner distribution function of low dimensional plaintext by using the bilinear property of Wigner distribution function. Computer simulation results show that this method can not only enlarge the key space, but also break through the linear characteristic of the traditional optical encryption technology. So it can significantly improve the safety of the encryption system.
Modern space telescopes are demanded to have a very large aperture in order to achieve high resolution. The notion of
the sparse aperture systems introduces a new solution to make the telescopes practicable. It is significant to simulate
sparse aperture systems before their application in space observation. The multiple mirror telescope (MMT) is one type
of sparse aperture systems and Golay3 is the configuration serving as a good start. The method to simulate Golay3 MMT
is investigated. The fundamental principle of optical surfaces simulation using the optical design program is discussed. It
is proposed that Golay3 MMT simulation can be accomplished by programming to establish surface files with the aid of
the interface of this program. The structure of Golay3 MMT in which three sub-mirrors replace the monolithic spherical
primary mirror is analyzed. The formulas determining locations of sub-mirrors on the spherical primary mirror are
deduced. The surface file representing the primary mirror is created by external programming and defining properties of
rays passing through it. The simulation procedures are introduced in detail. A simulation example is given out and
evaluated. It proves that the simulation method is reasonable and effective, and has significant reference values to
simulate sparse aperture systems with other structures.
The surface curvature of the progressive addition lenses varies gradually from the distance-viewing area to the
near-viewing area. The curvature of the principal meridional curve varies progressively from point to point to provide a
predetermined dioptric focal power at each point according to a predetermined power law. Several kinds of power laws
along meridian line including linear combination and polynomials, are illustrated. The details for determining the
coefficient and order of the polynomial are also introduced. Based on different power laws along meridian lines, the
results of the computer evaluation are given out. Progressive addition lenses corresponding to different forms of
meridional power laws have been manufactured with Satisloh VFT-compact machine. The lenses manufactured have
been measured using the Class Plus lens analyzer to provide sphere, cylinder, and axis values across the surface of the
lens, and distortion distributions are also presented. The results of measurement indicate that the performances of
progressive addition lenses are consistent with those of the computer evaluation. These results are shown that the lenses
have more wide distance-viewing or near-viewing areas and short corridor but with higher level of astigmatism in the
peripheral areas while the curvature along the median line is constant in the distance zone and the rate of meridional
dioptric variation is quicker, on the contrary, the lenses have more narrow distance-viewing or near-viewing areas and
long corridor. The comparison and analysis prove that determining the power law along the meridian line is an important
task in designs for progressive addition lenses.
Sparse aperture telescopes represent a promising technology for increasing the effective diameter of an optical system
while reducing the weight and the size. Multiple-mirror telescope (MMT) and multiple-telescope telescope (MTT) are
two types of sparse aperture systems. The primary mirror of MMT consists of a number of segments that are all parts of a
single primary-mirror conic. The configuration of the sparse aperture is related to the performance of the MMT. Golay
configuration is nonredundant sparse aperture. Entrance pupil characteristics of Golay 6 MMT are studied to research the
relationships between the sub-mirrors on the primary mirror and the shapes of sub-apertures on the entrance pupil of
Golay 6. Overlay factor and efficiency factor are proposed to achieve the optimal fill factor on the entrance pupil. Given
the relative aperture of Golay 6 MMT, there is some concern that the fill factor on the entrance pupil is larger than the
overlay fill factor on the spherical sparse aperture primary mirror. The maximum fill factor and the maximal overlay
factor are discussed, and the tangency condition when sub-mirrors of Golay 6 MMT are tangency is derived. Two
Cassegrain telescopes having a spherical primary mirror with Golay6 configuration and with an aspherical secondary
mirror are designed. The fill factor on the entrance pupil can be larger than the overlay factor on the primary mirror at the
certain occasion. Based on the relationships between the fill factor and the overlay factor, the rational parameters of
sub-mirrors on the primary mirror can be selected.
High resolution imaging from space telescope for surveillance and astrometry is currently limited by launch vehicles
and systems cost. The weight of the telescope is one of major factors which limits the vehicles to be placed in orbit.
Sparse aperture optical system uses a reduced aperture area to synthesize the optical performance of a filled aperture. It
is more promising in virtue of its light weight, low cost and larger synthetic aperture. The sparse aperture optical system
has two types, i.e. the multiple-mirror telescope (MMT) and the multiple-telescope telescope (MTT). A MMT of
Golay3 sparse aperture optical system is investigated that three sub-mirrors are located on a spherical primary mirror.
Three sub apertures of Golay3 are elliptic that in fact the circular sub-mirrors of spherical primary mirror are projected
on the entrance pupil. The relationships between fill factor, radius of sub-mirrors and F number of the primary mirror
are presented. The analytical formula is also completed, which shows that the maximum fill factor is limited by F
number of the primary mirror. When the aperture radius is equal to curvature radius of the primary mirror
approximately, the shape of sub-apertures exhibits to be elliptic obviously. The maximum fill factor reaches the largest
one at that time. Modulation Transfer Function (MTF) of Golay3 system is studied. MTF is the correlation of three
elliptic sub-apertures. The sub-MTFs are different from those of sub-mirrors located on a plane. The formula is verified
by designing two Cassegrain telescopes which primary mirror is made up of three sub-mirrors of Golay3 configuration
with Zemax optical program. Three sub-mirrors of primary mirror share a common asphercial secondary mirror. The
errors caused by tilt and piston of three sub-apertures are also given out. Because of the loss of MTF for the sparse
aperture optical system, the image quality is decreased. Wiener filter technique is utilized to improve the image quality
for the sparse aperture system.
