We present a compact dual-view endoscope imaging system with a field of view (FOV) of ±80° and F/# of 3.4. The endoscope consists of two optical configurations for increasing FOV within the volume constraint. The front view configuration is a fisheye lens with a FOV of ±55°, and the side view configuration is a panoramic annular lens that covers the remaining FOV. The two configurations are combined by a hybrid lens that consists of center refractive portion and side catadioptric portion. Both the front and rear surfaces of the hybrid lens are aspherized with the use of annularly stitched Q-type aspheres. Thus, a compact endoscope is successfully implemented with fewer lenses, with a total length of 11.5 mm and a maximum diameter of 5.5 mm. The modulation transfer function at 167 lp/mm is above 0.4 over the entire FOV. The relative illumination is more than 0.65 and the optical distortion is within 10%. Moreover, the near telecentric condition is fulfilled and supports constant magnification focusing.
Modern advanced manufacturing and testing technologies allow the application of freeform optical elements. Compared with traditional spherical surfaces, an optical freeform surface has more degrees of freedom in optical design and provides substantially improved imaging performance. In freeform optics, the representation technique of a freeform surface has been a fundamental and key research topic in recent years. Moreover, it has a close relationship with other aspects of the design, manufacturing, testing, and application of optical freeform surfaces. Improvements in freeform surface representation techniques will make a significant contribution to the further development of freeform optics. We present a detailed review of the different types of optical freeform surface representation techniques and their applications and discuss their properties and differences. Additionally, we analyze the future trends of optical freeform surface representation techniques.
A combination method using numerical orthogonal polynomials and overlapping averaging is presented for freeform surface estimation. The whole effective aperture of freeform surface is decomposed into multiple overlapped subapertures. The corresponding local surface over each subaperture is reconstructed by numerical orthogonal polynomials suited for general shaped aperture. Then, the whole freeform surface is obtained by overlapping averaging approach from multiple local surfaces. The performance of the presented combination method is discussed and demonstrated by examples and further verified by an experiment. The results show that the combination method could reach nanometer accuracy. Meanwhile, the local deformations of freeform surface can be characterized finely.
The conjugate differential method has been applied to the absolute test of flat, cylindrical, and axicon surfaces. In the
previous work, simulations and correspond experiments have been carried out to verify the feasibility of the method. To
analyze the influences of different factors upon the measurement result, the conjugate differential method is discussed in
detail. Considering the characteristics of the test surface such as surface types and surface profiles, the application ranges
of the conjugate differential method are discussed into three parts. According to the three surface types using the
conjugate differential method, the method can be extended to the absolute test of the spherical surfaces based on
spherical coordinate system. The reconstructed errors caused by different aberrations expressed as Zernike polynomial
terms show that they are more sensitive to high order aberration terms of the surface under test. And for surfaces with
different frequency distributions, the surface with less mid-spatial frequency information is less sensitive to the sampling
frequency. The influence from the other factors in interferometric test are also discussed into three parts. The influences
from the uncertainty of shifts are correlated with the increased aperture diameters, since the integration error caused by
the shift error increases gradually with the expanding of the integration path. The integration error changes by the
influences from the coherent noise and pixel noise related to pixel deviations. The reconstructed deviations get increased
while the peak pixel deviation is increasing. For the balance of the differential deviation and integration error, the
optimization of sampling resolution should take considered for accuracy improvement.
Human retina is different from other ocular tissues, such as cornea, crystalline lens and vitreous because of high scattering performance. As an anisotropic tissue, we cannot neglect its impact on the polarization state of the scattered light. In this paper, Mie scattering and radiative transfer theory are applied to analyze the polarization state of backscattered light from four types of retinal tissues, including neural retina, retinal pigment epithelial (RPE), choroid and sclera. The results show that the most backscattered zones in different depths have almost the same electrical fields of Jones vector, which represents the polarization state of light, whether neural retina layer is under normal incidence or oblique incidence. Very little change occurs in the polarization of backscattered light compared to that of the incident light. Polarization distribution of backward scattered light from neural retina layer doesn’t make apparent effects on polarization phase shifting in spectral domain OCT because its thickness is far less than photon mean free path, while other retinal tissues do not meet this rule.
