Equivalent Focal Length Research Articles

Accuracy evaluation for in-situ machining reference points binocular measurement based on credibility probability

Passive binocular measurement systems are being increasingly utilized in the in-situ industries of automobiles, aviation, and aerospace, etc. due to their excellent qualities of accuracy, efficiency, and cost performance. Whereas the barrier of evaluating the accuracy of measured objects resulted from the unequal equivalent focal length and quantization of pixels, has limited their further development and application of high requirements for in-situ machining, e.g., the measurement of machining reference points for the positioning of robotic drilling in aerospace manufacturing. In this paper, an accuracy evaluation method is proposed to address the problem. Firstly, the unequal equivalent focal length is considered to improve the accuracy of 3D reconstruction. Next, the credibility probability model is developed to calculate the probability of the observed error in the public view of the binocular measurement system and indicates the direction of improvement. Finally, the in-situ experiment is carried out to validate the method within the effective public view range of 300 mm × 300 mm. The experiment results show that the RMSs of observed errors are superior to 0.035 mm, and the credibility probabilities are all higher than 0.91; the maximum 3D reconstruction accuracy improvement is 60.3%, with the error reduced from 0.078 mm to 0.031 mm.

Focal length, EFL, and the eye.

The focal length is often called the effective focal length, or efl instead, and although this is acceptable for a lens in air, it is not otherwise correct. The eye is used as an example here for an optical system where the object is in air and the image is in fluid. Welford, Aberrations of Optical Systems (1986) has paraxial equations that are consistent with historical use while also clearly defining efl. These are based on power at a surface having to be the same for light traveling in both directions (n '/f '). The focal length f ' is the actual physical distance from the 2nd principal point to the paraxial focus, and the equivalent focal length, or efl, is the focal length divided by the image index (f '/n '). Separately, when the object is in air, the efl is shown to act at the nodal point, with the lens system represented by either an equivalent thin lens at the principal point with a focal length or a different equivalent thin lens in air at the nodal point with an efl. The rationale for using effective instead of equivalent for efl is unclear, but efl is used more as a symbol than as an acronym.

Systems of generalized harmonic lenses for image formation

Subject of study. The simplest scheme comprising two harmonic lenses is considered, which allows the formation of an image with higher quality than that obtained using each of these lenses individually owing to the accurate selection of the heights of their microreliefs. Method. Two harmonic lenses with coupled microrelief heights are fabricated using the direct laser writing method on the photoresist. An experiment is conducted on the formation of images by the system comprising two harmonic lenses and an individual harmonic lens. Main results. A “HarmLens” software for modeling of the systems comprising harmonic and diffractive lenses is designed. Modeling is performed within the geometric optic approximation using the ray tracing method. The possibility of obtaining a significant reduction in the displacement of the primary focal plane in comparison with the individual harmonic lens case is demonstrated by the specific selection of the microrelief height in this system. The system of two harmonic lenses is demonstrated to form an image with an average contrast exceeding the average contrast of the image formed by the individual harmonic lens by 1.4 times. The point spread function of the system comprising two harmonic lenses is experimentally demonstrated to be 1.6 times narrower than that of the individual harmonic lens with an equivalent focal length. Practical significance. The system of two harmonic lenses proposed in this work allows a sharper image than the image formed by an individual harmonic lens to be obtained. The system of two harmonic lenses can be adopted in machine vision systems where the compact arrangement of the objective’s elements is more important than the high quality of the formed image.