Sparse aperture optical systems use a reduced aperture area to synthesize optical performance of a filled aperture. The
relative arrangement of sub-apertures is a key for the design of sparse aperture. Golay configurations are a series of
sparse apertures which are nonredundant configurations and have uniform MTF. A novel sparse aperture configuration
named pseudo-Golay6 is proposed, which is also nonredundant configuration. It is based on the analysis of one
dimensional array arrangement and array optimization. The relative arrangement of the sub-apertures of pupil is similar
with the Golay's. The sub-apertures are arranged on the sides of the equilateral triangle. It has advantage of simple
configuration and uniform MTF. The arrangement of the sub-apertures is analyzed, and the MTF is also studied. Image
simulation of the pseudo-Golay6 is developed, and it has been compared with the performance of Golay6. The results
show that the array of pseudo-Golay6 is nonredundant and has uniform arrangement at the spatial frequency space. The
sub-MTFs of pseudo-Golay6 are not overlap except at zero frequency. The cutoff spatial frequency is highest at the
direction of π3, the cutoff spatial frequency is lowest at the direction of π6, . The practical effective diameter of
pseudo-Golay6 is larger than that of Golay6 ,and the highest cutoff spatial frequency is higher than that of Golay6 with
the same fill factor. At each different direction, the sub-MTF arrangement of pseudo-Golay6 is less uniform than that of
Progressive addition lenses design is focused on utilizing the shape of lens surface, which is not rotationally symmetric, and provides power addition. The lenses should meet power variation progressively without allowing the aberrations to attain detrimental values. The principle and e idea of designing progressive addition lenses are introduced. Several kinds of design methods are illustrated, and their advantages and drawbacks are also represented. Based on one of design methods, which the distance and near power points are determined firstly, then an umbilic line of progressive dioptric power is optimized to satisfy realistic requirements on stability of power and binocular compatibility, the form of the progressive power surface will be gotten, a progressive addition lens design that matches the particular visual needs of the patient is given out. Progressive addition lenses were manufactured with Satisloh VFT-compact machine. The lenses manufactured were measured using the Class Plus lens analyzer to provide sphere and cylinder across the surface of the lens. The results of measurement show that the lenses having a progressive power surface with a near portion and a distance portion, the near portion being of higher power than the distance portion, the form of the progressive power surface of the lens is effective to distribute surface astigmatism. In the current study, it is also shown that the optical characteristics of the different progressive addition lenses designs are significantly different from one another. The lenses designed and manufactured meet the needs. Compared with the lenses designed using Seiko software, the performance is similar with each other.
The quest for finer angular resolution in space-borne systems leads to larger aperture of the optical systems. Unfortunately, the primary mirror diameter for space telescopes is limited by volume and mass constraints of current launch vehicles as well as the scaling laws of manufacturing costs. The goal of sparse-aperture systems is to synthesize a larger effective collection aperture with a configuration of smaller sub-apertures. The modulation transfer function (MTF) of the sparse-aperture systems is depressed, resulting in a low-contrast and unsatisfactory SNR image. The optimization of the aperture is necessary to achieve a sparse-aperture configuration with more uniform MTF. In this paper, a novel sparse-aperture system composed of dual three sub-apertures is proposed. The optimization criterion of dual three sub-aperture is given, which is directly linked by the maximum spatial frequency ρR (or practical resolution) and the diameters of the sub-apertures. An optimized sparse-aperture configuration and the parameters of the configuration are given, i.e. the sites of each aperture, which varies with the different fill factor. Simulation images both optimized and un-optimized configuration for dual three sub-aperture are shown. Wiener filter is applied to restore the detail in the images of sparse-aperture systems. The loss of mid-spatial frequency information is irretrievable corresponding to the frequency (ρR) that MTF is a zero. So configuration optimization is a key aspect of the design for sparse-aperture systems.
Sparse-aperture imaging systems are desirable for aerospace applications because they can capture the same resolution as a filled aperture while reducing the systems’ size and weight. A novel sparse-aperture model named dual three-sub-aperture is proposed. By comparing with the famous Golay 6, dual three-sub-aperture is regarded as a better configuration for aerospace remote sensing. But the images of sparse-aperture systems become blurry because of the modulation transfer function (MTF) loss. It is necessary to optimize the image quality by image restoration process. In order to achieve ideal images, image filter technique has been studied. First, the imaging simulations of dual three-sub-aperture system and the Golay 6 with different fill factor are generated. The images formed by these systems are recovered by means of proper filters. Then different kinds of noises and different noise levels are added, various filters with different parameters are applied to recover these images. And the optimal deblurred images are gained. Through the quantitative evaluations of its image quality it is shown that the mentioned filter technique can be used to effectively improve the quality of the images degraded by the MTF’s loss, i.e. the details in images can be enhanced and its edges be sharpened.