Focal Length Measurement Research Articles

Focal length and radius of curvature measurement using coherent gradient sensing and Fourier fringe analysis

A procedure for the measurement of focal length and radius of curvature of a lens using coherent gradient sensing system and Fourier transform fringe analysis technique has been demonstrated. Light from the laser illuminates the specimen and the wavefront emerging from the specimen is tested using coherent gradient sensing interferometer. The fringe pattern corresponding to the test wavefront is stored, and analyzed using Fourier fringe analysis technique. The slope of the wavefront in the direction of shear has been evaluated. It provides the information regarding exact location of points corresponding to the focus/center of curvature of the lens. High accuracy and precision has been achieved.

Calibration method for high-accuracy measurement of long focal length with Talbot interferometry

In this paper, a new calibration method for accurate long focal-length measurements, based on Talbot interferometry, is presented. Error analysis is derived in detail by the numerical method, and an effective way to improve the accuracy is proposed. By this method, the systematic errors that are the main factors effecting accuracy are calibrated and reduced. Both simulation and experiments have been carried out to prove the effectiveness and advantages of the proposed method as compared to conventional approaches. The experimental results reveal that the relative error is lower than 0.02%, and the repeatability is better than 0.05%. This method is especially useful for measuring long focal-length lenses.

Alternative method for measuring effective focal length of lenses using the front and back surface reflections from a reference plate

We present a simple method for measuring the effective focal length without determining the location of principle plane of the lens. The method is based on the measurement of confocal backreflection axial responses from the front and back surfaces of a reference plate with known refractive index and thickness. We proved the concept by measuring the effective focal lengths of thin singlet lenses and complex microscope objectives. The theoretical limit of measurement precision varies depending on the numerical aperture of the lens. This method can provide an alternative focal length measurement method for complex lenses or lenses that are permanently attached to other structures. Measurement errors were analyzed theoretically and improvements in measurement accuracy were discussed.

Focal length measurement based on Hartmann–Shack principle

A novel means of focal length measurement is proposed based upon Hartmann–Shack principle of wavefront detection. Mathematical approaches of focal length measurement are deduced without the necessity of knowing the position of lens principle plane. In experiment, laser sources with wavelength of 633nm and 780nm are separately used and focal length of three pieces of doublets is measured under two wavelengths mentioned above. As were shown by the results, this method of focal length measurement could not only accurately measure lens focal length, but also evaluate chromatic aberration of them. Since the intensity of light is detected by CCD, optical characteristics of lens beyond the range of visible light are also measurable when response range of CCD allows. This new means of focal length measurement is characterized by high accuracy, fast measuring and easy to setup, thereby, it is applicable in wide fields of area.

基于哈特曼-夏克波前测量原理的焦距测量

A novel means of lens focal length measurement was proposed based on Hartmann-Shack principle of wavefront detection.Mathematical approaches of focal length measurement were deduced.In the experiments,laser sources with wavelength of 633 nm and 780 nm were separately used and focal length of three pieces of doublets were measured by the two wavelengths.The results show that the measured result can truly reflect the designed focal length by using 633 nm wavelength laser beam,which indicates that this measurement method is feasible and reliable.Meanwhile,the measured result by using 780 nm wavelength laser beam shows larger differences compared with its 633 nm counterpart,which reveals that this method can also be used to evaluate residual spherical aberrations,chromatic aberrations and manufacturing tolerance.

基于光栅多缝衍射的转角法测量微透镜焦距

基于光栅多缝衍射的转角法测量微透镜焦距

Thermally Tunable Polymer Microlenses for Biological Imaging

We present polydimethylsiloxane (PDMS) microlenses capable of thermally tuning their focal lengths via optically transparent indium tin oxide (ITO) microheaters. Microlenses with various diameters are created by molding PDMS over microstructures of reflowed photoresist. Due to a relatively large thermal expansion coefficient, these PDMS microlenses exhibit measurable thermal expansion with relatively small temperature changes. By adjusting the temperature of the microlenses using ITO microheaters, we can actively control their radii of curvature and focal lengths without requiring moving mechanical components. To demonstrate the tunability of the microlenses, we characterize temperature-dependent changes by focal length and magnification factor measurements. We also investigate the ability to use the microlenses for tunable observation of cells, demonstrating their potential application to biological imaging.