Multilayer defects which reside on the top or inside the multilayer are one of the most critical concerns in the extreme ultraviolet lithography (EUVL) manufacturing process. We proposed the transport of intensity equation and partial least-square regression (TIE & PLSR) method to inspect the defect and reconstruct its geometric parameters: height and full width at half maximum (FWHM). The transport of intensity equation (TIE) is employed to retrieve the phase of the multilayer defect from the two scattering images, which collected at two adjacent propagation distances. Comparing the simulated ideal phase, the phase deformations caused by different top heights and widths of the defects are analyzed. The optical properties maximum, minimum and fitting Zernike coefficients are used to parameterize the phase deformation. Partial least-squares regression (PLSR) is applied to associate the optical properties of the phase deformation with the geometric parameters of the defects, and reconstruct geometric parameters of the measured defect from the established data library. The reconstruction error is less than 0.2% in simulation experiment.
An absolute testing method for cylindrical surfaces is presented in a null test setup with a computer-generated hologram. The absolute test exploits the symmetry of cylinders, which allows us to introduce a certain shift of the test surface both parallel to and rotated about the centerline while the null test condition is still maintained. With two shifts of the cylindrical surface, four measurements belonging to two groups in conjugate positions can be accomplished to obtain the absolute differential map with the interferometer and null optics errors removed. The absolute surface can be obtained by wavefront reconstruction from local differential data. A simulation of the method is presented to estimate the error propagation. Experimental absolute test results of a concave cylindrical surface with 100-mm radius are given. The measured profiles are compared with those obtained from a commercial profiler, showing a difference of less than 15 nm (root-mean-square).
Multi-beam interference will exist in the cavity of Fizeau interferometer due to the high reflectivity of test optics. The random phase shift error will be generated by some factors such as the environmental vibration, air turbulence, etc. Both these will cause phase retrieving error. We proposed a non-iterative approach called Carrier Squeezing Multi-beam Interferometry (CSMI) algorithm, which is based on the Carrier squeezing interferometry (CSI) technique to retrieve the phase distribution from multiple-beam interferograms with random phase shift errors. The intensity of multiple-beam interference was decomposed into fundamental wave and high-order harmonics, by using the Fourier series expansion. Multi-beam phase shifting interferograms with linear carrier were rearranged by row or column, to fuse one frame of spatial-temporal fringes. The lobe of the fundamental component related to the phase and the lobes of high-order harmonics and phase shift errors were separated in the frequency domain, so the correct phase was extracted by filtering out the fundamental component. Suppression of the influence from high-order harmonic components, as well as random phase shift error is validated by numerical simulations. Experiments were also executed by using the proposed CSMI algorithm for mirror with high reflection coefficient, showing its advantage comparing with normal phase retrieving algorithms.
A method for measuring the focal length of the lens and the radius of curvature of the spherical surface using wavefront difference method is proposed. Based on Fizeau interferometer, an experimental system for focal length measurements is set up to verify the principle. Based on the point diffraction interferometer, an experimental system for radius of curvature measurements is proposed to verify the proposed method. With the focal length testing system, both the positive and negative lens experimental results indicate that the measurement accuracy is less than 0.16%under normal experimental environment. With the radius of curvature testing system, the radius of curvature of spherical mirrors and the surface figure can be measured in a higher precision simultaneously. The experimental results indicate that the measurement accuracy is in the order of 10-4 .