Automatic Extraction Of Interior Orientation Data In Aerial Photography Using Image Matching Method

The Interior Orientation is a set of parameters that have been determined to transform the coordinates of the camera photo, that is the coordinates of the pixel leading to the coordinates of the image. This parameter is used to calibrate the camera before use so as to produce a precise measurement from an aerial photograph. This orientation parameter consists of a calibrated and equivalent camera focal length, lens distortion, principal point, fiducial mark location, camera resolution, and flatness of the focal plane. All of these parameters are attached to or contained on the camera sensor and the values of these parameters can usually be known from the camera's report page. In this work, the author wants to obtain pixel coordinates from the Fiducial Mark in the base image (Window Search) automatically, therefore a Fiducial Mark template was created which is formed from a piece of a photo image frame to determine the Fiducial Mark coordinate values from the base image ( Window Search), the basis of this programming is to use the concept of photogrammetry, which uses Image Matching techniques. The Image Matching process was developed from the C ++ Language programming algorithm platform, this was done in order to speed up computational results. There are a number of techniques for doing Image Matching, in this study the authors conducted using the Normalized Cross-Correlation Image Matching. In statistics Normalized Cross-Correlation is between two random variables by determining the size of how closely the two variables are different simultaneously. Similarly, Normalized Cross-Correlation in Image Matching is a measurement by calculating the degree of similarity between two images. This level of similarity is determined by Normalized Cross-Correlation (NCC). The Least Square Image Matching method is used to increase the accuracy of the coordinates of the conjugation points.

Algorithm for calculating anastigmatic three-mirror telescopes. II. Spherical primary mirror case

A version of the general algorithm (Terebizh 2019; 2020) for calculating anastigmatic three-mirror telescopes is presented, assuming a spherical shape of the primary mirror. This case is of particular interest in connection with the creation of large telescopes. The input parameters are the natural characteristics of the telescope: equivalent focal length and relative diameters of mirrors; the result is a wide field of view design with all conic surfaces, free of the four major third-order aberrations. The ranges of values of input parameters in which acceptable solutions exist are clarified, and examples of optical systems of two main types are given. The sphericity condition of the primary mirror imposes strict requirements for the rest of the characteristics of three-mirror anastigmats, which significantly narrows the class of practically attractive systems.

Target distance measurement method using monocular vision

Most existing machine vision-based location methods mainly focus on the spatial positioning schemes using one or two cameras along with non-vision sensors. To achieve an accurate location, both schemes require processing a large amount of data. In this study, the authors propose a novel method, which requires much less amount of data to be processed for measuring target distance using monocular vision. Based on the geometric model of camera imaging, the parameters of the camera (such as camera's focal length and equivalent focal length.), as well as the principle of analogue signal being transformed into a digital signal, the authors derive the relationship among the target distance, field of view, equivalent focal length and camera resolution. Experimental results show that the proposed method can effectively and accurately achieve the target distance measurement.

A real-time fisheye video correction method based on Android smart-phone GPU

We propose a fisheye camera calibration algorithm, in which the center of the distortion and equivalent focal length of the fisheye camera are obtained by the contour constraint, and the distortion parameters are calculated by linear constraint and Levenberg-Marquardt (LM) optimization algorithm. According to the obtained camera parameters, the fisheye image can be corrected by cubic-box-mapping-method (CBMM). The result shows that for checkerboard images the calibration algorithm demonstrates a high-accuracy of about 0.6727 pixels in the average reprojection root-mean-square error (RMSE). Based on the calibration algorithm, the ream-time fisheye video correction is implemented on an android smart-phone. In the implementation, a direct mapping method is used to simplify the cubic box mapping method, and a heterogeneous architecture with a graphics processing unit (GPU) is built to accelerate the algorithm. Lastly, a fisheye video stream of 1280×1280 resolution is timely corrected on the smart-phone with a speed of 25 frames/sec.

Production of a Strain-Measuring Device with an Improved 3D Printer.

A traditional strain measurement sensor needs to be electrified and is susceptible to electromagnetic interference. In order to solve the fluctuations in the analog electrical signal in a traditional strain gauge operation, a new strain measurement method is presented here. It uses a photographic technique to display the strain change by amplifying the change of the pointer displacement of the mechanism. A visual polydimethylsiloxane (PDMS) lens with a focal length of 7.16 mm was added to a smartphone camera to generate a lens group acting as a microscope to capture images. It had an equivalent focal length of 5.74 mm. Acrylonitrile butadiene styrene (ABS) and nylon amplifiers were used to test the influence of different materials on the sensor performance. The production of the amplifiers and PDMS lens is based on improved 3D printing technology. The data obtained were compared with the results from finite element analysis (FEA) to verify their validity. The sensitivity of the ABS amplifier was 36.03 ± 1.34 µε/µm, and the sensitivity of the nylon amplifier was 36.55 ± 0.53 µε/µm.