Focusing X-Rays with Curved Multiplate Crystal Cavity

An overview is given of the study on X-ray focusing using the Fabry-Perot type multi-plate silicon crystal cavities consisting of compound refractive lenses. Silicon (12 4 0) is used as the back reflection for cavity resonance at the photon energy of 14.4388 keV. Measurements of focal length of the transmitted beam through the crystal cavities show enhanced focusing effect due to the presence of back diffraction. Also, an incident beam with ultrahigh energy resolution can improve the focusing owing to the wider acceptance angle of the back diffraction. Considerations based on the excitation of dispersion surface within the framework of X-ray dynamical diffraction theory are also presented to reveal the origin of this enhanced focusing.

Application of Newton’s method to determine the focal length of lenses using a lateral shearing interferometer and cyclic path optical configuration setup

We present a technique for the focal length measurement of lenses applying Newton's method, using a cyclic path optical configuration (CPOC) and a wedge shear plate (WSP). Two point sources of orthogonal linearly polarized light waves that have a known longitudinal separation between them are generated using CPOC. Selecting a particular state of polarization (s or p), the corresponding point source is made to coincide with the back focal point of the test lens (TL). The collimation of the output beam from TL is tested using the WSP. With a change in the state of polarization, a spherical wavefront would emerge from TL because the corresponding point source is situated slightly away from the focal plane of TL. The radius of curvature of the emerging spherical wavefront from TL approximated as image distance is evaluated by analyzing the shear fringes produced by WSP. Appropriate formulae for the determination of the focal length of TL, from the image distance and known longitudinal separation between the sources, are derived using Newton's method. Results obtained for a positive doublet lens of nominal focal length of 500.0 mm is presented.

基于Talbot-Moiré法测量透镜焦距的莫尔条纹的图像处理

Based on Talbot effect and Moire fringes of Ronchi gratings,focal length measurement of the long focal length is carried out. The focal length of measured lens can be figured out accurately according to its relation to the slope coefficient of Moire fringes. To get the slope of Moire fringes, the image of Moire fringes is mainly filtered or smoothed by mathematics morphological method to enhance the contrast of fringes effectively. Then the filtered image is processed by thinning to single pixel width. The fringes are labeled to fitting lines to calculate the slope coefficient accurately,and the error of focal length is 0.10%.

激光二极管端面抽运固体激光器的热效应和热透镜焦距测量

激光二极管端面抽运固体激光器的热效应和热透镜焦距测量

Laser differential confocal ultra-long focal length measurement

A new laser differential confocal focal-length measurement method is proposed for the measurement of an ultra-long focal-length. The approach proposed uses the property of an axial intensity curve that the absolute zero precisely corresponds to the focus of the objective in a differential confocal focusing system (DCFS) to measure the variation in position of DCFS focus with and without a measured ultra-long focal-length lens (UFL), uses the distance between the two focuses to obtain the UFL focal-length, and thereby achieving the precise measurement of ultra-long focal-length. The method has a high focusing precision, a strong anti-interference capability and a short measurement light-path. The theoretical analyses and preliminary experimental results indicate that the relative measurement error is about 0.01% when the method is used for the measurement of back-focus-distance (BFD).

Simultaneous measurement of focal length and index of refraction of a microlens using a compound microscope

The fabrication of microlenses has spurred a lot of interest and resulted in multiple techniques of fabrication in the past decade. However the metrology of these lenses has received less attention and remains a complex and time-consuming task that does not allow frequent control during development and manufacturing. We propose a simple technique based on a standard compound microscope that would allow measuring the focal length of a plano-convex lens and at the same time obtain a measure of the index of refraction of the lens material. The method relies on observing the different images of an object placed in the illumination path of the microscope. Among these images, some are created by the light going through the lens and others by its reflection on the surface. We show that with the image distance and size it is possible to retrieve the focal length and the average index of refraction of the lens material in the case of quasi-spherical lenses. The accuracy obtained by the technique is better than a few per cent and its cost is negligible as it only uses existing equipment.

Technique for the focal-length measurement of positive lenses using Fizeau interferometry

We present what we believe is a new technique for the focal-length measurement of positive lenses using Fizeau interferometery. The technique utilizes the Gaussian lens equation. The image distance is measured interferometrically in terms of the radius of curvature of the image-forming wavefront emerging from the lens. The radii of curvature of the image-forming wavefronts corresponding to two different axial object positions of known separation are measured. The focal length of the lens is determined by solving the equations obtained using the Gaussian lens equation for the two object positions. Results obtained for a corrected doublet lens of a nominal focal length of 200.0 mm with a measurement uncertainty of +/-2.5% is presented.

