It is necessary to fit the discrete sampling value of the optical element surface obtained by measuring equipment, because the results of fitting are useful for manufacturing and optical design. The commonly used fitting methods are X-Y polynomial approximation, Zernike polynomial approximation and radial basis function (RBF) approximation. Compared with others, radial basis function is more suitable to fit the complex optical surface. However, the further improvement of fitting accuracy and cost are limited by the fixed shape parameter of the classic RBF approximation. In this paper, we propose the sparse radial basis function approximation with spatially variable shape parameters to fit discretely sampled optical surfaces. Our main purpose is to improve fitting accuracy and to reduce computational cost. Then, we analyze the impact of the spatial distribution of RBF nodes on fitting. Finally, we compare the accuracy and cost between the classic RBF approximation and the sparse RBF approximation with spatially variable shape parameters by fitting various complex surface.
During the fabricating procedure of optical elements, computer-controlled tools will introduce some periodic structured errors, named mid-spatial frequency errors, which may scatter the laser beams, create filamentous spots or even damage the optical components in Inertial Confinement Fusion (ICF) high power laser system. Transverse translation diverse phase retrieval (TTDPR) is an ingenious phase retrieval method for measuring aspheric and freeform surfaces. In this paper, we explore the measurement of optical elements with mid-spatial frequency errors by using TTDPR. First, we briefly introduce the features of mid-spatial frequency errors and establish the relation between mid-spatial frequency errors and diffraction pattern. Second, with the knowledge of the mid-spatial frequency error, we analyze the feasibility of optical elements with mid-spatial frequency error measurement by using TTDPR. In order to improve the convergence and measurement accuracy of phase retrieval algorithm, initial inputs are optimized for the following iterative phase retrieval algorithm. Results indicate that a 50% higher reconstruction accuracy can be achieved, when the initial input is the ideal lens to recover the phase of lens with mid-spatial frequency errors. For TTDPR, sub-aperture illuminated with overlapping part among adjacent sub-apertures will improve accuracy of iterative phase algorithm than never overlapped sub-aperture, while it encumbers the efficiency of iterative phase retrieval algorithm. Based on the characteristics of the particular optical surfaces, the influence of major parameter of sub-aperture including the size of sub-aperture and the overlapped proportion among adjacent sub-aperture to accuracy and efficiency of TTDPR are also discussed.
In inertial confinement fusion high energy system, the mid-spatial frequency (MSF) errors of optical elements induced by computer numerical control tools lead to damage to the optical system. Based on the characteristics of the mid-spatial frequency errors, it is measured by using phase retrieval technology. Compared with conventional measurement methods such as interferometry, MSF errors can be measured by phase retrieval without complex measurement systems and large aperture optical elements with MSF errors can be measured via phase retrieval in theory. In this paper, we compare multiple phase retrieval algorithms that are used to measure optical element with MSF errors and explore approaches to improve the quality of results. First, we briefly introduce the feature of MSF errors and the relation between the wavefront of optical element with MSF errors and its diffraction pattern. Second, multiple phase retrieval algorithms including error-reduction (ER) algorithm, hybrid input-output (HIO) algorithm and oversampling smoothness (OSS) algorithm are adapted for the measurement of MSF errors. According to the bandwidth and structure characteristics of MSF errors, the convergence speed and the accuracy of above algorithms are discussed and compared. Then, according to the characteristics of different algorithms, different retrieved wavefront phase via using these algorithms are integrated to improve the accuracy of results. Last, based on the feature of MSF errors, the priori knowledge of algorithms is also discussed to further gear up the convergence speed and the accuracy of algorithms.
The ripple errors of the lens lead to optical damage in high energy laser system. The analysis of sidelobe on the focal plane, caused by ripple error, provides a reference to evaluate the error and the imaging quality. In this paper, we analyze the diffraction characteristics of sidelobe of optical elements with ripple errors. First, we analyze the characteristics of ripple error and build relationship between ripple error and sidelobe. The sidelobe results from the diffraction of ripple errors. The ripple error tends to be periodic due to fabrication method on the optical surface. The simulated experiments are carried out based on angular spectrum method by characterizing ripple error as rotationally symmetric periodic structures. The influence of two major parameter of ripple including spatial frequency and peak-to-valley value to sidelobe is discussed. The results indicate that spatial frequency and peak-to-valley value both impact sidelobe at the image plane. The peak-tovalley value is the major factor to affect the energy proportion of the sidelobe. The spatial frequency is the major factor to affect the distribution of the sidelobe at the image plane.