Automatic calibration method for the full parameter of a camera-projector system

We propose an automatic calibration method using grid-structured light for the full parameter of a camera-projector system, including principal points, equivalent focal length, image distortion coefficients, the rotation matrix, and translation vectors between the camera and projector. Grid-structured light is projected onto a board, camera image intersection points are extracted, and three-dimensional intersection points are computed according to a homography matrix. Finally, the full parameter of a camera-projector system is solved based on stereo vision. No manual intervention is required during image processing, which simplifies the operations and improves efficiency. The image-processing kernel problem involves both automatic detection and intersection point matching. (1) The proposed intersection point detection method utilizes multiscale fusion. At each level of the image pyramid, intersection points are searched according to gray distribution and geometrical characteristics. With the gray-gravity method, coordinates are achieved with subpixel intersection point precision. Therefore, the location precision exceeds 0.5 pixel. (2) The proposed matching method employs belief propagation. Taking intersection points as nodes, a Bayesian network is established according to the Markov random field hypothesis. The image intersection point matching problem between a camera and the projector is then transformed into a maximum a posteriori estimation problem. Ultimately, 15 images are used to calibrate the full parameter of a camera-projector system. The results indicate that the reprojection error exceeds 0.15 pixel.

A low-cost, accurate strain measurement using multi-view amplification mechanism and visual polydimethylsiloxane lens

Strain sensors are widely applied in the industry requiring specific signal amplifiers and signal readers. However, the devices are unable to read data quickly and intuitively. The present study introduces a highly accurate, repeatable, mold-free strain sensor comprising of an amplification mechanism and a smart-phone microscope. Generation of the amplification mechanism using rapid prototyping especially 3D printing is summarized and evaluated. The sensitivity of the proposed amplifier is (39.47 ± 1.34) for nylon and (37.74 ± 2.41) for ABS. A visual polydimethylsiloxane (PDMS) lens with a focal length of 7.23 mm is attached to the iphone6 camera, performing as a microscope for image acquisition, which provides an equivalent focal length of 6.7 mm and a resolution of 0.691 µm.

Infrared LEDs-Based Pose Estimation With Underground Camera Model for Boom-Type Roadheader in Coal Mining

Accurate and reliable pose estimation of a boom-type roadheader is of great importance in order to maintain the efficiency of automatic coal mining. The stability and accuracy of conventional measurement methods are difficult to be guaranteed on account of vibration noise, magnetic disturbance, electrostatic interference, and other factors in an underground environment. In this paper, a vision-based non-contact measurement method for cutting-head pose estimation is presented, which deploy a 16-point infrared LED target on the boom-type roadheader to tackle the low-illumination, high-dust, and complicated background. By establishing a monocular vision measurement system, the cutting-head pose is estimated through processing the LED target images obtained from an explosion-proof industrial camera mounted on the roadheader. After analyzing the measurement mechanism, an underground camera model based on the equivalent focal length is built to eliminate refraction errors caused by the two-layer glasses for explosion-proof and dust removal. Then, the pose estimation processes, including infrared LEDs feature point extraction, spot center location, and an improved P4P method based on dual quaternions, are carried out. The influence factors of cutting-head pose estimation accuracy are further studied by modeling, and the error distribution of the main parameters is investigated and evaluated. The numerical simulation and experimental evaluation are designed to verify the performance of the proposed method. The results show that the pose estimation error is in line with the numerical prediction, achieving the requirements of cutting-head pose estimation in underground roadway construction in the coal mine.