A white-light microscopy interferometer was developed for measurement of the 3D profile and roughness.10X, 20X and 50X Mirau interference microscope objectives with the numerical aperture of 0.3, 0.4 and 0.55 were designed, manufactured and then provided as the accessories. Thickness deviation between beam splitter plate and reference mirror plate as well as the numerical aperture will both affect the contrast of interference fringe, according to optical modeling and image evaluation. The former would generate dispersion and then decrease the fringe contrast, while the latter would not produce dispersion separately but impact the amount of dispersion when thickness deviation exists, and their influence on fringe contrast was based on the expression of white-light interference intensity. Simulations for interference fringes from Mirau interference microscope objectives with different NA and thickness deviation were implemented, demonstrated that the fringe contrast will be falling with NA and thickness deviation increasing. A standard step with the nominal step value of 110 nm was used to calibrate the white-light microscopy interferometer, showing that less than1nm deviation can be reached.
A new ultra-wide-angle projection function called fovea-stereographic is described and characterized by the relative relationship between the radial distortion level and the object field-of-view (FOV) angle, creating a high-resolution wide foveal image and adequate peripheral information to be processed within a limited computational time. The paper also provides the design results of an innovative fast fovea-stereographic fisheye lens system with a 170 deg of FOV that shows a more than 58.8% (100 deg) high-resolution central foveal image and at least 15% more peripheral information than any other light projection. Our lens distortion curve, in addition to its modulation transfer function, produces a high-resolution projection for real-time tracking and image transmission applications.
In practical optical measurements, the wavefront data are recorded by pixelated imaging sensors. The closed-form analytical base polynomial will lose its orthogonality in the discrete wavefront database. For a wavefront with an irregularly shaped aperture, the corresponding analytical base polynomials are laboriously derived. The use of numerical orthogonal polynomials for reconstructing a wavefront with a general shaped aperture over the discrete data points is presented. Numerical polynomials are orthogonal over the discrete data points regardless of the boundary shape of the aperture. The performance of numerical orthogonal polynomials is confirmed by theoretical analysis and experiments. The results demonstrate the adaptability, validity, and accuracy of numerical orthogonal polynomials for estimating the wavefront over a general shaped aperture from regular boundary to an irregular boundary.
A 1.5mm focal length, F/4and F/3.75, miniature fisheye all spherical optical lens systems with 220 degree full field of view are designed in this paper, a brief discussion for a series of limiting factors is achieved, the performance evaluation is done by ZEMAX optical design and analysis software, which shows that the two designed fisheye lenses are perfect lateral color and axial chromatic aberration corrected, the maximum wavefront OPD at the full FOV is 0.6λ and 1.2λ, the RMS spot size is 3.75-3.9microns across the full FOV in both lens systems, and have diffraction encircled energy, as above 80% energy can be included in 4.8 μm radius circle. Finally, the modulation transfer function of these two designs produces a high-resolution projection with uniform in brightness over the entire range of field angles for security, monitoring, and tracking applications.
Freeform complex surfaces with steep variations in local areas cannot be fitted by analytical functions with high accuracy in the whole aperture in optics. A framework with a combination of Zernike polynomials as base function with radial basis function method is presented to improve reconstruction accuracy for freeform complex surfaces with circular aperture. The algorithm of the framework is analyzed, and the performance of the method is investigated and verified by numerical experiments. The proposed method is accurate and highly adaptable, which could be applied in modern optical manufacturing and measurement.
There exists three variables in the radiative transfer equation based on dynamic energy conservation, including polar
angle, azimuth angle and normalized penetrate depth. In order to solute this equation with double integral on polar angle
and azimuth angle, the first step is to introduce proper method to isolate azimuthal dependency from polar angle. In this
paper, we propose a novel phase matrix expansion with Zernike polynomials, which represents the probability of
scattering events. The results show that it can provide a new improved strategy for the solution of radiative transfer
equations in Discrete-Ordinate Method (DOM), which is different from commonly used Fourier series and Legendre
polynomials expansion and we make conclusion that there are three principles for polynomials’ selection, including
orthogonal performance, special theorem for polynomial derivation and triangle function generation.
Axicon surfaces are widely used in nowadays optical engineering, requiring accurate metrology for these highly aspheric
surfaces. In this contribution, we present a complete approach to determine the shape deviation of axicons in an absolute
manner. The setup is an interferometric null configuration using a computer generated hologram (CGH) as null optics. We
demonstrate an absolute shifting method and the calibration issues connected with measuring the absolute cone angle.