A traditional tracking device obtain the attitude angle by analyzing the spots position on photodetector. However, the attainable angular measurement accuracy depends on the field of view (FOV), number of pixels of the photodetector and the centroiding algorithm. In this paper, we present a high-precision attitude angle measuring system based on Talbot interferometry using cross-gratings and four wedge plates, which can acquire the real-time change of incident angle along two axis. The specific structure of the system is introduced, and the formula for calculating the relative angle is derived. The tracking accuracy is analyzed to be better than 0.2 arcsecond, which is dependent on the grating period, the distance between the two gratings and the gray scale of image. The Simulation results show that the RMS error of relative angle is better than 0.1 arcsecond both in x and y direction.
Large-aperture and long focal-length lens is widely used in high energy laser system. The method based on Talbot interferometry is a reliable method to measure the focal length of such elements. By employing divergent beam and two gratings of different periods, this method could realize full-aperture measurement, higher accuracy and better repeatability. However, it does not take into account the spherical aberration of the measured lens resulting in the moiré fringes bending, which will introduce measurement error. Furthermore, in long-focal measurement with divergent beam, this error is an important factor affecting the measurement accuracy. In this paper, we propose a new spherical aberration compensation method, which could significantly reduce the measurement error. Characterized by central-symmetric scanning window, the proposed method is based on the relationship between spherical aberration and the lens aperture. Angle data of moiré fringes in each scanning window is retrieved by Fourier analysis and statistically fitted to estimate a globally optimum value for spherical-aberration-free focal length calculation. Simulation and experiment have been carried out. Compared to the previous work, the proposed method is able to reduce the relative measurement error by 50%. The effect of scanning window size and shift step length on the results is also discussed.
A panoramic long-wave infrared athermal system is introduced in this paper. The proposed system includes a panoramic annular lens (PAL) block providing a stereo field of view of (30 deg – 100 deg) × 360 deg without the need to move its components. Moreover, to ensure the imaging quality at different temperatures, a refractive/diffractive hybrid lens is introduced to achieve optical passive athermalization. The system operates in a spectral band between 8 and 12 μm, with a total length of 175 mm and a focal length of 3.4 mm. To get a bright and clear image, the aperture of the system was set to f/1.15. The introduction of aspherical surface and even-order diffractive surface not only eliminates the differential thermal but also makes the structure simple and lightweight and improves the image quality. The results show that the modulation transfer function below 20 lp/mm of the system is above 0.2 at each temperature ranging from −20°C to +60°C, which is close to the diffraction limit. The system is suitable to be applied in an uncooled infrared focal plane array detector and will serve as a static alert system. It has a number of pixels of 640×480, and the pixel size is 25 μm.
Star-tracker plays an important role in satellite navigation. Considering the satellites on
near-Earth orbit, the system usually has two optical systems: one for observing the profile
of Earth and the other for capturing the positions of stars. In this paper, we demonstrate a
novel kind of dual-channel optical observation system of star-tracker with non-blind area
PAL imaging system based on dichroic filter, which can combine both different
observation channels into an integrated structure and realize the feature of miniaturization.
According to the practical usage of star-tracker and the features of dichroic filter, we set
the ultraviolet band as the PAL channel to observe the Earth with the FOV ranging from
40°-60°, and set the visible band as the front imaging channel to capture the stars far away
from this system with the FOV ranging from 0°-20°. Consequently, the rays of both
channels are converged on the same image plane, improving the efficiency of pixels of
detector and reducing the weight and size of whole star-tracker system.
We propose a novel design of panoramic annular lenses (PAL) for the imaging of 360° surroundings
with a large field of view (FOV) ranging from 30°~105°, which can partly realize the zooming function.
Its wavelength band is between 486 and 656 nanometers. The conventional vari-focal PAL is based on
the axial shift of some optical components, which will make the blind zone larger and out of the
sensing area, while our design is based on the lateral shift, which can make some imaging area zoom in,
keep the area of blind zone stay the same, and minimize the whole scale of this system. In order to
change the focal length of conventional PAL system, we introduce several pairs of free-form surfaces
(Alvarez surfaces) which can be regarded as several plano-spherical lenses and change the focal power
of the whole optical system. As we set two different configurations (long focal length and wide angle),
all of the optical parameters are designed and optimized with the help of the software (Zemax).
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