Stray light protection system of the AZT-33VM telescope focal plane, Sayan astronomical complex

Developed according to quasi-Ritchey–Chretien, the AZT-33VM telescope is designed for up to 2.8-deg wide-field survey observations; it has inner position of the focal plane and the prefocal lens corrector installed at 0.12 of the equivalent focal length from the image plane. Classic methods to calculate direct stray light protection system in two-mirror systems allow us to find the optimal configuration of the baffles providing minimum obscuration of the entrance pupil. The design of stray light protection baffles for a future large rectangular detector 260 × 124 mm was proposed. The baffles were calculated from axisymmetric condition in a plane passing through the system centerline and a point of the detector perimeter. Using the ray-tracing method, we simulated optimized baffles for a rectangular detector. We assessed obscuration of the entrance pupil with an optimal design baffle as well their advantages for the modulation transfer function.

Research on the calibration technology of an underwater camera based on equivalent focal length

Calibration is one of the most crucial and inevitable processes in vision technology, whose performance can significantly affect the measurement accuracy of the vision system. To compensate for coefficients of water factors, the conventional calibration technology for the underwater camera generally introduces several higher-order distortion coefficients, which, unfortunately, suffer poor stability, low efficiency, as well as computational complexity. To overcome these drawbacks, a newish calibration method based on equivalent focal length is proposed in this paper. The method takes the refraction distortion of water factors as equivalent focal length changing to cause. Applying the invariance principle of linear perspective projection, distortion correction should first be carried out. Subsequently, the internal and external parameters of the camera are calculated by using Zhang's calibration method based on the camera linear model, which simplifies the process of underwater camera calibration. Finally, the experimental results show that the calibration method can effectively improve the accuracy of the underwater camera.

Economic fabrication of a novel hybrid planar Grating/Fresnel lens for miniature spectrometers.

We propose a new technique to fabricate a highly specialized optical element, a hybrid planar Grating/Fresnel lens (G-Fresnel), which is particularly useful to improve or enable more-affordable miniature/portable spectrometers. Both the Fresnel and the grating surface are fabricated simultaneously by sandwiching soft PDMS between a hard grating and a pre-replicated negative Fresnel surface. Several adhesion reduction techniques are also investigated that help improve both fabrication and cost efficiency (by reducing the solidification time) as well as the lifetime of the mold. Alignment errors are systematically analyzed, and their effects on the G-Fresnel lens evaluated. A compact fabrication platform was built, which is smaller than a volume of 160☓140☓106 mm3 to fit into a conventional vacuum drying oven, for the fabrication of a G-Fresnel lens with a diameter of 25.4 mm, an equivalent focal length of 25 mm, and a blazed grating pattern with 600 lines/mm spacing. The solidification time was reduced to 2 hours thanks to the improved adhesion reduction technique that permits a PDMS drying-temperature as high as 65 °C. The fabricated G-Fresnel lens was evaluated with regard to both geometrical fabrication precision and optical performance. The measured results, using a step gauge and atomic force microscopy, confirm that this replication technique produces high-quality replicates of the master surface-profile. Furthermore, a prototype spectrometer that uses a G-Fresnel lens was built and evaluated. The spectrometer fits within a volume of about 100 mm☓50 mm☓30 mm, and it operates across a wide wavelength spectrum (450 nm to 650 nm). Both the calculation based on the optical software ZEMAX and the experimental measurements are consistent and confirm that the spectrometer with the G-Fresnel lens can provide a spectral resolution of better than 1.2nm.

Operational Measurements for Infrared Camera Characterization

The detection, location, identification and recognition are very important activities for the air forces. Imaging systems are tools used for those functions, so it is mandatory to characterize those systems to really know their actual operational limits. This paper presents a set of measurements for spectral, radiometric and spatial camera characterization to be applied to imaging systems operating in the thermal infrared. A SC5600 camera manufactured by FLIR® Systems was used and assembled with lenses of 27 or 54 mm equivalent focal length. The camera spectral characterization was done by comparison to a calibrated system composed by thermal source, monochromator and a broadband reference detector. The radiometric characterization was performed using an extensive blackbody (CI Systems) for temperatures between 10 and 55 °C to evaluate the camera accuracy and obtain the calibration curves. The spatial characterization was carried out using the same extensive blackbody and 2 standard USAF 1951 machined targets, one made of steel and other of aluminum, serving as masks for the blackbody. Using recycled material, a homemade extended blackbody for outdoor use was built. The results obtained using the 2 blackbodies in laboratory were similar.