Experimental results are shown for the metrology of a 90° cone angle sample.
Computer-generated holograms (CGHs) allow to transfer the high 2D-positioning accuracy of modern lithography equipment into high precision 3D-shape measurements, e.g. in CGH asphere metrology. In this contribution, we give a detailed look into the characterization of steep topologies with CGHs on the example of a 90 deg axicon surface, requiring rather high line densities in the hologram. Several aspects gain importance with increasing CGH line densities when measuring dimensional quantities such as the cone angle of the surface: misalignment of the setup, fabrication effects of the CGH rigorous effects of the high density grating, and effects due to wavelength variations of the interferometer. This paper presents the experimental approach for the cone angle measurement and a systematic analysis of its measurement uncertainty, focusing on the specifics of this null test CGH measurement.
A portable phase-shifted interferometer with multiply usages is described. Several techniques are studied and used in this interferometer. In order to test an optical piece with obscuration or irregular edge, we study the seed-algorithm for wavefront reconstruction. For testing a corner cube reflector (CCR), we investigate the model to calculate its exit wavefront and angle error. To measure the figure of a convex or concave spherical surface, we develop a series of reference transmission spheres.
A practical system is described to measure the retardation of wave plates with phase-shifted method. The tested wave plate is put in and the original angle between the axis of it and the analyzer is random, not 45 degree. For the measurement is made rapidly and automatically, a standard wave plate act as a compensator, the stepping motor is used to drive the analyzer to realize phase shifting and a grating encoder is used to measure its rotating angle. At the same time, while the beam comes out from the analyzer, the photoelectric detector gets its intensity, and then the signals is magnified, filtered and sent to computer through its serial port. The results show the system has the advantages of costing little time and high accuracy.
A combination of computer generated hologram (CGH) with a small liquid crystal display, phase-shifting detection, and Twyman-Green interferometer is used to test an aspheric. This method resolves the problem of real-time produce CGH. In the paper, a method of producing real-time computer generated hologram is proposed in which a small liquid crystal display is adopted as a recording material. The making principle of the real-time computer generated hologram is described. The experimental result is better.
Reference lenses play an important role in test of spherical surfaces. In this condition, the ray reflected from the tested spherical surface goes the same way as that from the last surface of the reference lenses. If the two rays go different way, the focus of the reference lenses is not coincidence with its last surface’s curvature center, and system error is produced. The deviations between the focus and the curvature center of the last surface for a series of reference lenses are studied in this paper.
The optical quality and frequency response of an interferometer is influenced by its primary parts, for example its collimating input system, its reference lenses, its reference flat, its stop, etc. An interferometer is set up with optical design software to study the full view of influence by them in this paper. The data and curve is also given in this paper making sure the system error induced by them is less than 0.01λ (λis wavelength).
There is very strong need to test mid-frequency power spectrum density (PSD) for optical surface used in high power laser system, aerospace high resolution camera, astronomy optical system, and X-ray optics, etc. To improve measurement accuracy and remove the error, the calibration of frequency response function for a phase-shifted interferometer must be done before PSD is tested by this interferometer. In this paper, the intensity function contributed by three plane-waves interference is given at first. On basis of this function, the sinusoidal phase grating with variable frequency formed by two plane-waves interference with appropriate ratio of two amplitudes is discussed and is used to calibrate the frequency response function of an interferometer. A test example is given and some error sources are pointed out and studied.
A torus is a kind of aspherical surface, different from quadratic rotary surface. It plays an important role in special optical systems. However, up to now there is no effective method to test its wavefront. In this paper, a method is proposed using long wavelength (10.6 micrometers ) IR interferometry to test a torus, whose curvature radii is different from submillimeter deducing to micrometer, the principle is also given. Then a example torus is tested in self-developed IR spherical interferometer. When this torus is placed in typical positions along the optical axis, some interferograms are shown. According to these interferograms the wavefront error and the difference of two radii can be obtained and shown in this paper.
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