Design and fabrication of a negative microlens array

An operation model of a negative microlens array is demonstrated. The array consists of two kinds of materials with different refractive indices. First of all, a positive microlens array with 256×256 elements serving as a pattern is fabricated by argon ion beam etching on the quartz. The diameter and average corona height of the element are 28 and 0.638 μm, respectively. The spacing between two neighboring elements is 2 μm. In the second phase, after being coated by epoxy, the positive microlens array pattern is spun and baked, leading to a complex negative microlens array. Surface stylus measurement shows that the surface of the positive quartz microlens array is smooth and uniform. Focal length measurement of the negative microlens array indicates that the focal length region with −731±3 μm is in good agreement with the theoretical calculation value of −729 μm.

An Anatomical Study of the Visual Capabilities of the Green Turtle, Chelonia mydas

Several aspects of vision in juvenile and adult Green Turtles (Chelonia mydas) are examined, with special reference to retinal anatomy such as oil droplet topography, transmission electron microscopy of photoreceptors, spectral transmission measurements of the ocular media (cornea, lens, and vitreous humor), and measurements of focal length and optical sensitivity. A detailed study of the distribution of the different color classes of oil droplets shows that all oil droplets are found in high concentrations (>1000 mm−2) in the central/temporal parts of the retina. Red oil droplets were the largest, followed by yellow and clear. Oil droplet size varied in different parts of the retina. On average, red oil droplets were found in fewer numbers compared to yellow and clear oil droplets. Two types of clear oil droplets were identified: those that fluoresced under UV illumination and those that did not. We found that the majority (78.5%) of colorless oil droplets fluoresced when viewed under UV light. Spectral transmission measurements of the ocular media show that wavelengths to approximately 325 nm are transmitted. This may suggest ultraviolet (UV) vision in Green Turtles. The optical sensitivity of the Green Turtle eye was relatively low, suggesting an adaptation to high light intensities commonly experienced by this species.

Simple focal-length measurement technique with a circular Dammann grating

A novel technique for focal-length measurements with a circular Dammann grating is presented. In the back focal plane of the lens under test, a one-order circular Dammann grating with limited aperture will produce double-humped radial rings. The separation between the two lobes varies with the displacement of the observed plane from the focal plane of the lens. By searching for the position at which the separation is minimal, the focal point of the lens can be located and hence the back focal length can be determined. Experimental results demonstrated that this method is efficient and can be used effectively for a quick check of focal length.

Colour vision and visual ecology of the blue-spotted maskray, Dasyatis kuhlii Müller & Henle, 1814

Relatively little is known about the physical structure and ecological adaptations of elasmobranch sensory systems. In particular, elasmobranch vision has been poorly studied compared to the other senses. Virtually nothing is known about whether elasmobranchs possess multiple cone types, and therefore the potential for colour vision, or how the spectral tuning of their visual pigments is adapted to their different lifestyles. In this study, we measured the spectral absorption of the rod and cone visual pigments of the blue-spotted maskray, Dasyatis kuhlii, using microspectrophotometry. D. kuhlii possesses a rod visual pigment with a wavelength of maximum absorbance (lambda(max)) at 497 nm and three spectrally distinct cone types with lambda(max) values at 476, 498 and 552 nm. Measurements of the spectral transmittance of the ocular media reveal that wavelengths below 380 nm do not reach the retina, indicating that D. kuhlii is relatively insensitive to ultraviolet radiation. Topographic analysis of retinal ganglion cell distribution reveals an area of increased neuronal density in the dorsal retina. Based on peak cell densities and using measurements of lens focal length made using laser ray tracing and sections of frozen eyes, the estimated spatial resolving power of D. kuhlii is 4.10 cycles per degree.

A low cost technique for automated measurement of focal length using Lau effect combined with Moiré readout

A low cost, accurate and relatively simple technique based on the Lau effect coupled with Moiré readout for measuring the focal length of collimating lenses is demonstrated. The method is based on defocusing the collimating lens and measuring the corresponding variation in the inclination angle of the Moiré fringes. Details of theoretical background, experimental arrangement and error analysis are presented. Experimental results of the measurements are in close agreement with the true values.

Atomic beam focusing with a curved magnetic mirror

Reflective atom optics has been experimentally realized with a continuous flux of cold atoms by using a magnetized videotape. We have studied the behaviour of a slow atomic beam with a velocity of 20 m s−1 incident at different angles on the surface of a curved magnetic mirror. Focusing of the beam has been demonstrated and this induces an amplification up to a factor 3 of the fluorescence emitted by the atoms around the focal point. We deduced the shape of our reflector from the focal length measurements and show that the result is completely consistent with those obtained from the reflection of a red diode laser beam on the curved mirror.