High‐resolution photography of clouds from the surface: Retrieval of optical depth of thin clouds down to centimeter scales

AbstractThis paper describes the approach and presents initial results, for a period of several minutes in north central Oklahoma, of an examination of clouds by high‐resolution digital photography from the surface looking vertically upward. A commercially available camera having 35 mm equivalent focal length up to 1200 mm (nominal resolution as fine as 6 µrad, which corresponds to 9 mm for cloud height 1.5 km) is used to obtain a measure of zenith radiance of a 30 m × 30 m domain as a two‐dimensional image consisting of 3456 × 3456 pixels (12 million pixels). Downwelling zenith radiance varies substantially within single images and between successive images obtained at 4 s intervals. Variation in zenith radiance found on scales down to about 10 cm is attributed to variation in cloud optical depth (COD). Attention here is directed primarily to optically thin clouds; COD less than about 2. A radiation transfer model used to relate downwelling zenith radiance to COD and to relate the counts in the camera image to zenith radiance permits determination of COD on a pixel‐by‐pixel basis. COD for thin clouds determined in this way exhibits considerable variation, for example, an order of magnitude within 15 m, a factor of 2 within 4 m, and 25% (0.12 to 0.15) over 14 cm. This approach, which examines cloud structure on scales 3 to 5 orders of magnitude finer than satellite products, opens new avenues for examination of cloud structure and evolution.

First astrometric observations of space debris with the MéO telescope

The MéO (for Métrologie Optique) telescope is the Satellite and Lunar Laser Ranging (SLR) dedicated telescope of Observatoire de la Côte d’Azur (France) located at plateau de Calern. The telescope uses an altazimuth mount. The motorization of the mount has a capability of 6 deg/s allowing the follow up of Low Earth Orbits (LEO) satellites, as well as Medium Earth Orbits (MEO) and geostationary (GEO) satellites, and the Moon. The telescope has a primary mirror of 1.54 m. It uses a Nasmyth focus equipped with an EMCCD camera. The telescope field of view, defined by the equivalent focal length and the size of the camera, is currently 3.4 arcmin × 3.4 arcmin. Space debris observation with an optical telescope ideally requires a large field of view, accurate pointing, a fast slew rate, a high sensitivity, accurate astrometric positions, and a precise method for orbit propagation. The challenge is to obtain accurate orbits for all debris without compromising the field of view. The MéO telescope has a larger diameter than the ones habitually used for space debris tracking. It should improve the current accuracy of observations in the GEO region. For LEO, such sensitivity should allow observations of small pieces of debris at low altitudes. This paper presents the preliminary experiments carried out to benefit from the high astrometric quality of the instrument, namely the method developed to extract and to compute the astrometric positions of LEO and MEO satellites, as a test of the capabilities of such an instrument (very small field of view, but large aperture) for space debris tracking. Furthermore, we analyse the ability of MéO to keep track of an object for which only a preliminary orbit (computed by the Laplace method from previous observations) is known, so that high precision measurements can be obtained and the object can be catalogued with an updated orbit. The feasibility of our astrometric methods was tested throughout 2010. This paper presents the methods used and the difficulties encountered. The originality of our paper does not strictly reside in the methods used but in their adaptation to a telescope presenting such a small field of view. We discuss our first results obtained for LEO and MEO satellites. In particular, we give an estimate of the astrometric errors for the geodetic satellite Lageos-1 by comparing its positions deduced from our reduction strategy with those obtained from a reference orbit. We also present research to use the Laplace method to produce preliminary orbital elements. In this context, we discuss a novel improvement to the Laplace method. To put it in a nutshell, this article provides original results covering all fields of orbit estimation, from satellites tracking to preliminary orbit determination.

Estimating forest leaf area using cover and fullframe fisheye photography: Thinking inside the circle

This study compares circular fisheye photography and destructive leaf area index ( L) estimation with two alternative indirect methods for estimating L in broad-leaved forest: fullframe fisheye photography and cover photography. Fullframe fisheye photography differs from circular fisheye photography in that the images have a reduced field of view; the zenithal range of 0°–90° extends to the corners of the rectangular image, roughly doubling image resolution compared to circular fisheye images. Cover images are obtained by pointing a 70 mm equivalent focal length lens (in 35 mm format) straight upwards. Cover and L were measured in twelve stands of a 17 years old Eucalyptus marginata forest that had been planted at four initial densities: 625, 1250, 2500 and 10,000 trees per hectare. L, from destructive sampling, averaged between 2 and 2.4 for stands planted at between 1250 and 10,000 trees ha −1 but was only 1.3 for the stands planted at 625 trees ha −1. Cover photography provided good indirect estimates of L assuming a spherical leaf distribution, except in the stands with 10,000 trees ha −1. These trees appeared to have a more horizontal leaf angle based on the calculated zenithal extinction coefficient for those stands (∼0.7). Rapid and automated analysis of cover images using WinSCANOPY 2006 yielded similar results to manual image analysis using Adobe Photoshop. Estimates of L from fullframe fisheye photography were better correlated with L from destructive sampling than L estimated from circular fisheye photography, but neither performed as well as cover photography. Photographic methods that use a single threshold to separate sky and foliage appear less sensitive to the camera's gamma function than methods that use a two-value threshold. Higher resolution (>8 megapixel) cameras and better lenses, may further improve L estimation using fullframe fisheye photography. We recommend that cover photography be used for routine L estimation in broadleaf forest until it is demonstrated that fisheye methods can provide similar accuracy.

Estimation of leaf area index in eucalypt forest with vertical foliage, using cover and fullframe fisheye photography

This study compared fullframe fisheye photography and cover photography with destructive leaf area index ( L) estimation and the Licor LAI-2000 plant canopy analyser (PCA) in plantations of the vertical leaved species Eucalyptus globulus. Fullframe fisheye photography differs from circular fisheye photography in that the images have reduced field of view such that the zenithal range of 0–90° extends to the corners of the rectangular image, roughly doubling image resolution compared to circular images. Cover images instead are obtained by pointing a 70 mm equivalent focal length lens (in 35 mm format) straight upwards. Measurements of cover and indirect estimates of plant area index ( L t) were made in 12 stands of 6–8 years old Eucalyptus globulus. L was measured using destructive sampling and allometry in nine of these stands and ranged from 2.5 to 6.6. Both foliage cover and L t from the PCA were well correlated with L from allometry, but fullframe fisheye photography provided poor estimates of L despite corrections for foliage clumping. Sampling location had a significant effect on estimates of crown porosity, crown cover and zenithal clumping index from cover photography. The zenithal extinction coefficient ( k), calculated from L, crown porosity and cover, ranged from 0.14 to 0.25 and appeared to decrease as L increased; hence, we were unable to obtain an unambiguous estimate of k for E. globulus stands. Nonetheless, the study showed that L can be estimated from foliage cover with similar certainty to that of the PCA. We conclude that the greatest challenge facing indirect estimation of L in forests using photographic methods is to separate the effects of foliage angle from those of foliage clumping.

Studies of the characteristic parameters for a flattened-Gaussian beam through a defocusing lens

By introducing an equivalent focal length, analytical propagation equations of the characteristic parameters for a flattened-Gaussian beam through a defocusing lens in free space are obtained on the basis of Collins diffraction formula and definition of high-order intensity moments. The parametric characteristics of beam width, kurtosis parameter and power in the bucket are analyzed and discussed analytically or numerically. Numerical results show that the effects of different kinds or values of defocusing coefficient of the lens on these parameters are different. It is concluded that the action of the lens with different defocusing coefficient can be compensated by a series of lenses with different focal length in theory.